Soil moisture calculation - Revision history

Froehlich: /* Soil type */ language, clarification

2022-05-27T09:50:56Z

Soil type: language, clarification

← Older revision		Revision as of 02:50, 27 May 2022
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	===Soil type===		===Soil type===

	The soil moisture simulation is based on the non-linear calculation of the individual soil layers. The soil is divided into different soil layers. Each layer is ~~calculated~~ and ~~(if existing) adjusted~~ with the layers above or below. The parameters for the soil moisture calculation are the following physical soil properties:		The soil moisture simulation is based on the non-linear calculation of the individual soil layers. The soil is divided into different soil layers with different soil textures. Each layer is simulated individually and interacts with the layers above or below. The parameters for the soil moisture calculation are the following physical soil properties for the soil textures of each individual layer:
	* wilting point (<code>WP</code>)		* wilting point (<code>WP</code>)
	* field capacity (<code>FK</code>)		* field capacity (<code>FK</code>)
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	* maximum infiltration capacity (<code>MaxInf</code>)		* maximum infiltration capacity (<code>MaxInf</code>)
	* maximum rate of capillary rise (<code>MaxKap</code>)		* maximum rate of capillary rise (<code>MaxKap</code>)
	* Assignment to a soil ~~type~~: sand, silt, clay		* Assignment to a soil category: sand, silt, clay

	As few as one or as many as six soil layers ~~are possible~~. A division into three layers has proven to yield the best results. That is why the entered layers are always ~~distributed~~ into three layers in BlueM internally.		As few as one or as many as six soil layers can be entered. A division into three layers has proven to yield the best results. That is why the entered layers are always transformed into three calculation layers in BlueM internally.

	* infiltration layer (standard thickness = 20 [cm])		* infiltration layer (standard thickness = 20 [cm])
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	[[Bild:Theorie_Abb38.gif\|thumb\|300px\|Abbildung 38: Example of the aggregation of soil layers for the root layer]]		[[Bild:Theorie_Abb38.gif\|thumb\|300px\|Abbildung 38: Example of the aggregation of soil layers for the root layer]]

	The new characteristic soil parameters for the internally used layers are calculated by ~~weighing~~ the original parameters of the original layers according to the original thickness of these layers.Saturated hydraulic conductivity is calculated according to conservation of continuity of the flow. For vertical ~~Flow~~ the velocity <code>v</code> is to be constant within a layer for a given flow due to the continuity of the flow. Therefore the hydraulic gradient is no longer constant.		The new characteristic soil parameters for the internally used layers are calculated by weighting the original parameters of the original layers according to the original thickness of these layers. Saturated hydraulic conductivity is calculated according to conservation of continuity of the flow. For vertical flow the velocity <code>v</code> is to be constant within a layer for a given flow due to the continuity of the flow. Therefore the hydraulic gradient is no longer constant.


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	:<code>k<sub>f,v</sub></code> = saturated hydraulic conductivity of the internally used layer [mm/h]		:<code>k<sub>f,v</sub></code> = saturated hydraulic conductivity of the internally used layer [mm/h]

	The ~~Aggregation~~ of the layers is depicted in [[:Bild:Theorie_Abb38.gif\|Abbildung 38]].<br clear="all"/>		The aggregation of the layers is depicted in [[:Bild:Theorie_Abb38.gif\|Abbildung 38]].<br clear="all"/>

	==Interception==		==Interception==

Froehlich: remove hierarchy extension template

2015-01-09T14:41:11Z

remove hierarchy extension template

← Older revision		Revision as of 07:41, 9 January 2015
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	~~<div style="float:left; margin:0 10px 10px 0">__TOC__</div>~~		{{BlueM.Sim_nav}}
	{{~~HierarchieKopf~~}}		{{BlueMTheory_nav}}
	~~<br clear="all"/>~~
			__TOC__
	All process-values which are calculated through soil moisture simulation are depicted in the following picture.		All process-values which are calculated through soil moisture simulation are depicted in the following picture.
	[[Bild:Theorie_Abb39.gif\|thumb\|~~300px~~\|~~left~~\|Abbildung 39: calculated process-values through soil moisture simulation]]~~<br clear="all"/>~~		[[Bild:Theorie_Abb39.gif\|thumb\|600px\|center\|Abbildung 39: calculated process-values through soil moisture simulation]]

	==Hydrological Response Units (HRUs)==		==Hydrological Response Units (HRUs)==
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	If Runoff is determined through soil moisture simulation, the HRU concept is applied. This results in a catchment being sub-sectioned into a various amount of hydrological homogenous areas.		If Runoff is determined through soil moisture simulation, the HRU concept is applied. This results in a catchment being sub-sectioned into a various amount of hydrological homogenous areas.

