On the drop and aerosol size dependence of aqueous sulfate formation in a continental cumulus cloud

Atmospheric Environment Vol. 26A, No. 13, pp. 2309-2321, 1992.

0004-6981/92 $5.00+0.00 © 1992 Pergamon Press Ltd

Printed in Great Britain.

ON THE DROP AND AEROSOL SIZE DEPENDENCE OF AQUEOUS SULFATE FORMATION IN A CONTINENTAL CUMULUS CLOUD G. J. H. ROELOFS Institute of Meteorology and Oceanography, University of Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands (First received 30 July 1991 and in final form 12 February 1992) Abstract--An entraining air parcel model including microphysical and chemical processes is used to investigate the drop size dependence of pollutant concentrations in a growing cloud under continental background conditons. For the calculation of the chemical processes, the drop size of the cloud drops and their initial dry particle size before activation is taken into account. The size dependence of the pollutant concentration in drops smaller than 8 #m radius is mainly influenced by the activation and fast condensationai growth of recently entrained particles. In drops larger than 20 #m radius the main process influencing the drop size dependence of the pollutant concentration is coalescence between drops. The size dependence in drops between 8 and 20/zm radius is determined by the drops activated at the cloud base and the drops growing on particles that are entrained at higher altitudes, the influence of the latter rapidly increasing with height. Drops that are growing on large particles are polluted with initial aerosol matter to such an extent that sulfate production by oxidation is not significant in them. In drops growing on small particles the initial aerosol load has relatively little influence on the chemical processes in the drop. Oxidation of S(IV), especially by ozone, takes place mainly in these drops. The dependence of chemical processes on initial dry particle size holds throughout most of the cloud, until coalescence starts playing a role. If the cloud evaporates before producing precipitation-sized drops, the increase of aerosol mass due to cloud chemical processes is found to have taken place in the aerosol accumulation mode. If precipitationsized drops were produced during the cloud stage, the soluble volume fraction of the aerosol matter has increased throughout the aerosol size distribution, but mainly in the accumulation mode. Key word index: Aerosols, cloud chemistry, drop size dependence, oxidation, pH, sulfate.

1. INTRODUCTION In recent years an increasing number of cloud modeling studies has been focused on the drop size dependence of pollutant concentrations and aqueousphase chemical reactions. Simultaneously, measurements have been reported which indicate that the solute composition and concentration in cloud drops vary significantly with drop size (Noone et ai., 1988; Ogren et al., 1989). Generally, two types of model that focus on drop size dependent chemistry can be distinguished. In the first place there are models that are applied to nearcloud-base conditions. Based on an initial aerosol size distribution, they calculate a continuous development of the drop size of, and aqueous pollutant concentrations in the individual particles as they become activated and undergo condensational growth (e.g. Twohy et al., 1989). A number of these models consider the occurrence of aqueous-phase chemical processes in the particles (Rood and Currie, 1989; Pandis et al., 1990; Ayers and Larson, 1990; Hegg and Larson, 1990). The simulation results indicate that drops growing on small aerosol particles have smaller sizes but dilute faster than those growing on large aerosol particles. Oxidation of S(IV) by 03 tends to take place mainly in the former drops which are less acidic. Also

it was found that the smaller drops readily take up NH3 from the gas phase, while from larger ones NH3 escapes. Since these models are not concerned with altitudes higher than approximately 150 m above the cloud base, they do not consider entrainment of particles from outside the parcel and coalescence between cloud drops. The second type of model considers a complete cloud development, either based on an entraining air parcel (e.g. Flossmann et al., 1987) or a 2D-cloud model (Lee, 1986). Lee found an increase of drop pH with increasing drop size; Flossmann on the other hand found the opposite. Flossmann also concluded that the main sulfur mass is always associated with the main water mass in the cloud, and that the in-drop concentration of sulfate produced by oxidation increases with drop size up to a drop radius of 20/an radius, and becomes almost independent of drop size for larger radii due to coalescence. As a result of the inclusion of entrainment and coalescence processes in these models, drops of a certain size could not be assigned to the initial dry particle size of the drops. In an earlier paper we presented a simulation of the cloud chemical development under continental background conditions (Roelofs, 1992). It primarily dealt with the distribution of the sulfate initially present in the aerosols and the sulfate produced by the aqueous-

2309

2310

G.J.H. ROELOFS

phase oxidation of S(IV) by 03 and H 2 0 2 over the drop sizes. It was found that the oxidation-produced sulfate is significant in drops with radii larger than 10/~m when compared to the initial aerosol sulfate, and that the concentrations of all chemical species undergo a homogenization with drop size for drops larger than 20 #m radius. Apart from the cloud base, the model results could not be used to investigate the influence of the dry aerosol particle size on the chemical evolution in the drops that develop on them. This was caused by the fact that each drop size category formed a sort of bulk mixture on its own in which drops of the same size but different levels of pollution were averaged. In the present study this problem is met by the use of a two-dimensional drop size distribution in which both drop size and initial dry particle size are considered. When applied to continental background conditions, the drop size dependent results are qualitatively similar as those described above. In this paper attention will be given to the influence of the initial dry particle size on the chemical development of individual drops throughout the cloud parcel's ascent, and an analysis will be given of the way in which a partly soluble ammonium sulfate aerosol distribution is processed by aqueous-phase chemistry during cloud formation. 2. MODEL DESCRIPTION

