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The lapse rate is the rate at which an atmospheric variable, normally
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied on ...
in
Earth's atmosphere The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing f ...
, falls with
altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
. ''Lapse rate'' arises from the word ''lapse'', in the sense of a gradual fall. In dry air, the adiabatic lapse rate is 9.8 °C/km (5.4 °F per 1,000 ft). It corresponds to the vertical component of the spatial gradient of
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied on ...
. Although this concept is most often applied to the Earth's
troposphere The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. From ...
, it can be extended to any gravitationally supported parcel of gas.


Definition

A formal definition from the ''Glossary of Meteorology''(Glossary of Meteorology)
/ref> 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: :\Gamma = -\frac where \Gamma (sometimes L) is the lapse rate given in
unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * ''Unit'' (a ...
s of temperature divided by units of altitude, ''T'' is temperature, and ''z'' is altitude.


Convection and adiabatic expansion

The temperature profile of the atmosphere is a result of an interaction between
thermal conduction Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its ''thermal conductivity'', and is denoted . Heat spontaneously flows along a te ...
,
thermal radiation Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
, and natural convection. Sunlight hits the surface of the earth (land and sea) and heats them. They then heat the air above the surface. If
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes: * ''electromagnetic radiation'', such as radio waves, microwaves, infrared, vi ...
were the only way to transfer energy from the ground to space, the
greenhouse effect The greenhouse effect is a process that occurs when energy from a planet's host star goes through the planet's atmosphere and heats the planet's surface, but greenhouse gases in the atmosphere prevent some of the heat from returning directly ...
of gases in the atmosphere would keep the ground at roughly . However, when air is hot, it tends to expand, which lowers its density. Thus, hot air tends to rise and carry internal energy upward. This is the process of
convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the c ...
. 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. When a parcel of air expands, it pushes on the air around it, doing thermodynamic work. An expansion or contraction of an air parcel without inward or outward heat transfer is an
adiabatic process In thermodynamics, an adiabatic process (Greek: ''adiábatos'', "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, a ...
. Air has low
thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
, and the bodies of air involved are very large, so transfer of heat by conduction is negligibly small. Also, in such expansion and contraction, intra-atmospheric radiative heat transfer is relatively slow and so negligible. Since the upward-moving and expanding parcel does work but gains no heat, it loses
internal energy The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
so that its temperature decreases. The adiabatic process for air has a characteristic temperature-pressure curve, so the process determines the lapse rate. When the air contains little water, this lapse rate is known as the dry adiabatic lapse rate: the rate of temperature decrease is ( per 1,000 ft) (3.0 °C/1,000 ft). The reverse occurs for a sinking parcel of air.Danielson, Levin, and Abrams, ''Meteorology'', McGraw Hill, 2003 When the lapse rate is less than the adiabatic lapse rate the atmosphere is stable and convection will not occur. Only the
troposphere The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. From ...
(up to approximately of altitude) in the Earth's atmosphere undergoes
convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the c ...
: the
stratosphere The stratosphere () is the second layer of the atmosphere of the Earth, located above the troposphere and below the mesosphere. The stratosphere is an atmospheric layer composed of stratified temperature layers, with the warm layers of air ...
does not generally convect. However, some exceptionally energetic convection processes, such as volcanic
eruption column An eruption column or eruption plume is a cloud of super-heated ash and tephra suspended in gases emitted during an explosive volcanic eruption. The volcanic materials form a vertical column or plume that may rise many kilometers into the air ...
s and
overshooting top An overshooting top (or penetrating top) is a dome-like protrusion shooting out of the top of the anvil of a thunderstorm and into the lower stratosphere. When an overshooting top is present for 10 minutes or longer, it is a strong indication th ...
s associated with severe supercell thunderstorms, may locally and temporarily inject convection through the
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 ...
and into the stratosphere. Energy transport in the atmosphere is more complex than the interaction between radiation and convection.
Thermal conduction Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its ''thermal conductivity'', and is denoted . Heat spontaneously flows along a te ...
, evaporation,
condensation Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor ...
,
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 hai ...
all influence the temperature profile, as described below.


