Physics Of Weather

Type of physical science: Classical physics

Field of study: Thermodynamics

The thermal structure of the earth's atmosphere determines the development of large-scale weather systems, the dispersion of atmospheric pollutants, and the potential for severe weather. A clear understanding of the thermodynamic processes of the atmosphere is important in many applications, including weather prediction, the completion of environmental impact studies, and the modification of select weather phenomena.

Overview

Earth's atmosphere is a giant heat engine that converts radiant energy from the sun into the kinetic energy of atmospheric winds. Rising air motions associated with atmospheric circulations are responsible for the formation of important weather phenomena such as clouds, precipitation, and severe storms. Depending upon the vertical variation of air temperature, rising air motions may be either enhanced or suppressed by buoyant forces, so the thermal structure of the atmosphere is a key factor in the development of weather.

For the larger-scale motions of the atmosphere, the acceleration of air in the vertical direction is always small. Therefore, an approximate balance exists between the downward force of gravity and the upward force because of the decline in air pressure with height. Motions that satisfy this approximate balance are said to be hydrostatic. The rate at which pressure decreases with height depends on the air density, and, since air behaves as an ideal gas, the density at any given pressure level is determined by the air temperature. Assuming a hydrostatic balance, the pressure at any level of the atmosphere may then be determined from a knowledge of the surface pressure and the vertical distribution of temperature.

Vertical air motions and air temperature are strongly interdependent. This may be understood by considering the buoyant force that acts on a rising air parcel--a small, isolated mass of air that neither mixes nor exchanges heat with the surrounding air. As the parcel rises through the atmosphere, it expands in response to the decrease in atmospheric pressure. During expansion, the parcel works to push back the air in the surrounding atmosphere. If the expansion can be considered adiabatic--that is, if the parcel does not lose or gain heat--the work is done at the expense of the energy associated with the random motions of the parcel's air molecules, the internal energy. Therefore, the temperature of the parcel will decrease as it rises through the atmosphere. In a hydrostatic atmosphere, the first law of thermodynamics may be used to show that the temperature of the parcel will decrease with increasing altitude at a rate of 9.8 Kelvins per kilometer. This rate of temperature decrease is called the dry adiabatic lapse rate.

The buoyant force experienced by the air parcel will depend on how the density of the parcel compares with that of its environment. If the temperature of the air parcel is less than that of the surrounding air, it will experience a downward buoyant force, which acts to return it to the level at which it originated. Similarly, if the air parcel has a temperature that is greater than its surroundings, it will experience a buoyant force, which acts to accelerate its upward motion.

Since the temperature of a parcel changes with its motion, it is useful to define a related thermodynamic variable that is conserved during adiabatic air movements. Potential temperature is defined as the temperature an air parcel would have if it were adiabatically expanded or compressed to a standard pressure of 100 kilopascals. Air temperature and pressure uniquely determine the potential temperature. While the potential temperature of a rising air parcel is constant, that of the surrounding atmosphere may differ from one level to another. The variation of the potential temperature of the atmosphere with height determines whether vertical air motions will be enhanced or suppressed by buoyant forces. If the potential temperature increases with height, the atmosphere is said to be stable, since rising or sinking air parcels will experience buoyant forces that act to return them to their original level. Similarly, an unstable atmosphere is one in which the potential temperature decreases with height.

The presence of water vapor has only a slight effect on the thermodynamic properties of air unless condensation takes place. If the temperature of an air parcel becomes cool enough, water vapor in the parcel will condense to form droplets of liquid water. The potential energy lost by the condensing water molecules is transferred to the surrounding air molecules as latent heat, so the temperature of a rising air parcel in which condensation takes place will decrease less rapidly than the temperature of a parcel in which it does not. The so-called wet adiabatic lapse rate is not constant but depends on temperature and pressure. The altitude at which a rising parcel of surface air begins to experience condensation is called the lifting condensation level. This level is often a good estimate of the altitude at which the bases of convective clouds are found.

If the lapse rate of the atmospheric environment--the rate at which air temperature decreases with increasing altitude--is intermediate between the wet adiabatic lapse rate and the dry adiabatic lapse rate, the atmosphere is said to be conditionally unstable. In such an environment, a rising parcel of surface air will experience a downward buoyant force unless it is lifted high enough that condensation occurs and the release of latent heat causes its temperature to exceed that of its surroundings. The altitude above which the parcel becomes positively buoyant and continues to rise without an external source of lifting is called the level of free convection.

