CIATION ACHERS THE PHYSICS OF PRECIPITATION IN THE ATMOSPHERE' ROLAND J. BOUCHER United States Weather Bureau, East Boston, Massachusetts
AMONG the earliest plausible theories of the formation ture. The amount of water condensed is limited only of precipitation was that of Hutton, a British geologist by the amount of the moist air lifted sufficiently to cool of the 18th century. He believed that rain was pro- it below its saturation temperature. This cooling duced by the mixing of humid masses of air having dif- process is generally considered to be adiabatic. This ferent temperatures. Hi ideas were based on the fact theory seems to agree very well with observed phenomthat the capacity of a mass of air to contain water ena and is the one which we hold today. decreases more rapidly than in direct proportion to the Here are a few examples of how a moist current is lifted to cause cooling and condensation: temperature. The following table giving the satur* tion specific humidity for certain temperatures-shows (1) Convection; the number of grams of water vapor per kilogram of (2) Forced ascent of moist air current over a cold saturated air, a t a pressure of 1000 millibars: wedge; moist air by undercutting cold (3) Lifting of .warm "c. v. 1kr. "c. &I@. , air; and (4) Orographic lifting of moist air. -4" ".,a la 1U.t - 10 1.79 20 14.7 Just for the+sakeof completeness there are two other 0 3.80 25 20.0 ways in which condensation may occur. These are 26.9 30 the cooling of moist air by (1) radiation to space and (2) From this it can be seen that when two masses of air, contact with a cold surface. These, and especially the both saturated and a t different temperatures, are contact cooling process, are particularly important in mixed, the mixture is too cold forit to hold all the water the formation of fog, but do not produce precipitation. vapor originally contained in the pparate masses. For a long time condensation and precipitation were Consequently, some of the water vapor must drop out confused, and the terms even used interchangeably. to condense either as a cloud or as precipitation. It was believed that if conditions were sufficientfor inWhiie it is perfectly true that a small amount of pre- tense condensation, there should immediately follow cipitation might be realized from such a process, it intense precipitation. But this did not agree with obdoes not occur on a large enough scale to account for served facts, for there is much cloudiness which fails to even a light rainfall, not to mention the innumerable produce any precipitation. It was finally realized that cases when the two conditions of saturation and tem- some sort of release was necessary to start the process perature difference are not satisfied. It might also of precipitation from existing cloudiness. Before we be added that the release of the latent heat of condensa- examine the hypotheses dealing with this mechanism, tion would tend to raise the temperature of the mix- it might be well to go over a few fundamental ideas on ture and hence lessen the amount of precipitation pos- condensation. It has been proved beyond reasonable doubt that atsible. Yet in spite of its shortcomings, this theory of the formation of rain was accepted for about 100 years, mospheric condensation cannot occur on a wholesale scale without nuclei of condensation. Condensation or until near the end of the 19th century. The next concept of the primary cause for condeusa- without the help of nuclei would require a tremendous tion and precipitation was that of dynamic coolig in degree of supersaturation in the atmosphere far beyond ascending air currents. As the air rises, it expands be- any value ever observed. The reason for this is that cause of reduced pressure, thereby lowering its tempera- owing to the effects of surface tension, the vapor pres'Onvex surface is greater than that Over a sure Over ' Presented a t the 238th meeting of the New England Associa- plane S~rfaceby an amount which varies inversely with tion of Chemistry Teachers, Boston College, December 7, 1946. 204
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the radius of curvature. For a very small drop the vapor pressure becomes excessively high. For this reason it is impossible for a drop to form as its vapor pressure would approach infinity at the start of its .. existence. This is quite evident from the following expression for the diierence in the vanor nressure near the dron from that near a plane surface:
. .
