TALSIM Docs - Benutzerbeiträge [de]

Unterteilung in Systemelemente/en

2021-08-30T10:49:26Z

Haghani:

<languages/>

{{Navigation|vorher=Systemabgrenzung|hoch=Arbeitsschritte zur Modellerstellung|nachher=Systemlogik}}

In order to divide a water resources system into individual [[Special:MyLanguage/Beschreibung der Systemelemente|system elements]] it is vital to consider the problem which the model is used for and the existing data basis.

Basically there are two possible ways for the division of the system. It can be divided either catchment-based or grid-based. In addition, all hydrological structures relevant to the problem must be identified and represented by a suitable [[Special:MyLanguage/Beschreibung der Systemelemente|system element]], e.g. dams by [[Special:MyLanguage/Speicher|storage]], extractions by [[Special:MyLanguage/Verbraucher|consumer]], etc. Often there are several feasible solutions.

The preliminary work for dividing a river basin is usually done with a GIS.

==Catchment-based Division==

Criteria for the division can be:

*Catchment properties (topography)
* Punctual changes of the outflow by
** Inflows
** Point sources
** Extractions
* Location of hydrological structures
* Location of gauging stations
* Flow type and geometry

The results of this division are digital catchment boundaries and river sections. If the available data initially results in a rough division, it can be subdivided even further, especially if, due to the problem at hand, certain processes in the waterbody can no longer be represented with the intitial division. In the following, a high resolution water resources system is compared to a low resolution water resources system:

{| class="wikitable"
|-
| [[Datei:System_räumlich_hochaufgelöst.png|400px]] || [[Datei:System_räumlich_geringaufgelöst.png|400px]]
|-
|
*As the accuracy of system mapping increases, the importance of hydraulics in the waterbodies increases.
*The parameters of the runoff concentration only refer to the surface runoff in the corresponding sub-catchments, resp. interflow and base flow.
*The illustration of flood-routing within the waterbodies is possible.
||
*Simple approaches to the calculation of runoff generation usually manage better with a rough system illustration.
*Both, the surface runoff in the sub-catchments and the flood-routing that occur in the waterbodies are included in the parameters of the runoff concentration.
*The illustration of flood-routing within the waterbodies is hardly possible.
|-
|}

[[Datei:Teilgebiet_Auswahl_Systemelemente.png|thumb| Sub-catchments can be defined via a [[Einzugsgebiet|Rainfall-Runoff Model]][[Datei:Systemelement001.png|20px]] or can be visualised through a [[Special:MyLanguage/Einleitung|hydrograph]][[Datei:Systemelement002.png|20px]] at the output]]

The next step is to decide which system elements are to be used to map the sub-catchments, depending on the problem and the data basis. Alongside the system element [[Special:MyLanguage/Einzugsgebiet|sub-basin]], which brings the load into the system via a precipitation-runoff simulation, the system element [[Special:MyLanguage/Einleitung|point source]] can feed the outflow from the sub-catchment directly into the system via a hydrograph. The latter is of course only possible if a hydrograph is available. Then it is the solution using the fewest computational resources, which in addition (with good quality of the input data) also illustrates the actual outflow behavior in a realistic manner. If, however, for example, a forecast is to be calculated with changed land use conditions or if the hydrograph is not long enough, it is advisable to use the system element [[Special:MyLanguage/Einzugsgebiet|sub-basin]]. In Talsim-NG the selection of the system element for sub-catchments can also vary from sub-catchment to sub-catchment.

Once the system elements are defined, the [[Special:MyLanguage/Systemlogik|flow network]] is created, i.e. the flow relationships between the elements are defined.

== Grid-based Division==

In grid-based division, water is generally passed from one cell to the next according to its flow direction.

The transfer from one cell to the next varies depending on the flow component:
* Surface runoff is incorporated into the runoff generation process of the next cell, i.e. it is treated like additional precipitation.
* Interflow is fed into the cascade of storages of the next cell's interflow.
* Base flow is fed into the cascade of storages of the next cell's base flow.

Translations:Unterteilung in Systemelemente/3/en

2021-08-30T10:49:26Z

Haghani:

Basically there are two possible ways for the division of the system. It can be divided either catchment-based or grid-based. In addition, all hydrological structures relevant to the problem must be identified and represented by a suitable [[Special:MyLanguage/Beschreibung der Systemelemente|system element]], e.g. dams by [[Special:MyLanguage/Speicher|storage]], extractions by [[Special:MyLanguage/Verbraucher|consumer]], etc. Often there are several feasible solutions.

Speicher/en

2021-08-30T10:48:25Z

Haghani:

<languages/>

{{Navigation|vorher=Verzweigung|hoch=Beschreibung der Systemelemente|nachher=Speicher mit Wasserkraftanlagen}}

[[Datei:Systemelement006.png|50px|none]]

Storages are used to store an inflow and, depending on the current storage content and operating rules, to release water for different uses to up to three different system elements. With the possibility to [[Special:MyLanguage/Betriebsregelkonzept|regulate and control]] releases, it is an extremely flexible system element with a variety of options. Originally, the storage element was developed to represent reservoirs behind dams, but it can also be used to model other storages such as flood control reservoirs or similar.
Additionally, it is possible to optionally simulate the addition of water to the storage by precipitation, as well as losses from the storage by evaporation and infiltration.

The storage system element can also be used to simulate [[Special:MyLanguage/Speicher mit Wasserkraftanlagen|hydro power plants]].

==Rating Curve==

The storage rating curve defines the relationship between storage volume, water level and surface area.
It forms the basis for all calculation options that depend on not only the storage volume but also the water level and/or the surface area e.g., precipitation/losses, flow over a weir, pressurized flow through pipes.

==Releases==
The term release is used to describe any discharge of water according to operating rules from the storage to the downstream area through regulated or unregulated outlets. This includes controlled releases through operating and bottom outlets as well as releases via a spillway.

Releases are often related to operating rules, therefore, it is possible or sometimes also necessary to define several releases for each outlet.

===Calculation Options===

Independent of the selected calculation option, releases can always be scaled with a system state/control cluster, which makes it possible to model complex [[Special:MyLanguage/Betriebsregelkonzept|operating rules]], which are not only dependent on states within the storage, but also on other states within the river basin.

====Release per Timestep / Release Sequence====

With this option, you define the release values by directly entering (up to 365) values. During the simulation, these values are then used as release values for the individual simulation timesteps in the given order.

====Function (+ Hydrograph/Time Series)====

With this option, releases are defined as functions of storage volume by entering the nodes of the function. These releases can additionally be scaled with a factor, an annual, weekly and/or daily pattern (and, as with all calculation options, with a system state or a control cluster) or with a factor and a time series.

The following function types are available:

{|
|
KNL
|Rating curve
|-
|
LAM
|Pool-based operating plan
|-
|
XYZ
|Time-dependent function
|}

=====Rating Curve=====

The rating curve consists of a time-independent functional relationship between releases and storage volume. You can specify whether the function should be interpolated linearly between the entered nodes or whether the function should be interpreted as a step function.

=====Pool-Based Operating Plan=====

With the option pool-based operating plan, the storage is divided into different pools which vary over the year and these pools are each assigned a fixed release amount. A pool-based operating plan is defined by entering a number of releases with ascending amounts and specifying the corresponding storage volume for each release amount at different times of the year.

The areas between the entered nodes can be interpreted as steps. However, it is also possible to interpolate linearly in time and/or between the release amounts.<br clear="all" />

<gallery mode="nolines" widths=600px heights=200px>
Datei:Lamellenplan_EN.png|Comparison of a pool-based operating plan in the two- and three-dimensional representation, <br/>Interpretation: constant block (steps)
Datei:Lamellenplan_linear_interpoliert_EN.png|Comparison of a pool-based operating plan in the two- and three-dimensional representation, <br/>Interpretation: linearly interpolated (both in time and between pools)
</gallery>

=====Time-Dependent Function=====

A time-dependent function is very similar to a pool-based operating plan, but a bit more flexible: the releases defined at different time periods only have to be of equal number but not in value, and they do not necessarily have to be ascending. This makes it possible to define arbitrary functions with individual nodes for release amounts and storage volumes for different time periods.

By default the functions are interpreted as steps with constant values between the entered nodes. However, it is also possible to interpolate linearly in time and/or between the entered storage-release value pairs.<br clear="all" />

====Weir Overflow====

The release is calculated using the weir formula according to Poleni as free / submerged overflow.

====Pressure Pipeline====

The release is calculated according to the Prandtl-Colebrook and Darcy-Weisbach formulas.

====Turbine====

Based on the characteristics of the turbine, the flow through the turbine is determined depending on the storage level and the downstream water level, such that the desired power output is maintained as long as the maximum possible flow rate of the outlet is not exceeded. See also the page on [[Special:MyLanguage/Speicher_mit_Wasserkraftanlagen|hydropower plants]].

===Limits===

The [[Special:MyLanguage/Betriebsregeltypen|maximum physically possible output]] of individual outlets can be entered as functions of storage volume, causing releases to be limited to these values. It is also possible to specify a minimum permissible release value, below which the release will be set to 0.

===Internal Dependencies===

Internal dependencies are used to define the [[Special:MyLanguage/Betriebsregeltypen|priorities in case of multiple competing releases from one storage]]. One or more releases can be reduced if another release exceeds a certain amount or if the storage volume falls below a certain value.

The limits for releases and storage volumes for internal dependencies are entered as constant values, which can however be scaled with daily, weekly and/or annual patterns.

If several releases are to be reduced simultaneously, the order in which they should be reduced must also be specified.

Example:
''If release B > 0 and the storage volume S < X, then reduce release A by the amount of release B, but at most to a minimum value of zero.''

This means that there is a linear relatioship between A and B until B is equal to the value of A. If the value of B rises any further, A still remains zero.

==Precipitation/Losses==

An addition of water caused by precipitation onto the storage's surface or losses caused by evaporation or infiltration can be considered via two options:

* Constant pattern (daily, weekly and/or annual pattern)
* Time series

These can be additionally scaled by a factor.
Precipitation, evaporation and infiltration values must be provided as a linear unit such as e.g. mm. During the simulation, the provided values are converted to water volumes by multiplying with the current storage surface area.

Translations:Speicher/7/en

2021-08-30T10:48:24Z

Haghani:

==Releases==
The term release is used to describe any discharge of water according to operating rules from the storage to the downstream area through regulated or unregulated outlets. This includes controlled releases through operating and bottom outlets as well as releases via a spillway.

Betriebsregeltypen/en

2021-08-30T10:47:13Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a storage. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the storage for other purposes play a decisive role. A storage should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]storage B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Storage A to storage B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of storage B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Storage==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a storage, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined storage volumes, but not maintaining discharges below the set storage volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the storage, additional discharges used for energy production are stopped when the storage volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between storage content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective storage volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the storage volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no storage volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two storages are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/57/en

2021-08-30T10:47:13Z

Haghani:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]storage B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Storage A to storage B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of storage B and the scaling derived from it.

Betriebsregeltypen/en

2021-08-30T10:46:21Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a storage. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the storage for other purposes play a decisive role. A storage should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]Reservoir B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Reservoir A to reservoir B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of reservoir B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Storage==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a storage, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined storage volumes, but not maintaining discharges below the set storage volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the storage, additional discharges used for energy production are stopped when the storage volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between storage content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective storage volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the storage volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no storage volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two storages are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/24/en

2021-08-30T10:46:20Z

Haghani:

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the storage for other purposes play a decisive role. A storage should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

Betriebsregeltypen/en

2021-08-30T10:46:03Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a storage. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the reservoir for other purposes play a decisive role. A reservoir should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]Reservoir B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Reservoir A to reservoir B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of reservoir B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Storage==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a storage, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined storage volumes, but not maintaining discharges below the set storage volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the storage, additional discharges used for energy production are stopped when the storage volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between storage content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective storage volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the storage volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no storage volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two storages are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/12/en

2021-08-30T10:46:03Z

Haghani:

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a storage. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

Transportstrecke/en

2021-08-30T10:45:16Z

Haghani:

<languages/>

{{Navigation|vorher=Einleitung|hoch=Beschreibung der Systemelemente|nachher=Verbraucher}}
__TOC__
[[Datei:Systemelement003.png|50px|none]]
Transport reaches simulate the translation and retention behavior of natural water courses or pipelines. There are different approaches for the calculation of pipes or natural channels.

The following options are implemented:
[[Datei:Berechnungsoptionen_Transportstrecke_EN.png|frame|none|Calculation options for transport reaches]]

==Translation==

The inflow wave is output at the outlet with a time offset that corresponds to the flow time in the transport reach. If the flow time is smaller than the simulation time step, the translation behavior is not visible in the simulation results.

==Non-Pressurized Pipeline==

This option encompasses flow routing calculation for pipes according to Kalinin-Miljukov. The parameters required by the Kalinin-Miljukov method are estimated internally according to /Euler, 1983/ for circular pipes, and for non-circular profiles, are determined from the hydraulic diameter and the cross-sectional area when completely filled.

{|
|Characteristic length: ||<math>L=0.4 \cdot \frac{D}{I_S}~\mbox{[m]} </math>
|-
|Retention constant: ||<math>0.64 \cdot L \cdot \frac{D^2}{Q_v} ~\mbox{[s]}</math>
|-
|}

with:
{|style="margin-left: 40px;"
|<math>D~\mbox{[m]}</math>: || Circular pipe diameter or hydraulic diameter
|-
|<math>I_S~\mbox{[-]}</math>: || Slope of the pipe
|-
|<math>Q_v ~\mbox{[m³/s]}</math>: || Discharge capacity of the pipe when completely filled
|-
|}

The discharge capacity of the pipe when completely filled is calculated according to the flow law of Prandtl-Colebrook:

<math>Q_v=A_v \left [ -2 \cdot \lg \left [\frac{251 \cdot \nu}{D \sqrt{2 g D I_S}} + \frac{k_b}{3.71 \cdot D} \right ] \cdot \sqrt{2gDI_s} \right ]</math>

with:
{|style="margin-left: 40px;"
|<math>A_v~\mbox{[m²]}</math>: || Cross-sectional area of the profile
|-
|<math>\nu~\mbox{[m²/s]}</math>: || Kinematic viscosity
|-
|<math>k_b ~\mbox{[m³/s]}</math>: || Operating roughness
|-
|<math>g ~\mbox{[m/s²]}</math>: || Gravitational acceleration
|-
|}

Using the characteristic length <math>L</math>, the length of the transport reach <math>L_g</math> is divided into <math>n</math> calculation sections of equal length with

::<math>n=L_g/L</math> (where <math>n</math> is an integer number)

Parameters are adjusted as follows for the individual calculation sections:

::<math>L^*=L_g/n</math>
::<math>K^*=K \cdot L^*/L</math>

Based on these parameters, after calculating the following recursion formula <math>n</math> times,

<math>Q_{a,i}=Q_{a,i-1}+C_1 \cdot \left(Q_{z,i-1} - Q_{a,i-1} \right ) + C_2 \cdot \left(Q_{z,i}-Q_{z,i-1} \right) </math>

with:
{|style="margin-left: 40px;"
|<math>Q_z</math>: || Inflow to calculation section
|-
|<math>Q_a</math>: || Outflow from calculation section
|-
|<math>i</math>: || Current calculation time step
|-
|<math>i-1</math>: || Previous calculation time step
|-
|<math>dt</math>: || Calculation time interval
|-
|<math>C_1=1- e^{-dt/K^*}</math> ||
|-
|<math>C_2=1- \frac{K^*}{dt}/C_1</math> ||
|-
|}
produces the outflow at the end of the pipe.
This approximation method derived from Kalinin-Miljukov is identical to the linear storage cascade used for calculating runoff concentration. This means the flow ina transport reach can be simulated using a linear storage cascade consisting of <math>n</math> storages with the retention constant <math>K^*</math>.

