Vertical Discretizations: Some Basic Ideas

Abstract

This chapter introduces some key ideas in the design of vertical discretizations for atmospheric models. Various choices of vertical coordinate are possible, and the most widely used ones are introduced. The requirement to retain certain conservation properties can constrain or determine aspects of the discretization: this is illustrated using the Simmons and Burridge angular momentum and energy conserving scheme for hydrostatic models. Another important set of issues surrounds the ability to capture hydrostatic balance and wave dispersion accurately and to avoid computational modes: some implications for the vertical discretization are discussed.