Atmospheric thermodynamics

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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 describe and explain such phenomena as the properties of moist air, the formation of clouds, atmospheric convection, boundary layer meteorology, and vertical instabilities in the atmosphere. Atmospheric thermodynamic diagrams are used as tools in the forecasting of storm development. Atmospheric thermodynamics forms a basis for cloud microphysics and convection parameterizations used in numerical weather models and is used in many climate considerations, including convective-equilibrium climate models.

Contents

Overview

The atmosphere is an example of a non-equilibrium system. [1] Atmospheric thermodynamics describes the effect of buoyant forces that cause the rise of less dense (warmer) air, the descent of more dense air, and the transformation of water from liquid to vapor (evaporation) and its condensation. Those dynamics are modified by the force of the pressure gradient and that motion is modified by the Coriolis force. The tools used include the law of energy conservation, the ideal gas law, specific heat capacities, the assumption of isentropic processes (in which entropy is a constant), and moist adiabatic processes (during which no energy is transferred as heat). Most of tropospheric gases are treated as ideal gases and water vapor, with its ability to change phase from vapor, to liquid, to solid, and back is considered one of the most important trace components of air.

Advanced topics are phase transitions of water, homogeneous and in-homogeneous nucleation, effect of dissolved substances on cloud condensation, role of supersaturation on formation of ice crystals and cloud droplets. Considerations of moist air and cloud theories typically involve various temperatures, such as equivalent potential temperature, wet-bulb and virtual temperatures. Connected areas are energy, momentum, and mass transfer, turbulence interaction between air particles in clouds, convection, dynamics of tropical cyclones, and large scale dynamics of the atmosphere.

The major role of atmospheric thermodynamics is expressed in terms of adiabatic and diabatic forces acting on air parcels included in primitive equations of air motion either as grid resolved or subgrid parameterizations. These equations form a basis for the numerical weather and climate predictions.

History

In the early 19th century thermodynamicists such as Sadi Carnot, Rudolf Clausius, and Émile Clapeyron developed mathematical models on the dynamics of fluid bodies and vapors related to the combustion and pressure cycles of atmospheric steam engines; one example is the Clausius–Clapeyron equation. In 1873, thermodynamicist Willard Gibbs published "Graphical Methods in the Thermodynamics of Fluids."

Thermodynamic diagram developed in the 19th century is still used to calculate quantities such as convective available potential energy or air stability. Skew-T.gif
Thermodynamic diagram developed in the 19th century is still used to calculate quantities such as convective available potential energy or air stability.

These sorts of foundations naturally began to be applied towards the development of theoretical models of atmospheric thermodynamics which drew the attention of the best minds. Papers on atmospheric thermodynamics appeared in the 1860s that treated such topics as dry and moist adiabatic processes. In 1884 Heinrich Hertz devised first atmospheric thermodynamic diagram (emagram). [2] Pseudo-adiabatic process was coined by von Bezold describing air as it is lifted, expands, cools, and eventually precipitates its water vapor; in 1888 he published voluminous work entitled "On the thermodynamics of the atmosphere". [3]

In 1911 von Alfred Wegener published a book "Thermodynamik der Atmosphäre", Leipzig, J. A. Barth. From here the development of atmospheric thermodynamics as a branch of science began to take root. The term "atmospheric thermodynamics", itself, can be traced to Frank W. Verys 1919 publication: "The radiant properties of the earth from the standpoint of atmospheric thermodynamics" (Occasional scientific papers of the Westwood Astrophysical Observatory). By the late 1970s various textbooks on the subject began to appear. Today, atmospheric thermodynamics is an integral part of weather forecasting.

Chronology

Applications

Hadley Circulation

The Hadley Circulation can be considered as a heat engine. [4] The Hadley circulation is identified with rising of warm and moist air in the equatorial region with the descent of colder air in the subtropics corresponding to a thermally driven direct circulation, with consequent net production of kinetic energy. The thermodynamic efficiency of the Hadley system, considered as a heat engine, has been relatively constant over the 1979~2010 period, averaging 2.6%. Over the same interval, the power generated by the Hadley regime has risen at an average rate of about 0.54 TW per yr; this reflects an increase in energy input to the system consistent with the observed trend in the tropical sea surface temperatures.

