Tides on unstructured meshes

Abstract

Unstructured mesh methods offer flexibility in representing variable coastlines and bathymetries in ocean circulation models. They propose other advantages allowing, for example, to define high resolution in certain regions of global mesh without invoking nesting methods.However, already existing finite-difference structured mesh models often outperform them as their computations per mesh node are less expensive. Nevertheless, due to the big variety of discretizations possible with unstructured mesh methods - finite element or finite volume - and the freedom in mesh design, the existing setups are not necessarily optimal in terms of accuracy and numerical efficiency. The search for optimal approach presents an important direction of current research. This thesis partly contributes in this direction. Two finite element and one finite volume method are compared with respect to their ability to faithfully simulate tides on meshes of the European Continental Shelf. Judged by computational efficiency and the absence of stabilization the preference is given to the semi-implicit models based on finite volumes after Chen et al. (2003) or on the non-conforming finite element method.One of the proposed models is further validated in simulating M2 and K1 tidal constituents on a fine mesh. Its performance in balancing energy and calculating residual currents is analyzed. The influence of the open boundary condition is also discussed. The results obtained in this analysis indicate, that the model skills are more sensitive to errors in open boundary conditions and depth representation than to changes in the spatial or temporal discretization schemes. This dictates the next step - implementing algorithms that systematically improve model parameters and open boundary forcing. It is the second major goal of this thesis.In the thesis the adjoint model is generated by adapting automatic differentiation technique. It computes the sensitivities of a cost function, which is a measure for the misfit between observed and simulated model fields, with respect to the depth, the bottom friction coefficients and the open boundary values. The sensitivities are compared in M2 and K1 tidal simulations and on a coarse and fine meshes. Regions of strong sensitivities for each tidal constituent are identified. It turns out that the sensitivities on the coarse and fine meshes do not match. If mesh is coarse it is missing dynamics that are tuned. In contrast, on the fine mesh the sensitivities with respect to, for example, depth identify islands missing from the mesh. This suggests to use adjoint models for mesh refinements.Further, the adjoint model is coupled to a Broyden-Fletcher-Goldfarb-Shanno algorithm, and the parameters are optimized on the coarse mesh. The error in coastline representation and mesh resolution is partly projected on the parameter sensitivities, which leads to a tendency in less realistic values unless strong regularization is used. This shows that tuning parameters for the wrong reason is something that should be avoided. This thesis proposes to use the sensitivities first for mesh refinements and in a second step for parameter optimization.