Abstract
In decision-making processes, reliability and risk aversion play a decisive role. This paper presents a framework for stochastic optimization of control strategies for groundwater nitrate pollution from agriculture under hydraulic conductivity uncertainty. The main goal is to analyze the influence of uncertainty in the physical parameters of a heterogeneous groundwater diffuse pollution problem on the results of management strategies, and to introduce methods that integrate uncertainty and reliability in order to obtain strategies of spatial allocation of fertilizer use in agriculture. A hydro-economic modeling approach is used for obtaining the allocation of fertilizer reduction that complies with the maximum permissible concentration in groundwater while minimizes agricultural income losses. The model is based upon nonlinear programming and groundwater flow and mass transport numerical simulation, condensed on a pollutant concentration response matrix. The effects of the hydraulic conductivity uncertainty on the allocation of nitrogen reduction among agriculture pollution sources are analyzed using four formulations: Monte Carlo simulation with pre-assumed parameter field, Monte Carlo optimization, stacking management, and mixed-integer stochastic model with predefined reliability. The formulations were tested in an illustrative example for 100 hydraulic conductivity realizations with different variance. The results show a high probability of not meeting the groundwater quality standards when deriving a policy from just a deterministic analysis. To increase the reliability several realizations can be optimized at the same time. By using a mixed-integer stochastic formulation, the desired reliability level of the strategy can be fixed in advance. The approach allows deriving the trade-offs between the reliability of meeting the standard and the net benefits from agricultural production. In a risk-averse decision making, not only the reliability of meeting the standards counts, but also the probability distribution of the maximum pollutant concentrations. A sensitivity analysis was carried out to assess the influence of the variance of the hydraulic conductivity fields on the strategies. The results show that the larger the variance, the greater the range of maximum nitrate concentrations and the worst case (or maximum value) that could be reached for the same level of reliability. © 2011 Elsevier Ltd.
