Conceptual and analytical models
Experience with simulations based on models derived from first principles (FPMs) often leads to recognition of model-solution behaviors that are distinctive yet sufficiently generic that it becomes worthwhile to build conceptual or analytical models showing similar behavior. Even solutions of high-order nonlinear partial differential equations, observed in localized sub-domains and/or for certain time-intervals, can show simpler behavior such as waves or exponential growth or decay that would be mostly described by low-order or weakly nonlinear or even linear models. Also, the deviations from simpler behavior can sometimes be modeled in less-simple ways, that are still simpler than the FPM. For example, low-order dynamical system models such as Lorenz 1963 or Lorenz 1984 may be formally derived from an FPM by expanding all fields in orthogonal basis functions and dropping all but a few terms. Another approach, known as linear inverse modeling, obtains a linear operator A from the evolution of a covariance matrix C(t)=exp(tA)C(0), and replaces the nonlinear dynamics by stochastic forcing estimated using the fluctuation-dissipation relation.
Dry core GCM
Conventionally the instantaneous state of the atmosphere is taken to comprise the values at each space point of the 3D velocity, two thermodynamic variables (assuming an equation of state) and the densities of water vapor and other gas constituents with identifiable chemical or physical roles. The oceans are similarly composed, with gas constituents replaced by salinity and other solutions or trace constituents. An earth-system model would add components for the land surface (including snow and ice) and biosphere, anthropogenic effects etc. The evolution of the complete system includes exogenous forcing, primarily insolation and anthropogenic forcing. However it is commonly practiced to discard or severely simplify all but the dry atmosphere component with a single gas (air) component.
QG, etc. models
Another class of models obtained by exclusion of processes or other complications includes shallow-water and quasi-geostrophic and other highly idealized models. These have certain advantages over full FPMs such as possessing analytic solutions (or at least solution-existence proofs), (non-canonical) Hamiltonian structure or other conservation properties, and amenability to regularity estimates or other formal analyses. These models often exhibit sufficiently complex phenomena such as fronts, plumes and vortices, that they lend insight into the mechanisms of such phenomena observed in FPMs. Also these models can be simulated for extremely long time durations or in huge ensembles and so they provide test cases to compare highly reliable solutions with various approximation methods.