Abstract Bayesian inference using Markov Chain Monte Carlo (MCMC) provides an explicit framework for stochastic calibration of hydrogeologic models accounting for uncertainties; however, the MCMC sampling entails a large number of model calls, and could easily become computationally unwieldy if the high-fidelity hydrogeologic model simulation is time consuming. This study proposes a surrogate-based Bayesian framework to address this notorious issue, and illustrates the methodology by inverse modeling a regional MODFLOW model. The high-fidelity groundwater model is approximated by a fast statistical model using Bagging Multivariate Adaptive Regression Spline (BMARS) algorithm, and hence the MCMC sampling can be efficiently performed. In this study, the MODFLOW model is developed to simulate the groundwater flow in an arid region of Oman consisting of mountain-coast aquifers, and used to run representative simulations to generate training dataset for BMARS model construction. A BMARS-based Sobol’ method is also employed to efficiently calculate input parameter sensitivities, which are used to evaluate and rank their importance for the groundwater flow model system. According to sensitivity analysis, insensitive parameters are screened out of Bayesian inversion of the MODFLOW model, further saving computing efforts. The posterior probability distribution of input parameters is efficiently inferred from the prescribed prior distribution using observed head data, demonstrating that the presented BMARS-based Bayesian framework is an efficient tool to reduce parameter uncertainties of a groundwater system.

中文翻译：

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区域地下水流模型的基于代理的灵敏度量化和贝叶斯反演

摘要 使用马尔可夫链蒙特卡罗 (MCMC) 的贝叶斯推理为考虑不确定性的水文地质模型的随机校准提供了明确的框架；然而，MCMC 采样需要大量的模型调用，如果高保真水文地质模型模拟耗时，很容易在计算上变得笨拙。本研究提出了一个基于代理的贝叶斯框架来解决这个臭名昭著的问题，并通过对区域 MODFLOW 模型进行逆向建模来说明该方法。高保真地下水模型通过使用 Bagging Multivariate Adaptive Regression Spline (BMARS) 算法的快速统计模型近似，因此可以有效地执行 MCMC 采样。在这项研究中，MODFLOW 模型用于模拟阿曼干旱地区的地下水流，该地区由山地-沿海含水层组成，并用于运行具有代表性的模拟以生成用于 BMARS 模型构建的训练数据集。还采用基于 BMARS 的 Sobol 方法来有效计算输入参数敏感性，这些敏感性用于评估和排列它们对地下水流模型系统的重要性。根据敏感性分析，从MODFLOW模型的贝叶斯反演中筛选出不敏感的参数，进一步节省了计算量。输入参数的后验概率分布是使用观察到的头部数据从规定的先验分布中有效地推断出来的，