Atmospheric thermodynamics

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Atmospheric thermodynamics is the study of
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
-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 Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
, 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 Thermodynamic diagrams are diagrams used to represent the thermodynamic states of a material (typically fluid) and the consequences of manipulating this material. For instance, a temperature–entropy diagram (Temperature–entropy diagram, T–s ...
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.

# Overview

The atmosphere is an example of a non-equilibrium system. 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 In physics, the Coriolis force is an fictitious force, inertial or fictitious force that acts on objects in motion within a rotating reference frame, frame of reference that rotates with respect to an Inertial frame of reference, inertial fram ...
. The tools used include the law of energy conservation, the
ideal gas law The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first s ...
, specific heat capacities, the assumption of
isentropic process In thermodynamics, an isentropic process is an idealized thermodynamic process that is both Adiabatic process, adiabatic and Reversible process (thermodynamics), reversible. The work (physics), work transfers of the system are frictionless, and th ...
es (in which
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
is a constant), and moist
adiabatic process In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qu ...
es (during which no energy is transferred as heat). Most of tropospheric gases are treated as ideal gases and
water vapor (99.9839 °C) , - , Boiling point , , - , specific gas constant , 461.5 Joule, J/(Kilogram, kg·K) , - , Heat of vaporization , 2.27 Megajoule, MJ/kg , - , Heat capacity , 1.864 Kilojoule, kJ/(kg·K) Water vapor, water vapour or ...
, 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 In chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, stru ...
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 Mass transfer is the net movement of mass from one location (usually meaning stream, Phase (matter), phase, fraction or component) to another. Mass transfer occurs in many processes, such as Absorption (chemistry), absorption, evaporation, dryi ...
, 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 parcel In fluid dynamics, within the framework of continuum mechanics, a fluid parcel is a infinitesimal, 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 rema ...
s 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 Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Nicolas Léonard Sadi Ca ...
, 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 Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics Thermodynamics i ...
published "Graphical Methods in the Thermodynamics of Fluids." 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 process In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qu ...
es. In 1884
Heinrich Hertz Heinrich Rudolf Hertz ( ; ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's Maxwell's equations, equations of electrom ...
devised first atmospheric thermodynamic diagram (
emagram An emagram is one of four thermodynamic diagrams used to display temperature lapse rate and moisture content profiles in the atmosphere. The emagram has axes of temperature (T) and pressure (p). In the emagram, the dry adiabats make an angle of ab ...
). 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". In 1911 von
Alfred Wegener Alfred Lothar Wegener (; ; 1 November 1880 – November 1930) was a German climatologist, geologist, geophysicist, meteorologist, and Polar regions of Earth, polar researcher. During his lifetime he was primarily known for his achievemen ...
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

*1751 Charles Le Roy recognized dew point temperature as point of saturation of air *1782
Jacques Charles Jacques Alexandre César Charles (November 12, 1746 – April 7, 1823) was a French inventor, scientist, mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematica ...
made hydrogen balloon flight measuring temperature and pressure in Paris *1784 Concept of variation of temperature with height was suggested *1801–1803
John Dalton John Dalton (; 5 or 6 September 1766 – 27 July 1844) was an English chemist, physicist and meteorologist. He is best known for introducing the atomic theory into chemistry, and for his research into Color blindness, colour blindness, which ...
developed his laws of pressures of vapours *1804
Joseph Louis Gay-Lussac Joseph Louis Gay-Lussac (, , ; 6 December 1778 – 9 May 1850) was a French people, French chemist and physicist. He is known mostly for his discovery that water is made of two parts hydrogen and one part oxygen (with Alexander von Humboldt), ...
made balloon ascent to study weather *1805 Pierre Simon Laplace developed his law of pressure variation with height *1841 James Pollard Espy publishes paper on convection theory of cyclone energy *1856 William Ferrel presents dynamics causing
westerlies The westerlies, anti-trades, or prevailing westerlies, are prevailing winds from the west toward the east in the middle latitudes between 30 and 60 degrees latitude. They originate from the high-pressure areas in the horse latitudes and trend to ...
*1889 Hermann von Helmholtz and John William von Bezold used the concept of potential temperature, von Bezold used adiabatic
lapse rate 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 measurement, measured with a thermome ...
and pseudoadiabat *1893 Richard Asman constructs first aerological sonde (pressure-temperature-humidity) *1894 John Wilhelm von Bezold used concept of equivalent temperature *1926 Sir Napier Shaw introduced tephigram *1933 Tor Bergeron published paper on "Physics of Clouds and Precipitation" describing precipitation from supercooled (due to condensational growth of ice crystals in presence of water drops) *1946 Vincent J. Schaeffer and Irving Langmuir performed the first
cloud seeding Cloud seeding is a type of weather modification that aims to change the amount or type of Precipitation (meteorology), precipitation that falls from clouds by dispersing substances into the air that serve as Cloud condensation nuclei, cloud cond ...
experiment *1986 K. Emanuel conceptualizes tropical cyclone as Carnot heat engine

