Convective available potential energy

2025-10-16T20:59:22Z

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{{Short description|Measure of instability in the air as a buoyancy force}}
{{Technical|date=November 2014}}
[[File:Convective instability animation 12Z 21Z Jan08.gif|thumb|350px|right|A skew-T plot showing a morning sounding with a large hydrolapse followed by an afternoon sounding showing the cooling (red curve moving to the left) which occurred in the mid-levels resulting in an unstable atmosphere as surface parcels have now become negatively buoyant. The red line is temperature, the green line is the dew point, and the black line is the air parcel lifted.]]

In [[meteorology]], '''convective available potential energy''' (commonly abbreviated as '''CAPE'''),<ref>{{cite journal | author = M. W. Moncrieff, M.J. Miller | year = 1976 | title = The dynamics and simulation of tropical cumulonimbus and squall lines | journal = Q. J. R. Meteorol. Soc. | volume = 120 | pages = 373–94 | doi = 10.1002/qj.49710243208 |bibcode = 1976QJRMS.102..373M | issue = 432 }}</ref> is a measure of the capacity of the atmosphere to support upward air movement that can lead to cloud formation and storms. Some atmospheric conditions, such as very warm, moist, air in an atmosphere that cools rapidly with height, can promote strong and sustained upward air movement, possibly stimulating the formation of [[Cumulus cloud|cumulus]] clouds or [[cumulonimbus cloud|cumulonimbus]] (thunderstorm) clouds. In that situation the potential energy of the atmosphere to cause upward air movement is very high, so CAPE (a measure of potential energy) would be high and positive. By contrast, other conditions, such as a less warm air parcel or a parcel in an atmosphere with a [[Inversion (meteorology)|temperature inversion]] (in which the temperature increases above a certain height) have much less capacity to support vigorous upward air movement, thus the potential energy level (CAPE) would be much lower, as would the probability of thunderstorms.

More technically, CAPE is the integrated amount of [[Work (physics)|work]] that the upward (positive) [[Buoyancy|buoyancy force]] would perform on a given mass of air (called an [[air parcel]]) if it rose vertically through the entire atmosphere. Positive CAPE will cause the air parcel to rise, while negative CAPE will cause the air parcel to sink.
Nonzero CAPE is an indicator of [[atmospheric instability]] in any given [[atmospheric sounding]], a necessary condition for the development of [[Cumulus cloud|cumulus]] and [[Cumulonimbus cloud|cumulonimbus]] clouds with attendant [[severe weather]] hazards.

== Mechanics ==
[[File:B and LCL-LFC.jpg|thumb|right|300px|A Skew-T diagram with important features labeled]]
CAPE exists within the [[conditional instability|conditionally unstable]] layer of the [[troposphere]], the [[free convective layer]] (FCL), where an ascending air parcel is warmer than the ambient air. CAPE is measured in [[joule]]s per kilogram of air (J/kg). Any value greater than 0 J/kg indicates instability and an increasing possibility of thunderstorms and hail. Generic CAPE is calculated by [[Integral|integrating]] vertically the local buoyancy of a parcel from the [[level of free convection]] (LFC) to the [[equilibrium level]] (EL):
<math display="block">\mathrm{CAPE} = \int_{z_\mathrm{f}}^{z_\mathrm{n}} g \left(\frac{T_\mathrm{v,parcel} - T_\mathrm{v,env}}{T_\mathrm{v,env}}\right) \, dz</math>

Where <math>z_\mathrm{f}</math> is the height of the level of free convection and <math>z_\mathrm{n}</math> is the height of the equilibrium level (neutral buoyancy), where <math>T_\mathrm{v,parcel}</math> is the [[virtual temperature]] of the specific parcel, where <math>T_\mathrm{v,env}</math> is the virtual temperature of the environment (note that temperatures must be in the Kelvin scale), and where <math>g</math> is the [[standard gravity|acceleration due to gravity]]. This integral is the work done by the buoyant force minus the work done against gravity, hence it's the excess energy that can become kinetic energy.

CAPE for a given region is most often calculated from a [[thermodynamic diagrams|thermodynamic]] or [[atmospheric sounding|sounding]] diagram (e.g., a [[Skew-T log-P diagram]]) using air [[temperature]] and [[dew point]] data usually measured by a [[weather balloon]].

