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Lapse rate

Lapse rate

Overview
The lapse rate is defined as the rate of decrease with height for an atmospheric variable. The variable involved is 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...

 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 not simply the rate of change. While most often applied to Earth's 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...

 the concept can be extended to any gravitationally supported ball of gas.

A formal definition from the Glossary of Meteorology is:
The decrease of an atmospheric variable with height, the variable being temperature unless otherwise specified.
The term applies ambiguously to the environmental lapse rate and the process lapse rate, and the meaning must often be ascertained from the context.

The atmospheric lapse rate describes the reduction, or lapse of air temperature that takes place with increasing altitude.
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Encyclopedia
The lapse rate is defined as the rate of decrease with height for an atmospheric variable. The variable involved is 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...

 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 not simply the rate of change. While most often applied to Earth's 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...

 the concept can be extended to any gravitationally supported ball of gas.

Definition


A formal definition from the Glossary of Meteorology is:
The decrease of an atmospheric variable with height, the variable being temperature unless otherwise specified.
The term applies ambiguously to the environmental lapse rate and the process lapse rate, and the meaning must often be ascertained from the context.

The atmospheric lapse rate describes the reduction, or lapse of air temperature that takes place with increasing altitude. Lapse rates related to changes in altitude can also be developed for other properties of the atmosphere.

In the lower regions of the atmosphere (up to altitudes of approximately 40,000 feet [12,000 m]), temperature decreases with altitude at a fairly uniform rate. Because the atmosphere is warmed by conduction from Earth's surface, this lapse or reduction in temperature normal with increasing distance from the conductive source.

Although the actual atmospheric lapse rate varies, under normal atmospheric conditions the average atmospheric lapse rate results in a temperature decrease of 3.5°F (1.94°C) per 1,000 feet (304 m) of altitude.

The measurable lapse rate is affected by the moisture content of the air (humidity). A dry lapse rate of 5.5°F (3.05°C) per 1,000 feet (304 m) is often used to calculate temperature changes in air not at 100% relative humidity. A wet lapse rate of 3°F (1.66°C) per 1,000 feet (304 m) is used to calculate the temperature changes in air that is saturated (i.e., air at 100% relative humidity). Although actual lapse rates do not strictly follow these guidelines, they present a model sufficiently accurate to predict temperate changes associated with updrafts and downdrafts. This differential lapse rate (dependent upon both difference in conductive heating and adiabatic expansion and compression) results in the formation of warm downslope winds (e.g., Chinook winds, Santa Anna winds, etc.).
The atmospheric lapse rate, combined with adiabatic cooling and heating of air related to the expansion and compression of atmospheric gases, present a unified model explaining the cooling of air as it moves aloft and the heating of air as it descends downslope.

Atmospheric stability can be measured in terms of lapse rate (i.e., the temperature differences associated with vertical movement of air). A high lapse rate indicates a greater than normal change of temperature associated with a change in altitude and is characteristic of an unstable atmosphere.

Although the atmospheric lapse rate (also known as the environmental lapse rate) is most often used to characterize temperature changes, many properties (e.g., atmospheric pressure) can also be profiled by lapse rates.

See also Air masses and fronts; Land and sea breeze; Seasonal winds

Mathematical definition


In general, a lapse rate is the negative of the rate of temperature change with altitude change, thus:


where is the lapse rate given in units of temperature divided by units of altitude, T = temperature, and z = altitude.


Note: In some cases, or can be used to represent the adiabatic lapse rate in order to avoid confusion with other terms symbolized by , such as the specific heat ratio
Heat capacity ratio
The heat capacity ratio or adiabatic index or ratio of specific heats, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume . It is sometimes also known as the isentropic expansion factor and is denoted by \gamma or \kappa . The latter symbol kappa is...

 or the psychrometric constant
Psychrometric constant
The psychrometric constant \gamma relates the partial pressure of water in air to the air temperature. This lets one interpolate actual vapor pressure from paired dry and wet thermometer bulb temperature readings....

.

Types of lapse rates


There are two types of lapse rate:
  • Environmental lapse rate – which refers to the actual change of temperature with altitude for the stationary atmosphere (i.e. the temperature gradient
    Temperature gradient
    A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature gradient is a dimensional quantity expressed in units of degrees per unit length...