==Cross-Section (Open Channel)==

As with non-pressurized pipelines, the translation and retention behavior is simulated using flow routing according to Kalinin-Miljukov. The characteristic length required as a parameter for the Kalinin-Miljukov method is derived from the steady uniform flow relationship according to Manning-Strickler /Rosemann, 1970/.

[[Datei:Schema_charakteristische_Länge_EN.png|400px]]

The channel is divided into individual segments with the characteristic length. For each segment, the calculation of flow routing is carried out using [[Special:MyLanguage/Berechnungsschema von Speichern|nonlinear storage calculation]] with the help of the steady uniform flow relation.

==Rating Curve (Open Channel)==

If the flow behavior of the transport reach is known, e.g. from previous hydraulic calculations, a rating curve defining the relationship between water level, cross sectional area and discharge can be used.

Translations:Transportstrecke/21/en

2021-08-30T10:45:16Z

Haghani:

[[Datei:Schema_charakteristische_Länge_EN.png|400px]]

The channel is divided into individual segments with the characteristic length. For each segment, the calculation of flow routing is carried out using [[Special:MyLanguage/Berechnungsschema von Speichern|nonlinear storage calculation]] with the help of the steady uniform flow relation.

Unterteilung in Systemelemente/en

2021-08-30T10:44:49Z

Haghani:

<languages/>

{{Navigation|vorher=Systemabgrenzung|hoch=Arbeitsschritte zur Modellerstellung|nachher=Systemlogik}}

In order to divide a water resources system into individual [[Special:MyLanguage/Beschreibung der Systemelemente|system elements]] it is vital to consider the problem which the model is used for and the existing data basis.

Basically there are two possible ways for the division of the system. It can be divided either catchment-based or grid-based. In addition, all hydrological structures relevant to the problem must be identified and represented by a suitable [[Special:MyLanguage/Beschreibung der Systemelemente|system element]], e.g. dams by [[Special:MyLanguage/Speicher|reservoir]], extractions by [[Special:MyLanguage/Verbraucher|consumer]], etc. Often there are several feasible solutions.

The preliminary work for dividing a river basin is usually done with a GIS.

==Catchment-based Division==

Criteria for the division can be:

*Catchment properties (topography)
* Punctual changes of the outflow by
** Inflows
** Point sources
** Extractions
* Location of hydrological structures
* Location of gauging stations
* Flow type and geometry

The results of this division are digital catchment boundaries and river sections. If the available data initially results in a rough division, it can be subdivided even further, especially if, due to the problem at hand, certain processes in the waterbody can no longer be represented with the intitial division. In the following, a high resolution water resources system is compared to a low resolution water resources system:

{| class="wikitable"
|-
| [[Datei:System_räumlich_hochaufgelöst.png|400px]] || [[Datei:System_räumlich_geringaufgelöst.png|400px]]
|-
|
*As the accuracy of system mapping increases, the importance of hydraulics in the waterbodies increases.
*The parameters of the runoff concentration only refer to the surface runoff in the corresponding sub-catchments, resp. interflow and base flow.
*The illustration of flood-routing within the waterbodies is possible.
||
*Simple approaches to the calculation of runoff generation usually manage better with a rough system illustration.
*Both, the surface runoff in the sub-catchments and the flood-routing that occur in the waterbodies are included in the parameters of the runoff concentration.
*The illustration of flood-routing within the waterbodies is hardly possible.
|-
|}

[[Datei:Teilgebiet_Auswahl_Systemelemente.png|thumb| Sub-catchments can be defined via a [[Einzugsgebiet|Rainfall-Runoff Model]][[Datei:Systemelement001.png|20px]] or can be visualised through a [[Special:MyLanguage/Einleitung|hydrograph]][[Datei:Systemelement002.png|20px]] at the output]]

The next step is to decide which system elements are to be used to map the sub-catchments, depending on the problem and the data basis. Alongside the system element [[Special:MyLanguage/Einzugsgebiet|sub-basin]], which brings the load into the system via a precipitation-runoff simulation, the system element [[Special:MyLanguage/Einleitung|point source]] can feed the outflow from the sub-catchment directly into the system via a hydrograph. The latter is of course only possible if a hydrograph is available. Then it is the solution using the fewest computational resources, which in addition (with good quality of the input data) also illustrates the actual outflow behavior in a realistic manner. If, however, for example, a forecast is to be calculated with changed land use conditions or if the hydrograph is not long enough, it is advisable to use the system element [[Special:MyLanguage/Einzugsgebiet|sub-basin]]. In Talsim-NG the selection of the system element for sub-catchments can also vary from sub-catchment to sub-catchment.

Once the system elements are defined, the [[Special:MyLanguage/Systemlogik|flow network]] is created, i.e. the flow relationships between the elements are defined.

== Grid-based Division==

In grid-based division, water is generally passed from one cell to the next according to its flow direction.

The transfer from one cell to the next varies depending on the flow component:
* Surface runoff is incorporated into the runoff generation process of the next cell, i.e. it is treated like additional precipitation.
* Interflow is fed into the cascade of storages of the next cell's interflow.
* Base flow is fed into the cascade of storages of the next cell's base flow.

Translations:Unterteilung in Systemelemente/15/en

2021-08-30T10:44:49Z

Haghani:

The transfer from one cell to the next varies depending on the flow component:
* Surface runoff is incorporated into the runoff generation process of the next cell, i.e. it is treated like additional precipitation.
* Interflow is fed into the cascade of storages of the next cell's interflow.
* Base flow is fed into the cascade of storages of the next cell's base flow.

ASCII-Datensatz/en

2021-08-30T10:43:45Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Schnittstellen: Import/Export|nachher=Import/Export Zeitreihen}}
A data set contains all information about a system (e.g. flow network, input parameters, etc.) and is obtained by [[Special:MyLanguage/Bereich_Varianten#Variante_exportieren|exporting a scenario]] for example under ''D:\Talsim-NG\Customers\Auftraggeber_1\projectData\Example\dataSets''. Depending on the size of the system, the dataset consists of a varying number of files: the more data and system elements are included in the system, the more files are created.

The created data set can be passed on to other editors. They can [[Special:MyLanguage/Bereich_Varianten#Variante_importieren|import]] the data set into their Talsim model. For this, the *.SYS file is necessary.

Below, an overview of all possible files is presented.

{| class="wikitable"
|-
! Suffix !! Data
|-
| [[Special:MyLanguage/ALL-Datei|*.ALL]] || General information about the project
|-
| [[Special:MyLanguage/BOA-Datei|*.BOA]] ||Soil texture
|-
| [[Special:MyLanguage/BOD-Datei|*.BOD]] || Soil type
|-
| [[Special:MyLanguage/EIN-Datei|*.EIN]] || Point sources
|-
| [[Special:MyLanguage/EZG-Datei|*.EZG]] || Subcatchments
|-
| [[Special:MyLanguage/EXT-Datei|*.EXT]] || External time series
|-
| [[Special:MyLanguage/FKT-Datei|*.FKT]] || Functions with function values
|-
| [[Special:MyLanguage/HYO-Datei|*.HYO]] || Hydrology, evaporation, humidity, sunshine, wind
|-
| [[Special:MyLanguage/JGG-Datei|*.JGG]] || [[Special:MyLanguage/Belastungsdefinition / Modellinput#Jahresgang erstellen|Annual Patterns]]
|-
| [[Special:MyLanguage/KAL-Datei|*.KAL]] || Calibration factors
|-
| [[Special:MyLanguage/KTR-Datei|*.KTR]] || Control functions
|-
| [[Special:MyLanguage/LNZ-Datei|*.LNZ]] || Land use
|-
| [[Special:MyLanguage/PRO-Datei|*.PRO]] || Simulation settings for short-term simulations/design storms, parameters for model rains, flood wave statistics
|-
| [[Special:MyLanguage/QUA-Datei|*.QUA]] || [[Special:MyLanguage/Belastungsdefinition / Modellinput#Stoffparameter|Quality parameters]]
|-
| [[Special:MyLanguage/RFD-Datei|*.RFD]] || Precipitation distribution
|-
| [[Special:MyLanguage/SCE-Datei|*.SCE]] || Settings for scenario simulation
|-
| [[Special:MyLanguage/SIMINFO-Datei|*.SIMINFO]] || Information about the simulation
|-
| [[Special:MyLanguage/SYS-Datei|*.SYS]] || Flow network
|-
| [[Special:MyLanguage/TAL-Datei|*.TAL]] || Settings for all storage elements
|-
| [[Special:MyLanguage/TEM-Datei|*.TEM]] || Settings for temperature modelling
|-
| [[Special:MyLanguage/TGG-Datei|*.TGG]] || [[Special:MyLanguage/Belastungsdefinition / Modellinput#Tagesgang erstellen|Daily patterns]]
|-
| [[Special:MyLanguage/TRS-Datei|*.TRS]] || Settings for all transport elements
|-
| [[Special:MyLanguage/TXT-Datei|*.TXT]] || Description of all system elements, control clusters, system states
|-
| [[Special:MyLanguage/UPD-Datei|*.UPD]] || Update configuration
|-
| [[Special:MyLanguage/VAR-Datei|*.VAR]] || Consumer
|-
| [[Special:MyLanguage/VER-Datei|*.VER]] || Diversions
|-
| [[Special:MyLanguage/WGG-Datei|*.WGG]] || [[Special:MyLanguage/Belastungsdefinition / Modellinput#Wochengang erstellen|Weekly patterns]]
|-
| [[Special:MyLanguage/ZIE-Datei|*.ZIE]] || Objective function
|}

Besides, two result data sets are automatically saved after a scenario has been simulated.

Firstly, the zipped data set '''*.WLZIP''' contains all results for the simulation. It is created under ''D:\Talsim-NG\Customers\Auftraggeber_1\projectData\Beispiel\dataBase\Beispiel_Data''. When unpacking the zipped file, the files *.WEL and *.WELINFO are the output. Depending on the [[Special:MyLanguage/Belastungsdefinition / Modellinput#Stoffparameter|quality parameters]], there is the possibility of more output files.

{| class="wikitable"
|-
! Suffix !! Data
|-
| *.CHLO.WEL || Chloride loads and concentrations of all system elements
|-
| *.CHLO.WELINFO || Respective labeling of the file *.CHLO.WEL
|-
| *.KALI.WEL || Potassium loads and concentrations of all system elements
|-
| *.KALI.WELINFO || Respective labeling of the file *.KALI.WEL
|-
| *.KTR.WEL || Simulation results of all control functions
|-
| *.KTR.WELINFO || Respective labeling of the file *.KTR.WEL
|-
| *.WEL || Simulation results of all system elements
|-
| *.WELINFO || Respective labeling of the file *.WEL
|}

Secondly, the zipped data set '''*.ERGZIP''' is created under ''D:\Talsim-NG\Customers\Auftraggeber_1\projectData\Beispiel\dataBase\Beispiel_Data\result''. When the zipped file is unpacked, the following files are the output.

{| class="wikitable"
|-
! Suffix !! Data
|-
| *.[[Special:MyLanguage/BLZ-Datei|BLZ]] || Balance results
|-
| *.LOG ||
|-
| *.MAX ||
|-
| *.SIMEND ||
|-
| *.SIMINFO ||
|-
| *.WELINFO ||
|-
| *.WMX||
|-
|}

Translations:ASCII-Datensatz/4/en

2021-08-30T10:43:44Z

Haghani:

{| class="wikitable"
|-
! Suffix !! Data
|-
| [[Special:MyLanguage/ALL-Datei|*.ALL]] || General information about the project
|-
| [[Special:MyLanguage/BOA-Datei|*.BOA]] ||Soil texture
|-
| [[Special:MyLanguage/BOD-Datei|*.BOD]] || Soil type
|-
| [[Special:MyLanguage/EIN-Datei|*.EIN]] || Point sources
|-
| [[Special:MyLanguage/EZG-Datei|*.EZG]] || Subcatchments
|-
| [[Special:MyLanguage/EXT-Datei|*.EXT]] || External time series
|-
| [[Special:MyLanguage/FKT-Datei|*.FKT]] || Functions with function values
|-
| [[Special:MyLanguage/HYO-Datei|*.HYO]] || Hydrology, evaporation, humidity, sunshine, wind
|-
| [[Special:MyLanguage/JGG-Datei|*.JGG]] || [[Special:MyLanguage/Belastungsdefinition / Modellinput#Jahresgang erstellen|Annual Patterns]]
|-
| [[Special:MyLanguage/KAL-Datei|*.KAL]] || Calibration factors
|-
| [[Special:MyLanguage/KTR-Datei|*.KTR]] || Control functions
|-
| [[Special:MyLanguage/LNZ-Datei|*.LNZ]] || Land use
|-
| [[Special:MyLanguage/PRO-Datei|*.PRO]] || Simulation settings for short-term simulations/design storms, parameters for model rains, flood wave statistics
|-
| [[Special:MyLanguage/QUA-Datei|*.QUA]] || [[Special:MyLanguage/Belastungsdefinition / Modellinput#Stoffparameter|Quality parameters]]
|-
| [[Special:MyLanguage/RFD-Datei|*.RFD]] || Precipitation distribution
|-
| [[Special:MyLanguage/SCE-Datei|*.SCE]] || Settings for scenario simulation
|-
| [[Special:MyLanguage/SIMINFO-Datei|*.SIMINFO]] || Information about the simulation
|-
| [[Special:MyLanguage/SYS-Datei|*.SYS]] || Flow network
|-
| [[Special:MyLanguage/TAL-Datei|*.TAL]] || Settings for all storage elements
|-
| [[Special:MyLanguage/TEM-Datei|*.TEM]] || Settings for temperature modelling
|-
| [[Special:MyLanguage/TGG-Datei|*.TGG]] || [[Special:MyLanguage/Belastungsdefinition / Modellinput#Tagesgang erstellen|Daily patterns]]
|-
| [[Special:MyLanguage/TRS-Datei|*.TRS]] || Settings for all transport elements
|-
| [[Special:MyLanguage/TXT-Datei|*.TXT]] || Description of all system elements, control clusters, system states
|-
| [[Special:MyLanguage/UPD-Datei|*.UPD]] || Update configuration
|-
| [[Special:MyLanguage/VAR-Datei|*.VAR]] || Consumer
|-
| [[Special:MyLanguage/VER-Datei|*.VER]] || Diversions
|-
| [[Special:MyLanguage/WGG-Datei|*.WGG]] || [[Special:MyLanguage/Belastungsdefinition / Modellinput#Wochengang erstellen|Weekly patterns]]
|-
| [[Special:MyLanguage/ZIE-Datei|*.ZIE]] || Objective function
|}

Zeitreihenverwaltung/en

2021-08-30T10:43:21Z

Haghani:

<languages/>

{{Navigation|vorher=Menüleiste Systemverwaltung|hoch=Hauptseite|nachher=Einzelfenster von Modellkomponenten}}

Time series can be stored in TALSIM-NG's own time series manager, where they are classified by the type of data and the station they belong to. There they can be viewed graphically and edited tabularly. A basic statistics' tool, which can calculate average values for a defined period of time as well as other statistics, is also integrated in the time series manager.

=== Opening the Time Series Manager===

The time series manager can be accessed via the ''Menu bar → Time series → Time series manager''. The '''Talsim-User Selection''' window, where you are required to choose a user to proceed, appears. If you want to create and edit time series, you should choose your username and confirm with '''OK'''. If you log in using another username, you can only see the stations and time series, but you cannot edit or delete them.

[[Datei:Zeitreihe001_EN.png|Datei:Zeitreihe001EN_.png|500px]]
[[Datei:Zeitreihe002_EN.png]]

If you are logged in with your username and have not created any time series yet, an empty '''TalsminNG - TS Explorer''' opens. This explorer can be customized using '''View''', '''Folder''', as well as the '''folder icon'''.

