Downscaling Crop Water Sensitivity Index Using Monotone Piecewise Cubic Interpolation

Crop-water production functions quantitatively describe the relationship between crop yield and field evapotranspiration. The crop water sensitivity indexes of crop-water production functions, a key factor for optimizing irrigation scheduling in case of water scarcity, are usually obtained from field experiments or other sources for crop growth stages, while their values in shorter intervals are preferred for practical irrigation scheduling. We proposed a method to downscale the sensitivity index from growth stages to shorter intervals by monotone piecewise cubic interpolation of the cumulative sensitivity index curve. This method was used to estimate sensitivity indexes in irrigation intervals of about 10 d for corn and wheat in central Shanxi Province of China. Results showed that the downscaled sensitivity index could reflect the impact of water stress on crop growth both at different growth stages and within each stage. Scenario analysis of water stress at a single growth stage of wheat showed the rationality of downscaling water sensitivity index from growth stages to shorter intervals through interpolation of cumulative sensitivity index, and this proposed downscaling method was superior to the traditional linear downscaling method.