Parameter estimation with uncertainty quantification is essential in groundwater modeling to ensure model quality; however, parameter estimation, especially for non-Gaussian distributed parameters in highly heterogeneous aquifers, is still a great challenge. The ensemble smoother with multiple data assimilation (ES-MDA) is one of the most popular and effective ensemble-based data assimilation algorithms. However, it only works for multi-Gaussian fields, since two-point statistics are used to estimate the co-relation between parameters and state variables. The probability conditioning method (PCM) has the capability to integrate nonlinear flow data into facies simulation, but it has an assumption of homogeneity within each facies. Full characterization of facies and estimates of hydraulic conductivity within each facies are equally important. This work firstly modifies the original PCM, introducing a new probability assignment method, to consider within-facies heterogeneities, and then it is further combined with the ES-MDA to estimate non-Gaussian distributed hydraulic parameters in a groundwater model. The proposed method is evaluated using a two-facies case and a three-facies case in groundwater modeling. Both cases demonstrate that the modified PCM is effective for facies delineation, especially to identify high heterogeneities in each facies, as well as non-Gaussian characteristics with good connectivity within certain facies. The results also show that the performances of data reproduction and model prediction are of high accuracy and low uncertainty, which is attributed to the accurate characterization of the non-Gaussian parameters in the heterogeneous aquifers used.

具有不确定性量化的参数估计对于地下水建模至关重要，以确保模型质量；然而，参数估计，尤其是高度非均质含水层中非高斯分布参数的估计，仍然是一个巨大的挑战。具有多个数据同化的集成平滑器（ES-MDA）是最流行和最有效的基于集成的数据同化算法之一。但是，它仅适用于多高斯场，因为两点统计用于估计参数和状态变量之间的相互关系。概率条件方法（PCM）具有将非线性流数据集成到相模拟中的能力，但它假设每个相内均质。充分表征相和估算每个相中的水力传导率同样重要。这项工作首先修改了原始PCM，引入了一种新的概率分配方法，以考虑相内异质性，然后将其与ES-MDA进一步结合以估算地下水模型中的非高斯分布水力参数。在地下水建模中，使用两相情况和三相情况对提出的方法进行了评估。两种情况均表明，经修改的PCM可有效地描述相，特别是识别每个相中的高异质性，以及在某些相中具有良好连通性的非高斯特征。结果还表明，数据再现和模型预测的性能具有较高的准确性和较低的不确定性，这归因于所使用的非均质含水层中非高斯参数的准确表征。