	[[Bild:Theorie_Abb43.gif\|thumb\|left\|Abbildung 42: Assignment of soil type and land use to a HRU]]		[[Bild:Theorie_Abb43.gif\|thumb\|left\|Abbildung 43: Assignment of soil type and land use to a HRU]]

	The depicted assignment of land use and soil type is valid for each HRU. The resulting amount of water out of a HRU is applied at the outlet of the elemt. Therefore all HRUs discharge their Water with the same time delay, independent of their position within the catchment.		The depicted assignment of land use and soil type is valid for each HRU. The resulting amount of water out of a HRU is applied at the outlet of the elemt. Therefore all HRUs discharge their Water with the same time delay, independent of their position within the catchment.
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	==Literature==		==Literature==
	<references/>		<references/>

	~~{{HierarchieFuss}}~~

	[[Kategorie:BlueM Theorie]]		[[Kategorie:BlueM Theorie]]

Mkissel at 10:46, 25 July 2013

2013-07-25T10:46:52Z

← Older revision		Revision as of 03:46, 25 July 2013
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	The new characteristic soil parameters for the internally used layers are calculated by weighing the original parameters of the original layers according to the original thickness of these layers.Saturated hydraulic conductivity is calculated according to conservation of continuity of the flow. For vertical Flow the velocity <code>v</code> is to be constant within a layer for a given flow due to the continuity of the flow. Therefore the hydraulic gradient is no longer constant.		The new characteristic soil parameters for the internally used layers are calculated by weighing the original parameters of the original layers according to the original thickness of these layers.Saturated hydraulic conductivity is calculated according to conservation of continuity of the flow. For vertical Flow the velocity <code>v</code> is to be constant within a layer for a given flow due to the continuity of the flow. Therefore the hydraulic gradient is no longer constant.

	Bei senkrechter Strömung soll aufgrund der Kontinuität der Strömung die Geschwindigkeit <code>v</code> bei gegebener Durchflussmenge in einer programminternen Schicht denselben Wert besitzen. Damit ist das hydraulische Gefälle nicht mehr konstant.

	:<math>k_{f,v} = \frac{\sum d}{\left ( \frac{d_1}{k_1} + \cdots + \frac{d_i}{k_i} + \cdots + \frac{d_n}{k_n} \right )}</math>		:<math>k_{f,v} = \frac{\sum d}{\left ( \frac{d_1}{k_1} + \cdots + \frac{d_i}{k_i} + \cdots + \frac{d_n}{k_n} \right )}</math>

Mkissel at 12:12, 4 March 2013

2013-03-04T12:12:02Z

← Older revision		Revision as of 05:12, 4 March 2013
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	[[Bild:Theorie_Abb43.gif\|thumb\|left\|Abbildung 42: Assignment of soil type and land use to a HRU]]		[[Bild:Theorie_Abb43.gif\|thumb\|left\|Abbildung 42: Assignment of soil type and land use to a HRU]]

	The depicted assignment of land use and soil type is valid for each HRU. The resulting amount of water out of a HRU is applied at the outlet of the elemt. Therefore all HRUs discharge their Water with the same time delay, ~~independant~~ of their position within the catchment.		The depicted assignment of land use and soil type is valid for each HRU. The resulting amount of water out of a HRU is applied at the outlet of the elemt. Therefore all HRUs discharge their Water with the same time delay, independent of their position within the catchment.

	Soil moisture calculation is computationally intensive and therefore very time-consuming. This is especially true if there are many HRUs in each sub-catchment.		Soil moisture calculation is computationally intensive and therefore very time-consuming. This is especially true if there are many HRUs in each sub-catchment.
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	:<code>Kap(t)</code> = capillary-rise		:<code>Kap(t)</code> = capillary-rise

	Infiltration, Percolation, Evaporation, Transpiration, Interflow and Capillary-Rise are dependent of the current soil moisture. In the simulation this dependency is described by the following function curves.		Infiltration, Percolation, Evaporation, Transpiration, Interflow and Capillary-Rise are dependent on the current soil moisture. In the simulation this dependency is described by the following function curves.

	[[Bild:Theorie_Abb40.gif\|thumb\|500px\|Abbildung 40: Depiction of selected soil process functions]]		[[Bild:Theorie_Abb40.gif\|thumb\|500px\|Abbildung 40: Depiction of selected soil process functions]]

Mkissel at 09:52, 27 February 2013

2013-02-27T09:52:57Z

Mkissel at 16:44, 26 February 2013

2013-02-26T16:44:40Z

← Older revision		Revision as of 09:44, 26 February 2013
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	Soil moisture calculation is computationally intensive and therefore very time-consuming. This is especially true if there are many HRUs in each sub-catchment.		Soil moisture calculation is computationally intensive and therefore very time-consuming. This is especially true if there are many HRUs in each sub-catchment.
	br clear="all"/>		<br clear="all"/>

	===Land use===		===Land use===

Mkissel: First Translation Draft complete

2013-02-26T16:42:06Z

First Translation Draft complete

← Older revision		Revision as of 09:42, 26 February 2013
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	====Evaporation====		====Evaporation====

			For the evaporation out of the soil the determined potential evaporation, which was adjusted to land use, is converted into evaporation for fallow land.
	~~Für die Bodenverdunstung wird die an die Landnutzung angepasste~~, ~~potentielle Verdunstung auf eine potentielle Verdunstung für Brachland umgerechnet~~.

