Conditional symmetric instability: Difference between revisions

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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 aan inclined plane with respect to the two axes mentioned and that is why it can give rise to a so-called "slantwise convection" if the air parcel is almost saturated and moved laterally and vertically in a CSI area. This concept is mainly used in meteorology to explain the mesoscale formation of intense [[Rainband|precipitation bands]] in an otherwise stable region, such as in front of a [[warm front]].<ref name="AMS">{{cite web | url= http://glossary.ametsoc.org/wiki/Conditional_symmetric_instability | title= Slantwise convection | publisher= [[American Meteorological Society]] | work= Meteorology Glossary | accessdate= August 23, 2019}}</ref><ref name="AMS2">{{cite web | url= http://glossary.ametsoc.org/wiki/Symmetric_instability | title= SymetricSymmetric instability | publisher= [[American Meteorological Society]] | work= Meteorology Glossary | accessdate= August 23, 2019}}</ref> The same phenomenon is also applicable to oceanography.

==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|author1-link=Charles A. Doswell III}}

</ref> :

::* '''If <math>\theta_e</math> diminish with altitude leads to unstable airmass'''

::* '''If <math>\theta_e</math> remains the same with altitude leads to neutral airmass'''

::* '''If <math>\theta_e</math> increase with altitude leads to stable airmass.'''

===Inertial Stability===

[[File:Tourbillon total faible.png|thumb|Dark zones are regions of weak inertial stability in atmopshericatmospheric circulation.]]

In the same way, a lateral displacement of an air particle changes its absolute vortexvorticity η<math>\eta</math>. TheThis latteris consistsgiven by the sum of the planetary vorticity, <math>f</math>, the [[Coriolis parameter]], and <math>\zeta</math>, the [[Geostrophic wind|geostrophic vortex]] (or relative) vorticity of the parcel:<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_rv}{\partial x} - \frac{\partial u_ru}{\partial y} \right ] + f = \zeta + f \qquad \qquad </math></center>}}

Where :

* <math>v</math> and <math>u</math> are the meridional and zonal geostrophic velocities respectively.

* Vg is the component of the [[geostrophic wind]] in the motion direction

*<math>x</math> and <math>y</math> correspond to the zonal and meridional coordinates.

* x is the displacement in this direction.

* ''<math>f</math>'' is the [[Coriolis parameter]], which describes the component of vorticity around the local vertical that results from the rotation of the reference frame.

* ''<math>f</math>'' increases towards the poles and decreases towards the equator

* ''<math>\zeta</math>'' variesis accordingthe torelative vorticity around the pressurelocal gradient:vertical. positiveIt foris afound rotationby anti-clockwisetaking andthe negativevertical forcomponent aof the curl of the clockwisegeostrophic rotationvelocity.

<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 .<ref name="Moore" />.

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= 10–53 | archive-url= https://web.archive.org/web/20141221040317/http://www.comet.ucar.edu/class/rfc_hydromet/03-1/docs/Moore/Mesoinstab/Meso-proc.ppt | archive-date= December 21, 2014 | url-status= dead }}</ref><ref name=Schultz>{{cite journal | language = en | title= The Use and Misuse of Conditional Symmetric Instability | first1= David M. | last1 = Schultz | first2= Philip N. | last2= Schumacher | journal = [[Monthly Weather Review]] | volume = 127 | issue = 12 | pages = 2709 | date = December 1999 | doi = 10.1175/1520-0493(1999)127<2709:TUAMOC>2.0.CO;2| publisher= [[American Meteorological Society|AMS]] | s2cid= 708227 | issn = 1520-0493| doi-access = free }}</ref>

| title= Mesoscale Processes | publisher= [[University Corporation for Atmospheric Research|UCAR]] | accessdate= August 23, 2019 | date= 2001 | pages= 10-53 }}</ref><ref name=Schultz>{{cite journal | language = en | format= pdf | url = http://journals.ametsoc.org/doi/pdf/10.1175/1520-0493%281999%29127%3C2709%3ATUAMOC%3E2.0.CO%3B2 | title= The Use and Misuse of Conditional Symmetric Instability | first1= David M. | last1 = Schultz | first2= Philip N. | last2= Schumacher | journal = [[Monthly Weather Review]] | volume = 127 | issue = 12 | date = December 1999 | doi = 10.1175/1520-0493(1999)127<2709:TUAMOC>2.0.CO;2| publisher= [[American Meteorological Society|AMS]] | accessdate=August 23, 2019 | issn = 1520-0493}}</ref> :

*<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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;Lateral movement A

Horizontal accelerations (to the left or right of a surface <math> \scriptstyle M_g </math>) are due to an increase/decrease in the <math> \scriptstyle M_g </math> of the environment in which the particle moves. In these cases, the particle accelerates or slows down to adjust to its new environment. Particule A undergoes a horizontal acceleration that gives it positive [[buoyancy]] as it moves to colder air and decelerates as it moves to a region of smaller <math> \scriptstyle M_g </math>. The particle rises and eventually becomes colder than its new environment. At this point, sheit has negative buoyancy and begins to descend. In doing so, <math> \scriptstyle M_g </math> increases and the particle returns to its original position.<ref name = "Moore"/><ref name=Schultz/>

;Vertical displacement B

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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 .<ref name = "Moore"/>.

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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==Potential effects==

[[File:Snowcsi.gif|thumb|Zones of CSI (solid blue) and banded snow (dash green) along dethe warm front, near the low pressure area.]]

CSI is usually embedded in large areas of vertical upward motion. The ideal situation is a geostrophic flow from the South with wind speeds that increase with height. The environment is well mixed and close to saturation. Since the flow is unidirectional, the u component of the wind can be set equal to zero, which establishes a symmetrical flow perpendicular to the temperature gradient in the air mass. This type of flow is typically found in baroclinic atmospheres with cold air to the west.<ref name=Schultz/>

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forms along the front, near the low pressure area and the CSI.

{{clr}}

===SlantiseSlantwise 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 ana 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 ana 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 .<ref name=Schultz/>. As the motion is in an area near saturation, the particle remains very close to the [[Lapse rate#Moist adiabatic lapse rate|moist adiabatic lapse rate]] which gives it a limited [[Convective available potential energy]] (CAPE). The rate of climb in a slantwise convection zone ranges from a few tens of centimeters per second to a few meters per second.<ref name=Schultz/>. This is usually below the climbing speed limit in a [[cumulonimbus]], iei.e. 5 &nbsp;m/s, which gives [[lightning]] and limit the occurrence of it with CSI.<ref name=Schultz/>. It is however possible in:<ref name=Schultz/>

* 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 &nbsp;m/s.<ref name=Schultz/> This effect is associated with the descent to the ground of the ''[[Sting jet]]''.<ref name="Vaughan">{{cite web | language = en | format = ppt | url = http://eumetrain.org/data/2/236/236.pptx | title = Sting Jets | author = Geraint Vaughan | website = eumetrain.org | accessdate=December 18, 2014}}</ref>

==References==