A new smoother method for treating different timescales in variational data assimilation for coupled systems

Coupled atmosphere-ocean models are increasingly being used in numerical weather prediction (NWP). However, current data assimilation (DA) methods that are used to initialise these models are unable adequately to account for the different dynamical timescales in the atmosphere and ocean. In the context of variational DA, operational centres have developed weakly (or quasi-strongly) coupled DA systems, in which a separate optimization procedure is performed to estimate the atmosphere and ocean states, and information is passed between the two through an outer loop step or through cycling of the assimilation system. In such systems it is challenging to combine the short assimilation windows needed for the atmospheric assimilation with longer windows that are ideally needed for the more-slowly evolving ocean. In this work we propose a new method for treating the different timescales in the context of coupled variational data assimilation. After running the standard coupled assimilation for several short assimilation windows, a long-window minimization is introduced to update the ocean analysis, starting from the output of the short-window assimilations. To illustrate the proposed scheme we develop a new idealised model with an appropriate separation of timescales. Using this idealised model we show how our new scheme significantly improves the accuracy of the ocean analysis when compared with the current approach. When the system is then cycled with the coupled model, improvements in the ocean analyses translate into enhanced accuracy in the atmospheric fields. Furthermore, we illustrate how the new scheme enables the assimilation of late-arriving observations that are not available to the short-window assimilations. The new method shows strong potential for treating different dynamical timescales in coupled DA for NWP.