Metropolis-Hastings Markov Chain Monte Carlo Approach to Simulate van Genuchten Model Parameters for Soil Water Retention Curve

Abstract

The soil water retention curve (SWRC) is essential for assessing water flow and solute transport in unsaturated media. The van Genuchten (VG) model is widely used to describe the SWRC; however, estimation of its effective hydraulic parameters is often prone to error, especially when data exist for only a limited range of matric potential. We developed a Metropolis-Hastings algorithm of the Markov chain Monte Carlo (MH-MCMC) approach using R to estimate VG parameters, which produces a numerical estimate of the joint posterior distribution of model parameters, including fully-quantified uncertainties. When VG model parameters were obtained using complete range of soil water content (SWC) data (i.e., from saturation to oven dryness), the MH-MCMC approach returned similar accuracy as the widely used non-linear curve-fitting program RETC (RETention Curve), but avoiding non-convergence issues. When VG model parameters were obtained using 5 SWC data measured at matric potential of around −60, −100, −200, −500, and −15,000 cm, the MH-MCMC approach was more robust than the RETC program. The performance of MH-MCMC are generally good (R2 > 0.95) for all 8 soils, whereas the RETC underperformed for coarse-textured soils. The MH-MCMC approach was used to obtain VG model parameters for all 1871 soils in the National Cooperative Soil Characterization dataset with SWC measured at matric potentials of −60 cm, −100 cm, −330 cm, and −15,000 cm; the results showed that the simulated SWC by MH-MCMC model were highly consistent with the measured SWC at corresponding matric potential. Altogether, our new MH-MCMC approach to solving the VG model is more robust to limited coverage of soil matric potential when compared to the RETC procedures, making it an effective alternative to traditional water retention solvers. We developed an MH-MCMC code in R for solving VG model parameters, which can be found at the GitHub repository.

An Analytical Solution for Variable Viscosity Flow in Fractured Media: Development and Comparative Analysis With Numerical Simulations

“…This process simulates many samples with the developed analytical model and allows us to determine the posterior probability distribution functions (PDFs) of the model parameters. To accomplish this, we rely on the widely utilized Markov chain Monte Carlo technique (MCMC), which has been successfully employed by several authors in the field of Hydrogeology (e.g., Du et al., 2022; Linde et al., 2017; Rajabi & Ataie‐Ashtiani, 2016; Wang et al., 2019; Wei et al., 2023; Younes et al., 2016). MCMC is a Bayesian inference method where parameters are treated as random variables.…”

“…To accomplish this, we rely on the widely utilized Markov chain Monte Carlo technique (MCMC), which has been successfully employed by several authors in the field of Hydrogeology (e.g., Du et al, 2022;Linde et al, 2017;Rajabi & Ataie-Ashtiani, 2016;Wang et al, 2019;Wei et al, 2023;Younes et al, 2016). MCMC is a Bayesian inference method where parameters are treated as random variables.…”

Inverse Estimation of Soil Hydraulic Parameters in a Landslide Deposit Based on a DE-MC Approach

“…The Markov chain Monte Carlo (MCMC) method, as a formal Bayesian method, is widely used to obtain a posterior probabilistic distribution of the inversely estimated parameter [30][31][32]. In particular, the MCMC method, based on the adaptive difference evolution algorithm [33], can effectively explore the parameter space toward the higher probability density region, which has become a commonly-used approach to analyze uncertainties of parameterization in hydrological models.…”