During condensation and cloud formation, the potential temperature of an air parcel is not conserved. Yet, it is possible to define an equivalent potential temperature that is conserved.

Equivalent potential temperature is the potential temperature an air parcel would have if all of its water vapor were condensed and the latent heat added to the parcel. When the equivalent potential temperature of the atmospheric environment decreases with height, the atmosphere is said to be convectively unstable. Under these conditions, if a layer of air is lifted through a large enough distance, the bottom of the layer will experience a greater heating because of the release of latent heat than will the top. Thus, the layer will become unstable even if the original lapse rate within the layer was stable. Most outbreaks of severe weather occur when the atmosphere is convectively unstable.

Once clouds form, some liquid water droplets and/or ice crystals within the cloud may grow large enough to fall to the earth as precipitation. At middle latitudes, most clouds contain some ice, and the growth of ice particles dominates the production of precipitation. This results from the fact that the amount of water vapor that is needed within a cloud for the growth of an ice crystal is significantly less than that needed for the growth of a liquid cloud droplet of the same size. Ice crystals, therefore, will grow at the expense of liquid droplets within the same cloud. The droplets evaporate and supply water vapor to the growing ice particles. Once the ice crystal has grown to a large enough size by vapor deposition, it will fall through the cloud and grow further by the collection of other cloud particles until it reaches precipitation size.

Atmospheric conditions that control local weather phenomena, such as clouds and precipitation, are determined by the large-scale motions of the earth's atmosphere, which are, in turn, driven by radiant energy from the sun. Near Earth's equator, the total solar energy incident at the top of the atmosphere exceeds the energy emitted by the atmosphere to space in the form of infrared radiation. By contrast, the polar regions of Earth's atmosphere lose more energy to space than they receive from the sun. The net effect is to increase the internal energy of the atmosphere near the equator and to deplete that energy near the poles. The winds of Earth's atmosphere play a dominant role in transporting excess energy poleward to balance the energy deficit at high latitudes.

In a hydrostatic atmosphere, the gravitational potential energy of an air column bears a constant ratio, about 0.4, to the internal energy. If internal energy is either added by heating or converted to kinetic energy, the gravitational potential energy changes to maintain the same ratio.

Therefore, it is convenient to treat gravitational potential energy and internal energy together as the total potential energy. The amount of potential energy available to drive atmospheric circulations depends on the distribution of potential temperature. In the case of a stable and horizontally uniform atmosphere, no potential energy would be available for conversion to kinetic energy. Thus, the north-south temperature gradient created by the latitudinal variation in solar heating makes energy available to atmospheric circulation systems.

The portion of the potential energy that is available for conversion to kinetic energy during an adiabatic redistribution of air to create a horizontally uniform and stable atmosphere is called the available potential energy. Such a redistribution of air requires the sinking of cold air and the rising of warm air so that gravitational potential energy and internal energy are released simultaneously. At middle latitudes, these rising and sinking motions occur in association with large-scale circulations around low-pressure systems that develop along fronts. As warm air collides with and is lifted over cold air along the frontal boundary, potential energy is converted into kinetic energy from the developing circulation. Most significant weather events at middle latitudes are associated with this type of circulation system.

Applications

The concepts of atmospheric thermodynamics are of considerable practical importance in many areas of atmospheric science, including weather analysis and forecasting, the assessment of environmental impact, and weather modification.

Much of Earth's weather results from the interaction of adjacent air masses having different characteristics of temperature and moisture content. It is therefore important to be able to follow the motions of air masses by identifying characteristic properties that are conserved during their motion. Since most air motions are approximately adiabatic, air parcels will tend to move along surfaces of constant potential temperature. If the mixing ratio--the ratio of the mass of water vapor to the mass of dry air in an air parcel--is plotted on a map representing a surface of constant potential temperature, the motions of air masses become apparent, since mixing ratio is a conserved quantity outside regions where condensation occurs. Such an analysis is called an isentropic analysis.