    )
  • The adiabatic
    Adiabatic process
    In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...

     lapse rates
    – which refer to the change in temperature of a parcel of air as it moves upwards (or downwards) without exchanging heat with its surroundings. The temperature change that occurs within the air parcel reflects the adjusting balance between potential energy
    Potential energy
    In physics, potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule...

    and kinetic energy
    Kinetic energy
    The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

    of the molecules of gas that comprise the moving air mass. There are two adiabatic rates:
    • Dry adiabatic lapse rate
    • Moist (or saturated) adiabatic lapse rate

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
International Civil Aviation Organization
The International Civil Aviation Organization , pronounced , , is a specialized agency of the United Nations. It codifies the principles and techniques of international air navigation and fosters the planning and development of international air transport to ensure safe and orderly growth...

 (ICAO) defines an international standard atmosphere (ISA) with a temperature lapse rate of or from sea level to 11 km . From 11 km or 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 layer in which the temperature increases with height.

Dry adiabatic lapse rate



The dry adiabatic lapse rate (DALR) is the rate of temperature decrease with height for 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 dry or unsaturated air rising under adiabatic conditions. Unsaturated air has less than 100% relative humidity
Relative humidity
Relative humidity is a term used to describe the amount of water vapor in a mixture of air and water vapor. It is defined as the partial pressure of water vapor in the air-water mixture, given as a percentage of the saturated vapor pressure under those conditions...

; i.e. its actual temperature is higher than its 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...

. The term adiabatic means that no heat transfer occurs into or out of the parcel. Air has low thermal conductivity
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....

, and the bodies of air involved are very large, so transfer of heat by conduction
Heat conduction
In heat transfer, conduction is a mode of transfer of energy within and between bodies of matter, due to a temperature gradient. Conduction means collisional and diffusive transfer of kinetic energy of particles of ponderable matter . Conduction takes place in all forms of ponderable matter, viz....

 is negligibly small.

Under these conditions when the air rises (for instance, by 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....

) it expands, because the pressure is lower at higher altitudes. As the air parcel expands, it pushes on the air around it, doing work
Work (thermodynamics)
In thermodynamics, work performed by a system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system. As such, thermodynamic work is a generalization of the concept of mechanical work in mechanics. Thermodynamic work encompasses...

 (thermodynamics). Since the parcel does work but gains no heat, it loses internal energy
Internal energy
In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal...

 so that its temperature decreases. The rate of temperature decrease is per 1,000 m ( per 1,000 ft) (3.0°C/1,000 ft). The reverse occurs for a sinking parcel of air.

Since for adiabatic process:

the first law of thermodynamics
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

 can be written as

Also since : and :
we can show that:

where is the specific heat at constant pressure and is the specific volume
Specific volume
In thermodynamics, the specific volume of a substance is the ratio of the substance's volume to its mass. It is the reciprocal of density:In thermodynamics, the specific volume of a substance is the ratio of the substance's volume to its mass...

.

Assuming an atmosphere in hydrostatic equilibrium
Hydrostatic equilibrium
Hydrostatic equilibrium or hydrostatic balance is the condition in fluid mechanics where a volume of a fluid is at rest or at constant velocity. This occurs when compression due to gravity is balanced by a pressure gradient force...

:


where g is the standard 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...

 and is the density. Combining these two equations to eliminate the pressure, one arrives at the result for the DALR,.

Saturated adiabatic lapse rate


When the air is saturated
Saturation (chemistry)
In chemistry, saturation has six different meanings, all based on reaching a maximum capacity...

 with water vapor
Water vapor
Water vapor or water vapour , also aqueous vapor, is the gas phase of water. It is one state of water within the hydrosphere. Water vapor can be produced from the evaporation or boiling of liquid water or from the sublimation of ice. Under typical atmospheric conditions, water vapor is continuously...

 (at its 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...

), the moist adiabatic lapse rate (MALR) or saturated adiabatic lapse rate (SALR) applies. This lapse rate varies strongly with temperature. A typical value is around (1.5°C/1,000 ft).

The reason for the difference between the dry and moist adiabatic lapse rate values is that latent heat
Latent heat
Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a process that occurs without a change in temperature. A typical example is a change of state of matter, meaning a phase transition such as the melting of ice or the boiling of water. The term was...

 is released when water condenses, thus decreasing the rate of temperature drop as altitude increases. This heat release process is an important source of energy in the development of thunderstorms. An unsaturated parcel of air of given temperature, altitude and moisture content below that of the corresponding dewpoint cools at the dry adiabatic lapse rate as altitude increases until the dewpoint line for the given moisture content is intersected. As the water vapor then starts condensing the air parcel subsequently cools at the slower moist adiabatic lapse rate if the altitude increases further.

The saturated adiabatic lapse rate is given approximately by this equation from the glossary of the American Meteorology Society:

where:
font style="vertical-align:-10%;"> = Wet adiabatic lapse rate, K/m
font style="vertical-align:-55%;"> = Earth's gravitational acceleration
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...

 = 9.8076 m/s2
font style="vertical-align:-10%;"> = Heat of vaporization of water, J/kg
font style="vertical-align:-15%;"> = The ratio of the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

 of water vapor to the mass of dry air, kg/kg
font style="vertical-align:+15%;"> = The universal gas constant = 8,314 J kmol−1 K−1
font style="vertical-align:+20%;"> = The molecular weight of any specific gas, kg/kmol = 28.964 for dry air and 18.015 for water vapor
= The specific gas constant of a gas, denoted as
= Specific gas constant of dry air = 287 J kg−1 K−1
= Specific gas constant of water vapor = 462 J kg−1 K−1
font style="vertical-align:-10%;"> =The dimensionless ratio of the specific gas constant of dry air to the specific gas constant for water vapor = 0.6220
font style="vertical-align:+15%;"> = Temperature of the saturated air, K
font style="vertical-align:-30%;"> = The specific heat of dry air at constant pressure, J kg−1 K−1

Significance in meteorology


The varying environmental lapse rates throughout the Earth's atmosphere are of critical importance in meteorology
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...

, particularly within 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....

. They are used to determine if the 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 rising air will rise high enough for its water to condense to form cloud
Cloud
A cloud is a visible mass of liquid droplets or frozen crystals made of water and/or various chemicals suspended in the atmosphere above the surface of a planetary body. They are also known as aerosols. Clouds in Earth's atmosphere are studied in the cloud physics branch of meteorology...

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 cloud
Cumulonimbus cloud
Cumulonimbus is a towering vertical cloud that is very tall, dense, and involved in thunderstorms and other inclement weather. Cumulonimbus originates from Latin: Cumulus "Heap" and nimbus "rain". It is a result of atmospheric instability. These clouds can form alone, in clusters, or along a cold...

s (thunder clouds).

As unsaturated air rises, its temperature drops at the dry adiabatic rate. The 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...

 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
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...

, 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
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) absent mechanical lift, in which case, the parcel must be heated from below to its 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...

. The 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...

 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
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...

 drops is around per 1,000 m. Given a difference in temperature 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...

 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
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...

. 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
Inversion (meteorology)
In meteorology, an inversion is a deviation from the normal change of an atmospheric property with altitude. It almost always refers to a temperature inversion, i.e...

 of convective inhibition
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....

, or if lifting continues, deep, moist convection (DMC) may ensue, as a parcel rises to 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), after which it enters 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) and usually rises 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).

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 over many land masses. In these conditions, the likelihood of 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, showers or even thunderstorm
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 is increased.

Meteorologists use radiosonde
Radiosonde
A radiosonde is a unit for use in weather balloons that measures various atmospheric parameters and transmits them to a fixed receiver. Radiosondes may operate at a radio frequency of 403 MHz or 1680 MHz and both types may be adjusted slightly higher or lower as required...

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
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...

, examples of which include 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...

s and tephigram
Tephigram
A tephigram is one of four thermodynamic diagrams commonly used in weather analysis and forecasting. The name evolved from the original name "T-\phi-gram" to describe the axes of temperature and entropy used to create the plot...

s. (See also Thermals).

The difference in moist adiabatic lapse rate and the dry rate is the cause of foehn wind phenomenon (also known as "Chinook wind
Chinook wind
Chinook winds , often called chinooks, commonly refers to foehn winds in the interior West of North America, where the Canadian Prairies and Great Plains meet various mountain ranges, although the original usage is in reference to wet, warm coastal winds in the Pacific Northwest.Chinook is claimed...

s" in parts of North America).

See also

  • Adiabatic process
    Adiabatic process
    In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...

  • Atmospheric thermodynamics
    Atmospheric thermodynamics
    Atmospheric thermodynamics is the study of heat to work transformations in the earth’s atmospheric system in relation to weather or climate...

  • Fluid mechanics
    Fluid mechanics
    Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...

    • Fluid dynamics
      Fluid dynamics
      In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

  • Foehn wind

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