P. Squires Evolution of Cloud Droplet Laboratory of Atmospheric Physics Spectra: The Ellect ol Desert Research Institute University of Nevada System Nuclei Spectra Reno, Nev. 89507

Abstract complexities arise in the case of stratocumulus and even The particles on which cloud drops nucleate are thought to more so in the case of fog. be of mixed and somewhat variable constitution. Conse- Thus the specific relationship between nuclei and quently, in the discussion of cloud formation, a number of cloud droplet spectra appears in its simplest form in the simplifications and approximations are introduced that can case of cumulus, where a simple kinematic and thermo- in fact be justified a posteriori. Provided that the spectrum of critical supersaturations of the particles is known (rather dynamic model may realistically be taken as represent- than, for example, their size distribution), the resulting ing the major atmospheric event. theory can be used to predict the concentration of droplets in clouds with errors of order 50%. Thus, the theory can 2. Theoretical approaches explain, for example, the systematic difference between maritime and continental clouds. Some of the errors may The theoretical discussion of cloud formation usually be attributed to sampling problems and some to instrumental begins after the condensation nuclei have become haze problems; a more accurate check on the theory would require droplets. There exists a veritable hierarchy of approxi- the use of improved instrumentation to characterize the mations that result in simplified equations. Thus, the aerosol, and the conduct of a cloud-forming experiment under rather well-controlled conditions. transfer of vapor to a growing droplet and of heat from it is treated as a steady state process. Ventilation 1. Introduction effects due to sedimentation and the interactions of the Clouds form by a kind of macroscopic heterogeneous diffusion fields of one droplet with those of its neighbors nucleation of unstably growing water droplets on a are ignored. Continuum physics fails to describe mass selected group of particles, the so-called cloud nuclei or and heat transfer in the immediate vicinity of a drop- cloud condensation nuclei, as first discussed quantita- let with a radius comparable with the mean free path tively by Howell (1949). This nucleation type event is of air and vapor molecules. Following Fuchs (1934), this therefore one of the meeting places between two fields is dealt with approximately by introducing the notion of inquiry: aerosol physics, including the formation, of a "boundary sphere" at a distance from the drop growth, and elimination of particles; and cloud physics, surface of the order of a mean free path. Within this including the hydrologic cycle and the profound thermo- sphere, transfers are supposed to occur by molecular- dynamic influence of clouds on the lower troposphere. kinetic processes. These considerations have the effect of making the rate of growth of a small droplet de- The relationship between these particles and cloud pendent on the thermal accommodation coefficient droplet spectra has been studied most intensively in (which is usually assumed to be unity) and on the ac- connection with convective clouds. Cumulus clouds have commodation coefficient for water molecules, which will a basic kinematic simplicity in that cloud formation may be referred to here as the "sticking" coefficient. Experi- reasonably be supposed to occur as a result of the mental values for this coefficient center at about 0.04, steady, adiabatic expansion of moist air. Radiative ef- though they cover a wide range. In addition, a number fects may be disregarded because characteristic updraft of approximations are usually used to describe how the velocities correspond to cooling rates of order 10?oC per equilibrium vapor pressure of a solution droplet de- day. No doubt other more complex nucleation events pends on its radius and on the nucleus. For example, occur within a cumulus cloud as a result of the in-mixing it is typically assumed that the nucleus is entirely solu- of the air into which it grows; but since the real moisture ble, that the van't Hoff factor does not change as the supply for cloud formation comes from the well-mixed, droplet grows and becomes more dilute, and that the relatively homogeneous subcloud layer, the microphysical surface tension and density of the solution are equal stage is essentially set at the time of the original nuclea- to those of water. These simplifications are justified only tion of unstably growing droplets. if the solution is dilute. Indeed, as discussed below, the This simplifying element is absent in many other "dilute solution" assumption would appear to represent cloud systems. For example, in the case of a middle-level an acceptable approximation. cloud forming in an area of general rising motion, char- acteristic cooling rates due to expansion are not so large The analysis traces out how the relative humidity that radiative effects are obviously negligible. Similar rises at first more or less linearly as a result of the steady expansion of the air and how its rise is slowed as suc- i Paper presented at the International Cloud Physics Con- cessive groups of nuclei become unstable and begin to ference, 26 July 1976, Boulder, Colo. absorb significant quantities of water. The maximum

