Weak temperature gradient approximation: Difference between revisions

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== 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|gravity waves]].<ref name=":2" /> In the tropics, where Coriolis force is negligibly small, these [[Gravity wave|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 regions of precipitating convection and clear-sky region. 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>

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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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 energy and humidity. This solves the limitation of such models of understanding the distribution of precipitation as a prescribed vertical motion constrains precipitation. <ref name=":2" /><ref name=":1" />

Using the WTG framework, many different processes have been studied and better understood. These include, the Walker Cell<ref>{{Cite journal |last=Bretherton |first=Christopher S. |last2=Sobel |first2=Adam H. |date=2002-10-15 |title=A Simple Model of a Convectively Coupled Walker Circulation Using the Weak Temperature Gradient Approximation |url=https://journals.ametsoc.org/view/journals/clim/15/20/1520-0442_2002_015_2907_asmoac_2.0.co_2.xml |journal=Journal of Climate |language=EN |volume=15 |issue=20 |pages=2907–2920 |doi=10.1175/1520-0442(2002)015<2907:ASMOAC>2.0.CO;2 |issn=0894-8755}}</ref>, the diurnal cycle of convection<ref>{{Cite journal |last=Ruppert |first=James H. |last2=Hohenegger |first2=Cathy |date=2018-06-15 |title=Diurnal Circulation Adjustment and Organized Deep Convection |url=https://journals.ametsoc.org/view/journals/clim/31/12/jcli-d-17-0693.1.xml |journal=Journal of Climate |language=EN |volume=31 |issue=12 |pages=4899–4916 |doi=10.1175/JCLI-D-17-0693.1 |issn=0894-8755}}</ref>, self-aggregation<ref>{{Cite journal |last=Sessions |first=Sharon L. |last2=Sugaya |first2=Satomi |last3=Raymond |first3=David J. |last4=Sobel |first4=Adam H. |date=2010-06-27 |title=Multiple equilibria in a cloud‐resolving model using the weak temperature gradient approximation |url=https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2009JD013376 |journal=Journal of Geophysical Research: Atmospheres |language=en |volume=115 |issue=D12 |doi=10.1029/2009JD013376 |issn=0148-0227}}</ref>, tropical cyclone formation<ref>{{Cite journal |last=Raymond |first=David J. |last2=Sessions |first2=Sharon L. |date=2007-03 |title=Evolution of convection during tropical cyclogenesis |url=https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2006GL028607 |journal=Geophysical Research Letters |language=en |volume=34 |issue=6 |doi=10.1029/2006GL028607 |issn=0094-8276}}</ref>, the Madden Julian Oscillation<ref>{{Cite journal |last=Chikira |first=Minoru |date=2014-02-01 |title=Eastward-Propagating Intraseasonal Oscillation Represented by Chikira–Sugiyama Cumulus Parameterization. Part II: Understanding Moisture Variation under Weak Temperature Gradient Balance |url=https://journals.ametsoc.org/view/journals/atsc/71/2/jas-d-13-038.1.xml |journal=Journal of the Atmospheric Sciences |language=EN |volume=71 |issue=2 |pages=615–639 |doi=10.1175/JAS-D-13-038.1 |issn=0022-4928}}</ref>... The WTG has also been used as a parametrization in for large-scale motion in cloud-permitting models.<ref name=":4" />

Using the WTG framework, many different processes have been studied and better understood. These include, the Walker Cell, the diurnal cycle of convection, self-aggregation, tropical cyclone formation, the Madden Julian Oscillation... The WTG has also been used as a parametrization in for large-scale motion in cloud-permitting models.<ref name=":4" />