Sensitivity analysis of Doorenbos and Kassam (1979) crop water production function

Doorenbos and Kassam’s (1979) equation and the multiplicative and additive forms of it that were developed by Rao et al. (1988) were extensively used in optimization models and deficit irrigation planning. Although these equations were validated and successfully used by several investigators to predict crop yield at several locations, however, some signs of anomalies exist. This paper present the results of sensitivity analysis of these equations for potato crop in relation to three parameters namely maximum evapotranspiration (PET), actual evapotranspiration (AET) and crop yield response factor (Ky). Results show that plus error of PET and Ky and minus error of AET results in over predicting of relative yield (Yr). For a specific error value of Ky, when water shortage increases, error percentage of estimated Yr by Doorenbos and Kassam (1979) equation and by multiplicative and additive forms of Rao et al. (1988) equation increases. For a specific error value of PET or AET, however, when water shortage increases, error percentage of estimated Yr by Doorenbos and Kassam (1979) equation and by multiplicative form of Rao et al. (1988) equation decreases while error percentage of estimated Yr by additive form of Rao et al. (1988) equation increases. Sensitivity of Doorenbos and Kassam (1979) equation and additive form of Rao et al. (1988) equation is equal for plus or minus error of Ky and AET but their sensitivities are greater for minus error of PET than plus error. However, sensitivity of multiplicative form of Rao et al. (1988) equation is greater for minus error of Ky and PET and plus error of AET. It was shown that error percentage on estimation of Yr by multiplicative form of Rao et al. (1988) equation arising from error of PET, AET or Ky is less than additive form. In addition, calculated Yr by multiplicative equation is higher than additive form and the difference between two forms of this equation increases severely when water shortage increases. According to the results, it is recommended that multiplicative form of Rao et al. (1988) equation instead of additive form be used in optimization models and deficit irrigation planning.