Mathematics of the adiabatic lapse rate

These calculations use a very simple model of an atmosphere, either dry or moist, within a still vertical column at equilibrium.


Dry adiabatic lapse rate

Thermodynamics defines an adiabatic process as: :P \mathrmV = -\frac the
first law of thermodynamics The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amou ...
can be written as :m c_\text \mathrmT - \frac = 0 Also, since the density \rho = m/V and \gamma = c_\text/c_\text, we can show that: :\rho c_\text \mathrmT - \mathrmP = 0 where c_\text is the
specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of he ...
at constant pressure. Assuming an atmosphere in
hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetar ...
:Landau and Lifshitz, ''Fluid Mechanics'', Pergamon, 1979 :\mathrmP = -\rho g \mathrmz where ''g'' is the
standard gravity The standard acceleration due to gravity (or standard acceleration of free fall), sometimes abbreviated as standard gravity, usually denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth ...
. Combining these two equations to eliminate the pressure, one arrives at the result for the dry adiabatic lapse rate (DALR), :\Gamma_\text = -\frac = \frac = 9.8\ ^\text/\text


Moist adiabatic lapse rate

The presence of water within the atmosphere (usually the troposphere) complicates the process of convection. Water vapor contains latent
heat of vaporization The enthalpy of vaporization (symbol ), also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy ( enthalpy) that must be added to a liquid substance to transform a quantity of that substance into a gas. ...
. As a parcel of air rises and cools, it eventually becomes saturated; 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, forming
cloud In meteorology, a cloud is an aerosol consisting of a visible mass of miniature liquid droplets, frozen crystals, or other particles suspended in the atmosphere of a planetary body or similar space. Water or various other chemicals may ...
, 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 (or ''wet'') adiabatic lapse rate. The release of latent heat is an important source of energy in the development of thunderstorms. While the dry adiabatic lapse rate is a constant ( per 1,000 ft, ), the moist adiabatic lapse rate varies strongly with temperature. A typical value is around , (, , ). The formula for the moist adiabatic lapse rate is given by: :\Gamma_\text = g\, \frac where: :


Environmental lapse rate

The environmental lapse rate (ELR), is the rate of decrease of temperature with altitude in the stationary atmosphere at a given time and location. As an average, the
International Civil Aviation Organization The International Civil Aviation Organization (ICAO, ) is a specialized agency of the United Nations that coordinates the principles and techniques of international air navigation, and fosters the planning and development of international ...
(ICAO) defines an international standard atmosphere (ISA) with a temperature lapse rate of or from sea level to 11 km or . From 11 km up to 20 km or , the constant temperature is , which is the lowest assumed temperature in the ISA. The standard 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 an
inversion Inversion or inversions may refer to: Arts * , a French gay magazine (1924/1925) * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ...
layer in which the temperature increases with altitude.