Tropical cyclone Carnot cycle

Air is being moistened as it travels toward convective system. Ascending motion in a deep convective core produces air expansion, cooling, and condensation. Upper-level outflow visible as an anvil cloud is eventually descending conserving mass (rysunek - Robert Simmon). Anvil convection.jpg
Air is being moistened as it travels toward convective system. Ascending motion in a deep convective core produces air expansion, cooling, and condensation. Upper-level outflow visible as an anvil cloud is eventually descending conserving mass (rysunek – Robert Simmon).

The thermodynamic behavior of a hurricane can be modelled as a heat engine [5] that operates between the heat reservoir of the sea at a temperature of about 300K (27 °C) and the heat sink of the tropopause at a temperature of about 200K (−72 °C) and in the process converts heat energy into mechanical energy of winds. Parcels of air traveling close to the sea surface take up heat and water vapor, the warmed air rises and expands and cools as it does so causes condensation and precipitation. The rising air, and condensation, produces circulatory winds that are propelled by the Coriolis force, which whip up waves and increase the amount of warm moist air that powers the cyclone. Both a decreasing temperature in the upper troposphere or an increasing temperature of the atmosphere close to the surface will increase the maximum winds observed in hurricanes. When applied to hurricane dynamics it defines a Carnot heat engine cycle and predicts maximum hurricane intensity.

Water vapor and global climate change

The Clausius–Clapeyron relation shows how the water-holding capacity of the atmosphere increases by about 8% per Celsius increase in temperature. (It does not directly depend on other parameters like the pressure or density.) This water-holding capacity, or "equilibrium vapor pressure", can be approximated using the August-Roche-Magnus formula

(where is the equilibrium or saturation vapor pressure in hPa, and is temperature in degrees Celsius). This shows that when atmospheric temperature increases (e.g., due to greenhouse gases) the absolute humidity should also increase exponentially (assuming a constant relative humidity). However, this purely thermodynamic argument is subject of considerable debate because convective processes might cause extensive drying due to increased areas of subsidence, efficiency of precipitation could be influenced by the intensity of convection, and because cloud formation is related to relative humidity.[ citation needed ]

See also

Special topics

Related Research Articles

<span class="mw-page-title-main">Carnot heat engine</span> Theoretical engine

A Carnot heat engine is a theoretical heat engine that operates on the Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded by Benoît Paul Émile Clapeyron in 1834 and mathematically explored by Rudolf Clausius in 1857, work that led to the fundamental thermodynamic concept of entropy. The Carnot engine is the most efficient heat engine which is theoretically possible. The efficiency depends only upon the absolute temperatures of the hot and cold heat reservoirs between which it operates.

<span class="mw-page-title-main">Heat engine</span> System that converts heat or thermal energy to mechanical work

In thermodynamics and engineering, a heat engine is a system that converts heat to usable energy, particularly mechanical energy, which can then be used to do mechanical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, particularly electrical, since at least the late 19th century. The heat engine does this by bringing a working substance from a higher state temperature to a lower state temperature. A heat source generates thermal energy that brings the working substance to the higher temperature state. The working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a lower temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid. During this process, some heat is normally lost to the surroundings and is not converted to work. Also, some energy is unusable because of friction and drag.

<span class="mw-page-title-main">Thermodynamics</span> Physics of heat, work, and temperature

Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology.

<span class="mw-page-title-main">Troposphere</span> Lowest layer of Earths atmosphere

The troposphere is the lowest layer of the atmosphere of Earth. It contains 75% of the total mass of the planetary atmosphere and 99% of the total mass of water vapor and aerosols, and is where most weather phenomena occur. From the planetary surface of the Earth, the average height of the troposphere is 18 km in the tropics; 17 km in the middle latitudes; and 6 km in the high latitudes of the polar regions in winter; thus the average height of the troposphere is 13 km.

<span class="mw-page-title-main">Water vapor</span> Gaseous phase of water

Water vapor, water vapour or aqueous vapor is the gaseous 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. Water vapor is transparent, like most constituents of the atmosphere. Under typical atmospheric conditions, water vapor is continuously generated by evaporation and removed by condensation. It is less dense than most of the other constituents of air and triggers convection currents that can lead to clouds and fog.

<span class="mw-page-title-main">Lapse rate</span> Vertical rate of change of temperature in atmosphere

The lapse rate is the rate at which an atmospheric variable, normally temperature in Earth's atmosphere, falls with altitude. 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. The saturated air 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 to 9.2 °C/km, as obtained from the International Civil Aviation Organization (ICAO). The environmental lapse rate is the decrease in temperature of air with altitude for a specific time and place. It can be highly variable between circumstances.

