Ensemble Kalman Filtering with One-Step-Ahead Smoothing for Efficient Data Assimilation into One-Way Coupled Models
This work considers the filtering problem in one-way coupled state-space systems (state-2 dependent on state-1), for which the well-known joint ensemble Kalman filter (EnKF) is the standard solution. In this scheme, the two states of the coupled models are jointly updated with the incoming observations (of both states) using a Kalman correction step. In this work, we resort to the one-step-ahead (OSA) formulation of the filtering problem, which reverses the classical order of ``forecast then update steps’’, to build efficient schemes for data assimilation into one-way coupled systems. Joint filtering with OSA smoothing introduces an extra smoothing step for both states with the future observations of both variables in a fully Bayesian consistent framework, followed by an analysis step of both states, each by its own observation. The extra OSA smoothing step enables a more efficient use of the observations to inject more information into the system and to mitigate for the suboptimal character of EnKF framework. We further show that state-2 can be updated only by its own observations during the smoothing step, thereby enabling a more efficient implementation of the filtering system as a set of two EnKFs acting on the physics and the biology. We present and discuss results of numerical experiments conducted with a one-way coupled Lorenz-96 model to demonstrate the efficiency of the proposed approach.
Ms. Naila Raboudi KAUST