co

A B0 30 60

Distance (A)Fig. 3. Plot ofd(In I)/ds along the line A-B ofFig.2A. The two highest peaks should correspond tophosphate molecules ofDNA backbones, whereasthe small peak in the center may be due to theshallow bases inside the minor groove.

well preserved, presumably since the ends ofthe DNA segments are fixed by TAPO. PureTAPO solution on a similar gold substratecan be imaged only in the constant-currentmode and appears as a crystalline structureof squares 3 A on a side. The absence ofimaging in the gap-modulated mode isprobably due to a negligible modification ofthe work function of gold by TAPO.

In Fig. 1, which is a d(ln I)/ds map, twolong, partially overlapping segments of dou-ble-stranded DNA molecules are shown.The two segments ofDNA molecules showa typical helical conformation. The perio-dicity of the helix ranges from 25 A for thelower segment to 35 A for the upper one.Reproducible results have been obtained inseveral samples. At low magnification (as inFig. 1), images in the constant-currentmode are essentially the same, except forminor details in those segments where themolecule is marked by TAPO.

In Fig. 2A, which is a d(ln I)/ds map, asection of the DNA molecule is shown at amuch greater magnification (60 A by 36 A)and is a three-dimensional top-view repre-sentation with simulated illumination at anangle of 650 from the plane. The variouscolors represent the shading and their se-quence has been chosen to increase thecontrast. The molelcular structure of theDNA shows up dramatically. The two sec-tions of approximately rectangular shape(20 A by 15 A) in Fig. 2A form an angle of40° with the molecular axes and clearlyrepresent the shallow minor grooves of thehelix separated by an imperfectly imagedregion that corresponds to the deep majorgroove. The poor imaging of the majorgroove is probably due to the tip trying toenter the groove and drawing current from

IS SEPTEMBER I989

its sides, thus blurring the image. Due to theillumination technique used, the purple-redcolor spots correspond to local maxima.This kind of image representation enhancesthe small peak clearly visible in the middle ofFig. 3, which corresponds to the purple-redspots at the center ofthe rectangles, whereasin a relative height map representation itwould not be resolved. A standard model ofthe B-DNA double helix is shown in Fig. 2Bfor comparison. The model is composed ofphosphate molecules aligned along theDNA backbones and inner bases (dashedlines). In order to make a direct connectionwith the experimental result, the line A-B inFig. 2A has been redrawn in the approxi-mate location on the model. The agreementis remarkable: the periodicity of the helixis approximately 35 A; the width of theminor groove is 12 to 15 A. The slightdifference in the helix angle with respect tothe model is due to local tilting that isprobably caused by interaction with thesubstrate. A plot of d(ln I)/ds is shown inFig. 3 along the line A-B of Fig. 2A.The association ofthe structure of d(In I)l

ds to the different molecules or moleculargroups is a much harder task. A possibleinterpretation is that phosphate molecules ofthe backbone, which are negatively chargedand thus increase the local work function,are associated with the purple-red spots onthe long side of the rectangles correspond-ing to the two highest peaks of Fig. 3. Thelarger blue-green colored structures wouldthen be associated with sugar molecules andbases. Five purple-red bars corresponding tothe intermediate peak in Fig. 3 should also

be noticed on the long axes of the rectan-gles: they might be due to the shallow basesinside the minor groove.The image of Fig. 2A presumably shows

naked DNA, although the possibility of thepresence of water molecules and TAPObound to the DNA cannot be ruled out.Further experimental work is needed for acomplete understanding of such a problem.However, the results reported here alreadyshow the great potential of the method forthe characterization and possible sequentia-tion of the DNA.

REFERENCES AND NOTES

1. G. Binnig and H. Rohrer, IBMJ. Res. Dev. 30, 355(1986).

2. __ Ch. Gerber, H. Weibel, Phys. Rev. Lett. 50,120 (1983).

