The 2-D model extends vertically from the surface up to 120 km with a vertical resolution of 1 km, and latitudinally from -85 to 85 with a 5^o resolution. Log-pressure height is used as the vertical coordinate. As in Garcia and Solomon (1983), the dynamical fields and temperature are governed by a set of zonally-averaged quasi-geostropic equations of thermodynamics, momentum, and mass continuity, expressed in the transformed Eulerian mean (TEM) framework (symbol definition listed in Appendix A).

where

Note that in these equations, z represents the pressure altitude defined as z = 7 ln(p/p₀) where p₀ is the surface pressure. In Equation (1), thermodynamics is driven by solar heating (Q_S), infrared heating (Q_IR), and small scale diffusive transport of heat (D_q) by wave and molecular diffusion processes, given as:

where K_yy is the meridional eddy diffusivity coefficient, K_zz the vertical diffusivity coefficient, and K_T is the molecular thermal conductivity coefficient. The temperature and wind fields are advected by the transformed Eulerian mean circulation (v* and w*, also called residual circulation), a quantity that is more representative of the actual motions of air parcels in the meridional plane (see discussions in Andrews et al. 1987).The zonal momentum forcing (Equation (2)) is caused by planetary wave (F_R), gravity (F_G), and tidal wave (F_T) dissipation and breaking.

The governing equations can be combined to form a diagnostic equation for the mean circulation, represented by the streamfunction (Garcia and Solomon, 1983):

where is related to the residual velocities as:

The coefficients of the stream function equation (7) are functions of the mean zonal wind and temperature:

The forcing term C_F on the right-hand side of Equation (7):

Therefore, the circulation determined by Equation (7) is driven by the latitudinal gradient of the diabatic heating and the vertical gradient of the wave momentum forcing. Central to the improvements made in SOCRATES are the different ways in which these radiative and dynamic forcings are derived; these will be described in detail in the next section.