	:<math>\mbox{Eva}(\theta(t)) = \begin{cases} 0, & \theta(t) \le \mbox{WP} \\ \mbox{f}_{Eva} \cdot \left ( \frac{\theta(t)-\mbox{WP}}{\mbox{GPV}-\mbox{WP}} \right ), & \theta(t) > \mbox{WP} \end{cases}</math>		:<math>\mbox{Eva}(\theta(t)) = \begin{cases} 0, & \theta(t) \le \mbox{WP} \\ \mbox{f}_{Eva} \cdot \left ( \frac{\theta(t)-\mbox{WP}}{\mbox{GPV}-\mbox{WP}} \right ), & \theta(t) > \mbox{WP} \end{cases}</math>

Mkissel at 16:37, 26 February 2013

2013-02-26T16:37:41Z

← Older revision		Revision as of 09:37, 26 February 2013
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	:<code>n<sub>TP</sub></code> = Krümmungsparameter der Transpirationsfunktion		:<code>n<sub>TP</sub></code> = Krümmungsparameter der Transpirationsfunktion

	~~Die Programmparameter werden intern berechnet~~. ~~Der Anwender muss lediglich die Bodenkennwerte~~ <code>k<sub>f</sub></code>, <code>WP</code>, <code>FK</code> ~~und~~ <code>GPV</code> ~~angeben~~.		Programparameters are calculated internally. The user only needs to supply the characteristic soil parameters <code>k<sub>f</sub></code>, <code>WP</code>, <code>FK</code> and <code>GPV</code>.

	~~Die Simulation erfolgt mit einem neu entwickelten~~ [[Speicherbaustein\|~~Baustein~~]] ~~zur Simulation von Speichern~~, ~~deren Prozessfunktionen bereichsweise~~ linear ~~abzubilden sind~~.		The simulation takes place with a newly developed [[Speicherbaustein\|Building-Block]]for the simulation of reservoirs, whichs process function are to mapped through a stepwise linear approach.

	====Infiltration====		====Infiltration====
	[[Bild:Infiltration.png\|thumb\|300px\|~~Infiltrationsfunktion~~ in BlueM ~~im Vergleich zur Funktion nach~~ {{:Literatur:Holtan_1961\|Holtan}} ~~am Beispiel eines Sandbodens~~]]		[[Bild:Infiltration.png\|thumb\|300px\|Infiltration function in BlueM in comparison to the function according to {{:Literatur:Holtan_1961\|Holtan}} for a sand-soil]]
	~~Der ursprüngliche Ansatz nach~~ {{:Literatur:Holtan_1961}}:		The original approach according to {{:Literatur:Holtan_1961}}:
	:<math>\mbox{Inf}(\theta(t)) = \mbox{a}_v \cdot \left ( \mbox{GPV} - \theta(t) \right )^{1,4} + k_f</math>		:<math>\mbox{Inf}(\theta(t)) = \mbox{a}_v \cdot \left ( \mbox{GPV} - \theta(t) \right )^{1,4} + k_f</math>
	:~~mit~~		:with
	:<code>a<sub>v</sub></code> = ~~Vegetationsparameter~~ (~~zwischen~~ 0,1 ~~und~~ 1,0)		:<code>a<sub>v</sub></code> = Vegetation parameter (between 0,1 and 1,0)

	~~wird~~ in BlueM ~~in modifizierter Form angewandt~~:		is used in a modified form in BlueM:

	:<math>\mbox{Inf}(\theta(t)) = \begin{cases} \mbox{MaxInf} + k_f, & 0 < \theta(t) < 0,1 \cdot \mbox{nFK} \\ \mbox{MaxInf} \cdot \left( \frac{\mbox{GPV} - \theta(t)}{\mbox{GPV} - 0,1 \cdot \mbox{nFK}} \right) ^{1,4} + k_f, & \theta(t) \ge 0,1 \cdot \mbox{nFK} \end{cases}</math>		:<math>\mbox{Inf}(\theta(t)) = \begin{cases} \mbox{MaxInf} + k_f, & 0 < \theta(t) < 0,1 \cdot \mbox{nFK} \\ \mbox{MaxInf} \cdot \left( \frac{\mbox{GPV} - \theta(t)}{\mbox{GPV} - 0,1 \cdot \mbox{nFK}} \right) ^{1,4} + k_f, & \theta(t) \ge 0,1 \cdot \mbox{nFK} \end{cases}</math>

