Data assimilation by field alignment

Classical formulations of data assimilation, whether sequential, ensemble-based or variational, are amplitude adjustment methods. Such approaches can perform poorly when forecast locations of weather systems are displaced from their observations. Compensating position errors by adjusting amplitudes can produce unacceptably “distorted” states, adversely affecting analysis, verification and subsequent forecasts.

There are many sources of position error. It is non-trivial to decompose position error into constituent sources and yet correcting position errors during assimilation can be essential for operationally predicting strong, localized weather events such as tropical cyclones.

In this paper, we propose a method that accounts for both position and amplitude errors. The proposed method assimilates observations in two steps. The first step is field alignment, where the current model state is aligned with observations by adjusting a continuous field of local displacements, subject to certain constraints. The second step is amplitude adjustment, where contemporary assimilation approaches are used. We demonstrate with 1D and 2D examples how applying field alignment produces better analyses with sparse and uncertain observations.