3. J. A. N. Zasadzinski, J. Schneir, J. Gurley, V. Elings,P. K. Hansma, Science 239, 1013 (1988).

4. A. M. Baro et al., Nature 315, 253 (1985).5. G. Travaglini, H. Rohrer, M. Amrein, H. Gross,

Surf. Sci. 181, 380 (1987).6. T. P. Beebe et al., Science 243, 370 (1989).7. B. Marchon et al., Phys. Rev. Lett. 60, 1166 (1988).8. S. Selci, A. Cricenti, R. Generosi, E. Gori, G.

Chiarotti, Inst. Phys. Conf: Ser. 93 (vol. 1), 281(1988).

9. A. Cricenti, S. Selci, R. Generosi, E. Gori, G.Chiarotti, J. Microsc. 152, 789 (1988).

10. S. Selci, A. Cricenti, R. Generosi, E. Gori, G.Chiarotti, Surf Sci. 211, 143 (1989).

11. A. Cricenti, S. Seki, R. Generosi, E. Gori, G.Chiarotti, Solid State Commun. 70, 897 (1989).

12. W. Djaczenko and C. C. Cimmino, J. Cell Biol. 57,859 (1973).

13. M. Amrein, A. Stasiak, H. Gross, E. Stoll, G.Travaglini, Science 240, 514 (1988).

14. We thank L. Ferrari and A. Gavrilovich for helpfulassistance. Supported by a grant from "ProgettoFinalizzato Materiali e Dispositivi per l'Elettroni&adello Stato Solido" of the Consiglio Nazionale delleRicerche.1 May 1989; accepted 16 June 1989

Aerosols, Cloud Microphysics, andFractional Cloudiness

BRUCE A. ALBRECHT

Increases in aerosol concentrations over the oceans may increase the amount of low-level doudiness through a reduction in drizzle-a process that regulates the liquid-water content and the energetics of shallow marine clouds. The resulting increase inthe global albedo would be in addition to the increase due to enhancement inreflectivity associated with a decrease in droplet size and would contribute to a coolingof the earth's surface.

T WOMEY et al. (1) ARGUED THAT IN- increase in the number ofCCN may have acreases in aerosols due to either natu- significant impact on the microphysics ofral or man-made causes can increase clouds and thus climate. Ship trails (2, 3)

cloud reflectivity by increasing the number provide evidence that under proper condi-of cloud condensation nuclei (CCN). Be- tions increases in aerosol concentrations cancause there may be few CCN over the locally increase the reflectivity of shallowoceans away from continental influence, any marine stratocumulus clouds. Charlson et al.

(4) discussed the possible interaction be-

Department of Meteorology, Pennsylvania State Univer- tween cloud reflectivity and the productionsity, University Park, PA 16802. of dimethylsulfide (DMS) by phytoplank-

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ton and the possible impact on dimate. Ingeneral, however, the effects of cloud pro-cesses on climate are not well understood.Although the impact that aerosols may

have on cloud reflectivity has been ad-dressed, there has been little considerationof their effect on the amount of cloudiness.In earlier studies (1, 4), the liquid-watercontent was assumed to remain constant asthe aerosol concentration increased. Thepossibility that liquid-water content mayvary with CCN concentration was raised byCharlson et al. (4), and they noted that theseeffects are difficult to quantify. Twomey etal. (1) argued that changes in the globalalbedo due to changes in cloud amountwould be largely offset by changes in thelongwave radiation budget. Such a balancewould be the case for high (upper-tropo-spheric) clouds ifthe radiation budget at thetop of the atmosphere were the only consid-eration. The vertical distribution ofradiativeheating and the surface energy budget, how-ever, are sensitive to the amount of highclouds (5, 6). In addition, any changes in thefractional amount of low clouds, whichform over large areas of the subtropics andthe tropics and are linked closely to themarine atmospheric boundary layer, will im-pact the total radiative budget becausechanges in the amount of low cloudinesshave little effect on the longwave radiationemitted to space but have a large effect onthe amount of solar radiation reflected backto space. Randall et al. (7), for example,argued that a 4% change in the amount ofmarine stratocumulus could offset thewarming resulting from a doubling of CO2concentrations.

