Convective available potential energy

Meteorology

Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...

, convective available potential energy (CAPE)
, sometimes, simply, available potential energy (APE), is the amount of energy

Energy

In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

a parcel

Air parcel

In fluid dynamics, within the framework of continuum mechanics, a fluid parcel is a very small amount of fluid, identifiable throughout its dynamic history while moving with the fluid flow. As it moves, the mass of a fluid parcel remains constant, while—in a compressible flow—its volume may...

of air would have if lifted a certain distance vertically through the atmosphere. CAPE is effectively the positive buoyancy

Buoyancy

In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...

of an air parcel and is an indicator of atmospheric instability, which makes it valuable in predicting severe weather

Severe weather

Severe weather phenomena are weather conditions that are hazardous to human life and property.- Examples Include :Severe weather can occur under a variety of situations, but three characteristics are generally needed: a temperature or moisture boundary, moisture, and , instability in the...

. It is a form of fluid instability found in thermally stratified atmospheres in which a colder fluid overlies a warmer one. As explained below, when an air mass is unstable, the element of the air mass that is displaced upwards is accelerated by the pressure differential between the displaced air and the ambient air at the (higher) altitude to which it was displaced. This usually creates vertically developed clouds from convection, due to the rising motion, which can eventually lead to thunderstorms. It could also be created in other phenomenon, such as a cold front. Even if the air is cooler on the surface, there is still warmer air in the mid-levels, that can rise into the upper-levels. However, if there is not enough water vapor present, there is no ability for condensation, thus storms, clouds, and rain will not form.

Mechanics

CAPE exists within the conditionally unstable layer of the troposphere

Troposphere

The troposphere is the lowest portion of Earth's atmosphere. It contains approximately 80% of the atmosphere's mass and 99% of its water vapor and aerosols....

, the free convective layer

Free convective layer

In atmospheric sciences, the free convective layer is the layer of conditional or potential instability in the troposphere. It is a layer of positive buoyancy and is the layer where deep, moist convection can occur. On an atmospheric sounding, it is the layer between the level of free...

(FCL), where an ascending air parcel is warmer than the ambient air. CAPE is measured in joule

Joule

The joule ; symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended in applying a force of one newton through a distance of one metre , or in passing an electric current of one ampere through a resistance of one ohm for one second...

s per kilogram of air (J/kg). Any value greater than 0 J/kg indicates instability and the possibility of thunderstorms. Generic CAPE is calculated by integrating

Integral

Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...

vertically the local buoyancy of a parcel from the level of free convection

Level of free convection

The level of free convection is the altitude in the atmosphere where the temperature of the environment decreases faster than the moist adiabatic lapse rate of a saturated air parcel at the same level....

(LFC) to the equilibrium level

Equilibrium level

In meteorology, the equilibrium level , or level of neutral buoyancy , or limit of convection , is the height at which a rising parcel of air is at a temperature of equal warmth to it....

(EL):

Where

and

are, respectively, the heights of the levels of free convection and equilibrium (neutral buoyancy),

is the virtual temperature

Virtual temperature

In atmospheric thermodynamics, the virtual temperature T_v of a moist air parcel is the temperature at which a theoretical dry air parcel would have a total pressure and density equal to the moist parcel of air.-Description:...

of the specific parcel,

is the virtual temperature of the environment, and

is the acceleration due to gravity

Standard gravity

Standard gravity, or standard acceleration due to free fall, usually denoted by g0 or gn, is the nominal acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely , or about...

. CAPE for a given region is most often calculated from a thermodynamic

Thermodynamic diagrams

Thermodynamic diagrams are diagrams used by scientists and engineers to represent the thermodynamic states of a material and the consequences of manipulating this material...

or sounding

Atmospheric sounding

An atmospheric sounding is a measurement of vertical distribution of physical properties of the atmospheric column such as pressure, temperature, wind speed and wind direction , liquid water content, ozone concentration, pollution, and other properties...

diagram (e.g., a Skew-T log-P diagram

Skew-T log-P diagram

A Skew-T Log-P diagram is one of four thermodynamic diagrams commonly used in weather analysis and forecasting. In 1947, N. Herlofson proposed a modification to the emagram which allows straight, horizontal isobars, and provides for a large angle between isotherms and dry adiabats, similar to that...

) using air temperature

Temperature

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

and dew point

Dew point

The dew point is the temperature to which a given parcel of humid air must be cooled, at constant barometric pressure, for water vapor to condense into liquid water. The condensed water is called dew when it forms on a solid surface. The dew point is a saturation temperature.The dew point is...

data usually measured by a weather balloon

Weather balloon

A weather or sounding balloon is a balloon which carries instruments aloft to send back information on atmospheric pressure, temperature, humidity and wind speed by means of a small, expendable measuring device called a radiosonde...

.

