Analysis of the upscaling problem – A case study for the barotropic dynamics in the North Sea and the German Bight

Abstract

The upscaling problem is investigated using the barotropic dynamics of the North Sea and the German Bight as an example. The impact of small scale perturbations of bathymetry, bottom roughness, wind forcing, and boundary forcing is quantified using a two-dimensional linear barotropic model for the entire North Sea with 5 km resolution. The model is solved in the spectral domain for the dominant M2 tide. Comparisons with results from a fully nonlinear 3D circulation model show that the main circulation features are well captured by the spectral model. The impact of different types of perturbations is estimated by inversion of the model using the perturbation covariance matrix as input. Case studies with white noise and fully correlated noise are presented. It is shown that the German Bight area stands out in its sensitivity with respect to small scale uncertainties of bathymetry. Small scale changes of bottom roughness have a particularly strong effect in the English Channel. Small scale wind perturbations have a significant local effect only in very shallow near coastal areas. It is shown that uncorrelated noise introduced along an open boundary around the German Bight only has a very local effect. Perturbations with long correlation length are shown to lead to significant far field effects along the east coast of England. It is demonstrated that this effect is related to the boundary conditions used for the North Sea model. In a next step a German Bight grid with 1 km resolution is nested into the North Sea grid and the spectral model is solved in a two way nested configuration. It is shown that there are some significant local and far field effects caused by the change of resolution in this coastal area. Finally, the potential impact of observations taken in coastal areas is investigated by evaluating the Kalman a posteriori distribution of analysis vectors based on different assumptions about model errors. The area of influence of a single tide gauge is quantified for the case where the model errors are dominated by boundary forcing errors. The results show a strong dependence on spatial correlation properties of the errors.