Optimal control of irrigation systems : an analysis of water allocation rules

Abstract

A feasibility study of an irrigation development proposal should include an analysis of the effects of water supply conditions on the degree to which development objectives are expected to be realised. A method of making this analysis was developed based on procedures for solving two problems. These were; (a) optimally allocating a property's available supply of water among competing crops, and, (b) optimally controlling an open channel distribution system to meet temporally and spatially varying water demand. The procedure developed for solving (a) was applied.

A stochastic dynamic programming procedure was developed to optimally schedule the irrigation of a single crop, subject to constraints on the timing of water availability and total application depth. A second procedure was developed, employing a constrained differential dynamic programming algorithm, for determining optimal irrigation schedules for use with variable application depth systems, and when several crops compete for an intra-seasonally limited supply of water. This procedure was called, as frequently as water supply conditions allowed, to provide short-term irrigation schedules in a computer simulation of the optimal irrigation of several crops. An application system model was included in these procedures to transform a crop water-use production function into the required irrigation water-use production function. This transformation was a function of the application device type and the mean application depth.

From an analysis of the on-property effects of water supply conditions, it was concluded that in order to achieve high economic and irrigation efficiencies, water supply conditions must be sufficiently flexible to allow the application system operator to vary the mean application depth but not necessarily the time periods of water availability. Additionally, irrigation scheduling procedures which seek economically optimum strategies offer the potential to achieve a maximum level of net benefit at levels of water availability significantly lower than has previously been used for design purposes.