Statistical sensitivity analysis and water quality

In this paper, concepts and methods of statistical sensitivity analysis (SA) of computer models are reviewed and discussed in relation to water quality analysis and modelling. The starting point of this approach is based on modelling the uncertainty of the computer code by probability distributions. Despite the fact that computer models are generally speaking non-stochastic, in the sense that if we rerun the code we get the same result, the stochastic approach turns out to be useful to understand how the input uncertainty is propagated through the computer code into the output uncertainty. We follow the standard approach to SA which is based on variance decomposition and consider three levels of SA. At the Orst or preliminary level, we discuss DOE and response surface methodologies in order to get a first estimate of the input influences on the model output. At the second level, going further into modelling the relationship between computer model inputs and outputs, we assume that different computer runs are independent. We then discuss techniques derived from Monte Carlo input simulations and regression analysis. At the third level, recognizing that, since the computer model is actually non-stochastic, the errors are often smoother than independent errors, we consider the geostatistical SA which is based on assuming that the error of the computer code emulator is a stochastic process with positive correlation which gets higher as two inputs get closer.