Abstract Bayesian inference provides a mathematically elegant and robust approach to constrain numerical model predictions with system knowledge and observations. Technical challenges, such as evaluating a large number of models with long runtimes, have restricted the application of Bayesian inference to groundwater modeling. To overcome such technical challenges, we use Gaussian process emulators to replace a transient regional groundwater MODFLOW model for computing objective functions during model constraining. The regional model is designed to assess the potential impact of a proposed coal seam gas (CSG) development on groundwater levels in the Richmond River catchment, Clarence-Moreton Basin, Australia. The emulators were trained using 4000 snapshots derived from the MODFLOW model and subsequently used to replace the MODFLOW model in an Approximate Bayesian Computation (ABC) scheme. ABC was deemed the more appropriate choice as it relaxes the need to derive an explicit likelihood function that the formal Bayesian analysis requires. The study demonstrated the flexibility of the Gaussian process emulators, which can accurately reproduce the original model behavior at a fraction of the computational cost (from hours to seconds). The gain in computational efficiency using the proposed approach allows the global calibration and uncertainty algorithms to become more feasible for computationally demanding groundwater models. Based on the ABC analysis, the probability for the simulated CSG development causing a water table change of more than 0.2 m was less than 5%. In addition to a probabilistic estimate of the prediction, an added value of emulator-assisted ABC inference is providing information on the extent to which observations can constrain parameters and predictions, as well as the flexibility to include various quantitative and qualitative parameter constraining information.

中文翻译：

---

支持仿真器的近似贝叶斯计算 (ABC) 和计算成本高的地下水模型的不确定性分析

摘要 贝叶斯推理提供了一种数学上优雅而稳健的方法，可以通过系统知识和观察来约束数值模型预测。技术挑战，例如评估大量运行时间长的模型，限制了贝叶斯推理在地下水建模中的应用。为了克服这些技术挑战，我们使用高斯过程模拟器来代替瞬态区域地下水 MODFLOW 模型，以在模型约束期间计算目标函数。该区域模型旨在评估拟议的煤层气 (CSG) 开发对澳大利亚克拉伦斯-摩顿盆地里士满河集水区地下水位的潜在影响。模拟器使用源自 MODFLOW 模型的 4000 个快照进行训练，随后用于在近似贝叶斯计算 (ABC) 方案中替换 MODFLOW 模型。ABC 被认为是更合适的选择，因为它放宽了导出正式贝叶斯分析所需的显式似然函数的需要。该研究证明了高斯过程仿真器的灵活性，它可以以很少的计算成本（从几小时到几秒）准确地再现原始模型行为。使用所提出的方法提高计算效率允许全局校准和不确定性算法对于计算要求高的地下水模型变得更加可行。根据 ABC 分析，模拟 CSG 开发导致地下水位变化大于 0 的概率。2m小于5%。除了预测的概率估计之外，模拟器辅助 ABC 推理的附加价值是提供关于观察可以约束参数和预测的程度的信息，以及包括各种定量和定性参数约束信息的灵活性。