An adaptive Gaussian process-based iterative ensemble smoother for data assimilation

Liu

et al. 2019

Vadose Zone Journal

Self Cite

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.

Section: Discussionmentioning

confidence: 99%

Efficient Bayesian Inverse Modeling of Water Infiltration in Layered Soils

Gao

Liu

et al. 2019

Vadose Zone Journal

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“…Since the posterior confidence interval is the parameter space of interest and it only occupies a small proportion of the prior distribution, a GP surrogate can be conveniently refined by adding more base points chosen from this zone Ju et al 2018a). Based on this idea, we integrate the GP surrogate construction with the MCMC method.…”

Section: Adaptively Refined Gp Surrogatementioning

confidence: 99%

“…Sun et al (2014) and Marrel et al (2008) applied the GP model to predict the monthly streamflow and the radionuclide transport in groundwater, respectively. Ju et al (2018a) proposed an adaptive GP-based iterative ensemble smoother to improve the computational efficiency of data assimilation. Thus, we can adaptively construct a locally accurate surrogate over the posterior distribution to avoid the computational burden in constructing a globally accurate one over the prior distribution.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian Monitoring Design for Streambed Heat Tracing: Numerical Simulation and Sandbox Experiments

et al. 2018

Groundwater

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Heat tracing methods have been widely employed for subsurface characterization. Nevertheless, there were very few studies regarding the optimal monitoring design for heat tracing in heterogeneous streambeds. In this study, we addressed this issue by proposing an efficient optimal design framework to collect the most informative diurnal temperature signal for Bayesian estimation of streambed hydraulic conductivities. The data worth (DW) was measured by the expected relative entropy between the prior and posterior distributions of the conductivity field. An adaptively refined Gaussian process surrogate was employed to alleviate the computational burden, resulting in at least three orders of magnitude of speed-up. The applicability of the optimal experimental design framework was evaluated by both numerical and sandbox experimental cases. Results showed that the most informative locations centered in the transition zones among the main patterns of the hydraulic conductivity field, while the most informative times centered in a short period after the minimum/maximum temperature appeared. With the fixed number of measurements, extending the calibration period was more beneficial than increasing the monitoring frequency in improving the estimation results. To our best knowledge, this work is the first study on Bayesian monitoring design for streambed characterization with the heat tracing method. The method and results can provide guidance on selecting monitoring strategies under budget-limited conditions.

“…In this way, many unnecessary evaluations of f H ( m ) can be avoided. More recently, another approach that adaptively refines a data‐driven surrogate over the posterior distribution is proposed, which has shown to be highly efficient (Gong & Duan, ; Ju et al, ; Zhang et al, ).…”

Section: Introductionmentioning

confidence: 99%

Inverse Modeling of Hydrologic Systems with Adaptive Multifidelity Markov Chain Monte Carlo Simulations

Water Resources Research

Man

Lin

et al. 2018

Self Cite

Markov chain Monte Carlo (MCMC) simulation methods are widely used to assess parametric uncertainties of hydrologic models conditioned on measurements of observable state variables. However, when the model is CPU‐intensive and high dimensional, the computational cost of MCMC simulation will be prohibitive. In this situation, a CPU‐efficient while less accurate low‐fidelity model (e.g., a numerical model with a coarser discretization or a data‐driven surrogate) is usually adopted. Nowadays, multifidelity simulation methods that can take advantage of both the efficiency of the low‐fidelity model and the accuracy of the high‐fidelity model are gaining popularity. In the MCMC simulation, as the posterior distribution of the unknown model parameters is the region of interest, it is wise to distribute most of the computational budget (i.e., the high‐fidelity model evaluations) therein. Based on this idea, in this paper we propose an adaptive multifidelity MCMC algorithm for efficient inverse modeling of hydrologic systems. In this method, we evaluate the high‐fidelity model mainly in the posterior region through iteratively running MCMC based on a Gaussian process system that is adaptively constructed with multifidelity simulation. The error of the Gaussian process system is rigorously considered in the MCMC simulation and gradually reduced to a negligible level in the posterior region. Thus, the proposed method can obtain an accurate estimate of the posterior distribution with a small number of the high‐fidelity model evaluations. The performance of the proposed method is demonstrated by three numerical case studies in inverse modeling of hydrologic systems.