# Meteorology, Dynamic

## Meteorology, Dynamic

a branch of meteorology dealing with the theoretical study of atmospheric processes in the troposphere and lower stratosphere and using equations of hydrodynamics, thermodynamics, and radiation theory. Only the theories of electric, acoustic, and optical phenomena in the atmosphere are outside the concerns of dynamic meteorology.

The main task of dynamic meteorology is weather forecasting—specifically, the development of numerical methods of forecasting meteorological elements (pressure, temperature, wind, cloudiness, precipitation, visibility) for various periods through study of the general circulation of the atmosphere, that is, of the system of large-scale transfers of air over our planet. Dynamic meteorology also deals with more limited problems—analysis of the origin and behavior of atmospheric waves and vortices of various scale, the components of general circulation (fronts of atmospheric and jet streams), and atmospheric turbulence and convection.

Attempts at a theoretical explanation of isolated features of atmospheric circulation date back to the first half of the 18th century (British scientist G. Hadley). Early in the 19th century, P. Laplace established the theoretical relationship between changes in atmospheric pressure and altitude and temperature (the barometric formula) and thereby laid the foundations for a statics of the atmosphere. The first half of the 19th century saw the birth of thermodynamics, which was soon used in explaining individual atmospheric processes (such as the foehn). However, it was not until the 1880’s, in work of the German scientists H. Hertz, W. Bezold and others, that the theory of adiabatic processes (that is, processes in which heat exchange can be ignored) in an atmosphere containing water vapor was formulated. This theory was not developed further until the 20th century (by the British scientist W. N. Shaw, the Norwegian scientists A. Refsdal and J. Bjerknes, and others). In the first half of the 19th century the French scientist G. Coriolis proposed a theorem of relative motion on the rotating earth, which made it possible to apply equations of hydrodynamics, formulated by L. Euler as far back as the 18th century, to meteorological problems. In a number of studies begun in 1856, W. Ferrel (USA) provided the first theoretical model of the general circulation of the atmosphere based on the equations of hydrodynamics. This helped to establish dynamic meteorology as a scientific discipline. H. Helmholtz made a major contribution to the development of dynamic meteorology in the 1880’s by proposing a theoretical model of general circulation for a surface of discontinuity (an atmospheric front). In 1897, V. Bjerknes laid the foundation with his theorems of circulation and vortex generation for the “physical hydrodynamics” of the atmosphere as a compressible fluid of the most general type (a baroclinic fluid) in which density distribution depends on the distribution of both pressure and temperature. In 1904 he formulated the problem of weather forecasting as one of solving equations of atmospheric thermohydrodynamics. The development of V. Bjerknes’ ideas determined further advances in dynamic meteorology. Early in the 20th century, M. Margules in Austria, V. Bjerknes, and others constructed a theory of atmospheric fronts; Margules also laid the foundations for an energetics of the atmosphere. At the same time an intensive study was made of atmospheric turbulence, which determines a vertical exchange of heat, moisture, colloidal admixtures, and momentum in the atmosphere.

Rapid development of dynamic meteorology began in the USSR in the 1920’s. A Soviet school of dynamic meteorology appeared, headed by A. A. Fridman. As early as 1914, Fridman, together with the Swedish scientist T. Hesselberg, estimated for the first time the orders of magnitude of the basic meteorological elements (pressure, temperature, humidity) and their variability, making it possible to simplify the equations of dynamic meteorology. In 1922, Fridman constructed and analyzed in detail a general equation for determining velocity curl, the characteristics of the local rotation of a medium about instantaneous axes in a moving fluid; this turned out later to be of fundamental importance in the theory of weather forecasting. In 1931, N. E. Kochin solved the problem of stability loss at the intersurface of two air masses, which is involved in the formation of cyclones. In 1935 he developed a theory of the general circulation of the atmosphere, using the concept of planetary boundary layers. A. A. Dorodnitsyn (1938, 1940) found a theoretical solution to the problem of the effect of a mountain ridge on an airstream, and in 1940 he calculated the course of temperature over a 24-hour period.

The work of I. A. Kibel’ was a fundamental step in solving the chief practical task of dynamic meteorology: weather forecasting. His work provided a method of forecasting a field of pressure and temperature over a 24-hour period (1940). The fundamentals of the hydrodynamic method of long-term forecasting were established in the work of E. M. Blinova (1943). One of the basic problems of dynamic meteorology, the interrelationship of fields of pressure and wind in the atmosphere, was investigated by the Swedish scientist C. G. Rossby in 1938 and successfully solved by A. M. Obukhov in the USSR in 1949. This problem was subsequently generalized in the works during the 1950’s of I. A. Kibel’ and A. S. Monin, making it possible in the 1960’s to move on to more accurate methods of weather forecasting. The first numerical pressure forecasts were carried out in 1951 by the American scientist J. Charney. The works of G. I. Marchuk and N. I. Buleev (1953; USSR) and K. Hinkelman (Federal Republic of Germany) were a major step in forecasting theory. For the first time they took into consideration the effect that processes over large areas have on atmospheric changes in the area to be forecast. The appearance of electronic computers in the 1950’s and the rapid development of computer mathematics have stimulated intensive development of many branches of dynamic meteorology.

