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This paper combines a risk-based two-stage stochastic robust programming (RTSRP) model into an agricultural-ecological system dynamics (AESD) to conduct agricultural-ecological water resources management. It integrates the chance- constrained programming, conditional risk-at-value, two-stage stochastic robust programming with the AESD model. The RTSRP model improves upon the TSRP model by introducing the risk control measurements. The agricultural-ecological dynamic system (AEDS) model can build water connections amid wheat, field corn, seed corn, economic crops, woodland, meadow, and city greening and farmland shelterbelts. Besides, the ecological service value is transformed into the irrigation benefit of ecological sector to guide water allocation amid sub-ecological sectors at a more applicable detailed scale. It can tradeoff relationships between economic benefit and ecological recovery by formulating two enlarging ecological areas scenarios. The combinations of the RTSRP model and the AEDS model can get optimal water allocation schemes, and simulate future sustainable degree (SD) of optimal water allocation schemes and explore relationships amid water allocation, economic benefit, and SD and risk and robustness of model. It is used to the middle reaches of the Heihe River Basin in China to verify its application. The results show that water allocation schemes have different responses on various risk scenarios. Higher water allocation corresponds to bigger water shortage risk and higher robustness of the model. The economic benefit positive with water allocation is contradictory with SD. Enlarging ecological areas contributes to improvements of economic benefit and ecological recovery, but not the SD under the condition of enough water resources. [ABSTRACT FROM AUTHOR]

A two-stage joint chance-constrained programming is proposed based on the two-stage stochastic programming, the robust interval programming and the joint chance-constrained programming. In this study, the previous method combining interval order relations and interval possibility degrees is interpreted from the view of robust programming and then is rewritten according to the frame of robust stochastic programming and robust fuzzy programming. Based on the concept of interval possibility degree, the interval chance constrained programming is proposed and a joint chance-constrained method is generated by combining interval with the random and fuzzy chance-constrained programming. The established model is applied in agricultural water planning in an arid region. The results show that the model can provide decision makers with various planting schemes under different risk levels. According to the response of the results in different risk scenarios, decision makers can get the general impression on the influence degree of uncertainties. The analysis on the results can also show the advantage of the established model in handling multiple uncertainties and making tradeoff among different factors like the unit net benefits, penalty and water demand of crops as well as water supply. According to the comparison with the traditional two-step-method-based interval two-stage chance-constrained method, the optimality robustness and the high reference value of the established model can be proved. [ABSTRACT FROM AUTHOR]