Radiative influences on drop and cloud condensation

nuclei equilibrium in stratocumulus

James Marquis and Jerry Y. HarringtonDepartment of Meteorology, Pennsylvania State University, University Park, Pennsylvania, USA

Received 30 August 2004; accepted 17 February 2005; published 20 May 2005.

[1] Radiative heating and cooling occurs throughout most of a stratocumulus cloudlayer. Shortwave (SW) heating of individual drops can be strong enough that droptemperatures at equilibrium deviate by as much as 6�C from the surroundingenvironment. These large temperature differences lead to substantial errors when theclassical equation for vapor growth is used. A new form of the vapor growth equation isderived for cases of strong radiative heating. The new equation is used to assess theequilibrium supersaturation (seq) state of drops and cloud condensation nuclei (CCN)within a stratocumulus cloud. Longwave (LW) cloud top cooling has two primaryeffects on seq. It tends to reduce seq for large drops to values as low as �6%, providingfor drop growth at subsaturations. It also tends to reduce the critical supersaturation andsize at which larger CCN activate to become growing cloud drops. In contrast, LWheating of cloud base suppresses the growth of cloud drops and CCN. Larger CCN(sizes between 0.5 and 5 mm) lose their Kohler curve maximum, indicating restrictedCCN growth. Solar heating produces seq up to 20% for drops with sizes between 500and 1000 mm, indicating strong evaporation of drizzle drops. Since solar absorptionincreases more slowly with drop size than LW emission, a minimum appears in theKohler curves at sizes between 20 and 100 mm, suggesting a preferred size range forvapor growth in SW heated clouds. Like LW heating, SW heating causes suppression ofgrowth for larger CCN.

Citation: Marquis, J., and J. Y. Harrington (2005), Radiative influences on drop and cloud condensation nuclei equilibrium in

stratocumulus, J. Geophys. Res., 110, D10205, doi:10.1029/2004JD005401.

1. Introduction

[2] It is well-known that near cloud boundaries, clouddrops experience significant radiative heating/cooling,which alters the vapor growth rates of the drops [e.g.,Roach, 1976]. These radiative heating and cooling ratescan be large, reaching values of nearly �15 K h�1 forcloud-top longwave (LW) cooling and nearly 2 K h�1 forsolar, or shortwave (SW), heating. In the case of stratiformboundary layer clouds, LW cooling influences the develop-ment of the drop size spectrum once the drops reach cloudtop [e.g., Austin et al., 1995]. Roach [1976], Barkstrom[1978], and Guzzi and Rizzi [1980] have shown that LWradiation begins to strongly influence drop growth at radii ofaround 10 mm. Beyond this size, the LW influence increaseswith size and begins to dominate drop growth. If dropsspend at least 10 min at cloud top [Harrington et al., 2000],LW cooling can produce significant broadening of the dropsize spectrum leading to quicker initiation of the collectionprocess [Hartman and Harrington, 2005a] and perhaps amore prolific drizzle process [Austin et al., 1995]. The LWinfluence appears to have its strongest influence on drop

growth at intermediate and larger drop concentrations (N ^200 cm�3) [Hartman and Harrington, 2005a].[3] Though the influence of LW cooling on drop growth

has been studied somewhat extensively over the past 20 years,few studies have examined the influence of SW heating onthe growth of drops. (The two notable exceptions are Davies[1985], who examined how LW and SW radiation alters theequilibrium value of supersaturation, and Ackerman et al.[1995], who included LW and SW heating influences ondrop growth in a one-dimensional model of boundary layerstratiform clouds.) That this is the case is notable because,unlike LW cooling, SW heating occurs throughout most, orall, of a stratocumulus cloud deck. One can imaginetherefore that SW heating may have an important, suppres-sive effect on the growth of drops within stratiform clouds.Indeed, the studies of Hartman and Harrington [2005a,2005b] show that for solar zenith angles between 0� and60� SW heating suppresses the vapor growth of cloud dropsand, in certain situations, this can cause a suppression ofcollection growth.[4] While almost all prior studies examined radiative

influences on drop growth with an eye on collection rates,few studies have focused primarily on vapor growth rates.Interestingly, Guzzi and Rizzi [1980] showed that drops withradii ^10 mm have enhanced growth rates due to cloud top

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, D10205, doi:10.1029/2004JD005401, 2005

Copyright 2005 by the American Geophysical Union.0148-0227/05/2004JD005401$09.00

D10205 1 of 13

LW cooling, whereas smaller drops (r ] 10 mm) tend tohave their growth suppressed. It turns out that this result isdue to the fact that the drop absorption efficiency (Qabs)increases rapidly between 5 and 10 mm (see Figure 5a below),which allows r ^ 10 mm drops to cool in the LW, whereassmaller drops have weak to nonexistent cooling rates. There-fore drops with r^ 10 mm can persist in slightly subsaturatedenvironments [Roach, 1976]. Unlike LWcooling, theQabs forSW radiation increases slowly with size. As Hartman andHarrington [2005a] have shown, this leads to strong suppres-sion of vapor growth for drops with r ^ 200 mm.[5] Reflecting on these previous studies, the following

question comes to mind: When radiative influences areimportant, under what conditions are water drops of varioussizes in equilibrium with the surrounding vapor field?Because radiative influences alter drop temperatures, thesupersaturation at which drops are in equilibrium with thesurrounding environment (seq, or the Kohler equation) maybe substantially altered. It would therefore seem that knowl-edge of how seq is affected in radiatively heated/cooledstratocumulus would be important for studies of dropgrowth. Alas, even though the radiatively influenced growthhas been studied for over 20 years, radiative affects on dropequilibrium have been relatively ignored, with the onlyexceptions being Roach [1976] and the recent work byConant et al. [2002].[6] The study by Roach [1976] was perhaps the only one

to examine LW cooling effects on seq for cloud drops. Hisidealized studies showed that (1) the critical supersaturation(maximum) in the Kohler curve (scrit) is reduced and hasnegative values. Furthermore, the radius associated with scrit(critical radius, or rcrit) is reduced substantially (Figure 1).This is important because the maximum is typically used asa demarcation between cloud condensation nuclei (CCN,left of the maximum) and activated CCN or growing drops(right of the maximum). Since seq increases with size forCCN, this region can be thought of as one in which CCNgrowth is restricted. Conversely, seq decreases for activated

