High‐dimensional ensemble Kalman filter with localization, inflation, and iterative updates

Abstract Accurate estimation of forecast‐error covariance matrices is an essential step in data assimilation, which becomes a challenging task for high‐dimensional data assimilation. The standard ensemble Kalman filter (EnKF) may diverge due to both the limited ensemble size and the model bias. In this article, we propose to replace the sample covariance in the EnKF with a statistically consistent high‐dimensional tapering covariance matrix estimator to counter the estimation problem under high dimensions. A high‐dimensional EnKF scheme combining covariance localization with the inflation method and an iterative update structure is developed. The proposed assimilation scheme is tested on the Lorenz‐96 model with spatially correlated observation systems. The results demonstrate that the proposed method could improve the assimilation performance under multiple settings.