[[Datei:Zeitreihe003_EN.png]]

===Create New Station===

Time series are principally assigned to stations, e.g. measuring stations. For this reason a station should be created first. To do this, right-click on the ''Explorer → New Station''. A window, where you can enter the name of the station and confirm with '''OK''', will appear.

[[Datei:Zeitreihe004_EN.png]] [[Datei:Zeitreihe005_EN.png|Datei:Zeitreihe005_EN.png]]

Subsequently, a new station, as well as 15 subfolders are created. These subfolders present the different types of the hydrological, hydrometeorological, or storage-dependent variables that can be saved as time series in the TS Explorer.

[[Datei:Zeitreihe006_EN.png]]

You have a choice of the following options when you right-click on the new station in the explorer.

{| class="wikitable" style="width:70%"
|-
|'''New Station''' ||A new empty station with 15 subfolders is created.
|-
|'''Edit Station''' ||The dialog window ''Edit of a Talsim time series station'', in which information about the selected station can be edited, is opened.
|-
|'''Delete Station''' ||The marked station and all associated time series are deleted. This operation cannot be undone.
|-
|'''Copy to Clipboard''' || The list of time series associated with the station as well as their metadata is copied to the clipboard.
|-
|'''New Time Series''' ||A new time series associated with the selected station is created.
|-
|'''Release Edit-lock''' ||Releases the edit-lock of the station, so it can be edited by another user.
|-
|}

=== Create New Time Series===

To create a time series, right-click on the ''Station → New Time Series'' in the [[Special:MyLanguage/Belastungsdefinition / Modellinput#Zeitreihenverwaltung|time series explorer]]. A window will open, prompting you to enter the name of the new time series. Confirm with '''OK'''.

[[Datei:Zeitreihe007_EN.png|Datei:Zeitreihe007_EN.png]]

The following attributes are displayed for each time series in the explorer:

{| class="wikitable" style="width:70%"
|-
|'''Name''' ||Name of the time series.
|-
|'''ID''' ||Identification number of a time series. ID corresponds to the ID of the binary file, stored in the system data. Caution: Not to be confused with the ID of a simulation in the model and on the server.
|-
|'''Type''' ||Hydrological, hydrometeorological, storage-dependent or geological variable. With this setting the time series is assigned to one of the 15 subfolders of the station. Default value: discharge.
|-
|'''Unit''' ||Unit of the values. Default value: m³/s.
|-
|'''Interpretation''' ||Information about the time series values, i.e. how to understand the timestamp and the value stored in it. Caution: wrongly set interpretations inevitably lead to incorrect results. For example, precipitation [mm] is usually a sum per timestep. Default value: Current_value (linear_interpolation)
|-
|'''Origin''' ||Origin of the time series. Default value: measured.
|-
|'''from''' ||Date and time of the start of the time series. Default value: Day and time of creation.
|-
|'''to''' ||Date and time of the end of the time series. Default value: Day and time of creation.
|-
|'''Data points''' ||Number of data points. Default value: 0
|-
|}

[[Datei:Zeitreihe008_EN.png]]

The created time series is assigned the chosen name and a consecutive ID number. The other attributes are filled with the default values.

You can use the following buttons if you right-click on the time series in the explorer.

{| class="wikitable" style="width:70%"
|-
|'''Edit Time Series''' ||The selected time series can be edited.
|-
|'''Chart''' ||The time series can be displayed as a graph over time or as a duration curve.
|-
|'''Edit Values''' ||Values with date are added to the selected time series. Values can also be edited or deleted.
|-
|'''Statistics''' ||Calculates a statistical overview of the time series.
|-
|'''Import Time Series''' ||An existing time series can be imported.
|-
|'''Export Time Series''' ||The selected time series can be exported.
|-
|'''Delete Time Series''' ||The selected time series is deleted. This operation cannot be undone.
|-
|'''Release Edit-lock''' ||Releases the edit-lock of the time series, so it can be edited by another user..
|-
|'''Refresh Attributes''' ||After adjusting the attributes of a time series, those attributes are updated in the explorer.
|-
|}

Edit Time Series

To adjust the attributes of a time series, right-click on ''Time Series → Edit Time Series'' in the time series manager.

[[Datei:Zeitreihe009_EN.png]]

The following dialog window, where you can edit the attributes, opens. The attributes assigned to identification and settings, which are displayed in black, can be adjusted with a double-click. By clicking OK all time series attributes can be saved.

[[Datei:Zeitreihe010_EN.png]]

{| class="wikitable" style="width:70%"
|-
|rowspan="2" style="text-align:center" |'''Identification'''
|''Description''
|Description of the time series

|-
|''Name''
|Name of the time series

|-
|rowspan="8" style="text-align:center"|'''Settings'''
|''Altitude masl''
|Height of the measuring station in meters above sea level
|-
|''Coordinate-X''
|X-coordinate of the measuring station
|-
|''Coordinate-Y''
|Y-coordinate of the measuring station
|-
|''Interpretation''
|Information about the time series values, i.e. how to understand the timestamp and the value stored in it. Caution: wrongly defined interpretations inevitably lead to incorrect results.
Choice of: [[Datei:00036_EN.png|mini]]
*BlockLeft
*BlockRight
*Instantaneous_(Linear_Interpolation)
*Cumulative
*CumulativePerTimeStep
*Undefined

|-
|''Memo''
|Description of the origin of the time series and other additional information
|-
|''Origin''
|Origin of the time series
Choice of:
*derived
*measured
*imported
*manual
*simulated
*miscellaneous
*synthetic
|-
|''Type''
|Hydrological, hydrometeorological, storage-dependent or geological variable
With this setting the time series is assigned to one of the 15 subfolders of the station.
Choice of:
*area
*discharge
*evaporation
*humidity
*mass movement
*precipitation
*pressure
*soil process
*storage
*sunshine
*temperature
*unknown
*velocity
*water level
*wind
|-
|Unit
|Unit of the variable
Choice of:
?,empty, number, class, mm/m, percent, h/d, 0/00, ml/l, mm, m, cm, km, hm, dm, l/ha, l/km², l/m², mNN, m², km², ha, cm², mm², dm², m³/m, m³, Tsd. m³, Mio. m³, l, hl,
km³, cm³, mm³, m/s, mm/d, mm/h, mm/min, l/s/km², m/h, m/d, l/s/ha, m/s², m³/s, l/s, m³/d, m³/h, l/h, l/d, °C, kg, g, mg, t, s, min, h, d, w, mon, a, Datum,
A, bar, pa, hpa, Grad, Rad, kg/m³, mg/l, g/l, l/kg, ml/g, Grad_C, kg/s, y/n
|-
|}

===Time Series Values===

After a new time series is created and edited, values can be added to it. To do this, right-click on the ''Time Series → Edit Value''. If a time series with values already exists, the values can be edited or deleted.

[[Datei:Zeitreihe0011_EN.png]]

You can use the following buttons:

{| class="wikitable"
|-
|'''Edit''' ||Selected values of the time series can be edited.
|-
|'''Add''' ||Values can be added to the time series.
|-.
|'''Delete''' ||Selected values of the time series can be deleted. This operation cannot be undone.
|-
|}

====Add Values to Time Series====

To add new values to the time series, click on '''add'''. The following ''TalsimNGZreProvider'' window opens. This indicates that the time series does not contain any values yet, and is, therefore, not stored on the server on in the database. By clicking '''OK''' the window for editing the time series values opens.

[[Datei:Zeitreihe012_EN.png|Datei:Zeitreihe012_EN.png]] [[Datei:Zeitreihe013_EN.png]]

Here you can use the following buttons:

{| class="wikitable"
|-
|'''Insert Row''' ||A row is inserted above the selected cell.
|-
|'''Add Row''' || A row is added to the end of the time series.
|-
|'''Remove Row''' ||The selected row is removed.
|-
|'''Graph''' ||The time series is displayed graphically.
|-
|'''Check dates''' ||The date of the time series is checked. This means that the date must be ascending in time.
|-
|'''Write values''' ||The time series and its values are stored on the server and in the database. Additionally, a binary file, named after the ID of the time series, is created in the system data.
|-
|'''Delete values''' ||All values are deleted.
|-
|}

The 'Edit time series' window shows the active time series, as well as the date, which by default corresponds to the date of creating the time series, unless it has been manually changed. Here you can manually enter a date and its corresponding value. You can also copy a time series with dates and values e.g. from Excel and click on the first cell of the table and paste it there (key combination: Ctrl+V).

When the values are inserted, the time series can be displayed using '''Graph'''.

[[Datei:Zeitreihe014_EN.png|Datei:Zeitreihe014_EN.png]]

In the next step the date is checked. If the dates are ascending, a window with "Check successful!" will appear. Otherwise an error message will be displayed.

[[Datei:Zeitreihe015_EN.png|Datei:Zeitreihe015_EN.png]] [[Datei:Zeitreihe016_EN.png|Datei:Zeitreihe016_EN.png]]

If all values are complete and the date is successfully checked, the values are written. In the appearing window, click '''Yes''' to confirm, '''No''' or '''Cancel''' to cancel.

[[Datei:Zeitreihe017_EN.png|Datei:Zeitreihe017_EN.png]]

The implementation of the values into the time series has been successful if the following confirmation window appears. Completing this step, saves the time series in the time series database as well as in the system data as a binary file, and exports the time series to the server. The editing window can now be closed.

[[Datei:Zeitreihe018_EN.png|Datei:Zeitreihe018_EN.png]]

====Edit Values of the Time Series====

Time series can be edited by right-clicking on the ''Time Series → Edit Values → Edit''. The active time series and its appropriate date is displayed. Now you can select the time period for which you want to make changes to load it into the edit window. The data will be displayed accordingly. With the other buttons you can edit the time series as described under [[Special:MyLanguage/Belastungsdefinition / Modellinput#Werte zur Zeitreihe hinzufügen|''Add Values to Time Series'']].

[[Datei:Zeitreihe019_EN.png]]

<div class="mw-translate-fuzzy">
====[[Special:MyLanguage/Werte in der Zeitreihe löschen|Delete Values of the Time Series]]====
</div>

===Display Time Series Graphically===

A time series can be displayed graphically by right-clicking on ''Time Series → Charts''. You have the choice between a [[Special:MyLanguage/Ganglinie|hydrograph]] (Time series chart) and a [[Special:MyLanguage/Dauerlinie|duration curve]].

[[Datei:Zeitreihe020_EN.png]] [[Datei:Zeitreihe021_EN.png]]

=== Evaluate Time Series Statistically===

Right-clicking ''Time Series → Statistics'' opens a statistics tool with which you can calculate severlal statistical measures for a predefined period. Furthermore, you can perform a low water or flood analysis. The results are displayed once you click on '''Calculate''' after entering the required data.

[[Datei:Zeitreihe022_EN.png]]

<div class="mw-translate-fuzzy">
===Import Time Series===
</div>

<div class="mw-translate-fuzzy">
=== Export Time Series===
</div>

<div class="mw-translate-fuzzy">
===Delete Time Series===
</div>

<div class="mw-translate-fuzzy">
===Release Edit-Lock===
</div>

Translations:Zeitreihenverwaltung/32/en

2021-08-30T10:43:21Z

Haghani:

|-
|''Memo''
|Description of the origin of the time series and other additional information
|-
|''Origin''
|Origin of the time series
Choice of:
*derived
*measured
*imported
*manual
*simulated
*miscellaneous
*synthetic
|-
|''Type''
|Hydrological, hydrometeorological, storage-dependent or geological variable
With this setting the time series is assigned to one of the 15 subfolders of the station.
Choice of:
*area
*discharge
*evaporation
*humidity
*mass movement
*precipitation
*pressure
*soil process
*storage
*sunshine
*temperature
*unknown
*velocity
*water level
*wind
|-
|Unit
|Unit of the variable
Choice of:
?,empty, number, class, mm/m, percent, h/d, 0/00, ml/l, mm, m, cm, km, hm, dm, l/ha, l/km², l/m², mNN, m², km², ha, cm², mm², dm², m³/m, m³, Tsd. m³, Mio. m³, l, hl,
km³, cm³, mm³, m/s, mm/d, mm/h, mm/min, l/s/km², m/h, m/d, l/s/ha, m/s², m³/s, l/s, m³/d, m³/h, l/h, l/d, °C, kg, g, mg, t, s, min, h, d, w, mon, a, Datum,
A, bar, pa, hpa, Grad, Rad, kg/m³, mg/l, g/l, l/kg, ml/g, Grad_C, kg/s, y/n
|-
|}

Zeitreihenverwaltung/en

2021-08-30T10:43:09Z

Haghani:

<languages/>

{{Navigation|vorher=Menüleiste Systemverwaltung|hoch=Hauptseite|nachher=Einzelfenster von Modellkomponenten}}

Time series can be stored in TALSIM-NG's own time series manager, where they are classified by the type of data and the station they belong to. There they can be viewed graphically and edited tabularly. A basic statistics' tool, which can calculate average values for a defined period of time as well as other statistics, is also integrated in the time series manager.

=== Opening the Time Series Manager===

The time series manager can be accessed via the ''Menu bar → Time series → Time series manager''. The '''Talsim-User Selection''' window, where you are required to choose a user to proceed, appears. If you want to create and edit time series, you should choose your username and confirm with '''OK'''. If you log in using another username, you can only see the stations and time series, but you cannot edit or delete them.

[[Datei:Zeitreihe001_EN.png|Datei:Zeitreihe001EN_.png|500px]]
[[Datei:Zeitreihe002_EN.png]]

If you are logged in with your username and have not created any time series yet, an empty '''TalsminNG - TS Explorer''' opens. This explorer can be customized using '''View''', '''Folder''', as well as the '''folder icon'''.

[[Datei:Zeitreihe003_EN.png]]

===Create New Station===

Time series are principally assigned to stations, e.g. measuring stations. For this reason a station should be created first. To do this, right-click on the ''Explorer → New Station''. A window, where you can enter the name of the station and confirm with '''OK''', will appear.

[[Datei:Zeitreihe004_EN.png]] [[Datei:Zeitreihe005_EN.png|Datei:Zeitreihe005_EN.png]]

Subsequently, a new station, as well as 15 subfolders are created. These subfolders present the different types of the hydrological, hydrometeorological, or storage-dependent variables that can be saved as time series in the TS Explorer.

[[Datei:Zeitreihe006_EN.png]]

You have a choice of the following options when you right-click on the new station in the explorer.

{| class="wikitable" style="width:70%"
|-
|'''New Station''' ||A new empty station with 15 subfolders is created.
|-
|'''Edit Station''' ||The dialog window ''Edit of a Talsim time series station'', in which information about the selected station can be edited, is opened.
|-
|'''Delete Station''' ||The marked station and all associated time series are deleted. This operation cannot be undone.
|-
|'''Copy to Clipboard''' || The list of time series associated with the station as well as their metadata is copied to the clipboard.
|-
|'''New Time Series''' ||A new time series associated with the selected station is created.
|-
|'''Release Edit-lock''' ||Releases the edit-lock of the station, so it can be edited by another user.
|-
|}

=== Create New Time Series===

To create a time series, right-click on the ''Station → New Time Series'' in the [[Special:MyLanguage/Belastungsdefinition / Modellinput#Zeitreihenverwaltung|time series explorer]]. A window will open, prompting you to enter the name of the new time series. Confirm with '''OK'''.

