Hydrological Model J2000g - Revision history

Chr at 10:47, 5 December 2011

2011-12-05T10:47:53Z

Chr at 15:54, 28 November 2011

2011-11-28T15:54:39Z

← Older revision		Revision as of 15:54, 28 November 2011
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		+	[[de:Hydrologisches_Modell_J2000g]]
	==Abstract==		==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 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.

Claudia: /* Precipitation Correction */

2010-02-12T17:11:11Z

Precipitation Correction

← Older revision		Revision as of 17:11, 12 February 2010
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	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.		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 Precipitation Correction===
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	For the daily precipitation correction the two error terms are calculated explicitly.		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).		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 Loss====
	[[Bild: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)]]		[[Bild: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)]]

Claudia: /* Input Data - Model Driver */

2010-02-12T17:09:41Z

Input Data - Model Driver

← Older revision		Revision as of 17:09, 12 February 2010
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	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).		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)'''		* '''@dataSetAttribs (attribute of the dataset)'''

Claudia: /* Distribution and Attribute Tables */

2010-02-12T17:08:45Z

Distribution and Attribute Tables

← Older revision		Revision as of 17:08, 12 February 2010
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	==Distribution and Attribute Tables==		==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.		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===		===Model Unit Attribute Table===

Claudia: /* Snow Cover Calculation */

2010-02-12T17:06:23Z

Snow Cover Calculation

← Older revision		Revision as of 17:06, 12 February 2010
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	<math> SM_p = TMF \cdot (T_{melt} - Tbase) </math> [mm/d]		<math> SM_p = TMF \cdot (T_{melt} - Tbase) </math> [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~~. 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==		==Soil Water Budget==

Claudia: /* Model Unit Attribute Table */

2010-02-12T17:05:39Z

Model Unit Attribute Table

← Older revision		Revision as of 17:05, 12 February 2010
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	* '''ID''' - a clear numeric ID		* '''ID''' - a clear numeric ID
	* '''X''' - the easting of the centre (centroid) as Gauss-Krüger coordinate		* '''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		* '''area''' - the area of the model unit in m²
	* '''elevation''' - the mean elevation of the model unit in m above N.N.		* '''elevation''' - the mean elevation of the model unit in m above N.N.
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	* '''hgeoID''' - a clear numeric ID for the hydrological unit of the model unit (serves as allocation to the hydrogeology 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.	+	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===		===Soil Attribute Table===

Claudia: /* Abflusskonzentration und Abflussverzögerung */

2010-02-12T16:56:49Z

Abflusskonzentration und Abflussverzögerung

← Older revision		Revision as of 16:56, 12 February 2010
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	The ground water recharge is seen as source for the basis runoff (BQ) now.		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).

Claudia: /* Bodenwasserhaushalt */

2010-02-12T16:56:13Z

Bodenwasserhaushalt

← Older revision		Revision as of 16:56, 12 February 2010
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	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. 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. Schneeschmelzwasser wird an das folgende Modul als Input weitergegeben.

−	==~~Bodenwasserhaushalt~~==	+	==Soil Water Budget==
−	~~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~~.	+	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:
		+

−	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]		<math>SQ = \Theta^{DFB} \cdot Inflow </math> [mm/d]
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	<math>INF = (1 - \Theta^{DFB}) \cdot Inflow</math> [mm/d]		<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]		<math>SSQ = \tan\alpha \cdot LVD \cdot EW </math> [mm/d]
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	<math>GWR = (1 - \tan\alpha) \cdot LVD \cdot EW </math> [mm/d]		<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==		==Abflusskonzentration und Abflussverzögerung==
	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.		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.

Claudia: /* Schneedeckenberechnung */

2010-02-12T16:54:25Z

Schneedeckenberechnung

← Older revision		Revision as of 16:54, 12 February 2010
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	<math> es = 0.6108 \cdot e^{\frac{17.27 \cdot T}{237.3 + T}} </math> [kPa]		<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]		<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. Schneeschmelzwasser wird an das folgende Modul als Input weitergegeben.

	==Bodenwasserhaushalt==		==Bodenwasserhaushalt==

← Older revision		Revision as of 10:47, 5 December 2011
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	===Model Unit Attribute Table===		===Model Unit Attribute Table===
	Each model unit needs to be described with specific attributes for the modeling. These are:		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		* '''ID''' - a clear numeric ID
	* '''X''' - the easting of the centre (centroid) as Gauss-Krüger coordinate		* '''X''' - the easting of the centre (centroid) as Gauss-Krüger coordinate
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	===Soil Attribute Table===		===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.		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.

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	===Land Use Attribute Table===		===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:		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.		* '''LID''' - a clear numeric ID with which the connection to the model unit table is generated.
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	===Hydrogeology Attribute Table===		===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:		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.		* '''GID''' - a clear numeric ID with which the connection to the model unit table is generated.
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	==Input Data - Model Driver==		==Input Data - Model Driver==
−	[[~~Bild~~:dateFile.jpg\|thumb\|sample for an input data table]]	+	[[File:dateFile.jpg\|thumb\|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:		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:

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	===Monthly Precipitation Correction===		===Monthly Precipitation Correction===
−	[[~~Bild~~:Richter.jpg\|thumb\|Monthly percental precipitation errors in measurement for slightly sheltered stations, concentrated regionally (Richter 1995)]]	+	[[File:Richter.jpg\|thumb\|Monthly percental precipitation errors in measurement for slightly sheltered stations, concentrated regionally (Richter 1995)]]

	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):		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):
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	For this purpose, correction functions were derived on the basis of the tabled error values according to Richter (1995).		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 Loss====
−	[[~~Bild~~: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)]]	+	[[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)]]

	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:		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:
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	====Wind Error====		====Wind Error====
−	[[~~Bild~~:WindFehler.jpg\|thumb\|Characteristic of the relative correction function for the wind error based on the tabled values by Richter (1995) (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)]]
	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:		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:

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	===Extraterrestrial Radiation===		===Extraterrestrial Radiation===
−	[[~~Bild~~:radiation.jpg\|thumb\|Annual course of extraterrestrial radiation (Ra), global radiation (Rg) and net radiation (Rn) for a position in the Thuringian Forrest]]	+	[[File:radiation.jpg\|thumb\|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 / 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:		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: