Lapse rate
The lapse rate is the rate at which an atmospheric variable, normally
Lapse rate corresponds to the vertical component of the spatial gradient of temperature. Although this concept is most often applied to the Earth's troposphere, it can be extended to any gravitationally supported parcel of gas.
Definition
A formal definition from the Glossary 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:
where (sometimes ) is the lapse rate given in
Convection and adiabatic expansion
The temperature profile of the atmosphere is a result of an interaction between thermal conduction, thermal radiation, 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 were the only way to transfer energy from the ground to space, the greenhouse effect of gases in the atmosphere would keep the ground at roughly 333 K (60 °C; 140 °F).[6]: 60
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. 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
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 9.8 °C/km (5.4 °F per 1,000 ft) (3.0 °C/1,000 ft). The reverse occurs for a sinking parcel of air.[7]
When the lapse rate is less than the adiabatic lapse rate the atmosphere is stable and convection will not occur.[6]: 63
Only the
Energy transport in the atmosphere is more complex than the interaction between radiation and convection. Thermal conduction, evaporation, condensation, precipitation all influence the temperature profile, as described below.
Mathematics of the adiabatic lapse rate
The following calculations use a very simple model of an atmosphere. In this model, an atmosphere is either dry or moist and exists within a still vertical column at equilibrium.
Dry adiabatic lapse rate
Thermodynamics defines an adiabatic process as:
the first law of thermodynamics can be written as
Also, since the density and , we can show that:
where is the
Assuming an atmosphere in hydrostatic equilibrium:[9]
where g is the standard gravity. Combining these two equations to eliminate the pressure, one arrives at the result for the dry adiabatic lapse rate (DALR),[10]
Moist adiabatic lapse rate
The presence of water within the atmosphere (usually the troposphere) complicates the process of convection. Water vapor contains latent
While the dry adiabatic lapse rate is a constant 9.8 °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 around 5 °C/km, (9 °F/km, 2.7 °F/1,000 ft, 1.5 °C/1,000 ft).[12] The formula for the moist adiabatic lapse rate is given by:[13]
where:
, wet adiabatic lapse rate, K/m , Earth's gravitational acceleration = 9.8076 m/s2 , heat of vaporizationof water = 2501000 J/kg, specific gas constantof dry air = 287 J/kg·K, specific gas constant of water vapour = 461.5 J/kg·K , the dimensionless ratio of the specific gas constant of dry air to the specific gas constant for water vapour = 0.622 , the water vapour pressureof the saturated air, the mixing ratio of the mass of water vapour to the mass of dry air[14] , the pressure of the saturated air , temperature of the saturated air, K , the specific heatof dry air at constant pressure, = 1003.5 J/kg·K
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
Effect on weather
This section relies largely or entirely on a single source. (March 2022) |
The varying environmental lapse rates throughout the Earth's atmosphere are of critical importance in
As unsaturated air rises, its temperature drops at the dry adiabatic rate. The
The difference between the dry adiabatic lapse rate and the rate at which the dew point drops is around 4.5 °C per 1,000 m. Given a difference in temperature and dew 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 lose buoyancy. 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 (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 thunderstorms is increased.
Meteorologists use
The difference in moist adiabatic lapse rate and the dry rate is the cause of
See also
- Adiabatic process
- Atmospheric thermodynamics
- Fluid dynamics
- Foehn wind
- Lapse rate climate feedback
- Scale height
Notes
References
- ISBN 978-0-521-83970-9.
- ISBN 978-0-495-01162-0.
- ISBN 978-1-4020-0390-5.
- ISBN 978-90-277-2769-5.
- ^ a b Richard M. Goody; James C.G. Walker (1972). "Atmospheric Temperatures" (PDF). Atmospheres. Prentice-Hall. Archived from the original (PDF) on 2016-06-03.
- ISBN 9780072420722.
- ^ "The stratosphere: overview". UCAR. Retrieved 2016-05-02.
- ^ Landau and Lifshitz, Fluid Mechanics, Pergamon, 1979
- ISBN 978-0-7167-1088-2. problem 11
- ^ "Dry Adiabatic Lapse Rate". tpub.com. Archived from the original on 2016-06-03. Retrieved 2016-05-02.
- .
- ^ "Saturation adiabatic lapse rate". Glossary. American Meteorological Society.
- ^ "Mixing ratio". Glossary. American Meteorological Society.
- ISBN 978-92-9194-004-2. Doc 7488-CD.
- ISBN 978-0-19-513271-7.
Further reading
- Beychok, Milton R. (2005).
- R. R. Rogers and M. K. Yau (1989). Short Course in Cloud Physics (3rd ed.). Butterworth-Heinemann. ISBN 978-0-7506-3215-7.
External links
- Definition, equations and tables of lapse rate from the Planetary Data system.
- National Science Digital Library glossary:
- An introduction to lapse rate calculation from first principles from U. Texas