The Neelin-Zeng Quasi-Equilibrium Tropical Circulation Model (QTCM1), is an intermediate complexity atmospheric model, designed to occupy the niche between general circulations models (GCMs) and simple models. The model formulation makes use of the constraints placed on the flow by deep convection, as represented by quasi-equilibrium (QE) convective parameterizations, hence the Q in QTCM. Analytical solutions for tropical flow [8, 7] under strict QE conditions (plus additional approximations) appeared useful enough to motivate development of a model that could employ these where appropriate and yet not be completely bound by them, as discussed below. The derivation from the primitive equations and the equations for the resulting atmospheric model are given in [1]. The numerical implementation developed at the UCLA Department of Atmospheric Sciences, initially by Neelin and Zeng and now by other members of the Climate Systems Interactions group, including H. Su, C. Chou and M. Munnich is more fully discussed in [1, 2]. In order to consistently simulate the tropical climatology, interannual variability and intraseasonal variability, a suite of physical parameterizations has been included, including a simple land model and a radiation package, all aimed at being simpler to run and analyze than a GCM, and yet being a reasonable approximation under suitable conditions to what would be included in a GCM. This manual describes the implementation of the resulting numerical model.
Regarding the atmospheric dynamics, QE convective closures and model formulation: QE convective closures posit that moist convective elements tend to act quickly compared to the large scale flow, and tend to dissipate the buoyancy available to moist overturning motions within a vertical column. Convective available potential energy (CAPE) is one measure of this. The tendency to generate CAPE at large-scales is assumed to be roughly balanced by dissipation in small-scale convective activity to establish a statistical ``quasi-equilibrium'' among variables affecting buoyancy. Typically, this implies a relation between the temperature profile through the column and the boundary layer moisture and temperature. One parameterization that makes this explicit in a simple manner is the Betts-Miller convective scheme. A convective profile is established by a moist adiabat arising from the boundary layer. Temperature is restored toward this profile when deep convection occurs. In moist convective regions, temperature will thus tend to have a vertical profile close to this convective profile.
QTCM1 takes the shape of this convective temperature profile and uses it as a basis function for temperature in a Galerkin-like representation of vertical structure. A basis function for baroclinic velocity is computed from the implied vertical profile of the baroclinic pressure gradients, according to the hydrostatic equation. And the implied vertical velocity profile is computed from this according to continuity. Barotropic motions add an additional basis function. The primitive equations are projected on these vertical structures. In deep convective regions, this should be an efficient basis set to capture much of the most important motions, compared to a GCM running the same convection scheme. Away from deep convective regions, QE will not apply, but the Galerkin-like representation of vertical structure still tends to capture deep motions for the dry dynamics. Within a Rossby radius of deformation (25 degrees or so) this should still be a reasonable approximation. At higher latitudes, it is simply a highly truncated Galerkin representation.
The reduction of the vertical degrees of freedom considerably cuts computational time. The current version takes approximately 5 minutes of CPU time to run one year of model simulation on a Sun Ultra 80 workstation (1.5 minutes on a Pentium-4/Linux workstation). A GCM with only a few layers would have the same speed, but an advantage of the current approach is that it is more quantitative in and near deep convection zones. For tropical climate, this appears to be quite significant. In analyzing the results, it can be helpful to consider the moist static energy budget and the gross moist stability, as discussed in [1, 11].
When using the model, please note that there are trade-offs to the approach. It is always necessary to consider for each application whether the approximations are within their range of validity. Often this will have to be tested for the particular phenomenon of interest. We also note that the model does not assume strict QE, although it is set up to be most accurate when QE tends to apply. Although we find QE assumptions can be useful for some scales and phenomena, this does not mean that it will apply in all situations. In particular, QE assumes that an ensemble of convective elements is acting together. At sufficiently small scales this assumption will cease to hold well. With these caveats, we note that there do seem to be a variety of phenomena for which the model can be useful to the climate research community.
The current version of the model includes the following major features: