In atmospheric science, the weak temperature gradient approximation (WTG) is a theoretical framework used to simplify the equations governing tropical atmospheric dynamics and circulation.
[1][2] The assumption of horizontal homogeneity of temperature follows from observations of free tropospheric temperature in the tropical regions as well as early work on the simplified equations governing tropical circulation.
It is understood to occur as a result of the weak Coriolis force in the tropics.
Density or buoyancy fluctuations in a stably stratified fluid lead to the formation of gravity waves.
[3] In the tropics, where Coriolis force is negligibly small, these gravity waves prove to be very effective at smoothing out buoyancy gradients, in a process called gravity-wave adjustment or buoyant equalization.
[3] These pressure differences can also be analyzed using the Navier-Stokes momentum equation in the tropics with the Coriolis parameter
This shows that for small Rossby numbers in the extra-tropics, density (and with it temperature) perturbations are much larger than in the tropical regions.
[3] The assumption of negligible horizontal temperature gradient has significant implications for the study of the interactions between large scale circulation and convection in the tropics.
Although, the WTG does not directly apply to the humidity field, latent heat release from phase changes related to convective activity affects temperature and therefore moisture must also be considered.
[3] The WTG approximation allows for models and studies to fix the free tropospheric temperature profile, usually using the reversible moist adiabat.
The use of the moist adiabat is not only supported by observations but also by the fact that gravity waves efficiently disperse the vertical structure of deep convective areas across the tropics.
The first, classical interpretation is that the large scale circulation creates conditions for atmospheric convection to occur.
[3] The alternate, more important interpretation is that the surface fluxes and latent heat effects are processes which control the large scale circulation.
In this case, a heat source would cause a temperature anomaly which, in the WTG, would get smoothed out by gravity waves.
Due to energetic constraints, this would lead to a large-scale vertical motion to cool the column.
[3] Using this framework, a coupling between large scale vertical motion and diabatic heating in the tropics is achieved.
The weak temperature gradient approximation is often used in models with limited domains as a way to couple large-scale vertical motion and small scale diabatic heating.
Generally, this has been done by neglecting horizontal free-tropospheric temperature variations (to first order), while explicitly retaining fluid dynamical aspects and diabatic processes.
[7] Many studies implemented the WTG constraint in radiative-convective equilibrium (RCE) models, by fixing the mean virtual temperature profile.
Although these models usually treat temperature prognostically while constraining the large-scale vertical motion, using the WTG approximation, large scale vertical motion becomes a diagnostic variable, dependent on static stability and humidity.
These include, both synoptic processes such as the Walker Cell[9] and the Madden Julian Oscillation[10] and also mesoscale processes such as, the diurnal cycle of convection,[11] convective self-aggregation[12] and tropical cyclone formation.