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There are a lot of uncertainties in the water resources system, which makes the water allocation plan have very risky. In order to analyze the risks of water resources allocation under uncertain conditions, a new methodology called the stochastic simulation-based risk assessment approach is developed in this paper. First, the main hydrological stochastic variable is fitted by a proper probability distribution. Second, a suitable two-stage stochastic programming is constructed to obtain the expected benefit and optimized water allocation targets. Third, the Monte Carlo method is used to obtain a suitable stochastic sample of the hydrological variable. Fourth, a pre-allocated water optimization model is proposed to obtain optimized actual benefit. The methodology can give a way for risk analysis of water allocation plans obtained by uncertain optimization models, which provides reliable assistance to water managers in decision-making. The proposed methodology is applied to the Zhanghe Irrigation District and the risk of water allocation plan obtained under the randomness of annual inflow is assessed. In addition, three different division methods of the annual inflow are applied in the first step, namely three levels, five levels and seven levels, respectively. From the results, the risk of water allocation scheme obtained by TSP model is 0.372–0.411 and decreases with the increase of number of hydrological levels. Considering both the risk and model complexity, seven hydrological levels are recommended when using TSP model to optimize water allocation under stochastic uncertainty.

A stochastic simulation-based risk assessment method for water allocation under the uncertainty