Ensemble Kalman Filtering with One-Step-Ahead Smoothing

Abstract

The ensemble Kalman filter (EnKF) is widely used for sequential data assimilation. It operates as a succession of forecast and analysis steps. In realistic large-scale applications, EnKFs are implemented with small ensembles and poorly known model error statistics. This limits their representativeness of the background error covariances and, thus, their performance. This work explores the efficiency of the one-step-ahead (OSA) smoothing formulation of the Bayesian filtering problem to enhance the data assimilation performance of EnKFs. Filtering with OSA smoothing introduces an updated step with future observations, conditioning the ensemble sampling with more information. This should provide an improved background ensemble in the analysis step, which may help to mitigate the suboptimal character of EnKF-based methods. Here, the authors demonstrate the efficiency of a stochastic EnKF with OSA smoothing for state estimation. They then introduce a deterministic-like EnKF-OSA based on the singular evolutive interpolated ensemble Kalman (SEIK) filter. The authors show that the proposed SEIK-OSA outperforms both SEIK, as it efficiently exploits the data twice, and the stochastic EnKF-OSA, as it avoids observational error undersampling. They present extensive assimilation results from numerical experiments conducted with the Lorenz-96 model to demonstrate SEIK-OSA’s capabilities.

Towards an End-to-End Analysis and Prediction System for Weather, Climate, and Marine Applications in the Red Sea

“…We have physics (Sivareddy et al 2019). We are currently working on tuning DART for WRF, and on testing newly introduced ensemble assimilation schemes (Hoteit et al 2015;Raboudi et al 2018).…”

Enhancing ensemble data assimilation into one‐way‐coupled models with one‐step‐ahead smoothing

“…Ensemble OSA‐smoothing filters involve two update steps with the same data, in a fully Bayesian consistent way and under the common Gaussian assumptions (Ait‐El‐Fquih et al ., 2016; Raboudi et al ., 2018). Starting from an analysis ensemble, , EnKF OSA first performs a standard forecast step to obtain a forecast ensemble, .…”

“…Here, SC‐EnKF OSA is derived by applying the EnKF OSA to the more general OWC system (), by applying the equations in Raboudi et al . (2018, section 2b) to the augmented state X n . The scheme therefore involves two joint update steps (smoothing and analysis) and two coupled model integrations (forecast and pseudo‐forecast).…”

A particle‐filter based adaptive inflation scheme for the ensemble Kalman filter

“…We also perform the same study in two more challenging scenarios, involving more pronounced systematic errors, one of which uses a perturbed state model in the two algorithms and the other a perturbed observation model. In these experiments, the filters' performances are evaluated based on the root MSE (RMSE) misfits between the reference states and their filter analysis states, averaged over all variables and over the last 200 assimilation cycles (e.g., equation 44 of Raboudi et al, 2018). For the inflation, we consider the analysis estimates and associated error variances averaged over the A07 (variance = 0.85) 1,780 1,790 1,800 1,810 1,820 1,780 1,790 1,800 1,810 1,820 1,780 1,790 1,800 1,810 1,820 1,780 1,790 1,800 1,810 1,820 1,780 1,790 1,800 1,810 1,820 1,780 1,790 1,800 1,810 1,820 1,780 1,790 1,800 1,810 1,820 1,780 1,790 1,800 1,810 1,820…”