Irrigation scheduling under a limited water supply

Abstract The problem of scheduling irrigation at weekly intervals for a single crop when water supply is limited is considered. The mathematical formulation is based on a dated water-production function, weekly soil-water balance, and a heuristic assumption that water stress in the early weeks of a crop-growth stage leads to suboptimal yields. The allocation problem is solved at two levels, growth stages, and weeks. At the first level, the dated water-production function is maximized by dynamic programming to obtain optimal allocations for growth stages. At the second, the water allocated to each growth stage is re-allocated to satisfy weekly water deficits within the stage in a sequential order, beginning with the 1st week of the stage. Water delivery and soil-water storage constraints are included at both levels. The model is applied to a field problem to derive weekly irrigation programmes for cotton under various levels of seasonal water supply and initial soil moisture.