Bulletin American Meteorological Society 29

Unauthenticated | Downloaded 10/03/21 10:33 PM UTC 30 Vol. 58, No. 1, January 1977 value is reached when the absorption of water and re- of the growing drops is most critical for the cloud-form- lease of heat match the rate of expansion, and thereafter ing process at the time when they approach their critical the supersaturation declines. To a first approximation, size. In the case of a nucleus consisting of a pure soluble the concentration of cloud droplets that form is equal electrolyte, the effective molar ratio of solute to solvent to the concentration of nuclei with critical supersatura- has by then fallen to about Sc/2 (Sc in absolute units), tions less than the maximum value reached in the so that if the critical supersaturation is of order 10"2, ambient air. the critical droplet solution is indeed somewhat dilute, It is generally believed that atmospheric condensation though this does not always mean that the van't Hoff nuclei are not the pure soluble electrolytes that are factor is very close to its value at infinite dilution (e.g., usually discussed in connection with cloud formation in the case of H2SO* it is still about 2). Thus, since cloud but are mixed particles consisting in part of insoluble formation usually involves only particles for which Sc components. Some evidence on this question has been is of order 10~2 or smaller, in the case of critical droplets obtained by Twomey and Severynse (1964) and Twomey there is some a posteriori justification for the approxi- (1965) who estimated the sizes of natural cloud nuclei mations that depend on the "dilute solution" assump- by means of diffusion battery measurements. The diffu- tion. Also, the presence of an insoluble component will sion coefficient of these particles was smaller than would by that time have only a reduced influence. be expected if they were wholly soluble; this finding There is some plausibility, therefore, to the commonly led to the conclusion that they contained an insoluble adopted notion that the most important single property component. of a complex nucleus is its critical supersaturation. However, Katz and Kocmond (1973) measured the Thus, if the spectrum of critical supersaturations is size distribution of an NaCl aerosol prepared in the known, the theoretical discussion of cloud formation laboratory using an electrical aerosol analyzer and found may reasonably be carried out as if the nuclei were that even with a pure soluble aerosol, the particles with simple soluble particles of the appropriate size. a given critical supersaturation, Sc, were 2-3 times larger than theory would indicate—indeed, somewhat larger 3. Experimental checks than indicated by the work of Twomey and Severynse The first attempt to check whether theory correctly for natural particles. This work tends to call in question predicted the way a cloud forms was made by Twomey the basic theory of Kohler that relates the size of a and Squires (1959) in the simplest way possible, by mea- soluble particle to its critical supersaturation, and there suring the spectrum of the critical supersaturation Sc is a need for further investigations along these lines. of cloud nuclei in the air below a cumulus and the In contrast to the results of Katz and Kocmond, H. C. concentration of droplets in the cloud. This type of Gerber (personal communication, 1976) has recently ob- experiment has been repeated several times, and, in tained some results that confirm Kohler's theory. general, there has been agreement between observed and The many approximations used in discussing cloud computed droplet concentrations to within about 30- formation, some of which are fairly crude, are justified 50%. This result is about as good as could be expected by two considerations. First, the question of the nature in such an experiment considering the approximations of the nuclei. Obviously, a complete physical and chemi- used in the theory, the difficulty of the measurements, cal description of the nucleus population is beyond our and the serious sampling problems that