The basic equations of dynamic meteorology consider a layer of atmosphere 20-30 km deep—a thin layer in comparison to the average radius of the earth (6,374 km). About 98 percent of the entire mass of the atmosphere is concentrated in this layer; this is due to the force of gravity, one of the basic forces affecting a small volume (“particle”) of air. The earth’s atmosphere in this layer is a medium that is dense enough to be considered continuous and to have applied to it the laws of continuum mechanics: the law of conservation of mass, which makes possible the continuity equation, and the law of change of momentum. The main forces operating on a particle of air, aside from the force of gravity, are the deflecting force of the earth’s rotation (the Coriolis force) and the dissipative forces of turbulent friction. The main features of the motions considered in dynamic meteorology are the slowness of the speed of wind in relation to the speed of sound and the large influence of the force of gravity.

The dynamics of atmospheric processes on every possible scale is closely linked to the influx of heat. The application of the first principle of thermodynamics to atmospheric processes gives the so-called heat flux equation, under the effect of the three main sources of heat in the atmosphere: radiant and turbulent heat influxes and the emission of energy in phase transitions of moisture from one state to another (vapor, liquid, ice). The thermodynamic parameters of the atmosphere—pressure, temperature, and density—are linked by the equation of state.

Equations determining the transfer of radiant energy in the atmosphere, the transfer of moisture, and the conditions of cloud formation and precipitation are added to the equations listed above. Boundary conditions on the earth’s surface link air temperature to the temperature of the surfaces of continents and oceans. Air and ocean currents also prove to be interrelated. Thus, a complete statement of the task of dynamic meteorology must include the determination of the pressure, density, temperature, and humidity of the air, the three components of wind, and the conditions of formation of clouds and precipitation in relation to the quantities characterizing the state of the ocean and dry land. This problem is extremely complex and is solved only when very major simplifications are made. The development of dynamic meteorology is closely related to the development of methods of solving the nonlinear equations of mathematical physics.

The basic problems of dynamic meteorology follow. (1) The study of the general circulation of the atmosphere. The integration of the equations of dynamic meteorology over long periods, taking into account, as much as possible, heat and moisture exchange in the atmosphere and the thermal and dynamic interaction of ocean and atmosphere, has made it possible to create a mathematical model of the general circulation of the atmosphere that corresponds in its main features to the data of observations. By varying the outer parameters, it is possible to explain the causes of anomalies of climate and to establish the climate patterns of former geological epochs. This work is also of importance for long-term weather forecasting theory. The available empirical information on the earth’s atmosphere is not yet entirely adequate for building a complete model of the general circulation of the atmosphere. In this connection, the investigation of global atmospheric processes by studying radiation transfer, convection, and other processes is an important task of dynamic meteorology.

(2) The study of turbulence in the atmosphere and hydrosphere. The role of turbulent exchange in the atmosphere is very great; with rare exceptions, all atmospheric motion is in essence turbulent. In order to develop and perfect the theory of turbulence it is necessary not only to work out mathematical models but also to develop subtle experimental methods for determining the local and integral characteristics of turbulent exchange.

(3) Weather forecasting. The problem is arbitrarily divided into three parts: short-term forecasting for periods up to three days, long-term forecasting (forecasts for five to ten days, for a month, or even for a season), and forecasts of local weather conditions. Since the 1960’s, short-term synoptic forecasts (mostly of the distribution of pressure and other meteorological elements over a wide area) by the methods of dynamic meteorology have been used widely in a number of countries with highly developed computer technology (the USSR, the USA, Great Britain, France, Sweden, Norway). Long-term forecasts have also been drawn up experimentally for individual elements (for example, mean temperature and pressure) on the basis of dynamic meteorology. The methods of these forecasts are more closely related to models of the general circulation of the atmosphere than are the methods of short-term forecasting. Forecasts of local weather conditions are at present mostly empirical and are based on forecasts of the general synoptic situation. The theoretical approaches to this kind of forecasting are labor-consuming and complicated; they are drawn up on the basis of dynamic meteorology only experimentally and at the best computer-equipped forecasting centers. The widespread use of ultrahigh-speed electronic computers will make it possible to work out forecast maps that will show not only the long-lasting features of a meteorological regime but also the short-lived features that cause changes in weather conditions over a small area.

### REFERENCES

*Osnovy dinamicheskoi meteorologii*. Leningrad, 1955.

Belinskii, V. A.

*Dinamicheskaia meteorologiia*. Moscow-Leningrad, 1948.

Marchuk, G. I.

*Chislennye metody v prognoze pogody*. Leningrad, 1967.

Iudin, M. I.

*Novye metody i problemy kratkosrochnogo prognoza pogody*. Leningrad, 1963.

Monin, A. S.

*Prognoz pogody kak zadacha fiziki*. Moscow, 1969.

Kibel’, I. A.

*Vvedenie v gidrodinamicheskie metody kratkosrochnogo prognoza pogody*. Moscow, 1957.

*Meteorologiia i gidrologiia za 50 let Sovetskoi vlasti*. Edited by E. K. Fedorov. Leningrad, 1967.

E. M. DOBRYSHMAN