Hydrological Model J2000g

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Latest revision as of 10:47, 5 December 2011

Abstract

The Model J2000g was developed as a simplified hydrological model to calculate temporally aggregated, spatially allocated hydrological target sizes. The representation and calculation of the hydrological processes is carried out one-dimensionally for an arbitrary number of points in the space. These model points enable the use of different distribution concepts (Response Units, grid cells, catchment areas) without further model adjustments.

The temporal discretization of the modeling can be carried out in daily or monthly steps. During the modeling the following processes are calculated for each time step: regionalization of punctual existing climate data to the referring model units, calculation of global and net radiation as access for the evaporation calculation, calculation of the land-cover-specific potential evaporation according to Penman-Monteith, snow accumulation and snowmelt, soil water budget, groundwater recharge, retardation in runoff (translation and retention). The individual processes are described in more detail below.

Distribution and Attribute Tables

The model J2000g is not bound to any specific distribution concept because the processes are calculated on the basis of points in the space that are independent of each other (1D-model concept). These points can represent different space units, e.g. single station positions, polygons, grid cells, catchment areas or subcatchments but also rather administrative units such as field unit or administrative districts. In the following text the term “model unit” is used for these points.

Model Unit Attribute Table

Each model unit needs to be described with specific attributes for the modeling. These are:

Sample for a model unit-parameter-table

ID - a clear numeric ID
X - the easting of the centre (centroid) as Gauss-Krüger coordinate
Y - the northing of the centre (centroid) as Gauss-Krüger coordinate
area - the area of the model unit in m²
elevation - the mean elevation of the model unit in m above N.N.
slope - the mean slope of the model unit in degree
aspect - the aspect of the model unit in degree from North clockwise
soilID - a clear numeric ID for the soil type (serves as allocation to the soil attribute table)
landuseID - a clear numeric ID for the land use/land cover type (serves as allocation to the land use table)
hgeoID - a clear numeric ID for the hydrological unit of the model unit (serves as allocation to the hydrogeology table)

The model unit attribute table contains the attribute names in the first row. These must not be changed because they are used as variable name for the attribute generation during the model parameterization. The second row contains the minimal possible value of the referring attribute, whereas the third one contains the maximum possible value. In the fourth row the physical unit of the attribute needs to be entered. Then, as many rows as needed are given that contain the attribute values of the single model units. The table needs to be completed by a comment row which starts with the comment symbol (#). The tab (\t) has to be used to separate the rows.

Soil Attribute Table

Sample for a soil attribute table

The soil attribute table contains soil-physical characteristics for each soil unit that occurs in the area. In the current model version only the usable field capacity for each decimeter is needed. On the basis of the field capacity the maximum storage capacity of the soil water storage is calculated in dependence of the effective root depth of the vegetation on the model unit during the model parameterization.

The format of the soil attribute table is very similar to the model units attribute table. The table can be started with an arbitrary number of comment rows that need to be started with the comment symbol (#). In the first interpreted row the attribute names need to be given. The spelling is very important here. The following attributes need to be included:

SID - clear numeric ID with which the connection to the model unit table is generated
depth - depth of the soil in cm
fc_sum - entire usable field capacity of the soil in mm
fc_1 bis fc_n - usable field capacity for each decimeter in mm/dm

To complete the table, a comment row must be given (introduced with #). The tab (\t) has to be used to separate the rows.

Land Use Attribute Table

sample for a land use attribute table

The land use attribute table contains vegetation parameters that are nearly exclusively needed for the evaporation calculation according to Penman-Monteith. In the table the following attributes need to be given for each land use unit and land cover unit that occurs in the area:

LID - a clear numeric ID with which the connection to the model unit table is generated.
description - a description as text
albedo - albedo [0 ... 1]
RSC0_1 bis RSC0_12 - the stomatal resistances for good water availability for the months January (RSC0_1) to December (RSC0_12) in s/m
LAI_d1 bis LAI_d4 - the area leaf index in m²/m² for the Julian Days 110 (d1), 150 (d2), 250 (d3) and 280 (d4) for a terrain height of 400 m above N.N.
effHeight_d1 bis effHeight_d4 - effective vegetation height in meter for the Julian Days 110 (d1), 150 (d2), 250 (d3) und 280 (d4) for a terrain height of 400 m above N.N.
rootDepth - the effective root depth in dm

To complete the table, a comment row must be given (introduced with #). The tab (\t) has to be used to separate the rows.

Hydrogeology Attribute Table

sample for a hydrogeology attribute table

In the hydrogeology attribute table the maximum possible ground water recharge rates per time unit are set up for each hydrogeologic unit. It only contains the following two attributes:

GID - a clear numeric ID with which the connection to the model unit table is generated.
mxPerc - the maximum possible percolation rate (ground water recharge rate) per time interval in mm per time unit

To complete the table, a comment row must be given (introduced with #). The tab (\t) has to be used to separate the rows.

Input Data - Model Driver

sample for an input data table

For the model run climate time series of an arbitrary number of climate and precipitation stations are needed. The time series have to be preprocessed in the referring formatted data files. The files have the following format:

Rows 1 to 13 contain meta information about the data. They are arranged in blocks which are started with descriptions which in turn are started with the AT-symbol (@). Multiple entries per row are separated via the tab (\t).

@dataSetAttribs (attribute of the dataset)
- missingDataVal - value that marks missing data
- dataStart - start date of the dataset (DD.MM.JJJJ HH:MM)
- dataEnd - end date of the dataset (DD.MM.JJJJ HH:MM)
- tres - termporal resolution (days "d", months "m")
@statAttribVal (attributes of the climate stations)
- name - the names of the climate stations
- ID - a numeric, clear ID
- elevation - the elevation of the station in m above N.N.
- x - easting as Gauss-Krüger-coordinate
- y - northing as Gauss-Krüger-coordinate
- dataColumn - describes the column in which the data for the referring station can be found

In the following rows the actual data for each time step is listed – starting with:

@dataVal

The format is Date, Time followed by Data that is separated by the tab.

Installation and Start

Model Initialization

Regionalization

The regionalization module is used for the transfer of punctual values to the model units. The procedure was taken from the hydrological Model J2000 without any changes and is arranged in the following steps:

Calculation of a linear regression between the station values and the station heights for each time step. Thereby, the coefficient of determination (r²) and the slope of the regression line (b_H) is calculated.
Definition of the n gaging stations which are nearest to the particular model unit. The number n which needs to be given during the parameterization is dependent on the density of the station net as well as on the position of the individual stations.
Via an Inverse-Distance-Weighted Method (IDW) the weightings of the n stations are defined dependently on their distances for each model unit. Via the IDW-method the horizontal variability of the station data is taken into account according to its spatial position.
Calculation of the data value for each model unit with the weightings from point 3 and an optional elevation correction for the consideration of the vertical variability. (The elevation correction is only carried out when the coefficient of determination –calculated under point 1 – goes beyond the threshold of 0.7.)

The calculation of the data value for each model unit (DW_U) without elevation correction is carried out with the weightings (W(i)) and the values (MW(i)) of each n gaging station according to:

$DW_{U} = \sum_{i=1}^{n}MW(i) \cdot W(i)$

For the calculation with elevation correction the elevation difference (HD(i)) between the gaging station and the model unit as well as the slope of the regression line (b_H) are taken into account. Thus, the data value for the model unit (DW_U) is calculated according to:

$DW_U = \sum_{i=1}^{n}\left(\left(HD(i) \cdot b_H + MW(i)\right) \cdot W(i)\right)$

Precipitation Correction

Precipitation values partly show a clear systematic error in measurement which is caused instrument-determined or due to the selection of the instrument position. This error in measurement has two causes: (1) the moistening error and evaporation error, which each depends on the type of the instrument and (2) the wind error which emerges due to the drifting of the precipitations. Both errors in measurement are strongly dependent on the type (rain or snow) of the precipitation amount.

For the correction of both errors a correction method according to Richter (1995) is used which is applied in the same way in the Model J2000. The procedure for the evaporation correction differs with regard to the temporal resolution of the precipitation data.

Monthly Precipitation Correction

Monthly percental precipitation errors in measurement for slightly sheltered stations, concentrated regionally (Richter 1995)

The corrected precipitation (P_korr) is calculated for monthly time steps on the basis of the decrease of the measured precipitation (P_m) and the percental monthly error in measurement (MF_t) (see adjacent table):

$P_{korr} = P_m + P_m \cdot \frac{MF_t}{100}$

Daily Precipitation Correction

For the daily precipitation correction the two error terms are calculated explicitly. For this purpose, correction functions were derived on the basis of the tabled error values according to Richter (1995).

