reactive scavenging of pollutants by rain: a modeling approach

Atma~btric EmOa~Rmt Vol. 20. No. $, pp. 1015-1024, 1986 0004-69Sl/~6 S3.00 + 0.00 ~rinted in Great Britmn. Pergamon Press Ltd.

REACTIVE SCAVENGING OF POLLUTANTS BY RAIN: A MODELING APPROACH

SUDARSHAN KUMAR Environmental Science Department, General Motors Research Laboratories, Warren, MI 48090-9055,

U.S.A.

(First recehz.d 14 February 1985 and receit~*d for publication 26 September 1985)

AMtraet--An Eulerian model for rain scavenging of pollutants (Kumar, 1985) has been extended to take into account the processes of absorption of multiple pollutant species and chemical reactions within the raindrops. Model simulations have been performed to compare the rates of S(IV) oxidation by O3 and HaO3. A compmimn of these two oxidation paths indicates that for raindrops, oxidation by O3 can be the dominating path at pH values near or above 4.'/. However, oxidation by H=O2 will dominate at lower pH values. Oxidation of S(IV) catalyzed by Fe(IIl) and Mn(ll) is potentially a very important path but there are many uncertainties regarding the magnitude and the pH dependence of the reaction rates as well as the presence of catalytic synergism between Fe(III) and Mn(ll).

At lower temperatures, solubilities of SO,, O3 and H=O2 increase while the rate constants for oxidation reactions decrease. Model simulations indicate that, all other conditions remaining the same, [SO~ "2 ] in raindrops would increase at lower temperatures but [NO~" ], which is produced solely as a result of HNO3 absorption, would not change. The lower [SO~"I in winter rains is thus, most likely, a result of the fimited availability of oxidants. As a result of model simulations, it was also found that formaldehyde (HCHO) does not bind any appreciable amount of S(IV) in raindrops and that the [SO~" a'l and [S(IV)] in raindrops are not affected by the presence of HCHO in the atmosphere.

Key word index: Acid precipitation, acid rain, reactive scavenging model, precipitation scavenging.

I. INTRODUCTION

The processes of trace gas absorption and aerosol scavenging by hydrometeors followed by aqueous- phase reactions are responsible for the acidification of rain. All of thcse processes can occur either in-cloud or below-cloud. The contribution of in-cloud and below- cloud processes in influencing the chemical composition of rain varies from event to event. The scavenging of aerosols below clouds by falling rain is not an efficient process because of the low scavenging efficiency for aerosols with diameters between 0.I and 1.0/~m. This is the so called Greenfield gap (Pruppacher and Klett, 1978). The importance of below-cloud gaseous scavenging depends on many factors including the pH of raindrops as they fall from the cloud.base. For example, below-cloud scavenging of SO, and its subsequent oxidation to SO~ 2 depends highly on the initial pH of the raindrops because the effective solubility of SO2 decreases with increasing raindrop acidity. On the other hand, the incorporation of HNO2 in drops does not have'a significant dependence on raindrop pH (Kumar, 1985) because of the very high solubility of HNO~ in water.

The contribution of below.cloud scavenging to the ionic composition of rain has also been studied in field experiments. In a recent study of ¢Ioudwater and rainwater composition in the Adirondacks, Castillo et al. (1983) concluded that in one particular rain event, below-cloud scavenging contributed only negligibly to the composition of rainwater (the rainwater com-

position was virtually identical to the cloudwater composition), while in another case, below-cloud scavenging was responsible for 45 % of the total ion concentration in the rainwater. Their second case highlights the importance of below-cloud scavenging in contributing to the ionic composition of rain at ground level.

A number of Lagrangian models (Adamowicz, 1979; Durham et al., 1981; Adewuyi and Carmichael, 1982) have been formulated to describe the problem of trace gas absorption by falling raindrops. In a previous work (Kumar, 1985), an Eulerian model was formulated to describe the simultaneous processes of gas-phase de- pletion and aqueous-phase accumulation of pollutant species during a rain event. This model enables one to follow the space-time profiles of a trace pollutant species in the gas phase as well as in the aqueous phase. In this work, the model is extended to include the processes of multiple-species absorption and chemical reactions in the aqueous phase.

Because of its Eulerian nature, the model is capable of accommodating any realistic initial vertical profile of gas-phase concentrations. In addition, one can incorporate time-dependent initial aqueous-phase concentration, at the cloud-base. At this stage, the dynamics of air motion during a rain event are not included. Fisher (1982) and Molenkamp (1983) have attempted to couple the dynamics of air motion and precipitation production with the uptake of pollutants by precipitation. However, they do not include detailed chemistry within the raindrops. The emphasis in this

1015

1016 SUDAltSHAN KUMAR

work is to develop a model that includes aqueous- phase chemical reactions associated with scavenging of a number of pollutant species.

