A simple and efficient method for global sensitivity analysis based on cumulative distribution functions

AbstractVariance-based approaches are widely used for Global Sensitivity Analysis (GSA) of environmental models. However, methods that consider the entire Probability Density Function (PDF) of the model output, rather than its variance only, are preferable in cases where variance is not an adequate proxy of uncertainty, e.g. when the output distribution is highly-skewed or when it is multi-modal. Still, the adoption of density-based methods has been limited so far, possibly because they are relatively more difficult to implement. Here we present a novel GSA method, called PAWN, to efficiently compute density-based sensitivity indices. The key idea is to characterise output distributions by their Cumulative Distribution Functions (CDF), which are easier to derive than PDFs. We discuss and demonstrate the advantages of PAWN through applications to numerical and environmental modelling examples. We expect PAWN to increase the application of density-based approaches and to be a complementary approach to variance-based GSA

Global Sensitivity Analysis of environmental models:Convergence and validation

AbstractWe address two critical choices in Global Sensitivity Analysis (GSA): the choice of the sample size and of the threshold for the identification of insensitive input factors. Guidance to assist users with those two choices is still insufficient. We aim at filling this gap. Firstly, we define criteria to quantify the convergence of sensitivity indices, of ranking and of screening, based on a bootstrap approach. Secondly, we investigate the screening threshold with a quantitative validation procedure for screening results. We apply the proposed methodologies to three hydrological models with varying complexity utilizing three widely-used GSA methods (RSA, Morris, Sobol’). We demonstrate that convergence of screening and ranking can be reached before sensitivity estimates stabilize. Convergence dynamics appear to be case-dependent, which suggests that “fit-for-all” rules for sample sizes should not be used. Other modellers can easily adopt our criteria and procedures for a wide range of GSA methods and cases