Interactions of Dynamics and Observations in a Four-Dimensional Variational Assimilation

A four-dimensional (4D) variational assimilation (4DVAR) seeks an optimal balance between observations scattered in time and space over a finite 4D analysis volume and a priori information. In some cases, 4DVAR is able to closely fit both observations and the a priori initial estimate by making very small changes to the initial conditions that correspond to those rapidly growing perturbations that have large amplitude at the observation locations and times. Some observations may occur at locations and times for which the amplitudes of rapidly growing perturbations are not large. To fit such data, larger changes to the initial conditions are necessary. Such cases may result in amplification of the analysis increments away from the observation locations. This situation occurs generally for surface data, because of the damping effect of surface exchange processes. These interactions are seen in experiments using single observations. To further explore the impact of surface data in 4DVAR, experiments were conducted with and without ERS-1 C-band measurements of backscatter. As expected and in contrast to conventional approaches, the impact is not confined to the lower troposphere and the analysis increments are balanced. The study focuses on the case of a small intense North Atlantic storm that struck the coast of Norway on New Year's Day 1992. The scatterometer data have a significant, apparently positive, impact on the 4DVAR analysis in this case. The example using scatterometer data also demonstrates the ease with which 4DVAR assimilates nonstandard data, which have a complex, highly nonlinear relationship with the model variables.