2. MODEL DESCRIPTION---CHEMICAL

2.1. Aqueous phase equilibria

Raindrops falling from the doud-bnse through the polluted layer are exposed to a number of pollutant species. Gaseous species that have a major influence on the chemical composition of rain are CO2, SOs, NO, NO:, HNO:, NHs, H2Oz and 03. These species are absorbed by raindrops (at

d[SO~2]/dt = 3.1 x 10S[HSO~ "] [03]

+ 2.2 x 10'[SO; 2'1 [03] M s- L (2)

The rate of oxidation of S(IV) by O3 shows a strong pH dependence. Bemuse both [HSO~'.1 and [SO~ 2] decrease with decreasing pH, the oxidation rate also decreases as the drops become more acidic. The stoichiometry for S(IV)-Os reactions can he represented by

HSO~ + 03 --* H + + SO~ =, SO~" 2 + 03 --* SO22. (3)

Hydrogen peroxide (H,O,) is formed in the atmosphere and has been measured at ppb levels in the atmosphere by

rates that depend on the muss-transfer coelficlents of these species), and undergo dissociation and e~maiml rexctions in the aqueous phase. The Henry's law solubility constants and aqueons-phase equilibria eonstants of various SlX~ies of importance are given in Table 1. Alglnming CO~IUIllt praetlra, the temperature dependence ofequilibrium constants is given by the relationship (Denbigh, 1971)

d In K AH ° (1)

dT RT 2

where AH ° is the increase in enthalpy for the equilibrium process, R is the univemd gas constant and Tis the absolute temperature. The liquid-phase dism~ation equilibria generally have time constants much smaller than the aqueous- phase oxidation reactions (Eigen tn a/., 1964). It is assumed that the solubility and dissociation equilibria listed in Table 1 are 'fast' compared to the chemical reactions in the drops.

2.2. Formation of sulfote m the ra~rops

Two of the most important oxidizing agents for S(IV) in the aqueous-phase are O3 and H20:. The kinetics of aqueous- phase oxidation of S(IV) by O: has been the subject of a number of investigations [Edckson a al. (1977k Lawson et al. (1978), Muhe (1983), and Penkett eta/. (1979)'1. The work of Erkkson tn a/. (1977) is in excellent agreement with that of Maahe (1983) and includes an expression that specifies the individual contributions of various S(IV) species in the formation of SO~ :. Specifically, the rate expression given by Erickson et al. (1977) is

various investigators (Kok eta/., 1978; Oroblicki, 1984). It is highly soluble in water and is a strong oxidizing agent for S(IV) in the aqueous phase. The oxidation of S(IV) by H20, has also been studied by many authors including Penkett et al. (1979), Martin and Damschen (1981), and MeArdle and Hoffmann (1983). In this work, the rate expression due to Martin and Damsehen (1981) was chosen

d[SOX2]/dt - 5.2 x 107[H ÷] [H202.1 ['HSO~] M s- 1 (4)

which is consistent with the stoichiometry

HSOf + H,O2 + H + -+ 2H + + SOl ". (5)

The S(IV) oxidation by H202 is an acid.catalyzed reaction and the rate of reaction, unlike that of S(IV) and 03, is essentially independent of pH.

Auto-oxidation of SOa in the aqueous phase, catalyzed by various transition metals, can also be an important source of SO~ ~ in precipitation. This path for production ofSO~" will be considered in a later section. Another possible path for S(IV) oxidation in the aqueous phase is through reactions with dissolved NO2. Recently, Lee and Schwartz (1982) and Ellison and Eckert (1984) have studied this system. Lee and Schwartz (1982) determined second-order rate constants for reactions of NO2 (aq) and various S(IV) species. However, there are considerable uncertainties in the pH-dependence and reaction stoichiometry because of the unresolved mech. anism of the reaction path. This reaction system deserves further study and is not included in the model set out in this paper.

Table 1. F.quilibrium processes and values of equilibrium constants

K2~. &H ° (M or M atm - l ) (kcal tool") Ref.

1. HsO ~- H + + OH - 1.80 ( - 16)* 13.35 (SM)t 2. COa(g) ~ CO2(aq) 3.40(-2) -4.85 (SM) 3. COa(aq) ~ H + + HCOi " 4.47(-7) 1.83 (SM) 4. HCO~" ~ H + +CO~ "2 4.68(-11) 3.55 (SM) 5. SO2 (g) ~ SO2 (aq) 1.24 - 6.29 ( M )

t, + 6. SO2(aq)~,~H +HSO~ 1.32(-2) -3.90 (M)

k.6

7. HSO~ ~ H + +SO~ 2 6.42(-8) -2.84 (M) k..p

8. HNO3 (g) ~ HNOs (aq) 2.1 ( + 5) - - (SW) 9. HNO3(aq) ~ H ÷ + NO~ 15.4 - 17.3 (SW)

10. NHs (g) ,~"" NH: (aq) 58.9 -8.17 (SM) 11. NH:(aq)~NH4 + OH- 1.70(-5) 0.865 (SM) 12. HaOa(g)~-HaOa(aq) 7.1 (+4) - 13.8 (MD) 13. Os (g) ~-O3 (aq) 1.23(-2) -5.04 (BP) 14, HCHO(g)~,~CH:(OH)z 7.0(+3) - 12.85 (BE)

*The notation 1.80(-16) denotes 1.8 x I0-t6. tSMmSillen and Martell (1964), M--Muhs (1982), SW--Schwanz and White

(1981), MD--Martin and Damschen (1981), BPmBriner and Perrottet (1939), BE--~AI and Evans (1966).