CAPE is effectively positive buoyancy, expressed ''B+'' or simply ''B''; the opposite of [[convective inhibition|convective inhibition (CIN)]], which is expressed as ''B-'', and can be thought of as "negative CAPE". As with CIN, CAPE is usually expressed in J/kg but may also be expressed as m<sup>2</sup>/s<sup>2</sup>, as the values are equivalent. In fact, CAPE is sometimes referred to as ''positive buoyant energy'' (''PBE''). This type of CAPE is the maximum energy available to an ascending parcel and to moist convection. When a layer of CIN is present, the layer must be eroded by surface heating or mechanical lifting, so that [[convective boundary layer]] parcels may reach their [[level of free convection]] (LFC).

On a sounding diagram, CAPE is the ''positive area'' above the LFC, the area between the parcel's virtual temperature line and the environmental virtual temperature line where the ascending parcel is warmer than the environment. Neglecting the virtual temperature correction may result in substantial relative errors in the calculated value of CAPE for small CAPE values.<ref>{{cite journal | author = [[Charles A. Doswell III]], E.N. Rasmussen |date=December 1994 | title = The Effect of Neglecting the Virtual Temperature Correction on CAPE Calculations | journal = Weather and Forecasting | volume = 9 | issue = 4 | pages = 625–9 | doi = 10.1175/1520-0434(1994)009<0625:TEONTV>2.0.CO;2|bibcode = 1994WtFor...9..625D | doi-access = free }}</ref> CAPE may also exist below the LFC, but if a layer of CIN ([[subsidence]]) is present, it is unavailable to deep, moist convection until CIN is exhausted. When there is mechanical lift to [[Saturated fluid|saturation]], [[cloud base]] begins at the [[lifted condensation level]] (LCL); absent forcing, [[cloud base]] begins at the [[convective condensation level]] (CCL) where heating from below causes spontaneous buoyant lifting to the point of [[condensation]] when the [[convective temperature]] is reached. When CIN is absent or is overcome, saturated parcels at the LCL or CCL, which had been small [[cumulus cloud]]s, will rise to the LFC, and then spontaneously rise until hitting the stable layer of the equilibrium level. The result is deep, moist convection (DMC), or simply, a thunderstorm.

When a parcel is unstable, it will continue to move vertically, in either direction, dependent on whether it receives upward or downward forcing, until it reaches a stable layer (though momentum, gravity, and other forcing may cause the parcel to continue). There are multiple types of CAPE, ''downdraft CAPE'' (''DCAPE''), estimates the potential strength of rain and evaporatively cooled [[downdraft]]s. Other types of CAPE may depend on the depth being considered. Other examples are ''surface based CAPE'' (''SBCAPE''), ''mixed layer'' or ''mean layer CAPE'' (''MLCAPE''), ''most unstable'' or ''maximum usable CAPE'' (''MUCAPE''), and ''normalized CAPE'' (''NCAPE'').<ref name="SPC parameters">{{cite web |last=Thompson |first=Rich |title=Explanation of SPC Severe Weather Parameters |publisher=[[Storm Prediction Center]] |year=2006 |url=http://www.spc.noaa.gov/exper/mesoanalysis/help/begin.html |access-date=2007-05-30 }}</ref>

Fluid elements displaced upwards or downwards in such an atmosphere expand or compress [[adiabatically]] in order to remain in pressure equilibrium with their surroundings, and in this manner become less or more dense.

If the adiabatic decrease or increase in density is ''less'' than the decrease or increase in the density of the ambient (not moved) medium, then the displaced fluid element will be subject to downwards or upwards pressure, which will function to restore it to its original position. Hence, there will be a counteracting force to the initial displacement. Such a condition is referred to as ''convective stability''.

On the other hand, if adiabatic decrease or increase in density is ''greater'' than in the ambient fluid, the upwards or downwards displacement will be met with an additional force in the same direction exerted by the ambient fluid. In these circumstances, small deviations from the initial state will become amplified. This condition is referred to as ''[[convective instability]]''.<ref>{{Cite book| last = Shu | first = Frank | title = The Physics of Astrophysics, volume II: Gas dynamics | year = 1992 | publisher = University Science Books | isbn=978-0-935702-65-1| bibcode = 1992pavi.book.....S }}</ref>

Convective instability is also termed ''static instability'', because the instability does not depend on the existing motion of the air; this contrasts with [[Dynamic instability (fluid mechanics)|dynamic instability]] where instability is dependent on the motion of air and its associated effects such as [[dynamic lifting]].