[[Datei:Zeitreihe007_EN.png|Datei:Zeitreihe007_EN.png]]

The following attributes are displayed for each time series in the explorer:

{| class="wikitable" style="width:70%"
|-
|'''Name''' ||Name of the time series.
|-
|'''ID''' ||Identification number of a time series. ID corresponds to the ID of the binary file, stored in the system data. Caution: Not to be confused with the ID of a simulation in the model and on the server.
|-
|'''Type''' ||Hydrological, hydrometeorological, storage-dependent or geological variable. With this setting the time series is assigned to one of the 15 subfolders of the station. Default value: discharge.
|-
|'''Unit''' ||Unit of the values. Default value: m³/s.
|-
|'''Interpretation''' ||Information about the time series values, i.e. how to understand the timestamp and the value stored in it. Caution: wrongly set interpretations inevitably lead to incorrect results. For example, precipitation [mm] is usually a sum per timestep. Default value: Current_value (linear_interpolation)
|-
|'''Origin''' ||Origin of the time series. Default value: measured.
|-
|'''from''' ||Date and time of the start of the time series. Default value: Day and time of creation.
|-
|'''to''' ||Date and time of the end of the time series. Default value: Day and time of creation.
|-
|'''Data points''' ||Number of data points. Default value: 0
|-
|}

[[Datei:Zeitreihe008_EN.png]]

The created time series is assigned the chosen name and a consecutive ID number. The other attributes are filled with the default values.

You can use the following buttons if you right-click on the time series in the explorer.

{| class="wikitable" style="width:70%"
|-
|'''Edit Time Series''' ||The selected time series can be edited.
|-
|'''Chart''' ||The time series can be displayed as a graph over time or as a duration curve.
|-
|'''Edit Values''' ||Values with date are added to the selected time series. Values can also be edited or deleted.
|-
|'''Statistics''' ||Calculates a statistical overview of the time series.
|-
|'''Import Time Series''' ||An existing time series can be imported.
|-
|'''Export Time Series''' ||The selected time series can be exported.
|-
|'''Delete Time Series''' ||The selected time series is deleted. This operation cannot be undone.
|-
|'''Release Edit-lock''' ||Releases the edit-lock of the time series, so it can be edited by another user..
|-
|'''Refresh Attributes''' ||After adjusting the attributes of a time series, those attributes are updated in the explorer.
|-
|}

Edit Time Series

To adjust the attributes of a time series, right-click on ''Time Series → Edit Time Series'' in the time series manager.

[[Datei:Zeitreihe009_EN.png]]

The following dialog window, where you can edit the attributes, opens. The attributes assigned to identification and settings, which are displayed in black, can be adjusted with a double-click. By clicking OK all time series attributes can be saved.

[[Datei:Zeitreihe010_EN.png]]

{| class="wikitable" style="width:70%"
|-
|rowspan="2" style="text-align:center" |'''Identification'''
|''Description''
|Description of the time series

|-
|''Name''
|Name of the time series

|-
|rowspan="8" style="text-align:center"|'''Settings'''
|''Altitude masl''
|Height of the measuring station in meters above sea level
|-
|''Coordinate-X''
|X-coordinate of the measuring station
|-
|''Coordinate-Y''
|Y-coordinate of the measuring station
|-
|''Interpretation''
|Information about the time series values, i.e. how to understand the timestamp and the value stored in it. Caution: wrongly defined interpretations inevitably lead to incorrect results.
Choice of: [[Datei:00036_EN.png|mini]]
*BlockLeft
*BlockRight
*Instantaneous_(Linear_Interpolation)
*Cumulative
*CumulativePerTimeStep
*Undefined

|-
|''Memo''
|Description of the origin of the time series and other additional information
|-
|''Origin''
|Origin of the time series
Choice of:
*derived
*measured
*imported
*manual
*simulated
*miscellaneous
*synthetic
|-
|''Type''
|Hydrological, hydrometeorological, reservoir-dependent or geological variable
With this setting the time series is assigned to one of the 15 subfolders of the station.
Choice of:
*area
*discharge
*evaporation
*humidity
*mass movement
*precipitation
*pressure
*soil process
*storage
*sunshine
*temperature
*unknown
*velocity
*water level
*wind
|-
|Unit
|Unit of the variable
Choice of:
?,empty, number, class, mm/m, percent, h/d, 0/00, ml/l, mm, m, cm, km, hm, dm, l/ha, l/km², l/m², mNN, m², km², ha, cm², mm², dm², m³/m, m³, Tsd. m³, Mio. m³, l, hl,
km³, cm³, mm³, m/s, mm/d, mm/h, mm/min, l/s/km², m/h, m/d, l/s/ha, m/s², m³/s, l/s, m³/d, m³/h, l/h, l/d, °C, kg, g, mg, t, s, min, h, d, w, mon, a, Datum,
A, bar, pa, hpa, Grad, Rad, kg/m³, mg/l, g/l, l/kg, ml/g, Grad_C, kg/s, y/n
|-
|}

===Time Series Values===

After a new time series is created and edited, values can be added to it. To do this, right-click on the ''Time Series → Edit Value''. If a time series with values already exists, the values can be edited or deleted.

[[Datei:Zeitreihe0011_EN.png]]

You can use the following buttons:

{| class="wikitable"
|-
|'''Edit''' ||Selected values of the time series can be edited.
|-
|'''Add''' ||Values can be added to the time series.
|-.
|'''Delete''' ||Selected values of the time series can be deleted. This operation cannot be undone.
|-
|}

====Add Values to Time Series====

To add new values to the time series, click on '''add'''. The following ''TalsimNGZreProvider'' window opens. This indicates that the time series does not contain any values yet, and is, therefore, not stored on the server on in the database. By clicking '''OK''' the window for editing the time series values opens.

[[Datei:Zeitreihe012_EN.png|Datei:Zeitreihe012_EN.png]] [[Datei:Zeitreihe013_EN.png]]

Here you can use the following buttons:

{| class="wikitable"
|-
|'''Insert Row''' ||A row is inserted above the selected cell.
|-
|'''Add Row''' || A row is added to the end of the time series.
|-
|'''Remove Row''' ||The selected row is removed.
|-
|'''Graph''' ||The time series is displayed graphically.
|-
|'''Check dates''' ||The date of the time series is checked. This means that the date must be ascending in time.
|-
|'''Write values''' ||The time series and its values are stored on the server and in the database. Additionally, a binary file, named after the ID of the time series, is created in the system data.
|-
|'''Delete values''' ||All values are deleted.
|-
|}

The 'Edit time series' window shows the active time series, as well as the date, which by default corresponds to the date of creating the time series, unless it has been manually changed. Here you can manually enter a date and its corresponding value. You can also copy a time series with dates and values e.g. from Excel and click on the first cell of the table and paste it there (key combination: Ctrl+V).

When the values are inserted, the time series can be displayed using '''Graph'''.

[[Datei:Zeitreihe014_EN.png|Datei:Zeitreihe014_EN.png]]

In the next step the date is checked. If the dates are ascending, a window with "Check successful!" will appear. Otherwise an error message will be displayed.

[[Datei:Zeitreihe015_EN.png|Datei:Zeitreihe015_EN.png]] [[Datei:Zeitreihe016_EN.png|Datei:Zeitreihe016_EN.png]]

If all values are complete and the date is successfully checked, the values are written. In the appearing window, click '''Yes''' to confirm, '''No''' or '''Cancel''' to cancel.

[[Datei:Zeitreihe017_EN.png|Datei:Zeitreihe017_EN.png]]

The implementation of the values into the time series has been successful if the following confirmation window appears. Completing this step, saves the time series in the time series database as well as in the system data as a binary file, and exports the time series to the server. The editing window can now be closed.

[[Datei:Zeitreihe018_EN.png|Datei:Zeitreihe018_EN.png]]

====Edit Values of the Time Series====

Time series can be edited by right-clicking on the ''Time Series → Edit Values → Edit''. The active time series and its appropriate date is displayed. Now you can select the time period for which you want to make changes to load it into the edit window. The data will be displayed accordingly. With the other buttons you can edit the time series as described under [[Special:MyLanguage/Belastungsdefinition / Modellinput#Werte zur Zeitreihe hinzufügen|''Add Values to Time Series'']].

[[Datei:Zeitreihe019_EN.png]]

<div class="mw-translate-fuzzy">
====[[Special:MyLanguage/Werte in der Zeitreihe löschen|Delete Values of the Time Series]]====
</div>

===Display Time Series Graphically===

A time series can be displayed graphically by right-clicking on ''Time Series → Charts''. You have the choice between a [[Special:MyLanguage/Ganglinie|hydrograph]] (Time series chart) and a [[Special:MyLanguage/Dauerlinie|duration curve]].

[[Datei:Zeitreihe020_EN.png]] [[Datei:Zeitreihe021_EN.png]]

=== Evaluate Time Series Statistically===

Right-clicking ''Time Series → Statistics'' opens a statistics tool with which you can calculate severlal statistical measures for a predefined period. Furthermore, you can perform a low water or flood analysis. The results are displayed once you click on '''Calculate''' after entering the required data.

[[Datei:Zeitreihe022_EN.png]]

<div class="mw-translate-fuzzy">
===Import Time Series===
</div>

<div class="mw-translate-fuzzy">
=== Export Time Series===
</div>

<div class="mw-translate-fuzzy">
===Delete Time Series===
</div>

<div class="mw-translate-fuzzy">
===Release Edit-Lock===
</div>

Translations:Zeitreihenverwaltung/19/en

2021-08-30T10:43:09Z

Haghani:

{| class="wikitable" style="width:70%"
|-
|'''Name''' ||Name of the time series.
|-
|'''ID''' ||Identification number of a time series. ID corresponds to the ID of the binary file, stored in the system data. Caution: Not to be confused with the ID of a simulation in the model and on the server.
|-
|'''Type''' ||Hydrological, hydrometeorological, storage-dependent or geological variable. With this setting the time series is assigned to one of the 15 subfolders of the station. Default value: discharge.
|-
|'''Unit''' ||Unit of the values. Default value: m³/s.
|-
|'''Interpretation''' ||Information about the time series values, i.e. how to understand the timestamp and the value stored in it. Caution: wrongly set interpretations inevitably lead to incorrect results. For example, precipitation [mm] is usually a sum per timestep. Default value: Current_value (linear_interpolation)
|-
|'''Origin''' ||Origin of the time series. Default value: measured.
|-
|'''from''' ||Date and time of the start of the time series. Default value: Day and time of creation.
|-
|'''to''' ||Date and time of the end of the time series. Default value: Day and time of creation.
|-
|'''Data points''' ||Number of data points. Default value: 0
|-
|}

Zeitreihenverwaltung/en

2021-08-30T10:42:51Z

Haghani:

<languages/>

{{Navigation|vorher=Menüleiste Systemverwaltung|hoch=Hauptseite|nachher=Einzelfenster von Modellkomponenten}}

Time series can be stored in TALSIM-NG's own time series manager, where they are classified by the type of data and the station they belong to. There they can be viewed graphically and edited tabularly. A basic statistics' tool, which can calculate average values for a defined period of time as well as other statistics, is also integrated in the time series manager.

=== Opening the Time Series Manager===

The time series manager can be accessed via the ''Menu bar → Time series → Time series manager''. The '''Talsim-User Selection''' window, where you are required to choose a user to proceed, appears. If you want to create and edit time series, you should choose your username and confirm with '''OK'''. If you log in using another username, you can only see the stations and time series, but you cannot edit or delete them.

[[Datei:Zeitreihe001_EN.png|Datei:Zeitreihe001EN_.png|500px]]
[[Datei:Zeitreihe002_EN.png]]

If you are logged in with your username and have not created any time series yet, an empty '''TalsminNG - TS Explorer''' opens. This explorer can be customized using '''View''', '''Folder''', as well as the '''folder icon'''.

[[Datei:Zeitreihe003_EN.png]]

===Create New Station===

Time series are principally assigned to stations, e.g. measuring stations. For this reason a station should be created first. To do this, right-click on the ''Explorer → New Station''. A window, where you can enter the name of the station and confirm with '''OK''', will appear.

[[Datei:Zeitreihe004_EN.png]] [[Datei:Zeitreihe005_EN.png|Datei:Zeitreihe005_EN.png]]

Subsequently, a new station, as well as 15 subfolders are created. These subfolders present the different types of the hydrological, hydrometeorological, or storage-dependent variables that can be saved as time series in the TS Explorer.

[[Datei:Zeitreihe006_EN.png]]

You have a choice of the following options when you right-click on the new station in the explorer.

{| class="wikitable" style="width:70%"
|-
|'''New Station''' ||A new empty station with 15 subfolders is created.
|-
|'''Edit Station''' ||The dialog window ''Edit of a Talsim time series station'', in which information about the selected station can be edited, is opened.
|-
|'''Delete Station''' ||The marked station and all associated time series are deleted. This operation cannot be undone.
|-
|'''Copy to Clipboard''' || The list of time series associated with the station as well as their metadata is copied to the clipboard.
|-
|'''New Time Series''' ||A new time series associated with the selected station is created.
|-
|'''Release Edit-lock''' ||Releases the edit-lock of the station, so it can be edited by another user.
|-
|}

=== Create New Time Series===

To create a time series, right-click on the ''Station → New Time Series'' in the [[Special:MyLanguage/Belastungsdefinition / Modellinput#Zeitreihenverwaltung|time series explorer]]. A window will open, prompting you to enter the name of the new time series. Confirm with '''OK'''.

[[Datei:Zeitreihe007_EN.png|Datei:Zeitreihe007_EN.png]]

The following attributes are displayed for each time series in the explorer:

{| class="wikitable" style="width:70%"
|-
|'''Name''' ||Name of the time series.
|-
|'''ID''' ||Identification number of a time series. ID corresponds to the ID of the binary file, stored in the system data. Caution: Not to be confused with the ID of a simulation in the model and on the server.
|-
|'''Type''' ||Hydrological, hydrometeorological, reservoir-dependent or geological variable. With this setting the time series is assigned to one of the 15 subfolders of the station. Default value: discharge.
|-
|'''Unit''' ||Unit of the values. Default value: m³/s.
|-
|'''Interpretation''' ||Information about the time series values, i.e. how to understand the timestamp and the value stored in it. Caution: wrongly set interpretations inevitably lead to incorrect results. For example, precipitation [mm] is usually a sum per timestep. Default value: Current_value (linear_interpolation)
|-
|'''Origin''' ||Origin of the time series. Default value: measured.
|-
|'''from''' ||Date and time of the start of the time series. Default value: Day and time of creation.
|-
|'''to''' ||Date and time of the end of the time series. Default value: Day and time of creation.
|-
|'''Data points''' ||Number of data points. Default value: 0
|-
|}

[[Datei:Zeitreihe008_EN.png]]

The created time series is assigned the chosen name and a consecutive ID number. The other attributes are filled with the default values.

You can use the following buttons if you right-click on the time series in the explorer.

{| class="wikitable" style="width:70%"
|-
|'''Edit Time Series''' ||The selected time series can be edited.
|-
|'''Chart''' ||The time series can be displayed as a graph over time or as a duration curve.
|-
|'''Edit Values''' ||Values with date are added to the selected time series. Values can also be edited or deleted.
|-
|'''Statistics''' ||Calculates a statistical overview of the time series.
|-
|'''Import Time Series''' ||An existing time series can be imported.
|-
|'''Export Time Series''' ||The selected time series can be exported.
|-
|'''Delete Time Series''' ||The selected time series is deleted. This operation cannot be undone.
|-
|'''Release Edit-lock''' ||Releases the edit-lock of the time series, so it can be edited by another user..
|-
|'''Refresh Attributes''' ||After adjusting the attributes of a time series, those attributes are updated in the explorer.
|-
|}

Edit Time Series

To adjust the attributes of a time series, right-click on ''Time Series → Edit Time Series'' in the time series manager.

[[Datei:Zeitreihe009_EN.png]]

The following dialog window, where you can edit the attributes, opens. The attributes assigned to identification and settings, which are displayed in black, can be adjusted with a double-click. By clicking OK all time series attributes can be saved.