Equivalent potential temperature, commonly referred to as theta-e, is a quantity that is conserved during changes to an air parcel's pressure, even if water vapor condenses during that pressure change. It is therefore more conserved than the ordinary potential temperature, which remains constant only for unsaturated vertical motions.

<span class="mw-page-title-main">Cloud physics</span> Study of the physical processes in atmospheric clouds

Cloud physics is the study of the physical processes that lead to the formation, growth and precipitation of atmospheric clouds. These aerosols are found in the troposphere, stratosphere, and mesosphere, which collectively make up the greatest part of the homosphere. Clouds consist of microscopic droplets of liquid water, tiny crystals of ice, or both, along with microscopic particles of dust, smoke, or other matter, known as condensation nuclei. Cloud droplets initially form by the condensation of water vapor onto condensation nuclei when the supersaturation of air exceeds a critical value according to Köhler theory. Cloud condensation nuclei are necessary for cloud droplets formation because of the Kelvin effect, which describes the change in saturation vapor pressure due to a curved surface. At small radii, the amount of supersaturation needed for condensation to occur is so large, that it does not happen naturally. Raoult's law describes how the vapor pressure is dependent on the amount of solute in a solution. At high concentrations, when the cloud droplets are small, the supersaturation required is smaller than without the presence of a nucleus.

<span class="mw-page-title-main">Convective available potential energy</span> Measure of instability in the air as a buoyancy force

In meteorology, convective available potential energy, is the integrated amount of work that the upward (positive) buoyancy force would perform on a given mass of air if it rose vertically through the entire atmosphere. Positive CAPE will cause the air parcel to rise, while negative CAPE will cause the air parcel to sink. Nonzero CAPE is an indicator of atmospheric instability in any given atmospheric sounding, a necessary condition for the development of cumulus and cumulonimbus clouds with attendant severe weather hazards.

<span class="mw-page-title-main">Index of meteorology articles</span>

This is a list of meteorology topics. The terms relate to meteorology, the interdisciplinary scientific study of the atmosphere that focuses on weather processes and forecasting.

<span class="mw-page-title-main">Wet-bulb temperature</span> Temperature read by a thermometer covered in water-soaked cloth

The wet-bulb temperature (WBT) is the temperature read by a thermometer covered in water-soaked cloth over which air is passed. At 100% relative humidity, the wet-bulb temperature is equal to the air temperature ; at lower humidity the wet-bulb temperature is lower than dry-bulb temperature because of evaporative cooling.

<span class="mw-page-title-main">Thermodynamic diagrams</span> Diagram showing the thermodynamic states of a material

Thermodynamic diagrams are diagrams used to represent the thermodynamic states of a material and the consequences of manipulating this material. For instance, a temperature–entropy diagram may be used to demonstrate the behavior of a fluid as it is changed by a compressor.

<span class="mw-page-title-main">Convective instability</span> Ability of an air mass to resist vertical motion

In meteorology, convective instability or stability of an air mass refers to its ability to resist vertical motion. A stable atmosphere makes vertical movement difficult, and small vertical disturbances dampen out and disappear. In an unstable atmosphere, vertical air movements tend to become larger, resulting in turbulent airflow and convective activity. Instability can lead to significant turbulence, extensive vertical clouds, and severe weather such as thunderstorms.

<span class="mw-page-title-main">Level of free convection</span>

The level of free convection (LFC) is the altitude in the atmosphere where an air parcel lifted adiabatically until saturation becomes warmer than the environment at the same level, so that positive buoyancy can initiate self-sustained convection.

<span class="mw-page-title-main">Lifted condensation level</span>

The lifted condensation level or lifting condensation level (LCL) is formally defined as the height at which the relative humidity (RH) of an air parcel will reach 100% with respect to liquid water when it is cooled by dry adiabatic lifting. The RH of air increases when it is cooled, since the amount of water vapor in the air remains constant, while the saturation vapor pressure decreases almost exponentially with decreasing temperature. If the air parcel is lifting further beyond the LCL, water vapor in the air parcel will begin condensing, forming cloud droplets. The LCL is a good approximation of the height of the cloud base which will be observed on days when air is lifted mechanically from the surface to the cloud base.

The convective condensation level (CCL) represents the height where an air parcel becomes saturated when heated from below and lifted adiabatically due to buoyancy.

<span class="mw-page-title-main">Free convective layer</span>

In atmospheric sciences, the free convective layer (FCL) is the layer of conditional or potential instability in the troposphere. It is a layer in which rising air can experience positive buoyancy (PBE) so that deep, moist convection (DMC) can occur. On an atmospheric sounding, it is the layer between the level of free convection (LFC) and the equilibrium level (EL). The FCL is important to a variety of convective processes and to severe thunderstorm forecasting.

