Mathematical modeling of cloud chemistry in the Los Angeles basin

Atmospheric Environment Vol. 24A, No. 5, pp. 989 1006, 1990. Printed in Great Britain.

000~6981/90 $3.00+0.00 Pergamon Press plc

M A T H E M A T I C A L M O D E L I N G O F C L O U D C H E M I S T R Y IN T H E LOS ANGELES BASIN CHRISTIAN SEIGNEUR*

and ANTHONYM .

WEGRECKI

Bechtel Environmental, Inc., P.O. Box 3965, San Francisco, CA 94119, U.S.A. (First received 17 January 1989 and in final form 26 duly 1989)

Abstract--A mathematical model of cloud chemistry was evaluated with the cloud chemistry data collected by Richards et al. (1983, Atmospheric Environment 17, 911-914) from 1981 to 1985 in stratus clouds in the

Los Angeles Basin. The model simulates atmospheric chemistry including gas-phase chemistry, aqueousphase chemistry and droplet mass transfer, vertical transport, rainfall and turbulent diffusion. Evaluation of the model entailed two major parts. First, the equilibrium chemistry is evaluated with a total of 52 case studies. Then, the model with treatment of cloud chemistry, vertical transport and diffusion is evaluated with two case studies. The results of the model simulations show the importance of vertical transport in determining the chemical composition of stratiform clouds. The sensitivity of sulfate, nitrate, ammonium and hydrogen ion concentrations to precursor levels,various chemical kinetic and cloud microphysical parameters and various environmental conditions is discussed. Key word index: Sulfate, nitrate, cloud chemistry, mathematical modeling, Los Angeles.

1. I N T R O D U C T I O N

The formation of sulfate (SO 2 - ) and nitrate (NO3) species in the Los Angeles Basin is a topic of great importance in air quality because these species lead to increased aerosol concentrations, visibility degradation and acid deposition. Several field programs were conducted from 1981 to 1985 to characterize the reactants, products, kinetics and mechanisms of stratus cloud chemistry in the Los Angeles Basin (Richards, 1990). The experimental results obtained during these field programs are very comprehensive and constitute a unique data base for a detailed investigation of the chemistry of stratus clouds in the Los Angeles Basin. Some topics of particular interest for our understanding of cloud chemistry in the Los Angeles Basin include the following: (i) Evaluation of the equilibrium chemistry and kinetics of SO 2- and N O 3 formation in clouds. (ii) Identification of the most important chemical pathways leading to SO~- and NO 3 formation. (iii) Investigation of the relationships between precursors and acid species concentrations, (iv) Analysis of the sensitivity of cloud chemistry to various meteorological and chemical parameters.

using some of the early data of Richards (1990) as input to a detailed chemical kinetic mechanism of cloud chemistry. However, the most recent data of Richards (1990) provide a more complete data base which can be used to perform a more comprehensive evaluation of a cloud chemistry model. In particular, the data collected in 1985 provide unique information regarding the evolution of an air parcel in a stratus cloud for time periods of up to 3 h. These data also include measurements of both gas and aqueous-phase concentrations of formaldehyde and acetaldehyde. A comprehensive computerized mathematical model of cloud chemistry and physics was used to investigate the chemical and physical processes that govern the formation of acidic species in clouds. First, the performance of the model treatment of equilibrium chemistry is evaluated. Then, the model is used to investigate the chemical pathways and transport processes that lead to acid formation in clouds and to study the sensitivity of the acid concentrations to various chemical and meteorological parameters.

2. DESCRIPTION OF THE C L O U D M O D E L

These topics have been addressed to some extent by Seigneur and Saxena (1984) and Seigneur et al. (1985) *Present address: ENSR Consulting and Engineering, 1320 Harbor Bay Parkway, Alameda, CA 94501, U.S.A. 989

The mathematical model used in this study provides a detailed treatment of the gas-phase and aqueousphase atmospheric chemistry and some treatment of the basic cloud transport processes. The transport processes which are treated in the cloud model include vertical transport of pollutants due to the cloud updraft, vertical and horizontal turbulent diffusion, and rainfall through the cloud and the mixing layer. This model is an updated version of the model of Seigneur and Saxena (1988). In addition, a cloud

990

CHRISTIAN SEIGNEURand

microphysics model was used to calculate a consistent set of meteorological input data to the cloud model. This section presents a description of the major features of the model.