Here p, is the vapor pressure near the drop, p, is the vapor pressure near the plane surface, o is the density of the vapor, pis the density of the liquid, T is the surface tension of the liquid, and r is the radius of the drop. Fortunately there are present in the atmosphere a t all times plenty of hygroscopic nuclei, which consist for the most part of fine salt particles. These hygroscopic particles not only furnish nuclei of finite size for the droplet to start on but their attraction for water allows condensation to begin at considerably lower vapoi pressures than would otherwise be possible. Depending upon the nature and size of these particles, it may be possible for condensation to begin a t relative humidities as low as 97 per cent. Because of the lower vapor pressures required for condensation on convex surfaces of relatively large radii of curvature, condensation will first take place on the larger nuclei. The smaller ones which require a greater degree of saturation will become active only if there is an insufficient number of the larger nuclei present. The rate of growth of the droplets varies as an inverse function of the drop size according to the following expression : oP = AP
+ 8 K ( D - Do)t
Here a is the drop diameter at time t, A is the initial drop diameter, K is the diffusion coefficient of water vapor in air, and ( D - Do) is the difference between water vapor density in the atmosplpre and a t the surface. Using this expression, we find that two drops initially of 0.2 and 2.0 microns diameter, respectively, will reach a size of 10.0 and 10.2 microns a t the same time. The nuclei vary considerably in size, hut became of the change in rate of growth as the droplet size increases, all drops tend t o reach their maximum size a t about the same time. This property produces clouds with a fairly uniform droplet size which, as we shall see, is a deterrent to precipitation since it prevents amalgamation of the droplets to the size necessary for rain. The maximum size of the droplets formed by condensation is limited by the amount of the water available. This is generally considered to be on the order of 50 microns in diameter. The water vapor condensed into cloud form can he regarded as a colloidal suspension of water in air. This suspension may be stable, in which case the droplets do not coalesce and there is no precipitation, or it may be unstable, in which case there is droplet coagula-
.
tion and subsequent precipitation. The conditions under which a cloud will remain stable are as follows: (1) A uniform electrical charge on all the cloud droplets-that is, a charge of the same magnitude and polarity; (2) A uniform size of cloud droplets; (3) . . A uniform temverature of cloud elements so that there e k t s no appreciable difference in vapor pressure between one part of the cloud and another; and (4) A uniform motion of cloud elements which implies lack of turbulence which might force collisions between droplets and result in amalgamation. The nonfulfillment of any of these conditions will result in colloidal instability which, if of su5cient magnitude, will cause the droplets to coalesce and result in precipitation. There is considerable evidence to show that raindrops result principally from coalescence of cloud particles and that little if any rain results from the growth of certain particles a t the expense of others. The analysis of rainwater shows that the chloride concentration is practically the same as that in cloud water. If selective growth occurred on any large scale, the rainwater should show a weaker concentration. A German meteorologist, Defant, who measured over 10,000 raindrops, found that tbeir masses are integral multiples of a standard size, showing that the larger drops were probably formed from smaller droplets. It seems logical to assume that the most rapid coagulation should occur from collisions between cloud particles of unlike size which, because of their different size, will fall a t different velocities. The larger will overtake the smaller and will also coalesce with all the drops in their path unless carrying high electrical charges of the same sign. To illustrate this process, let us assume that a cloud contains one gram of liquid water per cubic meter, consisting of droplets 20 microns'in diameter formed by condensation on hygroscopic nuclei. By collision between a few droplets, probably through turbulence within the cloud, often observed, a number of 25micron drops form. These will immediately begin to fall relative to the 20-micron drops and in eight minutes will attain a diameter of 10@microns. With only an additional fall of 1500 ft. through the cloud, the 100micron drops will grow to 1 mm. or 1000 microns. Drops of this size are classified as moderate rain. It is evident from this example that the rain-forming process, once the conditions have been established, is a very rapid one. The final size of the drop after leaving the base of the cloud will depend on four factors: (1) Size of original cloud particle; (2) The liquid water content of the cloud; (3) The depth, i. e., vertical thickness of the cloud layer, through which the drop falls; and (4) The vertical velocity of the ascending air cnrrent which is essential to produce the initial condensation. The higher the velocity, the
JOURNAL OF CHEMICAL EDUCATION
longer the drop will remain in the cloud and the larger it will grow. The following table gives comparative drop sizes and fall velocities of various types of liquid precipitation: Diameter, mm.
Fall velocity, m/sec.
Mist 0.1 0.25 Drizzle '0.2 0.75 Light rain 0.45 2.00 Rain 1.0 4.00 Heavy rain 1.5 5.00 Very heavy rain 2.1 6.00 Cloudburst 7.00 3.0 Maximum uossible drou size* 5.0 8.00 * Drops larger than 5 mm. will break up inta s d e r drops.