Moistening Loss and Evaporation Loss

Moistening loss and evaporation losses by Hellmann precipitation gauges separated for the summer half year and winter half year in dependence of the daily value of the precipitation amount (according to Richter) and the adjusted correction function (Krause 2001)

For a continual error correction of the moistening loss and evaporation loss continual correction functions were adjusted to the tabled values by Richter (1995). They are shown in the adjacent figure. The correction functions were derived each separately for the winter half year (November till April) and summer half year (May till October). With these functions the moistening loss and evaporation loss is calculated in mm for precipitations <= 9 mm according to:

$BV_{Som} = 0.08 \cdot \ln(N) + 0.225$

$BV_{Win} = 0.05 \cdot \ln(N) + 0.13$

If the amount of precipitation is greater than 9 mm, a constant error of 0.47 mm in the summer half year and of 0.3 mm in the winter half year is assumed.

Wind Error

Characteristic of the relative correction function for the wind error based on the tabled values by Richter (1995) (Krause 2001)

The calculation of the wind error of the precipitation measurement with the Hellman precipitation gauge is also carried out according to the tabled error values from Richter (1995) which was adjusted to the referring continual correction functions. For the correction it is differentiated whether the precipitation was rain or snow. The way of internal differentiation is described further below. The relative correction value is calculated as follows:

$WK_s = 0.5424 \cdot N^{-0.211}$ for snow

$WK_r = 0.1421 \cdot N^{-0.519}$ for rain.

The corrected precipitation value (P_K) is finally calculated on the basis of the value (P_M), the relative correction value for the wind error (WK_s, WK_r) as well as the moistening loss and evaporation loss (BV_Som, BV_Win) as follows:

$P_K = P_M + P_M \cdot WK_{s,r} + BV_{Som,Win}$

Radiation Calculation

For the evaporation calculation according to Penman-Monteith, the net radiation is needed as initial value and can be calculated on the basis of the global radiation. If the global radiation is not available, it can be defined approximately on the basis of the sunshine duration. For this purpose, a number of intermediate calculations are necessary. The following calculations act on the assumption of a daily modeling. When the model runs in monthly time steps, the calculations listed below are carried out on the 15th of each month. The resulting terms are then accumulated on the basis of the days per month.

Extraterrestrial Radiation

Annual course of extraterrestrial radiation (Ra), global radiation (Rg) and net radiation (Rn) for a position in the Thuringian Forrest

The extraterrestrial radiation (Ra) is the short-wave radiation energy flux of the sun at the upper boarder of the atmosphere. Ra is calculated for a specific place in dependence of its latitude (lat in radians), the declination of the sun (decl in radians), the solar constant (Gsc in MJ / m²min), the hour angle at sundown (ws in radians) and the inverse relative distance between earth and sun (dr in radians) according to:

$Ra = \frac{24\cdot60}{\pi} \cdot Gsc \cdot dr \cdot \left(ws \cdot \sin(lat) \cdot \sin(decl) + \cos(lat) \cdot \cos(decl) \cdot \sin(ws)\right)$

The solar constant (Gsc in MJ / m²min) results from the Julian Date (jD [1... 365,366]) as follows:

$Gsc = 0.08139 + 0.00291 \cdot \cos\left(\frac{\pi}{180} \cdot (jD - 15)\right)$ [MJ / m²min]

The relative distance between earth and sun (dr in radians) results from the Julian Date (jD [1... 365,366]) as follows:

$dr = 1 + 0.033 \cdot \cos\left(\frac{2\pi}{365} \cdot jD\right)$ [rad.]

The declination of the sun (decl in radians) results from the Julian Date (jD [1... 365,366]) as follows:

$decl = 0.40954 \cdot \sin(0.0172 \cdot (jD - 79.35))$ [rad.]

The hour angle at sundown (ws in radians) results from the latitude (lat in radians) and the declination (decl in radians) as follows:

$ws = \arccos(-1 \cdot \tan(lat) \cdot \tan(decl))$ [rad.]

Global Radiation

The global radiation (Rg) is calculated on the basis of the extraterrestrial radiation (Ra in MJ/m²d) and the degree of cloudiness. At this, the degree of cloudiness is approximated on the basis of the relation of the measured sunshine duration (D in h/d) to the astronomic possible sunshine duration (S₀ in h/d) with the help of the Angström formula. Thus, Rg is calculated as follows:

$Rg = Ra \cdot \left(a + b \cdot \frac{S}{S_0}\right)$ [MJ/m²d]

The coefficients a and b need to be estimated for the position. Often 0.25 is used for a and 0.50 is used for b.

The maximum astronomic possible sunshine duration (S₀ in h) is calculated on the basis of the hour angle at sundown (ws in radians) as follows:

$S_0 = \frac{24}{\pi \cdot ws}$ [h/d]

Net Radiation

The net radiation (Rn in MJ/m²d) results from the single radiation components and provides the energy for the evaporation. The net radiation is calculated on the basis of the difference of the global radiation (Rg in MJ/m²d) and the effective long-wave radiation (Rl in MJ/m²d). The global radiation is reduced by the albedo (alpha) of the referring land cover.

$Rn = (1 - \alpha) \cdot Rg - Rl$

The effective long-wave radiation (Rl in MJ/m²d) is calculated on the basis of the Bolzmann constant (Bk = 4.903E-9 MJ/K⁴m²d), the absolute air temperature (Tabs in K), the actual vapor pressure of the air (ea in kPa), the actual global radiation (Rg in MJ/m²d) and the maximum global radiation for unclouded sky (Rg0 in MJ/m²d):

$Rl = Bk \cdot Tabs^4 \cdot (0.34 - 0.14 \cdot \sqrt{ea}) \cdot \left(1.35 \cdot \frac{Rg}{Rg0} - 0.35 \right)$ [MJ/m²d]

The actual vapor pressure of the air (ea in kPa) is calculated on the basis of the saturation vapor pressure (es in kPa) and the relative humidity (U in %) according to the following equation:

$ea = es \cdot \frac{U}{100}$ [kPa]

The saturation vapor pressure of the air (es in kPa) results from the air temperature (T in °C) according to:

$es = 0.6108 \cdot e^{\frac{17.27 \cdot T}{237.3 + T}}$ [kPa]

The maximum global radiation for uncovered sky (Rg0 in MJ/m²d) results from the extraterrestrial radiation (Ra in MJ/m²d) and the terrain height (h in m above N.N.) as follows:

$Rg0 = (0.75 + 2\cdot10^{-5} \cdot h) \cdot Ra$ [MJ/m²d]

Evaporation Calculation

The calculation of the potential evaporation can be carried out according to Penman-Monteith or Haude. The advantage of the Penman-Monteith method is the higher physical basis. However, much more input data is needed. For the calculation according to Haude only air temperature and relative humidity are required.

Potential Evaporation according to Penman-Monteith

The calculation of the Bestandesverdunstung according to Penman-Monteith (PET in mm/d) is calculated as follows:

$PET = \frac{1}{L_d} \cdot \frac{s \cdot (Rn - G) + \rho \cdot c_P \cdot \frac{es - ea}{r_a}}{s + \gamma \cdot \left(1 + \frac{r_s}{r_a}\right)}$ [mm/d]

with:

L_d : latent heat of evaporation [MJ/kg]

s : slope of the vapor pressure curve [kPa / K]

Rn : net radiation [MJ/m²d]

G : soil heat flux [MJ/m²d]

$ρ$ : density of the air [kg/m³]

c_P : specific heat capacity of the air (=1.031E-3 MJ/kg K]

es : saturation vapor pressure of the air [kPa]

ea : actual vapor pressure of the air [kPa]

$γ$ : psychrometer constant [kPa / K]

r_a : aerodynamic resistance of the land cover [s/m]

r_s : surface resistance of the land cover [s/m]

The latent heat of evaporation (L_d in MJ/kg) results from the air temperature according to the following equation:

$L_d = \frac{2501 - 2.361 \cdot T}{1000}$ [MJ/kg]

The slope of the saturation vapor pressure curve (s in kPa/K) is calculated on the basis of the air temperature:

$s = \frac{4098 \cdot 0.6018 \cdot e^{\frac{17.27 \cdot T}{T + 237.3}}}{(T+237.3)^2}$ [kPa/K]

The soil heat flux (G in MJ/m²d) results from the net radiation (Rn in MJ/m²d):

$G = 0.1 \cdot Rn$ [MJ/m²d]

The density of the air ( $ρ$ in kg/m³) results from the air pressure (p in kPa) and the virtual temperature (vT in K):

$\rho = 3.486 \cdot \frac{p}{vT}$ [kg/m³]

If the air pressure (p in kPa) is not available as value, it can be calculated approximately on the basis of the terrain height (h in m ü.NN) and the absolute air temperature (Tabs in K) according to the following equation:

$p = \frac{1013 \cdot e^{\left(-1\cdot\frac{9.811}{8314.3 \cdot Tabs} \cdot h\right)}}{10}$ [kPa]