arise. Strictly reach. Methods exist for exploring the size distribution speaking, the aerosol measurements should be made just over the relevant range of sizes (down to about r = below cloud base, and the cloud droplet measurements, 0.01 /um), but even the average chemical constitution is together with vertical velocity measurements, should be poorly understood, and it is totally unknown whether made very soon afterward just above this point. This is droplet growth rates may be affected by the presence in impracticable with a single aircraft, so that inevitably the nuclei (or some of them) of very small proportions the results tend to be confused by fluctuations in at- of surface active materials, as suggested, for example, by mospheric properties. Better controlled experiments 3 Mazin (1974). Consequently, no amount of computa- were carried out in a 3000 m chamber by Volkovitskiy tional elaboration is likely to enable us to realistically and Laktionov (1969) with generally similar results, explain initial cloud droplet spectra without additional though with less scatter than in the experiments con- physical insight into the nature of the nuclei. ducted in the free air. Second, the question of representativeness: existing All these experiments depend on the measurement of approximate theories indicate that the initial droplet the spectrum of Sc. There are reasons to think that the spectrum near the base of a cumulus depends on the accuracy of such measurements may not have been very preexisting aerosol and on the updraft speed, both of good in all cases. Comparisons were made between sev- which vary in time and space. To seek to explain drop- eral thermal diffusion chambers of rather similar design let spectra except in terms of mean properties is there- at Ft. Collins in 1970. When natural nuclei were used, fore impracticable. the various chambers differed by up to about 50%, The size distribution of the aerosol would, apparently, whereas with artificial aerosols, the differences were be a poor guide to its cloud-forming properties. In this even greater. More serious still, Alofs and Carstens connection, it is worthwhile to recall that the behavior (1976) have concluded from a theoretical analysis that

Unauthenticated | Downloaded 10/03/21 10:33 PM UTC Bulletin American Meteorological Society 31 thermal diffusion chambers of typical design are subject in the body of the cloud that increase in frequency to an uncertainty of a factor of 2 at 5 = 10~2, and up to with increasing height. a factor of 10 at S = 10~3. Regarding the initial droplet spectrum (to be found The effect of errors in the determination of the Sc in the lower part of a cumulus), neither turbulence nor spectrum may be estimated using the approximate theo- entrainment would seem likely to be significant. During ries of Twomey (1959) or Sedunov (1967). Representing the critical cloud-forming event, the supersaturation the Sc spectrum by N(SC) ~ cSck, where N is the concen- rises to a maximum and then begins to decline. With tration of nuclei with critical supersaturations less than usual cumulus updraft speeds, this event occupies only Sc, Twomey's treatment leads to the result that the con- a shallow layer, of order 20 m deep. The depth of this centration of droplets n formed in an updraft of critical layer is very small compared with the width of velocity V is given by a cumulus updraft. Over such a shallow layer, notable fluctuations in the vertical velocity are not likely; in /(fc+2) k/a+2) 2/(fc+2) 3k/[m+2)] n = [2-rrkB(3/2, V2)]~* 0 c v fact, updrafts are often observed to be rather smooth near the base of a cumulus. where 6 is a function of the pressure and temperature Rooth (1957) had suggested that with a small value at which condensation occurs. of the sticking coefficient, droplet growth at small sizes The values of k are typically less than unity, so that would be retarded. As a result, droplets would spend an error in c of 50% would cause an error of at least a longer time growing through the small sizes (below 30% in n. Errors of the magnitude suggested by Alofs r = 1 /mi), where the Raoult effect due to the dissolved and Carstens would obviously be more than sufficient nucleus is appreciable. This would increase the relative to explain the discrepancies typically found between ob- growth advantage of droplets formed on larger nuclei served and predicted cloud droplet concentrations, quite with lower Sc values and so tend to broaden the spec- apart from other errors, such as those due to sampling. trum. Indeed, Warner (1969b) found that as the sticking From the formula for n, it may be noted that the coefficient used in a model calculation decreased, the influence of V on n depends on