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

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