An unconventional approach for assimilating aliased radar radial velocities

An aliasing operator is introduced to mimic the effect of aliasing that causes discontinuities in radial-velocity observations, and to modify the observation term in the costfunction for direct assimilations of aliased radar radial-velocity observations into numerical models. It is found that if the aliasing operator is treated as a part of the observation operator and applied to the analysed radial velocity in a conventional way, then the analysis is not ensured to be aliased (or not aliased) in consistency with the aliased (or not aliased) observation at every observation point. Thus, the analysis-minus-observation term contains a large alias error whenever an inconsistency occurs at an observation point. This causes fine-structure discontinuities in the costfunction. An unconventional approach is thus introduced to apply the aliasing operator to the entire analysis-minus-observation term at each observation point in the observation term of the costfunction. With this approach, the costfunction becomes smooth and concave upwards in the vicinity of the global minimum. The usefulness of this approach for directly assimilating aliased radar radial-velocity observations under certain conditions is demonstrated by illustrative examples.