The cloud dynamical processes are described by the equations for a simple entraining air parcel (e.g. Pruppacher and Klett, 1978). The model makes a distinction between aerosols and drops. An aerosol particle will be considered a drop when its dry radius exceeds the critical dry radius at the ambient supersaturation, following the equations presented in Flossmann et al. (1985). Condensational growth of aerosols and drops is calculated using the droplet growth equation (Pruppacber and Klett, 1978), of which the linearized version from H/inel (1987) is used. In order to enhance the distinction between drops with the same drop size but different levels of pollution, a two-dimensional drop size distribution is considered by the model. In the first place drops are categorized according to their wet radius a, and in the second place to the initial dry radius R of the particles they grow on. The drop concentration as function of drop radius is given by:

f(a) = ff(a, R) dR,

(1)

wheref(a, R) denotes the concentration of drops with radius a which grow on particles with initial dry radius R. Coalescence between drops is simulated by the Kovetz and Olund solution of the stochastic collection equation (Pruppacher and Klctt, 1978). Coalescence results not only in interactions between drops of different radius, but also of different initial dry radius.

Therefore the collection equation is reformulated

as:

k i-I

df(ak, Rz) = ~. ~. B,.~.~K,.jf(a,, Rz)f(a~, R.) dt i=t j=l m=1 -f(a,,

R,) ~ ~ K,,kf(a,, R,),

(2)

i=lm=l

where Bi,j.k is the redistribution kernel as defined in Pruppacher and Klett (1978) and Kl.j is the collection kernel which is evaluated according to Hall (1980). The actual dry size of the chemical contents of a drop after collection of other drops will be larger than before collection took place. However, according to (2) the resulting drop is assigned to the dry size category in which the largest of the colliding drops (the collector drop) was placed. Impaction scavenging of aerosol particles by drops, and collision and coagulation between aerosol particles are not considered. The first process does not significantly enhance the amount of aerosol matter in the drops (Flossman et ai., 1985); the second process is significant only at a time scale much larger than that characterizing cloud development (see for example fig. 7-4 in Warneck, 1988). The atmospheric trace gases considered are SO2, NH3, HNO3, Oa, H202 and CO2. Gas and aerosol concentrations are modified as a result of entrainment which brings air from outside, into the air parcel. Gas concentrations are further modified by dissolution of the gases into drops. The rate at which a gaseous species s crosses the gas-liquid interface of a drop of radius a is given by: dc,.i 3ks =--(c,.l~- Hsc,.i) , dt a

(3)

where g and I denote the gas and liquid phases. The mass transfer coefficientk, describes the diffusion of s in the gas phase towards the drop. In view of their relativelyshort time scalesfor the chemical conditions considered, processes involving transport through the drop's surface and the internal mixing in the drop are assumed to take place instantaneously (Schwartz, 1988). Values of temperature-dependent Henry constants H. for the gases considered are listedin Table I.

Table 1. Henry's law coefficients Species

Hs, o*

-AH/~2?

Source~:

SO2 NHs HNO3 CO 2 03 H202

3.33 (-2)~ 7.05 ( - 4) 1.95 ( - 7) 1.32 3.56 5.49 ( - 7)

3120 4085

1, 3 1, 3 2, 4 1, 3 1, 3 2

2423 2560 6620

*H, =H, o exp(AH/~t)((I/T)-(1/298)); H, o in tool f~) mol- i~.ot,r. tAnl~K). ~:I:Nair and Peters(1989),2:Pandisand Seinfeld(1989),3: Overton et al.(1979),4: Durham et aL (1981). §Numbers between bracketsdenote powers of I0.

Aqueous sulfate formation in cloud

2311

Table 2. Equilibrium and reverse rate constants for dissociation reactions

H20=H+ +OH H2SO3=H÷ +HSO~ HSO~ =H÷ +SO 2NH3 = O H - +NH2 HNO3=H ÷ +NO~ H2CO3=H÷ +HCO3

Ko*

k,t

- AH/~t~.

Source§

1.0(-14)11 1.7(-2) 6.0(-8) 1.7 ( - 5) 15.4 4.3(-7)

1.3(+11) 2.0(+8) 1.0(+ 11) 3.4 (+ 10) 1.0 (+8) 5.6(+4)

-6716 2090 1120 -4325 0 -913

1, 3 1, 3 1, 3 1, 2 1, 3 1,3

*K = (kr/kr) = K o exp( - AH/.~I)(1/T- 1/298); K o in tool ~- 1. l"k, in s-1.

