Quantitative comparison of models for barotropic response of homogeneous basins

Numerous three-dimensional models that solve the shallow water equations have been proposed to describe the processes of circulation and mixing in large bodies of water. The utility of those models is often demonstrated by comparison of computed variables with field observations. However, both the hydrodynamic data and the boundary conditions that drive the model have unknown measurement uncertainties and a limited spatial coverage, which limit the validity of this approach. A series of simple benchmark problems with analytical solutions is proposed to evaluate a particular model's suitability to efficiently and accurately reproduce a wide range of characteristic hydrodynamic phenomena in natural lakes. The test problems focus on the representation of free and forced oscillations in homogeneous water bodies (barotropic response). This is not intended as a substitute for model validation against field data but, rather, as a necessary step in the initial model testing and selection. To illustrate this approach. the proposed test problems are used to compare a finite-element and a finite-difference free-surface hydrostatic model.