	~~wobei zu beachten ist, dass diese Funktion lediglich die~~ '''~~potentielle~~ Infiltration''' ~~beschreibt - die tatsächliche~~ Infiltration ~~wird durch den zur Verfügung stehenden Bestandsniederschlag beschränkt~~. Die Modifizierung ergibt sich aus der Überlegung, dass bei einem sehr trockenen Boden auf den es regnet, die im Boden vorhande Luft nicht entweichen kann und somit die maximale Infiltration limitiert, sodass dieses nicht weiter exponentiell ansteigt, wie nach dem ursprünglichen Ansatz nach Holtan ("~~Blumentopfeffekt~~").		it needs to be noted that this function only describes the '''potential Infiltration'''. Actual Infiltration is limited to the available amount of rain. The modification is a results of the consideration that if it rains on a very dry soil the air within the soil cannot escape and thereby limits the maximum infiltration. This leads to a stop of exponential increase in contrast to the original approach of Holtan. ("Flowerpot effect")

	====~~Perkolation~~====
			====Percolation====

	:<math>\mbox{Perk}(\theta(t)) = \begin{cases} 0, & \theta(t) \le \mbox{f}_{PK} \cdot \mbox{nFK} + \mbox{WP} \\ k_f \cdot \left ( \frac{\theta(t) - \left ( \mbox{f}_{PK} \cdot \mbox{nFK} + \mbox{WP} \right )}{\mbox{GPV} - \left ( \mbox{f}_{PK} \cdot \mbox{nFK} + \mbox{WP} \right )} \right )^{n_{PK}}, & \theta(t) > \mbox{f}_{PK} \cdot \mbox{nFK} + \mbox{WP} \end{cases}</math>		:<math>\mbox{Perk}(\theta(t)) = \begin{cases} 0, & \theta(t) \le \mbox{f}_{PK} \cdot \mbox{nFK} + \mbox{WP} \\ k_f \cdot \left ( \frac{\theta(t) - \left ( \mbox{f}_{PK} \cdot \mbox{nFK} + \mbox{WP} \right )}{\mbox{GPV} - \left ( \mbox{f}_{PK} \cdot \mbox{nFK} + \mbox{WP} \right )} \right )^{n_{PK}}, & \theta(t) > \mbox{f}_{PK} \cdot \mbox{nFK} + \mbox{WP} \end{cases}</math>

	:mod. ~~Ansatz nach~~ {{:Literatur:Ostrowski_1992}}, {{:Literatur:Bear_1998}}		:mod. approach according to {{:Literatur:Ostrowski_1992}}, {{:Literatur:Bear_1998}}

	:''→ zu modifizieren in [[Talk:Bodenfeuchtesimulation#Perkolation nach van Genuchten\|Ansatz nach van Genuchten]]''		:''→ zu modifizieren in [[Talk:Bodenfeuchtesimulation#Perkolation nach van Genuchten\|Ansatz nach van Genuchten]]''
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	====Interflow====		====Interflow====

	~~Der~~ Interflow ~~ist relativ unabhängig von den Bodenparametern und hängt neben der Bodenfeuchte lediglich vom Gefälle der jeweiligen Elementarfläche ab~~ (~~siehe~~ Bug 28):		Interflow is realtivly independent of soil parameters and depends on soil moisture and slope of the individual HRU. (refer to Bug 28):

	:<math>\mbox{Int}(\theta(t)) = \begin{cases} 0, & \theta(t) \le \mbox{f}_{1,Int} \cdot \mbox{nFK} \\ \theta(t)^{\mbox{n}_{Int}} \cdot \frac{I}{\sqrt{1+I^2}}, & \mbox{f}_{1,Int} \cdot \mbox{nFK} < \theta(t) \le \mbox{f}_{2,Int} \cdot \mbox{nFK} \\ \mbox{f}_{2,Int} \cdot \mbox{nFK}, & \theta(t) > \mbox{f}_{2,Int} \cdot \mbox{nFK} \end{cases}</math>		:<math>\mbox{Int}(\theta(t)) = \begin{cases} 0, & \theta(t) \le \mbox{f}_{1,Int} \cdot \mbox{nFK} \\ \theta(t)^{\mbox{n}_{Int}} \cdot \frac{I}{\sqrt{1+I^2}}, & \mbox{f}_{1,Int} \cdot \mbox{nFK} < \theta(t) \le \mbox{f}_{2,Int} \cdot \mbox{nFK} \\ \mbox{f}_{2,Int} \cdot \mbox{nFK}, & \theta(t) > \mbox{f}_{2,Int} \cdot \mbox{nFK} \end{cases}</math>

