A Global C-Staggered Composite Model for Shallow Water Equations with Latitude–Longitude Grid and Reductions in the Polar Regions

Abstract

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 describes a composite model using them side by side. The first is a well-known method for latitude–longitude grids and was used from 75[Formula: see text][Formula: see text]S until 75[Formula: see text][Formula: see text]N. The second is a recently developed scheme for reduced grids and was used only in the polar regions. The similarity between the two methods allows the use of small adaptations in their approximations to obtain consistency and mass conservation also in the transition between the two regions. The composite model combines advantages of the other two schemes and has a smaller computational cost. Numerical tests indicated order 2 of convergence, prevention of grid-imprinting errors, and avoidance of nonlinear instability. This model has numerical properties that may lead to efficient implementations with massive parallel computation.