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[[File:Northeast Snowfall Impact Scale.gif|thumb|[[Weather radar]] loop showing intense snow bands (lighter color) due to CSI ahead of a [[warm front]].]]
'''Conditional symmetric instability''', or '''CSI''', is a form of [[convective instability]] in a fluid subject to temperature differences in a uniform rotation [[frame of reference]] while it is thermally stable in the vertical and dynamically in the horizontal (inertial stability). The instability in this case develop only in
==Principle==
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An air particle at a certain altitude will be stable if its adiabatically modified temperature during an ascent is equal to or cooler than the environment. Similarly, it is stable if its temperature is equal or warmer during a descent. In the case where the temperature is equal, the particle will remain at the new altitude, while in the other cases, it will return to its initial level4.
In the diagram on the right, the yellow line represents a raised particle whose temperature remains at first under that of the environment (stable air) which entails no convection. Then in the animation, there is warming surface warming and the raised particle remains warmer than the environment (unstable air). A measure of hydrostatic stability is to record the variation with the vertical of the [[equivalent potential temperature]] (<math>\theta_e</math>):<ref name="Doswell">{{cite web |url= http://www.cimms.ou.edu/~doswell/csidisc/CSI.html |archiveurl=https://web.archive.org/web/20150227203926/http://www.cimms.ou.edu/~doswell/csidisc/CSI.html|archivedate=February 27, 2015| title= CSI Physical Discussion | website = www.cimms.ou.edu | author1= [[Charles A. Doswell III]] | publisher= [[Cooperative Institute for Mesoscale Meteorological Studies|CIMMS]] | accessdate= August 23, 2019}}
</ref>
::* '''If <math>\theta_e</math> diminish with altitude leads to unstable airmass'''
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===Inertial Stability===
[[File:Tourbillon total faible.png|thumb|Dark zones are regions of weak inertial stability in atmopsheric circulation.]]
In the same way, a lateral displacement of an air particle changes its absolute vortex η. The latter consists of <math>f</math>, the [[Coriolis parameter]], and <math>\zeta</math>, the [[Geostrophic wind|geostrophic vortex]]:<ref name="Doswell"/><ref name="MF-2">{{cite web|language=French | url= http://www.meteofrance.fr/publications/glossaire?articleId=152385 | title= Instabilité barocline | publisher= [[Météo-France]] | accessdate= August 23, 2019 | work= Glossaire météorologique }}</ref>
<center><math>\eta= \left[ \frac{\partial v_r}{\partial x} - \frac{\partial u_r}{\partial y} \right ] + f = \zeta + f \qquad \qquad </math></center>
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* ''<math>\zeta</math>'' varies according to the pressure gradient: positive for a rotation anti-clockwise and negative for a clockwise rotation.
<math>\eta</math> can be positive, null or negative depending on the conditions in which the move is made. As the absolute vortex is almost always positive on the [[synoptic scale]], one can consider that the atmosphere is generally stable for lateral movement. Inertial stability is low only when <math>\eta</math> is close to zero. Since <math>f</math> is always positive, <math>\eta \le 0 </math> can be satisfied only on the anticyclonic side of a strong maximum of [[jet stream]] or in a [[Ridge (meteorology)|barometric ridge]] at altitude, where the derivative velocities in the direction of displacement in the equation give a significant negative value
The variation of the [[angular momentum]] indicate the stability:<ref name="Doswell"/><ref name="Moore">{{cite web | language = en | format= ppt | url= http://www.comet.ucar.edu/class/rfc_hydromet/03-1/docs/Moore/Mesoinstab/Meso-proc.ppt | author= James T. Moore
| title= Mesoscale Processes | publisher= [[University Corporation for Atmospheric Research|UCAR]] | accessdate= August 23, 2019 | date= 2001 | pages=
*<math>\Delta M_g = 0 </math>, the particle then remains at the new position because its momentum has not changed
*<math>\Delta M_g > 0 </math>, the particle returns to its original position because its momentum is greater than that of the environment
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; Slantwise displacement C
Only case C is unstable. Horizontal acceleration combines with a vertical upward disturbance and allows oblique displacement. Indeed, the <math> \scriptstyle \theta_e </math> of the particle is larger than the <math> \scriptstyle \theta_e </math> of the environment. While the momentum of the particle is less than that of the environment. An oblique displacement thus produces a positive buoyancy and an acceleration in the oblique displacement direction which reinforces it
The condition for having conditional symmetric instability in an otherwise stable situation is therefore that:<ref name = "Doswell"/><ref name = "Moore"/><ref name=Schultz/>
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forms along the front, near the low pressure area and the CSI.
{{clr}}
===Slantise convection===
[[File:Instabilité symétrique conditionnelle.svg|thumb|Upward movement in an area of CSI gives clouds, downward movement clears the sky.]]
If a particle is climbing in an CSI zone, it will cool down and the water vapor will condense upon saturation, giving cloud and precipitation by oblique convection. For example, in front of a warm front, the air mass is stable because the mild air overcomes a cold mass. The geostrophic equilibrium brings back any particle moving perpendicularly from the center of the depression towards it. However, an upwardly oblique displacement by [[synoptic scale]] upward acceleration in an CSI layer produces parallel bands of heavy rainfall.<ref name="Schultz"/><ref>{{cite web | language = en | url= http://www.crh.noaa.gov/lmk/?n=paper-1/17/94 | title= Vertical Motion Forcing Mechanisms Responsible for the Production of a Mesoscale very heavy snow band across Northern Kentucky | publisher = [[National Weather Service]] | author= Theodore W. Funk | author2= James T. Moore}}</ref>
Conditional symmetric instability affects a layer that can be thin or very large in the vertical, similar to hydrostatic convection. The thickness of the layer determines the enhancement of convective [[precipitation]] within a region otherwise [[wikt:stratiform|stratiform]] clouds
* The trailing precipitation region of [[mesoscale convective system]]s.
* Wintertime convection because the lower and colder [[tropopause]] is helping the ionization of upward moving ice crystals.
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=== Subsidence ===
Conversely, if the particle slide downward, it will warm up and become relatively less saturated, dissipating clouds. The snow produced at higher altitude by the slantwise convection will also [[Sublimation (phase transition)|sublimate]] in the descending flow and accelerate. It can give it a speed of descent reaching the 20
==References==
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