Numerical uncertainties in discretization of the shallow-water equations for weather predication models

Abstract Uncertainties in the simulation of fluid dynamics in weather predication models have several sources: uncertainties in the initial conditions, uncertainties of the governing equations in simulating real atmosphere and ocean states, and uncertainties in the numerical implementation of the governing equations. In this chapter, we discuss the uncertainties arising from the discretization of the shallow-water equations (SWE), with focus on the numerical design for the global grid model. Numerical design of a SWE includes model selecting a grid and staggering scheme based on the form of the equations to be discretized, applying and devising consistent and stable numerical methods that are suitable for the discretization grid, and using numerical techniques to remove computational modes and increase the stability and efficiency of numerical simulation. The discussions are presented for the three most commonly used grids in modern global atmospheric and oceanic modeling, the Cartesian grid, the icosahedral grid, and the cubed-sphere grid.