In this report, I discuss the relation be-tween CCN concentrations and the fraction-al cloudiness of marine stratocumulus andfair-weather cumulus clouds. The mecha-nism I propose as a link between fractionalcloudiness and aerosols is precipitation,which for shallow clouds is principally in theform of drizzle. I suggest that in oceanicregions where concentrations of CCN arelow, an increase in CCN decreases the meandroplet size, which reduces drizzle produc-tion and thus increases the cloud liquidwater and the fractional cloudiness.The extensive marine stratocumulus

clouds contribute about a third ofthe earth'sglobal albedo (4). They are generally cappedby a strong inversion and are maintained byvertical mixing that is, under most condi-tions, driven by radiative cooling near cloudtop (8). The stratocumulous decks oftenbecome broken and eventually give way tobroken, shallow cumuli along the flow onthe eastern side ofthe subtropical highs. Thegeographical location of the transition fromstratocumulus to cumulus and the fractional

Fig. 1. Droplet concentration as a function of 10 \the mean volume droplet radius r, for droplets - 9in the range of r = 1 to 16 ,um. For a given 96 2liquid-water content L and number density N, L ° 7= (4/3) rr,3pN, where p is the density of water X 8-\(4). Measurements were obtained during air- 5craft ascents and descents made with the Na- -7 4tional Center for Atmospheric Research o(NCAR) Electra during FIRE (20) in horizon- c 6-0tally homogeneous clouds ranging in depth 1 8from 150 to 500 m in June and July of 1987 at 5locations about 400 to 500 km southwest of 0 20 40 60 80 100 120Los Angeles. The values are averages over a 20- Droplet concentration (cm3)m layer centered 100 m above cloud base andwere made with a Partide Measurements Systems (PMS) forward scattering spectrometer probe whereL = (4/3)irp r?Ni, and the sum is over different droplet sizes sampled. The solid line shows the relationbetween N and r, for a constant L of 0.08 g-3. Numbers refer to cases in Table 1. The shaded symbolscorrespond to the cases where drizzle (0) or significant drizzle (U) as defined in Table 1 was observed.

cloudiness associated with trade-wind cu-muli are two important factors that regulatelow-level cloudiness over the earth's oceans.

Shallow maritime clouds precipitate moreeasily than continental clouds (9). Althoughstratocumulus clouds typically have depthsof only about 250 to 500 m, they oftenprecipitate (10-13). Battan and Braham (14)detected radar echoes, indicative of precipi-tation, from oceanic cumulus clouds withtops as low as 2000 m near Puerto Rico,whereas over the central United States ech-oes were detected only from clouds withtops -4000 m. Squires (15) concluded thatthe difference in the precipitation produc-tion between continental and maritimeclouds was related to differences in CCNconcentrations. Larger cloud droplets (radi-us r . 15 jLm) have been observed inshallow, warm cumulus when concentra-tions of CCN were low (16). The warm-cloud simulations of Takahashi (17) forclouds with a depth of approximately 1.5km show that drizzle production decreasessignificantly for CCN concentrations greaterthan 150 cm-3. Twomey and Wojcie-chowski (18) noted that enhanced removalby precipitation may in part result in the lowCCN concentrations over the oceans. Thesemodeling and observational results suggestthat CCN concentrations are important inmodulating the drizzle process in shallowclouds.The drizzle produced in marine stratocu-

mulus clouds may have an important impacton the cloud liquid-water content. In acloud system studied with aircraft measure-ments off the coast of California on 13 June1976, a precipitation rate of approximately1 mm per day was estimated (10, 11). Theremoval of water from the cloud by drizzlewas about equal to the moistening of theboundary layer by evaporation from theocean. If there were no compensating verti-cal flux of water vapor from the surface,drizzle at this rate would have depleted all

the water in this cloud in approximately 1hour. The drorlet concentration was about30 to 40 cm- and the droplet distributionwas broad (12). This is a particularly inter-esting case because several ship trails wereevident in visible satellite images near thearea where the aircraft measurements weremade. In contrast, on two other flights (5and 17 June) no ship trails were observed,the droplet distribution was narrower thanthat on 13 June, and no drizzle was ob-served (12). The low droplet count and thebroad spectrum on 13 June support the idea(2, 19) that ship trails form in regions oflowCCN concentrations.Low CCN concentrations appear to be

important for the production of drizzle inshallow clouds. Microphysical observations