<span class="mw-page-title-main">Atmospheric convection</span> Atmospheric phenomenon

Atmospheric convection is the result of a parcel-environment instability in the atmosphere. Different lapse rates within dry and moist air masses lead to instability. Mixing of air during the day expands the height of the planetary boundary layer, leading to increased winds, cumulus cloud development, and decreased surface dew points. Convection involving moist air masses leads to thunderstorm development, which is often responsible for severe weather throughout the world. Special threats from thunderstorms include hail, downbursts, and tornadoes.

<span class="mw-page-title-main">Atmospheric instability</span> Condition where the Earths atmosphere is generally considered to be unstable

Atmospheric instability is a condition where the Earth's atmosphere is considered to be unstable and as a result local weather is highly variable through distance and time. Atmospheric stability is a measure of the atmosphere's tendency to discourage vertical motion, and vertical motion is directly correlated to different types of weather systems and their severity. In unstable conditions, a lifted thing, such as a parcel of air will be warmer than the surrounding air. Because it is warmer, it is less dense and is prone to further ascent.

<span class="mw-page-title-main">Glossary of meteorology</span> List of definitions of terms and concepts commonly used in meteorology

This glossary of meteorology is a list of terms and concepts relevant to meteorology and atmospheric science, their sub-disciplines, and related fields.

References

  1. Junling Huang & Michael B. McElroy (2015). "Thermodynamic disequilibrium of the atmosphere in the context of global warming". Climate Dynamics. 45 (11–12): 3513–3525. Bibcode:2015ClDy...45.3513H. doi:10.1007/s00382-015-2553-x. S2CID   131679473.
  2. Hertz, H., 1884, Graphische Methode zur Bestimmung der adiabatischen Zustandsanderungen feuchter Luft. Meteor Ztschr, vol. 1, pp. 421–431. English translation by Abbe, C. – The mechanics of the earth's atmosphere. Smithsonian Miscellaneous Collections, 843, 1893, 198–211
  3. Zur Thermodynamik der Atmosphäre. Pts. I, II. Sitz. K. Preuss. Akad. Wissensch. Berlin, pp. 485–522, 1189–1206; Gesammelte Abhandlugen, pp. 91–144. English translation Abbe, C. The mechanics of the earth's atmosphere. Smithsonian Miscellaneous Collections, no 843, 1893, 212–242.
  4. Junling Huang & Michael B. McElroy (2014). "Contributions of the Hadley and Ferrel Circulations to the Energetics of the Atmosphere over the Past 32 Years". Journal of Climate. 27 (7): 2656–2666. Bibcode:2014JCli...27.2656H. doi: 10.1175/jcli-d-13-00538.1 . S2CID   131132431.
  5. Emanuel, K. A. Annual Review of Fluid Mechanics, 23, 179–196 (1991)

Further reading

  1. Bohren, C.F. & B. Albrecht (1998). Atmospheric Thermodynamics. Oxford University Press. ISBN   978-0-19-509904-1.
  2. Curry, J.A. and P.J. Webster, 1999, Thermodynamics of Atmospheres and Oceans. Academic Press, London, 467 pp (textbook for graduates)
  3. Dufour, L. et, Van Mieghem, J. – Thermodynamique de l'Atmosphère, Institut Royal Meteorologique de Belgique, 1975. 278 pp (theoretical approach). First edition of this book – 1947.
  4. Emanuel, K.A.(1994): Atmospheric Convection, Oxford University Press. ISBN   0-19-506630-8 (thermodynamics of tropical cyclones).
  5. Iribarne, J.V. and Godson, W.L., Atmospheric thermodynamics, Dordrecht, Boston, Reidel (basic textbook).
  6. Petty, G.W., A First Course in Atmospheric Thermodynamics, Sundog Publishing, Madison, Wisconsin, ISBN   978-0-9729033-2-5 (undergraduate textbook).
  7. Tsonis Anastasios, A. (2002). An Introduction to Atmospheric Thermodynamics. Cambridge University Press. ISBN   978-0-521-79676-7.
  8. von Alfred Wegener, Thermodynamik der Atmosphare, Leipzig, J. A. Barth, 1911, 331pp.
  9. Wilford Zdunkowski, Thermodynamics of the atmosphere: a course in theoretical meteorology, Cambridge, Cambridge University Press, 2004.