The virtual temperature (vT in K) results from the air pressure (p in kPa), the absolute air temperature (Tabs in K) and the actual vapor pressure of the air (ea in kPa):

$vT = \frac{Tabs}{1 - 0.378 \cdot \frac{ea}{p}}$ [K]

The psychrometer constant ( $γ$ in kPa / K) is calculated on the basis of the specific heat capacity of the air (=1.031E-3 MJ/kg K), the air pressure (p in kPa), the relation of the molecular weight of dry and humid air (VM = 0.622) and the latent heat of evaporation (L_d in MJ/kg):

$\gamma = \frac{c_P \cdot p}{VM \cdot L_d}$

The surface resistance of the land cover (r_s in s/m) results from the leaf area index LAI, the stomatal resistance for the given point in time (rsc in s/m) and the surface resistance of an uncovered surface (rss = 150 s/m) as follows:

$r_s = \frac{1}{\frac{1 - 0.7^{LAI}}{rsc}+\frac{0.7^{LAI}}{rss}}$

The aerodynamic roughness of the land cover (r_a in s/m) results from the wind speed (v in m/s) and the effective vegetation height (eH in m)

$r_a = \frac{9.5}{v} \cdot \ln\left(\frac{2}{0.1 \cdot eH}\right)^2$ [s/m] for stands with eH < 10 m

$r_a = \frac{20}{0.41^2 \cdot v}$ [s/m] for stands with eH >= 10 m

Potential Evaporation according to Haude

The potential evaporation according to Haude is calculated on the basis of the saturation deficit of the air and an empirical, dimensionless Haude-factor (hF). The saturation deficit results from the saturation vapor pressure (es in kPa) and the relative air humidity (U in %). The Haude-factor has to be defined for different vegetation types. The calculation of the potential evaporation (PET in mm) is carried out according to:

$PET = es \cdot \left(1 - \frac{U}{100}\right) \cdot hF$

The saturation vapor pressure of the air (es in kPa) results from the air temperature (T in °C):

$es = 0.6108 \cdot e^{\frac{17.27 \cdot T}{237.3 + T}}$ [kPa]

Snow Cover Calculation

The snow cover calculation is implemented as simple accumulation and snowmelt approach. The method decides on the basis of the air temperature whether water is saved as snow on a model unit or whether potentially existing snow melts and produces snowmelt runoff. For this purpose, two temperatures are calculated from the minimum temperature (T_min), average temperature (T_avg) and maximum temperature (T_max) of the referring time step:

The accumulation temperature as: $T_{acc} = \frac{T_{min}+T_{avg}}{2}$ [°C] and

the snowmelt temperature as: $T_{melt} = \frac{T_{avg}+T_{max}}{2}$ [°C]

If the accumulation temperature (T_acc) lies on or below a threshold (Tbase) that needs to be given by the user, it is assumed that potentially occurring precipitation falls as snow. It is then saved on the model unit.

If the snowmelt temperature goes beyond the temperature threshold Tbase, the snowmelt is calculated with the help of a simple snowmelt factor (TMF). For this purpose, a potential snowmelt rate is calculated on the basis of the TMF (in mm/d K), the temperature threshold and the snowmelt temperature:

$SM_p = TMF \cdot (T_{melt} - Tbase)$ [mm/d]

This potential snowmelt rate is then compared to the actual saved snow water equivalent which is then partly or fully melted. The resulting snowmelt water is passed on as input to the following module.

Soil Water Budget

The soil water budget module serves as allocator of the input (precipitation and snowmelt) to the output paths (evaporation, direct runoff, ground water recharge). The central element is the soil storage which is dimensioned via the usable field capacity of the rooted soil area. The maximum fill volume can be adjusted by a multiplicative user-controlled calibration parameter (FCA).

First, the input (precipitation and snowmelt) is allocated to the evaporation until the potential evaporation is reached. The surplus (inflow) is then allocated in direct runoff (SQ) and infiltration (INF), in dependence of the relative soil saturation ( $Θ$ ) and a calibration parameter (DFB). The calculation is carried out as follows:

$SQ = \Theta^{DFB} \cdot Inflow$ [mm/d]

$INF = (1 - \Theta^{DFB}) \cdot Inflow$ [mm/d]

The infiltration (INF) is allocated to the soil storage until it is completely saturated. If there is a surplus (excess water EW), it is allocated to the two paths interflow (SSQ) and ground water recharge (GWR) in dependence of the slope ( $α$ ) and a calibration parameter (LVD). The calculation is carried out according to the following equation:

$SSQ = \tan\alpha \cdot LVD \cdot EW$ [mm/d]

$GWR = (1 - \tan\alpha) \cdot LVD \cdot EW$ [mm/d]

The ground water recharge is seen as source for the basis runoff (BQ) now.

Runoff Concentration and Retardation in Runoff

The runoff concentration and retardation in runoff is represented as simple function of the catchment area for the three runoff components (direct runoff, SQ, intermediate runoff SSQ and basis runoff BQ). For this purpose, the generation rates of the three components are accumulated area-weighted and are lead by their own linear cascade (Nash-cascade). For each of the three cascades the user has to determine the following two parameters: number of storages (n) and retention coefficient (k).

