Horizontal Discretizations: Some Basic Ideas

Abstract

This chapter will introduce some key ideas in the construction of horizontal discretizations for atmospheric models. One important topic is the ability of different schemes to capture wave propagation accurately. The von Neumann method for analysing numerical wave propagation is presented and applied to some simple schemes to demonstrate the advantages of staggered grids in finite difference models. Another important topic is whether the discretization respects the conservation properties of the differential equations being solved. An introduction to the topic is given, using energy conservation as an illustrative example.