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<div class="mw-translate-fuzzy">
{{Navigation|vorher=|hoch=Beschreibung der Systemelemente|nachher=Einleitung}}
{{{Navigation|before=|high=Description of the system elements|after=Introduction}}
[[Datei:Systemelement001.png|50px|none]] The simulation of natural catchment areas requires calculating the processes of runoff generation, distribution and concentration. The methods of calculation used are described below.
[[File:System Element001.png|50px|none|Symbol System Element Catchment Area]]The simulation of natural catchment areas requires the determination of load generation, flow branching and runoff concentration. The methods of calculation used are described below.
</div>




==Load Generation==
==Load Generation==


The load formation describes the determination of precipitation for the considered catchment area. Only one precipitation is used per catchment area. If there are several precipitation stations in the catchment area, it is useful to divide the area into several system elements 'catchment area', until only one precipitation can be assigned to each element.
Load generation is the process of determining the precipitation for the considered catchment area. In Talsim-NG, each sub-basin uses only one precipitation source. If there are several precipitation measurement stations in the catchment area, you can either divide the area into several sub-basins or aggregate precipitation sources, until only one precipitation source can be assigned to each element.




==Runoff generation of paved/unpaved surfaces==
==Runoff Generation for Permeable/Impermeable Areas==


The runoff generation determines the effective precipitation from the rainfall. From this, the components surface runoff, infiltration, evaporation and interflow are derived. A snow calculation is performed at temperatures below zero °C and is based on the Snow-Compaction-Method. Regarding the algorithms of the method, reference is made to the relevant literature.
Runoff generation determines the amount of effective precipitation from the rainfall. From this, the components surface runoff, infiltration, evaporation and interflow are derived. By defaut, snow calculation is carried out at temperatures below zero °C and is based on the Snow-Compaction-Method. Regarding the algorithms of the method, reference is made to the relevant literature.
The natural process from precipitation to runoff is divided into individual phases for the mathematical simulation. In the runoff generation phase, the precipitation (system load) is divided into the "effective precipitation" directly reaching the runoff, and the losses not affecting the runoff (moistening, trough, evaporation and infiltration losses). Therefore, this phase is also called load distribution. The resulting mathematical equation for the momentary load distribution is written as follows:
The natural process from precipitation to runoff is divided into individual phases for the mathematical simulation. In the runoff generation phase, the precipitation (system load) is divided into the "effective precipitation" which is transformed into runoff, and the losses not affecting runoff (wetting, depression, evaporation and infiltration losses). Therefore, this phase is also called load distribution. The resulting mathematical equation for the momentary load distribution is as follows:


<math>N_W(t) =N(t) -VP(t) -I(t) - \frac{dO}{dt} - \frac{dS}{dt}</math>
<math>N_W(t) =N(t) -VP(t) -I(t) - \frac{dO}{dt} - \frac{dS}{dt}</math>


mit:
with:
{|style="margin-left: 40px;"
{|style="margin-left: 40px;"
|<math>N_W</math>: || abflusswirksamer Niederschlag
|<math>N_W</math>: || Runoff-effective precipitation
|-
|-
|<math>N</math>: || Niederschlag
|<math>N</math>: || Precipitation
|-
|-
|<math>VP</math>: || potentielle Verdunstung
|<math>VP</math>: || Potential evaporation
|-
|-
|<math>I</math>: || Infiltration in den Bodenraum
|<math>I</math>: || Infiltration into the soil
|-
|-
|<math>O</math>: || Oberflächenwasservorrat
|<math>O</math>: || Surface water supply
|-
|-
|<math>S</math>: || Schneevorrat
|<math>S</math>: || Snow storage
|-
|-
|}
|}


Nachfolgend werden die in der Gleichung verwendeten Terme und deren Berechnung im Einzelnen erläutert.
In the following, the terms used in the equation and their calculation are explained in detail.




===Niederschlag N(t)===
===Precipitation N(t)===


Die Niederschlagsdaten müssen dem Simulationsmodell in Form von Regenreihen zur Verfügung gestellt werden. Hierbei ist es prinzipiell unerheblich, ob die Niederschlagsreihe ein Blockregen, ein Modellregen, ein gemessener natürlicher Regen, ein Regenspektrum oder eine langjährige Regenreihe ist. Je nach Zielsetzung der Simulationsrechnung ist die geeignete Belastung ausgewählt werden. Die Regenreihen stammen entweder aus der Zeitreihenverwaltung von Talsim-NG oder werden wie bei Anwendung einer Kurzfristprognose durch die Eingabe einer Regendauer, einer Niederschlagshöhe und der Wahl eines Modellregens direkt vor einer Simulation erzeugt.
Precipitation data must be provided to the simulation model in the form of time series. In principle, it is irrelevant whether the precipitation series is a block rain, a model rain, a time series of natural observed rainfall, a rain spectrum or a long-term rainfall time series. The appropriate load has to be selected depending on the objective of the simulation. The rainfall time series are either taken from the time series management of Talsim-NG or, when carrying out a short-term forecast, are generated by entering a duration, an amount and by selecting a model rain directly before a simulation.




===Verdunstung VP(t)===
=== Evaporation VP(t)===


Die Verdunstung wirkt sich in zweifacher Weise auf die Abflussbildung aus. Zum einen sind die Anfangsbedingungen im Einzugsgebiet (Benetzung und Muldenfüllung auf der Oberfläche sowie eingeschränkt auch die Bodenfeuchte bei durchlässigen Flächen) ein Resultat des vor dem betrachteten Niederschlagsereignis stattfindenden Verdunstungsgeschehens, zum anderen wird der zu berechnende abflusswirksame Niederschlag um den Betrag der momentanen Verdunstungsrate geschmälert.
Evaporation has a double effect on runoff generation. On the one hand, the initial conditions in the catchment area (interception and depression storage on the surface as well as to a limited degree the soil moisture of permeable areas) are a result of the evaporation taking place before the considered precipitation event. On the other hand, the current runoff-effective precipitation is affected by the amount of the current evaporation rate.
Die potentielle (energetisch mögliche) Verdunstung VP ist zeitlich und örtlich sehr unterschiedlich und einer genauen Berechnung nur schwer zugänglich. Aus ausgewerteten Messungen von 20 Stationen, deren Mittelwerte als Histogramm in dargestellt sind, wurde folgende Ausgleichsfunktion  ermittelt /BRANDT, 1979/.
 
The potential (energetically possible) evaporation VP varies in time and place and is very difficult to calculate exactly.
 
Talsim-NG offers multiple options for entering/calculating potential evaporation:
* Specification of an external time series with values for the potential evaporation
* Internal calculation of potential evaporation: the potential evaporation can be calculated internally based on temperature and, depending on the method, additional parameters. The following methods are available:
** Penman: requires the specification of average patterns or of time series for sunshine duration, wind speed and relative humidity
** Haude: requires the specification of average patterns or of a time series for relative humidity
** Turc: requires the specification of average patterns or of time series for sunshine duration and relative humidity
** Blaney-Criddle: simplistic method requiring only the specification of a latitude which is used internally to derive the sunshine duration.
* Specification of a fixed evaporation rate per year: when using this option, the entered annual value is distributed inner-annually using the compensation function according to Brandt (see below).
 
====Compensation functions====
The following compensation functions according to Brandt are used to distribute entered annual values for evaporation over the year and to convert daily values to hourly values.
 
Using evaluated measurements of 20 stations, the mean values of which are presented in the following histogram, the following compensation function was determined /BRANDT, 1979/.


<math>VP=(0.96+0.0033 \cdot i) \cdot \sin\frac{2\pi}{365}(i-148)+158</math>
<math>VP=(0.96+0.0033 \cdot i) \cdot \sin\frac{2\pi}{365}(i-148)+158</math>


mit:
with:
{|style="margin-left: 40px;"
{|style="margin-left: 40px;"
|<math>i</math>: || laufender Tag des Abflussjahres
|<math>i</math>: || current day of the hydrological year
|-
|-
|<math>i=1</math>: || 1. November
|<math>i=1</math>: || November 1
|-
|-
|}
|}


Die jährliche potentielle Gesamtverdunstungshöhe beträgt 642 mm. Liegen keine gemessenen Verdunstungswerte vor, kann optional dieser normierte Jahresgang der potentiellen Verdunstung für die Berechnung der aktuellen Verdunstung herangezogen werden. Ist das gewählte Berechnungszeitintervall kleiner als ein Tag, wird mittels des dargestellten Tagesgangs letztendlich die potentielle Verdunstung für jedes Berechnungszeitintervall ermittelt. Ist das Berechnungsintervall &le; 1 Tag entfällt die Berücksichtigung des Tagesganges.
The total annual potential evaporation height in this sample is 642 mm. If no measured evaporation values are available, this normalized annual potential evaporation pattern can optionally be used to calculate the current evaporation. If the simulation time step is less than one day, the potential evaporation for each time step is additionally determined using the daily pattern displayed below. If the calculation interval is more than 1 day, the daily pattern is not taken into account.
<gallery mode="packed" heights=300px">
<gallery mode="packed" heights=300px">
Datei:Jahresgang_ETpot.png|Jahresgang der potentiellen Verdunstung nach /BRANDT, 1979/
Datei:Jahresgang_ETpot_EN.png|Annual pattern of potential evaporation according to /BRANDT, 1979/
Datei:Tagesgang_ETpot.png|Tagesgang der potentiellen Verdunstung als Vielfaches der mittleren Tagesverdunstung
Datei:Tagesgang_ETpot_EN.png|Daily pattern of potential evaporation as a multiple of the mean daily evaporation
</gallery>
</gallery>


===Surface Water Storage (Impermeable Areas) O===


===Oberflächenwasservorrat (versiegelter Flächenanteil) O===
For impermeable areas, snow storage and infiltration can be neglected, so that the balance equation is simplified as follows:
 
Bei den versiegelten Flächenanteilen kann neben dem Schneevorrat auch die Infiltration vernachlässigt werden, so dass sich die Bilanzgleichung wie folgt vereinfacht:


<math>N_W(t)=N(t)-VP(t)-\frac{dO}{dt}</math>
<math>N_W(t)=N(t)-VP(t)-\frac{dO}{dt}</math>


wobei die Oberflächenwasservorratsänderung <math>dO/dt</math> die Benetzung der Oberfläche sowie die Auffüllung und Entleerung (durch Verdunstung) der Mulden repräsentiert.[[Datei:Schema_Modellansatz_Benetzungs-_und_Muldenverlust.png|thumb|Schema der Modellansätze Benetzungs- und Muldenverlust]]
The change in surface water storage <math>dO/dt</math> represents the wetting of the surface as well as the filling and emptying (by evaporation) of depressions.[[Datei:Schema_Modellansatz_Benetzungs-_und_Muldenverlust_EN.png|thumb|Schematic of wetting and depression losses]]
Als Benetzungsverlust <math>BV</math> für versiegelte Flächen wird folgender Standardwert angesetzt.
The following default value <math>BV</math> is used as wetting loss for impermeable areas.


<math>BV = 0.5 \mbox{ mm}</math>
<math>BV = 0.5 \mbox{ mm}</math>


Der Muldenverlust MV wird durch den Anwender vorgegeben. Der Standard- und gleichzeitig Maximalwert im Modell beträgt 4 mm  
Depression losses (MV) are specified by the user. The default and simultaneously maximum value in the model is 4 mm.
Der Muldenverlust stellt den Mittelwert für eine geneigte Oberfläche dar. Da die Mulden jedoch nicht gleichmäßig verteilt sind und erfahrungsgemäß bereits ein Abfluss einsetzt, bevor überall die komplette Muldenauffüllung erreicht ist, wird unterstellt, dass jeweils
Depression losses represent an average value for an sloped surface. Since depressions are not evenly distributed and runoff already begins before all depressions are completely filled, it is assumed that
* 1/3 der versiegelten Fläche einen verminderten Muldenverlust von 1/3·MV
* 1/3 of the impermeable area has a reduced depression loss of 1/3&sdot;MV
* 1/3 der versiegelten Fläche den mittleren Muldenverlust von 3/3·MV
* 1/3 of the impermeable area has the average depression loss of MV
* 1/3 der versiegelten Fläche einen erhöhten Muldenverlust von 5/3·MV
* 1/3 of the impermeable area has an increased depression loss of 5/3&sdot;MV
aufweist. Somit kommt es bereits zum Abfluss, wenn der um die Verdunstungsrate verminderte Niederschlag den Benetzungsverlust und 1/3 des Muldenverlustes übersteigt (bei trockener Vorgeschichte). Die o.g. Annahmen sind in der folgenden Abbildung schematisch skizziert.
Therefore, runoff already occurs when the precipitation reduced by the evaporation rate exceeds the wetting loss and 1/3 of the depression losses (in case of dry starting conditions). The assumptions described above are shown as a schematic in the following figure.