CAPE is effectively positive buoyancy

Buoyancy

, expressed B+ or simply B; the opposite of convective inhibition (CIN)

Convective inhibition

Convective inhibition is a numerical measure in meteorology that indicates the amount of energy that will prevent an air parcel from rising from the surface to the level of free convection....

, 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 m²/s², 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

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. CAPE may also exist below the LFC, but if a layer of CIN (subsidence

Subsidence

Subsidence is the motion of a surface as it shifts downward relative to a datum such as sea-level. The opposite of subsidence is uplift, which results in an increase in elevation...

) is present, it is unavailable to deep, moist convection until CIN is exhausted. When there is mechanical lift to saturation, cloud base

Cloud base

This article refers to meteorology. For the airborne base of the TV series Captain Scarlet and the Mysterons, see Cloudbase.The cloud base is the lowest altitude of the visible portion of the cloud...

begins at the lifted condensation level

Lifted condensation level

The lifted condensation level or lifting condensation level is formally defined as the height at which the relative humidity of an air parcel will reach 100% when it is cooled by dry adiabatic lifting...

(LCL); absent forcing, cloud base

Cloud base

begins at the convective condensation level

Convective condensation level

The convective condensation level represents the height where an air parcel becomes saturated when lifted adiabatically to achieve buoyant ascent. It marks where cloud base begins when air is heated from below to the convective temperature, without mechanical lift...

(CCL) where heating from below causes spontaneous buoyant lifting to the point of condensation

Condensation

Condensation is the change of the physical state of matter from gaseous phase into liquid phase, and is the reverse of vaporization. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition....

when the convective temperature

Convective temperature

The convective temperature is the approximate temperature that air near the surface must reach for cloud formation without mechanical lift. In such case, cloud base begins at the convective condensation level , whilst with mechanical lifting, condensation begins at the lifted condensation level...

is reached. When CIN is absent or is overcome, saturated parcels at the LCL or CCL, which had been small cumulus cloud

Cumulus cloud

Cumulus clouds are a type of cloud with noticeable vertical development and clearly defined edges. Cumulus means "heap" or "pile" in Latin. They are often described as "puffy" or "cotton-like" in appearance. Cumulus clouds may appear alone, in lines, or in clusters...

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 downdrafts. 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).

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 the 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.

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 where instability is dependent on the motion of air and its associated effects such as dynamic lifting.

Significance to thunderstorms

Thunderstorm

A thunderstorm, also known as an electrical storm, a lightning storm, thundershower or simply a storm is a form of weather characterized by the presence of lightning and its acoustic effect on the Earth's atmosphere known as thunder. The meteorologically assigned cloud type associated with the...

s form when air parcel

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 atmosphere

Earth's atmosphere

The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

is warm at the surface and lower levels of the troposphere

Troposphere

The troposphere is the lowest portion of Earth's atmosphere. It contains approximately 80% of the atmosphere's mass and 99% of its water vapor and aerosols....

where there is mixing

Mixed layer

The oceanic or limnological mixed layer is a layer in which active turbulence has homogenized some range of depths. The surface mixed layer is a layer where this turbulence is generated by winds, cooling, or processes such as evaporation or sea ice formation which result in an increase in salinity...

(the planetary boundary layer (PBL)

Planetary boundary layer

The planetary boundary layer , also known as the atmospheric boundary layer , is the lowest part of the atmosphere and its behavior is directly influenced by its contact with a planetary surface. On Earth it usually responds to changes in surface forcing in an hour or less...

), 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

Lapse rate

The lapse rate is defined as the rate of decrease with height for an atmospheric variable. The variable involved is temperature unless specified otherwise. The terminology arises from the word lapse in the sense of a decrease or decline; thus, the lapse rate is the rate of decrease with height and...

. When the rising air parcel cools more slowly than the surrounding atmosphere, it remains warmer and less dense

Density of air

The density of air, ρ , is the mass per unit volume of Earth's atmosphere, and is a useful value in aeronautics and other sciences. Air density decreases with increasing altitude, as does air pressure. It also changes with variances in temperature or humidity...

. The parcel continues to rise freely (convectively

Convection

Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....

; without mechanical lift) through the atmosphere until it reaches an area of air less dense (warmer) than itself.

The amount of and shape of the positive area modulates the speed of updrafts, extreme CAPE can result in explosive thunderstorm development; such rapid development usually occurs when CAPE stored by a capping inversion

Capping inversion

A capping inversion is an elevated inversion layer that caps a convective boundary layer.The boundary layer is the part of the atmosphere which is closest to the ground. Normally, the sun heats the ground, which in turn heats the air just above it. Thermals form when this warm air rises into the...

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

Tornadogenesis

Tornadogenesis is the process by which a tornado forms. There are many types of tornadoes, and each type of tornado can have several different methods of formation. Scientific study is ongoing, as some aspects of tornado formation remain a mystery....