2.1. Generaldescription The cloud model represents the physical and chemical processes that take place in a column of air extending from ground level to the top of the cloud layer. This column of air is advected with the mean wind flow. This Lagrangian model is depicted in Fig. 1. The concentrations of chemical species are governed within each cell by the following partial differential and algebraic equations. ~Ci(z, t)

- V, aCi(z, t) aCi(z, t) ~z + v.~ 6 ( w )

~-----~=

K=~

+ R~(z,t)

Ci(z, t) = El(Z, t) where

Ct(z,t) = concentration of species i z t V. Vd ~5(w)

= altitude above ground level = time = updraft velocity = raindrop fall velocity = Kronecker index, equal to 0 for gaseous species and to 1 for aqueous species K= = vertical eddy-diffusion coefficient Ri(z, t)= reaction rate of species i Ei(z,t)=gas/droplet and/or aqueous equilibrium of species i.

ANTHONY

M. WEGRECKI

The updraft and raindrop velocities are calculated by means of a cloud microphysics model. The vertical eddy-diffusion coefficient is selected according to the vertical temperature profile (atmospheric stability). The reaction rate and chemical equilibrium are calculated by the chemical kinetic and equilibrium equations. 2.2.

Cloud microphysics

The treatment of liquid water microphysics follows the formulation of Kessler (1969). Because temperatures observed in Los Angeles stratus clouds were above freezing, it was not necessary to include treatment of ice particles. The microphysical processes that govern the water mixing ratios include condensation, evaporation, autoconversion of cloud droplets to rain drops and collection of cloud droplets by raindrops. In addition, vertical transport by updraft and precipitation affects the water mixing ratios in each layer. The fall velocities of rain drops are calculated according to the formulation of Wobus et al. (1971). The cloud microphysical processes are summarized in Fig. 2. The governing equations are presented in Appendix A. It may be noted that if the distribution of water between its various phases (i.e. vapor, cloud droplets and rain drops) is known, it is then possible to apply the cloud microphysics model to the determination of one of the input data such as the updraft velocity. This mode of application is particularly useful because measurements of liquid water content, precipitation and relative humidity (r.h.) are generally available more readily than updraft velocities. The concentration of chemical species was assumed to be the same for cloud water and rain water for a given time and height.

cloud top

/

-

~

1

aircraft measurements~

meanwind rain

Cloudbase

I

t

t

diffusion

updraft oround

level time

= tt

time - t2

Fig. 1. Schematic description of the Lagrangian cloud model and its evaluation with cloud data.

Mathematical modeling of cloud chemistry

Evaporation

L w

Condensation

Cloud

Water

991

3. PREPARATION OF'THE MODEL INPUT DATA

Water Vapor

Autoconverslon Collection

LEvaporstion

F

JvI

Rain

Water

I

Precipitation

Fig. 2. Schematic description of the cloud microphysical processes.

2.3. Chemical kinetic mechanism The chemical kinetic mechanism consists of three major components: (i) a gas-phase chemical kinetic mechanism, (ii) a gas~troplet mass transfer component and (iii) an aqueous-phase chemical kinetic mechanism. The gas-phase chemistry is simulated according to the Carbon-Bond Mechanism IV (CBM-IV) (Whitten and Gery, 1986). A reaction was added to treat the oxidation of SO2 by OH radicals to form H2SO4 and HO2 radicals. The gas-phase homogeneous hydrolysis of N205 was updated according to the kinetics reported by Sverdrup et al. (1987). The gasphase chemical kinetic mechanism consists of a set of 71 reactions among 30 chemical species and is presented in Appendix B. The treatment of gas-droplet mass transfer is described by Seigneur and Saxena (1988). It includes Henry's law equilibrium at the gas-droplet interface for all species and gas-phase diffusion and droplet diffusion for radicals. Diffusion processes are assumed not to be rate limiting for molecular species. The droplets are assumed to be well mixed. The aqueous-phase chemical kinetic mechanism is described by Seigneur and Saxena (1988). It consists in a set of 18 gas~lroplet equilibria, 13 ionic equilibria, two hydration equilibria and 30 chemical reactions. This mechanism treats the aqueous formation of SO 2- and NO3 as well as radical chemistry. This aqueous-phase mechanism was updated to reflect recent kinetic and mechanistic results on the aqueous chemistry of SO 2- and N O 3 formation. The kinetics reported by Huie and Neta (1987) was used for the oxidation of S(IV) by OH radicals. The mechanisms of Martin and Hill (1987a, b) were selected to represent the oxidation of S(IV) by 0 2 when catalyzed by Fe and Mn. In addition, chemical equilibria for acetaldehyde were added. These changes in the mechanism of Seigneur and Saxena (1988) are presented in Appendix C.

