Application of the bias aware Ensemble Kalman Filter with Confirming Option (Bias-CEnKF) in groundwater flow data assimilation
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摘要:
集合卡尔曼滤波（Ensemble Kalman Filter，EnKF）方法已广泛应用于地下水水流和污染物运移模拟相关问题的求解。但前人研究多建立在同化系统预报模型是准确的基础上，忽视了模型概化的不确定性。当模型概化不准确时，将导致预报偏差，可能带来错误的系统估计。因此，文章提出考虑模型预报偏差的迭代式集合卡尔曼滤波（Bias aware Ensemble Kalman Filter with Confirming Option，Bias-CEnKF）方法。以地下水水流数据同化为例，研究模型概化存在不确定条件下，边界条件、初始条件、源汇项概化不准确时新方法的有效性。结果表明，当预报模型概化不准确时，使用标准EnKF方法进行数据同化，可能会导致滤波发散，造成同化失败。Bias-CEnKF方法不仅保留了较好的同化性能，同时减小了参数、变量、偏差项非线性关系带来的不一致性。针对文章中4种情景，Bias-CEnKF同化获得的含水层渗透系数场以及水头场均接近真实场，且预报结果可靠。本研究进一步提升了模型概化不确定时EnKF方法的适用性，为实际野外复杂条件下地下水水流数据同化问题提供了可靠的方法。
Abstract:The Ensemble Kalman Filter (EnKF) has been widely applied for real-time simulation of groundwater flow and solute transport. The majority of previous studies tend to assume no bias in forecast models, therefore ignoring the model uncertainties. This assumption, however, may be invalid when a conceptual model is not accurately generalized. As a result, forecast bias will lead to incorrect estimation of the system parameters or states. In this work, a bias aware Ensemble Kalman Filter with Confirming Option (Bias-CEnKF) is proposed to take into account the forecast bias by the model during the filtering process. The proposed method is tested in a real-time groundwater simulation considering model uncertainties, by setting inaccurate boundary conditions, initial conditions and recharge items. The results show that the standard EnKF may lead to filter divergence and assimilation failure, if the forecast model is not accurately generalized. Instead, Bias-CEnKF not only achieves better performances, but also reduces the inconsistency caused by the nonlinear relationship among the parameters, variables and bias corrections. Four scenarios are investigated, with the results showing the aquifer hydraulic conductivities and heads obtained by Bias-CEnKF are close to the real values, and the prediction results are also more reliable. This study further improves the applicability of the EnKF under the uncertain condition of model generalization, and provides a reliable method for groundwater data assimilation under complex field conditions.
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表 1 EnKF、Bias-EnKF和Bias-CEnKF同化结果对比
Table 1. Assimilation results of EnKF, Bias-EnKF and Bias-CEnKF
情景 Y场RMSE H场RMSE EnKF Bias-EnKF Bias-CEnKF EnKF Bias-EnKF Bias-CEnKF 情景1 1.70 0.79 0.75 1.52 0.63 0.56 情景2 0.80 0.63 0.60 0.75 0.46 0.36 情景3 1.72 0.68 0.68 1.10 0.54 0.48 情景4 1.48 0.56 0.56 2.25 0.39 0.34 
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