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.