Water is essential for crop production and best use of available water must be made for efficient crop production and high yields. This requires a proper understanding of the effect of water rainfall and/or irrigation on crop growth and yield under different growing conditions.
For application in planning, design and operation of irrigation schemes, it is possible to analyze the effect of water supply on crop yields. Water deficits in crops, and the resulting water stress on the plant, have an effect on crop evapotranspiration and crop yield. The relationship between crop yield and water supply can be determined when crop water requirements and actual crop water use, on the one hand, and maximum and actual crop yield on the other, can be quantified.
In the FAO 56 approach, the response of yield to water supply is quantified by the yield response factor (Ky), which relates the relative yield decrease (1-Ya/Ym) to relative evapotranspiration deficit (1-ETa/ETc). Hence, the Ky values for most crops are derived on the assumption that the relationship between relative yield (Ya/Ym) and relative evapotranspiration (ETa/ETc) is linear and is valid for water deficits of up to about 50% or 1 - ETa/ETc = 0.5.
In field conditions, water deficit of a given magnitude, expressed in the ratio of actual crop evapotranspiration (ETa) to potential crop evapotranspiration (ETc), may either occur continuously over the total growing period of the crop or it may occur during any stage of the individual growth periods.
FAO Irrigation and Drainage Paper No. 33 empirically derived yield-response factors (Ky) for individual growth stages (i.e. establishment, vegetative, flowering, yield formation, or ripening period) as well as for the total growing period. These factors are yield response factors for water stress in specified physiological growth stage (i) and over the total growing period of crops, and are given by:
= actual yield (corresponding to ETa)
Ym = maximum theoretical yield (corresponding to ETc) [kg/ha]
ETa = actual crop evapotranspiration
ETc = potential crop evapotranspiration
Ky = yield response factor to water stress, which comes from the Crop Library.
Ya/Ym is the relative yield fraction. Solving for Ya/Ym:
However, if water stress cannot be considered as constant throughout the growing period but occurs with different magnitude at different periods of the growing season, the expected total relative yield fraction should be calculated at a smaller timestep and aggregated for the season. In the MABIA method, relative yield fractions will be calculated on a daily timestep, and the multiplicative product of the yield fractions from all days will be used as the relative yield fraction for the season. (For details and justification for this approach, see Dirk Raes, Sam Geerts, Emmanuel Kipkorir, Joost Wellens, and Ali Sahli, Simulation of yield decline as a result of water stress with a robust soil water balance model. Agricultural Water Management, 81: 335-357, 2006.)
indicates the product of the N terms within the square brackets,
N = length of the growing season [days]
i = day number within the growing season [1..N]
s = crop stage corresponding to day i [1-4]
Ky,s = yield-response factor for crop stage s, from the Crop Library
Ls = length of crop stage s
ETa,i = actual evapotranspiration at day i
ETc,i = potential evapotranspiration at day i.
To obtain the actual yield, multiply the seasonal relative yield fraction by the maximum theoretical yield:
Market Value = Ya * Area * Price
Market Value = Total market value for crop
Ya = actual yield [kg/ha]
Area = cultivated area [ha]
Price = unit market price for crop [$/kg]