Optimal Stochastic Multicrop Seasonal and Intraseasonal Irrigation Control

Abstract

Optimal seasonal multicrop irrigation water allocation and optimal stochastic intraseasonal (daily) irrigation scheduling are carried out using a two-stage decomposition approach based on a stochastic dynamic programming methodology. In the first stage the optimal seasonal water and acreage allocation among several crops or fields is defined using deterministic dynamic programming with the objective of maximizing total benefits from all the crops. The optimization is based on seasonal crop production functions. Seasonal crop production functions are obtained using single-crop stochastic dynamic programming, which incorporates the physics of soil moisture depletion and the stochastic properties of precipitation. In the second stage optimal intraseasonal irrigation scheduling is performed using a single-crop stochastic dynamic programming algorithm, conditional on the optimal seasonal water allocation of stage one. Optimal daily irrigation decision functions are obtained as a function of root-zone soil moisture content and the currently available irrigation water. The methodology is applied to a case study characterized by four crops in which both the optimal irrigation applications and the optimal acreage for each crop are determined.