Efficient Bayesian Inverse Modeling of Water Infiltration in Layered Soils

Abstract

Core Ideas The adaptive GP‐based MCMC was efficient to estimate hydraulic parameters in soils. Accuracy of the estimated parameters was verified by simulating experimental results. These simulations revealed a significant effect of layered structure on soil water flow. Modeling water movement in heterogeneous soils, e.g., layered soils, is an essential but challenging task that requires accurate estimation of multiple sets of soil hydraulic parameters. Markov chain Monte Carlo (MCMC) is a popular but computationally expensive method for parameter estimation. An adaptive Gaussian process (GP)‐based MCMC method proposed in our previous work presents significant computational efficiency. Nevertheless, its performance was evaluated only for synthetic numerical cases and has not been experimentally validated. Furthermore, its applicability in estimating hydraulic parameters of layered soils is still unknown. In this study, we systematically evaluated the performance of the GP‐based MCMC method in estimating the layered soil hydraulic parameters through a water infiltration experiment. It was shown that the proposed method could provide reliable estimations that were very close to those given by the original‐model‐based MCMC but at a much lower computational cost. The simulated soil water dynamics using the estimated parameters revealed a significant effect of layered heterogeneity on water flow. The lower layer(s) with higher water suction may cause persistent unsaturated status of the upper layer(s) during infiltration.

Estimating vadose zone water fluxes from soil water monitoring data: a comprehensive field study in Austria

“…Higher values of these parameters signify a lower water retention capacity of the soil. According to results from Schül et al ( 2022) and Gao et al (2019), parameter uncertainty from calibration with daily soil water content measurements can be expected to be higher in coarse-textured soils (with a higher soil hydraulic conductivity and lower soil water retention capacity) than in fine-textured soils -which was the case in this study. We suppose that the more rapid water flow processes are less efficiently captured in daily soil water content measurements, which are consequently less efficient with respect to constraining the uncertainties in SHPs.…”

Comparison of Two Bayesian-MCMC Inversion Methods for Laboratory Infiltration and Field Irrigation Experiments

“…The discrepancy introduced by the ANN approximation should be identified and removed from the residual using the orthonormal basis generated by PCA before the calculation of the Bayesian likelihood function in each iteration [21]. However, the GP could automatically derive the statistical covariance of the randomly drew parameter sample and directly include the corresponding statistical covariance in the likelihood function of each iteration [29]. This difference leads to a relatively more complex and more time consuming MCMC sampling process of the ANN-based model compared with that of the GP-based model.…”

“…Given the optimal hyper-parameters, the conditional GP mean u |Y (u) and variance σ 2 |Y (u) for an arbitrary parameter sample u can be obtained. The GP surrogate can easily be coupled with the Bayesian-MCMC parameter inversion algorithm and you can refer to [29] for the construction of the GP-based inversion framework.…”

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

“…A popular and promising Bayesian method, the so-called Markov Chain Monte Carlo (MCMC) approach, is now widely used for a variety of inverse problems in applied mathematics [18] and recently in hydrological simulations [19,20]. Thus, MCMC methods are likely to become useful for solving VG parameters.…”