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Markov chain Monte Carlo (MCMC) simulation methods are widely used to assessparametric uncertainties of hydrologic models conditioned on measurements ofobservable state variables. However, when the model is CPU-intensive andhigh-dimensional, the computational cost of MCMC simulation will beprohibitive. In this situation, a CPU-efficient while less accuratelow-fidelity model (e.g., a numerical model with a coarser discretization, or adata-driven surrogate) is usually adopted. Nowadays, multi-fidelity simulationmethods that can take advantage of both the efficiency of the low-fidelitymodel and the accuracy of the high-fidelity model are gaining popularity. Inthe MCMC simulation, as the posterior distribution of the unknown modelparameters is the region of interest, it is wise to distribute most of thecomputational budget (i.e., the high-fidelity model evaluations) therein. Basedon this idea, in this paper we propose an adaptive multi-fidelity MCMCalgorithm for efficient inverse modeling of hydrologic systems. In this method,we evaluate the high-fidelity model mainly in the posterior region throughiteratively running MCMC based on a Gaussian process (GP) system that isadaptively constructed with multi-fidelity simulation. The error of the GPsystem is rigorously considered in the MCMC simulation and gradually reduced toa negligible level in the posterior region. Thus, the proposed method canobtain an accurate estimate of the posterior distribution with a small numberof the high-fidelity model evaluations. The performance of the proposed methodis demonstrated by three numerical case studies in inverse modeling ofhydrologic systems.

Inverse modeling of hydrologic systems with adaptive multi-fidelity Markov chain Monte Carlo simulations