![Northeast Snowfall Impact Scale](https://upload.wikimedia.org/wikipedia/commons/7/7e/Northeast_Snowfall_Impact_Scale.gif)
Conditional symmetric instability, or CSI, is a form of
convective instability
In meteorology, convective instability or stability of an air mass refers to its ability to resist vertical motion. A ''stable'' atmosphere makes vertical movement difficult, and small vertical disturbances dampen out and disappear. In an ''unst ...
in a fluid subject to temperature differences in a uniform rotation
frame of reference
In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both mathema ...
while it is thermally stable in the vertical and dynamically in the horizontal (inertial stability). The instability in this case develop only in an 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
precipitation bands in an otherwise stable region, such as in front of a
warm front
A warm front is a density discontinuity located at the leading edge of a homogeneous warm air mass, and is typically located on the equator-facing edge of an isotherm gradient. Warm fronts lie within broader troughs of low pressure than cold fro ...
.
The same phenomenon is also applicable to oceanography.
Principle
Hydrostatic stability
![Convective_instability_animation_12Z_21Z_Jan08](https://upload.wikimedia.org/wikipedia/commons/2/2b/Convective_instability_animation_12Z_21Z_Jan08.gif)
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 Equivalent potential temperature, commonly referred to as theta-e \left( \theta_e \right), is a quantity that is conserved during changes to an air parcel's pressure (that is, during vertical motions in the Earth's atmosphere, atmosphere), even if w ...
(
):
[
]
::* If
diminish with altitude leads to unstable airmass
::* If
remains the same with altitude leads to neutral airmass
::* If
increase with altitude leads to stable airmass.
Inertial Stability
![Tourbillon total faible](https://upload.wikimedia.org/wikipedia/commons/6/67/Tourbillon_total_faible.png)
In the same way, a lateral displacement of an air particle changes its absolute vorticity
. This is given by the sum of the planetary vorticity,
, and
, the
geostrophic
A geostrophic current is an oceanic current in which the pressure gradient force is balanced by the Coriolis effect. The direction of geostrophic flow is parallel to the isobars, with the high pressure to the right of the flow in the Northern ...
(or relative) vorticity of the parcel:
Where :
*
and
are the meridional and zonal geostrophic velocities respectively.
*
and
correspond to the zonal and meridional coordinates.
* ''
'' is the
Coriolis parameter
The Coriolis frequency ''ƒ'', also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate ''Ω'' of the Earth multiplied by the sine of the latitude \varphi.
:f = 2 \Omega \sin \varphi.\,
The rotation rate ...
, which describes the component of vorticity around the local vertical that results from the rotation of the reference frame.
* ''
'' is the relative vorticity around the local vertical. It is found by taking the vertical component of the curl of the geostrophic velocity.
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
The synoptic scale in meteorology (also known as large scale or cyclonic scale) is a horizontal length scale of the order of 1000 kilometers (about 620 miles) or more. This corresponds to a horizontal scale typical of mid-latitude depressions (e. ...
, one can consider that the atmosphere is generally stable for lateral movement. Inertial stability is low only when
is close to zero. Since
is always positive,
can be satisfied only on the anticyclonic side of a strong maximum of
jet stream
Jet streams are fast flowing, narrow, meandering thermal wind, air currents in the Atmosphere of Earth, atmospheres of some planets, including Earth. On Earth, the main jet streams are located near the altitude of the tropopause and are west ...
or in a
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
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
indicate the stability:
*
, the particle then remains at the new position because its momentum has not changed
*
, the particle returns to its original position because its momentum is greater than that of the environment
*
, the particle continues its displacement because its momentum is smaller than that of the environment.
Slantwise movement
![Déplacement dans instabilité symétrique conditionnelle](https://upload.wikimedia.org/wikipedia/commons/c/cc/D%C3%A9placement_dans_instabilit%C3%A9_sym%C3%A9trique_conditionnelle.png)
Under certain stable hydrostatic and inertial conditions, slantwise displacement may, however, be unstable when the particle changes air mass or wind regime. The figure on the right shows such a situation. The displacement of the air particle is done with respect to kinetic moment lines (
) that increase from left to right and equivalent potential temperature (
) that increase with height.
;Lateral movement A
Horizontal accelerations (to the left or right of a surface
) are due to an increase/decrease in the
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
Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the p ...
as it moves to colder air and decelerates as it moves to a region of smaller
. The particle rises and eventually becomes colder than its new environment. At this point, it has negative buoyancy and begins to descend. In doing so,
increases and the particle returns to its original position.
