Crop requirements are calculated assuming a demand site with simplified hydrological and agro-hydrological processes such as precipitation, evapotranspiration, and crop growth emphasizing irrigated and rainfall agriculture. Non-agricultural land classes can be included as well. The following equations were used to implement this approach where subscripts LC is land cover, HU is hydro-unit, I is irrigated, and NI is non-irrigated:
PrecipAvailableForETLC = PrecipHU * AreaLC * 10 -5 * PrecipEffectiveLC
ETpotentialLC = ETreferenceHU * KcLC * AreaLC * 10 -5
PrecipShortfallLC,I = Max ( 0, ETpotentialLC,I - PrecipAvailableForETLC,I )
SupplyRequirementLC,I = (1 / IrrFracLC,I ) * PrecipShortfallLC,I
SupplyRequirementHU = S LC,I SupplyRequirementLC,I
The above four equations are used to determine the additional amount of water (above the available precipitation) needed to supply the evapotranspiration demand of the land cover (and total hydro unit) while taking into account irrigation efficiencies.
Based on the system of priorities, the following quantities can be calculated:
SupplyHU = Calculated by WEAP allocation algorithm
SupplyLC,I = SupplyHU * ( SupplyRequirementLC,I / SupplyRequirementHU )
ETActualLC,NI = Min (ETpotentialLC,NI , PrecipAvailableForETLC,NI )
ETActualLC,I = Min (ETpotentialLC,I , PrecipAvailableForETLC,I ) + IrrFracLC,I * SupplyLC,I
EFLC = ETActualLC / ETpotentialLC
As a result, the actual yield can be calculated with the following equation:
ActualYieldLC = PotentialYieldLC * Max ( 0, (1 - YieldResponseFactorLC * (1 - EFLC ) ) )
In the Irrigation Demands Only method, runoff is not calculated. In the Rainfall Runoff method, runoff to both groundwater and surface water can be calculated with the following equations:
RunoffLC = Max ( 0, PrecipAvailableForETLC - ETpotentialLC)
+ (PrecipLC * (1 - PrecipEffectiveLC ))
+ (1 - IrrFracLC,I ) * SupplyLC,I
RunoffToGWHU = S LC (RunoffLC * RunoffToGWFractionLC )
RunoffToSurfaceWaterHU = S LC (RunoffLC * (1 - RunoffToGWFractionLC ) )
Units and definitions for all variables above are:
Area [HA] - Area of land cover
Precip [MM] - Precipitation
PrecipEffective [%] - Percentage of precipitation that can be used for
evapotranspiration
PrecipAvailableForET [MCM] - Precipitation available for evapotranspiration
Kc [-] - FAO crop coefficient
ETreference [MM] - Reference crop evapotranspiration
ETpotential [MCM] - Potential crop evapotranspiration
PrecipShortfall [MCM] - Evapotranspiration deficit if only precipitation
is considered
IrrFrac [%] - Percentage of supplied water available for ET (i.e. irrigation
efficiency)
SupplyRequirement [MCM] - Crop irrigation requirement
Supply [MCM] - Amount supplied to irrigation (calculated by WEAP allocation)
EF [-] - Fraction of potential evapotranspiration satisfied
YieldResponseFactor [-] - Factor that defines how the yield changes when
the ETactual is less than the ETpotential.
PotentialYield [KG/HA] - The maximum potential yield given optimal supplies
of water
ActualYield [KG/HA] - The actual yield given the available evapotranspiration
Runoff [MCM] - Runoff from a land cover
RunoffToGW [MCM] - Runoff to groundwater supplies
RunoffToSurfaceWater [MCM] - Runoff to surface water supplies