Increasing the reliability of irrigation water raises the cost of water storage and the price that farmers must pay for water. Evaluating farmers’ willingness to pay (WTP) for water is key to determining the reliability of irrigation water achievable. This paper presents a probabilistic optimization method for estimating the WTP to avoid water shortage. A nonlinear programming model was formulated to model water use and estimate a single farmer’s WTP when water shortage occurs. The model was subsequently expanded to include the WTP of a group of farmers relying on Monte Carlo simulation. Results show that low water prices do not have any effect on water use when there is no shortage of water. Facing water shortage, farmers employ irrigation systems with high efficiency to reduce the use and cost of irrigation water. They also change the cropping pattern to cultivate crops with low water requirements. The farmers’ WTP for irrigation water during shortage is assessed probabilistically and is found to be highly variable.

Evolutionary algorithms (EAs) have become competitive solvers of a wide variety of water-resources optimization problems. Genetic programming (GP) has become a leading EA since its inception in 1985. This paper reviews the state-of-the-art of GP and its applications in water-resources systems analysis. A comprehensive knowledge about GP's theory and modeling approach is essential for its successful application in water-resources systems analysis. This review presents variants of GP that have been proven useful in various applications to water resources problems. Several examples of applications of GP in water-resources systems analysis are herein presented. This review reveals GP's capability and superiority compared to other conventional methods, which makes it suitable for solving a wide variety of water-related problems including rainfall-runoff modeling, streamflow sediment prediction, flood prediction and routing, evaporation and evapotranspiration forecasting, reservoir operation, groundwater modeling, water quality modeling, water demand forecasting, and water distribution systems.

This paper introduces a hybrid non-linear Muskingum model for flood routing. The proposed hybrid model has more degrees of freedom for fitting observed data than other non-linear Muskingum models. The main goal of this work is to develop a comprehensive model for outflow routing. The proposed hybrid model's predictive skill is evaluated with experimental, real and multimodal hydrograph-routing problems. The results confirm the predictive skill of the hybrid model based on the minimisation of the sum of the square deviation (SSD) between observed and routed outflows, the sum of the absolute value of the deviations (SAD) between the observed outflow and the computed outflow, and the deviations between the peak of the routed and actual outflows (DPO). Results from this study show the hybrid model improved the SSD by 79, 15 and 5%, SAD by 50, 2 and 5%, and the DPO by 77, 4 and 34% compared with the best alternative Muskingum model in solving the experimental, real and multimodal example problems, respectively.