~,- AH/~ in K. § 1: Nair and Peters (1989), 2: Overton et al. (1979), 3: Durham et al. (1981). IINumbers between brackets denote powers of 10.

The chemical evolution in the drops is calculated by solving a set of partial differential equations using a multistep method. For this purpose the dissociation equilibrium constants are split in a forward and reverse reaction rate. The dissociation reaction rates and corresponding reverse reaction rates are given in Table 2. The forward reaction rates are calculated by the combination of the reverse reaction rates and the temperature-dependent equilibrium constants. The oxidation rate of S(IV) by 0 3 is taken from Maahs (1983); the oxidation rate of S(IV) by H 2 0 2 is taken from Martin and Damschen (1981). Chemical development is calculated for each drop size category separately, so the concentration of dissolved species i for each drop size category is defined as c~(a, R). The average concentration of dissolved chemical species i as function of drop radius a is calculated according to:

ci(a ) =

~f (a, R)c,(a, R)dR , ~f(a, R) dR

(4)

or as function of the initial dry particle radius R according to:

ci(g ) =

~f (a, R)aa ci(a, g)da ~f (a, R)a 3 da

(5)

Gas-phase sulfate production and liquid-phase sulfate production in the unactivated aerosols is not considered in view of the relatively large time scales characterizing these processes (Seidl, 1989; Saxena and Seigneur, 1987). Further information on the model is given in Roelofs (1992).

3.1NI~ALIZATION

The initial concentration ci of a trace gas or the aerosol matter in air as a function of height z is given by:

ci(z) = c~(0)e x p ( - z/Hi),

(6)

with cj(0) the concentration of species i at ground level and H~ the scale height. Values of ci and H~ for the

Table 3. Initial concentrations and scale heights Species SO 2 NH 3 HNO 3 03 H20 2 CO 2 SO~-

Ground-level concentration 4.0 ppb 1.0 ppb 0.5 ppb 35.0 ppb 0.5 ppb 340 ppm 2.54 #g m -3

H~ (km) 2.0 2.0 2.0

3.5

species considered are listed in Table 3. At ground level, the concentration ratio of gaseous SO2 and aerosol sulfate has a value of 6 (mol: mol). All concentrations are typical of a continental background atmosphere (Warneck and Wurzinger, 1988). The parameters given by Jaenicke (1988) for rural aerosols are used to construct a three-modal aerosol size distribution which is used as input. The aerosol matter is assumed to consist of an internal mixture of soluble and insoluble material with a size-independent soluble volume ratio of 0.2. The soluble material is assumed to be ammonium sulfate. Silicate, which is found to be an important insoluble substance in aerosols (Jaenicke, 1988), is taken to be representative for all insoluble material. Smallest and largest dry aerosol radii considered are 0.01 and 2/~m. This interval is logarithmically divided into 48 size classes. Figure 1 shows the number distribution of the aerosols as a function of dry aerosol size at the initial parcel height. For the drop size distribution, the smallest and largest drop radii considered are 0.2 and 2000/~m, and this range is logarithmically divided into 60 size classes. The second dimension of the drop size distribution is divided into 16 dry-particle-size classes on a logarithmic scale, covering the same range as the aerosol size distribution. The temperature and humidity variations with height are taken from Lee et al. (1980). The initial height, radius, updraft velocity and entrainment coefficient of the air parcel are 1000 m, 350 m, 1 m s - 1 and 0.6. The initial relative humidity in the parcel is 99%.

2312

G. J. H. ROELOFS 10 4

I

........

I

'

I

......

I

I

t

the supersaturation near the cloud base has a value of 0.26%; the smallest aerosols that become drops at this value have a dry radius of approximately 0.062 #m. The liquid water content increases with height as a result ofcondensational growth of the drops. The drop concentration and the aqueous concentration of aerosol sulfate (relative to air) decrease with height due to entrainment of clearer air into the parcel. The same goes for the gaseous SO2 concentration, whose decrease is enhanced by dissolution in the cloud drops. Near the cloud top the drop concentration decreases further as a result of coalescence. The average cloudwater pH does not vary significantly with height. It has a maximum near the cloud base due to the rapid dilution of the drop's chemical contents as a result of condensational growth immediately upon activation of the aerosols. At higher elevations the dilution is counteracted by an increasing production of acidity resulting from the oxidation of S(IV). In the lower half of the cloud the rates of oxidation by 03 and by H202 are of the same order; in the upper half of the cloud the former becomes more important. The height dependence of the cloud pH and the sulfate concentrations is discussed in more detail in Roelofs (1992).

ill,,,I

102

i

10o

10-2

0.01

.......

0.1

1

10

dry aerosol radius (gin) Fig. 1. Initial aerosol size distribution (cm~)).