Hydrological Model J2000g

Latest revision as of 10:47, 5 December 2011

Contents

Abstract

Distribution and Attribute Tables

Model Unit Attribute Table

Soil Attribute Table

Land Use Attribute Table

Hydrogeology Attribute Table

Input Data - Model Driver

Installation and Start

Model Initialization

Regionalization

Precipitation Correction

Monthly Precipitation Correction

Daily Precipitation Correction

Moistening Loss and Evaporation Loss

Wind Error

Radiation Calculation

Extraterrestrial Radiation

Global Radiation

Net Radiation

Evaporation Calculation

Potential Evaporation according to Penman-Monteith

Potential Evaporation according to Haude

Snow Cover Calculation

Soil Water Budget

Runoff Concentration and Retardation in Runoff

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@@ Line 1: / Line 1: @@
-==Zusammenfassung==
+[[de:Hydrologisches_Modell_J2000g]]
-Das Modell J2000g wurde als vereinfachtes hydrologisches Modell entwickelt um zeitlich aggregierte, räumlich verteilte hydrologische Zielgrößen zu berechnen. Die Darstellung und Berechnung der hydrologischen Vorgänge erfolgt dabei eindimensional für eine beliebige Anzahl von Punkten im Raum. Durch diese Modellpunkte können unterschiedliche Distributionskonzepte (Response Units, Rasterzellen, Teileinzugsgebiete) gleichermaßen ohne weitere Modellanpassung eingesetzt werden.
+==Abstract==
+The Model J2000g was developed as a simplified hydrological model to calculate temporally aggregated, spatially allocated hydrological target sizes. The representation and calculation of the hydrological processes is carried out one-dimensionally for an arbitrary number of points in the space. These model points enable the use of different distribution concepts (Response Units, grid cells, catchment areas) without further model adjustments.
-Die zeitliche Diskretisierung der Modellierung kann entweder in Tagesschritten oder Monatschritten erfolgen. Während der Modellierung werden folgende Prozesse für jeden Zeitschritt berechnet: Regionalisierung von punktuell vorliegenden Klimadaten auf die jeweiligen Modelleinheiten, Berechnung von Global- und Nettostrahlung als Eingang für die Verdunstungsberechnung, Berechnung der landbedeckungsspezifischen potentiellen Verdunstung nach Penmam-Monteith, Schneeakkumulation und Schmelze, Bodenwasserhaushalt, Grundwasserneubildung, Abflussverzögerung (Translation und Retention). Die einzelnen Prozesse werden unten detailliert beschrieben.
+The temporal discretization of the modeling can be carried out in daily or monthly steps. During the modeling the following processes are calculated for each time step: regionalization of punctual existing climate data to the referring model units, calculation of global and net radiation as access for the evaporation calculation, calculation of the land-cover-specific potential evaporation according to Penman-Monteith, snow accumulation and snowmelt, soil water budget, groundwater recharge, retardation in runoff (translation and retention). The individual processes are described in more detail below.
 ==Distribution and Attribute Tables==
 The model J2000g is not bound to any specific distribution concept because the processes are calculated on the basis of points in the space that are independent of each other (1D-model concept). These points can represent different space units, e.g. single station positions, polygons, grid cells, catchment areas or subcatchments but also rather administrative units such as field unit or administrative districts. In the following text the term “model unit” is used for these points.
 ===Model Unit Attribute Table===
 Each model unit needs to be described with specific attributes for the modeling. These are:
-[[Bild:HruTab.jpg|thumb|Sample for a model unit-parameter-table]]
+[[File:HruTab.jpg|thumb|Sample for a model unit-parameter-table]]
 * '''ID''' - a clear numeric ID
 * '''X''' - the easting of the centre (centroid) as Gauss-Krüger coordinate
-* '''Y''' - the northing of the centre (centroid) as Gauss-Krüger coordinateder
+* '''Y''' - the northing of the centre (centroid) as Gauss-Krüger coordinate
 * '''area''' - the area of the model unit in m²
 * '''elevation''' - the mean elevation of the model unit in m above N.N.
@@ Line 22: / Line 22: @@
 * '''hgeoID''' - a clear numeric ID for the hydrological unit of the model unit (serves as allocation to the hydrogeology table)
 The model unit attribute table contains the attribute names in the first row. These must not be changed because they are used as variable name for the attribute generation during the model parameterization. The second row contains the minimal possible value of the referring attribute, whereas the third one contains the maximum possible value. In the fourth row the physical unit of the attribute needs to be entered. Then, as many rows as needed are given that contain the attribute values of the single model units. The table needs to be completed by a comment row which starts with the comment symbol (#). The tab (\t) has to be used to separate the rows.
 ===Soil Attribute Table===
-[[Bild:SoilTab.jpg|thumb|Sample for a soil attribute table]]
+[[File:SoilTab.jpg|thumb|Sample for a soil attribute table]]
 The soil attribute table contains soil-physical characteristics for each soil unit that occurs in the area. In the current model version only the usable field capacity for each decimeter is needed. On the basis of the field capacity the maximum storage capacity of the soil water storage is calculated in dependence of the effective root depth of the vegetation on the model unit during the model parameterization.
@@ Line 38: / Line 37: @@
 ===Land Use Attribute Table===
-[[Bild:LanduseTab.jpg|thumb|sample for a land use attribute table]]
+[[File:LanduseTab.jpg|thumb|sample for a land use attribute table]]
 The land use attribute table contains vegetation parameters that are nearly exclusively needed for the evaporation calculation according to Penman-Monteith. In the table the following attributes need to be given for each land use unit and land cover unit that occurs in the area:
 * '''LID''' - a clear numeric ID with which the connection to the model unit table is generated.
@@ Line 51: / Line 50: @@
 ===Hydrogeology Attribute Table===
-[[Bild:HgeoTab.jpg|thumb|sample for a hydrogeology attribute table]]
+[[File:HgeoTab.jpg|thumb|sample for a hydrogeology attribute table]]
 In the hydrogeology attribute table the maximum possible ground water recharge rates per time unit are set up for each hydrogeologic unit. It only contains the following two attributes:
 * '''GID''' - a clear numeric ID with which the connection to the model unit table is generated.
@@ Line 58: / Line 57: @@
 To complete the table, a comment row must be given (introduced with #). The tab (\t) has to be used to separate the rows.
-==Eingangsdaten - Modelltreiber==
+==Input Data - Model Driver==
-[[Bild:dateFile.jpg|thumb|Beispiel für eine Eingangsdatentabelle]]
+[[File:dateFile.jpg|thumb|sample for an input data table]]
-Für den Modellantrieb werden Klimazeitreihen von einer beliebigen Anzahl von Klima- und Niederschlagsstationen benötigt. Diese müssen in entsprechend formatierte Datendateien aufbereitet werden. Diese Dateien besitzen folgendes Format:
+For the model run climate time series of an arbitrary number of climate and precipitation stations are needed. The time series have to be preprocessed in the referring formatted data files. The files have the following format:
-Zeile 1 bis 13 enthalten Metainformationen zu den Daten. Diese sind in Blöcken angeordnet, die durch Beschreibungen beginnend mit dem AT-Zeichen (@) begonnen werden. Mehrere Einträge pro Zeile werden durch den Tabulator (\t) getrennt.
+Rows 1 to 13 contain meta information about the data. They are arranged in blocks which are started with descriptions which in turn are started with the AT-symbol (@). Multiple entries per row are separated via the tab (\t).
-* '''@dataSetAttribs (Attribute des Datensatzes)'''
+* '''@dataSetAttribs (attribute of the dataset)'''
-** missingDataVal - Wert der fehlende Daten kennzeichnet
+** missingDataVal - value that marks missing data
-** dataStart - Startdatum des Datensatzes (DD.MM.JJJJ HH:MM)
+** dataStart - start date of the dataset (DD.MM.JJJJ HH:MM)
-** dataEnd - Enddatum des Datensatzes (DD.MM.JJJJ HH:MM)
+** dataEnd - end date of the dataset (DD.MM.JJJJ HH:MM)
-** tres - zeitliche Auflösung (Tage "d", Monate "m")
+** tres - termporal resolution (days "d", months "m")
-* '''@statAttribVal (Attribute der Klimastationen)'''
+* '''@statAttribVal (attributes of the climate stations)'''
-** name - die Namen der Klimastationen
+** name - the names of the climate stations