Der Abflussbeiwert der versiegelten Flächen (nach Abdeckung der Anfangsverluste) wird mit <math>\Psi = 1</math> angesetzt. Bei der Festlegung des versiegelten Flächenanteils in einem Teileinzugsgebiet ist zu beachten, dass nicht alle befestigten oder versiegelten Flächen tatsächlich in eine Kanalisation entwässern.
The runoff coefficient of the impermeable areas (after covering the initial losses) is set at <math>\Psi = 1</math>. When determining the portion of impermeable areas for a sub-basin, you must take into account that not all paved or sealed surfaces actually drain into a sewer system.
Die kontinuierliche Bereitstellung der Benetzungs- und Muldenverluste erfolgt über die laufende Bilanzierung dieser Speicher und der Verdunstung.
The continuous provision of wetting and depression losses is achieved by continuously balancing the corresponding storages and the evaporation.




===Oberflächenwasservorrat (unversiegelter Flächenanteil) O===
===Surface Water Storage (Permeable Areas) O===


Der Oberflächenwasservorrat wird über die Bilanzierung eines Verlustspeichers in Abhängigkeit des gewählten Abflussbildungsansatzes berechnet. Einzelheiten dazu finden sich in den folgenden Abschnitten zur Berechnung der Infiltration bzw. abflusswirksamer Niederschlag.
The surface water storage of permeable areas is calculated by balancing a loss storage depending on the selected runoff generation approach. Details can be found in the following sections on the calculation of infiltration and runoff-effective precipitation.




===Infiltration bzw. abflusswirksamer Niederschlag I(t), N<sub>W</sub>(t)===
=== Infiltration and runoff-effective precipitation I(t), N<sub>W</sub>(t)===


Bei den durchlässigen Flächen kann die Infiltration in den Boden nicht vernachlässigt werden, da diese das Abflussgeschehen entscheidend prägt. Für die Berechnung wurden drei Ansätze im Modell implementiert:
In the case of permeable areas, infiltration into the soil cannot be neglected, since this has a decisive influence on the runoff. For the calculation three approaches are implemented in the model:
# Konstanter Abflussbeiwert <math>\Psi</math>
# Constant discharge coefficient <math>\Psi</math>
# Ereignisspezifischer Abflussbeiwert in Anlehnung an das Verfahren des Soil-Conservation-Service (SCS)
# Event-specific discharge coefficient based on the Soil-Conservation-Service (SCS) method
# Bodenfeuchtesimulation
# Soil moisture simulation




====Konstanter Abflussbeiwert &Psi;====
====Constant discharge coefficient &Psi;====


Bei Angabe eines <math>\Psi</math>-Wertes kommt nach Abdeckung der Anfangsverluste (Benetzungs- und Muldenverlust) der übrige Anteil des Niederschlages im Verhältnis des Abflussbeiwertes <math>\Psi</math> zum Abfluss und zwar unabhängig von der Vorgeschichte und den Merkmalen des Niederschlages (Höhe, Intensität, Dauer). Auf diesen Ansatz sollte nach Möglichkeit verzichtet werden, da hier der Prozess der Abflussbildung nur grob vereinfachend beschrieben wird.
If a <math>\Psi</math> value is given, the remaining part of the precipitation after covering the initial losses (wetting and depression losses) is converted to runoff by multplying with <math>\Psi</math>, independent of the antecedent conditions and the characteristics of the rainfall event (amount, intensity, duration). If possible, this approach should be avoided, since the process of runoff formation is greatly simplified.




====Ereignisspezifischer Abflussbeiwert in Anlehnung an das Verfahren des Soil-Conservation-Service (SCS)====
====Event-specific discharge coefficient based on the Soil-Conservation-Service (SCS) method====


Bei Angabe eines vom Bodentyp und der Bodennutzung abhängigen CN-Wertes (siehe /DVWK, 1991/) lässt sich ein vorgeschichtsabhängiger Anfangsverlust sowie eine vorgeschichtsabhängige Beziehung des Abflussbeiwertes von der bis zum betrachteten Zeitpunkt akkumulierten Niederschlagshöhe formulieren /Zaiss, 1987/; d.h. der Abflussbeiwert wächst mit zunehmendem Niederschlag im Verlauf des Ereignisses an.
Using a CN value that is dependent on the soil type and land use (see /DVWK, 1991/), the initial losses and a relationship between the runoff coefficient and the accumulated rainfall amount up to the current point in time can be derived, both of which are dependent on antecedent conditions /Zaiss, 1987/. With this approach, the runoff coefficient increases with increasing precipitation amount during the course of the rainfall event.
Die Quantifizierung der Vorgeschichte erfolgt über den 21-Tage-Vorregenindex <math>VN</math>
The quantification of the antecedent conditions is based on the 21-day-precipitation index <math>VN</math>.


<math>V_N=\sum_{j=1}^21 C(j)^j \cdot hN_j</math>
<math>V_N=\sum_{j=1}^21 C(j)^j \cdot hN_j</math>


mit:
with:
{|style="margin-left: 40px;"
{|style="margin-left: 40px;"
|<math>hN_j</math>: || Niederschlagshöhe des j-ten Vortags
|<math>hN_j</math>: || Precipitation amount of the j-th previous day
|-
|-
|<math>C(j)</math>: || Faktor, der den Einfluss des j-ten Vortags beschreibt
|<math>C(j)</math>: || Factor describing the influence of the j-th previous day
|-
|-
|}
|}


Der Einfluss der Jahreszeit wird durch einen Jahresgang des Faktors C wiedergegeben.
The impact of different seasons is represented by an annual pattern of the factor C.


<math>C=0.05 \cdot \sin\frac{2\pi}{365}(i+0.75)+0.85</math>
<math>C=0.05 \cdot \sin\frac{2\pi}{365}(i+0.75)+0.85</math>


mit:
with:
{|style="margin-left: 40px;"
{|style="margin-left: 40px;"
|<math>i</math>: || laufender Tag des Abflussjahres
|<math>i</math>: || current day of the hydrological year
|-
|-
|}
|}


