A global C-staggered composite model for shallow water equations 1 with latitude-longitude grid and reductions in the polar regions

To develop a numerical method for global geophysical fluids, we usually need to choose a spherical grid and numerical approximations to represent the partial derivative equations. Some alternatives include the use of finite differences or finite volumes with latitude-longitude or reduced grids. Each of these cases has some advantages and also some limitations. This paper presents a comparison between two methods and numerical tests with a composite model using them side by side. The first is a well-known method for latitude-longitude grids that was used from 75ºS until 75ºN. The second is a recently developed scheme for reduced grids that was used only in the polar regions. The similarity between these two methods allows a smooth transition in these two regions. Numerical tests with the composite model indicated order 2 of convergence, prevention of grid-imprinting errors, and a combination of the advantages of both schemes. The composite model has numerical properties that may lead to efficient implementations with massive parallel computation.