A new derivation of the shallow water equations in geographical coordinates and their application to the global barotropic ocean model (the DEBOT model)

Abstract

The purpose of this paper is to present a new global barotropic ocean model—the DEBOT model. The model is based on the shallow water equations which we newly express in geographical coordinates. The derivation includes the boundary conditions and the Reynolds tensor in a form used commonly in oceanography. The numerical model employs finite differences on an Arakawa-C grid in space and a generalized forward–backward scheme in time with a combined third-order Adams–Bashforth and fourth-order Adams–Moulton step. The validity of the model is demonstrated by the tests based on conservation integral invariants. As a practical application, we present ocean circulation simulations generated by the lunisolar tidal force.