4.1. Near the cloud base

Results referring to a height of 150m above the cloud base are given in Fig. 2. Figure 2a shows the drop number concentration as a function of drop radius. The influence of coalescence is not noticeable at this stage of the cloud because the drops have not grown large enough to reach significant collection efficiencies. Entrainment of unactivated particles from outside the parcel and their subsequent activation in the parcel is taking place hut the ranges of drop radii occupied by the entrained particles and the particles initially present in the parcel are relatively well separated. The size range smaller than approximately 2.5 ~m radius refers to recently entrained and activated particles, while the range larger than approximately 4/~m refers mainly to the particles initially present in the parcel. The drops with radii between 2.5 and 4/zm are a mixture of both.

At the beginning of the simulation the aerosols in the parcel are assumed to be in equilibrium with this value; their further growth is calculated as described earlier. Particles that become entrained are assumed to have an initial wet radius that is in equilibrium with a relative humidity of 95%.

4. RESULTS Table 4 lists values of microphysical and (bulk) chemical concentrations at three stages during the development of the cloud: near the cloud base, halfway up the ascent and near the cloud top. The cloud base is defined as the level where the supersaturation in the parcel becomes positive. This occurs approximately 30 m above the initial parcel height. At its maximum,

Table 4. Microphysical and chemical parameters at selected cloud parcel heights

Height above cloud base (m) Simulation time (s) Drop concentration (cm-3) Liquid water content (g m ~ ) [SO2]g (ppb) Bulk pH Aqueous sulfate ~g m,~) Contribution (%) to total sulfate by: oxidation by O a oxidation by H 2 0 2 nucleation scavenging

Near cloud base

Mid-cloud

Near cloud top

150 180 390 0.23 2.21 4.94 2.12

1600 1000 219 1.06 1.20 4.78 2.10

3400 1800 47 1.29 0.42 4.76 1.76

11

23 20 57

44 16 40

7

82

Aqueous sulfate formation in cloud (a) ~" 103 J

e?,

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00

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,,,,,,

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drop radius (gin)

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106 10-7 10-2

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3.0

. . . . .

10-2

,,'1

.

.

.

.

' ' " 1

10-1" 100 initial dry radius (lain)

Fig. 2. 150 m above the cloud base. (a) Drop size distribution (emma), (b) aqueous sulfate concentration (mol ~- 1) vs drop radius, (c) pH vs drop radius, (d) aqueous sulfate concentration (mol ~- 1) vs initial dry particle radius, (e) pH vs initial dry particle radius. (b) and (d): Sulfate produced by ozone oxidation ( . . . . ), sulfate produced by hydrogen-peroxide oxidation (.-..'),sulfate from nucleation scavenging of aerosols (---), total amount of sulfate (solid line).

Figures 2b and 2c show the concentrations of aqueous sulfate from the different sources and the pH as a function of drop radius. Due to their recent activation the drops with radii smaller than 2.5 #m undergo relatively fast condensational growth and

therefore their average aerosol sulfate concentration is seen to decrease with increasing drop radius. The concentration of sulfate produced by aqueous oxidation, on the other hand, increases with increasing drop size: larger drops in this range have on average longer

2314

G.J.H. ROELOFS

lifetimes and the amount of oxidation-produced sulfate is higher. Despite the initial neutrality of the aerosol material the drops smaller than 2.5 gm radius are to a high degree acidic. This is mainly due to the dissociation of aerosol ammonium in activated large particles which produces H +. This will be discussed later. Due to condensational growth the acidity decreases with increasing drop size. As mentioned earlier, drops with radii smaller than 2.5 #m grow on particles that were continuously entrained during the parcel's ascent thus far. All entrained particles whose dry size exceeds the critical dry size at the current supersaturation in the air parcel, become drops. Therefore a specific drop radius smaller than 2.5/~m cannot be assigned to a specific dry particle size. For drop radii larger than 4/zm, mainly associated with particles initially present at the parcel, drop size and initial dry size are related in such a way that large drops grow on large aerosols and vice versa. The aerosol sulfate concentration increases with drop size, demonstrating that the chemical contents of large activated aerosols undergo a slower dilution than those of small activated aerosols. This also follows from the drop size dependence of the pH. In drops with radii between 4 and 7/~m the sulfate production by oxidation of S(IV) contributes significantly to the total amount of sulfate. Figures 2d and 2e show the concentrations of aqueous sulfate from different sources and the average drop pH as a function of the initial dry particle radius (further denoted as IDP-radius). The concentration of aerosol sulfate increases with increasing IDP-radius. In drops growing on particles with a IDP-radius larger than 0.2 #m the sulfate produced by oxidation does not significantly contribute to the total amount of sulfate. In drops growing on smaller particles on the other hand it does, and the oxidation by O a is the most efficient due to the relatively high pH in these drops. The oxidation rate by Oa decreases sharply for drops growing on larger particles due to a similar pH decrease. The sulfate production due to oxidation by H202 is relatively pH-independent and shows no dependence on the IDP-radius. Unlike the previous figures, Figs 2d and 2e show no distinction between drops growing on entrained particles and drops growing on particles that were initially present. Therefore the ranges of the concentration variations with drop

