Bayesian Simultaneous Estimation of Unsaturated Flow and Solute Transport Parameters from a Laboratory Infiltration Experiment

Abstract

Numerical modeling has become an irreplaceable tool for the investigation of water flow and solute transport in the unsaturated zone. The use of this tool for real situations is often faced with lack of knowledge of hydraulic and soil transport parameters. In this study, advanced experimental and numerical techniques are developed for an accurate estimation of the soil parameters. A laboratory unsaturated flow and solute transport experiment is conducted on a large undisturbed soil column of around 40 cm length. Bromide, used as a nonreactive contaminant, is injected at the surface of the undisturbed soil, followed by a leaching phase. The pressure measurements at different locations along the soil column as well as the outflow bromide concentration are collected during the experiment and used for the statistical calibration of flow and solute transport. The Richards equation, combined with constitutive relations for water content and permeability, is used to describe unsaturated flow. Both linear and non-equilibrium mobile–immobile transport models are investigated for the solute transport. All hydraulic and mass transport parameters are inferred using a one-step Bayesian estimation with the Markov chain Monte Carlo sampler. The results prove that the pressure and concentration measurements are able to identify almost all hydraulic and mass transport parameters. The mobile–immobile transport model better reproduces the infiltration experiment. It produces narrower uncertainty intervals for soil parameters and predictive output concentrations.

Modeling of Flow and Transport in Saturated and Unsaturated Porous Media

“…Younes et al [39] developed advanced experimental and numerical techniques for an accurate estimation of the soil parameters. Bromide, used as a nonreactive contaminant, was injected at the surface of a large undisturbed soil column and followed by a leaching phase.…”

Probability Distribution for Water Fluxes in a Heterogeneous Unsaturated Zone Using an Ensemble of 1D Simulations

“…In order to assess the uncertainties associated with groundwater recharge and other hydraulic quantities, the probability distribution of the flux (or of other hydraulic quantities) is required. There are various methods for estimating the probability distribution of these quantities (Wu & Zeng, 2013), including considering specific forms of the probability distribution of model hydraulic parameters (e.g., Chen et al., 2018; Kosugi, 1996; Sánchez‐Vila et al., 2009; Zhai & Benson, 2006) and the Bayesian approach (e.g., Abbaspour et al., 1999; Feyen et al., 2003; Gao et al., 2019; Guber et al., 2009; Moreira et al., 2016; Schmidt‐Walter et al., 2020; Scholer et al., 2012; Tsai & Li, 2008; Xu & Valocchi, 2015; Younes et al., 2019). Another approach combines methods for parameter selection and the Bayesian approach (Vesselinov & Harp, 2012), with a Monte Carlo‐based estimation of the probability distributions (Mattis et al., 2015).…”

Use of Global Sensitivity and Data-Worth Analysis for an Efficient Estimation of Soil Hydraulic Properties

“…Bayesian DWA, performed a priori, allows to quantify the improvement of the posterior uncertainty of the estimated parameters when adding a type of measurement. The results reveal that an accurate estimation of the soil properties can be obtained if the target parameter values are located in the regions of high influence in the parameter space.Water 2020, 12, 736 2 of 15 and evaporation experiments [13], unsaturated transport experiments [14][15][16][17], and hydrogeophysical experiments [18,19].Laboratory experiments are often time consuming, expensive, and tricky because of the risk of non-identifiability of the accepted parameters which depends on the measured data. Global sensitivity analysis (GSA) has been employed by Younes et al, [7] to help assess unsaturated soil hydraulic parameters.…”

“…Water 2020, 12, 736 2 of 15 and evaporation experiments [13], unsaturated transport experiments [14][15][16][17], and hydrogeophysical experiments [18,19].…”