Efficient sensitivity/uncertainty analysis using the combined stochastic response surface method and automated differentiation: Application to environmental and biological systems

Estimation of uncertainties associated with model predictions is an importa nt component of the application of environmental and biological models. "Tr aditional" methods for propagating uncertainty, such as standard Monte Carl o and Latin Hypercube Sampling, however, often require performing a prohibi tive number of model simulations, especially for complex, computationally i ntensive models. Here, a computationally efficient method for uncertainty p ropagation, the Stochastic Response Surface Method (SRSM) is coupled with a nother method, the Automatic Differentiation of FORTRAN (ADIFOR). The SRSM is based on series expansions of model inputs and outputs in terms of a set of "well-behaved" standard random variables. The ADIFOR method is used to transform the model code into one that calculates the derivatives of the mo del outputs with respect to inputs or transformed inputs. The calculated mo del outputs and the derivatives at a set of sample points are used to appro ximate the unknown coefficients in the series expansions of outputs. A fram ework for the coupling of the SRSM and ADIFOR is developed and presented he re. Two case studies are presented, involving (1) a physiologically based p harmacokinetic model for perchloroethylene for humans, and (2) an atmospher ic photochemical model, the Reactive Plume Model. The results obtained agre e closely with those of traditional Monte Carlo and Latin hypercube samplin g methods, while reducing the required number of model simulations by about two orders of magnitude.