size for radii larger than 4 #m as shown in Figs 2b and 2c, and those of the concentration variations with IDP-radius as shown in Figs 2d and 2e, do not entirely overlap. Table 5 lists for three representative IDP-radii the average concentrations of the most abundant ionic species: H +, NH~, NO~, H S O ; , initial aerosol sulfate (denoted as S,cr), and sulfate produced by both oxidation reactions (denoted as So~). The concentrations are listed in descending order of magnitude. In the smallest activated particles, a significant amount of acidity is produced by the uptake and dissociation of gaseous H N O 3 and by the oxidation of S(IV), but it is to a large extent neutralized by the uptake and dissociation of NHa. In drops growing on the largest particles the uptake of HNO 3 and the oxidation of S(IV) account for only a small portion of the acidity present: here the largest amount of acidity is produced by the dissociation of a part of the aerosol ammonium into NH 3 and H +. In view of the dissociation equilibrium constant for NH~ the resulting aqueous concentration of NH3 in the activated large particles significantly exceeds its Henry's law equilibrium concentration, and therefore it escapes from the drops. Condensational growth after activation plays an important role: it causes a continuous dilution of the pollutants in the drop and this enables further dissociation of NH~. NH3 gas-phase diffusion limitations on one hand, and relatively high acidity levels in the drops which counteract the ammonium dissociation on the other hand, have as result that--with respect to NH 3 and N H ~ - - t h e adjustment towards chemical equilibrium between gas and liquid phase takes place only relatively slowly for these drops. 4.2. Mid-cloud Figure 3 shows the data referring to a height of 1600 m above the cloud base. For the size range dominated by condensational growth of recently entrained and activated aerosol particles (at this level up to approximately 8/~m radius), all concentration variations with drop size are qualitatively similar to those found in the near-cloud-base situation (Figs 3b and 3c). Specific drop radii larger than 8/zm now also refer to activated particles of widely varying dry size. Particles that were entrained and activated during the parcel's ascent thus far have grown significantly and

Table 5. Main ionic species and their concentration (tool d-t) in drops growing on particles with different initial dry size--150 m above the cloud base Initial dry radius (/an) 0.09 NH,+ NO 3 Sox HSO3 S,,r H+

0.33 0.11 (-3) 0.43 (-4) 0.18 (-4) 0.13 (-4) 0.12 (-4) 0.65 (-5)

NH4+ Sler H+ NO~Sox HSO~"

0.98 (-3) 0.49 (-3) 0.54 (-4) 0.45 (-4) 0.73 (-5) 0.22 (-5)

1.22 NH~ S,, r n+ NO~ Sox HSO~"

0.15 ( - I ) 0.78 (-2) 0.47 (-3) 0.27 (-4) 0.77 (-5) 0.21 (-6)

Bulk NH2 S,, r NO~ Sox HSO~ H+

0.24 ( - 3) 0.78 (-4) 0.47 (-4) 0.16 (-4) 0.12 (-4) 0.12 (-4)

AqueQus sulfate formation in cloud 10 3

(a)

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101

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10-2

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Fig. 3. As Fig. 2, but for 1600m above the cloud base.

are of sizes comparable to those of the particles that were in the parcel initially. Therefore a clear distinction based on drop size is no longer possible. At this level the former group of drops accounts for approximately 70% of the total number of drops. Coalescence starts playing a role in the formation of drops larger than 20 #m radius. On average the concentration of aerosol sulfate increases with drop size in these

drops due to collection of small and more polluted drops (see also Roelofs, 1992). In Figs 3d and 3e the aqueous sulfate concentrations and pH are given as a function of IDP-radius. The graphs are qualitatively similar to the results presented in Figs 2d and 2e. In the drops growing on the largest aerosol particles the concentration of sulfate produced by the oxidation of O3 is seen to increase

2316

G.J.H. ROELOFS

again with increasing IDP-radius, despite the relatively high acidity. The increasing concentration is however not due to oxidation in these drops, but to the collection of drops during whose lifetime a significant production of sulfate by oxidation by 0 3 has taken place. The concentrations of the most abundant ionic species as a function of IDP-radius are listed in Table 6. Due to the increase of the liquid water content, the aqueous concentrations of N O 3 and of the aerosol matter (S,c, in all drops, and NH~" in the drops growing on the largest particles) show a decrease when compared to the near-cloud-base situation. Due to the oxidation of S(IV) the decrease of the concentration of oxidation-produced sulfate is much less, and the concentration of H + has even increased in the drops growing on the smallest particles. The dissociation of aerosol ammonium in the drops with the largest IDP-radii has become significant. The gaseous NH 3 that is formed in this way becomes dissolved again in the more diluted drops. At this cloud level and under the conditions chosen, approximately 11% of the gaseous NH 3 dissolved in these drops was initially present as particulate matter in the large aerosols. 4.3. Near the cloud top Figure 4 shows the data referring to a height of 3400 m above the cloud base. The process of coalescence is very pronounced near the cloud top, resulting in an efficient production of drops with radii larger than 20 pm (Fig. 4a). Upon coalescence, drops of