== Significance to thunderstorms ==
[[Thunderstorm]]s form when [[air parcel]]s are lifted vertically. Deep, moist convection requires a parcel to be lifted to the LFC where it then rises spontaneously until reaching a layer of non-positive buoyancy. The [[Earth's atmosphere|atmosphere]] is warm at the surface and lower levels of the [[troposphere]] where there is [[mixed layer|mixing]] (the [[planetary boundary layer|planetary boundary layer (PBL)]]), but becomes substantially cooler with height. The temperature profile of the atmosphere, the change in temperature, the degree that it cools with height, is the [[lapse rate]]. When the rising air parcel cools more slowly than the surrounding atmosphere, it remains warmer and less [[Density of air|dense]]. The parcel continues to rise freely ([[convection|convectively]]; without mechanical lift) through the atmosphere until it reaches an area of air less dense (warmer) than itself.

The amount, and shape, of the positive-buoyancy area modulates the speed of [[updraft]]s, thus extreme CAPE can result in explosive thunderstorm development; such rapid development usually occurs when CAPE stored by a [[capping inversion]] is released when the "lid" is broken by heating or mechanical lift. The amount of CAPE also modulates how low-level [[vorticity]] is entrained and then stretched in the [[updraft]], with importance to [[tornadogenesis]]. The most important CAPE for [[tornado]]es is within the lowest {{convert|1|to|3|km|mi|abbr=on}} of the atmosphere, whilst deep layer CAPE and the width of CAPE at mid-levels is important for [[supercell]]s. [[Tornado outbreak]]s tend to occur within high CAPE environments. Large CAPE is required for the production of very large hail, owing to updraft strength, although a rotating updraft may be stronger with less CAPE. Large CAPE also promotes lightning activity.<ref name="climatology parameters">{{cite journal |last=Craven |first=Jeffrey P. |author2=H.E. Brooks |title=Baseline climatology of sounding derived parameters associated with deep moist convection |journal=[[National Weather Digest]] |volume=28 |pages=13–24 |date=December 2004 |url=http://www.nssl.noaa.gov/users/brooks/public_html/papers/cravenbrooksnwa.pdf }}</ref>

Two notable days for severe weather exhibited CAPE values over 5 kJ/kg. Two hours before the [[1999 Oklahoma tornado outbreak]] occurred on May 3, 1999, the CAPE value sounding at [[Oklahoma City, Oklahoma|Oklahoma City]] was at 5.89 kJ/kg. A few hours later, an [[Fujita scale|F5]] tornado ripped through the southern suburbs of the city. Also on May 4, 2007, CAPE values of 5.5 kJ/kg were reached and an [[Enhanced Fujita Scale|EF5]] [[Greensburg tornado|tornado]] tore through [[Greensburg, Kansas]]. On these days, it was apparent that conditions were ripe for tornadoes and CAPE wasn't a crucial factor. However, extreme CAPE, by modulating the updraft (and downdraft), can allow for exceptional events, such as the deadly F5 tornadoes that hit [[Plainfield, Illinois]] on August 28, 1990, and [[Jarrell, Texas]] on May 27, 1997, on days which weren't readily apparent as conducive to large tornadoes. CAPE was estimated to exceed 8 kJ/kg in the environment of the [[Plainfield Tornado|Plainfield storm]] and was around 7 kJ/kg for the [[1997 Prairie Dell-Jarrell tornado|Jarrell storm]].

Severe weather and tornadoes can develop in an area of low CAPE values. The [[April 2004 Utica tornado outbreak|surprise severe weather event]] that occurred in [[Illinois]] and [[Indiana]] on April 20, 2004, is a good example. Importantly in that case, was that although overall CAPE was weak, there was strong CAPE in the lowest levels of the troposphere which enabled an outbreak of minisupercells producing large, long-track, intense tornadoes.<ref name="Utica outbreak">{{cite conference |first=Albert E. |last=Pietrycha |author-link=Albert E. Pietrycha |author2=J.M. Davies |author3=M. Ratzer |author4=P. Merzlock |title=Tornadoes in a Deceptively Small CAPE Environment: The 4/20/04 Outbreak in Illinois and Indiana |book-title=Preprints of the 22nd Conference on Severe Local Storms |publisher=[[American Meteorological Society]] |date=October 2004 |location=Hyannis, Massachusetts |url=http://ams.confex.com/ams/11aram22sls/techprogram/paper_81569.htm }}</ref>

