Linear and non-linear optimization models for allocation of a limited water supply

One partial solution to the problem of ever-increasing demands on our water resources is optimal allocation of available water. A non-linear programming (NLP) optimization model with an integrated soil water balance was developed. This model is the advanced form of a previously developed one in which soil water balance was not included. The model also has the advantage of low computer run-time, as compared to commonly used dynamic programming (DP) models that suffer from dimensionality. The model can perform over different crop growth stages while taking into account an irrigation time interval in each stage. Therefore, the results are directly applicable to real-world conditions. However, the time trend of actual evapotranspiration (AET) for individual time intervals fluctuates more than that for growth-stage AETs. The proposed model was run for the Ardak area (45 km NW of the city of Mashhad, Iran) under a single cropping cultivation (corn) as well as a multiple cropping pattern (wheat, barley, corn, and sugar beet). The water balance equation was manipulated with net applied irrigation water to overcome the difficulty encountered with incorrect deep percolation. The outputs of the model, under the imposed seasonal irrigation water shortages, were compared with the results obtained from a simple NLP model. The differences between these two models (simple and integrated) became more significant as irrigation water shortage increased. Oversimplified assumptions in the previous simple model were the main causes of these differences. Copyright (C) 2004 John Wiley Sons, Ltd.