There are two other possible causes of coalescence of cloud particles. These will be mentioned briefly for the sake of completeness, but are considered unimportant for the reason that they are much too slow in action. One of these is the hydrodynamical attraction between two drops of equal size falling side by side, and the other, the molecular impact upon the droplets produced by Brownian movement. Among the most recent theories on the physical process of precipitation is one proposed by Bergeron, a Norwegian meteorologist, and Findeiseu, a German physicist, in the 30's. The main feature of this more recent theory is that it incorporates an explanation of the sudden release of precipitation which is frequently observed to take place from hitherto stable clond masses and satisfactorily explains the formation of snow. The theory is based on the physical fact that a t temperatures below freezing, the saturation vapor pressure with respect t o ice is less than with respect to supercooled water. It is an obsewed fact that in the atmosphere, liquid water droplets exist a t temperatures far below the freezing point, even as low as -20°C. Now if ice crystals are introduced into a cloud consisting of super-cooled clond droplets, the ice crystals will grow a t the expense of the droplets by virtue of the lower vapor pressure over ice. c Once the ice crystals grow large enough to acquire a fall velocity, further growth is insured as long as the cloud is of sufficient depth. I t matters not if the snowflakes melt, for they will then become raindrops; in fact, a large amount of rain during the cold season results from snowflakes which melt in the last few hundred feet of their fall. Since this theory postulates the presence of ice crystals, it is necessary t o explain how these may be formed. First, however, we must introduce another type of nuclei, nonhygroscopic sublimation nuclei. These do not act as condensation nuclei but have a shape and size suitable for the formation of ice crystals by sublimation of water vapor. It is presumed that when a
cloud is cooled, sublimation will occur on these nuclei at temperatures of from -lO°C. to -20°C. These crystals, once formed, will grow at the expense of other droplets in a cloud which may eventually evaporate completely, leaving only trails of ice crystals, the familiar 'I mares' tails" so frequently seen preceding a storm. This process probably goes on above a precipitation area. The ice crystals fall slowly downward into the lower cloud layers where the process is repeated until real precipitation is produced. I n this connection might be mentioned the recent experiment conducted by members of the General Electric Research Staff. This consisted of dropping particles of "dry ice" into a stable cloud mass from above and causing a very little, but nevertheless real, precipitation to fall out of the cloud. In this case the particles of "dry ice" act as a catalytic agent, causing a few cloud particles to become instantaneously transformed into ice crystals by virtue of the extremely low temperature of the "dry ice." The few ice crystals then grow at the expense of the other cloud droplets and start the precipitation process which apparently changes the cloud from a stable suspension to an unstable one. There are also two other means by which ice crystals can be introduced into a supercooledcloud: (1) It is possible for some of the supercooled droplets to pick up nuclei of crystallization (sublimation) by collision and become ice crystals; and (2) Collisions between supercooled droplets would probably also cause crystallization, just as s t i r k g of. supercooled water will cause crystallization. .. . . As can readily be imagined, the process of precipitation is very difficult to study; most of the knowledge about precipitation must be deduced from what can be observed and measured at the surface of the earth while the process itself takes place several thousand feet up. But meager as the knowledge is, afairly workable theory has been put together. There are still numerous points of uncertainty which furnish a wide field for further study and research. BIBILOGRAPHY (1) (2) (3)
(4) (5)
J. C., "Physid Meterology," Prentice Hall, Inc., New York, 1941. BFRGERON, T., Proces-Verbanz de 1'Assoc. de Met. de 1'U. G. G. I., Lisbonne, Septembre, 2933, Paris, 1935, Part 11, pp. 156-78. HOUGHMN. H. G., "~mblemaConnected with the Condensation and Precipitation Processes in the Atmosphere," Bulletin, American Meterological Society, April, 1938, pp. 152-9. HUMPHREYS, W. J., "Physics of the Air," McGraw-Hill Book Company, Inc., New York, 1940. PETPERSEN, S., "Weather Analysis and Forecasting," McGraw-Hill Book Campany, Inc., New York, 1940. &,BRIGHT,