Reactive scavenging of pollutants by rain I 017

2.3. Formation of nitrate m the raindrops

The solubility and reaction equilibria of aitrogen oxides in water have been studied in detail by Lee and Schwartz (1981a, b) and Schwartz and White (1981). The aqueous- phase equilibria of interest, in the N O = - H 2 0 system, are

2NO=(g) + H20 *-* 2H + + NO~ + NO~, NO(g) + NO2 (g) + HzO .., 2H + + 2NO[. (6)

If one considers only the equilibria, very high concentrations of HNO3 can be obtained at low NOz concentrations. However, at atmospheric eoncentrations, the rate of aqueous- plume oxidation of NO= is very slow reflecting the second- order kinetics of the aqueous-phase reactions and low physical sohibifity of NO and NO=. Therefore, over the time- scales of interest in the atmosphere, these aqueous-phase reactions are far from equilibrium and contribute negligibly to nitrate levels in precipitation.

The dissolution and decomposition of PAN (peroxyacetyl nitrate) in raindrops has also been suggested as a possible source of NO[ in rain. Peroxyacetyl nitrate is a commonly found pollutant species in urban areas (Spicer et ai~ 1983; Altshuller, 1983) and has been measured at ppb levels in various cities. Holdren et al. (1984) have estimated PAN solubility at 5Matm -I, while Lee et al. (1983) have estimated PAN solubility to be roughly 4 Matm- 1. The decomposition rate of PAN, as determined by Holdren et al. (1984) is 6.85 × 10-" s-~ at 25°C. Combining these results with typical PAN concentrations of a few ppb in the atmosphere leads to a very small contribution to lqOi levels in the raindrops. On the other hand, p.saons HNO~ is present as a trace pollutant in virtually all urban areas, and is highly soluble in water. Scavenging of HNO3 is thus a major source of NO[ in rainwater. Of course, NO~ in rainwater may result from HNO3 absorption at cloud level or through nitrate aerosol particles serving as cloud condensation nuclei. However, in this work only below-cloud gaseous scavenging and reaction pr _oc~___~_ are dealt with, and HNO3 absorption by raindrops is considered to be the only process responsible for production of NO~ in rain.

3. MODEL DESCRIPTION--PHYSICAL

The model presented in Kumar (1985) was extended to the case of multiple-species absorption and chemical reactions in the raindrops. The major assumptions of the model are: (i) Raindrops start at the cloud-hase and fall through the polluted layer, as shown schematically in Fig. 1, at their terminal velocities. The terminal velocity u of a drop depends on its radius r. It is assumed that the pollutant species are absorbed by the raindrops in the polluted layer. (ii) The drops are well-mixed internally. As a consequence, the aqueous-phasa concentration of any species within a drop is uniform and the resistance to mass transfer ties entirely in

.io .... ;;, ' ' ' [ I I I I I

I [ R a i n d r o p s I ] I

' I i I t : ' ,

i i' , , [ I i i [ll, i l l ,

. . . . . . . . . . . C l o u d . B a s e

P o l l u t e d L a y e r

x : L G r o u n d

Fig. 1. A =¢hemstic diqp'am of raindrops falling through the polluted layer.

the g u pham. The 8m-ldUUe mass-trama'er coefficient kw, for a particular ~=~_'__. can be calculated from the Fro=ring equation OFrondin& 1938). (iii) The model further assumes that all the drops are of a uniform =/ze ro comaponding to the mmfimum in the fraetional volume distribution of drops. The pctdominant drop radius r o is calculated from the Marshall-Palmer size distribution (Marshall and Palmer, 1948). The number of drops per unit volume of air, No, is such that iV, the liquid water content per unit volume ofair during rainfall, obeys the empirical relationship observed between W and rainfall intensity L

In order to formulate the equations describing the model proposed in this paper, first it should be noted that the species of interest can be divided into three classes: (it) All the pollutant species in the gas phase, e.g. SOu and 02. (b) The dissolved or hydrated form of the gas-phaze species in (a), e.& SO= (aq) and O3 (acO. (c) Species which are produced solely as a result of dissoci-

• ation or chemical reactions in the aqueous phase, e.g. HSO~, SO~ = and SO~ =. For a particular species in the gas phase, the concentration p(x, t) (in atm) at time t after the start of a rain event and distance x below cloud-base can be described by

0p(x, t ) ,DO2P(x ,O_4 , r~Nok , ( ro ){P(x , t )_c (x~} 0t ax =

(~)

where c(x,t) is the aqueous-phase concentration (in moles t ' -1 designated as M) of the hydrated form of spscics under consideration in predominant size drops and H is its Henry's law solubility constant (in M arm- =). The first term on the r.h.s, of Equation (7) describes the effect of turbulent diffusion (D is the turbulent diffusivity) and the _~o~__nd term describes the net mass transfer from the gas phase to the aqueous phase. The aqueous-phase concentration c(x, t) of the dissolved species is described by

Oc(x,t) . ,Oc(x,O 3k,(ro)f x " c(x,t)] , +alto, ax = , o R r

+ net rate of accumulation due to dissociation. (8)

For example, for the case of SOz (aq), we have

a[SO=] O[SO=] 3ks, so , f [SO=]~. +=*,o) = , o R r

- k6[SO=] + k - 6 [ H ÷ ] [HSO~ ] (9)

where the first term on the r.h.s, describes the mass transfer from the gas phase to the drop and the rest oftbe terms on the r.h& account for net accumulation due to dissociation. For a g3ecks in class (c), the equation for the aqueous-phase concentration c(x, 0 is simply

Oc(x, t) + u ( r o ) ~ - net rate of accumulation (10)

Ot due to dissociation and chemical reactions.