Damit schwankt der Wert C zwischen 0.8 < C < 0.9. Hierdurch wird erreicht, dass bei gleichem Vorregen zu unterschiedlichen Jahreszeiten unterschiedliche Vorregenindizes berechnet und damit eine veränderte Abflussbereitschaft in Rechnung gestellt wird.
As a result, the value of C ranges between 0.8 < C < 0.9. This ensures that different rainfall indices are calculated for the same amount of rainfall at different times of the year, thus taking into account different degrees of runoff readiness.
In Abhängigkeit von der auf diese Weise quantifizierten Vorgeschichte kann unter Verwendung der gebietsspezifischen und für mittlere Vorfeuchteverhältnisse gültigen CN-Werte ein aktueller Abflussbeiwert berechnet werden. In der folgenden Abbildung ist für unterschiedliche CN-Werte dargestellt, wie sich der aktuelle Abflussbeiwert in Abhängigkeit von der Vorgeschichte verändert.
Depending on the antecedent conditions quantified in this way, a current discharge coefficient can be calculated using the CN values specific to the area and valid for average previous conditions. The following figure shows how the current discharge coefficient for different CN-values changes depending on antecedent conditions.
Da sich im Verlaufe eines Regenereignisses durch die Durchfeuchtung des Bodens die Abflussbereitschaft eines Einzugsgebiets verändert, wird ebenfalls eine Anpassung des Abflussbeiwertes während eines Ereignisses als Funktion der kumulierten Niederschlagshöhe vorgenommen.
Since the runoff readiness of a catchment area changes during the course of a rainfall event due to soil moistening, the runoff coefficient is also adjusted during an event as a function of the cumulative precipitation amount.
<gallery mode="packed" heights=300px>
<gallery mode="packed" heights=300px>
Datei:Abhängigkeit_des_Abflussbeiwertes_von_der_Vorgeschichte.png|Abhängigkeit des Abflussbeiwertes von der Vorgeschichte
Datei:Abhängigkeit_des_Abflussbeiwertes_von_der_Vorgeschichte_EN.png|Dependence of the runoff coefficient on antecedent conditions
Datei:Abhängigkeit_des_Abflussbeiwertes_von_der_kumulierten_Niederschlagssumme.png|Abhängigkeit des Abflussbeiwertes von der kumulierten Niederschlagssumme
Datei:Abhängigkeit_des_Abflussbeiwertes_von_der_kumulierten_Niederschlagssumme_EN.png|Dependence of the runoff coefficient on the cumulative precipitation sum
</gallery>
</gallery>




====Bodenfeuchtesimulation====
====Soil Moisture Simulation====




=====Landnutzung=====
=====Land Use=====


Bei der Anwendung der Bodenfeuchtesimulation ist die Angabe von Landnutzungen notwendig. Aus den Angaben zur Landnutzung wird die Durchwurzelungstiefe benötigt, um die Dicke der Durchwurzelungsschicht zu ermitteln. Weitere Parameter der Landnutzung, die zur Berechnung der Interzeption und der Transpiration dienen, sind:
When using soil moisture simulation, it is necessary to specify the land use. From the information about land use, the rooting depth is needed to determine the thickness of the root layer. Further parameters of land use, which are used to calculate interception and transpiration, are
* Wurzeltiefe
* Root depth
* Bedeckungsgrad
* Coverage
* Jahresgang des Bedeckungsgrades
* Annual pattern of coverage
* Blattflächenindex
* Leaf area index
* Jahresgang des Blattflächenindexes
* Annual pattern of the leaf area index
Die Angabe von Haude-Faktoren zur besseren Berücksichtigung der Verdunstung je Landnutzung sind über Eingabe von Jahresgängen beliebig möglich und können den gewünschten Landnutzungen zugeordnet werden.
Haude factors entered as annual patterns can be assigned to each land use for a better consideration of the evaporation.




=====Bodentyp/ Bodenart=====
=====Soil Type / Soil Texture=====


[[Datei:Programminterne_Zusammenfassung_Bodenschichten.png|thumb|Beispiel der Zusammenfassung der Bodenschichten zu einer programminternen Schicht anhand der Durchwurzelungsschicht]]
[[Datei:Programminterne_Zusammenfassung_Bodenschichten_EN.png|thumb|Aggregation of soil layers to simulation layers]]
[[Datei:Schema_Bodenfeuchtesimulation.png|thumb|Mit der Bodenfeuchtesimulation berechnete Größen]]
[[Datei:Schema_Bodenfeuchtesimulation_EN.png|thumb|Variables calculated with the soil moisture simulation]]
Die Bodenfeuchtesimulation basiert auf einer nichtlinearen Berechnung der einzelnen Bodenhorizonte. Der Boden wird dabei in verschiedene Horizonte (Schichten) eingeteilt. Jede Schicht wird berechnet und mit den (falls vorhanden) darunter bzw. darüber liegenden Schichten abgeglichen. Als Parameter zur Bodenfeuchteberechnung dienen folgende bodenphysikalischen Größen:
The soil moisture simulation is based on a non-linear calculation of the individual soil layers. The soil is divided into different layers. Each layer is calculated individually and inflows and outflows reconciled with the layers below or above (if present). The following physical soil parameters are used as parameters for the soil moisture calculation:
* Welkepunkt (WP)
* Wilting point (WP)
* Feldkapazität (FK)
* Field capacity (FC)
* Gesamtporenvolumen (GPV)
* Total pore volume (TPV)
* Gesättigte Leitfähigkeit (kf-Wert)
* Saturated conductivity (kf value)
* Maximale Infiltrationskapazität (Max.Inf.)
* Maximum infiltration capacity (max. inf.)
* Maximale Rate des Kapillaraufstiegs (Max.Kap.)
* Maximum rate of capillary suction (max. cap.)
* Zuordnung zu einer Bodenart: Sand, Schluff, Ton
* Soil categorization: sand, silt, clay


Die mögliche Anzahl der Bodenschichten läuft von minimal einer bis maximal sechs. Die Erfahrung zeigte, dass die besten Ergebnisse mit einer Aufteilung in drei Schichten erzielt werden konnten. Aus diesem Grund werden die eingegebenen Schichten programmintern immer in drei Horizonte unterteilt.
The possible number of soil layers ranges from a minimum of one to a maximum of six. Experience has shown that the best results are achieved with a division into three layers. For this reason, the entered layers are always internally divided into three simulation layers:
* Infiltrationsschicht (Standarddicke [cm] = 20)
* Infiltration layer (standard thickness [cm] = 20)
* Durchwurzelte Schicht (Mindestdicke [cm] = 5)
* Root layer (minimum thickness [cm] = 5)
* Transportschicht (Mindestdicke [cm] = 5)
* Transport layer (minimum thickness [cm] = 5)


Die Berechnung der neuen Bodenkennwerte für die programmintern verwendeten Schichten erfolgt durch eine Gewichtung entsprechend den vorgegebenen original Dicken der Schichten. Im Fall der gesättigten Leitfähigkeit läuft die Berechnung nach dem Prinzip der Erhaltung der Kontinuität der Strömung ab. Bei senkrechter Strömung soll aufgrund der Kontinuität der Strömung die Geschwindigkeit v bei gegebener Durchflussmenge in einer programminternen Schicht denselben Wert besitzen. Damit ist das hydraulische Gefälle nicht mehr konstant.
The calculation of soil properties for the simulation layers is done by weighting them according to the given original thicknesses of the layers. In case of saturated conductivity the calculation is based on the principle of maintaining the continuity of the flow. For vertical flow, the velocity v at a given flow rate in one simulation layer should have the same value due to the continuity of the flow. Thus, the hydraulic gradient is no longer constant.