the slope of the nucleus dispersion of the initial spectrum did increase some- spectrum, which is defined by k. The exponent of V what. By comparing the model-produced spectra with varies from about 0.2 to 0.5 for k in the range 1/3 to 1, those observed in the lower parts of cumuli, he was the values typically found in nonurban areas. This de- able to obtain some indications as to the magnitude of pendence is in rather good agreement with the experi- the sticking coefficient for water vapor molecules, which mental results. were in general agreement with most of the determina- tions that have been made in the laboratory. Fitzgerald 4. Cloud droplet spectra (1970, 1972), using a similar value of 0.036, found rather Howell (1949) remarked that observed droplet spectra good agreement between observed and predicted spectra often seemed to be distinctly broader than those that of cloud droplets. would be predicted theoretically. Since the formation of In summary, above the cloud base region, spectra are rain by coalescence of droplets would seem likely to probably influenced by entrainment and turbulence— depend critically on dispersion of the droplet spectrum which are probably linked. The initial spectrum, to be formed by condensation, this question has been of con- found in the cloud base region, will be controlled by cern to cloud physicists for many years. the nucleus spectrum and the updraft speed, and its Belyaev (1961), Sedunov (1965), and Levin and correct prediction seems to depend on a knowledge of Sedunov (1968) concluded that a distinct spectrum the sticking coefficient. This is a poorly understood broadening would result from turbulence in the up- parameter, and one that could perhaps be influenced by draft. However, Warner (1969a, b) was not able to the presence of surface active materials. obtain this result. He found that a turbulent updraft, in general, though not always, would produce a spec- 5. Concluding remarks trum that differed little from that formed with a con- The concentration of droplets found in cumuli vary stant updraft velocity at a given level in the cloud. A over a range of order 10-1, the higher concentrations similar result was obtained by Bartlett and Jones (1972). being found in continental areas, where the concentra- Stepanov (1975) gave a more generalized treatment and tions of cloud nuclei are also high. It would appear that concluded that the earlier results were not really in our present measurement techniques and theories of conflict, the differences arising from the differing ways droplet growth are good enough to enable us to under- in which turbulence was taken into account. stand such gross differences in cloud microstructure. From the analysis of an extensive set of observations, As mentioned earlier, cloud formation resembles a Warner (1969a) was led to conclude that the entrain- nucleation event; in the whole ensemble of atmospheric ment of environmental air into the top of a cumulus in processes, only those that fall in this group are likely the manner suggested by Squires (1958) played an im- to be influenced by man's activities, whether advertent portant role in modifying droplet spectra. This effect or inadvertent. It would therefore seem desirable to is not present near cloud base (Warner, 1973), but it refine our understanding of this area one step further. appears to result in the formation of bimodal spectra For example, it would be useful to improve existing

Unauthenticated | Downloaded 10/03/21 10:33 PM UTC 32 Vol. 58, No. 1, January 1977 measurement techniques so that by using an aerosol of drop size spectrum. Izv. Acad. Sci. USSR Atmos. Oceanic known constitution and carrying out reproducible ex- Phys., Engl. Transl., 10, 228. periments in a well-controlled situation, it would be Rooth, C., 1957: On a special aspect of the condensation possible to check and modify existing theory to achieve process and its importance in the treatment of cloud particle growth. Tellus, 9, 372. a predictive accuracy considerably better than has been Sedunov, Y. S., 1965: Fine structure of clouds and its role achieved so far. in the formation of the cloud particle spectrum. Izv. Acad. The importance of the subject of cloud formation, Sci. USSR Atmos. Oceanic Phys., Engl. Transl., 1(7), 720. and its relation to the aerosol, needs little emphasis. It , 1967: Kinetics of the initial condensation stage on bears directly on the hydrologic cycle and on atmo- clouds. Izv. Acad. Sci. USSR Atmos. Oceanic Phys., Engl. spheric scavenging of the aerosol itself—both of which Transl., 3(1), 34. relate to practical problems of increasing importance. Squires, P., 1958: Penetrative downdrafts in cumuli. Tellus, 10, 381-389. References Stepanov, A. S., 