Uncertainty modeling and propagation for groundwater flow: a comparative study of surrogates

Abstract

AbstractWe compare sparse grid stochastic collocation and Gaussian process emulation as surrogates for the parameter-to-observation map of a groundwater flow problem related to the Waste Isolation Pilot Plant in Carlsbad, NM. The goal is the computation of the probability distribution of a contaminant particle travel time resulting from uncertain knowledge about the transmissivity field. The latter is modelled as a lognormal random field which is fitted by restricted maximum likelihood estimation and universal kriging to observational data as well as geological information including site-specific trend regression functions obtained from technical documentation. The resulting random transmissivity field leads to a random groundwater flow and particle transport problem which is solved realization-wise using a mixed finite element discretization. Computational surrogates, once constructed, allow sampling the quantities of interest in the uncertainty analysis at substantially reduced computational cost. Special emphasis is placed on explaining the differences between the two surrogates in terms of computational realization and interpretation of the results. Numerical experiments are given for illustration.