<math>kf_V=\frac{\sum_{i=1}^n d_i}{\sum_{i=1}^n \frac{d_i}{k_i}}</math>
<math>kf_V=\frac{\sum_{i=1}^n d_i}{\sum_{i=1}^n \frac{d_i}{k_i}}</math>


mit:
with:
{|style="margin-left: 40px;"
{|style="margin-left: 40px;"
|<math>d_i</math>: || anteilige Schichtdicke der jeweiligen Original-Schicht [mm]
|<math>d_i</math>: || proportional layer thickness of the respective original layer [mm]
|-
|-
|<math>k_i</math>: || gesättigte Leitfähigkeit der jeweiligen Original-Schicht [mm/h]
|<math>k_i</math>: || saturated conductivity of the respective original layer [mm/h]
|-
|-
|<math>kf_V</math>: || gesättigte Leitfähigkeit der programmintern verwendeten Schicht [mm/h]
|<math>kf_V</math>: || saturated conductivity of the simulation layer [mm/h]
|-
|-
|}
|}
[[Datei:Schema_aktuelle_Verdunstung.png|thumb|Schema der Ermittlung der aktuellen Verdunstung]]
[[Datei:Schema_aktuelle_Verdunstung_EN.png|thumb|Schematic of calculation of the actual evapotranspiration]]
Auf der Basis der bereichsweisen linearen Abbildung der die Bodenfeuchte beeinflussenden Prozessfunktionen Infiltration, aktuelle Verdunstung (Evaporation + Transpiration), Perkolation, Interflow und Kapillaraufstieg wird für eine Bodenschicht die Wasserbilanzgleichung gelöst. Die Eingangsgröße für die Evaporation und Transpiration ermittelt sich aus der potentiellen Verdunstung.
The water balance equation for a soil layer is solved on the basis of the piece-wise linear representation of the process functions which influence soil moisture: infiltration, current evaporation (evaporation + transpiration), percolation, interflow and capillary suction. The input variable for evaporation and transpiration is determined from the potential evaporation.
Die zu lösende Gleichung ist:
The equation to be solved is:


<math>\frac{dBF(t)}{dt}=Inf(t)-Perk(t)-Eva_{akt}(t)-Trans_{akt}(t)-Int(t)+Kap(t)</math>
<math>\frac{dBF(t)}{dt}=Inf(t)-Perk(t)-Eva_{akt}(t)-Trans_{akt}(t)-Int(t)+Kap(t)</math>


mit:
with:
{|style="margin-left: 40px;"
{|style="margin-left: 40px;"
|<math>BF(t)</math>: || aktuelle Bodenfeuchte
|<math>BF(t)</math>: || current soil moisture
|-
|-
|<math>Inf(t)</math>: || Infiltration in den Boden
|<math>Inf(t)</math>: || infiltration into the soil
|-
|-
|<math>Perk(t)</math>: || Perkolation (Durchsickerung)
|<math>Perk(t)</math>: || percolation (seepage)
|-
|-
|<math>Eva_{akt}(t)</math>: || aktuelle Evaporation
|<math>Eva_{akt}(t)</math>: || current evaporation
|-
|-
|<math>Trans_{akt}(t)</math>: || aktuelle Transpiration
|<math>Trans_{akt}(t)</math>: || current transpiration
|-
|-
|<math>Int(t)</math>: || Interflow
|<math>Int(t)</math>: || interflow
|-
|-
|<math>Kap(t)</math>: || Kapillaraufstieg
|<math>Kap(t)</math>: || capillary suction
|-
|-
|}
|}
[[Datei:Bodenprozessfunktionen.png|thumb|Darstellung ausgewählter Bodenprozessfunktionen]]
[[Datei:Bodenprozessfunktionen_EN.png|thumb|Display of selected soil process functions]]
Infiltration, Perkolation, Evaporation, Transpiration, Interflow und Kapillaraufstieg sind von der aktuellen Bodenfeuchte abhängig. In der Simulation wird diese Abhängigkeit durch folgende Funktionsverläufe beschrieben.
Infiltration, percolation, evaporation, transpiration, interflow and capillary suction depend on the current soil moisture. In the simulation, this dependence is described by the following functions.


<math>Inf(BF(t))=a_v \cdot \left(GPV-BF(t) \right)^{1.4}+k_f </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(Ansatz nach HOLTAN)
<math>Inf(BF(t))=a_v \cdot \left(GPV-BF(t) \right)^{1.4}+k_f </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(Approach according to HOLTAN)


<math>
<math>
Zeile 219: Zeile 231:
\end{cases}
\end{cases}
</math>
</math>
:::::::::::::::::(mod. Ansatz nach /OSTROWSKI, 1992/)
:::::::::::::::::(mod. approach according to /OSTROWSKI, 1992/)
<math>
<math>
Eva(BF(t)) =  
Eva(BF(t)) =  
Zeile 236: Zeile 248:
</math>
</math>


mit:
with:
{|style="margin-left: 40px;"
{|style="margin-left: 40px;"
|<math>a_v</math>: || Infiltrationsfaktor nach HOLTAN (in Talsim-NG <math>a_v=1</math>
|<math>a_v</math>: || infiltration factor according to HOLTAN (in Talsim-NG <math>a_v=1</math>)
|-
|-
|<math>k_f</math>: || Durchlässigkeitsbeiwert des gesättigten Bodens
|<math>k_f</math>: || coefficient of conductivity of saturated soil
|-
|-
|<math>nFK</math>: || nutzbare Feldkapazität (<math>nFK=FK-WP</math>)
|<math>nFK</math>: || available water capacity (<math>nFK=FK-WP</math>)
|-
|-
|<math>WP</math>: || Welkepunkt
|<math>WP</math>: || wilting point
|-
|-
|<math>FK</math>: || Feldkapazität
|<math>FK</math>: || field capacity
|-
|-
|<math>GPV</math>: || gesamtes Porenvolumen
|<math>GPV</math>: || total pore volume
|-
|-
|<math>f_{PK}</math>: || bodenabhängiger Skalierungfaktor der Perkolationsfunktion
|<math>f_{PK}</math>: || soil-dependent scaling factor of the percolation function
|-
|-
|<math>exp,PK</math>: || bodenabhängiger Krümmungsparameter der Perkolationsfunktion
|<math>exp,PK</math>: || soil-dependent curvature parameter of the percolation function
|-
|-
|<math>f_{Eva}</math>: || bodenabhängiger Skalierungsfaktor der Evaporationsfunktion
|<math>f_{Eva}</math>: || soil-dependent scaling factor of the evaporation function
|-
|-
|<math>f_{Trans}</math>: || bodenabhängiger Skalierungsfaktor der Transpirationsfunktion
|<math>f_{Trans}</math>: || soil-dependent scaling factor of the transpiration function
|-
|-
|<math>exp,Trans</math>: || Krümmungsparameter der Transpirationsfunktion
|<math>exp,Trans</math>: || curvature parameter of the transpiration function
|-
|-
|}
|}