Thus, for the case of SO~', we have

OESO[ 2] 4" u(ro) 0[SO[ =] =. k7 [HSO[ "] Ot ~x

-- k_ , [H+ ] [SOj'Z 3 -2.2 x 10'[SO~a][O=]. (11)

Similar equations can be written for each of the species in the two phases. Thus a system of coupled partial differential equations is obtained which must be solved simultaneously to obtain the concentration profiles of various species as a function of time and distance below dood-bme. However, certain simplifications can be made to reduce the number of equations in the system.

1018 S ~ KUM~

Nitric acid and ammonia lutve extremely high solubilities in water at pH values of intercst (< 5). These SaNs are absorbed by raindrops, undergo dimmcmtion in the aqueous phase, and do not take part in any reactions in the aqueous phase. Thus, their concentrations can be assumed to be independent of x and to decrease exponentially with time as 0Kumar, 1985)

p(t) = p,(0)exp ( - ~t) (12)

where p ~ 4xaoNok,. We further assume that the dissolved ammonia and nitric acid dissociate almost completely so that [NH3(aq)] < [ N H ; ] and [HNO3(ao.)] < [NO; ] . Db- solved COz in rain undergoes dissociation to form H +, HCO~, and CO; 2 ions. The HCO; and CO~ ~ ions do not take Part in any reactions and from the equilibrium constant values it can be readily shown that at pH values ~ 5, the contribution due to the dismciation of diseolved CO~ to me total [H*] is quite small. Therefore, dissolved CO z and its dissociation products can be safely neglected from the species in this system.

The system equations can be solved for any arbitrary initial and boundary conditions. However, in order to keep the simulation results s/mple and easy to interpret, the following were chosen. All the gas-phase species are assumed to be present at concentrations which are invariant with height at t = 0. The flux of gas-phase species at the ground and the cloud-base is also assumed to be zero. As the raindrops descend from the cloud-base, the concentrations of all aqueous-phase species, except [H+], at the cloud-base are assumed to be zero. The initial pH of raindrops can be specified at any given value. The coupled system of partial differential equations was solved by using the Galerkin method (Lapldus and Pinder, 1982) with chapeau functions as the basis functions to formulate ~ equations. The d ~ equations were then solved by a program called EPISODE (Hindmarsh and Byrne, 1975). EPISODE is an implementation of the Gear technique for solving a stiff system of ordinary differential equations.

4. MODEL SIMULATION EESULTS

A number of simulations have been performed with the objective of understanding the roles of various pollutants and the effects of certain key parameters in influencing the chemical composition of rain. In all the simulation results to be described, it is assumed the rain intensity I - 10 mm h - s, the height of the cloud- base above ground L ffi 1500m, and the vertical turbulent diffusivity D = 100 m 2 s - s. The water content per unit volume of air is given by W = 72 lO.as, where W is in mg m - 3 I is in mm h - ~ and No, the number of drops per unit volume ofair, is calculated to maintain W at the value indicated by I.

4.1. Role o f H202, 0~, HNO3 and NH3

In Fig. 2 are shown the aqueous-phase SO~ 2 and NO~ concentrations and pH in raindrops as a function of distance below cloud-base at t = 15 rain after the start of a rain event. For these simulations, initial conditions are as follows: SO 2 = 15 ppb, HNO3 = 2.0 ppb, H20 2 -- 2.5 ppb, Oa = 80 ppb and NH3 = 1.5 ppb. In addition, it is assumed that initial raindrop pH = 5.0 and temperature = 25°C. The initial ps -phase concentrations have been chosen to represent average summertime pollutant concentrations in the Northeastern United States under non- episodic conditions. For a detailed review of the

3.50 0

o

| soo

m, e0o _o ¢J

t 'oo J~

120o

|150o " 0.0

3.75 4.00 4.25 4.50 4.75 5.00

/ . . . . " . . . ",,4 o4-21 /p. [NO3"i", tl • -'" t , , / so4-a

",, " ~ t I . . . . . . NO3"

I t I ~'* t I ~ -

5.0 10.0 15.0 20.0 25.0 Concentration in Raindrops (taM)

Fig. 2. Sulfate and nitrate concentrations and pH in raindrops as a function of distance below cloud-base 15 rain after the start of a rain evenL Initial gas-phase concentrations [cese (A)]: SOz-15ppb , HNOs - 2 ppb, H2Oz = 2.5 ppb, O~ - 80 ppb and NH3

• - 1.5 ppb. Initial raindrop pH - 5.0.