Table 1. Cloud depth for observations shown inFig. 1. Drizzle was observed in the clouds asindicated; cases with significant observed drizzleare indicated by an "*". The drizzle characteriza-tions are, however, subjective because the drizzleareas in these clouds tend to be horizontallyinhomogeneous. To detect drizzle, I used mea-surements from a PMS Model X260 OpticalArray Probe to estimate droplet concentrations inthe radius range of r = 30 to 310 ,um. A cloud isdefined to contain drizzle if at any level in orbelow the cloud the droplet concentration exceeds10 cm-3 and the mean radius is greater than 40Lm. Clouds with patches ofdroplet concentrationof 20 cm-3 with a mean radius of 100 ,um wereclassified as significant drizzle. These classifica-tions are consistent with subjective observationsmade by observers on the aircraft.

Case Cloud depth Drizzle(m)

1 150 No2 240 Yes3 275 Yes4 255 No5 285 Yes6 265 Yes*7 490 Yes*8 500 Yes9 275 Yes*

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Fig. 3. Fractional cloudiness as a function ofspecified sea surface temperature from steady-state solutions obtained from a modified versionof the model described in (28) with a specifiedlarge-scale divergence D.. For these tests thesurface wind speed is specified as 8 m s-' and thethermodynamic structure above the inversion andthe radiative parameterization is that used in (27).These conditions are representative of the trade-winds. The low-level divergence is specified exter-nally. Simulations with a divergence of 3 x 106s 1 and no precipitation give a saturated cloudlayer and a fractional cloud cover of 1.0 at alltemperatures.

1.0

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0.6~

0.4

0.2

0.0

Do 5 x I I- I

(without precipitation)

Do=3x 106s-'

Do =5 x 104sl -

23 24 25 26 27 28 29Sea surface temperature (OC)

Fig. 2. Geostationary Operational EnvironmentalSatellite (GOES) West visible images from 14July 1987 at (A) 1515 UT and (B) 2315 UTshowing ship trails in an "H" pattern. The X's onthe 2315 UT image indicate the location of theship-trail intersections at 1515 UT. The 0 indi-cates the 1515 UT location of the eastern edge ofan east-west band ofclouds oflow reflectivity thatis located at about 32'N and 125°W.

in marine stratocumulus made during theFirst International Satellite Cloud Climatol-ogy Project Regional Experiment (FIRE),1987 (20), illustrate the inverse relationbetween droplet size and droplet concentra-tions (Fig. 1 and Table 1) and the frequentoccurrence of drizzle as the droplet concen-tration decreases. These observations areconsistent with the suggestion by Hudson(21) that lower CCN concentrations mayenhance the precipitation process in stratusclouds. The broadening of the droplet-sizespectra in maritime clouds appears to berelated to entrainment and mixing at thedoud top (22, 23). Nicholls (24) used amodel to show that the formation of a fewlarger drops was sufficient to produce appre-ciable amounts ofdrizzle. These larger drop-lets have a relatively long residence time inthe clouds as a result of random turbulentmotions and they grow by collision andcoalescence processes. Consequently, broad-ening of the droplet-size spectrum in mari-time clouds is important in regulating thegrowth oflarger droplets. Droplet spectra incontinental clouds can, however, remainnarrow even when drier air is entrained andmixed into the clouds (25).

Drizzle that reaches the surface removesCCN from the boundary layer and helps

15 SEPTEMBER I989

maintain the low CCN concentrations thatappear to be favorable for the generation ofprecipitation. For an idealized stratocumu-lus cloud 250 m thick with a drizzle rate of1 mm per day and drizzle droplets with amean radius of 100 ,um, each of whichforms by the collection of 1000 smallerdroplets, CCN would be depleted from thecloud layer at the rate of approximately1000 cm-3 per day even if each smallerdroplet contained only a single CCN. Inregions of high CCN concentrations, theremoval of aerosols by drizzle is inhibited,which may help maintain high concentra-tions.

