Distribution‐Based Global Sensitivity Analysis in Hydrology

Abstract

Global sensitivity analysis (GSA) is routinely used in academic setting to quantify the influence of input variability and uncertainty on predictions of a quantity of interest. Practical applications of GSA are hampered by its high computational cost, which arises from the need to run large (e.g., groundwater) models multiple times, and by its reliance on the analysis of variance, which formally requires input parameters to be uncorrelated. The former difficulty can be alleviated by replacing expensive models with inexpensive (e.g., polynomial) surrogates, while adoption of distribution‐based (rather than variance‐based) metrics can, in principle, overcome the latter but at significantly increased computational cost. To make use of distribution‐based GSA feasible for regional‐scale models with a large number of degrees of freedom, we supplement it with a surrogate model built with polynomial chaos expansions with analytically updated coefficients. We demonstrate the computational efficiency of our algorithm on a case study dealing with evaluation of the effects of temperature variability on annual evapotranspiration at the regional scale.

Characterizing the Influence of Multiple Uncertainties on Predictions of Contaminant Discharge in Groundwater Within a Lagrangian Stochastic Formulation

“…In case of correlated inputs, one has to move toward distribution‐based GSA metrics whose computation can be also handled resorting to PCE as shown in Ciriello et al (2019).…”

“…The key idea behind PCE is to approximate the response surface through an orthonormal polynomial basis in the parameter space to represent the model output to change in input parameters. PCE has been been employed for GSA (e.g., Crestaux et al, 2009) and has been applied to several hydrogeological problems (e.g., Ciriello et al, 2017, 2019; Oladyshkin et al, 2012). Specific applications of PCEs to address groundwater quality are also reported in the literature (Ciriello, Di Federico, et al, 2013; Oladyshkin et al, 2012; Riva et al, 2015).…”

Mutual information for explainable deep learning of multiscale systems

“…Their interpretation is ambiguous when spaces of correlated CVs are large [11,12] and QoIs are highly non-Gaussian [13,14], a situation representative of complex multiscale/multiphysics systems. In contrast, moment-independent GSA approaches are easy to interpret regardless of the nature of the data or data-generating process [15][16][17]; however, they require knowledge of the CV and QoI distributions or availability of sufficient data to approximate them. DNNs resolve the latter problem by cheaply generating large amounts of data.…”

Thermal experiments for fractured rock characterization: theoretical analysis and inverse modeling

“…The former strategy includes the development of accelerated Markov chain samplers, Hamiltonian Monte Carlo sampling, iterative local updating ensemble smoother, ensemble Kalman filters, and learning on statistical manifolds (Barajas-Solano et al, 2019;Boso & Tartakovsky, 2020bKang et al, 2021;Zhou & Tartakovsky, 2021). The latter strategy aims to replace an expensive forward model with its cheap surrogate/emulator/reduced-order model (Ciriello et al, 2019;Lu & Tartakovsky, 2020a. Among these techniques, various flavors of deep neural networks (DNNs) have attracted attention, in part, because they remain robust for large numbers of inputs and outputs (Zhou & Tartakovsky, 2021;Mo et al, 2020;Kang et al, 2021).…”