A variational approach for the reconstruction of regional scale Eulerian velocity fields from Lagrangian data

A method for the reconstruction of the mesoscale Eulerian velocity field based on Lagrangian data at given sampling period is presented. A variational approach is used, where information on the float positions are combined with a simple model constraint describing the motion of particles advected in a velocity field. The velocity field of a priori specified space scale is estimated minimizing a cost function which measures the distance between the observed float positions and the model predicted ones for each sampling period. The method is first implemented considering the time-independent approximation of the velocity correction during a time interval shorter than the typical time scale of the mesoscale field. In a second step, this approximation is relaxed to consider inertial oscillations superimposed on the mesoscale field. The method is tested on a numerical regional circulation on the Northwestern Mediterranean Sea, characterized by an Eulerian time scale significantly longer than the inertial period. The observational coverage of the region varies between 80% and 16% and the corresponding error in the velocity reconstruction varies from less than 10% to approximately 50%, with a sampling period of the day. For smaller sampling intervals, the reconstruction is further improved in the time-dependent approximation. Finally, the method is used to combine information from Lagrangian data and General Circulation Models. The results suggest the useful application of the method for assimilation studies.