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Integrated and holistic approach of water resources management is important for sustainability. Since the optimum use of water resources needs taking into account different environmental issues. Accordingly, the use of supportive models in decision making as an effective tool is significantly important. To addressing uncertainty in crop water allocation, several methodologies have been proposed. The most of these models consider rainfall as a stochastic variable affecting soil moisture. Applying a new methodology/model while considering the stochastic variable in nonnormal state and uncertainties for both irrigation depth and soil moisture looks more realistic. In this research, a mathematical model was developed based on Constraint-State equation optimization model and Beta function. The first and the second moments of soil moisture are used as constraints in optimization process. This model uses the soil moisture budget equation for a specific plant (winter wheat) on a weekly basis, considering the root depth, soil moisture, irrigation depth, rainfalls, evapotranspiration, leaching depth, soil physical properties and a stochastic variable. The model was written in MATLAB and was run for winter wheat in Badjgah, south of Iran. The results were compared with the results obtained from a simulation model. Based on the results, the optimum net irrigation depth of winter wheat including the rainfall was 306.2 mm. The insignificant difference of simulation and optimization results showed that, the optimization model works properly and is acceptable for optimization of irrigation depth, as its reliability index is 96.86 %.

Optimal Crop Water Allocation Based on Constraint-State Method and Nonnormal Stochastic Variable