-** ID - eine numerische, eindeutige Identifikationsnummer
+** ID - a numeric, clear ID
-** elevation - die Höhe auf der die Station liegt in m ü.N.N.
+** elevation - the elevation of the station in m above N.N.
-** x - Rechtswert als Gauss-Krüger-Koordinate
+** x - easting as Gauss-Krüger-coordinate
-** y - Hochwert als Gauss-Krüger-Koordinate
+** y - northing as Gauss-Krüger-coordinate
-** dataColumn - bezeichnet die Spalte in der die Daten für die jeweilige Station stehen
+** dataColumn - describes the column in which the data for the referring station can be found
-In den folgenden Zeilen stehen dann die eigentlichen Daten für jeden Zeitschritt, beginnend mit:
+In the following rows the actual data for each time step is listed – starting with:
 * '''@dataVal
-Das Format ist Datum Uhrzeit gefolgt von tabulatorgetrennten Daten.
+The format is Date, Time followed by Data that is separated by the tab.
-==Installation und Start==
+==Installation and Start==
-==Modellinitialisierung==
+==Model Initialization==
-==Regionalisierung==
+==Regionalization==
-Das Regionalisierungsmodul dient der Übertragung von punktuellen Messwerten auf die Modelleinheiten. Das Verfahren wurde aus dem hydrologischen Modell J2000 ohne Änderung übernommen und gliedert sich in folgende Schritte:
+The regionalization module is used for the transfer of punctual values to the model units. The procedure was taken from the hydrological Model J2000 without any changes and is arranged in the following steps:
-# Berechnung einer linearen Regression zwischen den Stationsmesswerten und den Stationshöhen für jeden Zeitschritt. Dabei wird das Bestimmtheitsmass (r<sup>2</sup>) und die Steigung der Regressionsgeraden (b<sub>H</sub>) bestimmt.
+# Calculation of a linear regression between the station values and the station heights for each time step. Thereby, the coefficient of determination (r<sup>2</sup>) and the slope of the regression line (b<sub>H</sub>) is calculated.
-# Bestimmung der n Messstationen, die der jeweiligen Modelleinheit am nächsten liegen. Die Zahl n, die während der Parametrisierung des Modells angegeben werden muss, ist von der Dichte des Stationsmessnetzes und der Lage der einzelnen Stationen abhängig.
+# Definition of the n gaging stations which are nearest to the particular model unit. The number n which needs to be given during the parameterization is dependent on the density of the station net as well as on the position of the individual stations.
-# Mit einem Inverse-Distance-Weighted (IDW) Verfahren werden die Wichtungen der n Stationen in Abhängigkeit von ihrer Entfernung für jede Modelleinheit bestimmt. Durch das IDW-Verfahren wird die horizontale Variabilität der Stationsdaten, entsprechend ihrer Lage im Raum, berücksichtigt.
+# Via an Inverse-Distance-Weighted Method (IDW) the weightings of the n stations are defined dependently on their distances for each model unit. Via the IDW-method the horizontal variability of the station data is taken into account according to its spatial position.
-# Berechnung des Datenwertes für jede Modelleinheit mit den Gewichten aus Punkt 3 und einer optionalen Höhenkorrektur zur Berücksichtigung der der vertikalen Variabilität. (Die Höhenkorrektur wird nur dann durchgeführt wenn das unter 1. berechnete Bestimmtheitsmass den Wert von 0.7 übersteigt.)
+# Calculation of the data value for each model unit with the weightings from point 3 and an optional elevation correction for the consideration of the vertical variability. (The elevation correction is only carried out when the coefficient of determination –calculated under point 1 – goes beyond the threshold of 0.7.)
-Die Berechnung des Datenwertes für jede Modelleinheit (DW<sub>U</sub>) '''ohne Höhenkorrektur''' erfolgt mit den Gewichten (W(i)) und den Messwerten (MW(i)) jeder der n Messtationen nach:
+The calculation of the data value for each model unit (DW<sub>U</sub>) '''without elevation correction''' is carried out with the weightings (W(i)) and the values (MW(i)) of each n gaging station according to:
 <math> DW_{U} = \sum_{i=1}^{n}MW(i) \cdot W(i) </math>
-Bei der Berechnung '''mit Höhenkorrektur''' wird außerdem noch die Höhendifferenz (HD(i)) zwischen der Messstation und der Modelleinheit und die Steigung der Regressionsgerade (b<sub>H</sub>) berücksichtigt. Der Datenwert für die Modelleinheit (DW<sub>U</sub>) ergibt sich damit nach:
+For the calculation '''with elevation correction''' the elevation difference (HD(i)) between the gaging station and the model unit as well as the slope of the regression line (b<sub>H</sub>) are taken into account. Thus, the data value for the model unit (DW<sub>U</sub>) is calculated according to:
 <math> DW_U = \sum_{i=1}^{n}\left(\left(HD(i) \cdot b_H + MW(i)\right) \cdot W(i)\right) </math>
-==Niederschlagskorrektur==
+==Precipitation Correction==
-Niederschlagsmesswerte weisen teilweise einen deutlichen systematischen Messfehler auf, der einerseits gerätebedingt, andererseits auf die Aufstellung des Messgerätes zurückzuführen ist. Dieser Messfehler lässt sich auf zwei Ursachen zurückführen: (1) den Benetzungs- und Verdunstungsfehler, der von der Art des Messgerätes abhängt und (2) den Windfehler, der aus der Verdriftung der Niederschläge resultiert. Beide Messfehler sind in hohem Maße von der Art (Regen oder Schnee) und der Niederschlagsmenge abhängig.
+Precipitation values partly show a clear systematic error in measurement which is caused instrument-determined or due to the selection of the instrument position. This error in measurement has two causes: (1) the moistening error and evaporation error, which each depends on the type of the instrument and (2) the wind error which emerges due to the drifting of the precipitations. Both errors in measurement are strongly dependent on the type (rain or snow) of the precipitation amount.
-Für die Korrektur beider Fehlergrößen wird ein Korrekturverfahren nach Richter (1995) eingesetzt, dass in gleicher Form auch im Modell J2000 zum Einsatz kommt. Das Verfahren zur Niederschlagskorrektur unterscheidet sich bezüglich der zeitlichen Auflösung der Niederschlagsdaten.
+For the correction of both errors a correction method according to Richter (1995) is used which is applied in the same way in the Model J2000. The procedure for the evaporation correction differs with regard to the temporal resolution of the precipitation data.
-===Monatliche Niederschlagskorrektur===
+===Monthly Precipitation Correction===
-[[Bild:Richter.jpg|thumb|Monatliche prozentuale Niederschlagsmessfehler für leicht geschützte Stationslagen, gebietsweise zusammengefasst (Richter 1995)]]
+[[File:Richter.jpg|thumb|Monthly percental precipitation errors in measurement for slightly sheltered stations, concentrated regionally (Richter 1995)]]
-Der korrigierte Niederschlag (P<sub>korr</sub>) berechnet sich bei monatlichen Zeitschritten durch die Erhöhung des  gemessenen Niederschlags (P<sub>m</sub>) durch den prozentualen monatlichen Messfehler (MF<sub>t</sub>) (siehe nebenstehende Tabelle) nach:
+The corrected precipitation (P<sub>korr</sub>) is calculated for monthly time steps on the basis of the decrease of the measured precipitation (P<sub>m</sub>) and the percental monthly error in measurement (MF<sub>t</sub>) (see adjacent table):
 <math> P_{korr} = P_m + P_m \cdot \frac{MF_t}{100} </math>
-===Tägliche Niederschlagskorrektur===
+===Daily Precipitation Correction===
-Für die tägliche Niederschlagskorrektur werden die beiden Fehlerterme explizit berechnet. Hierzu wurden aus den tabellierten Fehlerbeträgen nach Richter (1995) Korrekturfunktionen abgeleitet.
+For the daily precipitation correction the two error terms are calculated explicitly.
-====Benetzungs- und Verdunstungsverlust====
+For this purpose, correction functions were derived on the basis of the tabled error values according to Richter (1995).
-[[Bild:BVerr.jpg|thumb|Benetzungs- und Verdunstungsverluste von Hellmann-Niederschlagsmessern, getrennt für das Sommer- und Winterhalbjahr in Abhängigkeit des Tageswertes der Niederschlagshöhe (nach Richter 1995) und die daran angepassten Korrekturfunktionen (Krause 2001)]]
+====Moistening Loss and Evaporation Loss====
+[[File:BVerr.jpg|thumb|Moistening loss and evaporation losses by Hellmann precipitation gauges separated for the summer half year and winter half year in dependence of the daily value of the precipitation amount (according to Richter) and the adjusted correction function (Krause 2001)]]
-Für eine stetige Fehlerkorrektur des Benetzungs- und Verdunstungsverlustes wurden an die von Richter (1995) tabellierten Werte stetige Korrekturfunktionen angepasst, die in der nebenstehenden Abbildung dargestellt sind. Die Korrekturfunktionen wurden jeweils separat für das Winterhalbjahr (Nov. bis Apr.) und das Sommerhalbjahr (Mai bis Okt.) abgeleitet. Mit diesen Funktionen berechnet sich der Benetzungs- und Verdunstungsverlust in mm für Niederschläge <= 9 mm nach:
