Numerical models of the general circulation, climate and weather prediction
Model simulations of present-day and future climate conditions involve iterating the model
equations for perhaps tens to hundreds of years of simulated time depending on the question at hand. In order to solve these coupled equations, additional processes such as radiative transfer through the atmosphere with diurnal and seasonal cycles, surface friction and energy transfers and cloud formation and precipitation processes must be accounted for. These are coupled in the manner shown schematically in Figure 8.1. Beginning with a set of initial atmospheric conditions usually derived from observations, the equations are integrated forward in time repeatedly using time steps of several minutes to tens of minutes at a large number of grid points over the earth and at many levels vertically in the atmosphere; typically 10-20 levels in the vertical is common. The horizontal grid is usually of the order of several degrees latitude by several degrees longitude near the equator. Another, computationally faster, approach is to represent the horizontal fields by a series of two-dimensional sine and cosine functions (a spectral model). A truncation level describes the number of two-dimensional waves
that are included. The truncation procedure may be rhomboidal (R) or triangular (T); R15 (or T21) corresponds approximately to a 5° grid spacing, R30 (T42) to a 2.5° grid, and T102 to a 1° grid.