ambient measurements of various gaseous pollutants, the reader is referred to Altshuller (1983) and Blumenthal et al. (1984). In the simulation shown in Fig. 2, [ N O i ' ] and [ S O ; 2] increase with the distance below the cloud-base. On an equivalent basis, [SO~ 2] is roughly three times [NO~'] at ground level. The raindrop pH decreases from 5.0 at cloud-base to 4.2 at ground level. Figure 3 shows the [ N O i ' ] and [SO~ 2] in rain at ground level as a function of time. As the rain event progresses in time, the gas-phase concentrations of HNO3, SO2 and the oxidants decrease, which in turn account for reduced [NO~'] and [SO~ 2] and an increase in raindrop pH. [ S O i 23 decreases from 25 ~M at the start of the rain event to roughly half that value at the end of an hour. At the end of the same period, [NO~] decreases to less than one third of its initial value while the pH increases from 4.2 to 4.4. The rapid decrease in [ N O ~ ] is a direct consequence of the high solubility of HNO3 in water leading to a rapid reduction in gas-phase HNO3 concentration. The decrease in [SO~ 2] is a result ofthe rapid decline in the gas.phase H202 concentration and a slower decline in the gas-phase SO: and O~ concentrations.

... 30.0 5.0

2§.0

. ! 20.0

~ 16.0

10.0

U 0.0 0

. . . . . ___ pH 03

I t t t ' 4 . 0 10 20 30 40 sO 60

Time (rain)

4 . 8

4.6!_

4.4

4.2

Fig. 3. Sulfate, nitrate and pH in raindrops at ground level for case (A) as a function of time after the start of a

rain event.

Reactive scavenging of pollutants by rain 1019

Figure 4(a) shows [SO,~ z] in rain at ground level for a number of g~nulations. For the base case [Case (A)], [SO,~ z] decreases in an expected fashion as the rain event progrmes. When FIFO2 is the only oxidant for S(IV) oxidation [case (B), init ial ps-phase O3 ffi 0.0], less SO~, z is formed and the [SO,~ 2] decreases very rapidly. This is a consequence of the fact that H202, the only oxidant present, has a high solubiLity and its concentration in both the gas and aqueous phases decreases rapidly. The oxidation of S(IV) is thus Limited by the availability of an oxidant. For case (C), it is assumed that the gas-phase H20, concentration is zero and thus 03 is the only oxidant present. Unlike H202, the O3 concentration in the aqueous phase quickly approaches equilibrium with the gas phase and thus can be replenished as soon as it is consumed in the aqueous-phase reactions. Thus [SO,; =] at ground level for case (C) remains essentially comtttnt. Curve (D) shows [SO~ 2] for the case of NH3(g) ffi 0.0. Absence of NH3 results in slightly more acidic raindrops and a reduced rate ofSO~ 3 formation (via oxidation by 03). The [NO~ ] in raindrops is a direct result of absorption of HNO3 by the drops and is not affected by the changes in concentrations of H~O2 and O~. Slight differences in the pH values resulting from changes in the H~O2, O~ or NH~ concentrations do not affect the solubility of HNO3 in any significant way. Thus, the

(a )

30.0 i

2 5 . 0

~20.0

.c 15.0

10.0

S.O o

0.0 0

A - Bess Case 8 - 03 Absent C - H202 Absent

,~ " ~ ' ~ O - NH 3 AbHnt

. . . . . : ~ . _ _ c _ . . . . . . . . .

I I ! I I

1 o 20 30 40 50 60 Time (rain)

(b) 5 . 0

4 . 8

~ 4 . 6

.£ 4 , 4

4 . 2

4.0 0

A - BHe Case B - 03 Absent C - H202 Absent D - NH 3 Absent

. . . . . . ...-_--_"_':.= 2c_ . . . .

. / " I I l I I

1 0 20 30 4o 5o 8 0 Time (rain)

Fig. 4(a). Sulfate in mindropl at ground level for cases (A~ (B) [03 ab~st], (C) [HzOa absent] and (D) [NH 3 absent]. (b). pH ofmindrol~ at ground level for cases (A),

(a), (C) and (D)~

[NO~] in raindropsd0es not change for cases (B), (C) and (D).

It is worthwhile to compare the rate of oxidation of S(IV) by 03 and H,O, in raindrops. This comparison has been considered (e.g. Schwartz, 1984) for situations where an equilibrium exist| between the gas-phase and aqueous-phase concentrations of SO2, HzOz and O~. However, in below-cloud scavenging, the absorption of H202 in raindrops is mass-transfer limited and an equilibrium is not likely to exist between gas. and aqueous-phase concentrations of H20~. A comparison between the oxidation rates of S(IV) by O3 and H202 can be made by assuming that Oa in raindrops is at equilibrium with the gas phase while the H202 concentration in raindrops increases linearly with distance below cloud-base according to the expression in Kumar (1985). Such a comparison, baaed on verti- cally integrated aqucons-phase concentrations, is given in Table 2. It is clear that in the ambient situation where O3 concentrations are typically greater than HzO2 concentrations by a factor of 20 or more, below- cloud oxidation of S(IV) by O3 is significant and may even be more important than oxidation by H~O 2 for initial raindrop pH values/> 4.7. Ofcourse, the rate of oxidation by 03 decreases sharply with decreasing pH while that by HzO2 remains roughly constant. Consequently, at pH values below 4.7, S(IV) oxidation by H202 is Likely to dominate.