CCN, or growing drops, which we shall call unrestrictedgrowth. (2) As drop size increases, seq continues to de-crease, amplifying vapor growth (Figure 1). This effect hasbeen the focus of most previous studies. (3) Under moderateLW heating, such as at cloud base, seq increases with sizeand may therefore affect the activation of CCN. ThoughRoach [1976] first pointed out how cloud top LW coolingmay alter seq, he did not extend his analysis to large drops,which are much more strongly affected by radiation.[7] Given the current interest in black carbon aerosol

influences on cloud radiative properties [e.g., Ackerman etal., 2000; Feingold et al., 2004], there has been somerenewed interest in how radiation affects the equilibriumproperties of water drops. Conant et al. [2002] have shownthat water drops containing black carbon can be substan-tially heated by SW radiation. This has the effect ofincreasing scrit and thereby reducing the number of activatedCCN. Going beyond purely equilibrium arguments, Neneset al. [2002] considers the growth of CCN containing SW-heated black carbon and illustrates that CCN growth isindeed suppressed. This suppression is particularly impor-tant for giant CCN (GCCN), since it has been thought thatGCCN may help initiate the drizzle process [e.g., Feingoldet al., 1999]. Though interesting, one important limitation ofthese works is that the actual warming of the liquid of thedrop was neglected in order to isolate the black carboneffects.[8] In the present paper we examine two issues. We show

how radiative heating and cooling affects the equilibriumstate of cloud and drizzle drops within idealized stratocu-mulus. Second, we examine how radiation alters CCNthrough changes in the Kohler curve maximum. This secondissue may have important implications for the activation andgrowth of CCN.

2. Method

[9] In a radiatively altered cloud environment, whether adrop grows or evaporates depends not only on the ambientsaturation but also on the rate of radiative warming orcooling of the drop. The rate of radiative energy absorbedby a drop is derived in many publications [e.g., Roach,1976; Bott et al., 1990] and is given by

Qrad ¼ 4pr2Ed rð Þ; ð1Þ

Ed rð Þ ¼Z

Qabs r;lð Þ 1

2Fþ lð Þ þ F� lð Þ½ � � pB Ts;lð Þ

� �dl; ð2Þ

where Qabs is the drop absorption efficiency computedusing Mie theory, F + and F� are the upwelling anddownwelling radiative fluxes incident on the drop, respec-tively, and B(Ts, l) is the Planck function evaluated at thedrop temperature (drop emission). The function Ed is knownas the radiative effect. It is positive (heating) when theincident (absorbed) radiation is larger than than that emittedby the drop. It is negative (cooling) when emissiondominates. The function, Qrad, is the total drop heating orcooling in Watts.[10] The effect of net radiative heating or cooling is to

shift the equilibrium conditions of the drop with respect tothe surrounding vapor field (see Roach [1976] and Figure 1).

Figure 1. Kohler curves without (lines) and with (lineswith circles) longwave (LW) cooling with Ed = �20 W m�2

(see section 2) as a function of cloud condensation nuclei(CCN) radius.

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

2 of 13

D10205

To find this condition (seq), we set the condensational growthequation for a water drop to zero and solve for the supersat-uration (seq). Because radiative heating can lead to significantdrop-environment temperature differences, large errors areincurred when the classical vapor growth equation [e.g.,Roach, 1976] is used. In order to mitigate these errors, weredrive the classical condensational growth equation includ-ing radiation (equation (2)) using the method of Srivastavaand Coen [1991] (see Appendix A). This more accuratederivation leads to the following equation for the temperaturedifference between a drop and its environment,

DT ¼ Ts � T1 ¼ rsatr0sat

g

1þ gs� sradð Þ 1� a s� sradð Þ½ �; ð3Þ

and a more accurate expression for seq,

seq ¼A

r� Br3ccnr3 � r3ccn|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}

Standard Ko::hler Equation

�Crad �1

2

1

a2� Qrad

prGLva

12

: ð4Þ

All of the symbols in the equations above are defined inAppendix A. Though difficult to discern from equation (3),radiation has the effect of producing a temperature reduction(increase) of the drop with respect to the environment underradiative cooling (heating), which will become apparentshortly. When radiative effects are important, the equilibriumsupersaturation now has extra terms (equation (4)). The firstterm is due to surface tension, which increases the requiredequilibrium supersaturation (Kelvin term), and the secondterm reduces the equilibrium supersaturation because ofdissolved solute (Raoult term). These two terms comprisethe standard Kohler equation. The third and fourth termsaccount for radiative influences on seq and cause a reduction(increase) in seq during radiative cooling (heating).

2.1. Idealized Stratocumulus

[11] The interaction between drops and radiation havebeen most extensively studied within the context of strato-

cumulus clouds. This is understandable given that radiation(both SW and LW) have a strong influence on stratocumu-lus. Computation of seq requires profiles of temperature,pressure, and the radiative fluxes through the cloud (equa-tion (2)). Because these equations require only static pro-files, dynamic cloud model simulations are unnecessary.Instead, we compute the radiative fluxes through idealizedstratocumulus that are constructed using climatologicalsoundings. This simplification is not a serious limitationto our studies, since the constructed stratocumulus profilesare built to mimic those observed and produced by cloudmodels. Moreover, most radiation models are one dimen-sional, including the one used here, and only respond tovertical structure.[12] We construct idealized stratocumulus using the cli-

matological sounding for midlatitude summer derived fromMcClatchy et al. [1972]. The lower 1 km of the sounding ismodified so that the boundary layer (BL) is typical of thosecontaining stratocumulus. This is accomplished by lifting aparcel from the surface with a particular value of q andwater vapor mixing ratio (rv). The BL is assumed neutraluntil the lifted condensation level is reached (Figure 2a)above which all water vapor exceeding saturation is con-densed producing the classic stratocumulus liquid watermixing ratio profile (rl, Figure 2b). Cloud top is prescribedto be 1 km in all studies and, at this level, rl becomes zeroand we impose a cloud-top jump in q and rv similar to thoseobserved. It is important to note at this stage that theradiative fluxes were only minimally impacted by ourchoice of cloud-top jumps, hence these remain fixed inour simulations.[13] Computing the radiative fluxes through the cloud

layer requires not only rl but also a measure of dropconcentration (N). Since buoyantly driven stratocumulushave N that is approximately constant with height [e.g.,Nicholls, 1984; Stevens et al., 1996], we impose this as acondition in our simulations (Figure 2b). The radiativefluxes through the cloud layer are computed using thetwo-stream radiative transfer model described byHarringtonand Olsson [2001a], which has been used in numerous

Figure 2. Sample profiles of (a) q and rv and (b) rl and N for use in the radiative and seq calculations.

