Thelapse rate is the rate at which an atmospheric variable, normallytemperature inEarth's atmosphere, falls withaltitude.^[1][2]Lapse rate arises from the wordlapse (in its "becoming less" sense, not its "interruption" sense). In dry air, theadiabatic lapse rate (i.e., decrease in temperature of a parcel of air that rises in the atmosphere without exchanging energy with surrounding air) is 9.8 °C/km (5.4 °F per 1,000 ft). The saturated adiabatic lapse rate (SALR), or moist adiabatic lapse rate (MALR), is the decrease in temperature of a parcel of water-saturated air that rises in the atmosphere. It varies with the temperature and pressure of the parcel and is often in the range 3.6 to9.2 °C/km (2 to5 °F/1000 ft), as obtained from theInternational Civil Aviation Organization (ICAO). Theenvironmental lapse rate is the decrease in temperature of air with altitude for a specific time and place (see below). It can be highly variable between circumstances.

Lapse rate corresponds to the vertical component of thespatial gradient oftemperature. Although this concept is most often applied to the Earth'stroposphere, it can be extended to any gravitationally supportedparcel of gas.

A formal definition from theGlossary of Meteorology^[3] is:

The decrease of an atmospheric variable with height, the variable being temperature unless otherwise specified.

Typically, the lapse rate is the negative of the rate of temperature change with altitude change:

${\displaystyle \mathrm{\Gamma }=-\frac{\mathrm{d}T}{\mathrm{d}z}}$

where${\displaystyle \mathrm{\Gamma }}$ (sometimes${\displaystyle L}$) is the lapse rate given inunits of temperature divided by units of altitude,T is temperature, andz is altitude.^[a]

Theenvironmental lapse rate (ELR), is the actual rate of decrease of temperature with altitude in the atmosphere at a given time and location.^[6]

As an average, theInternational Civil Aviation Organization (ICAO) defines aninternational standard atmosphere (ISA) with a temperature lapse rate of6.50 °C/km^[7](3.56 °F or1.98 °C/1,000 ft) from sea level to 11 km(36,090 ft or6.8 mi). From 11 km up to 20 km(65,620 ft or12.4 mi), the constant temperature is−56.5 °C(−69.7 °F), which is the lowest assumed temperature in the ISA. Thestandard atmosphere contains no moisture.

Unlike the idealized ISA, the temperature of the actual atmosphere does not always fall at a uniform rate with height. For example, there can be aninversion layer in which the temperature increases with altitude.

The temperature profile of the atmosphere is a result of the interaction between radiative heating fromsunlight, cooling to space viathermal radiation, and upward heat transport vianatural convection (which carries hot air andlatent heat upward). Above thetropopause, convection does not occur and all cooling is radiative.

Within thetroposphere, the lapse rate is essentially the consequence of a balance between (a) radiative cooling of the air, which by itself would lead to a high lapse rate; and (b) convection, which is activated when the lapse rate exceeds a critical value; convection stabilizes the environmental lapse rate.^[8]

Sunlight hits the surface of the earth (land and sea) and heats them. The warm surface heats the air above it. In addition, nearly a third of absorbed sunlight is absorbed within the atmosphere, heating the atmosphere directly.^[9]

Thermal conduction helps transfer heat from the surface to the air; this conduction occurs within the few millimeters of air closest to the surface. However, above that thin interface layer, thermal conduction plays a negligible role in transferring heat within the atmosphere; this is because the thermal conductivity of air is very low.^{[10][11]: 387}

The air is radiatively cooled bygreenhouse gases (water vapor, carbon dioxide, etc.) and clouds emittinglongwave thermal radiation to space.^[12]

Ifradiation were the only way to transfer energy within the atmosphere, then the lapse rate near the surface would be roughly 40 °C/km and thegreenhouse effect of gases in the atmosphere would keep the ground at roughly 333 K (60 °C; 140 °F).^{[13]: 59–60}

However, when air gets hot or humid, its density decreases.^[14][15] Thus, air which has been heated by the surface tends to rise and carry internal energy upward, especially if the air has been moistened by evaporation from water surfaces. This is the process ofconvection. Vertical convective motion stops when a parcel of air at a given altitude has the same density as the other air at the same elevation.

Convection carries hot, moist air upward and cold, dry air downward, with a net effect of transferring heat upward. This makes the air below cooler than it would otherwise be and the air above warmer. Because convection is available to transfer heat within the atmosphere, the lapse rate in the troposphere is reduced to around 6.5 °C/km^[8] and the greenhouse effect is reduced to a point where Earth has its observed surface temperature of around 288 K (15 °C; 59 °F).