The data collected by Richards (1990) constitute a very comprehensive set for the evaluation of a cloud model. In particular, the data collected in the 1985 field program are very complete as gas-phase hydrocarbons were also measured during this program. All gas-phase concentrations were available in the clouds except H202, NH 3 and H N O 3. The latter two species, NH 3 and HNO3, are primarily in solution and their gas-phase concentrations can be neglected. The value of the gas-phase concentration of H202 needed to be calculated from the measured aqueousphase concentration according to Henry's Law. The concentration of PAN was always below the detection limit of 0.5 ppb. Concentrations of SO2, NO, NO2 and 03 which were monitored continuously, were also available below cloud base. Air samples were collected in canisters and analyzed for C 1 Clo paraffins, olefins and aromatics. Formaldehyde and acetaldehyde were collected both in the gas phase and in the aqueous phase. Aqueous-phase concentrations of nearly all solutes of interest were measured. No aqueous organic species concentrations were determined except formaldehyde and acetaldehyde concentrations. Species of potential interest which were not measured consist of hydroxymethane sulfonic acid (HMSA), and organic acids (formic and acetic acids). Uncertainties in the aqueous-phase concentrations were estimated to be about 5-10 per cent (Richards, 1990). The total S(IV) concentration was measured, however, it includes both dissolved SO 2 (i.e. H2SO3, HSO 3 and SO 2-) and S O 2 complexed as HMSA. Aerosols were measured in the clouds and their sampled chemical composition includes SO 2- , NO 3 and N H 2 . However, these aerosols represent all suspended droplets less than about 2 to 3 #m in diameter as selected by a cyclone inlet. For the purpose of the modeling, it was assumed that SO2,- , NO 3 and NH,~ were primarily present in the droplets sampled with the cloud water collector which selected droplets larger than about 3/~m in diameter. It should be noted that data on SO 2 - , NO 3, and N H 2 were not available below the cloud. Meteorological data needed for the model include the liquid water content as function of height, mean droplet radius, temperature, pressure and relative humidity vertical profiles, atmospheric stability, the updraft velocity and the rainfall rate. All these data were available from Richards (1990) except the atmospheric stability, updraft velocity and the rainfall rate. The atmospheric stability was estimated from the vertical temperature profile. It should be noted that the liquid water content, updraft velocity and rainfall rate are related by the equations of the cloud microphysics model. Therefore, one is allowed one unknown variable among the cloud physics variables. If the liquid water content and rainfall rate are known, it is then possible to estimate the updraft velocity. The

992

CHRISTIAN SEIGNEURand ANTHONYM. WEGRECKI

liquid water contents were obtained from the King probe when available or from the forward scattering spectrometer probe (FSSP) otherwise. Temperature and dew point temperatures were measured by the aircraft and were also available from radiosondes on certain days. Then, the updraft velocity was calculated by the cloud microphysics model as described in Appendix A. 4. EQUILIBRIUM CHEMISTRY