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

3 of 13

D10205

simulations of stratocumulus clouds [Olsson et al., 1998;Stevens et al., 1998;Harrington et al., 2000;Harrington andOlsson, 2001b; Hartman and Harrington, 2005a, 2005b].The configuration used here has six bands across the SWspectrum and 12 bands across the infrared. Since two-streammodels perform poorly at higher solar zenith angles (Qo ^50), errors will be incurred [Harshvardhan and King, 1992]in some of the results presented later. However, since solarabsorption is quite small at this large Qo producing lowheating rates, this limitation may not be severe. Neverthe-less, this limitation should be kept firmly in mind.[14] Example radiative heating rates for the idealized

stratocumulus are shown in Figure 3. The heating ratesshown are fairly typical for stratocumulus: The cloud topLW cooling rate is around �8 K h�1 and is strongest in theupper 50 m of the cloud layer. The SW heating, which iscomputed for overhead Sun (Qo = 0�) maximizes at roughly2 K h�1, with SW heating affecting much of the cloud layer.Longwave radiation can also heat cloud base as long as thesurface emitting temperature is greater than the temperatureof cloud base (Figure 3). Hence even when the surfacetemperature is the same as that of the overlying air (i.e., aneutral surface layer, DTsfc = 0�C), cloud base is heated byLW radiation.[15] The radiative fluxes so computed provide an estimate

of the radiative environment to which drops and CCN areexposed. We can therefore use the radiative fluxes providedby the radiation model to compute how seq (or the Kohlercurves) is modified throughout the cloud layer. As we shallsee, the results provide important insight into how clouddrop growth and CCN activation may be modified in acloud that is exposed to radiative influences.

2.2. Errors in Classical seq[16] As Roach [1976] first pointed out, cloud drops that

are exposed to radiative fluxes will have equilibrium tem-

peratures that deviate from those of the environment and isthe reason that seq (equation (4)) deviates from classicalKohler theory. In Figure 4 we have plotted the droptemperature difference, DT, at cloud top where LW coolingand SW heating are maximized. Even when SW heating isnot included, drops with r ] 200 mm have DT ] 1 K.However, larger drops show increasing temperature differ-ences. When LW cooling alone occurs (i.e., nocturnalsituations), the largest drizzle drops (r ^ 1000 mm) are asmuch as 3 K cooler than the environment, whereas understrong solar heating (Qo = 0�) these drops can be as much as4–6 K warmer than the environment. Note also that undersolar heating, drops tend to cool at sizes below approxi-mately 100–200 mm, whereas they warm at larger sizes.[17] The reason for this size-dependent DT behavior is

due to the water drop absorption efficiency (Qabs), shown in

Figure 3. Radiative heating rates as computed for thecloud shown in Figure 2. Shown are LW heating rates forsurface temperatures that are the same as, and 20�C greaterthan, the overlying air. SW heating rates are computed foroverhead Sun (Qo = 0�).

Figure 4. (a) Temperature difference between drop andenvironment (DT) for base case: N = 100 cm�3, a clouddepth of 300 m, and overhead Sun (Qo = 0�). Note that they-axis is logarithmic for negative DT to visualize thedifferences. (b) Difference between seq as calculated bySrivastava and Coen [1991] (ssc) and the classical formula-tion [e.g., Roach, 1976], (scl).

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

4 of 13

D10205

Figure 5a for two strongly absorbing SW bands and thestrong drop emission over a portion of the LW window. Inthe LW, Qabs increases rapidly with size, maximizing at r ’20 mm. In contrast, Qabs increases slowly with size in theSW, maximizing at large drop sizes. As Wiscombe et al.[1984] have pointed out, this behavior of the absorptionefficiency leads to a net warming of large drops. Since SWfluxes are generally much larger than LW fluxes, the SWabsorption overcomes cloud top LW cooling for drops withlarger radii (Figure 5b). Note that net cooling (Ed < 0) tendsto maximize at r � 18 mm. This is in the radius range ofcloud drops (10–20 mm), which are the most numerous, andis the reason that cloud top experiences a net cooling whenSW heating is present. As one might imagine, the size atwhich drops cross over from predominantly cooling topredominantly heating (around 200 mm in this case) changesdepending on the amount of SW heating (Qo) and depth inthe cloud. This will be examined in more detail later.

[18] The large temperature differences between biggerdrops and the environment leads to errors when the classicalexpression for drop growth is used. Figure 4b shows seqcomputed using the correction of Srivastava andCoen [1991](equation (4)) and compared with the classical expression[e.g., Roach, 1976]. When drops have radii ]200 mm, theerror in the equilibrium supersaturation is relatively small. Fordrizzle drops seq, and therefore drop growth and evaporation,can have an absolute error of as much as 6% in the supersat-uration. This is an impressive error indicating that the form ofthe growth equation given in Appendix A should be usedwhen computing drop growth in clouds when radiation isimportant. From this point forward, we use the corrected formof seq given by equation (4).

3. Longwave Effects

3.1. Equilibrium Supersaturation Effects

[19] Longwave radiation affects not only cloud top butalso cloud base (Figure 3) and has important consequencesfor seq. As Figure 4a shows, cloud drops that reside in theLW cooling region at cloud top have increasingly depressedtemperatures with size. Consequently, seq becomes smalleras the drop becomes large (Figure 1). Small drops areaffected by the curvature and solution terms requiring thespecification of a particular solute type. In all of oursimulations, pure (NH4)2SO4 CCN are assumed with aprescribed initial dry radius (rccn). Even a cursory examina-tion of Figure 1 illustrates two things. First, even modest-sized CCN (rccn � 0.2 mm) show a reduction in the criticalsupersaturation (scrit). In fact, larger CCN have scrit valuesthat are negative, indicating the possibility of activation atsubsaturation. Second, the radius at which scrit occurs, orrcrit, is much smaller as rccn increases. Both of thesecharacteristics are due to the fact that the amount of LWcooling experienced by a drop increases rapidly with dropsize (Figure 5). Hence larger drops can exist in subsaturatedenvironments when LW cooling is present.[20] Though LW cooling is maximized at cloud top, this

does not mean that radiative influences are confined to thatsmall region alone. In fact, LW cooling occurs over almostone half of the upper cloud, although this cooling is quiteweak between 850 and 900 m (Figures 3 and 6a). Further-more, even a neutral surface (DTsfc = 0�C) produces cloudbase LW heating that extends through the lower half of thecloud layer. Though weak, these radiative effects do alterseq. In Figure 6a, Ed and seq have been plotted as a functionof cloud depth and drop size. The LW radiative heating andcooling structure alters seq throughout the cloud layerproducing negative seq in the upper half of the cloud andpositive seq in the lower half. Most cloud drops have sizesbetween roughly 10 and 20 mm [Pruppacher and Klett,1997] and these drops are not strongly influenced byradiative effects except within the upper 50–75 m of thecloud. Even within the strong LW cooled region, clouddrops have seq ’ �0.1%. Because the radiative influence onseq is small for the most numerous drops, it is likelythat radiation has only a small effect on actual cloudsupersaturations (i.e., those developed through dynamic-microphysics interactions). Indeed, previous work of oursalso indicates that this is the case [e.g., Hartman andHarrington, 2005a].