[[Datei:Zeitreihe010_EN.png]]

{| class="wikitable" style="width:70%"
|-
|rowspan="2" style="text-align:center" |'''Identification'''
|''Description''
|Description of the time series

|-
|''Name''
|Name of the time series

|-
|rowspan="8" style="text-align:center"|'''Settings'''
|''Altitude masl''
|Height of the measuring station in meters above sea level
|-
|''Coordinate-X''
|X-coordinate of the measuring station
|-
|''Coordinate-Y''
|Y-coordinate of the measuring station
|-
|''Interpretation''
|Information about the time series values, i.e. how to understand the timestamp and the value stored in it. Caution: wrongly defined interpretations inevitably lead to incorrect results.
Choice of: [[Datei:00036_EN.png|mini]]
*BlockLeft
*BlockRight
*Instantaneous_(Linear_Interpolation)
*Cumulative
*CumulativePerTimeStep
*Undefined

|-
|''Memo''
|Description of the origin of the time series and other additional information
|-
|''Origin''
|Origin of the time series
Choice of:
*derived
*measured
*imported
*manual
*simulated
*miscellaneous
*synthetic
|-
|''Type''
|Hydrological, hydrometeorological, reservoir-dependent or geological variable
With this setting the time series is assigned to one of the 15 subfolders of the station.
Choice of:
*area
*discharge
*evaporation
*humidity
*mass movement
*precipitation
*pressure
*soil process
*storage
*sunshine
*temperature
*unknown
*velocity
*water level
*wind
|-
|Unit
|Unit of the variable
Choice of:
?,empty, number, class, mm/m, percent, h/d, 0/00, ml/l, mm, m, cm, km, hm, dm, l/ha, l/km², l/m², mNN, m², km², ha, cm², mm², dm², m³/m, m³, Tsd. m³, Mio. m³, l, hl,
km³, cm³, mm³, m/s, mm/d, mm/h, mm/min, l/s/km², m/h, m/d, l/s/ha, m/s², m³/s, l/s, m³/d, m³/h, l/h, l/d, °C, kg, g, mg, t, s, min, h, d, w, mon, a, Datum,
A, bar, pa, hpa, Grad, Rad, kg/m³, mg/l, g/l, l/kg, ml/g, Grad_C, kg/s, y/n
|-
|}

===Time Series Values===

After a new time series is created and edited, values can be added to it. To do this, right-click on the ''Time Series → Edit Value''. If a time series with values already exists, the values can be edited or deleted.

[[Datei:Zeitreihe0011_EN.png]]

You can use the following buttons:

{| class="wikitable"
|-
|'''Edit''' ||Selected values of the time series can be edited.
|-
|'''Add''' ||Values can be added to the time series.
|-.
|'''Delete''' ||Selected values of the time series can be deleted. This operation cannot be undone.
|-
|}

====Add Values to Time Series====

To add new values to the time series, click on '''add'''. The following ''TalsimNGZreProvider'' window opens. This indicates that the time series does not contain any values yet, and is, therefore, not stored on the server on in the database. By clicking '''OK''' the window for editing the time series values opens.

[[Datei:Zeitreihe012_EN.png|Datei:Zeitreihe012_EN.png]] [[Datei:Zeitreihe013_EN.png]]

Here you can use the following buttons:

{| class="wikitable"
|-
|'''Insert Row''' ||A row is inserted above the selected cell.
|-
|'''Add Row''' || A row is added to the end of the time series.
|-
|'''Remove Row''' ||The selected row is removed.
|-
|'''Graph''' ||The time series is displayed graphically.
|-
|'''Check dates''' ||The date of the time series is checked. This means that the date must be ascending in time.
|-
|'''Write values''' ||The time series and its values are stored on the server and in the database. Additionally, a binary file, named after the ID of the time series, is created in the system data.
|-
|'''Delete values''' ||All values are deleted.
|-
|}

The 'Edit time series' window shows the active time series, as well as the date, which by default corresponds to the date of creating the time series, unless it has been manually changed. Here you can manually enter a date and its corresponding value. You can also copy a time series with dates and values e.g. from Excel and click on the first cell of the table and paste it there (key combination: Ctrl+V).

When the values are inserted, the time series can be displayed using '''Graph'''.

[[Datei:Zeitreihe014_EN.png|Datei:Zeitreihe014_EN.png]]

In the next step the date is checked. If the dates are ascending, a window with "Check successful!" will appear. Otherwise an error message will be displayed.

[[Datei:Zeitreihe015_EN.png|Datei:Zeitreihe015_EN.png]] [[Datei:Zeitreihe016_EN.png|Datei:Zeitreihe016_EN.png]]

If all values are complete and the date is successfully checked, the values are written. In the appearing window, click '''Yes''' to confirm, '''No''' or '''Cancel''' to cancel.

[[Datei:Zeitreihe017_EN.png|Datei:Zeitreihe017_EN.png]]

The implementation of the values into the time series has been successful if the following confirmation window appears. Completing this step, saves the time series in the time series database as well as in the system data as a binary file, and exports the time series to the server. The editing window can now be closed.

[[Datei:Zeitreihe018_EN.png|Datei:Zeitreihe018_EN.png]]

====Edit Values of the Time Series====

Time series can be edited by right-clicking on the ''Time Series → Edit Values → Edit''. The active time series and its appropriate date is displayed. Now you can select the time period for which you want to make changes to load it into the edit window. The data will be displayed accordingly. With the other buttons you can edit the time series as described under [[Special:MyLanguage/Belastungsdefinition / Modellinput#Werte zur Zeitreihe hinzufügen|''Add Values to Time Series'']].

[[Datei:Zeitreihe019_EN.png]]

<div class="mw-translate-fuzzy">
====[[Special:MyLanguage/Werte in der Zeitreihe löschen|Delete Values of the Time Series]]====
</div>

===Display Time Series Graphically===

A time series can be displayed graphically by right-clicking on ''Time Series → Charts''. You have the choice between a [[Special:MyLanguage/Ganglinie|hydrograph]] (Time series chart) and a [[Special:MyLanguage/Dauerlinie|duration curve]].

[[Datei:Zeitreihe020_EN.png]] [[Datei:Zeitreihe021_EN.png]]

=== Evaluate Time Series Statistically===

Right-clicking ''Time Series → Statistics'' opens a statistics tool with which you can calculate severlal statistical measures for a predefined period. Furthermore, you can perform a low water or flood analysis. The results are displayed once you click on '''Calculate''' after entering the required data.

[[Datei:Zeitreihe022_EN.png]]

<div class="mw-translate-fuzzy">
===Import Time Series===
</div>

<div class="mw-translate-fuzzy">
=== Export Time Series===
</div>

<div class="mw-translate-fuzzy">
===Delete Time Series===
</div>

<div class="mw-translate-fuzzy">
===Release Edit-Lock===
</div>

Translations:Zeitreihenverwaltung/11/en

2021-08-30T10:42:50Z

Haghani:

Subsequently, a new station, as well as 15 subfolders are created. These subfolders present the different types of the hydrological, hydrometeorological, or storage-dependent variables that can be saved as time series in the TS Explorer.

Fenster der Systemelemente/en

2021-08-30T10:42:17Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Einzelfenster von Modellkomponenten|nachher=Einzugsgebietsfenster}}

The system elements in Talsim-NG are filled by using two types of windows.

==General Window of System Elements==

The settings, which are, to a large extent, similar for all elements, are predefined in a general window. This window opens automatically when creating a new system element. It contains the following tabs:

;Key
: 4-digit unique key of the element; the first letter is determined by the element type.
: Short description of the system element.
;Outflows
: Keys of the outflow elements. Depending on the type of element there is the possibility to assign one or more outflow elements. To do so, select the corresponding element from the list on the right side of the window and assign it to the desired outflow using the arrow key.
;Flow direction
: Display of the flow direction in the flow network map. This setting has no effect on the calculation.
;Symbol
: Symbol which shall represent the system element in the system plan. For each element type there are different options with a short description of what the symbols are intended for. The symbols have no influence on the calculation of the system element and a differentiation within an element type only serves to improve the clarity of the flow network map. Therefore, each user can make a distinction according to one's own criteria or use the default symbol.
;Description
: Detailed description of the system element.

<gallery widths=200px mode="nolines">
Datei:Fenster_Systemelemente_Kennung_EN.png|Key
Datei:Fenster_Systemelemente_Abläufe_EN.png|Outflows
Datei:Fenster_Systemelemente_Fließrichtung_EN.png|Flow direction
Datei:Fenster_Systemelemente_Symbol_EN.png|Symbol
Datei:Fenster_Systemelemente_Beschreibung_EN.png|Description
</gallery>

Later, this window can be opened by right-clicking on the system element and selecting ''Key'', ''Outflows'' or ''Flow direction'' from the appearing menu, also allowing changes to the settings.

==Properties of System Elements==

The second window shows the properties of a system element which will differ for each element type. The window contains the calculation methods for the system element, as well as the corresponding characteristics and parameters.

*[[Special:MyLanguage/Einzugsgebietsfenster|Sub-basin window]]
*[[Special:MyLanguage/Einzeleinleiterfenster|Point source window]]
*[[Special:MyLanguage/Transportstreckenfenster|Transport element window]]
*[[Special:MyLanguage/Verbraucherfenster|Consumer window]]
*[[Special:MyLanguage/Verzweigungsfenster|Diversion window]]
*[[Special:MyLanguage/Speicherfenster|Storage window]]

The properties can be opened by double-clicking on the system element or by right-clicking → ''Properties''.

Translations:Fenster der Systemelemente/10/en

2021-08-30T10:42:16Z

Haghani:

*[[Special:MyLanguage/Einzugsgebietsfenster|Sub-basin window]]
*[[Special:MyLanguage/Einzeleinleiterfenster|Point source window]]
*[[Special:MyLanguage/Transportstreckenfenster|Transport element window]]
*[[Special:MyLanguage/Verbraucherfenster|Consumer window]]
*[[Special:MyLanguage/Verzweigungsfenster|Diversion window]]
*[[Special:MyLanguage/Speicherfenster|Storage window]]

Anwendungsbeispiel: Umsetzung eines Betriebsplans/en

2021-08-30T10:41:27Z

Haghani:

<languages/>

{{Navigation|vorher=Berechungsschema/ Implementierung der Betriebsregeln|hoch=Betriebsregelkonzept|nachher=Begriffsdefinitionen}}

Taking the [https://de.wikipedia.org/wiki/Wehebachtalsperre Wehebach-Dam] as an example of use, the implementation of an operating plan in accordance with applying laws is illustrated.

The Wehebach-Dam is a multi-purpose storage used for water supply and flood protection. In addition, a standard discharge of 100 l/s to the downstream watercourse is to be maintained. The operator of the dam is the [http://www.wver.de Water association Eifel-Rur]. The operation responsibilities include the drinking water supply of the greater Aachen area, the northern Eifel region and the supply of service water for several industrial companies. The catchment area of the dam is 43.61 km², the average annual inflow is 21 million m³, and the storage capacity is 119.3%. Built as a rockfill dam, the construction of the storage was completed in 1983.

The following operating plan was drawn up for the Wehebach-Dam:

* ''Characteristics of the dam:''

:Max. content at crest level: 27.1M m³
:Capacity to the spillway: 25.06M m³
:Capacity level (normal water level): see flood control areas

* ''Release volume for water supply:''

The storage provides two water supply companies with drinking water. The companies request water via daily demand values. Concerning the water supply, it is set that up to 11 million m³ must be provided annually as drinking water, of which no more than 2.5 million m³ may be discharged each month.

* ''Standard discharge:''

The standard discharge is intended to provide a minimum flow downstream of the dam and is set depending on the inflow, as follows:

:{| cellspacing="0" cellpadding="5"
|   || Inflow || ≥ 200 l/s || → || Standard discharge || = || 200 l/s
|-
| 100 l/s ≤ || Inflow || < 200 l/s || → || Standard discharge || = || Inflow
|-
|   || Inflow || < 100 l/s || → || Standard discharge || = || 100 l/s
|}

Every water resources management year, not later than the end of March, 4 m³/s must be discharged to the downstream watercourse as a flushing wave over a period of 6 hours.

* ''Flood control areas:''

To ensure sufficing flood protection, a time-variable pool-based flood level is defined. The lower limit of the flood control areas is defined as the capacity level.

:{| cellspacing="0" cellpadding="5"
| 1.10. - 31.10. || Flood control area || = 1.00M m³ || Capacity level || = 24.06M m³
|-
| 1.11. - 30.11. || Flood control area || = 2.75M m³ || Capacity level || = 22.31M m³
|-
| 1.12. - 15.1. || Flood control area || = 4.50M m³ || Capacity level || = 20.56M m³
|-
| 16.1. - 31.3. || Flood control area || = 2.50M m³ || Capacity level || = 22.56M m³
|-
| 1.4. - 30.4. || Flood control area || = 1.75M m³ || Capacity level || = 23.31M m³
|-
| 1.5. - 30.9. || Flood control area || = 1.00M m³ || Capacity level || = 24.06M m³
|}

Clearance of flood control areas is done at the maximal permitted discharge.

* ''Maximal permitted discharge:''

As long as the normal water level has not yet been reached, no more than 5 m³/s may be discharged to the downstream watercourse.

If the normal water level of the dam is exceeded and the inflow exceeds the maximum discharge of 5 m³/s, no more than 5 m³/s may be discharged from the bottom outlet. Additional inflow is to be discharged via the spillway.

* ''Capacity curve of the spillway:''

The characteristic curve is given as a X-Y curve with interpolation points.

The realization of the operating plan considering the terminology described above, first requires the identification of all expectations and uses for the dam and a definition of the ''discharge functions''. The following information is provided only to illustrate the operating plan concept and does not claim to be complete or an accurate representation of actual conditions.

* '''''Use:''' Water supply''

:{| cellspacing="0" cellpadding="5"
| colspan="2" | <u>Temporal dependency:</u> || Constant annualized discharge function, variable demand
|-
| colspan="2" | <u>External dependencies:</u> || Yes
|-
|   || 1. Current water demand [m³/s]: || Factor1 (calculation rule: multiplication)
|-
|   || 2. Monthly balance of withdrawals: || Factor2 (calculation rule: multiplication)
|-
|   || 3. Annual balance of withdrawals: || Factor3 (calculation rule: multiplication)
|-
| colspan="2" valign="top" | <u>Discharge per time step:</u> || Calculation of the use 'water supply' with:<br/>
<code>Discharge = Factor1 × Factor2 × Factor3 × f(Storage volume)</code>
|}

:{| class="wikitable" cellspacing="0" cellpadding="5" border="1"
|- style="background-color:#CCCCCC;"
! width="300" | Conditions
! width="200" | Discharge functions
|-
| <u>Fulfillment of demand [%]:</u>

Period of validity: Jan. 1 - Dec. 31.

Explanation: Starting from a storage capacity of < 10 million m³, the fulfillment of demand is reduced to 80%. If the storage volume falls below 2 million m³, no more water is withdrawn.

| align="center" | [[Bild:Theorie_Bsp01.png|thumb|none]]
|- style="background-color:#CCCCCC;"
! Conditions !! System State Functions
|-
| <u>Actual water demand [m³/s]:</u>

(Factor 1)

Time reference: current value

Calculation rule: multiplication
| align="center" | No function necessary
|-
| <u>Monthly balance of discharge [-]:</u>

(Factor 2)

Time reference: monthly balance

Period of validity: Jan. 1 - Dec. 31.

Limit value: 2.5M m³

Calculation rule: multiplication
| align="center" | [[Bild:Theorie_Bsp02.png|thumb|none]]
|-
| <u>Annual balance of discharge [-]:</u>

(Factor 3)

Time reference: annual balance

Period of validity: Jan. 1 - Dec. 31.

Limit value: 11.0M m³

Calculation rule: multiplication
| [[Bild:Theorie_Bsp03.png|thumb|none]]
|}

* '''''Use:''' Flood Protection''

:{| cellspacing="0" cellpadding="5"
| <u>Time dependency:</u> || Yes
|-
| <u>External dependencies:</u> || No
|-
| valign="top" | <u>Discharge per time step:</u> || The use 'flood protection' is given directly as a function of the date.
<code>Discharge = f(storage volume)</code>
|}

:{| class="wikitable" cellspacing="0" cellpadding="5" border="1"
|- style="background-color:#CCCCCC;"
! width="300" | Conditions
! width="200" | Discharge Functions
|-
| Period of validity: Dec. 1 - Jan. 15.