. The most important CAPE for tornado

Tornado

A tornado is a violent, dangerous, rotating column of air that is in contact with both the surface of the earth and a cumulonimbus cloud or, in rare cases, the base of a cumulus cloud. They are often referred to as a twister or a cyclone, although the word cyclone is used in meteorology in a wider...

es is within the lowest 1 to 3 km (0.6 to 1.9 mi), whilst deep layer CAPE and the width of CAPE at mid-levels is important for supercell

Supercell

A supercell is a thunderstorm that is characterized by the presence of a mesocyclone: a deep, continuously-rotating updraft. For this reason, these storms are sometimes referred to as rotating thunderstorms...

s). Tornado outbreak

Tornado outbreak

While there is no single agreed upon definition, generally at least 6-10 tornadoes produced by the same synoptic scale weather system is considered a tornado outbreak. The tornadoes usually occur within the same day, or continue into the early morning hours of the succeeding day, and within the...

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.

Two notable days for severe weather exhibited CAPE values over 5,000 J/kg. Two hours before the 1999 Oklahoma tornado outbreak occurred on May 3, 1999, the CAPE value sounding at Oklahoma City

Oklahoma City, Oklahoma

Oklahoma City is the capital and the largest city in the state of Oklahoma. The county seat of Oklahoma County, the city ranks 31st among United States cities in population. The city's population, from the 2010 census, was 579,999, with a metro-area population of 1,252,987 . In 2010, the Oklahoma...

was at 5,885 J/kg. A few hours later, an F5

Fujita scale

The Fujita scale , or Fujita-Pearson scale, is a scale for rating tornado intensity, based primarily on the damage tornadoes inflict on human-built structures and vegetation...

tornado ripped through the southern suburbs of the city. Also on May 4, 2007 CAPE values of 5,500 J/kg were reached and an EF5

Enhanced Fujita Scale

The Enhanced Fujita Scale rates the strength of tornadoes in the United States based on the damage they cause.Implemented in place of the Fujita scale introduced in 1971 by Ted Fujita, it began operational use on February 1, 2007. The scale has the same basic design as the original Fujita scale:...

tornado

May 2007 Tornado Outbreak

The May 2007 Tornado Outbreak was an extended tornado outbreak that started on May 4, 2007, affecting portions of the Central United States. The most destructive tornado in the outbreak occurred on the evening of May 4 in western Kansas, where about 95% of the city of Greensburg in Kiowa County was...

tore through Greensburg, Kansas

Greensburg, Kansas

Greensburg is a city in and the county seat of Kiowa County, Kansas, United States. As of the 2010 census, the city population was 777. Greensburg is also home to the world's largest hand-dug well....

. 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

Plainfield, Illinois

Plainfield is a village in Will County, Illinois, United States. As of the 2007 special census, the population is 37,334.The Village includes land in Plainfield and Wheatland townships. Part of Plainfield is located in Kendall County...

on August 28, 1990 and Jarrell, Texas

Jarrell, Texas

Jarrell is a city in Williamson County, Texas, United States and is located about 12 miles north of Georgetown, Texas or about 38 miles north of Austin. and 1,448 according to a 2008 Census Bureau estimate.. The total population is 984 according to the 2010 census.-History:Founded in 1909 by real...

on May 27, 1997 on days which weren't readily apparent as conducive to large tornadoes. CAPE was estimated to exceed 8,000 J/kg in the environment of the Plainfield storm

Plainfield Tornado

The 1990 Plainfield tornado was a devastating tornado that occurred on the afternoon of Tuesday, August 28, 1990. The violent tornado killed 29 people and injured 353. It is the only F5 tornado ever recorded in August and the only F5 tornado to ever strike the Chicago area...

and was around 7,000 J/kg for the Jarrell storm.

Severe weather and tornadoes can develop in an area of low CAPE values. The surprise severe weather event that occurred in Illinois

Illinois

Illinois is the fifth-most populous state of the United States of America, and is often noted for being a microcosm of the entire country. With Chicago in the northeast, small industrial cities and great agricultural productivity in central and northern Illinois, and natural resources like coal,...

and Indiana

Indiana

Indiana is a US state, admitted to the United States as the 19th on December 11, 1816. It is located in the Midwestern United States and Great Lakes Region. With 6,483,802 residents, the state is ranked 15th in population and 16th in population density. Indiana is ranked 38th in land area and is...

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.

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

Troposphere

The troposphere is the lowest portion of Earth's atmosphere. It contains approximately 80% of the atmosphere's mass and 99% of its water vapor and aerosols....

, a hydrolapse (an area of rapidly decreasing dew point temperatures with height) results in the region where the moist boundary layer

Boundary layer

In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface where effects of viscosity of the fluid are considered in detail. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by diurnal...

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. Due 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

Convection

Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....

. 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 eventually escapes as a rapidly rising bubble of humid air triggering the development of a cumulus

Cumulus cloud

or cumulonimbus cloud.

External links

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Mechanics

Significance to thunderstorms

Example from meteorology

Further reading

External links