Abstract
Abstract. We propose new metrics to assist global sensitivity analysis, GSA, of hydrological and Earth systems. Our approach allows assessing the impact of uncertain parameters on main features of the probability density function, pdf, of a target model output, y. These include the expected value of y, the spread around the mean and the degree of symmetry and tailedness of the pdf of y. Since reliable assessment of higher-order statistical moments can be computationally demanding, we couple our GSA approach with a surrogate model, approximating the full model response at a reduced computational cost. Here, we consider the generalized polynomial chaos expansion (gPCE), other model reduction techniques being fully compatible with our theoretical framework. We demonstrate our approach through three test cases, including an analytical benchmark, a simplified scenario mimicking pumping in a coastal aquifer and a laboratory-scale conservative transport experiment. Our results allow ascertaining which parameters can impact some moments of the model output pdf while being uninfluential to others. We also investigate the error associated with the evaluation of our sensitivity metrics by replacing the original system model through a gPCE. Our results indicate that the construction of a surrogate model with increasing level of accuracy might be required depending on the statistical moment considered in the GSA. The approach is fully compatible with (and can assist the development of) analysis techniques employed in the context of reduction of model complexity, model calibration, design of experiment, uncertainty quantification and risk assessment.
Highlights
Our improved understanding of physical–chemical mechanisms governing hydrological processes on multiple scales of space and time and the ever increasing power of modern computational resources are at the heart of the formulation of conceptual models which are frequently characterized by marked levels of sophistication and complexity
Amongst the diverse available techniques to construct a surrogate model, we exemplify our approach by considering the generalized polynomial chaos expansion that has been successfully applied to a variety of complex environmental problems (Sudret, 2008; Ciriello et al, 2013; Formaggia et al, 2013; Riva et al, 2015; Gläser et al, 2016), other model reduction techniques being fully compatible with our global sensitivity analysis (GSA) framework
We introduce a set of new indices to be employed in the context of global sensitivity analysis, GSA, of hydrological and Earth systems
Summary
Our improved understanding of physical–chemical mechanisms governing hydrological processes on multiple scales of space and time and the ever increasing power of modern computational resources are at the heart of the formulation of conceptual models which are frequently characterized by marked levels of sophistication and complexity. Amongst the diverse available techniques to construct a surrogate model (see, e.g., Razavi et al, 2012a, b), we exemplify our approach by considering the generalized polynomial chaos expansion (gPCE) that has been successfully applied to a variety of complex environmental problems (Sudret, 2008; Ciriello et al, 2013; Formaggia et al, 2013; Riva et al, 2015; Gläser et al, 2016), other model reduction techniques being fully compatible with our GSA framework In this context, we investigate the error associated with the evaluation of the sensitivity metrics we propose by replacing the original (full) system model with the selected surrogate model.
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