As convection causes parcels of air to rise or fall, there is little heat transfer between those parcels and the surrounding air. Air has lowthermal conductivity, and the bodies of air involved are very large; so transfer of heat byconduction is negligibly small. Also, intra-atmospheric radiative heat transfer is relatively slow and so is negligible for moving air. Thus, when air ascends or descends, there is little exchange of heat with the surrounding air. A process in which no heat is exchanged with the environment is referred to as anadiabatic process.

Air expands as it moves upward, and contracts as it moves downward. The expansion of rising air parcels, and the contraction of descending air parcels, areadiabatic processes, to a good approximation. When a parcel of air expands, it pushes on the air around it, doingthermodynamic work. Since the upward-moving and expanding parcel does work but gains no heat, it losesinternal energy so that its temperature decreases. Downward-moving and contracting air has work done on it, so it gains internal energy and its temperature increases.

Adiabatic processes for air have a characteristic temperature-pressure curve. As air circulates vertically, the air takes on that characteristic gradient, called theadiabatic lapse rate. When the air contains little water, this lapse rate is known as the dry adiabatic lapse rate: the rate of temperature decrease is9.8 °C/km (5.4 °F per 1,000 ft) (3.0 °C/1,000 ft). The reverse occurs for a sinking parcel of air.^[16]

When the environmental lapse rate is less than the adiabatic lapse rate the atmosphere is stable and convection will not occur.^[13]: 63 The environmental lapse is forced towards the adiabatic lapse rate whenever air is convecting vertically.

Only thetroposphere (up to approximately 12 kilometres (39,000 ft) of altitude) in the Earth's atmosphere undergoesconvection: thestratosphere does not generally convect.^[17] However, some exceptionally energetic convection processes, such as volcaniceruption columns andovershooting tops associated with severesupercell thunderstorms, may locally and temporarily inject convection through thetropopause and into the stratosphere.

Energy transport in the atmosphere is more complex than the interaction between radiation and dry convection. Thewater cycle (includingevaporation,condensation,precipitation) transportslatent heat and affects atmospheric humidity levels, significantly influencing the temperature profile, as described below.

The following calculations derive the temperature as a function of altitude for a packet of air which is ascending or descending without exchanging heat with its environment.

Thermodynamics defines an adiabatic process as:

${\displaystyle P\mathrm{d}V=-\frac{V\mathrm{d}P}{\gamma }}$

thefirst law of thermodynamics can be written as

${\displaystyle m{c}_{\text{v}}\mathrm{d}T-\frac{V\mathrm{d}P}{\gamma }=0}$

Also, since the density${\displaystyle \rho =m/V}$ and${\displaystyle \gamma =c_{\text{p}}/c_{\text{v}}}$, we can show that:

${\displaystyle \rho c_{\text{p}}\mathrm{d}T-\mathrm{d}P=0}$

where${\displaystyle c_{\text{p}}}$ is thespecific heat at constant pressure.

Assuming an atmosphere inhydrostatic equilibrium:^[18]

${\displaystyle \mathrm{d}P=-\rho g\mathrm{d}z}$

whereg is thestandard gravity. Combining these two equations to eliminate the pressure, one arrives at the result for thedry adiabatic lapse rate (DALR),^[19]

${\displaystyle {\mathrm{\Gamma }}_{\text{d}}=-\frac{\mathrm{d}T}{\mathrm{d}z}=\frac{g}{c_{\text{p}}}=9.8{}^{\circ }\text{C}/\text{km}}$

The DALR (${\displaystyle {\mathrm{\Gamma }}_{\text{d}}}$) is the temperature gradient experienced in an ascending or descending packet of air that is not saturated with water vapor, i.e., with less than 100% relative humidity.

The presence of water within the atmosphere (usually the troposphere) complicates the process of convection. Water vapor contains latentheat of vaporization. As a parcel of air rises and cools, it eventually becomessaturated; that is, the vapor pressure of water in equilibrium with liquid water has decreased (as temperature has decreased) to the point where it is equal to the actual vapor pressure of water. With further decrease in temperature the water vapor in excess of the equilibrium amount condenses, formingcloud, and releasing heat (latent heat of condensation). Before saturation, the rising air follows the dry adiabatic lapse rate. After saturation, the rising air follows the moist (orwet) adiabatic lapse rate.^[20] The release of latent heat is an important source of energy in the development of thunderstorms.

