Ensemble smoother for optimizing tidal boundary conditions and wind forcing by assimilation of High-Frequency Radar surface currents measurements of the German Bight

An ensemble smoother scheme is presented to assimilate HF radar surface currents to improve tidal boundary conditions and wind forcings of a circulation model of the German Bight. To create an ensemble of dynamically realistic tidal boundary conditions, a cost function is formulated which is directly related to the probability of each perturbation. This cost function ensures that the perturbations are spatially smooth and that the structure of the perturbations satisfies approximately the harmonic linearized shallow water equations. Based on those perturbations an ensemble simulation is carried out using the full three-dimensional General Estuarine Ocean Model (GETM). Optimized boundary values are obtained using all observations within the assimilation period using the covariances of the ensemble simulation. The approach acts like a smoother scheme since all observations are taken into account. Since the scheme aims to derive the optimal perturbation, it might be called Ensemble Perturbation Smoother. The final analysis is obtained by rerunning the model using the optimal perturbation to the boundary conditions. The analyzed model solution satisfies thus the model equations exactly and does not suffer from spurious adjustments often observed with sequential assimilation schemes. Model results are also compared to independent tide gage data. The assimilation did also reduce the model error compared to those sea level observations. The same scheme has also been used to correct surface winds. Surface winds are crucial for accurately modeling the marine circulation in coastal waters. The method is validated directly by comparing the analyzed wind speed to in situ measurements and indirectly by assessing the impact of the corrected winds on sea surface temperature (SST) relative to satellite SST.