Equilibrium chemistry consists of gas-phase/ aqueous-phase equilibria and aqueous-phase ionic and hydration equilibria. Clearly, it is essential that these equilibria be properly treated in a model because they determine the aqueous-phase concentrations of the chemical species at a given time and govern the rates of aqueous-phase chemical kinetics. The input data to the equilibrium chemistry model consist of the total (i.e. gas and liquid) concentrations of the chemical species, the liquid water content and the temperature. The model, then, calculates the gasphase and liquid-phase concentrations of the various chemical species. The liquid-phase concentrations of the ionic species must satisfy electroneutrality and the pH is calculated according to the electroneutrality condition. This electroneutrality condition requires solving all gas-phase/aqueous-phase equilibria and aqueous-phase ionic and hydration equilibria by iteration until the concentrations of cations and anions become equal. An overall evaluation of the equilibrium chemistry is performed by comparing the measured and calculated pH values. If the calculated and measured pH values are in close agreement, it may be assumed that the model treats correctly the equilibrium chemistry. If there is a discrepancy between the calculated and measured pH values, there are two possible explanations: (i) The model fails to treat one or more equilibria correctly which leads to erroneous concentrations of some ions. (ii) The experimental data are incomplete or inaccurate and do not provide an adequate input data set for the model calculations. More specific evaluation of equilibrium chemistry can he performed when concentrations of several species involved in an equilibrium are available. This is the case for example when both gas-phase and aqueousphase concentrations of a species are available. We present and discuss in this section the results of the model performance evaluation for equilibrium chemistry. We first present the comparison of measured and calculated pH values. Then, we analyze the equilibrium chemistry of S(IV) and aldehydes for which both gas-phase and aqueous-phase concentrations are available. 4.1. Cloud droplet pH The cloud droplet pH was calculated for a total of 52 cases, including 10 cases from the 1981 data, I1

cases from the 1982 data, eight cases from the 1984 data, and 23 cases from the 1985 data. Cases for which data on anion and cation concentrations were significantly incomplete were not considered. Measurements of S(IV) in the aqueous phase did not differentiate between dissolved SO2, i.e. H2SO3, HSO 3 and SO~and SO2 complexed with HCHO as hydroxymethane sulfonic acid (HMSA). Therefore, we performed two types of simulations. In the first type of simulation, we assumed that no HMSA was present and that measured S(IV) corresponded solely to H2SO3, HSO 3 and SO 2-. (Note that in this case, the measured S(IV) concentrations may not verify Henry's Law equilibrium between gasphase SO2 and aqueous S(IV).) In the second type of simulation, we assumed that H2SO3, HSO3 and SO~- were in equilibrium with the measured SO2 gasphase concentration and that the remaining measured S(IV) concentration corresponded to HMSA. The normalized bias and absolute error in the H + concentrations are presented in Table 1 for each year of data. Overall, there is a bias toward the underprediction of the H ÷ concentration. The 1981 data set with HMSA and the 1984 data set are the only ones that show a trend toward overprediction of the H ÷ concentration. Among the 52 cases considered, the H + concentration is underpredicted 32 times and overpredicted 20 times. The calculated H + concentration is within a factor of 1.5 of the measured value 45 times out of 52; it is within a factor of two, 49 times out of 52. ' The largest discrepancies occur for case two (23-11-81) , where the H + concentration is underpredicted by 70%, case 14 (22-5-82) where it is underpredicted by 84% and case 52 (10-6-85) where it is overpredicted by 154%. If case 52 is discarded as an outlier from the 1985 data set, there is a clear trend toward underpredicting the H ÷ concentration in this data set by about 9%. The use of HMSA in the equilibrium calculations for the 1981 and 1982 data leads to higher H ÷ concentrations (i.e. lower pH values) because the anion concentration is higher. (If no HMSA is assumed, a large fraction of the input HSO3 concentration is redistributed into the gas phase.) Consequently, the bias shows less underprediction (or more overprediction) of the H + concentration. Overall, however, the absolute error is not affected by the assumption made for S(IV). It should be noted that only the cases where the measured S(IV) concentration constitutes a significant amount of the measured anion concentration show sensitivity to the HMSA assumption. There are about only eight such cases (Cases 3, 4, 5, 6, 9, 10, 13 and 14). 4.2. Equilibrium chemistry of S(IV) The concentrations of S(IV) were highest in 1981 and 1982. The use of gas in power plants the following years led to small S(IV) concentrations. According to our chemical kinetic mechanism, S(IV) may be present in the aqueous phase as dissolved SO2, i.e. H2SO3,

