集合卡尔曼滤波估计水文地质参数的局域化修正

集合卡尔曼滤波(Ensemble Kalman Filter,EnKF)作为一种有效的数据同化方法,在众多数值实验中体现优势的同时,也暴露了它使用小集合估计协方差情况下精度较低的缺陷。为了降低取样噪声对协方差估计的干扰并提高滤波精度,应用局域化函数对小集合估计的协方差进行修正,即在协方差矩阵中以舒尔积的形式增加空间距离权重以限制远距离相关。在一个二维理想孔隙承压含水层模型中的运行结果表明,局域化对集合卡尔曼滤波估计地下水参数的修正十分有效,局域化可以很好地过滤小集合估计中噪声的影响,节省计算量的同时又可以防止滤波发散。相关长度较小的水文地质参数(如对数渗透系数)更容易受到噪声的干扰,更有必要进行局域化修正。

Localization corrections for the estimation of hydrogeological parameters using ensemble Kalman filter

The ensemble Kaml an filter(EnKF)is a sophisticated sequential data assimilation method.The EnKF has proven to be efficient handling of strong nonlinear dynamics and large state spaces.However,EnKF uses are latively small ensemble of forecasts to estmiate the forecast error covariance,which can introduce spurious correlations that lead to excessive decrease of the ensemble variance and possibly filter divergence.The spurious correlations can be handled by a localization method.In the method,the ensemble covariance matrix is multiplied with a specified correlation matrix through a Schur product(entry-wise multiplication),which can effectively truncate the long-range spurious correlations produced by the limited ensemble size.The revised EnKF is tested numerically for a two-dmiensional synthetic case.The result shows that localization can largely reduce the sampling errors due to small ensembles size with high eficiency,as well as can avoid filter divergence to a large extent.Applications of localization for the EnKF are also necessary to conduct localized corrections for the estimation of hydrogeological parameters with relatively small values of the correlation length.