Figure 5. (a) Absorption efficiency (Qabs) averaged overtwo solar (near-IR, Dl = 1.3–1.9 mm and 1.9–2.5 mm) andone infrared (Dl = 9–10.5 mm) bands. (b) Shortwave (SW),LW, and combined (SW + LW) radiative heating as afunction of radius at cloud top for Qo = 0�.

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

5 of 13

D10205

[21] As drop size increases so does absorption andemission (Figure 5). For moderate drop sizes (or embryonicdrizzle, 20–100 mm), LW radiation alters seq throughout theupper and lower one third of the cloud layer (Figure 6). Forthese drops, seq = �0.1 to �1% are possible in the upperportion of the cloud layer, whereas within 50 m of cloudbase, seq takes on a smaller range of values (]0.1 to 0.2%).Since the cloud top effect is stronger and occurs throughouta deeper layer, it seems that significant enhancement ofvapor depositional growth would occur in this region. Thisis important as 20 to 100 mm drops are the precursors todrizzle initiation, hence the term embryonic drizzle as perHobbs and Rangno [1998]. Drizzle drops (r ^ 100 mm) areinfluenced by radiative heating and cooling throughout mostof the cloud layer. In the upper 100 m, seq varies between�0.1 and �6%, whereas within the lowest 100 m of thecloud, seq can reach 3%. Though drizzle drops growprimarily by collection, such large values of seq can affectthe final size of these larger drops [see, for example,Harrington et al., 2000].

[22] While the values of seq near cloud top are importantbecause radiatively enhanced growth can increase collectionin this high liquid water content region, cloud base heatingis also of interest. The main reason is that cloud base is theregion where CCN first activate and grow as cloud drops.Cloud base heating, as noted above (section 2), depends onthe temperature difference between the surface and theoverlying air (DTsfc). Figure 6b shows Ed and seq at cloudbase plotted as a function of DTsfc and drop radius. It isinteresting to note that even surface temperature depressionswith respect to the overlying air lead to cloud base LWheating because of the greater LW emission by the surface.This leads to an ever increasing seq commensurate withDTsfc. Though DTsfc = 20�C is extreme, even the moretypical DTsfc (up to 5�C) show strong influences on seq of upto 5%. Once surface temperatures are depressed by morethan about 7�C, cloud base cooling can be realized. How-ever, DTsfc depressions have to be fairly drastic (�10�C)before seq is substantially impacted. Though rare in manyplaces, such surface temperature depressions in the form ofsteep surface inversions occur regularly in Arctic regionseven during the summer months including beneath liquidstratus [e.g., Curry and Herman, 1985].

3.2. Influence on scrit and rcrit[23] Even though the radiative effect on cloud drops is not

large (Figure 5), that does not mean that the shape of theKohler curve for a given CCN is not impacted. Larger CCNhave Kohler curve maxima (scrit, rcrit) that peak at lowersupersaturations and larger sizes (Figure 1). Hence a smallamount of radiative heating or cooling may be sufficient toalter this small scrit value. For instance, Figure 7a shows rcritand scrit as a function of rccn near cloud top. Typically, rccnrange from 0.01 mm to values as large as 5 to 10 mm(GCCN). The cloud top LW cooling maximum reduces rcritand causes scrit to become negative for rccn ^ 0.3 mm. CCNwith a radius of 0.3 mm typically produce drops with radiinear 7 mm in the absence of radiation, which is exactlywhere LW radiative effects start to become significant(Figure 5). Furthermore, note that both rcrit and scrit areimpacted to a great degree throughout the upper 50 m of thecloud, even though the LW cooling rates are decreasingrapidly (Figure 3). This result is shown in greater detail inFigure 8a, which provides contours of rcrit and scrit through-out the cloud layer. Within the upper half of the cloud layer,large CCN (typically with rccn ^ 0.5 mm) have values of scritthat are negative (�0.1 to �0.3%) and much smaller rcrit(between 70 and 90 mm) as compared with hundreds of mm.Given that giant CCN (GCCN have rccn ^ 5 mm) growslowly to activation sizes [e.g., Nenes et al., 2001], GCCNthat make it to cloud top may rapidly reach sizes that canassist collection initiation [Feingold et al., 1999].[24] Perhaps as important, cloud base heating can ad-

versely affect the growth of small drops and CCN. Evenunder neutral surface conditions (DTsfc = 0�C, Figure 7b),the heating of larger CCN can completely remove theKohler curve maximum. A 0.5 mm radius CCN wouldrequire increasing supersaturations in order to grow to largersizes (Figure 7b). Since stratocumulus have supersaturationmaxima near cloud base that are no greater than a few tenthsof a percent [Cotton and Anthes, 1989; Pruppacher andKlett, 1997], the growth of large CCN would be severely

Figure 6. Ed (shaded, W m�2) and seq (contoured, %) forLW radiation only: (a) with DTsfc = 0�C as a function ofcloud depth and radius. Note that the Ed = 0 region islabeled and delinated by a narrow contour line. (b) at cloudbase (Z = 700 m) as a function of DTsfc and radius. Since thex-axis is linear, the Ed = 0 and the seq = 0 contours overlap.

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

6 of 13

D10205

restricted. Indeed, this effect occurs throughout much of thelower half of the cloud layer. As Figure 8a shows, CCNwith rccn ^ 0.3 mm no longer have Kohler curve maximaand would have restricted growth. Of course, this growthsuppression effect depends greatly on the surface tempera-ture. In Figure 8b, the CCN size at which the Kohler curvemaximum disappears (rnomax) is plotted as a function ofDTsfc and Z. Note that for DTsfc ^ �5�C, suppression ofCCN growth becomes important in the lower half of thecloud. As surface temperatures rise and cloud base warmingincreases, smaller CCN begin to show suppressed growth.For example, with neutral surface conditions (DTsfc = 0�C),rccn as small as 0.27 mm lose their Kohler curve maximum,effectively restricting their growth. Overall, cloud baseradiative heating may substantially suppress the growth oflarger CCN causing them to remain smaller in size. Sincemany CCN have sizes in the range between 0.2 and 0.5 mm[Pruppacher and Klett, 1997], LW radiative warming could

have an influence on early CCN growth and cloud micro-structure, including collection initiation. In the case ofGCCN, however, vapor growth suppression by radiativeheating becomes strong only when the drop has alreadyreached sizes important for collection growth [Feingold etal., 1999; Feingold and Chuang, 2002] (r ^ 20 mm). Notethat a GCCN with rccn = 5 mm has an seq that deviates fromclassical behavior only when the drop is already larger thanabout 25 mm (Figure 7b). This is due to the fact that thesolute effect is very strong and indicates that LW heating ofcloud base may have its strongest impact on an intermediaterange of CCN sizes (from 0.3 to perhaps 5 mm, as we shallsee later.) The intriguing implications of these seq curves forthe initial development of the drop size spectrum needs tobe tested in a full microphysical model, which will be doneas a part of our future work.

