|
== Physical Explanation ==
Free tropospheric temperature refers to the temperature found in the higher part of the troposphere where the influence from [[boundary layer]] effects is negligible. Although the framework is based on its gradients, this occurs as a result of gradients and fluctuations in [[buoyancy]]. AnyDensity stablyor stratifiedbuoyancy fluidfluctuations whichin undergoesa densitystably orstratified buoyancy fluctuations willfluid lead to the formation of gravity waves.<ref name=":2" /> 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.<ref>{{Cite journal |last=Bretherton |first=Christopher S. |last2=Smolarkiewicz |first2=Piotr K. |date=1989-03-15 |title=Gravity Waves, Compensating Subsidence and Detrainment around Cumulus Clouds |url=https://journals.ametsoc.org/view/journals/atsc/46/6/1520-0469_1989_046_0740_gwcsad_2_0_co_2.xml |journal=Journal of the Atmospheric Sciences |language=EN |volume=46 |issue=6 |pages=740–759 |doi=10.1175/1520-0469(1989)046<0740:GWCSAD>2.0.CO;2 |issn=0022-4928}}</ref> This effectively redistributes temperature between convective, precipitating regions and dryer regions. Due to the speed with which the gravity-wave adjustment occurs, the WTG not only considers negligible horizontal buoyancy gradients but also negligibly small temporal gradients. <ref name=":4">{{Cite journal |last=Adames |first=Ángel F. |date=2022-08-01 |title=The Basic Equations under Weak Temperature Gradient Balance: Formulation, Scaling, and Types of Convectively Coupled Motions |url=https://journals.ametsoc.org/view/journals/atsc/79/8/JAS-D-21-0215.1.xml |journal=Journal of the Atmospheric Sciences |language=EN |volume=79 |issue=8 |pages=2087–2108 |doi=10.1175/JAS-D-21-0215.1 |issn=0022-4928}}</ref>
Buoyancy is closely related to temperature, more specifically virtual temperature and virtual potential temperature, leading to the name Weak Temperature Gradient.<ref name=":3" />
</math>
scale analysis suggests that the difference in pressure at two equal heightheights <math>h</math> is
<math>
== Applications ==
This assumption of negligible horizontal temperature gradient has an effect on the study of the interaction between large scale circulation and convection at the tropics. Although, the WTG does not apply to the humidity field, latent heat release from phase changes of phase related to convective activity must be considered. 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 follows,is supported not only fromby observations, but also becauseby the fact that gravity waves efficiently spreaddisperse the vertical structure of deep convective areas aroundacross the tropics.<ref name=":2" /> From the conservation of dry static energy, the WTG can be used to derive the WTG balance equation
<math>
where Q is the diabatic heating from surface fluxes and latent heat effects, and <math>\omega</math> is the pressure velocity. This suggests that variations in a diabatic atmosphere allow for a formulation of equations for which temperature variations must follow a balance between vertical motions and diabatic heating.<ref name=":2" /><ref name=":4" />
There are two way to interpret this conclusion. The first, classical interpretation is that the large scale circulation creates conditions for atmospheric convection to occur. The alternate, more important interpretation is that the surface fluxes and latent heat effects are the 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.<ref name=":2" /> Using this framework, a coupling between large scale vertical motion and diabatic heating in the tropics is achieved.
=== Models ===
| 