Nonlinear uncertainty analysis for multiple criteria natural resource decision support systems

Abstract

The effects of uncertainties on the simulation component and the decision component of the USDA-ARS Water Quality Decision Support System (WQDSS) are studied. For the simulation component, a generalized second order covariance propagation equation for multiple response models is developed to account for model nonlinearities and complexities. The equation permits the calculation of the covariance matrix of several model responses as a function of their first and second order sensitivities to variations in model parameters and the cross moments of the parameter vector. The equation is complemented by developing an applied approach that aims to identify model nonlinearities, isolate response discontinuities, and simplify the computational efforts associated with analytical uncertainty analysis. As for the decision component, a generalized closed form solution of the WQDSS's decision model is derived to allow consideration of a vector of quantitative scale factors. The factors indicate the relative importance of the studied decision criteria. A procedure that is based on computing these scale factors and assigning importance orders proportional to the effects of the uncertainties on the scoring function transformation of the individual criteria is also developed and tested. To test the methodology, the covariance matrix of twelve model responses is estimated based on uncertainties in sixteen soil related parameters using (a) direct simulation, (b) first order propagation and (c) second order propagation. Comparing the first and second order propagated matrices to those resulting from actual simulations of four agricultural management systems attests to the superiority of the second order equation. The effects of uncertainties on the decision recommendations are identified through experimental combinations of three different importance orders and four possible alternative ranking schemes. Two of the importance orders and their associated scale factors are based on the uncertainties in evaluating decision criteria. The ranking methods are based on varying the point at which averaging of the data takes place with respect to the decision process. Results indicate that the decision model is less sensitive to changes in the point of averaging than it is with respect to variations in the importance orders and the scale factors.