+For a continual error correction of the moistening loss and evaporation loss continual correction functions were adjusted to the tabled values by Richter (1995). They are shown in the adjacent figure. The correction functions were derived each separately for the winter half year (November till April) and summer half year (May till October). With these functions the moistening loss and evaporation loss is calculated in mm for precipitations <= 9 mm according to:
 <math>BV_{Som} = 0.08 \cdot \ln(N) + 0.225 </math>
@@ Line 123: / Line 123: @@
 <math>BV_{Win} = 0.05 \cdot \ln(N) + 0.13 </math>
-Übersteigt die Niederschlagsmenge 9 mm wird ein konstanter Fehler von 0.47 mm im Sommer- und 0.3 mm im Winterhalbjahr angenommen.
+If the amount of precipitation is greater than 9 mm, a constant error of 0.47 mm in the summer half year and of 0.3 mm in the winter half year is assumed.
-====Windfehler====
+====Wind Error====
-[[Bild:WindFehler.jpg|thumb|Ausprägung der relativen Korrekturfunktion für den Windfehler basierend auf den tabellierten Werten in Richter (1995) (aus Krause 2001)]]
+[[File:WindFehler.jpg|thumb|Characteristic of the relative correction function for the wind error based on the tabled values by Richter (1995) (Krause 2001)]]
-Die Berechnung des Windfehlers der Niederschlagsmessung mit dem Hellmann Standardgerät erfolgt ebenfalls nach tabellierten Fehlerwerten aus RICHTER (1995) an die entsprechende stetige Korrekturfunktionen angepasst wurden. Bei der Korrektur wird unterschieden ob der Niederschlag als Regen oder Schnee gefallen ist. Wie diese Aufteilung intern erfolgt, wird weiter unten beschrieben. Der relative Korrekturbetrag berechnet sich als:
+The calculation of the wind error of the precipitation measurement with the Hellman precipitation gauge is also carried out according to the tabled error values from Richter (1995) which was adjusted to the referring continual correction functions. For the correction it is differentiated whether the precipitation was rain or snow. The way of internal differentiation is described further below. The relative correction value is calculated as follows:
-<math> WK_s = 0.5424 \cdot N^{-0.211} </math> für Schneeniederschlag
+<math> WK_s = 0.5424 \cdot N^{-0.211} </math> for snow
-<math> WK_r = 0.1421 \cdot N^{-0.519} </math> für Regenniederschlag.
+<math> WK_r = 0.1421 \cdot N^{-0.519} </math> for rain.
-Der korrigierte Niederschlagswert (P<sub>K</sub>) berechnet sich schliesslich aus dem Messwert (P<sub>M</sub>), dem relativen Korrekturbetrag für den Windfehler (WK<sub>s</sub>, WK<sub>r</sub>) und dem Benetzungs- und Verdunstungsverlust (BV<sub>Som</sub>, BV<sub>Win</sub>) nach:
+The corrected precipitation value (P<sub>K</sub>) is finally calculated on the basis of the value (P<sub>M</sub>), the relative correction value for the wind error (WK<sub>s</sub>, WK<sub>r</sub>) as well as the moistening loss and evaporation loss (BV<sub>Som</sub>, BV<sub>Win</sub>) as follows:
 <math>P_K = P_M + P_M \cdot WK_{s,r} + BV_{Som,Win} </math>
-==Strahlungsberechnung==
+==Radiation Calculation==
-Für die Verdunstungsberechnung nach Penman-Monteith wird die Nettostrahlung als Eingangswert benötigt. Diese kann aus der Globalstrahlung berechnet werden. Liegt die Globalstrahlung nicht als Messwert vor kann sie näherungsweise aus der Sonnenscheindauer bestimmt werden. Hierzu sind eine Anzahl von Teilberechnungen notwendig. Die folgenden Berechnungen gehen von einer täglichen Modellierung aus. Wird das Modell mit monatlichen Zeitschritten betrieben erfolgen die unten aufgeführten Berechnungen für den 15. Tag jeden Monats. Die resultierenden Terme werden dann anhand der Tage pro Monat aufsummiert.
+For the evaporation calculation according to Penman-Monteith, the net radiation is needed as initial value and can be calculated on the basis of the global radiation. If the global radiation is not available, it can be defined approximately on the basis of the sunshine duration. For this purpose, a number of intermediate calculations are necessary. The following calculations act on the assumption of a daily modeling. When the model runs in monthly time steps, the calculations listed below are carried out on the 15th of each month. The resulting terms are then accumulated on the basis of the days per month.
-===Extraterrestrische Strahlung===
+===Extraterrestrial Radiation===
-[[Bild:radiation.jpg|thumb|Jahresgang der extraterrestrischen Strahlung (Ra), Globalstrahlung (Rg) und Nettostrahlung (Rn) für einen Standort im Thüringer Wald]]
+[[File:radiation.jpg|thumb|Annual course of extraterrestrial radiation (Ra), global radiation (Rg) and net radiation (Rn) for a position in the Thuringian Forrest]]
-Die extraterrestrische Strahlung (Ra) ist der kurzwellige Strahlungsenergiefluss der Sonne an der Obergrenze der Atmosphäre. Ra berechnet sich für einen spezifischen Ort in Abhängigkeit von seiner geographischen Breite (lat in radians), der Deklination der Sonne (decl in radians), der Solarkonstante (Gsc in MJ / m<sup>2</sup>min), dem Stundenwinkel bei Sonnenuntergang (ws in radians) und der inversen relativen Distanz zwischen Erde und Sonne (dr in radians) nach:
+The extraterrestrial radiation (Ra) is the short-wave radiation energy flux of the sun at the upper boarder of the atmosphere. Ra is calculated for a specific place in dependence of its latitude (lat in radians), the declination of the sun (decl in radians), the solar constant (Gsc in MJ / m<sup>2</sup>min), the hour angle at sundown (ws in radians) and the inverse relative distance between earth and sun (dr in radians) according to:
 <math> Ra = \frac{24\cdot60}{\pi} \cdot Gsc \cdot dr \cdot \left(ws \cdot \sin(lat) \cdot \sin(decl) + \cos(lat) \cdot \cos(decl) \cdot \sin(ws)\right)</math>
-Die '''Solarkonstante''' (Gsc in MJ / m<sup>2</sup>min) ergibt sich aus der julianischen Tageszahl (jD [1... 365,366]) nach:
+The '''solar constant''' (Gsc in MJ / m<sup>2</sup>min) results from the Julian Date (jD [1... 365,366]) as follows:
 <math>Gsc = 0.08139 + 0.00291 \cdot \cos\left(\frac{\pi}{180} \cdot (jD - 15)\right)</math> [MJ / m<sup>2</sup>min]
-Die '''relative Distanz Erde Sonne''' (dr in radians) ergibt sich aus der julianischen Tageszahl (jD [1... 365,366]) nach:
+The '''relative distance between earth and sun''' (dr in radians) results from the Julian Date (jD [1... 365,366]) as follows:
 <math>dr = 1 + 0.033 \cdot \cos\left(\frac{2\pi}{365} \cdot jD\right)</math> [rad.]
-Die '''Deklination der Sonne''' (decl in radians) ergibt sich aus der julianischen Tageszahl (jD [1... 365,366]) nach:
+The '''declination of the sun''' (decl in radians) results from the Julian Date (jD [1... 365,366]) as follows:
 <math> decl = 0.40954 \cdot \sin(0.0172 \cdot (jD - 79.35)) </math> [rad.]
-Der '''Stundenwinkel bei Sonnenuntergang''' (ws in radians) ergibt sich aus der geographischen Breite (lat in radians) und der Deklination (decl in radians) nach:
+The '''hour angle at sundown''' (ws in radians) results from the latitude (lat in radians) and the declination (decl in radians) as follows:
 <math> ws = \arccos(-1 \cdot \tan(lat) \cdot \tan(decl)) </math> [rad.]
-===Globalstrahlung===
+===Global Radiation===
-Die Globalstrahlung (Rg) berechnet sich aus der extraterrestrischen Strahlung (Ra in MJ/m²d) und dem Bewölkungsgrad. Der Bewölkungsgrad wird hierbei aus dem Verhältnis der gemessenen Sonnenscheindauer (S in h/d) zur astronomisch möglichen Sonnenscheindauer (S<sub>0</sub> in h/d) unter Zuhilfenahme der Angström Formel approximiert. Rg berechnet sich damit nach:
+The global radiation (Rg) is calculated on the basis of the extraterrestrial radiation (Ra in MJ/m²d) and the degree of cloudiness. At this, the degree of cloudiness is approximated on the basis of the relation of the measured sunshine duration (D in h/d) to the astronomic possible sunshine duration (S<sub>0</sub> in h/d) with the help of the Angström formula. Thus, Rg is calculated as follows:
 <math> Rg = Ra \cdot \left(a + b \cdot \frac{S}{S_0}\right) </math> [MJ/m²d]
-Die Koeffizienten a und b müssen für den Standort geschätzt werden. Vielfach wird für a = 0.25 und für b = 0.50 eingesetzt.
+The coefficients a and b need to be estimated for the position. Often 0.25 is used for a and 0.50 is used for b.
-Die maximale '''astronomisch mögliche Sonnenscheindauer''' (S<sub>0</sub> in h) ergibt sich aus dem Stundenwinkel bei Sonnenuntergang (ws in radians) nach:
