Effects of sequential or simultaneous assimilation of observations and localization methods on the performance of the ensemble Kalman filter

Abstract The various implementations of the ensemble Kalman filter (EnKF) differ from each other in several ways. The effects of these differences are not yet well and completely explored and they include the use of sequential or simultaneous assimilation of observations and the application of localization to the observation error covariance matrix (R‐localization) or the background error covariance matrix (B‐localization). This study seeks to examine and better understand the effects of these differences, both individually and in combination. To that end, a B‐localized sequential scheme, a B‐localized simultaneous scheme, an R‐localized sequential scheme and an R‐localized simultaneous scheme are compared using a primitive equation two‐layer model with simulated observations and an imperfect model assumption. The comparisons in initial assimilation experiments show that the use of sequential or simultaneous assimilation and R‐/B‐localization impacts the accuracy of the EnKF analyses and forecasts. Diagnostic experiments show that the schemes generate different amounts of imbalance in the analysis as a result of systematic differences among the schemes in height gradient and wind increments. These disparities in analysis balance translate into accuracy differences during the subsequent forecast and analysis steps. Additional simplified experiments suggest that the differences caused by the sequential or simultaneous assimilation and the R‐/B‐localization are a function of the characteristic shape of the background error covariances in the model system. Several elements of the forecast‐assimilation system including the use of digital filter initialization, the number and type of observations, the ensemble size and the ratio of forecast error to observation error are identified that can significantly increase or decrease the magnitude of the observed differences caused by sequential or simultaneous assimilation and the R‐/B‐localization. Copyright © 2012 Royal Meteorological Society