Simplified Coefficient Methods (Rainfall Runoff & Irrigation Demands Only)

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, TS is timestep (e.g., month), 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 = S TSETActualLC / S TSETpotentialLC

As a result, the actual yield can be calculated with the following equation:

ActualYieldLC = PotentialYieldLC * Max ( 0, (1 - YieldResponseFactorLC * (1 - EFLC ) ) )

YieldLC = ActualYieldLC * AreaLC

MarketValueLC = YieldLC * MarketPriceLC

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
[-] - 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, averaged over the season (Planting Date to Harvest Date)
YieldResponseFactor
[-] - Seasonal factor that defines how the yield changes when ETActual is less than ETPotential (water stress).
PotentialYield
[KG/HA] - The maximum potential yield given optimal supplies of water
ActualYield [KG/HA] - The actual yield given the available evapotranspiration

Yield [KG] - Actual yield for the land class

MarketPrice [\$/kg] - Unit value of the crop.

MarketValue [\$] - Total value of the crop for the land class.
RunoffToGWFraction
[-] - Fraction of runoff that goes to groundwater

RunoffToGW [MCM] - Runoff to groundwater supplies

RunoffToSurfaceWater [MCM] - Runoff to surface water supplies