+The '''maximum astronomic possible sunshine duration''' (S<sub>0</sub> in h) is calculated on the basis of the hour angle at sundown (ws in radians) as follows:
 <math> S_0 = \frac{24}{\pi \cdot ws} </math> [h/d]
-===Nettostrahlung===
+===Net Radiation===
-Als resultierende der einzelnen Strahlungskomponenten ergibt sich die Nettostrahlung (Rn in MJ/m²d), die die Energie für die Verdunstung bereitstellt. Die Nettostrahlung ergibt sich aus der Differenz von Globalstrahlung (Rg in MJ/m²d) und der effektiven langwelligen Ausstrahlung (Rl in MJ/m²d) wobei die Globalstrahlung noch durch die Albedo (alpha) der jeweiligen Bodenbedeckung abgemindert wird, als:
+The net radiation (Rn in MJ/m²d) results from the single radiation components and provides the energy for the evaporation. The net radiation is calculated on the basis of the difference of the global radiation (Rg in MJ/m²d) and the effective long-wave radiation (Rl in MJ/m²d). The global radiation is reduced by the albedo (alpha) of the referring land cover.
 <math> Rn = (1 - \alpha) \cdot Rg - Rl </math>
-Die '''effektive langwellige Ausstrahlung''' (Rl in MJ/m²d) berechnet sich aus der Bolzmann Konstanten (Bk  = 4.903E-9 MJ/K<sup>4</sup>m²d), der absoluten Lufttemperatur (Tabs in K), dem aktuellen Dampfdruck der Luft (ea in kPa), der aktuellen Globalstrahlung (Rg in MJ/m²d) und der maximalen Globalstrahlung bei unbedecktem Himmel (Rg0 in MJ/m²d) nach:
+The '''effective long-wave radiation''' (Rl in MJ/m²d) is calculated on the basis of the Bolzmann constant (Bk  = 4.903E-9 MJ/K<sup>4</sup>m²d), the absolute air temperature (Tabs in K), the actual vapor pressure of the air (ea in kPa), the actual global radiation (Rg in MJ/m²d) and the maximum global radiation for unclouded sky (Rg0 in MJ/m²d):
 <math> Rl = Bk \cdot Tabs^4 \cdot (0.34 - 0.14 \cdot \sqrt{ea}) \cdot \left(1.35 \cdot \frac{Rg}{Rg0} - 0.35 \right)</math> [MJ/m²d]
-Der '''aktuelle Dampfdruck der Luft''' (ea in kPa) berechnet sich aus dem Sättigungsdampfdruck (es in kPa) und der relativen Feuchte (U in %) nach:
+The '''actual vapor pressure of the air''' (ea in kPa) is calculated on the basis of the saturation vapor pressure (es in kPa) and the relative humidity (U in %) according to the following equation:
 <math> ea = es \cdot \frac{U}{100} </math> [kPa]
-Der '''Sättigungsdampfdruck der Luft''' (es in kPa) ergibt sich aus der Lufttemperatur (T in °C) nach:
+The '''saturation vapor pressure of the air''' (es in kPa) results from the air temperature (T in °C) according to:
 <math> es = 0.6108 \cdot e^{\frac{17.27 \cdot T}{237.3 + T}} </math> [kPa]
-Die '''maximale Globalstrahlung bei unbedecktem Himmel''' (Rg0 in MJ/m²d) ergibt sich aus der extraterrestrischen Strahlung (Ra in MJ/m²d) und der Geländehöhe (h in m ü.N.N.) nach:
+The '''maximum global radiation for uncovered sky''' (Rg0 in MJ/m²d) results from the extraterrestrial radiation (Ra in MJ/m²d) and the terrain height (h in m above N.N.) as follows:
 <math> Rg0 = (0.75 + 2\cdot10^{-5} \cdot h) \cdot Ra </math> [MJ/m²d]
-==Verdunstungsberechnung==
+==Evaporation Calculation==
-Die Berechnung der potentiellen Verdunstung kann wahlweise nach Penman-Monteith oder Haude erfolgen. Der Vorteil der Berechnung nach Penman-Monteith ist die höhere physikalische Basiertheit allerdings werden auch deutlich mehr Eingangsdaten benötigt. Für die Berechnung nach Haude sind lediglich Lufttemperatur und relative Feuchte notwendig.
+The calculation of the potential evaporation can be carried out according to Penman-Monteith or Haude. The advantage of the Penman-Monteith method is the higher physical basis. However, much more input data is needed. For the calculation according to Haude only air temperature and relative humidity are required.
-===Potentielle Verdunstung nach Penman-Monteith===
+===Potential Evaporation according to Penman-Monteith===
-Die Berechnung der Bestandesverdunstung nach Penman-Monteith (PET in mm/d) erfolgt nach:
+The calculation of the Bestandesverdunstung according to Penman-Monteith (PET in mm/d) is calculated as follows:
 <math> PET = \frac{1}{L_d} \cdot \frac{s \cdot (Rn - G) + \rho \cdot c_P \cdot \frac{es - ea}{r_a}}{s + \gamma \cdot \left(1 + \frac{r_s}{r_a}\right)} </math> [mm/d]
-mit:
+with:
-L<sub>d</sub> : Latente Verdunstungswärme [MJ/kg]
+L<sub>d</sub> : latent heat of evaporation [MJ/kg]
-s : Steigung der Dampfdruckkurve [kPa / K]
+s : slope of the vapor pressure curve [kPa / K]
-Rn : Nettostrahlung [MJ/m²d]
+Rn : net radiation [MJ/m²d]
-G : Bodenwärmestrom [MJ/m²d]
+G : soil heat flux [MJ/m²d]
-<math>\rho</math> : Dichte der Luft [kg/m³]
+<math>\rho</math> : density of the air [kg/m³]
-c<sub>P</sub> : Spezifische Wärmekapazität der Luft (=1.031E-3 MJ/kg K]
+c<sub>P</sub> : specific heat capacity of the air (=1.031E-3 MJ/kg K]
-es : Sättigungsdampfdruck der Luft [kPa]
+es : saturation vapor pressure of the air [kPa]
-ea : aktueller Dampfdruck der Luft [kPa]
+ea : actual vapor pressure of the air [kPa]
-<math>\gamma</math> : Psychrometerkonstante [kPa / K]
+<math>\gamma</math> : psychrometer constant [kPa / K]
-r<sub>a</sub> : aerodynamischer Widerstand der Bodenbedeckung [s/m]
+r<sub>a</sub> : aerodynamic resistance of the land cover [s/m]
-r<sub>s</sub> : Oberflächenwiderstand der Bodenbedeckung [s/m]
+r<sub>s</sub> : surface resistance of the land cover [s/m]
-Die '''latente Verdunstungswärme''' (L<sub>d</sub> in MJ/kg) ergibt sich aus der Lufttemperatur nach:
+The '''latent heat of evaporation''' (L<sub>d</sub> in MJ/kg) results from the air temperature according to the following equation:
 <math>L_d = \frac{2501 - 2.361 \cdot T}{1000}</math> [MJ/kg]
-Die '''Steigung der Sättigungsdampfdruckkurve''' (s in kPa/K) berechnet sich aus der Lufttemperatur nach:
+The '''slope of the saturation vapor pressure curve''' (s in kPa/K) is calculated on the basis of the air temperature:
 <math>s = \frac{4098 \cdot 0.6018 \cdot e^{\frac{17.27 \cdot T}{T + 237.3}}}{(T+237.3)^2}</math> [kPa/K]
-Der '''Bodenwärmestrom''' (G in MJ/m²d) ergibt sich aus der Nettostrahlung (Rn in MJ/m²d) nach:
+The '''soil heat flux''' (G in MJ/m²d) results from the net radiation (Rn in MJ/m²d):
 <math>G = 0.1 \cdot Rn</math> [MJ/m²d]
-Die '''Dichte der Luft''' (<math>\rho</math> in kg/m³) ergibt sich aus dem Luftdruck (p in kPa) und der virtuellen Temperatur (vT in K) nach:
+The '''density of the air''' (<math>\rho</math> in kg/m³) results from the air pressure (p in kPa) and the virtual temperature (vT in K):
 <math>\rho = 3.486 \cdot \frac{p}{vT}</math> [kg/m³]
-Liegt der '''Luftdruck''' (p in kPa) nicht als Messwert vor kann er näherungsweise aus Geländehöhe (h in m ü.NN) und der absoluten Lufttemperatur (Tabs in K) wie folgt berechnet werden:
+If the '''air pressure''' (p in kPa) is not available as value, it can be calculated approximately on the basis of the terrain height (h in m ü.NN) and the absolute air temperature (Tabs in K) according to the following equation:
 <math> p = \frac{1013 \cdot e^{\left(-1\cdot\frac{9.811}{8314.3 \cdot Tabs} \cdot h\right)}}{10}</math> [kPa]
-Die virtuelle Temperatur (vT in K) ergibt sich aus dem Luftdruck (p in kPa), der absoluten Lufttemperatur (Tabs in K) und dem aktuellen Dampfdruck der Luft (ea in kPa) nach:
+The virtual temperature (vT in K) results from the air pressure (p in kPa), the absolute air temperature (Tabs in K) and the actual vapor pressure of the air (ea in kPa):
 <math>vT = \frac{Tabs}{1 - 0.378 \cdot \frac{ea}{p}}</math> [K]
-Die '''Psychrometerkonstante''' (<math>\gamma</math> in kPa / K) berechnet sich aus der spezifischen Wärmekapazität der Luft (=1.031E-3 MJ/kg K), dem Luftdruck (p in kPa), dem Verhältnis der Molgewichte von trockener und feuchter Luft (VM = 0.622) und der latenten Verdunstungswärme (L<sub>d</sub> in MJ/kg) nach:
+The '''psychrometer constant''' (<math>\gamma</math> in kPa / K) is calculated on the basis of the specific heat capacity of the air (=1.031E-3 MJ/kg K), the air pressure (p in kPa), the relation of the molecular weight of dry and humid air (VM = 0.622) and the latent heat of evaporation (L<sub>d</sub> in MJ/kg):
 <math> \gamma = \frac{c_P \cdot p}{VM \cdot L_d} </math>
-Der '''Oberflächenwiderstand der Bodenbedeckung''' (r<sub>s</sub> in s/m) berechnet sich aus dem Blattflächenindex (Leaf Area Index LAI), dem Stomatawiderstand zum gegebenen Zeitpunkt (rsc in s/m) und der Oberflächenwiderstand einer unbewachsenen Oberfläche (rss = 150 s/m) nach:
+The '''surface resistance of the land cover''' (r<sub>s</sub> in s/m) results from the leaf area index LAI, the stomatal resistance for the given point in time (rsc in s/m) and the surface resistance of an uncovered surface (rss = 150 s/m) as follows:
 <math> r_s = \frac{1}{\frac{1 - 0.7^{LAI}}{rsc}+\frac{0.7^{LAI}}{rss}} </math>