Figure 4(b) shows the pH of raindrops at ground level for cases A-D. The pH curves are consistent with the [SO22] curves in Fig. 4(a) and the [NOel in raindrops. For case (B) (H202 is the only oxidant), pH rises steadily from 4.3 to 4.6.

4.2. Summer vs winter conditions:, effect of temperature

In a number of studies (Galloway and Likens, 1981; Dasch and Cadle, 1985), it has been observed that [SO22] in rainwater decreases significantly in winter while the change in [NOel is not as significant. Obviously, numerous factors other than temperature influence the composition of rain. However, it is important to understand the effect of temperature on the chemical composition of rain. To that end, one simulation is performed [case (E) in Figs 5(a) and Co)], in which all the conditions are kept the mine as in case (A) but the temperature is reduced to 5°C. The equilibrium constants, reaction rate constants, and mass-transfer coefficients are functions of temperature, and the appropriate values of these constants are

Table 2. Equivalence between ambient H20, and Os for below-cloud

oxidation of S(IV)

pH Equivalence

$.6 1 ppb H202 ! 1.1 ppb Os 5.3 I ppb H202 "4.3 ppb 03 5.0 I ppb H202 = 17 ppb 03 4.7 I ppb H202 s 68 ppb 03 4.4 1 ppb HzO 2 z 271 ppb O~

1020 (a)

3 6 . 0

~ 3 0 . 0

~ 20.0

18.0

~10.0

S.O

0.0 0

(b) 30.0

2S.O

f20 .O

i 15.0

10.0

5.0

0.0 0

4.6

4.4

!!! 4.0

0

SUDARSHAN KUMAR

- , , , "'...~ F - Winter Conditions

I I I I I 10 20 30 40 50 60

Time (rain)

A - Base Case E - S e i n e as A e x c e p t T : 5°C F - W i n t e r C o n d i t i o n s

I I I l I 10 20 30 40 50 60

Time (rain)

F - Winter Conditions

I l I I I 10 20 30 40 50 60

Time (rain)

Fig. $(a). Sulfate in raindrops at ground level for cases (A), (E) [seine as (A) except temp.- 5°C] and (F) (wintertime conditions). (b). Nitrate in raindrops at wound level for cases (A), (E) and (F). (c). pH of

raindrops at ground level for cases (A), (E) and (F).

simulation [case (F)], it is assumed that the gas-phase SO, concentration is 10 ppb [lower than 15 ppb of case (A)] and the H20=, 03, HNO3 and NH~ concentrations are 0.5, 25, 1.0 and 0.4 ppb, respectively ['compared to 2.5, 80, 2.0 and 1.5 ppb, respectively, for case (A)'I. The temperature for case (F) is assumed to be 5°C.

Sulfate concentrations in rain at ground level are shown for cases (A), (E) and (F) in Fig. 5(a). It is interesting to note that ['SO~ ='l is higher by 20-25 % when temperature is reduced from 25 to 5°C, and all other conditions are held constant ['case (E)]. This increase in ['SO~='I is directly attribulable to higher aqueous-phase concentrations of H202, 03 and S(IV) species because of the increased solubilities of the gases at lower temperatures. Although the rate constants for reactions producing SO~ = are lower at 5°C, the increased aqueous-phase concentrations are suf- ficiently higher to produce a net increase in ['SO~ :] in rainwater. The ['SO~='I in rain for wintertime conditions [case (F)'I is lower than [.SO~='I for summertime conditions by a factor of 3 even though the ambient SO= concentration has been lowered by only 33 ~. Clearly, in our simulation of wintertime conditions, SO72 formation is limited by the availability of the oxidants H202 and 03. Hydrogen peroxide is readily washed out from the atmosphere and its concentration in the aqueous phase decreases rather fast. The concentration of 03 in the aqueous phase is not sufficient for formation of large amounts of SO~ 2. The [NO~"I in rain at ground level for cases (A), (E) and (F) is shown in Fig. 5(b). Lowering the temperature from 25 to 5°C alone does not change the [ 'NOel because ['NO~" "1 in rain is mass-transfer limited and the mass-transfer coefficient is not very temperature sen- sitive. For the wintertime conditions of case (F), ['NO~'I is reduced in almost exactly the same propor- tion as the ambient concentration of HNO3. If the ambient concentration of HNO3 were unaltered from summer to winter, the ['NO3"] in rain would remain the same.

These simulations help explain, in part, the obser- vations of seasonal dependence of I'SO~='I and ['NO~ ] in rain. Figure 5(c) shows the ground-level rain pH for cases (A), (E)and (F). The pH curves are consistent with [SO7 =] and ['NO3"I in Figs 5(a) and (b).

used. Generally, the gas-phase oxidant concentrations are much smaller in winter months than in summer months. Formation "of O3 and H202 is driven by photochemical activity which is significantly lower in winter. In addition, the amount of H202 formed decreases with decreasing relative humidity (Calvert and Stockwell, 1983). Thus, much lower concentrations of 03 and H202 are expected in the winter compared to the hot and humid summertime conditions in the Northeastern United States. In addition, the gas-phase SO=, HNO3 and NH3 concentrations are also generally lower in winter. In the winter case

4.3. Effect of initial raindrop pH One simulation was performed ['case (G)] with an

initial raindrop pH of 4.0, all other conditions remaining the same as in case (A). The results of simulations (A) and (G) are compared in Fig. 6. Significantly less SO~" is formed in case ((3) because of the decreased solubility of SO, at lower pH values and the inverse ['H + ] dependence of the oxidation rate of S(IV) by 03. As pointed out before, the oxidation rate of S(IV) by H202 remains euentially independent of pH because of the acid-catalyzed nature of the oxidation reaction.


