Optimisation of Parameters in a German Bight Circulation Model by 4DVAR Assimilation of Current and Water Level Observations

Abstract

Uncertain parameters in a 3D barotropic circulation model of the German Bight are estimated with a variational optimisation approach. Surface current measurements from a high frequency (HF) radar are used in combination with acoustic Doppler current profiler (ADCP) and tide gauge observations as input for a 4DVAR assimilation scheme. The required cost function gradients are estimated using an adjoint model code. The focus of the study is on systematic errors of the model with the control vector including parameters of the bathymetry, bottom roughness, open boundary forcing, meteorological forcing as well as the turbulence model. The model uses the same bathymetry, open boundary forcing, and metereological forcing as the operational model run at the Federal Maritime and Hydrographic Agency (BSH). The baroclinic BSH model is used as a reference to put the performance of the optimised model into perspective. It is shown that the optimised model has better agreement with HF radar data and tide gauge observations both within the fortnight training period and the test period 1 month later. Current profile measurements taken at two platforms indicate that both models have comparable error magnitudes at those locations. The optimised model was also compared with independent drifter data. In this case, drifter simulations based on the BSH model and the respective operational drift model including some surface wave effects were used as a reference. Again, these comparison showed very similar results overall, with some larger errors of the tuned model in very shallow areas, where no observations were used for the tuning and surface wave effects, which are only explicitly considered in the BSH model, play a more important role. The tuned model seems to be slightly more dissipative than the BSH model with more energy entering through the western boundary and less energy leaving toward the north. It also became evident that the 4DVAR cost function minimisation process is complicated by momentum advection, which leads to non-differentiable dependencies of the model with respect to the control vector. It turned out that the omission of momentum advection in the adjoint code still leads to robust estimates of descent directions.