Severe weather in the United States is most commonly associated with the southeasterly flow of warm moist air from the Gulf of Mexico near the surface of the earth and the westerly flow of cool dry air aloft. Under these conditions, the atmosphere is convectively unstable, and the change in wind direction with height favors the development of long-lived thunderstorms. If the afternoon heating of Earth's surface is sufficient, the resulting convective motions may trigger the formation of severe weather. One measure of atmospheric stability that is used in severe weather forecasting is the lifted index. To calculate this index, consider an imaginary parcel of air with a temperature equal to the forecast high temperature for the day and a moisture content equal to that averaged over the lower atmosphere. If one imagines such a parcel to rise to the middle of the atmosphere, about 50 kilopascals, its temperature there can be calculated on theoretical grounds. As it is lifted, the parcel's temperature decreases at the dry adiabatic lapse rate until it reaches its lifting condensation level. From that point upward, its temperature decreases more slowly at the wet adiabatic lapse rate. At its destination, the calculated temperature of the parcel is subtracted from the measured temperature of its environment to obtain the lifted index. A large negative lifted index indicates a high probability of severe weather. Lifted indexes more negative than about -2 are correlated with tornado-producing storms.

Atmospheric stability also has a profound influence on the rate at which atmospheric pollutants are diluted by mixing with air. Turbulent eddies, which are responsible for most of the mixing, may be enhanced by an unstable environment or suppressed by a stable environment. At night, the radiational cooling of Earth's surface and adjacent air typically produces a stable atmosphere in which the dilution of atmospheric pollutants is very slow. Pollutants may be transported large distances from their source by the wind before their concentrations are appreciably reduced. During the daylight hours, the lower atmosphere is generally unstable, and convective motions driven by solar heating mix pollutants upward efficiently.

Often, the layer mixed by convection is capped by a temperature inversion, a stable layer of air in which temperature increases with height. The depth of the atmospheric layer through which pollutants are mixed is an important factor in determining their concentrations.

Therefore, accurate modeling of air quality requires a knowledge of the level at which the upper-level inversion occurs. Normally, the height of the inversion is determined from temperature measurements taken at several altitudes by an instrumented balloon called a radiosonde.

Strong upper-air inversions are usually formed by sinking air motions, subsidence, associated with systems of high pressure. The convective mixing in the lower atmosphere prevents these sinking motions from extending all the way to Earth's surface, so only air parcels above the mixed layer move downward, and the adiabatic temperature increase the sinking motions experience results in the formation of a so-called subsidence inversion. Most severe air pollution episodes are caused by subsidence inversions created by slow-moving high-pressure systems.

Since weather is such an important factor in many economic endeavors, including agriculture, the prospect of weather modification has been the focus of much attention. Most attempts at weather modification are based on the fact that ice crystals, if they exist within a cloud at the correct concentration, will grow at the expense of water droplets in the same cloud and may eventually produce precipitation. If a cloud whose upper parts are at a temperature below 0 degrees Celsius has too little ice to produce precipitation efficiently, it may be possible to enhance the precipitation by introducing ice nuclei into the cloud particles, which promote the growth of ice crystals. The addition of ice nuclei into a cloud is referred to as cloud seeding.

Unfortunately, most studies on the enhancement of precipitation by cloud seeding have not been carried out with enough care to allow proper statistical evaluation of the results. With further study, however, this technique may eventually prove to be a useful tool for weather modification.

Context

By the early eighteenth century, it was already widely accepted that atmospheric winds must somehow be the result of differences in solar heating between the equator and the poles.

Nevertheless, the exact relationship between surface winds and the latitudinal variation in air temperature was not generally understood. In 1735, George Hadley proposed a model of the general circulation of the earth's atmosphere, in which atmospheric winds were driven by a single thermal circulation cell between the equator and the poles. The trade winds--the easterly winds in the tropics--were explained in terms of the deflection of winds in the circulation cell by the rotation of the earth. This model more firmly established the connection between solar heating and large-scale air motions. William Ferrel modified Hadley's model in 1856 to include three main circulation cells in order to account for observed winds at higher latitudes.

In 1903, when Max Margules first introduced the idea of total potential energy, an understanding of the energetics of middle-latitude cyclones or low-pressure systems began to emerge. Nevertheless, it was not until 1918 that Vilhelm and Jacob Bjerknes developed the polar front theory of cyclones and convincingly showed that those storms receive their energy from the interaction of air masses of different temperatures. In 1926, Sir Harold Jeffreys showed that middle-latitude cyclones play an important role in maintaining the general circulation. The concept of available potential temperature and its usefulness in the study of the general circulation were presented by Edward Lorenz in 1955.