	====Evaporation====		====Evaporation====


	Für die Bodenverdunstung wird die an die Landnutzung angepasste, potentielle Verdunstung auf eine potentielle Verdunstung für Brachland umgerechnet.		Für die Bodenverdunstung wird die an die Landnutzung angepasste, potentielle Verdunstung auf eine potentielle Verdunstung für Brachland umgerechnet.
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	:<math>\mbox{Trans}(\theta(t)) = \begin{cases} 0, & \theta(t) \le \mbox{f}_{TP} \cdot \mbox{nFK} + \mbox{WP} \\ \mbox{f}_{TP} \cdot \left ( \frac{\theta(t) - \mbox{f}_{TP} \cdot \mbox{nFK} + \mbox{WP}}{\mbox{GPV} - \mbox{f}_{TP} \cdot \mbox{nFK} + \mbox{WP}} \right )^{n_{TP}}, & \theta(t) > \mbox{f}_{TP} \cdot \mbox{nFK} + \mbox{WP} \end{cases}</math>		:<math>\mbox{Trans}(\theta(t)) = \begin{cases} 0, & \theta(t) \le \mbox{f}_{TP} \cdot \mbox{nFK} + \mbox{WP} \\ \mbox{f}_{TP} \cdot \left ( \frac{\theta(t) - \mbox{f}_{TP} \cdot \mbox{nFK} + \mbox{WP}}{\mbox{GPV} - \mbox{f}_{TP} \cdot \mbox{nFK} + \mbox{WP}} \right )^{n_{TP}}, & \theta(t) > \mbox{f}_{TP} \cdot \mbox{nFK} + \mbox{WP} \end{cases}</math>

	==~~Literaturangaben~~==		==Literature==
	<references/>		<references/>

Mkissel at 15:48, 26 February 2013

2013-02-26T15:48:56Z

← Older revision		Revision as of 08:48, 26 February 2013
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	:with:<code>k<sub>IC</sub></code> = 10.0 = Parameter to describe the fill rate of the interception reservoir [1/h] (Bug 409)		:with:<code>k<sub>IC</sub></code> = 10.0 = Parameter to describe the fill rate of the interception reservoir [1/h] (Bug 409)

	The maximum interception capacity for agricultural crops is {{:Literatur:Hoyningen-Huene_1983}}:		The maximum interception capacity for agricultural crops according to {{:Literatur:Hoyningen-Huene_1983}} is:

	:<math>\mbox{IC}_{max} = 0.935 + 0.498 \cdot LAI - 0.00575 \cdot LAI^2</math>		:<math>\mbox{IC}_{max} = 0.935 + 0.498 \cdot LAI - 0.00575 \cdot LAI^2</math>
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	==Soil moisture calculation==		==Soil moisture calculation==
	The water balance equation for the soil layer is solved by using a stepwise linear approach for the processes effecting soil moisture, ~~whch~~ are '''Infiltration''', '''Evaporation''', '''Transpiratin''', '''Percolation''', '''Interflow''' and '''Capillary-Rise'''. The input value for evaporation and transpiration is determined through the reduced potential evaporation due to interception evaporation.		The water balance equation for the soil layer is solved by using a stepwise linear approach for the processes effecting soil moisture, which are '''Infiltration''', '''Evaporation''', '''Transpiratin''', '''Percolation''', '''Interflow''' and '''Capillary-Rise'''. The input value for evaporation and transpiration is determined through the reduced potential evaporation due to interception evaporation.

	The equation to be solved is as follows:		The equation to be solved is as follows:
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	:with:		:with:
	:<code>θ(t)</code> = ~~aktuelle Bodenfeuchte~~		:<code>θ(t)</code> = current soil moisture
	:<code>Inf(t)</code> = ~~Infiltration in den Boden~~		:<code>Inf(t)</code> = infiltration into the soil
	:<code>Perk(t)</code> = ~~Perkolation (Durchsickerung)~~		:<code>Perk(t)</code> = percolation
	:<code>Eva<sub>akt</sub>(t)</code> = ~~aktuelle Evaporation~~		:<code>Eva<sub>akt</sub>(t)</code> = actual evaporation
	:<code>Trans<sub>akt</sub>(t)</code> = ~~aktuelle Transpiration~~		:<code>Trans<sub>akt</sub>(t)</code> = actual transpiration
	:<code>Int(t)</code> = ~~Interflow~~		:<code>Int(t)</code> = interflow
	:<code>Kap(t)</code> = ~~Kapillaraufstieg~~		:<code>Kap(t)</code> = capillary-rise

	Infiltration, ~~Perkolation~~, Evaporation, Transpiration, Interflow ~~und Kapillaraufstieg sind von der aktuellen Bodenfeuchte abhängig~~. In ~~der Simulation wird diese Abhängigkeit durch folgende Funktionsverläufe beschrieben~~.		Infiltration, Percolation, Evaporation, Transpiration, Interflow and Capillary-Rise are dependant of the current soil moisture. In the simulation this dependancy is described by the following function curves.

	[[Bild:Theorie_Abb40.gif\|thumb\|500px\|Abbildung 40: ~~Darstellung ausgewählter Bodenprozessfunktionen~~]]		[[Bild:Theorie_Abb40.gif\|thumb\|500px\|Abbildung 40: Depiction of selected soil process functions]]

