Using sparse polynomial chaos expansions for the global sensitivity analysis of groundwater lifetime expectancy in a multi-layered hydrogeological model

Abstract

The study makes use of polynomial chaos expansions to compute Sobol' indices within the frame of a global sensitivity analysis of hydrodispersive parameters in a simplified vertical cross-section of a segment of the subsurface of the Paris Basin. Applying conservative ranges, the uncertainty in 78 input variables is propagated upon the mean lifetime expectancy of water molecules departing from a specific location within a highly confining layer situated in the middle of the model domain. Lifetime expectancy is a hydrogeological performance measure pertinent to safety analysis with respect to subsurface contaminants, such as radionuclides. The sensitivity analysis indicates that the variability in the mean lifetime expectancy can be sufficiently explained by the uncertainty in the petrofacies, i.e. the sets of porosity and hydraulic conductivity, of only a few layers of the model. The obtained results provide guidance regarding the uncertainty modeling in future investigations employing detailed numerical models of the subsurface * Corresponding author, e-mail: konakli@ibk.baug.ethz.ch of the Paris Basin. Moreover, the study demonstrates the high efficiency of sparse polynomial chaos expansions in computing Sobol' indices for high-dimensional models.

Multiresolution Approach to Condition Categorical Multiple‐Point Realizations to Dynamic Data With Iterative Ensemble Smoothing

“…The model is inspired by the artificially induced flow resulting from the excavation of vertical shafts. The hydraulic impact of such perturbation has, for example, been monitored and studied at the Andra's Meuse/Haute-Marne since the operation of the Underground Research Laboratory (Benabderrahmane et al, 2014;Deman et al, 2015;Kerrou et al, 2017).…”

Uncertainty quantification and global sensitivity analysis for economic models

“…In this paper, we choose to follow the approach proposed by Sudret (2008), where the Sobol' indices are derived by directly post-processing the coefficients of the PCE. When combined with their sparse-regression-based calculation, this approach has been extensively shown to be computationally very efficient (see, e.g., Blatman and Sudret (2010b), Deman, Konakli, Sudret, Kerrou, Perrochet, and Benabderrahmane (2016)). Indeed, the Sobol' decomposition (equation (16)) of a truncated PC expansion M PC (θ) = α∈Ab α Ψ α (θ) can be derived analytically, as shown below.…”

A meta-modeling approach for spatio-temporal uncertainty and sensitivity analysis: an application for a cellular automata-based Urban growth and land-use change model

“…Since PCE reduces the computational expense of uncertainty propagation, it has been widely applied in complex environmental problems including water quality modeling (Moreau et al 2013), large scale socio-hydrologic modeling coupled with Agent-Based Models (Hu et al 2015), groundwater hydrogeological modeling (Deman et al 2016) and in other dynamic modeling examples such as crop modeling (Lamboni et al 2009) and seawater intrusion (Rajabi et al 2015). Moreover, an extensive review of basic principles and applications of PCE in computational fluid dynamics was conducted by Najm (2009).…”