Possibilistic Stochastic Water Management Model for Agricultural Nonpoint Source Pollution

Agricultural activities are the main contributors of nonpoint source water pollution within agricultural systems. In this study, a possibilistic stochastic water management (PSWM) model is developed and applied to a case study of water quality management within an agricultural system in China. This study is a first application of hybrid possibilistic chance-constrained programming approach to nonpoint source water quality management problems within an agricultural system. Hybrid uncertainties with the synergy of fuzzy and stochastic implications are effectively characterized by the PSWM model with the following advantages: (1) it improves upon the existing possibilistic and chance-constrained programming methods through direct incorporation of fuzziness and randomness within a general optimization framework; (2) it will not lead to more complicated intermediate models and thus have lower computational requirements; (3) its solutions offer flexibility in interpreting the results and reflect the interactional effects of uncertain parameters on system conditions variations; and (4) it can help examine the risk of violating system constraints and the associated consequences. The results of the case study show useful information for feasible decision schemes of agricultural activities, including the trade-offs between economic and environmental considerations. Moreover, a strong desire to acquire high agricultural income will run into the risk of potentially violating the related water quality standards, while willingness to accept low agricultural income will increase the risk of potential system failure (violating system constraints). The results suggest that the developed approach is also applicable to many practical problems where hybrid uncertainties exist.