# Applications

The Hadley Circulation can be considered as a heat engine. 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

The thermodynamic behavior of a hurricane can be modelled as a heat engine Emanuel, K. A. Annual Review of Fluid Mechanics, 23, 179–196 (1991) 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 In physics, the Coriolis force is an fictitious force, inertial or fictitious force that acts on objects in motion within a rotating reference frame, frame of reference that rotates with respect to an Inertial frame of reference, inertial fram ...
, 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 The Clausius–Clapeyron relation, named after Rudolf Clausius and Benoît Paul Émile Clapeyron, specifies the temperature dependence of pressure, most importantly vapor pressure, at a discontinuous phase transition between two phases of matter ...
shows how the water-holding capacity of the atmosphere increases by about 8% per Celsius increase in
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
. (It does not directly depend on other parameters like the
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
or
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek language, Greek letter Rho (letter), rho), although the Latin letter ''D'' ca ...
.) This water-holding capacity, or "
equilibrium vapor pressure Vapor pressure (or vapour pressure in English-speaking countries other than the US; American and British English spelling differences#-our, -or, see spelling differences) or equilibrium vapor pressure is defined as the pressure exerted by a v ...
", can be approximated using the August-Roche-Magnus formula :$e_s\left(T\right)= 6.1094 \exp \left\left( \frac \right\right)$ (where $e_s\left(T\right)$ is the equilibrium or
saturation vapor pressure Vapor pressure (or vapour pressure in English-speaking countries other than the US; American and British English spelling differences#-our, -or, see spelling differences) or equilibrium vapor pressure is defined as the pressure exerted by a v ...
in hPa, and $T$ is temperature in degrees Celsius). This shows that when atmospheric temperature increases (e.g., due to
greenhouse gases A greenhouse gas (GHG or GhG) is a gas that Absorption (electromagnetic radiation), absorbs and Emission (electromagnetic radiation), emits radiant energy within the thermal infrared range, causing the greenhouse effect. The primary greenhouse ...
) the
absolute humidity Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation (meteorology), precipitation, dew, or fog t ...
should also increase exponentially (assuming a constant
relative humidity Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation (meteorology), precipitation, dew, or fog t ...
). However, this purely thermodynamic argument is subject of considerable debate because convective processes might cause extensive drying due to increased areas of
subsidence Subsidence is a general term for downward vertical movement of the Earth's surface, which can be caused by both natural processes and human activities. Subsidence involves little or no horizontal movement, which distinguishes it from slope move ...
, efficiency of precipitation could be influenced by the intensity of convection, and because
cloud formation In meteorology, a cloud is an aerosol consisting of a visible mass of miniature liquid drop (liquid), droplets, ice crystals, frozen crystals, or other particulates, particles suspended in the atmosphere of a planetary body or similar space. ...
is related to relative humidity.

*
Atmospheric convection Atmospheric convection is the result of a Air parcel, parcel-environment instability, or temperature difference layer in the atmosphere. Different lapse rates within dry and moist air masses lead to instability. Mixing of air during the day which ...
* Atmospheric temperature * Atmospheric wave *
Chemical thermodynamics Chemical thermodynamics is the study of the interrelation of heat and Work (thermodynamics), work with chemical reactions or with physical changes of thermodynamic state, state within the confines of the laws of thermodynamics. Chemical thermodynam ...
*
Cloud physics 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 p ...
* Equilibrium thermodynamics *
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) and ...
*
Non-equilibrium thermodynamics Non-equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non-equilibrium state variables) that represent an ext ...
*
Thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

# Special topics

*Lorenz, E. N., 1955, Available potential energy and the maintenance of the general circulation, Tellus, 7, 157–167. *Emanuel, K, 1986, Part I. An air-sea interaction theory for tropical cyclones, J. Atmos. Sci. 43, 585, ( energy cycle of the mature hurricane has been idealized here as Carnot engine that converts heat energy extracted from the ocean to mechanical energy).