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In [[atmospheric science]], the '''weak temperature gradient approximation''' ('''WTG''') is a theoretical framework used to simplify the equations governing tropical atmospheric dynamics and circulation. The WTG approximation assumes that free [[Troposphere|tropospheric]] temperature in the [[tropics]] has negligible horizontal (and temporal) gradients compared to its vertical gradient.<ref name=":0">{{Cite journal |
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.<ref name=":2">{{Cite book |url=https://www.cambridge.org/core/books/clouds-and-climate/7B47159F7B050B71625111E40795D182 |title=Clouds and Climate: Climate Science's Greatest Challenge |date=2020 |publisher=Cambridge University Press |isbn=978-1-107-06107-1 |editor-last=Siebesma |editor-first=A. Pier |___location=Cambridge |editor-last2=Bony |editor-first2=Sandrine |editor-last3=Jakob |editor-first3=Christian |editor-last4=Stevens |editor-first4=Bjorn}}</ref><ref name=":3">{{Cite journal |last=Charney |first=Jule G. |date=1963-11-01 |title=A Note on Large-Scale Motions in the Tropics
In a multitude of theoretical, modelling and observational studies, the WTG has been applied to study [[Synoptic scale meteorology|synoptic]]- and [[Mesoscale meteorology|mesoscale]] phenomena in the tropics.
== Physical explanation ==
Free tropospheric temperature refers to the [[temperature]] in the upper layers of the troposphere where the influence from the surface and the [[boundary layer]] is negligible. Although the framework is formulated with the gradients of free tropospheric temperature, this phenomena occurs as a result of gradients and fluctuations in [[buoyancy]]. Density or buoyancy fluctuations in a stably stratified fluid lead to the formation of [[gravity wave]]s.<ref name=":2" /> In the tropics, where Coriolis force is negligibly small, these [[gravity wave]]s prove to be very effective at smoothing out buoyancy gradients, in a process called gravity-wave adjustment or buoyant equalization.<ref>{{Cite journal |
As, buoyancy is closely related to temperature (more specifically the [[virtual temperature]] and the virtual potential temperature) the framework is usually named Weak Temperature Gradient approximation.<ref name=":3" />
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=== Models ===
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.<ref>{{Cite journal |
Many studies implemented the WTG constraint in radiative-convective equilibrium (RCE) models, by fixing the mean virtual temperature profile.<ref name=":0" /> Often this creates opposing results with either dry, non-precipitating states or heavily-precipitating states, depending on the stability of the constrained temperature profile.<ref>{{Cite journal |
Bulk, single column models, can also be developed with the WTG. 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. Due to the strong coupling between vertical motion and precipitation, the WTG approach allows the study of precipitation distribution, also in the bulk setup.<ref name=":2" /><ref name=":1" />
Using the WTG framework, many different processes have been studied and better understood. These include, both synoptic processes such as the Walker Cell<ref>{{Cite journal |
== References ==
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