~2S.O

_ . . . . . . . . .

I S.O . . . . . . , . 2 " " ~ " "~ '

' ° ° I" ___(~)c._____"-'-'-.--..-::-, . . . . . 5.01 "'~"'~,- 0.0 , I l I I I

S.O0

4.75

4.50

4 . 2 5

i=

4.00

3.7§

0 10 20 30 40 60 SO Time (rain)

Fig. 6. Sulfate and pH in raindrops at ground level for cases (A) and (G) [tame as (A) except initial raindrop pH --- 4.0].

4.4. Effect of formaldehyde Formaldehyde is a ubiquitous component of urban

atmospheres and has been measured at levels ranging from a few ppb to tens of ppb (Altshuller, 1983). Ordinarily, the oxidation of S(IV) by H,O2 is fast and based on the kinetics of the system, H202 and S(IV) are not expected to coexist in clouds or rainwater. However, one potentially important step that needs to he considered is the absorption of HCHO in rainwater followed by reaction with S(IV) species to form an adduct. Formaldehyde (HCHO) is absorbed in water forming methylene glycol (CHt2(OH)2), the hydrate of HCHO. Formaldehyde is almost completely hydrated in aqueous solution, and its hydration has a half-life of less than 0.1 s at room temperature (Bell and Evans, 1966). The equilibrium relations can be written as

HCHO(g) ~ HCHO(aq)

HCHO(aq) ~ CH2 (OH)2. (I 3)

The effective solubility defined by H = [CH,(OH)2]/[HCHO(g)] is estimated to be 7 x 103 M a t m -1 at 25°C. In the aqueous phase, methylene glycol and I,ISO~ react to form an adduct called the hydroxymethane sulfonate (HMSA) ion.

CH2(OH)2 + HSO3 --* CH,OHSO~ + H20.

The forward and backward rate constants (k + and k_, respectively) for this equifibrium have been determined to be 3 M - l s - i and 4 × 1 0 - S s - I (Jacob and Hoffmann, 1983; Dusgupta et al., 1980). It has been suggested that in a cloud system, HSO~ may be bound in the adduct HMSA and thus make it unavailable for oxidation to SOl 2. For this reaction, it is relatively simple to calculate the time-constant T for approach to equilibrium. The inverse time-constant is given by

:-I = k+ [HSOf] +k+ [CH,(OH)2] +k_.

Thus, for typical aqueous-phase concentrations of I0 ~M HSO~ and 20/~M CI'12(OH)2, T = 120 rain. It is clear that in raindrops falling through the atmosphere, this reaction cannot approach equilibrium because of the short reaction time available. In a cloud environment, where the average life time of droplets is

about 30 rain, this reaction may play a more important role.

Table 3 shows a comparison of the concentrations of various aqueous-phase species in raindrops at ground level for cases (A)and (H). The conditions for cases (A) and (H) are exactly the same except for the presence of 15 ppb of gus-phase HCHO in case (H) at the start of the simulations. The calculations show that the concentrations of various S(IV) species and SOl 2 are almost exactly the same in these two cases. _BecJ__use of the short time available for reaction, a very small amount (0.2/~M) of HMSA is produced and a large amount of hydrated HCHO (methylene glycol) is present. The adduct formation would continue if longer reaction time were available. Thus, if a sample of rain collected at this time were to he stored, the HSO~ and CH2(OH)2 in the rainwater would react further and ultimately reach equilibrium levels. The HMSA concentration at equilibrium would he a few /~M.

4.5. Transition metal catalysis

Iron and manganese arc two of the most abundant transition metals in the atmosphere. Iron and manganese found in the atmosphere could be derived from the earth's crust and could also be emitted as a result of coal combustion. The oxidation of S(IV) is catalyzed by Fe(IlI) and Mn(II) and has been a subject of numerous investigations (Brimblecomhe and Spedding, 1974; Fuzzi, 1978; Martin, 1984). Hydrolysis of ferric ion results in the formation of various species including FeOH + 2 Fe(OH)~', Fe + 3, Fe2(OH), ÷ 4 and Fe(OH)~. Ferric salts become more soluble in water as the pH decreases. At high pH values, Fe(OH)a which is a difficultly soluble salt precipitates out. On the other hand, manganese salts are much more soluble and would exist primarily in the solution phase at concentrations typical of those found in rain. In the calculations, it is assumed that iron exists in the raindrops as soluble Fe(llI) and the total concentration of Fe(III), as well as Mn(II), in the raindrops stays at a fixed value as the drops fall through the atmosphere. Martin (1984) has reviewed the work on auto-oxidation of

Table 3. Comparison of the con~ntra- tiom ~M) of various aqueomt-phase ~pecies in rain for case* (A) and (H). All conditions in case (H) are the tame as in case (A) except for an additional 15 ppb of HCHO in the atmosphere at the start of the

rain event*

Case(A) Ca~(H)

HSO~ 3.381 3.366 SOl 2 3.663(- 3) 3.638(- 3) SO~(aq) 1.521(-2) 1.$17(-2) CH2(OH)2 - - 73.M HMSA - - 2.114(- !) SOl 2 22.70 22.67

*lpM ,= I/mlole t -I.

