Asynchronous data assimilation with the EnKF

This study revisits the problem of assimilation of asynchronous observations, or four-dimensional data assimilation, with the ensemble Kalman filter (EnKF). We show that for a system with perfect model and linear dynamics the ensemble Kalman smoother (EnKS) provides a simple and efficient solution for the problem: one just needs to use the ensemble observations (that is, the forecast observations for each ensemble member) from the time of observation during the update, for each assimilated observation. This recipe can be used for assimilating both past and future data; in the context of assimilating generic asynchronous observations we refer to it as the asynchronous EnKF. The asynchronous EnKF is essentially equivalent to the four-dimensional variational data assimilation (4D-Var). It requires only one forward integration of the system to obtain and store the data necessary for the analysis, and therefore is feasible for large-scale applications. Unlike 4D-Var, the asynchronous EnKF requires no tangent linear or adjoint model.