Maximal permitted discharge: 5 m³/s

Capacity level: 20.56M m³
| [[Bild:Theorie_Bsp04.png|thumb|none]]
|-
|Period of validity: 16 Jan - 31 March

Maximal permitted discharge: 5 m³/s

Capacity level: 22.56M m³
| [[Bild:Theorie_Bsp05.png|thumb|none]]
|-
| Period of validity: April 1 - April 30

Maximal permitted discharge: 5 m³/s

Capacity level: 23.31M m³/s
| [[Bild:Theorie_Bsp06.png|thumb|none]]
|-
| colspan="2" | For the remaining periods, the discharge functions are analogous.
|}

* '''''Use:''' Standard discharge''

:{| cellspacing="0" cellpadding="5"
| colspan="2" | <u>Time dependency:</u> || Yes
|-
| colspan="2" | <u>External dependencies:</u> || Yes
|-
|   || 1. Current inflow {m³/s]: || Factor 1 (calculation rule: multiplication)
|-
| colspan="2" valign="top" | <u>Discharge per time step:</u> || Calculation of the use 'standard discharge' with:<br/>
<code>Discharge = Factor × f(storage volume)</code>
|}

:{| class="wikitable" cellspacing="0" cellpadding="5" border="1"
|- style="background-color:#CCCCCC;"
! width="300" | Conditions
! width="200" | Discharge Functions
|-
| <u>Factor standard discharge [-]:</u>

Period of validity: Jan. 1 - Dec. 31.

Explanation: If the storage volume declines below 2 million m³, a standard discharge is no longer maintained.

| [[Bild:Theorie_Bsp07.png|thumb|none]]
|- style="background-color:#CCCCCC;"
! Conditions
! System State Functions
|-
| <u>Current inflow [m³/s]:</u>

(Factor 1)

Period of validity: Jan. 1 - Dec. 31.

Maximal permitted discharge: 5 m³/s

Explanation: If the inflow exceeds 0.2 m³/s, a discharge of 0.2 m³/s continues.

| [[Bild:Theorie_Bsp08.png|thumb|none]]
|}

[[Bild:Theorie_Abb26.png|thumb|Abbildung 26: Skalierte Abgabenfunktionen]]

For a selected time and an assumed initial storage volume of S<sub>0</sub> = 23K m³, all relations are plotted in [[:Bild:Theorie_Abb26.png|Abbildung 26]]. For illustration purposes, a different y-axis scale is chosen for the flood control function.

{| class="wikitable" cellspacing="0" cellpadding="5" border="1"
|- style="background-color:#CCCCCC;"
! Parameters !! Defaults !! Affected Parameters:
|-
| Time || January 30 || flood protection, water supply. (Factor1, Factor2)
|-
| Initial storage volume || 23M m³ || all discharge functions
|-
| Average daily inflow || 0.180 m³/s || standard discharge
|-
| Average water demand || 0.300 m³/s || discharge for water supply
|-
| Discharge for water supply since 1.Jan. || 0.750M m³ || discharge for water supply
|}

Translations:Anwendungsbeispiel: Umsetzung eines Betriebsplans/8/en

2021-08-30T10:41:27Z

Haghani:

The storage provides two water supply companies with drinking water. The companies request water via daily demand values. Concerning the water supply, it is set that up to 11 million m³ must be provided annually as drinking water, of which no more than 2.5 million m³ may be discharged each month.

Anwendungsbeispiel: Umsetzung eines Betriebsplans/en

2021-08-30T10:41:13Z

Haghani:

<languages/>

{{Navigation|vorher=Berechungsschema/ Implementierung der Betriebsregeln|hoch=Betriebsregelkonzept|nachher=Begriffsdefinitionen}}

Taking the [https://de.wikipedia.org/wiki/Wehebachtalsperre Wehebach-Dam] as an example of use, the implementation of an operating plan in accordance with applying laws is illustrated.

The Wehebach-Dam is a multi-purpose storage used for water supply and flood protection. In addition, a standard discharge of 100 l/s to the downstream watercourse is to be maintained. The operator of the dam is the [http://www.wver.de Water association Eifel-Rur]. The operation responsibilities include the drinking water supply of the greater Aachen area, the northern Eifel region and the supply of service water for several industrial companies. The catchment area of the dam is 43.61 km², the average annual inflow is 21 million m³, and the storage capacity is 119.3%. Built as a rockfill dam, the construction of the storage was completed in 1983.

The following operating plan was drawn up for the Wehebach-Dam:

* ''Characteristics of the dam:''

:Max. content at crest level: 27.1M m³
:Capacity to the spillway: 25.06M m³
:Capacity level (normal water level): see flood control areas

* ''Release volume for water supply:''

The reservoir provides two water supply companies with drinking water. The companies request water via daily demand values. Concerning the water supply, it is set that up to 11 million m³ must be provided annually as drinking water, of which no more than 2.5 million m³ may be discharged each month.

* ''Standard discharge:''

The standard discharge is intended to provide a minimum flow downstream of the dam and is set depending on the inflow, as follows:

:{| cellspacing="0" cellpadding="5"
|   || Inflow || ≥ 200 l/s || → || Standard discharge || = || 200 l/s
|-
| 100 l/s ≤ || Inflow || < 200 l/s || → || Standard discharge || = || Inflow
|-
|   || Inflow || < 100 l/s || → || Standard discharge || = || 100 l/s
|}

Every water resources management year, not later than the end of March, 4 m³/s must be discharged to the downstream watercourse as a flushing wave over a period of 6 hours.

* ''Flood control areas:''

To ensure sufficing flood protection, a time-variable pool-based flood level is defined. The lower limit of the flood control areas is defined as the capacity level.

:{| cellspacing="0" cellpadding="5"
| 1.10. - 31.10. || Flood control area || = 1.00M m³ || Capacity level || = 24.06M m³
|-
| 1.11. - 30.11. || Flood control area || = 2.75M m³ || Capacity level || = 22.31M m³
|-
| 1.12. - 15.1. || Flood control area || = 4.50M m³ || Capacity level || = 20.56M m³
|-
| 16.1. - 31.3. || Flood control area || = 2.50M m³ || Capacity level || = 22.56M m³
|-
| 1.4. - 30.4. || Flood control area || = 1.75M m³ || Capacity level || = 23.31M m³
|-
| 1.5. - 30.9. || Flood control area || = 1.00M m³ || Capacity level || = 24.06M m³
|}

Clearance of flood control areas is done at the maximal permitted discharge.

* ''Maximal permitted discharge:''

As long as the normal water level has not yet been reached, no more than 5 m³/s may be discharged to the downstream watercourse.

If the normal water level of the dam is exceeded and the inflow exceeds the maximum discharge of 5 m³/s, no more than 5 m³/s may be discharged from the bottom outlet. Additional inflow is to be discharged via the spillway.

* ''Capacity curve of the spillway:''

The characteristic curve is given as a X-Y curve with interpolation points.

The realization of the operating plan considering the terminology described above, first requires the identification of all expectations and uses for the dam and a definition of the ''discharge functions''. The following information is provided only to illustrate the operating plan concept and does not claim to be complete or an accurate representation of actual conditions.

* '''''Use:''' Water supply''

:{| cellspacing="0" cellpadding="5"
| colspan="2" | <u>Temporal dependency:</u> || Constant annualized discharge function, variable demand
|-
| colspan="2" | <u>External dependencies:</u> || Yes
|-
|   || 1. Current water demand [m³/s]: || Factor1 (calculation rule: multiplication)
|-
|   || 2. Monthly balance of withdrawals: || Factor2 (calculation rule: multiplication)
|-
|   || 3. Annual balance of withdrawals: || Factor3 (calculation rule: multiplication)
|-
| colspan="2" valign="top" | <u>Discharge per time step:</u> || Calculation of the use 'water supply' with:<br/>
<code>Discharge = Factor1 × Factor2 × Factor3 × f(Storage volume)</code>
|}

:{| class="wikitable" cellspacing="0" cellpadding="5" border="1"
|- style="background-color:#CCCCCC;"
! width="300" | Conditions
! width="200" | Discharge functions
|-
| <u>Fulfillment of demand [%]:</u>

Period of validity: Jan. 1 - Dec. 31.

Explanation: Starting from a storage capacity of < 10 million m³, the fulfillment of demand is reduced to 80%. If the storage volume falls below 2 million m³, no more water is withdrawn.

| align="center" | [[Bild:Theorie_Bsp01.png|thumb|none]]
|- style="background-color:#CCCCCC;"
! Conditions !! System State Functions
|-
| <u>Actual water demand [m³/s]:</u>

(Factor 1)

Time reference: current value

Calculation rule: multiplication
| align="center" | No function necessary
|-
| <u>Monthly balance of discharge [-]:</u>

(Factor 2)

Time reference: monthly balance

Period of validity: Jan. 1 - Dec. 31.

Limit value: 2.5M m³

Calculation rule: multiplication
| align="center" | [[Bild:Theorie_Bsp02.png|thumb|none]]
|-
| <u>Annual balance of discharge [-]:</u>

(Factor 3)

Time reference: annual balance

Period of validity: Jan. 1 - Dec. 31.

Limit value: 11.0M m³

Calculation rule: multiplication
| [[Bild:Theorie_Bsp03.png|thumb|none]]
|}

* '''''Use:''' Flood Protection''

:{| cellspacing="0" cellpadding="5"
| <u>Time dependency:</u> || Yes
|-
| <u>External dependencies:</u> || No
|-
| valign="top" | <u>Discharge per time step:</u> || The use 'flood protection' is given directly as a function of the date.
<code>Discharge = f(storage volume)</code>
|}

:{| class="wikitable" cellspacing="0" cellpadding="5" border="1"
|- style="background-color:#CCCCCC;"
! width="300" | Conditions
! width="200" | Discharge Functions
|-
| Period of validity: Dec. 1 - Jan. 15.

Maximal permitted discharge: 5 m³/s

Capacity level: 20.56M m³
| [[Bild:Theorie_Bsp04.png|thumb|none]]
|-
|Period of validity: 16 Jan - 31 March

Maximal permitted discharge: 5 m³/s

Capacity level: 22.56M m³
| [[Bild:Theorie_Bsp05.png|thumb|none]]
|-
| Period of validity: April 1 - April 30

Maximal permitted discharge: 5 m³/s

Capacity level: 23.31M m³/s
| [[Bild:Theorie_Bsp06.png|thumb|none]]
|-
| colspan="2" | For the remaining periods, the discharge functions are analogous.
|}

* '''''Use:''' Standard discharge''

:{| cellspacing="0" cellpadding="5"
| colspan="2" | <u>Time dependency:</u> || Yes
|-
| colspan="2" | <u>External dependencies:</u> || Yes
|-
|   || 1. Current inflow {m³/s]: || Factor 1 (calculation rule: multiplication)
|-
| colspan="2" valign="top" | <u>Discharge per time step:</u> || Calculation of the use 'standard discharge' with:<br/>
<code>Discharge = Factor × f(storage volume)</code>
|}

:{| class="wikitable" cellspacing="0" cellpadding="5" border="1"
|- style="background-color:#CCCCCC;"
! width="300" | Conditions
! width="200" | Discharge Functions
|-
| <u>Factor standard discharge [-]:</u>

Period of validity: Jan. 1 - Dec. 31.

Explanation: If the storage volume declines below 2 million m³, a standard discharge is no longer maintained.

| [[Bild:Theorie_Bsp07.png|thumb|none]]
|- style="background-color:#CCCCCC;"
! Conditions
! System State Functions
|-
| <u>Current inflow [m³/s]:</u>

(Factor 1)

Period of validity: Jan. 1 - Dec. 31.

Maximal permitted discharge: 5 m³/s

Explanation: If the inflow exceeds 0.2 m³/s, a discharge of 0.2 m³/s continues.

| [[Bild:Theorie_Bsp08.png|thumb|none]]
|}

[[Bild:Theorie_Abb26.png|thumb|Abbildung 26: Skalierte Abgabenfunktionen]]

For a selected time and an assumed initial storage volume of S<sub>0</sub> = 23K m³, all relations are plotted in [[:Bild:Theorie_Abb26.png|Abbildung 26]]. For illustration purposes, a different y-axis scale is chosen for the flood control function.

{| class="wikitable" cellspacing="0" cellpadding="5" border="1"
|- style="background-color:#CCCCCC;"
! Parameters !! Defaults !! Affected Parameters:
|-
| Time || January 30 || flood protection, water supply. (Factor1, Factor2)
|-
| Initial storage volume || 23M m³ || all discharge functions
|-
| Average daily inflow || 0.180 m³/s || standard discharge
|-
| Average water demand || 0.300 m³/s || discharge for water supply
|-
| Discharge for water supply since 1.Jan. || 0.750M m³ || discharge for water supply
|}

Translations:Anwendungsbeispiel: Umsetzung eines Betriebsplans/3/en

2021-08-30T10:41:13Z

Haghani:

The Wehebach-Dam is a multi-purpose storage used for water supply and flood protection. In addition, a standard discharge of 100 l/s to the downstream watercourse is to be maintained. The operator of the dam is the [http://www.wver.de Water association Eifel-Rur]. The operation responsibilities include the drinking water supply of the greater Aachen area, the northern Eifel region and the supply of service water for several industrial companies. The catchment area of the dam is 43.61 km², the average annual inflow is 21 million m³, and the storage capacity is 119.3%. Built as a rockfill dam, the construction of the storage was completed in 1983.

Beschreibung der Systemelemente/en

2021-08-30T10:40:34Z

Haghani:

<languages/>

{{Navigation|vorher=Modellkonzept|hoch=Hauptseite#Theoretische Grundlagen|nachher=Einzugsgebiet}}
In Talsim-NG, a river basin model is setup according to a modular principle. All relevant objects and processes of the [[Special:MyLanguage/Begriffsdefinitionen|water resources system]] are represented by system elements. These can be linked together as building blocks to represent the entire system including its interactions.

