基于多点地质统计与集合平滑数据同化方法识别非高斯渗透系数场

在冲积含水层中，由于岩相的非均质分布，渗透系数一般呈现出明显的非高斯特性（例如砂和黏土两种岩相），非高斯特性给地下水模型参数的推估带来了困难与挑战。目前广泛使用的集合平滑数据同化方法（ESMDA）虽然有效且计算成本较低，但仅适用于高斯场。多点地质统计方法虽已广泛用于模拟非高斯场，但其无法融入动态观测数据推估参数。基于多点地质统计方法中的直接采样法（DS）与集合平滑数据同化方法，构建一种新的数据同化框架（ESMDA-DS），既可保持参数场的非高斯特性，又可融合多源数据精确推估非高斯场。构建三个理想算例验证ESMDA-DS对非高斯参数场的推估效果，并探讨了不同类型观测数据对推估效果、水位与浓度预测精度的影响。三个理想算例包括仅融合水位数据（Case 1），同时融合水位与浓度数据（Case 2），同时融合水位、浓度与对数渗透系数数据（Case 3）。结果表明:ESMDA-DS方法结合了ESMDA与DS的各自优势，能有效融合观测数据推估渗透系数场，并保持参数场的非高斯特性。通过对比三个算例推估结果，Case 3的参数场推估效果最好，水位与浓度预测精度最高，Case 2次之，Case 1最差，表明融合多源数据可改善推估效果，提高预测精度。

Characterization of non-Gaussian hydraulic conductivity fields using multiple-point geostatistics and ensemble smoother with multiple data assimilation method

In alluvial aquifers, hydraulic conductivity usually follows non-Gaussian distribution due to litho-facies heterogeneity. It is still a great challenge to characterize the non-Gaussian aquifers. The ensemble smoother with multiple data assimilation (ESMDA) is an effective and low-cost inversion method, but only works for the Gaussian fields. The multiple-point geostatistics methods (MPS) are widely used to estimate the non-Gaussian fields, but cannot integrate dynamic data (e.g., piezometric head and concentration) for highly parameterized inversion. In this work, we developed a new data assimilation framework, ESMDA-DS, by coupling the Direct Sampling method (DS, one of Multiple-point geostatistics method) and ESMDA method. The performance of the ESMDA-DS is demonstrated by three synthetic cases. The influence of different observation data types on parameter estimation are also discussed. For Case 1, only piezometric head data are assimilated. For Case 2, both piezometric head and concentration data are assimilated simultaneously. For Case 3, the piezometric head, concentration and hydraulic conductivity observation data are assimilated together. The results show that the ESMDA-DS method can not only preserve the non-Gaussian pattern, but also incorporate the dynamic data to identify the non-Gaussian aquifers with a high resolution. Case 3 has the highest accuracy to estimate the non-Gaussian field and predict the evolution of piezometric head and concentration, Case 2, the second, and Case 1 the worst, which demonstrate that integration of multiple data can improve the accuracy of parameter estimation and has a better performance for model prediction.