Developing 4D-Var for Strongly Coupled Data Assimilation Using a Coupled Atmosphere–Ocean Quasigeostrophic Model

Abstract

Abstract Four-dimensional variational (4D-Var) data assimilation (DA) is developed for a coupled atmosphere–ocean quasigeostrophic application. Complications arise in coupled data assimilation (CDA) systems due to the presence of multiple spatiotemporal scales. Various formulations of the background error covariance matrix (), using different localization strategies, are explored to evaluate their impact on 4D-Var performance in a CDA setting. 4D-Var requires access to tangent linear and adjoint models (TLM/AM) to propagate information about the misfit between the forecast and observations within an optimization window. In practice, particularly for coupled models, the TLM and adjoint are often difficult to produce, and for some models are nonexistent in analytic form. Accordingly, a statistical data-driven alternative is also employed and evaluated to determine its feasibility for a 4D-Var CDA system. Using experiments conducted with a coupled atmosphere–ocean quasigeostrophic model, it is found that ensemble generation of flow-dependent error covariance statistics can increase the accuracy of 4D-Var CDA. When observing all variables, the hybrid climatological/flow-dependent constructions outperform either independently. The use of a hybrid matrix combined with a rapid updating ensemble transform Kalman filter (RU-ETKF) using either strongly or weakly CDA resulted in lower overall RMSE. The ocean component achieved its lowest RMSE when using a fully flow-dependent matrix generated using 4D-ETKF and using weakly CDA. These results show the importance of time scales and analysis update frequencies. The use of a statistically derived TLM/AM generated from the ETKF ensemble perturbations produces results similar to cases using the analytical coupled TLM/AM in 4D-Var.