Over the last decade, data assimilation methods based on the ensemble Kalman filter (EnKF) have been particularly explored in various geoscience fields to solve inverse problems. Although this type of ensemble methods can handle high-dimensional systems, they assume that the errors coming from whether the observations or the numerical model are multivariate Gaussian. To handle existing non-linearities between the observations and the variables to estimate, iterative methods have been proposed. In this paper, we investigate the feasibility of using the ensemble smoother and two iterative variants for the calibration of a synthetic 2D groundwater model inspired by a real nuclear storage problem in France. Using the same set of sparse and transient flow data, we compare the results of each method when employing them to condition an ensemble of multi-Gaussian groundwater flow parameter fields. In particular, we explore the benefit of transforming the state observations to improve the parameter identification performed by one of the two iterative algorithms tested. Despite the favorable case of a multi-Gaussian parameter distribution addressed, we show the importance of defining an ensemble size of at least 200 to obtain sufficiently accurate parameter and uncertainty estimates for the groundwater flow inverse problem considered.

在过去的十年中，已经在各个地球科学领域中特别探索了基于集合卡尔曼滤波器（EnKF）的数据同化方法来解决反问题。尽管这种集成方法可以处理高维系统，但它们假定误差来自观察值或数值模型是多元高斯模型。为了处理观测值和要估计的变量之间的非线性，提出了一种迭代方法。在本文中，我们研究了使用整体平滑器和两个迭代变量对法国实际核存储问题启发的合成二维地下水模型进行标定的可行性。使用相同的稀疏和瞬态流量数据集，我们将每种方法的结果用作一组多高斯地下水流量参数字段的条件时，将它们进行比较。特别是，我们探索了转换状态观测值以改进由测试的两个迭代算法之一执行的参数识别的好处。尽管解决了多高斯参数分布的有利情况，但我们仍显示了定义集合大小至少为200以获得对所考虑的地下水流反问题获得足够准确的参数和不确定性估计的重要性。