1975: Condensation growth of cloud drops Alofs, D. J., and J. C. Carstens, 1976: Numerical simulation in a turbulent medium in the low water content approxi- of a widely used cloud nucleus counter. J. Appl. Meteor., mation, incorporating diabatic effects. Izv. Acad. Sci. USSR 15, 350-354. Atmos. Oceanic Phys.., Engl. Transl., 11, 160. Bartlett, J. T., and P. R. Jonas, 1972: On the dispersion of Twomey, S., 1959: The nuclei of natural cloud formation, the sizes of droplets growing by condensation in turbulent Part 2, The supersaturation in natural clouds and the clouds. Quart. J. Roy. Meteor. Soc., 98, 150. variation of cloud droplet concentration. Geofis. Pura Belyaev, V. I., 1961: Drop-size distribution in a cloud during Appl., 43, 243. the condensation stages of development. Izv. Akad. Nauk , 1965: Size measurements of natural cloud nuclei. J. SSSR, Ser. Geofiz., 1209-1213. Rech. Atmos., 2, 113. Fitzgerald, J. W., 1970: A re-examination of the classical , and G. T. Severynse, 1964* On the relation between theory of the growth of a population of cloud droplets by sizes of particles and their ability to nucleate condensation condensation. Preprints, Conference on Cloud Physics (Ft. of natural clouds. J. Rech. Atmos., 1, 81. Collins), AMS, Boston, 111-112. , and P. Squires, 1959: The influence of cloud nucleus , 1972: A study of the initial phase of cloud droplet population on the microstructure and stability of con- growth by condensation: Comparison between theory and vective clouds. Tellus, 11, 408. observation. Ph.D. dissertation, Univ. of Chicago, Chicago, Volkovitskiy, O. A., and A. G. Laktionov, 1969: An investi- 111. gation of the initial stage of cloud formation in a chamber. Fuchs, N. A., 1934: On the rate of fine droplet evaporation Izv. Acad. Sci. USSR Atmos. Oceanic Phys., Engl. Transl., in a gaseous atmosphere. ,/. Exp. Tech. Phys., 4, 7. 5, 153. Howell, W. E., 1949: The growth of cloud drops in uni- Warner, J., 1969a: The microstructure of cumulus cloud: formly cooled air. J. Meteor., 6, 134. Part 1, General features of the droplet spectrum. J. Atmos. Katz, U., and W. C. Kocmond, 1973: An investigation of the Sci., 26, 1049. size-supersaturation relationship of soluble condensation , 1969b: The microstructure of cumulus cloud: Part 2, nuclei. J. Atmos. Sci., 30, 160-165. The effect on droplet size distribution of the cloud nucleus Levin, L. M., and Y. S. Sedunov, 1968: The theoretical model spectrum and updraft velocity. J. Atmos. Sci., 26, 1272. of the drop spectrum formation process in clouds. Pure , 1973: The microstructure of cumulus cloud: Part 4, Appl. Geophys., 69, 320. The effect on the droplet spectrum of mixing between Mazin, I. P., 1974: Mechanisms of formation of the cloud- cloud and environment. J. Atmos. Sci., 30, 256. •

announcements continued from page 28 graphic temperature map. The films show land areas chang- ing from their night shade of grey to black as the land is Time-lapse cloud films warmed to its maximum daytime temperature. Vertical Three 16 mm time-lapse films of weather patterns in the circulation in the Intertropical Convergence Zone is espe- northern half of the Western Hemisphere are available from cially interesting as a diurnal cycle of huge convective cell the California Institute of Earth, Planetary and Life Sci- developments, oscillating between intermediate grey and ences. The first of their kind, two of the films—"Hurri- bright white. Fifteen Pacific hurricanes were spawned here cane 1" and "Hurricane-2"—cover the weather from May in the summer of 1975. "Hurricane-3," recently made avail- 1975 to May 1976 in 40 min and were compiled from about able for distribution and covering weather from May to 16 000 individual photographs of the infrared (IR) emission October 1976, shows the unusual path of Hurricane Kath- from the Western Hemisphere. Each 24 h day is documented leen, circa 10 September 1976. each half hour with IR photos acquired by the Stationary Each film, "Hurricane-1" (covering May 1975-October Meteorological Satellite-2 (SMS-2), the second in the planned 1975), "Hurricane-2" (November 1975-May 1976), and "Hur- worldwide series of six geosynchronous, equator-based, mete- ricane-3" (May-October 1976) is available for $140.00 per orological satellites. copy. For further information, contact: California Institute Photographs of the IR emission from the earth and its of Earth, Planetary and Life Sciences, 12208 N.E. 137th atmosphere show the various temperatures in 256 shades of Place, Kirkland, Wash. 98033. grey, from black to white, indicating hot to cold. Thus, in these films the year's weather is visible as an evolving topo- Continued on page 32

Unauthenticated | Downloaded 10/03/21 10:33 PM UTC