4. Shortwave Influences

4.1. Equilibrium Supersaturation Effects

[25] Unlike LW radiative influences, SW radiation canproduce strong heating throughout a large fraction of thecloud layer (Figure 3). Of course, the strength of thisheating depends on the solar zenith angle, with Qo = 0�(overhead Sun) providing the strongest heating and Qo =90� (nocturnal) providing no heating. Near cloud top, SWheating reduces the effect of LW cooling while heating themiddle and lower portion of the cloud (Figure 3). While thisclassic structure of the radiative heating profiles is straight-forward, its impact on seq is not. For instance, recall thatbecause the drop absorption coefficient (Qabs) increasesmore slowly with size for SW radiation, smaller drops tendto experience a net cooling at cloud top, whereas largerdrops experience a net warming (Figures 4 and 5). Thisbehavior of Qabs alters the behavior of seq in the vicinity ofcloud top (Figure 9). At cloud top (Z = 1000 m), note thatseq no longer decreases continually with size as in the LWonly situation (e.g., Figures 1 and 4). Instead, the increase ofQabs with size for SW radiation produces a minimum in seqat roughly rmin = 100 mm and smin = �0.42%. Thisminimum coincides with the minimum in DT shown inFigure 4, as expected. Moreover, once SW heating domi-nates over LW cooling the drop’s temperature becomeselevated with respect to the environment, causing positiveseq. This occurs at a crossover size rcross = 200 mm. Whensolar radiation is active the minimum occurs throughout theupper cloud layer. At smaller Z where LW cooling is muchweaker, the SW effect dominates causing the minimumand rcross to migrate to smaller sizes with rmin ’ 20 mmnear midcloud (Figure 9a). Drizzle drops, having muchbigger surface areas, are strongly heated by SW radiation(Figure 4a). Such large heating rates produce very large seqvalues (up to 20%) for drizzle drops. These high seq occurthroughout all of the upper half of the cloud and must have apronounced effect on the vapor growth of drizzle drops.[26] While the seq of drizzle drops is not influenced by the

initial CCN radius, cloud drops are affected (Figure 9b). Asrccn increases, the solute effect causes rcrit to increase. SinceLW cooling is stronger than SW heating at these sizes, rcritoccurs at negative seq. However, the larger CCN (rccn^ 5 mm)have rcrit that approach rmin, leading to a loss of the Kohlercurve maximum similar to that caused by cloud base LW

Figure 7. (a) The scrit (left y-axis) and rcrit (right y-axis)without radiation and with cloud top LW cooling, (b) Theseq at cloud base for two different rccn. A variety of surface-air temperature differences (DTsfc) are plotted for rccn = 0.5and 5 mm.

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

7 of 13

D10205

heating. While growth is restricted because of the increasingseq with size, the equilibrium values occur at negative super-saturations over such a large range of radii that rapid vaporgrowth will still occur at cloud top.[27] A cloud-scale view of these influences illustrates that

SW heating has a strong effect throughout the entire cloudlayer (Figure 10a). While the smallest drops (r ] 10 mm) areonly weakly influenced by SW radiation (Ed ] 10 W m�2),larger drops are strongly affected. Drizzle drops with radiibetween 100 and 1000 mm experience total radiative heatingbetween Ed = 20 and 50 W m�2 which leads to seq between2 and 19%. The largest drizzle drops, 500 to 1000 mmradius, experience seq of at least 8% throughout all of thecloud layer.[28] Of course, the results presented above depend greatly

on Qo, which controls the strength of the SW radiativeheating. Figure 10b shows how Ed and seq vary as a functionof Qo and drop radius at cloud top. The SW heating isstrongest for the largest drops and the smallest Qo. WhenQo ] 60� SW heating is still important with Ed between

10 and 30 W m�2 for drops with radii ^ 500 mm. This leadsto seq between 2 and 8%. Furthermore, the location of theKohler curve minimum and rcross (i.e., the zero contour)are also affected by Qo. As SW heating decreases withincreasing Qo, the minimum deepens, becoming as small as�1%, and migrates toward larger sizes. At the same time,rcross ranges from around 200 mm at Qo = 0� to 300 mm atQo = 45�. Once Qo ^ 60� and SW heating becomes veryweak, the minimum and rcross begin to disappear.[29] As one might imagine, this seq structure in a SW

heated cloud has important implications for the growth ofcloud drops. In fact, Hartman and Harrington [2005a]found significant narrowing of the drop size distributionwhen SW radiation is active. Not surprisingly, this narrow-ing becomes apparent at sizes around 200 mm, which isroughly at the location of rcross, or where significant vaporgrowth restriction is expected to occur. The above-describedKohler curves are the reason for this behavior: The mini-mum and rcross confine drop growth to smaller sizes,effectively limiting some of the effects of collection, atleast for Qo ] 45�. We suspect that these effects will evenhave an influence on drizzle drops because seq is quite largethroughout much of the cloud layer and this would lead tolarge evaporation rates. Although unexplored by Hartmanand Harrington [2005a], rccn may also influence theseradiative effects on drop growth (Figure 9b).

4.2. Effects on rcrit and scrit[30] As Figure 9 makes clear, SW radiation has some

important effects on the shape of the Kohler curves.However, individual curves cannot easily convey radiativemodifications for the entire cloud. Instead, we use rcrit andscrit along with the newly defined rmin, smin, and rcross tocompactly examine how LWand SW radiation may alter thegrowth of small and large drops.[31] Figure 11 illustrates how rcrit and scrit vary with rccn

and cloud depth for overhead Sun (Qo = 0�). Comparingthis figure with that for LW radiation only (Figure 8a)illustrates how strongly SW radiation influences the Kohlercurve maximum. The first feature that stands out in com-parison to the LWonly case is that the region of negative seqat cloud top is severely reduced. This is not surprising giventhat SW radiation offsets the effects of LW cooling. Hencethe region of enhanced large and GCCN growth is severelyreduced. Second of all, the region over which the Kohlercurve maximum disappears (white area) has increased withrespect to the LW only case, reaching far into the upper halfof the cloud. Heating by SW radiation effectively restrictsCCN growth in the upper portion of the cloud. Note that thiswhite region bends sharply toward larger sizes in the upperhalf of the cloud. This is due to the slow increase in Qabs forsolar radiation as compared with that for LW radiation(Figure 5). Because of this, smaller CCN (rccn ] 0.5 mm)are only weakly affected by SW radiation. Larger CCN, onthe other hand, have larger rcrit and smaller scrit, allowingSW radiation to significantly alter the curve maximum.Thus the inclusion of SW radiation should restrict thegrowth of the larger CCN (rccn between 0.5 and 5 mm)throughout most of the cloud layer.[32] The effect described above turns out to be important

even at fairly high Qo. In order to show this, we haveplotted the CCN size at which the Kohler curve maximum

Figure 8. (a) The scrit (contoured, %) and rcrit (shaded,mm) as a function of Z and CCN size. Only LW radiation isincluded and DTsfc = 0�C. White (blank) region has noKohler curve maxima. (b) The rccn size beyond whichKohler curve maximum disappears (rnomax, contoured inmm, and shaded gray) as a function of Z and DTsfc.

