Using lagged covariances in data assimilation

This paper describes a novel method to incorporate significantly time-lagged data into a sequential variational data assimilation framework. The proposed method can assimilate data that appear many assimilation window lengths in the future, providing a mechanism to gradually dynamically adjust the model towards those data. The method avoids the need for an adjoint model, significantly reducing computational requirements compared to standard four-dimensional variational assimilation. Simulation studies are used to test the assimilation methodology in a variety of situations. The use of lagged covariances is shown to provide robust improvements to the assimilation quality, particularly if data at multiple lags are used to influence the cost function in each window. The methodology developed can be used to improve contemporary global reanalyses by incorporating time-lagged observations that may otherwise not be exploited to their full potential.