highly different chemical composition are mixed. Therefore the sulfate concentrations, as well as the pH, do not vary significantly with increasing drop size in drops larger than 20 pm radius (Figs 4b and 4c). The aerosol sulfate concentration shows a slight increase with drop size due to the continuous collection of small drops with relatively high aerosol sulfate concentrations. Figures 4d and 44: show the sulfate concentrations and the pH as a function of IDP-radius. The term 'initial dry particle radius' has however no practical significance at this level in view of the recombination of initial aerosol material that has occurred as a result of coalescence events. Figures 4d and 4e however demonstrate the significant homogenization of pollutant concentrations over the individual drops. This also follows from Table 7. 4.4. Cloud processing of the aerosols The simulation results are used to obtain an estimation of how the initial aerosol size distribution (Fig. 1) is processed during the cloud's lifetime. From Tables 5, 6 and 7 it may be derived that the soluble material comprised in the remaining particles will consist mainly of NH2, H ÷, NO~ and SO 2- . Their relative amounts in each particle mainly depend on the time that the particle has been activated, the relative importance of the aqueous chemical processes that have taken place during the droplet stage of the particle, the amount and nature of the drops that have been collected upon coalescence, and how nitric acid and ammonia are redistributed over the gas and liquid phase upon evaporation. To facilitate the comput-

Table 6. Main ionic species and their concentration (mol ~'- 1) in drops growing on particles with different initial dry size --1600 m above the cloud base Initial dry radius (/an) 0.09

0.33

1.22

Bulk

NH~"

0.20 (-4)

NH +

0.12 (-3)

NH2

0.40 (-2)

NH2

0.36 (-4)

H+

0.14 ( - 4 )

S,,,~

0.68 ( - 4 )

St,,.

0.21 ( - 2 )

H+

0.17 ( - 4 )

So. NO 3 HSOi S..r

0.90 (-5) 0.61 (-5) 0.49 (-5) 0.25 (-5)

H+ NO3 So~ HSO~

0.38 (-4) 0.54 (-5) 0.48 (-5) 0.23 (-5)

H+ Sol NO~ HSO~

0.28 (-3) 0.53 (--5) 0.36 (-5) 0.34 (-6)

S,,r So. NOi HSOi

0.12 (-4) 0.88 (-5) 0.61 (-5) 0.46 (-5)

Table 7. Main ionic species and their concentration (mol d- 1) in drops growing on particles with different initial dry size - 3400 m above the cloud base Initial dry radius (~m) 0.09

0.33

1.22

Bulk

H+

0.17 ( - 4 )

NH~

0.33 ( - 4 )

NH~

0.34 ( - 3 )

H+

0.18 ( - 4 )

NH 2 So, S,,~ HSO~ NO3

0.13 (-4) 0.84 (-5) 0.35 (-5) 0.27 ( - 5) 0.24 ( - 5)

H+ S,,, So, NO~ HSO~

0.22 (-4) 0.18 (-4) 0.73 (-5) 0.23 ( - 5) 0.22 ( - 5)

S,,, H+ Soz NO~ HSOi

0.18 (-3) 0.37 (-4) 0.82 (-5) 0.24 ( - 5) 0.20 ( - 5)

NHI So, S,°, HSO~ NO~

0.16 (-4) 0.85 (-5) 0.57 (-5) 0.25 ( - 5) 0.24 ( - 5)

Aqueous sulfate formation in cloud

(a)

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0 0

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i0 -I i0 0 initial dry radius (pro)

3.0

. . . . . . . .

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10 1

10 0

initial dry radius (l~m)

Fig. 4. As Fig. 2, but for 3400 m above the cloud base.

ations we assumed that all drops evaporate instantaneously, and that each evaporated drop yields one aerosol particle. Further we neglected the fact that after evaporation different chemical compositions will be found in different particles. Instead we assumed that both the initial aerosol sulfate and the sulfate formed during the cloud's lifetime are in a completely neutralized state after drop evaporation, so that the

final chemical composition of the soluble aerosol material is again (NH,)2SO,. In terms of final particle radius this may alter the results to some extent. Since it will be seen that the results are not qualitatively dependent on the final particle composition, this is not a serious error. The radius r of the dry material resulting from complete evaporation of a drop with radius a and IDP-radius R is then given by:

2318

G.J.H. ROELOFS

, _,

(3rm,(a,R) mu(a,R)-]'~'13 p. + ,, j )

in the drop immediately before evaporation, and M, is the molecular mass of ammonium sulfate. As a result of sulfate production during the drop stage, the eventual soluble volume fraction will be higher than before activation. When compared with each other, dry particles of the same size may show significant external mixing when considering the soluble volume fraction they contain. For instance, a large, recently activated particle may yield the same dry particle radius after complete evaporation as a smaller but earlier activated particle in which a substantial amount of sulfate is produced by oxidation.