== Example from meteorology ==
A good example of convective instability can be found in our own atmosphere. If dry mid-level air is drawn over very warm, moist air in the lower [[troposphere]], a [[hydrolapse]] (an area of rapidly decreasing dew point temperatures with height) results in the region where the moist [[boundary layer]] and mid-level air meet. As daytime heating increases mixing within the moist boundary layer, some of the moist air will begin to interact with the dry mid-level air above it. Owing to thermodynamic processes, as the dry mid-level air is slowly saturated its temperature begins to drop, increasing the [[adiabatic lapse rate]]. Under certain conditions, the lapse rate can increase significantly in a short amount of time, resulting in [[convection]]. High convective instability can lead to severe [[thunderstorms]] and [[tornadoes]] as moist air which is trapped in the boundary layer eventually becomes highly negatively buoyant relative to the adiabatic lapse rate and escapes as a rapidly rising bubble of humid air triggering the development of a [[Cumulus cloud|cumulus]] or [[cumulonimbus]] cloud.

== Limitations ==
As with most parameters used in [[meteorology]], there are some caveats to keep in mind, one of which is what CAPE represents physically and in what instances CAPE can be used. One example where the more common method for determining CAPE might start to break down is in the presence of [[tropical cyclones]] (TCs), such as tropical depressions, tropical storms, or [[hurricanes]].<ref>{{cite conference |title=Reversible CAPE in Tropical Cyclone Tornado Regimes |last1= Edwards |first1= Roger |author-link1= Roger Edwards (meteorologist)|last2= Thompson |first2= Richard |date= November 2014 |publisher= [[American Meteorological Society]] |location= Madison, WI |conference= 27th AMS Severe Local Storms Conference |doi= 10.13140/2.1.2530.5921 |url= https://www.researchgate.net/publication/270821803 }}</ref><ref>{{cite AV media |people= [[Roger Edwards (meteorologist)|Roger Edwards]] |date= July 7, 2017 |title= Tropical Cyclone Tornadoes: Dual-Pol Radar Applications and Reversible CAPE |type= YouTube Video |language= English |url= https://www.youtube.com/watch?v=_AhqdR_UNoM&ab_channel=NOAAWeatherPartners |access-date= December 27, 2021 |publisher= [[NOAA]]}}</ref>

The more common method of determining CAPE can break down near tropical cyclones because CAPE assumes that liquid water is lost instantaneously during [[condensation]]. This process is thus irreversible upon [[adiabatic]] descent. This process is not realistic for tropical cyclones. To make the process more realistic for tropical cyclones is to use Reversible CAPE (RCAPE for short). RCAPE assumes the opposite extreme to the standard convention of CAPE and is that no liquid water will be lost during the process. This new process gives parcels a greater [[density]] related to water loading.

RCAPE is calculated using the same formula as CAPE, the difference in the formula being in the [[virtual temperature]]. In this new formulation, we replace the parcel saturation [[mixing ratio]] (which leads to the [[condensation]] and vanishing of liquid water) with the parcel water content. This slight change can drastically change the values we get through the integration.

RCAPE does have some limitations, one of which is that RCAPE assumes no evaporation keeping consistent for the use within a TC but should be used sparingly elsewhere.

Another limitation of both CAPE and RCAPE is that currently, both systems do not consider [[entrainment (meteorology)|entrainment]].

== See also ==
{{Portal|Weather|Physics}}
* [[Atmospheric thermodynamics]]
* [[Lifted index]]
* [[Maximum potential intensity]]

== References ==
{{Reflist|colwidth=35em}}

== Further reading ==
* Barry, R.G. and Chorley, R.J. ''Atmosphere, weather and climate'' (7th ed) Routledge 1998 p. 80-81 {{ISBN|0-415-16020-0}}

== External links ==
*[https://earth.nullschool.net/#current/wind/surface/level/overlay=cape/winkel3 Map of current global CAPE]

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Convective available potential energy