Each system element has specific [[Special:MyLanguage/Begriffsdefinitionen|properties]] and methods, is able to process certain input variables and provides specific output variables (see [[Special:MyLanguage/Modellkonzept|model concept]]). The following table gives an overview of all system elements in Talsim-NG with their most important properties/methods as well as input and output variables:

{| class="wikitable"
|-
! Element || Important loads || Properties / methods || Element output
|-
| [[Special:MyLanguage/Einzugsgebiet|Sub-basin]] <br />[[Datei:Systemelement001.png|40px]] ||
*Precipitation
*Temperature
*Evaporation
||
*Soil properties/imperviousness
*Runoff generation
*Runoff distribution
*Runoff concentration
*...
||
*Surface runoff
*Baseflow
*Total discharge
*...
|-
| [[Special:MyLanguage/Einleitung|Point source]] <br />[[Datei:Systemelement002.png|40px]]|| ||
*Water input into the system
||
*Runoff
|-
| [[Special:MyLanguage/Transportstrecke|Transport reach]] <br />[[Datei:Systemelement003.png|40px]]||
*Inflow
||
*Translation
*Retention
||
*Runoff
|-
| [[Special:MyLanguage/Verbraucher|Consumer]] <br />[[Datei:Systemelement004.png|40px]]||
*Inflow
||
*Consumption behavior
*External contribution
*Return flow into the system
||
*Return flow
*External contribution
*Total discharge
|-
| [[Special:MyLanguage/Verzweigung|Diversion]] <br />[[Datei:Systemelement005.png|50px]]||
*Inflow
||
*Diversion rule
||
*Two outflows
|-
| [[Special:MyLanguage/Speicher|Storage]] <br />[[Datei:Systemelement006.png|50px]]||
*Inflow
optional:
*Precipitation
*Evaporation
||
*Storage rating curve
*Storage-surface rating curve
*Capacity of operational equipment
*Operating rules
*(Infiltration properties)
*...
||
*Releases
*Storage
*Water level
|-
| [[Special:MyLanguage/Zielpegel|System outlet]] <br />[[Datei:Symbol_Zielpegel.PNG]]||
*Inflow
||
||
|-
|}

Translations:Beschreibung der Systemelemente/3/en

2021-08-30T10:40:34Z

Haghani:

{| class="wikitable"
|-
! Element || Important loads || Properties / methods || Element output
|-
| [[Special:MyLanguage/Einzugsgebiet|Sub-basin]] <br />[[Datei:Systemelement001.png|40px]] ||
*Precipitation
*Temperature
*Evaporation
||
*Soil properties/imperviousness
*Runoff generation
*Runoff distribution
*Runoff concentration
*...
||
*Surface runoff
*Baseflow
*Total discharge
*...
|-
| [[Special:MyLanguage/Einleitung|Point source]] <br />[[Datei:Systemelement002.png|40px]]|| ||
*Water input into the system
||
*Runoff
|-
| [[Special:MyLanguage/Transportstrecke|Transport reach]] <br />[[Datei:Systemelement003.png|40px]]||
*Inflow
||
*Translation
*Retention
||
*Runoff
|-
| [[Special:MyLanguage/Verbraucher|Consumer]] <br />[[Datei:Systemelement004.png|40px]]||
*Inflow
||
*Consumption behavior
*External contribution
*Return flow into the system
||
*Return flow
*External contribution
*Total discharge
|-
| [[Special:MyLanguage/Verzweigung|Diversion]] <br />[[Datei:Systemelement005.png|50px]]||
*Inflow
||
*Diversion rule
||
*Two outflows
|-
| [[Special:MyLanguage/Speicher|Storage]] <br />[[Datei:Systemelement006.png|50px]]||
*Inflow
optional:
*Precipitation
*Evaporation
||
*Storage rating curve
*Storage-surface rating curve
*Capacity of operational equipment
*Operating rules
*(Infiltration properties)
*...
||
*Releases
*Storage
*Water level
|-
| [[Special:MyLanguage/Zielpegel|System outlet]] <br />[[Datei:Symbol_Zielpegel.PNG]]||
*Inflow
||
||
|-
|}

Betriebsregelkonzept/en

2021-08-30T10:39:02Z

Haghani:

<languages/>

{{Navigation|vorher=Berechnungsschema von Speichern|hoch=Hauptseite|nachher=Betriebsregeltypen}}

In order to achieve the best possible water resource management of storage systems, you need instructions that clearly define how water should be stored, released or distributed under given system loads and conditions. These instructions are summarized in an operating plan. An operating plan can consist of many individual instructions, e.g. the compliance with a certain release amount depending on the storage volume. An individual instruction can be called an operating rule.

Since the formulation of an operating rule is always associated with a corrective intervention in the natural flow behaviour, in order to be able to execute the operating rule you must also be able to change the flow in some way. Only few water resource management elements are suitable for this purpose. Normally these will be storages with adjustable releases. Apart from that, there are also controllable diversion structures or weirs. In Talsim-NG the system elements [[Special:MyLanguage/Speicher|storage]] and [[Special:MyLanguage/Verzweigung|diversion]] offer the possibility to be controlled by operating rules.

The purpose of all operating rules is to adapt system states of a water resources system in order to meet specified objectives. It is irrelevant where the system states and target variables occur, as long as the target variables can be influenced by a change in the system states.

In the following
*[[Special:MyLanguage/Betriebsregeltypen|typical operating rules]] for the operation of storages are presented,
*their principles are [[Special:MyLanguage/Abstraktion der Betriebsregeln|abstracted]],
*the [[Special:MyLanguage/Berechungsschema/ Implementierung der Betriebsregeln|implementation of a calculation scheme]] for the simulation is derived,
*and an [[Special:MyLanguage/Anwendungsbeispiel:_Umsetzung_eines_Betriebsplans|example]] demonstrates the implementation of an operating plan in Talsim-NG.

Translations:Betriebsregelkonzept/3/en

2021-08-30T10:39:01Z

Haghani:

Since the formulation of an operating rule is always associated with a corrective intervention in the natural flow behaviour, in order to be able to execute the operating rule you must also be able to change the flow in some way. Only few water resource management elements are suitable for this purpose. Normally these will be storages with adjustable releases. Apart from that, there are also controllable diversion structures or weirs. In Talsim-NG the system elements [[Special:MyLanguage/Speicher|storage]] and [[Special:MyLanguage/Verzweigung|diversion]] offer the possibility to be controlled by operating rules.

Betriebsregeltypen/en

2021-08-30T10:36:09Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a reservoir. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the reservoir for other purposes play a decisive role. A reservoir should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]Reservoir B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Reservoir A to reservoir B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of reservoir B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Storage==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a storage, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined storage volumes, but not maintaining discharges below the set storage volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the storage, additional discharges used for energy production are stopped when the storage volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between storage content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective storage volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the storage volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no storage volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two storages are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/87/en

2021-08-30T10:36:08Z

Haghani:

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two storages are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

Betriebsregeltypen/en

2021-08-30T10:35:54Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a reservoir. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the reservoir for other purposes play a decisive role. A reservoir should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]Reservoir B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Reservoir A to reservoir B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of reservoir B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Storage==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a storage, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined storage volumes, but not maintaining discharges below the set storage volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the storage, additional discharges used for energy production are stopped when the storage volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between storage content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective storage volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the storage volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no storage volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two reservoirs are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/85/en

2021-08-30T10:35:54Z

Haghani:

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no storage volume can be used as a reference value.

Betriebsregeltypen/en

2021-08-30T10:35:35Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a reservoir. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the reservoir for other purposes play a decisive role. A reservoir should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]Reservoir B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Reservoir A to reservoir B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of reservoir B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Storage==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a storage, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined storage volumes, but not maintaining discharges below the set storage volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the storage, additional discharges used for energy production are stopped when the storage volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between storage content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective storage volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the storage volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no reservoir volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two reservoirs are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/79/en

2021-08-30T10:35:35Z

Haghani:

:''If discharge B > 0 and the storage volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

Betriebsregeltypen/en

2021-08-30T10:35:21Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a reservoir. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the reservoir for other purposes play a decisive role. A reservoir should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]Reservoir B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Reservoir A to reservoir B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of reservoir B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Storage==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a storage, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined storage volumes, but not maintaining discharges below the set storage volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the storage, additional discharges used for energy production are stopped when the storage volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between storage content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective storage volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the reservoir volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no reservoir volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two reservoirs are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/76/en

2021-08-30T10:35:21Z

Haghani:

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between storage content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective storage volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

Betriebsregeltypen/en

2021-08-30T10:35:04Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a reservoir. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the reservoir for other purposes play a decisive role. A reservoir should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]Reservoir B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Reservoir A to reservoir B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of reservoir B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Storage==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a storage, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined storage volumes, but not maintaining discharges below the set storage volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the storage, additional discharges used for energy production are stopped when the storage volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between reservoir content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective reservoir volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the reservoir volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no reservoir volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two reservoirs are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/75/en

2021-08-30T10:35:04Z

Haghani:

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the storage, additional discharges used for energy production are stopped when the storage volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

Betriebsregeltypen/en

2021-08-30T10:34:45Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a reservoir. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the reservoir for other purposes play a decisive role. A reservoir should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]Reservoir B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Reservoir A to reservoir B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of reservoir B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Storage==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a storage, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined storage volumes, but not maintaining discharges below the set storage volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the reservoir, additional discharges used for energy production are stopped when the reservoir volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between reservoir content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective reservoir volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the reservoir volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no reservoir volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two reservoirs are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/73/en

2021-08-30T10:34:45Z

Haghani:

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined storage volumes, but not maintaining discharges below the set storage volume.

Betriebsregeltypen/en

2021-08-30T10:34:33Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a reservoir. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the reservoir for other purposes play a decisive role. A reservoir should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]Reservoir B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Reservoir A to reservoir B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of reservoir B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Storage==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a storage, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined reservoir volumes, but not maintaining discharges below the set reservoir volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the reservoir, additional discharges used for energy production are stopped when the reservoir volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between reservoir content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective reservoir volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the reservoir volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no reservoir volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two reservoirs are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/72/en

2021-08-30T10:34:33Z

Haghani:

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a storage, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

Betriebsregeltypen/en

2021-08-30T10:34:10Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a reservoir. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the reservoir for other purposes play a decisive role. A reservoir should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]Reservoir B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Reservoir A to reservoir B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of reservoir B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Storage==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a reservoir, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined reservoir volumes, but not maintaining discharges below the set reservoir volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the reservoir, additional discharges used for energy production are stopped when the reservoir volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between reservoir content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective reservoir volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the reservoir volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no reservoir volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two reservoirs are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/71/en

2021-08-30T10:34:10Z

Haghani:

==Rule Type 9: Priorities for Competing Discharges from a Storage==

Betriebsregeltypen/en

2021-08-30T10:33:50Z

Haghani:

<languages/>

{{Navigation|vorher=|hoch=Betriebsregelkonzept|nachher=Abstraktion der Betriebsregeln}}

The operating plan of a dam or a storage network is part of the official approval of plans and usually is available as a report or presentation. Its complexity can vary: it ranges from simply defining flood protection areas and setting a report and alarm plan to notify the supervisory authorities in exceptional situations to complex sets of rules concerning functional dependencies that derive discharges from varying system states.

As follows, principles to clarify the variety of possible regulations and reduce them to essential dependencies are presented. A concept is derived to represent most operating rules by a few basic calculation rules. The given selection does not claim to be complete, but it is likely to contain the rules applied in practice.

==Basic Principle: Verification of Physical Limits==

[[Datei:Theorie_Abb1.png|thumb|Figure 1: Dependency on storage capacity]]

When specifying discharges according to an operating rule, it is assumed that the outlet capacity is sufficient to meet these discharges. Thus, dimensioning the outlet element must consider the operating requirements. In principle, the physically possible discharge, given by the outlet's characteristic curve at full opening, sets the upper limit value.

If the pressure level or the outlet capacity is sufficient to discharge the desired quantity when fully opened, the discharge can be throttled to the intended level by closing a slide. If the pressure level is insufficient, only the hydraulically possible discharge can be discharged.

*Mathematical abstraction:
:All outlets obeying an operating rule are functions of the storage's volume and cannot exceed the outlets' maximum capacity when fully opened. As soon as the capacity of the outlets exceeds the required discharge, it can be adjusted by partially closing the control elements.

All discharge types from storages mentioned below are subject to this restriction.

==Rule Type 1: Definition of a Minimum Output or a Safely Dischargeable Maximum Output==

[[Datei:Theorie_Abb2.png|thumb|Figure 2: Example for minimum and maximum discharge as a function of storage capacity]]

* Dependency:
:The specification of a minimum or maximum discharge is based on requirements downstream of a reservoir. The maximal discharge is based on the discharge respective to a critical, downstream cross-section. Consequently, a hydraulic method exists for its determination. In contrast, there is no clear guideline for the minimum discharge. Often, ratios of MNQ or MQ are used. Independent of determining the minimum or maximum discharge, the basic principle to verify outlet elements' physical limits is applied. So, minimum and maximum discharge can only be discharged if the outlet capacity is sufficient at the given pressure level. Since, in reality, it is unlikely that the dimensioning of the outlet elements and the required discharge are conflicting, the reference to the dependence on the storage capacity content is rather theoretical but necessary to derive general laws.

* Mathematical abstraction:
:Minimum and maximum discharge are functions of the storage volume and follow the characteristic curve of fully opened outlets at a low filling level. As soon as the outlet elements' capacity is sufficient for the required discharge volume, the discharge can be kept constant by partially closing the control elements.

==Rule Type 2: Maintaining a Flood Protection Area, Possibly Timely Variable Over the Year==

[[Datei:Theorie_Abb3.png|thumb|Figure 3: Example of a function to maintain a flood protection area]]

* Dependency:
:The definition of a flood protection area as a minimum requirement only includes the designation of a volume, which has to be kept free for potential floodwater. The dimensioning is based on flood events with certain recurrence intervals. If the water level exceeds the mark of the protection area, an increased discharge to the downstream water of the storage ensures that the area is kept empty. Thus, this rule is reduced to a relation between discharge and storage volume, where the outlet capacity or a defined maximum discharge can serve as an upper limit for keeping the flood protection area empty. If the flood protection area is variable in time over the year, only the discharge of the respective storage volume is increased.

* Mathematical abstraction:
:There is a direct relation between storage capacity and release. If the storage capacity exceeds the mark of the flood protection area, a discharge occurs. If it remains below the mark, the discharge is set to zero.

==Rule Type 3: Direct Withdrawals from a storage for Drinking or Service Water ==

[[Datei:Theorie_Abb4.png|thumb|Figure 4: Example of a function for drinking or raw water withdrawal]]

* Dependency:
:Primarily, the current demand determines the volume of withdrawals from the storage, but it is also subject to temporal variations. The upper limits for withdrawals are generally set by water rights or defined maximum withdrawal volumes, which refer to selected periods such as a day, a month, a quarter, or a year. Initially, one only considers the current demand communicated by water suppliers, which constitutes a claim towards the storage. There is no connection to the actual storage and the respective storage volume.
:Whether the demand can be pleased by withdrawing water from the storage is determined by the actual storage volumes. To connect the water demand to the actual storage volumes, the structural implementation of withdrawal elements and means of anticipatory management are taken into account. For example, if particularly low storage volumes are reached, it is advisable to throttle withdrawals in advance to avoid the storage running empty and then completely failing at covering the demand during prolonged periods of low water <ref name="Schultz_1989">'''Schultz, G.A.''' (1989): Entwicklung von Betriebsregeln für die Wupper-Talsperre in Niedrig- und Hochwasserzeiten. Wasserwirtschaft 79 (7/8) S. 340-343</ref>. Hence, there is usually space reserved in a dam specifically used for drinking water supply. Its use is handled separately in respective operating plans.

* Mathematical abstraction:
:If the demand is exactly known and unchangeable, a direct relation between withdrawal and storage volume can be defined. However, the demand is subject to certain variations. For this reason, it is recommended to normalize the relationship between withdrawals and storage volume, where the current demand serves as a scaling factor. If the storage volume falls below a defined limit value, only a certain percentage of the current demand is satisfied. The limit value, as well as the form of the function, can be variable in time.

==Rule Type 4: Standard Discharge to Downstream Water==

[[Datei:Theorie_Abb5.png|thumb|Figure 5: Pool-based operating plan in a two-dimensional representation]]

* Dependency:
:The normal discharge to the downstream water should provide a discharge compensation for seasonal differences in the inflow. If a minimum discharge is required, it will be included in the normal discharge. A pool-based operating plan is used to describe the normal discharge. It divides the storage capacity into different areas and assigns a discharge to each pool-based operation. When determining the pool-based operating plan, the long-term discharge and other withdrawals from the reservoir for other purposes play a decisive role. A reservoir should collect water in periods of high inflow but still not overflow to have sufficient reserves in periods of low inflow. The coupling of the releases to the storage pool-based operation is a function of the storage volume. Since the system is supposed to react to variations of inflow during the year, the relationship between storage volume and discharge is usually variable over time.

* Mathematical abstraction:
:[[Datei:Theorie_Abb6.png|thumb|Figure 6: Comparison of a pool-based operating plan in a two- and three-dimensional representation]] Like for the previous rules, the output depends on the storage volume. Usually, a pool-based operating plan is displayed in two-dimensional diagrams. The X-axis shows the time of one year, while the Y-axis shows the storage capacity. Pool-based operations are depicted as lines of equal outputs.