A~ 2 0 : $ - N

1022 SUDARSHAN KUMAR

S(IV) in the presence of Fe(IIl) and Mn(H) catalysts and recommends different rate equations depending upon the pH (< 4 or > 5) and total S(IV) concentration (< 1 or > 100#M). The region of S(IV) concentrations of 1-I00 pM and pH 4--5 has been termed the transition region and there is a great deal of uncertainty in the catalytic oxidation rates in this region. This also happens to he precisely the region of interest in the rain and cloud system. Since the rate equations for this region arc not available, the rate of oxidation used in these simulations is an arithmetic average of the rates predicted by the four rate expres- sions given in Martin (1984), Obviously, the catalytic rate of formation of SO~'2 in these simulations must he considered uncertain.

Figure 7(a) shows the [SO~ 2] in raindrops at ground level as a function oftime for three cases. Case (A) is the base case, while cases (1) and (J) include transition metal catalyzed oxidation of S(IV) as detailed in the figure caption. Figure 7(b) shows the pH in raindrops for these three cases. It is clear that S(IV) oxidation catalyzed by Fe(IIl) and Mn(II) is potentially a very important path for SO~ 2 formation. This system should he investigated further to understand clearly the reaction mechanism, presence of catalytic

(a) 80,0

~ 5 0 . 0

40.0

.£ 30.0

i 20.0

10.0

0.0 0

Co) 5.0

4.8

4.6

W .~ 4,4 ' i

~ 4.2

:Z 4.0

3.8

I A - Base Case [ ' • ease Case ", 0.4 . M Mn (ll)[

--~',~,~. J - Case I + 2.0 FM Fe (Ill} [

10 20 30 40 SO 6O Time (rain)

A - Base Case I - Base Case * 0.4 #M Mn (11)

J - Case I * 2.0 taM Fa (111)

A __

- - ' - " ' T " "

3.6 , I I I I I I 0 10 20 30 40 50 60

Time (rain)

Fig. 7(a). Sulfate in raindrops at ground level for ~ (A). (1) [same as (A) except that raindrops contain Mn(ll) at a concentration of 0.4 imloles/- 1 "] and (J) [same as (I) except that raindrops also contain Fe(lll) at a cone. of 2.0 pmoles/- ~ ]. Co). pH of raindrops at ground level for

cases (A), (I) and (J).

synergism between Fe(IlI) and Mn(II), and the pH dependence of the rate constants involved.

5. CONCLUDING ItEMAItKS

An Eulerian model for reactive scavenging of pollutants has been developed. The model considers the processes of pollutant absorption followed by chemical reactions within the drops as they fall to the ground. Simulations can be performed for any given vertical profile of initial gas.phase concentrations and can take into account time-varying raindrop composition at the cloud-base.

We have attempted to gain an understanding of the roles of various pollutant species in influencing the chemical composition of rain. The role of 03 in oxidizing S(IV) in raindrops can be as important as that o f H 2 0 2 for pH values ~ 4.7 because the ambient concentrations of O3 are generally much higher and its absorption in raindrops, unlike that of H202, is not mass-transfer limited. S(IV) oxidation catalyzed by transition metals Fe(lIl) and Mn(ll) is potentially very important. However, there are many uncertainties in the rates of oxidation, synergistic effects, and reaction mechanisms involving transition metals. More work is needed in this area to clearly understand the role of transition metal catalyzed oxidation of S(IV).

The effect of temperature on aqueous-phase S(IV) chemistry was also studied. The sulfate concentration in raindrops increases with a decrease in temperature when the initial gas-phase concentrations and all other conditions are kept the same. The nitrate concentration, on the other hand, is not affected significantly by a decrease in temperature. The decrease in sulfate concentration in winter rains is thus, most likely, due to the fact that S(IV) oxidation in winter is limited by the availability of oxidants. The formation of the S(IV)-HCHO adduct is a slow process and is not important for below-cloud reactions in the raindrops. However, for cloud droplets whose average life-time is approximately 30 rain, this reaction may play a more important role.

It is probably apparent that experimental ver/fi- cation of the results of simulations in this study is difficult. However, the model simulations do help us understand the roles of various pollutant species and relative importance of different chemical reactions considered in the rain scavenging of pollutants. The model can be easily modified to include any additional chemical reactions as the understanding of aqueous- phase chemistry increases. There are many assumptions in the model including the invariance of temperature and size distribution of raindrops with distance below cloud-base. In addition, the model neglects the dynamics of air motion and precipitation production during a rain event. It would be necessary to include these processes as well as the in-cloud processes in a model before the model simulation results can be compared with field experiments.


A c ~ s - - ' l ~ author wishes to ad~i~owledga the help of Jerry Ortmann and Peter Berzins in carrying out the computations.

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reactive scavenging of pollutants by rain: a modeling approach

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