We present a four-dimensional ensemble Kalman filter (4D-LETKF) that approximately and efficiently solves a variational problem similar to that solved by 4D-VAR, and report numerical results with the Simplified-Parametrized primitive Equation Dynamics model, a simplified global atmospheric model. We discuss the relationship of 4D-LETKF to other ensemble Kalman filters and, in our simulations, compare it with two simpler approaches to assimilating asynchronous observations.

 We find that 4D-LETKF significantly improves on the approach of treating asynchronous observations as if they occur at the analysis time. For a sufficiently short analysis time interval, the approach of computing innovations from the background state at the observation times and treating those innovations as if they occur at the analysis time is comparable to 4D-LETKF, but for longer analysis intervals, we find that 4D-LETKF is superior to this approach.