A proposed method to determine yield response factors of different crops under deficit irrigation using inverse formulation approach

Yield response factors of a given crop can be determined following the FAO approach (Doorenbos and Kassam, 1979. Yield response to water. FAO Irrigation and Drainage Paper no. 33. Rome, Italy, pp. 1-40) either by applying deficit irrigation throughout the whole growing period, or at one stage of the crop growth while maintaining full irrigation at the other stages. In this study, an inverse formulation methodology is proposed to determine the stage wise yield response factors (modified kyi values) for eight crops in the Lower Indus Basin. The proposed inverse formulation was based on the multiplicative (Jensen, 1968. Water consumption by agricultural plants. Chapter 1. In: T.T. Kozlowski (Ed.) Water Deficits and Plant Growth Vol. II (pp 1-22). Academic Press, New York) and additive (Stewart et al., 1977. Determination and utilization of water production functions for principal California crops. W-67 California Contributory Project, University of California) approaches to determine yield response factors. To illustrate the applicability of the proposed inverse formulation, the widely used seasonal ky values of FAO Irrigation and Drainage Paper No 33 (Doorenbos and Kassam, 1979. Yield response to water. FAO Irrigation and Drainage Paper no. 33. Rome, Italy, pp. 1-40) were used to generate a data set of yields and evapotranspirations for the crops under study after applying theoretical levels of deficit irrigation at different growth stages using climatic and soil data of the Lower Indus Basin. This data set was then used to estimate the modified kyi values separately for the additive and the multiplicative approaches from the inverse formulations. Modified kyi values were found to be different for additive and multiplicative approaches but there was a good agreement between the relative yield reductions using modified kyi values and seasonal ky values. However, there was a complete mismatch between relative yield reductions using FAO 33 stage wise kyi values and using FAO 33 seasonal ky values. Modified kyi values, based on the proposed inverse formulation, may be more representative by taking into account the effects of deficit irrigation on crop production.