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

8 of 13

D10205

disappears (rnomax, Figure 12) as a function of Z and Qo.Again, CCN sizes larger than those shown in the figure losetheir Kohler curve maximum because of radiative heating,leading to restricted growth. What immediately stands out inthis figure is that restricted growth occurs throughout themajority of the cloud layer for most Qo. The upper part ofthe cloud layer has the largest rnomax with smaller valuesnear cloud base. In the upper 50 m of the cloud, rcrit needs tobe 80 mm before SW radiation can dominate over the strongLW cooling of cloud top. This is the reason that only thelargest CCN are affected in the upper 50 m. Moreover, notethat rnomax shows little influence of Qo in the lower half ofthe cloud. This is not surprising given that SW radiationaffects larger drops more than LW radiation. Consequently,LW heating dominates the modification to the Kohlercurves at cloud base.[33] If CCN become classical growing drops (i.e., be-

come larger than rcrit), the minimum and rcross shown inFigure 9 should significantly affect future growth. As thecontour image of Figure 13a shows, the minimum occurs

throughout the entire cloud deck and for most Qo. In theupper portion of the cloud, as expected, the minimumoccurs at negative supersaturations and at larger drop sizes(between 35 and 50 mm). This implies that rapid radiativelyenhanced growth should occur here but it is limited by therapid upturn in seq beyond the minimum. Moreover, sincercross is larger at cloud top (100 to 500 mm, Figure 13b) it isquite likely that collection growth could be initiated rapidly.The bigger drops so formed, however, would find them-selves with a large seq and subsequently evaporate at a rapidrate. Indeed, Hartman and Harrington [2005a] have shownevaporative narrowing of the drop size spectrum at r ^200 mm despite rapid collection growth. Though SWheating causes the upturn in seq at large sizes in theupper half of the cloud layer, the lower cloud experiencesa similar minimum that is due primarily to cloud baseLW heating. This LW heating leads to a minimum atpositive, small, supersaturations and at small sizes. Fur-thermore, it is dependent on rccn. However, the cloud base

Figure 9. (a) The seq plotted for small (left) and large(right) drops for Qo = 0� near cloud top. CCN size wasassumed to be rccn = 0.2 mm. (b) The seq plotted at cloud topwith Qo = 0� for a variety of rccn.

Figure 10. (a) The seq (logarithmically contoured, %) andEd (shaded) as a function of Z and drop size for Qo = 0�.X-axis is logarithmic so that the cloud top radiative effecton small drops is apparent. Ed = 0 shade is labeled. (b) The seq(contoured, %) and Ed (shaded) as a function of Qo = 0� anddrop size at cloud top. The seq = 0 and Ed = 0 coincide in thispart.

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

9 of 13

D10205

minimum is small enough that it may not have a significantimpact on the growth of smaller CCN. The implications ofthese curves for CCN growth will be explored in future work.

5. Summary and Concluding Remarks

[34] Radiative heating and cooling occur throughoutmost, if not all, of a stratocumulus cloud deck and thisimpacts the growth of cloud drops. Previous work hasfocused primarily on the fact that radiative effects can alterthe collection process [e.g., Austin et al., 1995]. However,since LW and SW radiation alters drop temperatures, theequilibrium saturation state (seq) of CCN and drops shouldalso be affected. This is important because seq provides ademarcation between growth and evaporation. In this studywe provided an estimate of how LW and SW radiationaffects seq throughout a stratocumulus cloud layer.[35] Since big drops have large absorption cross sec-

tions, strong heating by SW radiation can occur. This

leads to temperature differences between the drop and theenvironment which can be as large as 5–8�C. AsSrivastava and Coen [1991] have pointed out, the clas-sical equation for drop vapor growth can be significantlyin error for drop-environment temperature differences ofthis size. We therefore rederived the vapor growth equa-tion including radiative effects using the method ofSrivastava and Coen [1991]. This led to an improvedequation for vapor growth, and for seq, when strongradiative heating or cooling occurs. Idealized stratocumu-lus were constructed so that their main macroscopiccharacteristics match observations and cloud modelingstudies. These clouds were used to compute the radiativefluxes experienced by CCN and drops residing in thestratocumulus layer. When LW radiation alone is consid-ered, we found the following:[36] 1. Cloud top LW cooling can depress drop temper-

atures by up to 3�C for the largest (r ^ 100 mm) drops. Thisleads to seq between �0.1 and �6% for drops with radiibetween 100 and 1000 mm in the upper half of the cloud.Thus larger drops can grow in a subsaturated environment.[37] 2. Cloud top LW cooling causes a reduction in the

standard Kohler curve maximum such that the criticalsupersaturation, scrit, becomes negative and the criticalradius, rcrit, is significantly reduced for larger CCN. Hence

Figure 11. The rcrit (shaded, mm) and scrit (contoured, %)as a function of cloud depth and radius for Qo = 0�. Thewhite (blank) region contains no Kohler curve maxima.

Figure 12. CCN radius at which Kohler curve maximumdisappears (rnomax in mm, and shaded gray) as a function ofheight and Qo for DTsfc = 0�C.

Figure 13. (a) The rmin (shaded, mm) and smin (contoured,%) as a function of cloud depth and Qo. (b) The rcrosscontoured (mm) as a function of cloud depth and Qo.

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

10 of 13

D10205

the possibility exists for the activation and growth of largeCCN at cloud top.[38] 3. Cloud base LW warming leads to a continual

increase in seq with size for larger CCN. In other words,the Kohler curve maximum disappears indicating that thegrowth of larger CCN is restricted at cloud base. Typically,CCN with sizes (rccn) greater than 0.3 mm have restrictedgrowth. This growth suppression occurs even for surfacetemperatures that are depressed with respect to the overlyingair.[39] When SW radiation is included, the above results are

modified in the following way:[40] 1. The drop absorption coefficient (Qabs) increases

more slowly with radius for SW radiation than it does forLW radiation. However, since SW radiative fluxes are muchlarger than LW fluxes, SW effects dominate at drizzle dropsizes, leading to drop heating at r ^ 200 mm even at cloudtop. This leads to a situation where seq decreases to negativevalues with a subsequent return to positive values as dropradius increases. A minimum in the Kohler curve is there-fore produced at moderate sizes (50 to 200 mm for solarzenith angles (Qo) ] 60�. This minimum occurs throughoutmost of the cloud, though it is most pronounced near cloudtop and indicates a preferred size range for drop vaporgrowth in SW heated clouds.[41] 2. Drizzle drops are strongly heated by SW radiation,

leading to drop temperature elevations of up to 6�C. Thisleads to high seq, typically between a few percent and 15%,for drops with sizes between 100 and 1000 mm. As Hartmanand Harrington [2005a] have shown, this leads to rapidevaporation of larger drops and a subsequent suppression ofthe collection process.[42] 3. Since SW heating occurs throughout the cloud, the