-Die '''aerodynamische Rauhigkeit der Bodenbedeckung''' (r<sub>a</sub> in s/m) berechnet sich aus der Windgeschwindkeit (v in m/s) und der effektiven Wuchshöhe der Vegetation (eH in m)
+The '''aerodynamic roughness of the land cover''' (r<sub>a</sub> in s/m) results from the wind speed (v in m/s) and the effective vegetation height (eH in m)
-<math> r_a = \frac{9.5}{v} \cdot \ln\left(\frac{2}{0.1 \cdot eH}\right)^2</math> [s/m] für Bestände mit eH < 10 m
+<math> r_a = \frac{9.5}{v} \cdot \ln\left(\frac{2}{0.1 \cdot eH}\right)^2</math> [s/m] for stands with eH < 10 m
-<math> r_a = \frac{20}{0.41^2 \cdot v}</math> [s/m] für Bestände mit eH >= 10 m
+<math> r_a = \frac{20}{0.41^2 \cdot v}</math> [s/m] for stands with eH >= 10 m
-===Potentielle Verdunstung nach Haude===
+===Potential Evaporation according to Haude===
-Die potentielle Verdunstung nach Haude berechnet sich aus dem Sättigungsdefizit der Luft und einem empirischen, dimensionslosen Haude-Faktor (hF). Das Sättigungsdefizit ergibt sich aus dem Sättigungsdampfdruck (es in kPa) und der relativen Luftfeuchte (U in %). Der Haude-Faktor muss für unterschiedliche Vegetationsarten bestimmt werden. Die Berechnung der potentiellen Verdunstung (PET in mm) erfolgt nach:
+The potential evaporation according to Haude is calculated on the basis of the saturation deficit of the air and an empirical, dimensionless Haude-factor (hF). The saturation deficit results from the saturation vapor pressure (es in kPa) and the relative air humidity (U in %). The Haude-factor has to be defined for different vegetation types. The calculation of the potential evaporation (PET in mm) is carried out according to:
 <math> PET = es \cdot \left(1 - \frac{U}{100}\right) \cdot hF </math>
-Der '''Sättigungsdampfdruck der Luft''' (es in kPa) ergibt sich aus der Lufttemperatur (T in °C) nach:
+The '''saturation vapor pressure of the air''' (es in kPa) results from the air temperature (T in °C):
 <math> es = 0.6108 \cdot e^{\frac{17.27 \cdot T}{237.3 + T}} </math> [kPa]
-==Schneedeckenberechnung==
+==Snow Cover Calculation==
-Die Schneedeckenberechnung ist als einfacher Akkumulations- und Schmelzansatz implementiert. Das Verfahren entscheidet anhand der Lufttemperatur ob Wasser als Schnee auf einer Modelleinheit gespeichert wird oder ob potentiell vorhandener Schnee schmilzt und Schneeschmelzabfluss produziert. Hierzu werden zunächst zwei Temperaturen aus Minimum- (T<sub>min</sub>), Durchschnitts- (T<sub>avg</sub>) und Maximumtemperatur (T<sub>max</sub>) des jeweiligen Zeitschrittes berechnet:
+The snow cover calculation is implemented as simple accumulation and snowmelt approach. The method decides on the basis of the air temperature whether water is saved as snow on a model unit or whether potentially existing snow melts and produces snowmelt runoff. For this purpose, two temperatures are calculated from the minimum temperature (T<sub>min</sub>), average temperature (T<sub>avg</sub>) and maximum temperature (T<sub>max</sub>) of the referring time step:
-Die Akkumulationstemperatur als: <math>T_{acc} = \frac{T_{min}+T_{avg}}{2}</math> [°C] und
-die Schmelztemperatur als: <math>T_{melt} = \frac{T_{avg}+T_{max}}{2}</math> [°C]
+The accumulation temperature as: <math>T_{acc} = \frac{T_{min}+T_{avg}}{2}</math> [°C] and
-Liegt die Akkumulationstemperatur (T<sub>acc</sub>) gleich oder unterhalb eines vom Anwender anzugebenden Grenzwertes (Tbase) wird davon ausgegangen, dass eventuell auftretender Niederschlag als Schnee fällt. Dieser wird dann auf der Modelleinheit zwischengespeichert.
+the snowmelt temperature as: <math>T_{melt} = \frac{T_{avg}+T_{max}}{2}</math> [°C]
+If the accumulation temperature (T<sub>acc</sub>) lies on or below a threshold (Tbase) that needs to be given by the user, it is assumed that potentially occurring precipitation falls as snow. It is then saved on the model unit.
+If the snowmelt temperature goes beyond the temperature threshold Tbase, the snowmelt is calculated with the help of a simple snowmelt factor (TMF). For this purpose, a potential snowmelt rate is calculated on the basis of the TMF (in mm/d K), the temperature threshold and the snowmelt temperature:
-Wenn die Schmelztemperatur den Temperaturgrenzwert Tbase übersteigt wird Schneeschmelze mit Hilfe eines einfachen Schneeschmelzfaktors (TMF) berechnet. Hierzu wird eine potentielle Schneeschmelzrate aus TMF (in mm/d K), dem Temperaturgrenzwert und der Schmelztemperatur berechnet:
 <math> SM_p = TMF \cdot (T_{melt} - Tbase) </math> [mm/d]
-Diese potentielle Schmelzrate wird dann gegen das aktuell gespeicherte Schneewasseräquivalent verglichen, das dann teilweise oder vollständig geschmolzen wird. Das resultierende Schneeschmelzwasser wird an das folgende Modul als Input weitergegeben.
+This potential snowmelt rate is then compared to the actual saved snow water equivalent which is then partly or fully melted. The resulting snowmelt water is passed on as input to the following module.
+==Soil Water Budget==
+The soil water budget module serves as allocator of the input (precipitation and snowmelt) to the output paths (evaporation, direct runoff, ground water recharge). The central element is the soil storage which is dimensioned via the usable field capacity of the rooted soil area. The maximum fill volume can be adjusted by a multiplicative user-controlled calibration parameter (FCA).
+First, the input (precipitation and snowmelt) is allocated to the evaporation until the potential evaporation is reached. The surplus (inflow) is then allocated in direct runoff (SQ) and infiltration (INF), in dependence of the relative soil saturation (<math>\Theta</math>) and a calibration parameter (DFB). The calculation is carried out as follows:
-==Bodenwasserhaushalt==
-Das Bodenwasserhaushaltsmodul dient als Verteiler des Inputs (Niederschlag und Schneeschmelze) auf die Outputpfade (Verdunstung, Direktabfluss, Grundwasserneubildung). Zentrales Element ist der Bodenspeicher der durch die nutzbare Feldkapazität des durchwurzelten Bodenbereiches dimensioniert ist. Das maximale Füllvolumen kann durch einen multiplikativen, anwendergesteuerten Eichparameter (FCA) angepasst werden.
-Der Input (Niederschlag und Schneeschmelze) wird zunächst der Verdunstung zugeführt bis die potentielle Verdunstung erreicht ist. Der Überschuss (Inflow) wird dann in Direktabfluss (SQ) und Infiltration (INF), abhängig von der relativen Bodenwassersättigung (<math>\Theta</math>) und einem Eichparameter (DFB) aufgeteilt. Die Berechnung erfolgt nach:
 <math>SQ = \Theta^{DFB} \cdot Inflow </math> [mm/d]
@@ Line 299: / Line 305: @@
 <math>INF = (1 - \Theta^{DFB}) \cdot Inflow</math> [mm/d]
-Die Infiltration (INF) wird dem Bodenspeicher zugeschlagen bis dieser vollkommen gesättigt ist. Entsteht dann Überschuss (excess water EW) wird dieses in Abhängigkeit von der Hangneigung (<math>\alpha</math>) und einem Eichparameter (LVD) auf die beiden Pfade Interflow (SSQ) und Grundwasserneubildung (GWR) aufgeteilt. Die Berechnung erfolgt nach:
+The infiltration (INF) is allocated to the soil storage until it is completely saturated. If there is a surplus (excess water EW), it is allocated to the two paths interflow (SSQ) and ground water recharge (GWR) in dependence of the slope (<math>\alpha</math>) and a calibration parameter (LVD). The calculation is carried out according to the following equation:
 <math>SSQ = \tan\alpha \cdot LVD \cdot EW </math> [mm/d]
@@ Line 305: / Line 311: @@
 <math>GWR = (1 - \tan\alpha) \cdot LVD \cdot EW </math> [mm/d]
-Die Grundwasserneubildung wird im Folgenden als Quelle für den Basisabfluss (BQ) betrachtet.
+The ground water recharge is seen as source for the basis runoff (BQ) now.
-==Abflusskonzentration und Abflussverzögerung==
+==Runoff Concentration and Retardation in Runoff==
-Die Abflusskonzentration und Abflussverzögerung wird als einfache Funktion des Einzugsgebietes für die drei Abflusskomponenten (Direktabfluss SQ, Zwischenabfluss SSQ und Basisabfluss BQ). Hierzu werden die Bildungsraten der drei Komponenten flächengewichtet aufsummiert und durch eine jeweils eigene lineare Speicherkaskade (Nash-Kaskade) geleitet. Für jede dieser drei Kaskaden muss der Anwender die beiden Parameter Anzahl der Speicher (n) und Retentionskoeffizient (k) bestimmen.
+The runoff concentration and retardation in runoff is represented as simple function of the catchment area for the three runoff components (direct runoff, SQ, intermediate runoff SSQ and basis runoff BQ). For this purpose, the generation rates of the three components are accumulated area-weighted and are lead by their own linear cascade (Nash-cascade). For each of the three cascades the user has to determine the following two parameters: number of storages (n) and retention coefficient (k).