While the dry adiabatic lapse rate is a constant9.8 °C/km (5.4 °F per 1,000 ft,3 °C/1,000 ft), the moist adiabatic lapse rate varies strongly with temperature. A typical value is around5 °C/km, (9 °F/km,2.7 °F/1,000 ft,1.5 °C/1,000 ft).^[21] The formula for thesaturated adiabatic lapse rate (SALR) ormoist adiabatic lapse rate (MALR) is given by:^[22]

${\displaystyle {\mathrm{\Gamma }}_{\text{w}}=g\frac{\left(1+{\displaystyle \frac{H_{\text{v}}r}{R_{\text{sd}}T}}\right)}{\left(c_{\text{pd}}+{\displaystyle \frac{H_{\text{v}}^{2}r}{R_{\text{sw}}{T}^2}}\right)}}$

where:

${\displaystyle {\mathrm{\Gamma }}_{\text{w}}}$,	wet adiabatic lapse rate, K/m
${\displaystyle g}$,	Earth'sgravitational acceleration = 9.8067 m/s2
${\displaystyle H_v}$,	heat of vaporization of water =2501000 J/kg
${\displaystyle R_{\text{sd}}}$,	specific gas constant of dry air = 287 J/kg·K
${\displaystyle R_{\text{sw}}}$,	specific gas constant of water vapour = 461.5 J/kg·K
${\displaystyle ϵ=\frac{R_{\text{sd}}}{R_{\text{sw}}}}$,	the dimensionless ratio of the specific gas constant of dry air to the specific gas constant for water vapour = 0.622
${\displaystyle e}$,	the watervapour pressure of the saturated air
${\displaystyle r=\frac{ϵe}{p-e}}$,	themixing ratio of the mass of water vapour to the mass of dry air[23]
${\displaystyle p}$,	the pressure of the saturated air
${\displaystyle T}$,	temperature of the saturated air, K
${\displaystyle c_{\text{pd}}}$,	thespecific heat of dry air at constant pressure, = 1003.5 J/kg·K

The SALR or MALR (${\displaystyle {\mathrm{\Gamma }}_{\text{w}}}$) is the temperature gradient experienced in an ascending or descending packet of air that is saturated with water vapor, i.e., with 100% relative humidity.

This sectionrelies largely or entirely on asingle source. Relevant discussion may be found on thetalk page. Please helpimprove this article byintroducing citations to additional sources. Find sources: "Lapse rate" – news ·newspapers ·books ·scholar ·JSTOR(March 2022)

The varying environmental lapse rates throughout the Earth's atmosphere are of critical importance inmeteorology, particularly within thetroposphere. They are used to determine if theparcel of rising air will rise high enough for its water to condense to formclouds, and, having formed clouds, whether the air will continue to rise and form bigger shower clouds, and whether these clouds will get even bigger and formcumulonimbus clouds (thunder clouds).

As unsaturated air rises, its temperature drops at the dry adiabatic rate. Thedew point also drops (as a result of decreasing air pressure) but much more slowly, typically about2 °C per 1,000 m. If unsaturated air rises far enough, eventually its temperature will reach itsdew point, and condensation will begin to form. This altitude is known as thelifting condensation level (LCL) when mechanical lift is present and theconvective condensation level (CCL) when mechanical lift is absent, in which case, the parcel must be heated from below to itsconvective temperature. Thecloud base will be somewhere within the layer bounded by these parameters.

The difference between the dry adiabatic lapse rate and the rate at which thedew point drops is around4.5 °C per 1,000 m. Given a difference in temperature anddew point readings on the ground, one can easily find the LCL by multiplying the difference by 125 m/°C.

If the environmental lapse rate is less than the moist adiabatic lapse rate, the air is absolutely stable — rising air will cool faster than the surrounding air and losebuoyancy. This often happens in the early morning, when the air near the ground has cooled overnight. Cloud formation in stable air is unlikely.

If the environmental lapse rate is between the moist and dry adiabatic lapse rates, the air is conditionally unstable — an unsaturated parcel of air does not have sufficient buoyancy to rise to the LCL or CCL, and it is stable to weak vertical displacements in either direction. If the parcel is saturated it is unstable and will rise to the LCL or CCL, and either be halted due to aninversion layer ofconvective inhibition, or if lifting continues, deep, moist convection (DMC) may ensue, as a parcel rises to thelevel of free convection (LFC), after which it enters thefree convective layer (FCL) and usually rises to theequilibrium level (EL).