Kohler curve maximum is affected over a larger clouddepth. For Qo ] 60�, rccn ^ 0.3 lose their Kohler curvemaximum throughout a majority of the cloud layer. SinceQabs for SW radiation increases more slowly with size thanit does for LW radiation, the CCN size at which the Kohlercurve maximum disappears is smaller for LW radiation (assmall as 0.25 mm) as compared with SW radiation (as smallas 0.5 mm).[43] Given the above results, we expect that SW heating

may have a strong impact on the growth of embryonicdrizzle (20 to 100 mm) and drizzle-sized drops in strato-cumulus. Since seq is increased over much of the cloudlayer for these drops, significant evaporation could occurbefore the drops exit the cloud layer. Furthermore, LWheating of cloud base and SW heating of the entire cloudcauses a continual increase of seq with size for larger CCN.While the giant CCN (rccn ^ 5 mm) could still reach sizesthat may impact collection, large CCN (rccn between 0.5and 5 mm) may be more strongly impacted. This is due tothe fact that GCCN are only affected by radiation oncethey already swell to large sizes. Large CCN, in contrast,show strong LW heating influences at smaller sizes, whichmay impact their subsequent growth. However, cloud topLW cooling tends to greatly reduce the critical size andsupersaturation of large CCN. This could cause rapidgrowth of large CCN once cloud top is reached. Giventhe extent of radiative influences on drop equilibrium andthe rich parameter space that exists, it would seem thatfuture work should attempt to assess how radiation alters

the early growth of the drop size spectrum in a cloudmodel.

Appendix A: Derivation of seq

[44] For a spherical drop the classical equation for themass growth of cloud drops by vapor diffusion is given by

dm

dt¼ 4prDv* r1 � rs½ �; ðA1Þ

where m is the mass of a drop of radius r, r1 is the densityof the vapor in the atmosphere a large distance from thedrop, and rs is the vapor density at the surface of the drop.The diffiusivity of water vapor, D*v is modified for kineticeffects [see Pruppacher and Klett, 1997],[45] Following Srivastava and Coen [1991], we write the

vapor density as

r1 ¼ rsat T1ð Þ 1þ s½ �

rs ¼ rsat Tsð Þ 1þ sp� �

;ðA2Þ

where rsat(T1) and s are the saturation vapor density andthe supersaturation, respectively, in the atmosphere farfrom the cloud drop, rsat(Ts) is the saturation vapordensity at the surface of the cloud drop, and sp is theclassical equilibrium supersaturation over a curvedsolution drop (traditional Kohler curves),

sp ¼A

r� Br3ccnr3 � r3ccn

; ðA3Þ

where A is a coefficient containing the drop surfacetension, B is a function of the solute type, and rccn is theradius of the dry aerosol particle (see Pruppacher andKlett [1997] for coefficient equations). In order to arrive ata single equation for the vapor growth of a cloud drop, thedrop temperature (Ts) is typically removed from (A1). Thisis done by expanding rsat(Ts) in a Taylor Series around T1,

rsat Tsð Þ ’ rsat T1ð Þ þ @rsat T1ð Þ@T

DT þ @2rsat T1ð Þ@T2

DT2 þ � � �

DT ¼ Ts � T1: ðA4Þ

Classically, only the linear term in DT is retained since DTis typically small. Srivastava and Coen [1991] showed thatwhen DT is large, the final growth equation can besignificantly improved if the second-order term is alsoretained.[46] During condensation, evaporation, or radiative heat-

ing and cooling the temperature of the drop changes and thisalters the saturation vapor density. Traditionally, we assumea balance between latent heating, thermal diffusion, andradiative heating. While large drops do not necessarilyattain thermal balance during growth, this approximationis valid for our studies, since we are interested in equilib-rium. Thermal balance is given by

Lvdm

dt¼ 4prk*DT � Qradf ; ðA5Þ

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

11 of 13

D10205

where Lv is the latent heat of vaporization, k* is the thermaldiffusivity modified for kinetic effects [see Pruppacher andKlett, 1997], and Qrad is a term (see equation (1) in the maintext) that takes radiative heating and cooling into account.The factor, f, is the fraction of radiative cooling or heatingthat is due to the drop [see Austin et al., 1995].[47] An equation for DT can be derived by substitution of

equations (A2)–(A4) into equation (A1) and combining theresult with equation (A5),

DT ¼ rsatr0sat

g

1þ gs� sradð Þ 1� a s� sradð Þ½ �; ðA6Þ

which is equation (3) in the main text. Note that as Qrad ! 0in equation (A6), we recover the result of Srivastava andCoen [1991]. In the above equation we have defined thefollowing quantities,

r0sat ¼@rsat@T

jT1¼1

RvT1

Lves

RvT21� es

RvT21;

g ¼ LvDv*

k*r0sat;

a ¼ 1

2

rsatr00sat

r02sat

g

1þ g

�2

;

r00sat ¼@2rsat@T2

jT1¼2es

RvT31

1þ 1

2

Lv

RvT1

�2

� 2Lv

RvT1:

" #

srad ¼ sp �Qrad

4prDv*rsLv; ðA7Þ

where es is the saturation (equilibrium) vapor pressureevaluated at T1, and all other symbols are defined in thetext above. The behavior of equation (A6) is discussed inthe main text.[48] The equation for condensational mass growth, as

modified by radiation, can then be determined by substitut-ing equation (A6) into equation (A5), which gives

dm

dt¼ 4prG s� sradð Þ 1� a s� sradð Þ½ � � Qrad

Lv; ðA8Þ

G ¼ Dv*rsat1þ g

: ðA9Þ

Finally, to determine the equilibrium supersaturation (seq),we set dm/dt = 0 in equation (A8) and solve for s = seqwhich leads to

seq ¼A

r� B msð Þ

r3� Crad �

1

2

1

a2� Qrad

prGLva

12

; ðA10Þ

where Crad is

Crad ¼ Qrad

4prLvDv*rsat: ðA11Þ

Equation (A10) is given in the main text as equation (4).

[49] Acknowledgments. J. Marquis was supported by the Pennsyl-vania State University for summer undergraduate research. J. Harrington

would like to thank the National Science Foundation for support undergrant ATM-0234211.

