Sensitivity Analysis: An Operational Picture

Abstract

Sensitivity analysis (SA) is establishing as a fundamental discipline to support environmental systems modeling (Razavi et al., 2021; Saltelli et al., 2021 and reference therein).In particular, global SA (GSA) is gaining attention due to the possibility of characterizing the sensitivity of selected model output(s) with respect to model variables (or parameters) across the entirety of their space of definition (e.g., Pianosi et al., 2016;Razavi & Gupta, 2015). From a mathematical point of view, the global character of the SA is accommodated by treating the model variables as random ones (either discrete or continuous). The latter choice appears to be natural to code and treat quantitatively variability and led to the emergence of diverse GSA strategies over the last decades. The most well-known strategy is the variance-based GSA of Sobol (Homma & Saltelli, 1996;Owen, 1994;Sobol, 1993) according to which the degree of sensitivity of a model output is proportional to the amount of variance of the latter that is ascribable to the variability in one (or groups) variable(s). Recognition that the variance is insufficient to describe the model output uncertainty in case that its probability density function (pdf) deviates from Gaussianity, diverse strategies can be adopted by grounding the model output sensitivity onto the variations of: (a) distinct statistical moments (SMs) of the output pdf (Dell'Oca et al., 2017; (b) the whole output pdf (Borgonovo, 2007); (c) the cumulative distribution function of the output (Pianosi & Wagner, 2015, 2018. A different picture is adopted in derivative-based GSA in which the model output sensitivity is linked to average (in the model variables space) measures of the variations in the model output due to variations in the model variables (Campolongo et al.