Stochastic simulation of soil particle-size curves in heterogeneous aquifer systems through a Bayes space approach

Abstract

We address the problem of stochastic simulation of soil particle-size curves (PSCs) in heterogeneous aquifer systems. Unlike traditional approaches that focus solely on a few selected features of PSCs (e.g., selected quantiles), our approach considers the entire particle-size curves and can optionally include conditioning on available data. We rely on our prior work to model PSCs as cumulative distribution functions and interpret their density functions as functional compositions. We thus approximate the latter through an expansion over an appropriate basis of functions. This enables us to (a) effectively deal with the data dimensionality and constraints and (b) to develop a simulation method for PSCs based upon a suitable and well defined projection procedure. The new theoretical framework allows representing and reproducing the complete information content embedded in PSC data. As a first field application, we demonstrate the quality of unconditional and conditional simulations obtained with our methodology by considering a set of particle-size curves collected within a shallow alluvial aquifer in the Neckar river valley, Germany.