Die Programmparameter werden intern berechnet. Der Anwender muss lediglich die Bodenkennwerte kf, WP, FK und GPV angeben.
These parameters are calculated internally. The user only has to specify the soil parameters kf, WP, FC and TPV.
Die Berechnung der Bodenprozesse erfolgt mit einem neuentwickelten [[Special:MyLanguage/Berechnungsschema von Speichern|Baustein zur Simulation von Speichern]].
The soil processes is are solved using a [[Special:MyLanguage/Berechnungsschema von Speichern|component for the simulation of storage]].




=====Elementarflächen=====
=====Hydrologic Response Units=====


Wird mit der Bodenfeuchtesimulation die Abflussbildung berechnet, wird gleichzeitig das Elementarflächenkonzept angewandt. Ein Einzugsgebietselement wird dabei in beliebig viele hydrologisch homogene Flächen unterteilt, d.h. Flächen gleichen Bodentyps und gleicher Landnutzung.
When runoff generation is calculated using soil moisture simulation, the concept of hydrologic response units (HRUs) is applied. A catchment area is divided into a number of hydrologically homogeneous areas, i.e. areas of the same soil type and the same land use.
Für jede Elementarfläche gilt genau eine Zuordnung von Landnutzung und Bodentyp. Die aus einer Elementarfläche resultierende Wassermenge wird am Elementausgang angesetzt, d.h. alle Elementarflächen geben unabhängig ihrer Lage im Einzugsgebiet Wasser mit der gleichen zeitlichen Verzögerung ab.
For each hydrologic response unit there is exactly one assignment of land use and soil type. The discharge resulting from a hydrologic response unit is output from the sub-basin element to which the HRU belongs, i.e. all hydrologic response units release discharge with the same time delay, independent of their location within the sub-basin.
<gallery mode="packed" heights=200px>
<gallery mode="packed" heights=200px>
Datei:Aufteilung_EZG_in_Elementarflächen.png|Aufteilung eines Einzugsgebietselementes in Elementarflächen
Datei:Aufteilung_EZG_in_Elementarflächen.png|Division of a sub-basin element into hydrologic response units
Datei:Elementarflächen_Zuordnung_Bodentyp_Landnutzung.png|Zuordnung von Bodentyp und Landnutzung zu Elementarflächen
Datei:Elementarflächen_Zuordnung_Bodentyp_Landnutzung_EN.png|Assignment of soil type and land use to hydrologic response units
</gallery>
</gallery>




==Abflusskonzentration==
==Runoff Concentration==


Die Abflusskonzentration bestimmt die Verzögerung des Oberflächenabflusses aus dem Einzugsgebiet. Es wird eine Parallelspeicherkaskade mit drei Speichern für unbefestigte und eine Kaskade für befestigte Flächen benutzt. Der Abfluss der Komponenten Interflow und Grundwasser wird über einen linearen Einzelspeicher verzögert an den Elementausgang abgegeben.
Runoff concentration determines the delay of runoff from the catchment area. A parallel storage cascade with three reservoirs for permeable and one cascade for impermeable areas is used for surface runoff. The outflow of the components interflow and baseflow is output at the element outlet after passing through a single linear storage.
[[Datei:Abflusskonzentration.png|frame|none|Berechnung der Abflusskonzentration von Einzugsgebieten]]
[[Datei:Abflusskonzentration_EN.png|frame|none|Calculation of the runoff concentration of catchment areas]]

Aktuelle Version vom 17. Dezember 2020, 10:45 Uhr

Sprachen:
Systemelement001.png

The simulation of natural catchment areas requires calculating the processes of runoff generation, distribution and concentration. The methods of calculation used are described below.


Load Generation

Load generation is the process of determining the precipitation for the considered catchment area. In Talsim-NG, each sub-basin uses only one precipitation source. If there are several precipitation measurement stations in the catchment area, you can either divide the area into several sub-basins or aggregate precipitation sources, until only one precipitation source can be assigned to each element.


Runoff Generation for Permeable/Impermeable Areas

Runoff generation determines the amount of effective precipitation from the rainfall. From this, the components surface runoff, infiltration, evaporation and interflow are derived. By defaut, snow calculation is carried out at temperatures below zero °C and is based on the Snow-Compaction-Method. Regarding the algorithms of the method, reference is made to the relevant literature. The natural process from precipitation to runoff is divided into individual phases for the mathematical simulation. In the runoff generation phase, the precipitation (system load) is divided into the "effective precipitation" which is transformed into runoff, and the losses not affecting runoff (wetting, depression, evaporation and infiltration losses). Therefore, this phase is also called load distribution. The resulting mathematical equation for the momentary load distribution is as follows:

[math]\displaystyle{ N_W(t) =N(t) -VP(t) -I(t) - \frac{dO}{dt} - \frac{dS}{dt} }[/math]

with:

[math]\displaystyle{ N_W }[/math]: Runoff-effective precipitation
[math]\displaystyle{ N }[/math]: Precipitation
[math]\displaystyle{ VP }[/math]: Potential evaporation
[math]\displaystyle{ I }[/math]: Infiltration into the soil
[math]\displaystyle{ O }[/math]: Surface water supply
[math]\displaystyle{ S }[/math]: Snow storage

In the following, the terms used in the equation and their calculation are explained in detail.


Precipitation N(t)

Precipitation data must be provided to the simulation model in the form of time series. In principle, it is irrelevant whether the precipitation series is a block rain, a model rain, a time series of natural observed rainfall, a rain spectrum or a long-term rainfall time series. The appropriate load has to be selected depending on the objective of the simulation. The rainfall time series are either taken from the time series management of Talsim-NG or, when carrying out a short-term forecast, are generated by entering a duration, an amount and by selecting a model rain directly before a simulation.


Evaporation VP(t)

Evaporation has a double effect on runoff generation. On the one hand, the initial conditions in the catchment area (interception and depression storage on the surface as well as to a limited degree the soil moisture of permeable areas) are a result of the evaporation taking place before the considered precipitation event. On the other hand, the current runoff-effective precipitation is affected by the amount of the current evaporation rate.