	:~~mit~~:		:with:
	:<code>k<sub>f</sub></code> = ~~Durchlässigkeitsbeiwert des gesättigten Bodens~~		:<code>k<sub>f</sub></code> = saturated hydraulic conductivity
	:<code>nFK</code> = nutzbare ~~Feldkapazität~~ (<code>nFK = FK - WP</code>)		:<code>nFK</code> = available water capacity nutzbare (<code>nFK = FK - WP</code>)
	:<code>WP</code> = ~~Welkepunkt~~		:<code>WP</code> = wilting point
	:<code>FK</code> = ~~Feldkapazität~~		:<code>FK</code> = field capacity
	:<code>GPV</code> = ~~gesamtes Porenvolumen~~		:<code>GPV</code> = total pore volume
	:<code>I</code> = ~~Gefälle~~ [-]		:<code>I</code> = gradient [-]
	:<code>f<sub>PK</sub></code> = ~~bodenabhängiger Skalierungsfaktor der Perkolationsfunktion~~		:<code>f<sub>PK</sub></code> = soil specific scaling factor for the percolation function
	:<code>f<sub>Eva</sub></code> = ~~bodenabhängiger Skalierungsfaktor der Evaporationsfunktion~~		:<code>f<sub>Eva</sub></code> = soil specific scaling factor for the evaporation function
	:<code>f<sub>TP</sub></code> = ~~bodenabhängiger Skalierungsfaktor der Transpirationsfunktion~~		:<code>f<sub>TP</sub></code> = soil specific scaling factor for the transpiration function
	:<code>f<sub>1,Int</sub></code> = ~~bodenabhängiger Skalierungsfaktor für die Interflowfunktion~~		:<code>f<sub>1,Int</sub></code> = soil specific scaling factor for the interflow function
	:<code>f<sub>2,Int</sub></code> = ~~bodenabhängiger Skalierungsfaktor für die Interflowfunktion~~		:<code>f<sub>2,Int</sub></code> = soil specific scaling factor for the interflow function
	:<code>n<sub>Int</sub></code> = ~~bodenabhängiger Krümmungsparameter der Interflowfunktion~~		:<code>n<sub>Int</sub></code> = soil specific scaling factor for the interflow function
	:<code>n<sub>TP</sub></code> = Krümmungsparameter der Transpirationsfunktion		:<code>n<sub>TP</sub></code> = Krümmungsparameter der Transpirationsfunktion

Mkissel at 15:18, 26 February 2013

2013-02-26T15:18:05Z

← Older revision		Revision as of 08:18, 26 February 2013
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	To simplify things it is assumed that this approach is valid for wooded areas, although this approach was derived out of studies for agricultural crops.		To simplify things it is assumed that this approach is valid for wooded areas, although this approach was derived out of studies for agricultural crops.

			Futhermore the interception evaporation is calculated, which is subtracted from the potential evaporation which leads to a '''reduced potential evaporation''' remaining for the following processes of transpiration and evaporation.

	Im Weiteren wird die Interzeptionsverdunstung berechnet. Die ermittelte Interzeptionsverdunstung wird von der potentiellen Verdunstung abgezogen, so dass für die weiteren Prozesse Transpiration und Evaporation nur diese '''reduzierte potentielle Verdunstung''' zur Verfügung steht.

	==~~Bodenfeuchteberechnung~~==		==Soil moisture calculation==
	~~Auf der Basis der bereichsweisen linearen Abbildung der die Bodenfeuchte beeinflussenden Prozessfunktionen~~ '''Infiltration''', '''Evaporation''', '''~~Transpiration~~''', '''~~Perkolation~~''', '''Interflow''' ~~und~~ '''~~Kapillaraufstieg~~''' ~~wird für eine Bodenschicht die Wasserbilanzgleichung gelöst~~. ~~Die Eingangsgröße für die Evaporation und Transpiration ermittelt sich aus der durch die Interzeptionsverdunstung reduzierte potentiellen Verdunstung~~.		The water balance equation for the soil layer is solved by using a stepwise linear approach for the processes effecting soil moisture, whch are '''Infiltration''', '''Evaporation''', '''Transpiratin''', '''Percolation''', '''Interflow''' and '''Capillary-Rise'''. The input value for evaporation and transpiration is determined through the reduced potential evaporation due to interception evaporation.

	~~Die zu lösende Gleichung ist~~:		The equation to be solved is as follows:

	[[Bild:Theorie_Abb39b.gif\|thumb]]		[[Bild:Theorie_Abb39b.gif\|thumb]]
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	:<math>\frac{d\theta(t)}{d\mbox{t}} = \mbox{Inf}(t) - \mbox{Perk}(t) - \mbox{Eva}_{akt}(t) - \mbox{Trans}_{akt}(t) - \mbox{Int}(t) + \mbox{Kap}(t)</math>		:<math>\frac{d\theta(t)}{d\mbox{t}} = \mbox{Inf}(t) - \mbox{Perk}(t) - \mbox{Eva}_{akt}(t) - \mbox{Trans}_{akt}(t) - \mbox{Int}(t) + \mbox{Kap}(t)</math>

	:~~mit~~:		:with:
	:<code>θ(t)</code> = aktuelle Bodenfeuchte		:<code>θ(t)</code> = aktuelle Bodenfeuchte
	:<code>Inf(t)</code> = Infiltration in den Boden		:<code>Inf(t)</code> = Infiltration in den Boden

← Older revision		Revision as of 02:52, 27 February 2013
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	Providing Haude-Coefficients {{:Literatur:Haude_1954\|}}{{:Literatur:Haude_1955\|}} is possible by providing an annual pattern and ~~assiging~~ them to the desired land use. This allows for a better consideration of evaporation for each land use.		Providing Haude-Coefficients {{:Literatur:Haude_1954\|}}{{:Literatur:Haude_1955\|}} is possible by providing an annual pattern and assigning them to the desired land use. This allows for a better consideration of evaporation for each land use.

