Comparing Seven Variants of the Ensemble Kalman Filter: How Many Synthetic Experiments Are Needed?
Comparing Seven Variants of the Ensemble Kalman Filter: How Many Synthetic Experiments Are Needed?
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DOI：
10.1029/2018wr023374
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发表时间：
2018-09-01
影响因子：
5.4
通讯作者：
Marquart, Gabriele
中科院分区：
文献类型：
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作者：
Keller, Johannes;Franssen, Harrie-Jan Hendricks;Marquart, Gabriele
集合卡尔曼滤波（EnKF）是地球科学中常用的一种估计技术。将其作为状态向量预测和参数估计的数值工具。例如，EnKF可以帮助评估含水层的地热潜力。在这种应用中，EnKF通常用于小型或中型集成尺寸。因此，表征这些系综尺寸的EnKF行为是有意义的。对于7个集合尺寸（50、70、100、250、500、1000和2000）和7个EnKF变量（阻尼、迭代、局部、混合、对偶、正态得分和经典EnKF），我们为两个设置计算了1000个综合参数估计实验：一个二维示踪剂输运问题和一个注入井的二维流动问题。对于每个模型，合成实验之间唯一的区别是随机渗透率场的生成集。1,000个综合实验允许计算渗透率场表征的均方根误差（RMSE）的概率密度函数。比较不同EnKF变量、集合大小和流量/输送设置的平均均方根误差表明，需要多个合成实验来进行可靠的性能比较。在这项工作中，需要10个合成实验来正确区分小于10%的EnKF变体之间的RMSE差异。为了检测小于2%的RMSE差异，需要100个综合实验，集合大小分别为50、70、100和250。EnKF变体的总体排名强烈依赖于物理模型设置和集合大小。
The ensemble Kalman filter (EnKF) is a popular estimation technique in the geosciences. It is used as a numerical tool for state vector prognosis and parameter estimation. The EnKF can, for example, help to evaluate the geothermal potential of an aquifer. In such applications, the EnKF is often used with small or medium ensemble sizes. It is therefore of interest to characterize the EnKF behavior for these ensemble sizes. For seven ensemble sizes (50, 70, 100, 250, 500, 1,000, and 2,000) and seven EnKF variants (damped, iterative, local, hybrid, dual, normal score, and classical EnKF), we computed 1,000 synthetic parameter estimation experiments for two setups: a 2-D tracer transport problem and a 2-D flow problem with one injection well. For each model, the only difference among synthetic experiments was the generated set of random permeability fields. The 1,000 synthetic experiments allow to calculate the probability density function of the root-mean-square error (RMSE) of the characterization of the permeability field. Comparing mean RMSEs for different EnKF variants, ensemble sizes and flow/transport setups suggests that multiple synthetic experiments are needed for a solid performance comparison. In this work, 10 synthetic experiments were needed to correctly distinguish RMSE differences between EnKF variants smaller than 10%. For detecting RMSE differences smaller than 2%, 100 synthetic experiments were needed for ensemble sizes 50, 70, 100, and 250. The overall ranking of the EnKF variants is strongly dependent on the physical model setup and the ensemble size.