Effect on weather

The varying environmental lapse rates throughout the Earth's atmosphere are of critical importance in
meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...
, particularly within the
troposphere The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. From ...
. They are used to determine if the
parcel Parcel may refer to: * Parcels (band), an Australian modern soul band * Parcel (consignment), an individual consignment of cargo for shipment * ''Parcel'' (film), 2019 Bengali film * Parcel (package), sent through the mail or package delivery ...
of rising air will rise high enough for its water to condense to form
cloud In meteorology, a cloud is an aerosol consisting of a visible mass of miniature liquid droplets, frozen crystals, or other particles suspended in the atmosphere of a planetary body or similar space. Water or various other chemicals may ...
s, 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 form cumulonimbus clouds (thunder clouds). As unsaturated air rises, its temperature drops at the dry adiabatic rate. The
dew point The dew point is the temperature to which air must be cooled to become saturated with water vapor, assuming constant air pressure and water content. When cooled below the dew point, moisture capacity is reduced and airborne water vapor will c ...
also drops (as a result of decreasing air pressure) but much more slowly, typically about per 1,000 m. If unsaturated air rises far enough, eventually its temperature will reach its
dew point The dew point is the temperature to which air must be cooled to become saturated with water vapor, assuming constant air pressure and water content. When cooled below the dew point, moisture capacity is reduced and airborne water vapor will c ...
, and condensation will begin to form. This altitude is known as the lifting condensation level (LCL) when mechanical lift is present and the convective condensation level (CCL) when mechanical lift is absent, in which case, the parcel must be heated from below to its convective temperature. The cloud base will be somewhere within the layer bounded by these parameters. The difference between the dry adiabatic lapse rate and the rate at which the
dew point The dew point is the temperature to which air must be cooled to become saturated with water vapor, assuming constant air pressure and water content. When cooled below the dew point, moisture capacity is reduced and airborne water vapor will c ...
drops is around per 1,000 m. Given a difference in temperature and
dew point The dew point is the temperature to which air must be cooled to become saturated with water vapor, assuming constant air pressure and water content. When cooled below the dew point, moisture capacity is reduced and airborne water vapor will c ...
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 lose
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 ...
. 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 an inversion layer of convective inhibition, or if lifting continues, deep, moist convection (DMC) may ensue, as a parcel rises to the level of free convection (LFC), after which it enters the free convective layer (FCL) and usually rises to the
equilibrium level In meteorology, the equilibrium level (EL), or level of neutral buoyancy (LNB), or limit of convection (LOC), is the height at which a rising parcel of air is at the same temperature as its environment. This means that unstable air is now stable ...
(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 of cumulus clouds, showers or even
thunderstorm A thunderstorm, also known as an electrical storm or a lightning storm, is a storm characterized by the presence of lightning and its acoustic effect on the Earth's atmosphere, known as thunder. Relatively weak thunderstorms are somet ...
s is increased. Meteorologists use
radiosonde A radiosonde is a battery-powered telemetry instrument carried into the atmosphere usually by a weather balloon that measures various atmospheric parameters and transmits them by radio to a ground receiver. Modern radiosondes measure or calcula ...
s 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 as thermodynamic diagrams, examples of which include Skew-T log-P diagrams and tephigrams. (See also
Thermals A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
). The difference in moist adiabatic lapse rate and the dry rate is the cause of
foehn wind A Foehn or Föhn (, , ), is a type of dry, relatively warm, downslope wind that occurs in the lee (downwind side) of a mountain range. It is a rain shadow wind that results from the subsequent adiabatic warming of air that has dropped most of i ...
phenomenon (also known as " Chinook winds" in parts of North America). The phenomenon exists because warm moist air rises through orographic 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 by
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 hai ...
on the top and
windward Windward () and leeward () are terms used to describe the direction of the wind. Windward is ''upwind'' from the point of reference, i.e. towards the direction from which the wind is coming; leeward is ''downwind'' from the point of reference ...
sides of the mountain. As the air descends on the leeward side, it is warmed by adiabatic 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 an
arid A region is arid when it severely lacks available water, to the extent of hindering or preventing the growth and development of plant and animal life. Regions with arid climates tend to lack vegetation and are called xeric or desertic. Most ...
region on the leeward side of the mountain.


See also

*
Adiabatic process In thermodynamics, an adiabatic process (Greek: ''adiábatos'', "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, a ...
*
Atmospheric thermodynamics Atmospheric thermodynamics is the study of heat-to- work transformations (and their reverse) that take place in the earth's atmosphere and manifest as weather or climate. Atmospheric thermodynamics use the laws of classical thermodynamics, to des ...
*
Fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
*
Foehn wind A Foehn or Föhn (, , ), is a type of dry, relatively warm, downslope wind that occurs in the lee (downwind side) of a mountain range. It is a rain shadow wind that results from the subsequent adiabatic warming of air that has dropped most of i ...
* Lapse rate climate feedback * Scale height


Notes


References


Further reading

*
www.air-dispersion.com
*


External links



from the Planetary Data system. * National Science Digital Library glossary: *
Lapse Rate
*
Environmental lapse rate
*
Absolute stable air
* An introduction t

from U. Texas {{DEFAULTSORT:Lapse Rate Atmospheric thermodynamics Climate change feedbacks Fluid mechanics Spatial gradient Atmospheric temperature Vertical position