ReferencesAckerman, A. S., O. B. Toon, and P. V. Hobbs (1995), A model for particlemicrophysics, turbulentmixing, and radiative transfer in the stratocumulus-topped marine boundary layer and comparisons with measurements,J. Atmos. Sci., 52, 1204–1236.

Ackerman, A., O. Toon, D. Stevens, A. Heymsfield, V. Ramanathan, andE. Welton (2000), Reduction in tropical cloudiness by soot, Science,288, 1042–1047.

Austin, P. H., S. Siems, and Y. Wang (1995), Constraints on droplet growthin radiatively cooled stratocumulus, J. Geophys. Res., 100, 14,231–14,242.

Barkstrom, B. R. (1978), Some effects of 8–12 mm radiant energy transferon the mass and heat budgets of cloud droplets, J. Atmos. Sci., 35, 665–667.

Bott, A., U. Sievers, and W. Zdunkowski (1990), A radiation fog modelwith a detailed treatment of the interaction between radiative transfer andfog microphysics, J. Atmos. Sci., 47, 2153–2166.

Conant, W., A. Nenes, and J. Seinfeld (2002), Black carbon radiatativeheating effects on cloud microphysics and implications for the aerosolindirect effect: 1. Extended Kohler theory, J. Geophys. Res., 107(D21),4604, doi:10.1029/2002JD002094.

Cotton, W. R., and R. A. Anthes (1989), Storm and Cloud Dynamics, 883pp., Elsevier, New York.

Curry, J. A., and G. F. Herman (1985), Infrared radiative properties ofsummertime arctic stratus clouds, J. Clim. Appl. Meteorol., 24, 525–538.

Davies, R. (1985), Response of cloud supersaturation to radiative forcing,J. Atmos. Sci., 42, 2820–2825.

Feingold, G., and P. Y. Chuang (2002), Analysis of the influence of film-forming compounds on droplet growth: Implications for cloud micro-physical processes and climate, J. Atmos. Sci., 59, 2006–2018.

Feingold, G., W. Cotton, S. Kreidenweis, and J. Davis (1999), The impactof giant cloud condensation nuclei on drizzle formation in stratocumulus:Implications for cloud radiative properties, J. Atmos. Sci., 56, 4100–4117.

Feingold, G., H. Jiang, and J. Harrington (2004), Influences of soot oncloudiness, paper presented at International Conference on Clouds andPrecipitation, World Meteorol. Org., Bologna, Italy.

Guzzi, R., and R. Rizzi (1980), The effect of radiative exchange on thegrowth of a population of droplets, Contrib. Atmos. Phys., 53, 351–365.

Harrington, J. Y., and P. Q. Olsson (2001a), A method for the parameter-ization of cloud optical properties in bulk and bin microphysical models:Implications for arctic cloudy boundary layers, Atmos. Res., 57, 51–80.

Harrington, J. Y., and P. Q. Olsson (2001b), On the potential influence ofice nuclei on surface-forced marine stratocumulus cloud dynamics, J. Geo-phys. Res., 106, 27,473–27,484.

Harrington, J. Y., G. Feingold, and W. R. Cotton (2000), Radiative impactson the growth of a population of drops within simulated summertimearctic stratus, J. Atmos. Sci., 57, 766–785.

Harshvardhan, and M. D. King (1992), Comparative accuracy of diffuseradiative properties computed using selected multiple scattering approx-imations, J. Atmos. Sci., 50, 247–259.

Hartman, C., and J. Harrington (2005a), Radiative impacts on the growth ofdrops in simulated stratocumulus. Part I: Strong solar heating, J. Atmos.Sci., in press.

Hartman, C., and J. Harrington (2005b), Radiative impacts on the growth ofdrops in simulated stratocumulus. Part II: Solar zenith angle influences,J. Atmos. Sci., in press.

Hobbs, P. V., and A. L. Rangno (1998), Microstructure of low and middle-level clouds over the beaufort sea, Q. J. R. Meteorol. Soc., 124, 2035–2071.

McClatchy, R., R. Fenn, J. Selby, F. Voltz, and J. Garing (1972), Opticalproperties of the atmosphere, Tech. Rep. 411, Air Force Cambridge Res.Lab., Hanscom Air Force Base, Mass.

Nenes, A., S. Ghan, H. Abdul-Razzak, P. Y. Chuang, and J. H. Seinfeld(2001), Kinetic limitations on cloud droplet formation and impact oncloud albedo, Tellus, Ser. B, 53, 133–149.

Nenes, A., W. Conant, and J. Seinfeld (2002), Black carbon radiatativeheating effects on cloud microphysics and implications for the aerosolindirect effect: 2. Cloud microphysics, J. Geophys. Res., 107(D21), 4605,doi:10.1029/2002JD002101.

Nicholls, S. (1984), The dynamics of stratocumulus: Aircraft observationsand comparisons with a mixed layer model, Q. J. R. Meteorol. Soc., 110,783–820.

Olsson, P. Q., J. Y. Harrington, G. Feingold, W. R. Cotton, and S. M.Kreidenweis (1998), Exploratory cloud-resolving simulations of bound-ary layer Arctic stratus clouds. Part I: Warm season clouds, Atmos. Res.,47, 573–597.

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

12 of 13

D10205

Pruppacher, H. R., and J. D. Klett (1997), Microphysics of Clouds andPrecipitation, 954 pp., Springer, New York.

Roach, W. T. (1976), On the effect of radiative exchange on the grwoth bycondensation of a cloud or fog droplet, Q. J. R. Meteorol. Soc., 102,361–372.

Srivastava, R., and J. Coen (1991), New explicit equations for the accuratecalculation of growth and evaporation of hydrometeors by diffusion ofwater vapor, J. Atmos. Sci., 49, 1643–1651.

Stevens, B., G. Feingold, W. R. Cotton, and R. L. Walko (1996), Elementsof the microphysical structure of numerically simulated nonprecipitatingstratocumulus, J. Atmos. Sci., 53, 980–1007.

Stevens, B., W. R. Cotton, G. Feingold, and C.-H. Moeng (1998), Large-eddy simulations of strongly precipitating, shallow, stratocumulus-toppedboundary layers, J. Atmos. Sci., 55, 3616–3638.

Wiscombe, W. J., R. M. Welch, and W. D. Hall (1984), The effects of verylarge drops on cloud absorption. Part I: Parcel models, J. Atmos. Sci., 41,1336–1355.

�����������������������J. Marquis and J. Y. Harrington, Department of Meteorology,

Pennsylvania State University, 503 Walker Building, University Park, PA16802, USA. (jmarquis@mail.meteo.psu.edu)

D10205 MARQUIS AND HARRINGTON: RADIATIVE INFLUENCES ON DROP EQUILIBRIUM

13 of 13

D10205