Local modulation of precipitation pro-cesses by aerosols may help maintain thecontrast between ship trails and their envi-ronment. For example, satellite images overseveral hours on 14 July 1987 (Fig. 2) showwell-defined ship trails (an "H" pattern).The images show that the clouds both inand out of the trails were associated withstable cloud microphysical states. The mod-ulation ofprecipitation rates by aerosol vari-ations may contribute to the apparent stabil-ity of these two cloud states because thereappears to be little difference between mete-orological conditions in regions where shiptrails are observed and in areas where theyare not (12). Radke et al. (26) analyzed datacollected during an aircraft penetration of aship trail and found an increase in the liquidwater and a decrease in drizzle-size dropletsin the trail relative to in the environment.Likewise, the relatively complicated hori-zontal variations in cloud structure that areoften observed in visible satellite images ofmarine stratocumulus (Fig. 2) often have alifetime of several hours and in many casesare maintained by variations in the micro-physical structure of the clouds and notvariations in the temperature, moisture, andwind.

In addition to the direct removal of liquidwater and CCN from the cloud layer, drizzlein stratus clouds stabilizes the boundarylayer (11, 13). Stabilization results from aheating of the cloud layer as water vaporcondenses and a cooling of the subcloud

layer as some of the drizzle evaporates. Thisstabilization inhibits vertical mixing, a pro-cess that is critical to the maintenance ofmarine stratocumulus. For a drizzle rate of1 mm per day, a boundary layer 500 m deepwould be stabilized at a rate of 10°C km-'per day. In some cases, evaporation justbelow cloud base can form a stable layer ofsufficient strength that the cloud and thesubcloud layer can be completely decoupled(13). Because decoupling limits the trans-port of water from the surface to the cloudlayer, it may lead to conditions that allowthe cloud to break up. This process may beone mechanism that contributes to the tran-sition between marine stratocumulus andtrade cumulus as low-level air flows equator-ward in the subtropical highs.Although our present understanding is

insufficient to model the transition fromstratocumulus to trade cumulus, the effectsthat drizzle might have on the fractionalcloudiness associated with trade cumuli canbe estimated with a simple one-dimensionalmodel [(27-29); see also (30)] of the ther-modynamic structure of the trade-windboundary layer. In this model the structurerepresents that of an area that is assumed toinclude many (parameterized) convective el-ements and is on the order of a typical gridbox in a general circulation model. Theconvective and the radiative fluxes are pa-rameterized. I modified the model to in-clude precipitation by allowing a specifiedfraction of the parameterized cloud water tobe converted to precipitation and removedfrom the boundary layer.Although the fractional area of active fair-

weather cumuli (cloud elements associatedwith active updrafts) over the oceans mayonly be a few percent at any given time (31),total fractional cloud amount can be muchlarger, because it includes both passive (ordynamically inactive) and active cloud ele-ments (32). Although only active clouds areresponsible for vertical transport of energyand moisture, both passive and active cloudsare important for the radiation budget oftheboundary layer and the surface. The amountof passive cloudiness may critically depend

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on the initial liquid-water content of thecloud elements and the relative humidity inthe cloud layer (27). This effect is illustratedby the parameterization of fractional cloudamount (FC) (27) where FC = (SR - 1)/(SR - RH) and SR is the ratio of the totalwater (liquid and vapor) mixing ratio in thecloud to the saturation mixing ratio, and RHis the relative humidity of the environment.Cloud elements that form in an environmentwith a high RH (close to 1) will have a longlifetime, which contributes to a large FC. Incontrast, a cloud element with a small initialliquid-water content (SR only slightly largerthan 1) will be associated with a small FC.For typical conditions over subtropicaloceans, RH is between 0.8 and 1.0 and SRmay vary from 1.0 to 1.2 (27). For theseranges of variations, FC is sensitive to varia-tions in both RH and SR and thus to drizzle(27).

