Classical formulations of data-assimilation, whether sequential, ensemble-based or variational, can be viewed as amplitude-adjustment methods. Such approaches do not deal well with position errors, which can be seen readily, for example, when a forecast localized weather event is displaced from its observed location. The sources of position error are many and include errors in initial conditions, observations, model parameters and model structure. In the presence of sparse observations, typical assimilation approaches will tend to distort the state if the adjusted variables do not have a direct impact on position errors. In this sense, either by construction or due to computational limitations, popular methods are inadequate for handling inherently non-linear and hard to diagnose error sources. But correcting position errors revealed by sparse observations is essential for predicting strong, localized weather events such as tropical cyclones. Indeed, to ameliorate these problems, forecasters currently resort to crude procedures, such as bogussing.

In this paper, we propose a pre-processing step applicable for assimilation. In this step, called field alignment, the current model state is spatially aligned with observations by adjusting a continuous field of local displacements. This is accomplished by solving an auxiliary variational optimization problem in a preprocessing step. In contrast to other alignment techniques, our preprocessing step does not explicitly rely on the denition of a feature and displacements are valid in the continuum. Once aligned, a standard DA technique may be applied. We demonstrate this technique in a 2D framework under sparse, uncertain observations and show that applying this step produces better analyses and typically reduces the number of iterations to convergence during assimilation.