(7)

with m,, p,, m, and Pu referring to the mass and density of the soluble and insoluble material comprised in the drop. Since the soluble material is assumed to be (NH4)2SO4, ms can be calculated according to: m,(a,

4x

R)=-~-a3(cs..r(a, R)+Cso,,(a, R))M,,,

(8)

where Cs.., and Cso.are the concentrations of the initial aerosol sulfate and the sulfate produced by oxidation

.

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1 dry aerosol radius (j~n)

1

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10

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w

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o,

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0.2

.0

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1

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. . . . . . . .

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1 dry aerosol radius (jJm)

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10

. . . . . . . .

100

Fig. 5. (a) Aerosol volume concentration (normalized,/an 3 Cm~r5 ), (b) soluble volume fraction vs dry particle radius: initially (solid line), and after complete evaporation of the cloud drops at 150m (---), 1600 m (. . . . ) and 3400m (....) above the cloud base.

Aqueous sulfate formation in cloud The soluble volume fraction of the latter particle will however be higher than that of the former. The average soluble volume fraction of the particles with dry radius r is calculated by: ~,(r) =

1

--S ~ A(r, a, R)f(a, R)m,(a, R)dadR P, ,, A(r,a,R)f(a,R)[m~(~iR) +rn~£R)]dad R,

(9)

where A(r, a, R) has the value 1 if r(a, R)=r, and 0 otherwise. The average soluble volume fraction as given by (9) is essentially the same as the volume mixing ratio Mr defined by Jaenicke (1978). Figure 5a shows aerosol volume distributions as a function of dry particle radius for the initial aerosol size distribution and the aerosols remaining after an assumed complete evaporation of the cloud drops near the cloud base, halfway up the cloud and near the cloud top. The volume distributions are normalized with respect to the initial volume concentration in the air parcel. Due to the oxidation of S(IV), near the cloud base an increase of aerosol volume is noticed between 0.07 and 0.2 #m radius (cf. Fig. 2d). Allowing further development of the cloud, the size of the peak increases and it shifts towards larger aerosol sizes. Near the cloud top the aerosol volume between the radii 0.07 and 0.3 #m has decreased drastically due to the redistribution of the particulate matter caused by coalescence of the cloud drops. This results in an increased particle volume for radii larger than 2 #m. The evolution of the soluble fraction as a function of particle radius is shown in Fig. 5b. During the first half of the cloud development the average solubility of the particles increases between approximately 0.07 and 0.4 #m radius. Halfway up the cloud, particles with the highest soluble volume fraction are found between 0.1 and 0.2 #m radius. Their average soluble volume fraction has increased from initially 0.2 to more than 0.5. In the upper half of the cloud this maximum is not exceeded further, but due to coalescence of the drops the solubility increases throughout the particle size spectrum. The sudden increase of the soluble volume fraction at 2 #m results from the fact that initially no aerosols were assumed to be present with radii larger than this value, and the average solubility in this range is not influenced by particles that have not significantly undergone chemical evolution or collected other drops during their drop stage.

5. DISCUSSION Results were presented of a numerical simulation of a growing cloud under continental background conditions. The model considers entraining air parcel dynamics, detailed microphysics and aqueous-phase chemistry. The drop size distribution, which forms the

2319

basis for the chemistry calculations, is represented in a two-dimensional way, the first dimension being the drop radius, the second dimension being the initial dry radius of the drops. The aqueous concentrations of drop pollutants as function of drop size are found to be influenced to a large extent by processes of microphysical and dynamical nature. In small drops (up to radii of approximately 2.5 #m near the cloud base and 8/~m at higher altitudes) the total pollutant concentration shows a decrease with increasing drop size. They have only recently been activated and undergo relatively fast condensational growth (see, for example, fig. 13-2 in Pruppacher and Klett, 1978). Their aqueous sulfate production by oxidation is not yet significant when compared to the initial aerosol load. Near the cloud base, the drop size dependence of pollutant concentrations in drops larger than 4 ttm radius is mainly dominated by the size distribution and chemical composition of the aerosols initially present in the parcel. These drops show an increasing pollutant concentration with drop size. At higher altitudes the influence of earlier entrained and activated drops becomes increasingly important. Drops of a certain size can no longer be assigned to a certain dry aerosol size. Instead they grow on particles of widely varying dry sizes, resulting in a relative homogenization of the concentrations over the drop sizes when compared to the near-cloud-base situation. At still higher altitudes the process of coalescence becomes increasingly important in the formation of drops larger than 20 #m radius. Since coalescence is a stochastical process, the pollutant concentrations in the resulting drops are an average of the concentrations found in the smaller drops before coalescence, and eventually become relatively independent of drop size. We have not included drop break-up processes in our model. However, in view of the relative homogeneity of pollutant concentrations in the drops most liable to break up, and the size of resulting satellite drops (Hall, 1980), we do not expect a significant change of the drop size dependence of the pollutant concentrations. At higher altitudes than near the cloud base the concentration of the oxidation-produced sulfate significantly contributes to the total amount of sulfate in drops of approximately 8 #m radius and larger. The aqueous concentrations of pollutants are also studied as a function of the initial dry size of the drops. This size dependence remains fairly unambiguous throughout most of the cloud. The smallest activated aerosols are the most diluted (cf.Twohy et al., 1989), so the sulfate production by oxidation is most significant in these drops when compared to the initial aerosol load. Furthermore, a possible acidity load or acidityproducing property of the initial aerosol matter is least noticeable in these drops, and the sulfate production by oxidation by 03 can be most significant. The initial aerosol matter becomes increasingly important with increasing dry particle radius. In drops