Simulations made with and without pre-cipitation at different sea-surface tempera-tures using the model described above (Fig.3) show that for a specified large-scale diver-gence (which specifies the lar e-scale verticalvelocity) Do of 5 x 10-6 s-, FC decreasesby as much as 0.6 in the precipitating case.

i 1.10

cn% 1.00

£2C)co1-

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0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Precipitation efficiency

Fig. 4. The dependence of fractional cloudiness,RH, and SR for different specifications of aprecipitation efficiency factor. The removal ofwater by precipitation processes in the parameter-ized convective elements by the model is assumedto be (dl,/dz)pREcIp = -a 1 where z is height, l isthe cloud liquid water, and a is the precipitationefficiency factor in units of per kilometer. A zeroefficiency factor is no drizzle production and avalue of a = 1 corresponds to a decrease in thecloud liquid water (for no condensation) by lieover a cloud depth of 1 km. Solutions are for theconditions described in Fig. 3 with a sea-surfacetemperature of 26°C and D. of 5 x 10-6 s'.

1230

In addition, the response of the cloud coverto specified sea-surface temperature varia-tions is substantially altered by the inclusionof precipitation. For a weaker subsidencerate (Do = 3 x 10-6 s-'), FC is 1.0 at allsea-surface temperatures from 22° to 30°C ifprecipitation is not included because theseconditions give a deep boundary layer and asaturated cloud layer. With drizzle (Fig. 3),the cloud cover is reduced to about 0.40. Inaddition, FC increases from 0.2 to 0.6 (withDo = 5 x 10-6 s-1) as the surface windspeed (which regulates the evaporation fromthe surface) increases from 3 to 9 m s- .

When drizzle is included, FC is about 0.1and is insensitive to the specification of thewind speed.As a specified precipitation efficiency fac-

tor in the model is increased (which isequivalent to decreasing the CCN concen-tration), the water content (SR) of themodel clouds decreases (Fig. 4). There isthen less water available to evaporate in thecloud layer so that this layer dries and warmsrelative to the nonprecipitating case. Thiseffect results in a decrease in RH. Thus thedepletion ofcloud water by drizzle results ina large decrease in the FC because of de-creases in both SR and RH. The sensitivityofFC to the precipitation efficiency factor isgreatest just as the cloud fraction decreasesfrom totally cloudy conditions and the pre-cipitation rate is 0.4 to 0.6 mm per day.These sensitivity tests indicate that as theprecipitation efficiency of shallow cloudsdecreases, FC and its sensitivity to the sea-surface temperature and the surface windspeed increases.

It is difficult to quantify the effects thataerosol variations may have in altering theglobal albedo because theories of drizzleproduction and its effects on the structure ofthe marine stratocumulus and its role in thetransition from stratocumulus to trade cu-mulus clouds are incomplete. In addition,most climate models include only a cruderepresentation of shallow clouds and cloudprocesses in general (33). From albedo esti-mates (4), one can, however, deduce that a4% increase in the fractional cloudiness oflow clouds would result in an increase in theglobal albedo of about 0.02, which is equiv-alent to that attributed to the estimatedreflectivity change associated with a 30%increase in the CCN concentration. Becausechanges in cloud amount and reflectivitywork in concert to alter the cloud albedo,the effects of decreased drizzle would en-hance the feedbacks suggested by Charlsonet al. (4). From a climate modeling perspec-tive, these results are discouraging because,in general, the cloud problem has beenviewed as one of trying to relate cloudprocesses to the large-scale thermodynamic

and kinematic fields. If, however, aerosols(CCN) play a significant role in modulatingcloud processes and the associated globalalbedo, then an additional degree ofcompli-cation is added to the cloud problem.

REFERENCES AND NOTES

1. S. A. Twomey, M. Piepgrass, T. L. Wolfe, Tellus36B, 356 (1984).

2. J. H. Conover, J. Atmos. Sci. 23, 778 (1966).3. J. A. Coakley, Jr., R. L. Bernstein, P. A. Durkee,

Science 237, 1020 (1987).4. R. J. Charlson, J. E. Lovelock, M. 0. Andreae, S. G.