If the environmental lapse rate is larger than the dry adiabatic lapse rate, it has a superadiabatic lapse rate, the air is absolutely unstable — a parcel of air will gain buoyancy as it rises both below and above the lifting condensation level or convective condensation level. This often happens in the afternoon mainly over land masses. In these conditions, the likelihood ofcumulus clouds, showers or eventhunderstorms is increased.

Meteorologists useradiosondes to measure the environmental lapse rate and compare it to the predicted adiabatic lapse rate to forecast the likelihood that air will rise. Charts of the environmental lapse rate are known asthermodynamic diagrams, examples of which includeSkew-T log-P diagrams andtephigrams. (See alsoThermals).

The difference in moist adiabatic lapse rate and the dry rate is the cause offoehn wind phenomenon (also known as "Chinook winds" in parts of North America). The phenomenon exists because warm moist air rises throughorographic lifting up and over the top of a mountain range or large mountain. The temperature decreases with the dry adiabatic lapse rate, until it hits the dew point, where water vapor in the air begins to condense. Above that altitude, the adiabatic lapse rate decreases to the moist adiabatic lapse rate as the air continues to rise. Condensation is also commonly followed byprecipitation on the top andwindward sides of the mountain. As the air descends on the leeward side, it is warmed byadiabatic compression at the dry adiabatic lapse rate. Thus, the foehn wind at a certain altitude is warmer than the corresponding altitude on the windward side of the mountain range. In addition, because the air has lost much of its original water vapor content, the descending air creates anarid region on the leeward side of the mountain.^[24]

If the environmental lapse rate was zero, so that the atmosphere was the same temperature at all elevations, then there would be nogreenhouse effect. This doesn't mean the lapse rate and the greenhouse effect are the same thing, just that the lapse rate is a prerequisite for the greenhouse effect.^[25]

The presence of greenhouse gases on a planet causes radiative cooling of the air, which leads to the formation of a non-zero lapse rate. So, the presence of greenhouse gases leads to there being a greenhouse effect at a global level. However, this need not be the case at a localized level.

The localized greenhouse effect is stronger in locations where the lapse rate is stronger. In Antarctica, thermal inversions in the atmosphere (so that air at higher altitudes is warmer) sometimes cause the localized greenhouse effect to become negative (signifying enhanced radiative cooling to space instead of inhibited radiative cooling as is the case for a positive greenhouse effect).^[26][27]

A question has sometimes arisen as to whether a temperature gradient will arise in a column of still air in a gravitational field without external energy flows. This issue was addressed byJames Clerk Maxwell, who established in 1868 that if any temperature gradient forms, then that temperature gradient must be universal (i.e., the gradient must be same for all materials) or thesecond law of thermodynamics would be violated. Maxwell also concluded that the universal result must be one in which the temperature is uniform, i.e., the lapse rate is zero.^[28]

Santiago and Visser (2019) confirm the correctness of Maxwell's conclusion (zero lapse rate) provided relativistic effects are neglected. Whenrelativity is taken into account, gravity gives rise to an extremely small lapse rate, the Tolman gradient (derived by R. C. Tolman in 1930). At Earth's surface, the Tolman gradient would be about${\displaystyle {\mathrm{\Gamma }}_t=T_s\times ({10}^{-16}}$m${\displaystyle {}^{-1})}$, where${\displaystyle T_s}$ is the temperature of the gas at the elevation of Earth's surface. Santiago and Visser remark that "gravity is the only force capable of creating temperature gradients in thermal equilibrium states without violating the laws of thermodynamics" and "the existence of Tolman's temperature gradient is not at all controversial (at least not within the general relativity community)."^[29][30]

• Adiabatic process
• Atmospheric thermodynamics
• Fluid dynamics
• Foehn wind
• Lapse rate climate feedback
• Scale height

• Beychok, Milton R. (2005).Fundamentals Of Stack Gas Dispersion (4th ed.). author-published.ISBN 978-0-9644588-0-2.www.air-dispersion.com
• R. R. Rogers and M. K. Yau (1989).Short Course in Cloud Physics (3rd ed.). Butterworth-Heinemann.ISBN 978-0-7506-3215-7.

• Definition, equations and tables of lapse rate from the Planetary Data system.
• National Science Digital Library glossary:
  • Lapse Rate
  • Environmental lapse rate
  • Absolute stable air
• An introduction tolapse rate calculation from first principles from U. Texas

• Atmospheric thermodynamics
• Climate change feedbacks
• Fluid mechanics
• Meteorological quantities
• Spatial gradient
• Atmospheric temperature
• Vertical distributions

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