	These Haude-Coefficients scale the valid potential grass reference-evaporation for the time step by their ratio to the corresponding Haude-Coefficient for ~~gras~~.		These Haude-Coefficients scale the valid potential grass reference-evaporation for the time step by their ratio to the corresponding Haude-Coefficient for grass.


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	* Assignment to a soil type: sand, silt, clay		* Assignment to a soil type: sand, silt, clay

	As few as one or as many as six soil layers are possible. A division into three layers has proven to yield the best results. That is why the entered layers are ~~allways~~ distributed into three layers in BlueM internally.		As few as one or as many as six soil layers are possible. A division into three layers has proven to yield the best results. That is why the entered layers are always distributed into three layers in BlueM internally.

	* infiltration layer (standard thickness = 20 [cm])		* infiltration layer (standard thickness = 20 [cm])
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	[[Bild:Theorie_Abb38.gif\|thumb\|300px\|Abbildung 38: Example of the aggregation of soil layers for the root layer]]		[[Bild:Theorie_Abb38.gif\|thumb\|300px\|Abbildung 38: Example of the aggregation of soil layers for the root layer]]

	The new characteristic soil parameters for the internally used layers are calculated by weighing the original parameters of the original layers according to the original thickness of these layers.Saturated hydraulic conductivity is calculated according to conservation of continuity of the flow. For vertical Flow the velocity <code>v</code> is to be constant within a layer for a given flow due to the continuity of the flow. Therefore the hydraulic gradient ~~ist~~ no longer constant.		The new characteristic soil parameters for the internally used layers are calculated by weighing the original parameters of the original layers according to the original thickness of these layers.Saturated hydraulic conductivity is calculated according to conservation of continuity of the flow. For vertical Flow the velocity <code>v</code> is to be constant within a layer for a given flow due to the continuity of the flow. Therefore the hydraulic gradient is no longer constant.

	Bei senkrechter Strömung soll aufgrund der Kontinuität der Strömung die Geschwindigkeit <code>v</code> bei gegebener Durchflussmenge in einer programminternen Schicht denselben Wert besitzen. Damit ist das hydraulische Gefälle nicht mehr konstant.		Bei senkrechter Strömung soll aufgrund der Kontinuität der Strömung die Geschwindigkeit <code>v</code> bei gegebener Durchflussmenge in einer programminternen Schicht denselben Wert besitzen. Damit ist das hydraulische Gefälle nicht mehr konstant.
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	==Interception==		==Interception==
	In BlueM the ~~Inflow~~ to the interception reservoir (<code>Q<sub>zu<sub>IC</sub></sub></code>)is described as a linear function of the free interception reservoir.		In BlueM the inflow to the interception reservoir (<code>Q<sub>zu<sub>IC</sub></sub></code>) is described as a linear function of the free interception reservoir.

	:<math>Q_{zu_{IC}} = k_{IC} \cdot ( \mbox{IC}_{max} - \mbox{IC}_{akt})</math>		:<math>Q_{zu_{IC}} = k_{IC} \cdot ( \mbox{IC}_{max} - \mbox{IC}_{akt})</math>
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	:<code>LAI</code> = Leaf Area Index [-]		:<code>LAI</code> = Leaf Area Index [-]

	The rate of evaporation is assumed to be equal to the rate of potential evaporation (= <code>ET<sub>p</sub></code>).A simple differential equation can be derived due to the fact that inflow is equal to the amount of rain above the vegetation minus the rain which penetrates it :		The rate of evaporation is assumed to be equal to the rate of potential evaporation (= <code>ET<sub>p</sub></code>). A simple differential equation can be derived due to the fact that inflow is equal to the amount of rain above the vegetation minus the rain which penetrates it :

	:<math>\frac{\mbox{dIC}}{\mbox{d}t} = k_{IC} \cdot ( \mbox{IC}_{max} - \mbox{IC}(t)) - ET_p</math>		:<math>\frac{\mbox{dIC}}{\mbox{d}t} = k_{IC} \cdot ( \mbox{IC}_{max} - \mbox{IC}(t)) - ET_p</math>
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	To simplify things it is assumed that this approach is valid for wooded areas, although this approach was derived out of studies for agricultural crops.		To simplify things it is assumed that this approach is valid for wooded areas, although this approach was derived out of studies for agricultural crops.

