Background error covariances for a future coupled ocean–atmosphere data assimilation system: Case of tropical cyclone Batsirai

Abstract Ocean–atmosphere coupled data assimilation (DA) can be achieved through the specification of flow‐dependent ocean–atmosphere covariances in an ensemble–variational (EnVar) formulation of DA. Such a coupled EnVar relies on covariances that can be constructed directly from an ensemble of coupled forecasts. As a first step in this direction, background error covariances are investigated here for the case of the Tropical Cyclone (TC) Batsirai over the Indian Ocean. This is achieved by using the AROME‐Indian mesoscale model that is run over this domain and which is coupled to an ocean mixed‐layer model during the forecast. An ensemble of DAs (EDAs) for AROME‐Indian has thus been built in order to simulate associated background errors, while including ocean–atmosphere coupling in the forecast step of the EDA. The resulting EDA is found to simulate uncertainties in the track and intensity of TC Batsirai in a realistic way, when compared with the existing operational ensemble prediction system. It is then shown that estimated oceanic and atmospheric background error standard deviations exhibit flow‐dependent features that are consistent with the main physical processes in a TC and with longer memory effects in the ocean. Associated vertical cross‐covariance diagnostics are also found to be physically meaningful; for instance, with negative covariances between salinity and precipitation that correspond to salt dilution during tropical convective precipitation. Therefore, the resulting EDA and covariance diagnostics suggest that it would be worthwhile to conduct ocean–atmosphere coupled EnVar experiments.