The forecasting of weather by solving the fundamental equations describing the physics of the atmosphere has been realized only in recent years. The difficulty lies in part in the fact that the equations are very complicated and general solutions have not been forthcoming. In 1904, Vilhelm Bjerknes first suggested that forecasts might be made by solving the equations numerically. Lewis Fry Richardson showed, in 1922, that equations describing the state of the atmosphere could be reduced to many approximate algebraic equations using appropriate techniques. Since digital computers were not yet available, however, the computations needed to obtain solutions were too lengthy to allow the technique to be useful for weather forecasting. In 1937, Carl-Gustaf Arvid Rossby developed a simple equation for forecasting the movement of large-scale troughs and ridges of pressure in the middle atmosphere by using the concept of vorticity--the spin of air around a vertical axis. Rossby's equation assumed that the atmosphere was barotropic, that is, that the temperature of the atmosphere was uniform in the horizontal.

Thus, the equation was unable to predict changes in the strength of atmospheric disturbances that result from the release of available potential energy. Nevertheless, the first successful numerical forecasts performed in 1950 were based upon Rossby's work. By 1953, forecast models capable of predicting the development of middle-latitude cyclones were being integrated numerically. As more powerful generations of digital computers become available, numerical forecast models continue to include more detailed descriptions of the physics of weather.

Principal terms

AVAILABLE POTENTIAL ENERGY: that part of the total potential energy of the atmosphere that is available for conversion to the kinetic energy of atmospheric winds

DRY ADIABATIC LAPSE RATE: the rate at which the temperature of a dry air parcel decreases with altitude as it rises through the atmosphere

EQUIVALENT POTENTIAL TEMPERATURE: the potential temperature an air parcel would have if its water vapor were condensed and the latent heat added to the parcel

HYDROSTATIC BALANCE: the balance between the downward force of gravity and the upward force resulting from the decline in air pressure with altitude

LATENT HEAT: heat released during the condensation of water vapor to form liquid water or the vapor deposition of water vapor to form ice

POTENTIAL TEMPERATURE: the temperature an air parcel would have if it were adiabatically expanded or compressed to a standard pressure of 100 kilopascals

TOTAL POTENTIAL ENERGY: the sum of the internal energy and the gravitational potential energy of an air column

WET ADIABATIC LAPSE RATE: the rate of temperature decrease with altitude of a rising air parcel in which condensation occurs

Bibliography

Battan, Louis J. WEATHER. 2d ed. Englewood Cliffs, N.J.: Prentice-Hall, 1985. This book provides a concise qualitative treatment of the physics of weather. Battan has written several books on the subject of meteorology that are accessible to the general reader.

Friedman, Robert Marc. APPROPRIATING THE WEATHER: VILHELM BJERKNES AND THE CONSTRUCTION OF A MODERN METEOROLOGY. Ithaca, N.Y.: Cornell University Press, 1989. The author traces the development of meteorological thought that led to a modern understanding of middle-latitude cyclones. The relationship between the development of the commercial applications of meteorology and that of the science itself is explored. The career of the Norwegian meteorologist Vilhelm Bjerknes is central to the discussion.

Houghton, David D., ed. HANDBOOK OF APPLIED METEOROLOGY. New York: Wiley-Interscience, 1985. This handbook is designed as a comprehensive reference for the nonmeteorologist. In addition to a thorough treatment of the fundamentals of the theory, extensive discussions of most modern applications of atmospheric science are included. Mathematics is employed frequently; however, much of the material requires little mathematical sophistication.

Sutton, O. G. THE CHALLENGE OF THE ATMOSPHERE. Reprint. New York: Greenwood Press, 1969. This highly readable account of weather and climate provides a good overview of atmospheric physics at an elementary level. Sutton presents a well-integrated view of atmospheric circulation systems and their associated weather.

Wallace, John M., and Peter V. Hobbs. ATMOSPHERIC SCIENCE: AN INTRODUCTORY SURVEY. New York: Academic Press, 1977. This text gives a quantitative treatment of a wide range of topics in atmospheric science at an introductory level. The chapters on atmospheric thermodynamics, clouds and storms, and the general circulation are most relevant. Numerous biographical footnotes provide a historical background for the discussions.

The Behavior of Gases

Laws of Thermodynamics