:[[Datei:Theorie_Abb7.png|thumb|Figure 7: Pool-based operating plan with linear interpolation between successive time reference points]]This view is practical but not yet complete: A three-dimensional representation of a simple pool-based operating plan makes this clear. On the X-axis is the time, on the Y-axis the storage capacity is plotted, while the Z-axis shows the output directed upwards.

:The 3D image viewed from above gives the two-dimensional shape. Instead of taking constant blocks for the individual time horizons, a linear connection is also used often.

:[[Datei:Theorie_Abb8.png|thumb|Figure 8: Pool-based operating plan with two types of interpretation (selected month of May)]]For the individual periods - here months - different functional dependencies between storage capacity and outflow are considered. If the storage volume/discharge relation is also considered for a selected point in time, there are two possibilities to connect the discharge nodes. On the one hand, there is the possibility of linear interpolation, and on the other hand, a step function is possible.

:In two-dimensional space, this information is not visible and must be specified separately. However, there is usually the convention to assume that the output between two nodes is constant, i.e. to interpret the pool-based operating plan as shown above in the form of steps.<br clear="all" />

==Rule Type 5: Maintaining Defined Discharges to Downstream Waters (Increase of Low Water / Coverage of Demand)==

[[Datei:Theorie_Abb9.png|thumb|Figure 9: Example of a function between shortfalls and scaling factors for a storage
]]

* Dependency:
:In this case, the current discharge is determined by conditions downstream of a storage. At a cross-section of a water resources system, the so-called ''control point'', where the flow is dependent on the discharge from the upstream storage, a minimum flow is defined. The flow at the control point is composed of the discharge from upstream storages and the lateral inflows between the storages and the control point. If the current flow remains below the set minimum, an additional discharge from upstream storages is necessary. The volume of the additional discharge depends on the difference between the previously defined target flow and the actual flow. Whether the required discharge can be fully provided from the storage depends on the currently available stored volumes in the storage. The lower the level, the less favorable it is to provide additional water. In this context, the increase of low water/coverage of demand behaves completely identical to the drinking or service water withdrawal, with only the triggering factor differing. As mentioned before, a storage-dependent function is scaled by a factor, but this factor is now derived from a comparison between set values and current discharges.

* Mathematical abstraction:
:The determination of the additionally needed discharge is composed of several factors. Firstly, a volumetrically varying shortfall of water results from failing the target discharge. The shortfall of water is then implemented as a scaling factor to the discharge which can be defined by a function. The shortfall of water functions independently, while the scaling factor functions dependently.

[[Datei:Theorie_Abb10.png|thumb|Figure 10: Example of a function for increasing low water levels or meeting demand]]

:Secondly, it depends on the actual storage volume, if and how an additional discharge from the storage can be met. A normalized volume-dependent function and the needed discharge lead to a clear determination of the additional discharge volumes. The following [[:Datei:Theorie_Abb10.png||Fig. 10]] shows an example, where the complete provision of an increased target can only be achieved if the filling level of the storage is above a critical limit (25%).

:If more than one storage has an influence on the relevant control point or if, in principle, more than one storage facility is to be used to meet the demand, the required additional discharge is to be divided between the storages in accordance with the corresponding regulations. A distinction must be made between the direct and indirect influences of a storage on the control point. A direct influence is present if a discharge can have a direct effect on the flow conditions at the control point, i.e. the natural flow between the storage
and the control point can no longer be changed by regulation. If this is not the case, an indirect influence is given.

:All storages with a direct influence on the control point receive a shortfall factor and a volume-dependent, scalable function according to [[:Datei:Theorie_Abb10.png|Figure 10]]. Thus, depending on the shortfall quantities and the storage capacity, the actual discharge can be determined separately for each storage.

==Rule Type 6: Discharge Depending on the storage Inflow==

* Dependency: [[Datei:Theorie_Abb11.png|thumb|Figure 11: Direct dependency between storage and control point]]
:There is a direct dependency between the discharge from the storage and the current inflow to the storage. Similar to the pool-based operating plan, there is also an adaptation to different inflow situations. This is done to prevent depletion or overflowing or to obtain a variable discharge regime downstream. However, long-term inflow fluctuations are difficult to detect with this operating rule, since the observations are only carried out as snapshots and not continuously.

:To determine an inflow-dependent discharge, several components have to be considered. First of all, a relation between the current inflow and discharge must be defined. In addition to the current inflow, the current storage volume is important, because the relation inflow/outflow must not be valid for every filling level. Thus it is likely that the relation is ceded completely or the release quantities are adjusted if the storage level falls below a critical level.

:As this rule can lead to the co-occurrence of relatively small storage volumes and high inflows resulting in high discharge volumes, special attention must be paid to the basic principle of checking the physical limits.

* Mathematical abstraction: [[Datei:Theorie_Abb12.png|thumb|Figure 12: Example of functions for inflow-dependent discharge]]
:In this case, three functional dependencies play a part. First, there is a direct dependency between the current inflow and the discharge. The form of the function can be arbitrary. It is possible to reproduce only individual sections of the inflow, which corresponds to a partial approximation of the discharge to the duration curve of the inflow.

:Second, the inflow/discharge function can be superposed with the relationship between storage volume and discharge. For reasons of clarity, it is recommended to work with a normalized function. This makes it possible to influence the result of the inflow/discharge function for each storage volume, which is especially convenient for low filling levels.

:Finally, the required discharge has to be checked with regard to the outlet elements' capacity.

:[[Datei:Theorie_Abb13.png|thumb|left|Figure 13: Results of different inflow-dependent release strategies]]

:The examples below show how the interaction of different functions affects the discharges. The results are compared in the following figures as inflow and discharge duration lines.

:In the case of a linear relation between inflow and discharge and a constant factor for the storage volume, the duration line of the discharge is a curve corresponding to the inflow reduced by a certain percentage. If the storage volume factor remains constant, the duration line can be changed by varying the inflow/discharge relationship. An additional modification of the factor via the storage volume has the advantage of being able to respond to certain filling levels to prevent the storage from emptying or overflowing.

<br clear="all"/>

==Rule Type 7: Influence of Discharges Trough System States==

* Dependency:
:Rule 7, just as rule 6, is a continuation and generalization of the increase of low water as described in rules 5. Just like a discharge deficit at a cross-section or the storage inflow can influence the discharge, any other system state can. In general terms, this means that a discharge from a storage is triggered, increased, or reduced due to a certain system state. Basically, it is irrelevant where the system state occurs. All measurable variables that influence the transport and storage of water can be considered as system states, e.g. the filling of other storages, discharges, flow regime at a cross-section, a snow depth in the catchment area, current precipitation, or current soil moisture.

:As a requirement to apply those dependencies a detection of the system state is necessary. Practically, this means either that a measuring device must be available to determine needed parameters or the required values are calculated using a mathematical model. Parameters are only considered as snap-shots and not continuously.

:If several system states should influence the discharge, a superposition of the parameters according to a corresponding regulation is necessary.

* Mathematical abstraction:
:Mathematically, the influence of system states on the discharge can always be undertaken by scaling. Two functions are necessary for this. The first function describes the relationship between storage volume and discharge. The second one controls the dependency between the system state and a scaling factor. The connection is done by multiplying the discharge with the scaling factor.

[[Datei:Theorie_Abb13.5.png|thumb|Transition]]

:A simple example is given by a transition from storage A to storage B.

:The decisive discharge is the transition from A to B. The considered system state is the storage volume of B. It seems obvious that a discharge from A to B is only useful if storage A has sufficient provision and storage B has sufficient capacity to hold additional water. This results in the following simple functions:

:[[Datei:Theorie_Abb14.png|thumb|left|Figure 14: Example functions for linking a system state to a discharge]]Reservoir B takes 100% of the discharge from A as long as its filling level does not reach 70% of the maximum volume. Furthermore, it is undesirable to receive additional water for flood protection reasons. The scaling factor decreases from 70% filling level to zero. Starting at a filling level above 50% it becomes increasingly easy to transfer water from Reservoir A to reservoir B. The actual transfer, however, only results from the interaction of both functions, taking into account the current filling level of reservoir B and the scaling derived from it.

:For storage A, the definition of the discharge is in m³/s, while the function for storage B receives a unitless scaling factor. In principle, however, it is possible to exchange the meaning of the functions and to use a unitless function for storage A to scale the desired transfer volume for storage B.

==Rule Type 8: Influencing a Discharge with Balances==

Dependency: [[Datei:Theorie_Abb15.png|thumb|Figure 15 : Example of long-term monthly averages and moving 30 day averages of storage volumes]]
:This rule is an extension of rule 7. Instead of using a current state parameter, the balance of a system state is linked to discharge. It is important that there are set time boundaries for carrying out the balance. However, it is irrelevant whether the balance is interpreted as a sum or as an average. A function that displays scaling factors depending on the actual balance can then be used to influence discharges.

:In practice, this form of dependency is often found where water rights define maximum withdrawal volumes per time unit. But the application of a balance is also interesting regarding the long-term behaviour of storage filling levels or inflows. For example, a discharge could be reduced to build up provisions if the inflow of the past winter half-year was below a defined expected value. Another application is the comparison between long-term and current moving averages of storage filling levels. If the current values deviate from the long-term values by a certain amount, the discharge can be reduced or increased to compensate.

:If linking a discharge to several balances is desired, it is possible to superpose several balances (see example at the end of this chapter).

* Mathematical abstraction: [[Datei:Theorie_Abb16.png|thumb|Figure 16: Example of a rule for standard discharge]]
:The influence of the balance on the discharge is posed by two functions according to rule 7. In addition to the already necessary storage volume/discharge function, there is a relation between the balance and scaling factor. The scaling factor is taken from the difference between the actual balance and the expected value.

:The method is demonstrated with a simple example of a standard discharge.

:For storage A, long-term monthly mean values of the storage volumes and derived sliding 30-day mean values of the storage filling levels, as well as the rule for the standard discharge, are known.

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.

:[[Datei:Theorie_Abb17.png|thumb|left|Abbildung 17: Example functions to link a water balance with a discharge]]The relation between the deviation of the balance and the scaling factor indicates that only starting from a difference greater than 20% a change of the standard discharge takes place. In the case of a decrease of more than 20%, the standard discharge is reduced stepwise. If the actual moving 30-day average exceeds the long-term values by more than 20%, the standard discharge is increased continuously.

:In general, there is also the possibility to extend the relation by superposing and combining several water balances.

:The interaction between water balance and discharge function is explained below.

<br clear="all"/>

==Rule Type 9: Priorities for Competing Discharges from a Reservoir==

* Dependency: [[Datei:Theorie_Abb18.png|thumb|Figure 18: Example for assigning priorities via the position of functions]]
:If there are several discharges from a reservoir, it can occur that it is not possible to carry out all demanded discharges. In such a case, priorities need to be specified, which determine an order in which discharges are to be satisfied. The order of priorities is often a consequence of political decisions and is not subject to physical conditions.

:However, there are some priorities based on physical conditions. An example is turning off a turbine in times of water shortage in favor of securing the water supply. In practice, operating rules often meet this problem by fulfilling demands up to defined reservoir volumes, but not maintaining discharges below the set reservoir volume.

:Another way to describe priorities is to reduce a discharge A exactly by an amount, which is resulting from a second discharge B, with the discharge A never being smaller than zero.

* Practical example:
:The Wiehl dam gives a good example for the practical operating conditions of a dam. The Wiehl dam serves primarily as a drinking water supply and a means for flood protection, and secondarily for energy production. In addition, a minimum flow of 100 l/s has to be guaranteed downstream of the Wiehl dam. The first priority is the drinking water supply. In order to ensure sufficient water quality in the reservoir, additional discharges used for energy production are stopped when the reservoir volume falls below 70% of the total volume. As both the minimum discharge and the turbine discharge leave into the Wiehl, it would also be uncalled-for to maintain the minimum discharge if water was simultaneously discharged through the turbine. This results in a reduction of a discharge A (minimum discharge) by the amount of discharge B (turbine) as described above <ref name="Aggerverband_1999">'''Aggerverband''' (1999): Hydrologische Sicherheit der Genkel- und Aggertalsperre. Gutachten des Fachgebietes Ingenieurhydrologie und Wasserbewirtschaftung, TU Darmstadt</ref>.

* Mathematical abstraction: [[Datei:Theorie_Abb19.png|thumb||Figure 19: Example of a relation between two discharges]]
:Assuming that for each use, following the above rules, a functional dependency between reservoir content and discharge exists, a ranking of several uses is already given by the position of the function's nodes. Then, the respective reservoir volume from which the target discharge is no longer covered to 100% or even reduced to zero is decisive.

:In the example, the ranking of the uses is clearly visible. First, the turbine is switched off, then the increase of low water refrained from until only the discharge covering the water supply remains.

:In addition, it is possible to directly compare two or more discharges. Such a rule could be:

:''If discharge B > 0 and the reservoir volume S < X, then reduce discharge A by the amount of discharge B, with discharge A not being smaller than zero.''

:This means that a linear dependency exists between A and B until B is equal to the value of A. If B increases further, A remains constantly zero.

==Rule Type 11: Water Distribution==

* Dependency:
:If there is the need to distribute water within a water resources system, a distribution rule must be defined.

[[Datei:Theorie_Abb19.5.png|thumb|Diversion]]

:Two types of diversions can occur:
:# Diversion that exclusively follows hydraulic laws
:# Adjustable diversions

:In both cases, relations can always be defined as a function of the inflow. In the second case, these distribution rules represent an operating rule, since they directly influence the transport and storage behavior of water. The number of discharges is basically not limited. The difference to transitions at dams is that in this case no reservoir volume can be used as a reference value.

[[Datei:Theorie_Abb20.png|thumb|Figure 20 :Example of assignment functions for multiple sequences]]

* Practical example:
:The water supply of Windhoek, the capital of Namibia, is provided by three dams. However, the water withdrawal for the drinking water supply is only possible from one dam - the Von Bach Dam. The remaining two reservoirs are connected to the main dam by pipes. However, the volume transferred between Swakopport Dam and Von Bach Dam is not exclusively available for refilling the Von Bach Dam, but also serves to supply the town of Karibib with drinking water.

* Mathematical abstraction:
:[[Datei:Theorie_Abb21.png|thumb|left|Fig. 21: Example of a threshold concept for a division into two flows]]For the definition of division rules, functions depending on the current inflow are an appropriate representation. Thus, both a hydraulic description and a description serving the management of the storage are possible. For each discharge leaving the diversion structure, a distribution function has to be specified. If the functions are to be variable, scaling is recommended.

[[Datei:Theorie_Abb22.png|thumb|Figure 22: Example of a threshold concept with a distribution to serve several users
]]

:If the distribution functions cannot be pre-defined, but the discharge volumes rather result later from demand calculations, then a threshold concept is suitable, which in turn can work with scaling factors. The threshold is scaled by a factor and is therefore variable. As long as the inflow is lower than the threshold, the entire inflow is used to satisfy the demand. Only when the current inflow exceeds the threshold, the remaining amount is discharged.

:If a division into more than two discharges is necessary, the threshold concept can be successively applied several times. The order of the discharges determines the priorities of the water distribution.

==Literature==

<references/>

Translations:Betriebsregeltypen/66/en

2021-08-30T10:33:50Z

Haghani:

:If, for example, on May 1st the average value of the storage volume calculated from the last 30 days amounts to 5.6 million m³ and thus, according to [[:Datei:Theorie_Abb15.png|Fig. 15]], it deviates by 30% from the long-term average value of 8 million m³, a scaling factor of 0.5 results (see [[:Datei:Theorie_Abb16.png|Fig. 16]]). With this value, the standard discharge is reduced and delivers only 0.25m³/s at a current storage filling level of 40%, i.e. 50% less than intended.