A simple and effective approach to Global Sensitivity Analysis based on conditional output distributions

Predictions of environmental models are affected by unavoidable and potentially large uncertainty. When models are applied to understand dominant controls of the system under study, uncertainties will reduce our ability to choose between competing hypotheses. When they are used to support decision-making, uncertainties will reduce our ability to discriminate between different management options and undermine the defensibility of the decision-making process. Global Sensitivity Analysis (GSA) provides quantitative information about the contribution to the uncertainty in the model output arising from different input factors like, for instance, model parameters, boundary conditions or forcing data. GSA thus provides insights into the model behavior and potential for simplification, indicates where further data collection and research is needed or would be beneficial, and enhances the credibility of the modelling results. In this paper, we present a novel method to GSA based on the comparison of the unconditional distribution of the model output, i.e. when all input factors vary, and the conditional distribution when one of the input factors is fixed. The main advantages of our strategy are that, in contrast to other GSA approaches, it works equally well regardless of the output distribution shape, e.g. skewed or not-skewed; it can be focused on specific regions of the output distribution, for instance extreme values; and it provides additional information about the input ranges that map into these output regions (so called Factor Mapping). We test the method using a real-world hydrologi-cal modelling application, and compare it to a well-established method of variance-based sensitivity indices (Sobol's method). We finally discuss its advantages and limitations and outline directions for further research.