	~~Futhermore~~ the interception evaporation is calculated, which is subtracted from the potential evaporation which leads to a '''reduced potential evaporation''' remaining for the following processes of transpiration and evaporation.		Furthermore the interception evaporation is calculated, which is subtracted from the potential evaporation which leads to a '''reduced potential evaporation''' remaining for the following processes of transpiration and evaporation.


	==Soil moisture calculation==		==Soil moisture calculation==
	The water balance equation for the soil layer is solved by using a stepwise linear approach for the processes effecting soil moisture, which are '''Infiltration''', '''Evaporation''', '''~~Transpiratin~~''', '''Percolation''', '''Interflow''' and '''Capillary-Rise'''. The input value for evaporation and transpiration is determined through the reduced potential evaporation due to interception evaporation.		The water balance equation for the soil layer is solved by using a stepwise linear approach for the processes effecting soil moisture, which are '''Infiltration''', '''Evaporation''', '''Transpiration''', '''Percolation''', '''Interflow''' and '''Capillary-Rise'''. The input value for evaporation and transpiration is determined through the reduced potential evaporation due to interception evaporation.

	The equation to be solved is as follows:		The equation to be solved is as follows:
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	:<code>Kap(t)</code> = capillary-rise		:<code>Kap(t)</code> = capillary-rise

	Infiltration, Percolation, Evaporation, Transpiration, Interflow and Capillary-Rise are ~~dependant~~ of the current soil moisture. In the simulation this ~~dependancy~~ is described by the following function curves.		Infiltration, Percolation, Evaporation, Transpiration, Interflow and Capillary-Rise are dependent of the current soil moisture. In the simulation this dependency is described by the following function curves.

	[[Bild:Theorie_Abb40.gif\|thumb\|500px\|Abbildung 40: Depiction of selected soil process functions]]		[[Bild:Theorie_Abb40.gif\|thumb\|500px\|Abbildung 40: Depiction of selected soil process functions]]
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	:with:		:with:
	:<code>k<sub>f</sub></code> = saturated hydraulic conductivity		:<code>k<sub>f</sub></code> = saturated hydraulic conductivity
	:<code>nFK</code> = available water capacity ~~nutzbare~~ (<code>nFK = FK - WP</code>)		:<code>nFK</code> = available water capacity (<code>nFK = FK - WP</code>)
	:<code>WP</code> = wilting point		:<code>WP</code> = wilting point
	:<code>FK</code> = field capacity		:<code>FK</code> = field capacity
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	:<code>n<sub>TP</sub></code> = Krümmungsparameter der Transpirationsfunktion		:<code>n<sub>TP</sub></code> = Krümmungsparameter der Transpirationsfunktion

	~~Programparameters~~ are calculated internally. The user only needs to supply the characteristic soil parameters <code>k<sub>f</sub></code>, <code>WP</code>, <code>FK</code> and <code>GPV</code>.		Program parameters are calculated internally. The user only needs to supply the characteristic soil parameters <code>k<sub>f</sub></code>, <code>WP</code>, <code>FK</code> and <code>GPV</code>.

	The simulation takes place with a newly developed [[Speicherbaustein\|Building-Block]]for the simulation of reservoirs, whichs process function are to mapped through a stepwise linear approach.		The simulation takes place with a newly developed [[Speicherbaustein\|Building-Block]] for the simulation of reservoirs, whichs process function are to be mapped through a stepwise linear approach.

	====Infiltration====		====Infiltration====
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	:<math>\mbox{Inf}(\theta(t)) = \begin{cases} \mbox{MaxInf} + k_f, & 0 < \theta(t) < 0,1 \cdot \mbox{nFK} \\ \mbox{MaxInf} \cdot \left( \frac{\mbox{GPV} - \theta(t)}{\mbox{GPV} - 0,1 \cdot \mbox{nFK}} \right) ^{1,4} + k_f, & \theta(t) \ge 0,1 \cdot \mbox{nFK} \end{cases}</math>		:<math>\mbox{Inf}(\theta(t)) = \begin{cases} \mbox{MaxInf} + k_f, & 0 < \theta(t) < 0,1 \cdot \mbox{nFK} \\ \mbox{MaxInf} \cdot \left( \frac{\mbox{GPV} - \theta(t)}{\mbox{GPV} - 0,1 \cdot \mbox{nFK}} \right) ^{1,4} + k_f, & \theta(t) \ge 0,1 \cdot \mbox{nFK} \end{cases}</math>

	it needs to be noted that this function only describes the '''potential Infiltration'''. Actual Infiltration is limited to the available amount of rain. The modification is a results of the consideration that if it rains on a very dry soil the air within the soil cannot escape and thereby limits ~~the~~ maximum infiltration. This leads to a stop of exponential increase in contrast to the original approach of Holtan. ("Flowerpot effect")		it needs to be noted that this function only describes the '''potential Infiltration'''. Actual Infiltration is limited to the available amount of rain. The modification is a results of the consideration that if it rains on a very dry soil the air within the soil cannot escape and thereby limits maximum infiltration. This leads to a stop of exponential increase in contrast to the original approach of Holtan. ("Flowerpot effect")