The potential (energetically possible) evaporation VP varies in time and place and is very difficult to calculate exactly.

Talsim-NG offers multiple options for entering/calculating potential evaporation:

  • Specification of an external time series with values for the potential evaporation
  • Internal calculation of potential evaporation: the potential evaporation can be calculated internally based on temperature and, depending on the method, additional parameters. The following methods are available:
    • Penman: requires the specification of average patterns or of time series for sunshine duration, wind speed and relative humidity
    • Haude: requires the specification of average patterns or of a time series for relative humidity
    • Turc: requires the specification of average patterns or of time series for sunshine duration and relative humidity
    • Blaney-Criddle: simplistic method requiring only the specification of a latitude which is used internally to derive the sunshine duration.
  • Specification of a fixed evaporation rate per year: when using this option, the entered annual value is distributed inner-annually using the compensation function according to Brandt (see below).

Compensation functions

The following compensation functions according to Brandt are used to distribute entered annual values for evaporation over the year and to convert daily values to hourly values.

Using evaluated measurements of 20 stations, the mean values of which are presented in the following histogram, the following compensation function was determined /BRANDT, 1979/.

[math]\displaystyle{ VP=(0.96+0.0033 \cdot i) \cdot \sin\frac{2\pi}{365}(i-148)+158 }[/math]

with:

[math]\displaystyle{ i }[/math]: current day of the hydrological year
[math]\displaystyle{ i=1 }[/math]: November 1

The total annual potential evaporation height in this sample is 642 mm. If no measured evaporation values are available, this normalized annual potential evaporation pattern can optionally be used to calculate the current evaporation. If the simulation time step is less than one day, the potential evaporation for each time step is additionally determined using the daily pattern displayed below. If the calculation interval is more than 1 day, the daily pattern is not taken into account.

Surface Water Storage (Impermeable Areas) O

For impermeable areas, snow storage and infiltration can be neglected, so that the balance equation is simplified as follows:

[math]\displaystyle{ N_W(t)=N(t)-VP(t)-\frac{dO}{dt} }[/math]

The change in surface water storage [math]\displaystyle{ dO/dt }[/math] represents the wetting of the surface as well as the filling and emptying (by evaporation) of depressions.

Schematic of wetting and depression losses

The following default value [math]\displaystyle{ BV }[/math] is used as wetting loss for impermeable areas.

[math]\displaystyle{ BV = 0.5 \mbox{ mm} }[/math]

Depression losses (MV) are specified by the user. The default and simultaneously maximum value in the model is 4 mm. Depression losses represent an average value for an sloped surface. Since depressions are not evenly distributed and runoff already begins before all depressions are completely filled, it is assumed that

  • 1/3 of the impermeable area has a reduced depression loss of 1/3⋅MV
  • 1/3 of the impermeable area has the average depression loss of MV
  • 1/3 of the impermeable area has an increased depression loss of 5/3⋅MV

Therefore, runoff already occurs when the precipitation reduced by the evaporation rate exceeds the wetting loss and 1/3 of the depression losses (in case of dry starting conditions). The assumptions described above are shown as a schematic in the following figure.

The runoff coefficient of the impermeable areas (after covering the initial losses) is set at [math]\displaystyle{ \Psi = 1 }[/math]. When determining the portion of impermeable areas for a sub-basin, you must take into account that not all paved or sealed surfaces actually drain into a sewer system. The continuous provision of wetting and depression losses is achieved by continuously balancing the corresponding storages and the evaporation.


Surface Water Storage (Permeable Areas) O

The surface water storage of permeable areas is calculated by balancing a loss storage depending on the selected runoff generation approach. Details can be found in the following sections on the calculation of infiltration and runoff-effective precipitation.


Infiltration and runoff-effective precipitation I(t), NW(t)

In the case of permeable areas, infiltration into the soil cannot be neglected, since this has a decisive influence on the runoff. For the calculation three approaches are implemented in the model:

  1. Constant discharge coefficient [math]\displaystyle{ \Psi }[/math]
  2. Event-specific discharge coefficient based on the Soil-Conservation-Service (SCS) method
  3. Soil moisture simulation


Constant discharge coefficient Ψ

If a [math]\displaystyle{ \Psi }[/math] value is given, the remaining part of the precipitation after covering the initial losses (wetting and depression losses) is converted to runoff by multplying with [math]\displaystyle{ \Psi }[/math], independent of the antecedent conditions and the characteristics of the rainfall event (amount, intensity, duration). If possible, this approach should be avoided, since the process of runoff formation is greatly simplified.


Event-specific discharge coefficient based on the Soil-Conservation-Service (SCS) method

Using a CN value that is dependent on the soil type and land use (see /DVWK, 1991/), the initial losses and a relationship between the runoff coefficient and the accumulated rainfall amount up to the current point in time can be derived, both of which are dependent on antecedent conditions /Zaiss, 1987/. With this approach, the runoff coefficient increases with increasing precipitation amount during the course of the rainfall event. The quantification of the antecedent conditions is based on the 21-day-precipitation index [math]\displaystyle{ VN }[/math].

[math]\displaystyle{ V_N=\sum_{j=1}^21 C(j)^j \cdot hN_j }[/math]

with:

[math]\displaystyle{ hN_j }[/math]: Precipitation amount of the j-th previous day
[math]\displaystyle{ C(j) }[/math]: Factor describing the influence of the j-th previous day

The impact of different seasons is represented by an annual pattern of the factor C.

[math]\displaystyle{ C=0.05 \cdot \sin\frac{2\pi}{365}(i+0.75)+0.85 }[/math]

with:

[math]\displaystyle{ i }[/math]: current day of the hydrological year

As a result, the value of C ranges between 0.8 < C < 0.9. This ensures that different rainfall indices are calculated for the same amount of rainfall at different times of the year, thus taking into account different degrees of runoff readiness. Depending on the antecedent conditions quantified in this way, a current discharge coefficient can be calculated using the CN values specific to the area and valid for average previous conditions. The following figure shows how the current discharge coefficient for different CN-values changes depending on antecedent conditions. Since the runoff readiness of a catchment area changes during the course of a rainfall event due to soil moistening, the runoff coefficient is also adjusted during an event as a function of the cumulative precipitation amount.


Soil Moisture Simulation

Land Use

When using soil moisture simulation, it is necessary to specify the land use. From the information about land use, the rooting depth is needed to determine the thickness of the root layer. Further parameters of land use, which are used to calculate interception and transpiration, are

  • Root depth
  • Coverage
  • Annual pattern of coverage
  • Leaf area index
  • Annual pattern of the leaf area index

Haude factors entered as annual patterns can be assigned to each land use for a better consideration of the evaporation.