[
;Vertical displacement B
Vertical movements in this case result in negative buoyancy as the particle encounters warmer air ( increases with height) and horizontal acceleration as it moves to larger surfaces . As the particle goes down, its decreases to fit the environment and the particle returns to B.][
; Slantwise displacement C
Only case C is unstable. Horizontal acceleration combines with a vertical upward disturbance and allows oblique displacement. Indeed, the of the particle is larger than the 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:[
* the slope of is greater than that of
* Laterally displaced air is almost saturated.
]
Potential effects
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.[
The image to the right shows such a situation in winter with CSI associated with negative equivalent ]potential vorticity
In fluid mechanics, potential vorticity (PV) is a quantity which is proportional to the dot product of vorticity and stratification. This quantity, following a parcel of air or water, can only be changed by diabatic or frictional processes. It i ...
() near a warm front. Banded snow
forms along the front, near the low pressure area and the CSI.
Slantwise convection
If a particle is climbing in a 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
The synoptic scale in meteorology (also known as large scale or cyclonic scale) is a horizontal length scale of the order of 1000 kilometers (about 620 miles) or more. This corresponds to a horizontal scale typical of mid-latitude depressions (e. ...
upward acceleration in a CSI layer produces parallel bands of heavy rainfall.
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
In meteorology, precipitation is any product of the condensation of atmospheric water vapor that falls under gravitational pull from clouds. The main forms of precipitation include drizzle, rain, sleet, snow, ice pellets, graupel and hail. ...
within a region otherwise stratiform clouds.[ As the motion is in an area near saturation, the particle remains very close to the ]moist adiabatic lapse rate
The lapse rate is the rate at which an atmospheric variable, normally temperature in Earth's atmosphere, falls with altitude. ''Lapse rate'' arises from the word ''lapse'', in the sense of a gradual fall. In dry air, the adiabatic lapse rate is ...
which gives it a limited Convective available potential energy
In meteorology, convective available potential energy (commonly abbreviated as CAPE), is the integrated amount of work that the upward (positive) buoyancy force would perform on a given mass of air (called an air parcel) if it rose vertically thr ...
(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.[ This is usually below the climbing speed limit in a ]cumulonimbus
Cumulonimbus (from Latin ''cumulus'', "heaped" and ''nimbus'', "rainstorm") is a dense, towering vertical cloud, typically forming from water vapor condensing in the lower troposphere that builds upward carried by powerful Buoyancy, buoyant air ...
, i.e. 5 m/s, which gives lightning
Lightning is a naturally occurring electrostatic discharge during which two electric charge, electrically charged regions, both in the atmosphere or with one on the land, ground, temporarily neutralize themselves, causing the instantaneous ...
and limit the occurrence of it with CSI.[ It is however possible in:][
* The trailing precipitation region of ]mesoscale convective system
A mesoscale convective system (MCS) is a complex of thunderstorms that becomes organized on a scale larger than the individual thunderstorms but smaller than extratropical cyclones, and normally persists for several hours or more. A mesoscale con ...
s.
* Wintertime convection because the lower and colder tropopause
The tropopause is the atmospheric boundary that demarcates the troposphere from the stratosphere; which are two of the five layers of the atmosphere of Earth. The tropopause is a thermodynamic gradient-stratification layer, that marks the end of ...
is helping the ionization of upward moving ice crystals.
* In the eyewall
The eye is a region of mostly calm weather at the center of tropical cyclones. The eye of a storm is a roughly circular area, typically in diameter. It is surrounded by the ''eyewall'', a ring of towering thunderstorms where the most severe weat ...
during the deepening phase of mature hurricanes, although rarely as it is a region symmetrically neutral and is generally free of lightning activity.
Slantwise convection bands have several characteristics:[
# They are parallel
# They are parallel to the ]thermal wind
The thermal wind is the vector difference between the geostrophic wind at upper altitudes minus that at lower altitudes in the atmosphere. It is the hypothetical vertical wind shear that would exist if the winds obey geostrophic balance in the ...
# They move with the general circulation
# The space between the bands is proportional to the thickness of the CSI layer
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 sublimate in the descending flow and accelerate. It can give it a speed of descent reaching the 20 m/s.[ This effect is associated with the descent to the ground of the '' Sting jet''.]
References
External links
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{{Meteorological variables
Fluid mechanics
Meteorological concepts
Weather prediction
Physical oceanography
Atmospheric thermodynamics
Severe weather and convection