Warren, Nature 326, 655 (1987).5. T. P. Ackerman, K-N. Liou, F. P. J. Valero, L.

Pfister, J. Atmos. Sci. 45, 1606 (1988).6. G. L. Stephens and P. J. Webster, ibid. 41, 681

(1984).7. D. A. Randall, J. A. Coakley, C. W. Fairall, R. A.

Kropfli, D. H. Lenschow, Bull. Am. Meteorol. Soc.65, 1290 (1984).

8. D. K. Lilly, Q.J. R. Meteorol. Soc. 94, 292 (1968).9. See pp. 194-202 of F. H. Ludlam, Clouds and Storms

(Penn State Univ. Press, University Park, PA,1980), for an overview.

10. R. A. Brost, D. H. Lenschow, J. C. Wyngaard, J.Atmos. Sci. 39, 800 (1982).

11. , ibid., p. 818.12. B. A. Albrecht, R. Penc, W. H. Schubert, ibid. 42,

800 (1985).13. S. Nicholls, Q.J. R. Meteorol. Soc. 110, 783 (1984).14. L. J. Battan and R. R. Braham, Jr., J. Meteorol. 13,

587 (1956).15. P. Squires, Tellus 10, 262 (1958).16. E. E. Hindman II, P. V. Hobbs, L. F. Radke, J.

Atmos Sci. 34, 951 (1977).17. T. Takahashi, ibid. 33, 269 (1976).18. S. Twomey and T. A. Wojciechowski, ibid. 26, 684

(1969).19. S. A. Twomey, H. B. Howell, T. A. Wojciechowski,

ibid. 25, 333 (1968).20. B. A. Albrecht, D. A. Randall, S. Nicholls, Bull. Am.

Meteorol. Soc. 69, 618 (1988).21. J. G. Hudson, J. Atmos. Sci. 40, 490 (1983).22. M. B. Baker, R. G. Corbin, J. Latham. Q. J. R.

Meteorol. Soc. 106, 581 (1980).23. J. W. Telford and S. K. Chai, Pure Appl. Geophys.

119, 720 (1980).24. S. Nicholls, Q. J. R. Meteorol. Soc. 114, 1141

(1988).25. J. B. Jensen, P. H. Austin, M. B. Baker, A. M. Blyth,

J. Atmos. Sci. 42, 173 (1985).26. L. F. Radke, J. A. Coakley, Jr., M. D. King, in

preparation.27. B. A. Albrecht, J. Atmos. Sci. 38, 97 (1981).28. , A. K. Betts, W. H. Schubert, S. K. Cox,

ibid. 36, 73 (1979).29. B. A. Albrecht, Tellus 36A, 187 (1984).30. K. N. Liou and S. C. Ou, J. Geophys. Res. 94, 8599

(1989). These authors used a one-dimensional cli-mate model to assess the role of cloud droplet sizeon precipitation and cloudiness. Their general con-clusions support some of the ideas presented in thisreport.

31. H. Riehl, T. C. Yeh, J. S. Malkus, N. E. LaSeur, Q.J. R. Meteorol. Soc. 77, 598 (1951); E. Augstein, H.Richl, F. Ostapoff, V. Wagner, Mon. Weath. Rev.101, 101 (1973); H.-R. Cho, J. Atmos. Sci. 34, 87(1977).

32. R. B. Stull, J. Climatol. Appl. Meteorol. 24, 49(1985).

33. R. C. J. Somerville, Nature 315, 713 (1985).34. T. Ackerman, M. Baker, C. Fairall, P. Durkee, and

D. Lamb provided useful comments on this work.The suggestions and encouragement of C. Bohrenare greatly appreciated. E. Gherlone assisted withthe preparation of this manuscript. This researchwas supported by the National Science Foundationgrant 86-19854 and jointly with the National Oce-anic and Atmospheric Administration grant ATM86-11224.

3 April 1989; accepted 11 July 1989

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