Soil Type / Soil Texture
Aggregation of soil layers to simulation layers
Datei:Schema Bodenfeuchtesimulation EN.png
Variables calculated with the soil moisture simulation

The soil moisture simulation is based on a non-linear calculation of the individual soil layers. The soil is divided into different layers. Each layer is calculated individually and inflows and outflows reconciled with the layers below or above (if present). The following physical soil parameters are used as parameters for the soil moisture calculation:

  • Wilting point (WP)
  • Field capacity (FC)
  • Total pore volume (TPV)
  • Saturated conductivity (kf value)
  • Maximum infiltration capacity (max. inf.)
  • Maximum rate of capillary suction (max. cap.)
  • Soil categorization: sand, silt, clay

The possible number of soil layers ranges from a minimum of one to a maximum of six. Experience has shown that the best results are achieved with a division into three layers. For this reason, the entered layers are always internally divided into three simulation layers:

  • Infiltration layer (standard thickness [cm] = 20)
  • Root layer (minimum thickness [cm] = 5)
  • Transport layer (minimum thickness [cm] = 5)

The calculation of soil properties for the simulation layers is done by weighting them according to the given original thicknesses of the layers. In case of saturated conductivity the calculation is based on the principle of maintaining the continuity of the flow. For vertical flow, the velocity v at a given flow rate in one simulation layer should have the same value due to the continuity of the flow. Thus, the hydraulic gradient is no longer constant.

[math]\displaystyle{ kf_V=\frac{\sum_{i=1}^n d_i}{\sum_{i=1}^n \frac{d_i}{k_i}} }[/math]

with:

[math]\displaystyle{ d_i }[/math]: proportional layer thickness of the respective original layer [mm]
[math]\displaystyle{ k_i }[/math]: saturated conductivity of the respective original layer [mm/h]
[math]\displaystyle{ kf_V }[/math]: saturated conductivity of the simulation layer [mm/h]
Schematic of calculation of the actual evapotranspiration

The water balance equation for a soil layer is solved on the basis of the piece-wise linear representation of the process functions which influence soil moisture: infiltration, current evaporation (evaporation + transpiration), percolation, interflow and capillary suction. The input variable for evaporation and transpiration is determined from the potential evaporation. The equation to be solved is:

[math]\displaystyle{ \frac{dBF(t)}{dt}=Inf(t)-Perk(t)-Eva_{akt}(t)-Trans_{akt}(t)-Int(t)+Kap(t) }[/math]

with:

[math]\displaystyle{ BF(t) }[/math]: current soil moisture
[math]\displaystyle{ Inf(t) }[/math]: infiltration into the soil
[math]\displaystyle{ Perk(t) }[/math]: percolation (seepage)
[math]\displaystyle{ Eva_{akt}(t) }[/math]: current evaporation
[math]\displaystyle{ Trans_{akt}(t) }[/math]: current transpiration
[math]\displaystyle{ Int(t) }[/math]: interflow
[math]\displaystyle{ Kap(t) }[/math]: capillary suction
Display of selected soil process functions

Infiltration, percolation, evaporation, transpiration, interflow and capillary suction depend on the current soil moisture. In the simulation, this dependence is described by the following functions.

[math]\displaystyle{ Inf(BF(t))=a_v \cdot \left(GPV-BF(t) \right)^{1.4}+k_f }[/math]           (Approach according to HOLTAN)

[math]\displaystyle{ Perk(BF(t)) = \begin{cases} 0, & BF(t)\le f_{PK} \cdot nFK + WP \\ k_f \cdot \left(\frac{BF(t)-(f_{PK} \cdot nFK +WP)}{GPV-(f_{PK} \cdot nFK +WP)} \right)^{exp,PK}, & BF(t)\gt f_{PK} \cdot nFK + WP \end{cases} }[/math]

(mod. approach according to /OSTROWSKI, 1992/)

[math]\displaystyle{ Eva(BF(t)) = \begin{cases} 0, & BF(t)\le WP \\ f_{Eva} \cdot \left(\frac{BF(t)-WP}{GPV-WP} \right)^{exp,PK}, & BF(t)\gt WP \end{cases} }[/math]

[math]\displaystyle{ Trans(BF(t)) = \begin{cases} 0, & BF(t)\le f_{Trans} \cdot nFK + WP \\ f_{Trans} \cdot \left(\frac{BF(t)-(f_{Trans} \cdot nFK +WP)}{GPV-(f_{Trans} \cdot nFK +WP)} \right)^{exp,PK}, & BF(t)\gt f_{Trans} \cdot nFK + WP \end{cases} }[/math]

with:

[math]\displaystyle{ a_v }[/math]: infiltration factor according to HOLTAN (in Talsim-NG [math]\displaystyle{ a_v=1 }[/math])
[math]\displaystyle{ k_f }[/math]: coefficient of conductivity of saturated soil
[math]\displaystyle{ nFK }[/math]: available water capacity ([math]\displaystyle{ nFK=FK-WP }[/math])
[math]\displaystyle{ WP }[/math]: wilting point
[math]\displaystyle{ FK }[/math]: field capacity
[math]\displaystyle{ GPV }[/math]: total pore volume
[math]\displaystyle{ f_{PK} }[/math]: soil-dependent scaling factor of the percolation function
[math]\displaystyle{ exp,PK }[/math]: soil-dependent curvature parameter of the percolation function
[math]\displaystyle{ f_{Eva} }[/math]: soil-dependent scaling factor of the evaporation function
[math]\displaystyle{ f_{Trans} }[/math]: soil-dependent scaling factor of the transpiration function
[math]\displaystyle{ exp,Trans }[/math]: curvature parameter of the transpiration function

These parameters are calculated internally. The user only has to specify the soil parameters kf, WP, FC and TPV. The soil processes is are solved using a component for the simulation of storage.


Hydrologic Response Units

When runoff generation is calculated using soil moisture simulation, the concept of hydrologic response units (HRUs) is applied. A catchment area is divided into a number of hydrologically homogeneous areas, i.e. areas of the same soil type and the same land use. For each hydrologic response unit there is exactly one assignment of land use and soil type. The discharge resulting from a hydrologic response unit is output from the sub-basin element to which the HRU belongs, i.e. all hydrologic response units release discharge with the same time delay, independent of their location within the sub-basin.


Runoff Concentration

Runoff concentration determines the delay of runoff from the catchment area. A parallel storage cascade with three reservoirs for permeable and one cascade for impermeable areas is used for surface runoff. The outflow of the components interflow and baseflow is output at the element outlet after passing through a single linear storage.

Calculation of the runoff concentration of catchment areas