2320

G.J.H. ROELOFS

growing on the largest particles the sulfate production by oxidation remains insignificant when compared to the aerosol sulfate. These drops contain, however, high acidity levels, despite the fact that the initial soluble aerosol compound is ammonium sulfate. Due to their relatively low degree of dilution, aerosol ammonium partly dissociates into NHa, which escapes into the gas phase, and H +. A similar effect was found by Ayers and Larson (1990). The use of the entraining parcel model as the dynamical framework has as a result that mixing of entrained air within the cloud is assumed to take place immediately and homogeneously. In reality mixing takes place gradually and inhomogcneously, and thus determines, for example, when and where in the cloud the activation of the entrained particles takes place. The drop size dependence of the concentration of dissolved aerosol material can be strongly influenced by this (e.g. Flossmann, 1991). Considering the fact that mixing processes also influence the concentrations of trace gases in the cloud, it might be expected that the aqueous-phase chemistry will be affected as well. We have assumed that the initial aerosol soluble volume fraction is independent of aerosol size. Generally it is found that the soluble volume fraction increases with decreasing particle size (Winkler, 1974; Jaenicke, 1978) in such a way that the smallest particles are almost completely soluble. If the initial aerosols were assumed to consist entirely of (NH4)2SO # (i.e. ev= 1) the concentration of the soluble aerosol material would increase accordingly by a factor of 5 when compared to the case described here. The concentration of aerosol material found in individual drops would however still range over a few orders of magnitude (depending on their initial partitle size; see Figs 2d and 3d), and qualitatively the size dependence of the chemical processes would not change significantly. Further, the initial aerosol matter might have contained acidity already. Results of a simulation identical to the one described here but with NH4HSO4 as soluble aerosol material show an increased acidity and a decreased oxidation rate by 03, both due to the initial aerosol acidity load. Qualitatively, however, the dependence of the concentrations of chemical species on drop and particle radius are identical. The cloud bulk concentrations predicted by the model as a function of height show reasonable agreement with measurements (Tremblay, 1987; Leaitch et al., 1986). The amount of sulfate produced by aqueous oxidation (0.4#gm -3 near the cloud base to 1.1 #g m-3 near the cloud top) is in good accordance with the findings of Hegg and Hobbs (1982) and Hegg et al. (1984). The increasing pollutant concentration with increasing drop size, found near the cloud base, is verified by the measurements of Ogren et al. (1989). As yet no measurements are reported in the literature of size-dependent pollutant concentrations of cloud drops at higher altitudes than near the cloud base, but

it can be expected that they will rather yield a decrease with increasing drop size. However, the theoretical explanation of the findings of Ogren et al. (1989), namely that drops growing on small particles dilute relatively more than drops growing on large particles, and the implication of this for the chemical evolution of the drops (Twohy et al., 1989), is, on average, plausible for higher cloud altitudes as well. Aqueous-phase chemistry in a non-precipitating cloud changes an initial aerosol size distribution in such a way that the largest aerosol growth takes place on the smallest activated particles. Generally these are accumulation mode particles. If coalescence does not play a significant role during the cloud stage, their growth is not enough to allow a transition into the coarse mode, and the produced sulfate eventually benefits the accumulation mode. The development of the chemical growth of the particles during the cloud stage, as indicated by the simulation, is qualitatively consistent with measurements performed by Hering and Friedlander (1982) on the influence of different growth mechanisms on urban aerosol size distributions. Coalescence of cloud drops recombines the aerosol matter in such a way that additional coarse particles are formed, composed of initial aerosol matter and in-cloud-produced sulfate. This is accompanied by a significant decrease of the aerosol volume in the accumulation mode. The soluble volume fraction of the particles increases throughout the size distribution, with a maximum for the particles with radii between 0.1 and 0.3 pm. Particles, eventually present in this range, were initially the smallest particles activated during the cloud's lifetime. The initial dry particle size is, as a measure for distinction between drops, not applicable to cloud chemistry measurements. It determines, however, to a large extent the acidity and other pollution levels in cloud drops, and these are seen to range over a few orders of magnitude. The differences between pollution levels in drops may lead, when regarding them as a bulk solution, to significant supersaturations with respect to Henry's law in the case of weak acids such as S(IV) (Pandis and Seinfeld, 1991). When not accounted for in models, this in turn may lead to an underprediction of the sulfate production by oxidation. For modeling purposes the initial dry particle size of drops is therefore probably a useful tool as discriminator between drops.

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2321

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AE(A) 26:t3-E