Mathematical modeling of cloud chemistry

993

Table 1. Normalized bias and absolute error in H ÷ concentrations*

Data set

Normalized absolute Normalized bias(%)t error (%)J;

1981 1982 1984 1985 1985 (without case 52) All data

Number of samples

- 3 (+4) -9 (-2) +5 -2 -9

27 (31) 33 (29) 5 17 10

10 11 8 23 22

- 3 (0.2)

20 (20)

52

*The first value corresponds to simulations where no HMSA was assumed to be present; the value in parentheses corresponds to simulations where HMSA was assumed to be present. tThe normalized bias is defined as 1

N

i~ "-' [( [H ÷ ]i,c - [H + ]i, m)/(H +)i, m] where N is the number of data pairs, and subscripts c and m refer to calculated and measured values, respectively. :~The normalized absolute error is defined as 1

N

~ (I [n+],.c - [ H +]i,,I/[H +]i,,). 1~ i= 1

Table 2. Comparison of measured and calculated S(IV} concentrations Case Number 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 19 20 21

Date

Tape/pass

Measured pH

Measured S(IV) concentration ( , u M )

23/11/81 23/11/81 23/11/81 24/11/81 24/1.1/81 24/11/81 24/11/81 20/05/82 21/05/82 21/05/82 22/05/82 22/05/82 22/05/82 22/05/82 23/05/82 23/05/82 23/05/82 23/05/82

296/2 296/4 296/5 296/6 296/7 297/3 297/5 301/2 302/1 302/3 302/5 302/7 302/9 302/11 303]5 ~ 303/7 303/8 303/9

3.36 3.80 3.05 2.98 3.02 3.72 3.67 2.99 2.40 2.72 3.39 2.56 2.65 2.69 3.05 3.38 3.33 3.59

41 21 89 129 89 30 27 11 52 182 365 29 33 51 18 5 10 10

Calculated HSO 3 concentration (#M)* 0.061/0 0.027/0 0.007/0.006 0.380/0.342 0.197/0.182 0.047/0.039 0.003/0 0.098/0.095 0.062/0.061 0.536/0.497 23.8/50.99 0.045/0.044 0.035/0.034 0.122/0.117 0.001/0 0.004/0 0.010/0 0.024/0

* The first concentration represents the calculation assuming no HMSA, the second concentration represents the calculation assuming HMSA formation. The difference in the HSO~ concentration results from the difference in pH. Concentrations of H2SO3 and SO~- are negligible compared to the HSO3 concentration.

H S O ~ or S O ~ - or as a complex formed by reaction with H C H O . This complex, hydroxymethane sulfonic acid (HMSA), is formed by reaction of H C H O with H S O ~ . Its decomposition is a function of p H and occurs more slowly than its formation; at low pH, H M S A may, therefore, act as a reservoir of S(IV) in solution. At the p H values observed in the Los Angeles stratus clouds, dissolved SO2 is primarily in the form of H S O 3 . Therefore, S(IV) is present as H S O 3 or HMSA. The experimental data do not differentiate between H S O ~ or H M S A because S(IV) in solution is stabil-

ized by reaction with H C H O before analysis. Because the decomposition rate of H M S A is slow compared to its formation rate, H M S A cannot be assumed to be in equilibrium with H S O 3 and H C H O and the formation and decomposition reactions must be treated explicitly in the mechanism. Therefore, the presence of H M S A cannot be calculated by the equilibrium chemistry but must be assumed as an input. A comparison of measured and calculated S(IV) concentrations for the 18 cases for which S(IV) concentrations were measured is presented in Table 2. Cases from the 1985 field program were not included

994

CHRISTIAN SEIGNEURand ANTHONYM. WEGRECKI

because the measured S O 2 concentrations were < 1 ppb and were, therefore, zero within the measurement uncertainty. The calculated values represent HSO3 concentrations that were calculated from the equilibrium with the gas-phase SO2 concentrations. It appears clearly that the calculated HSO~ concentrations are consistently less than the measured S(IV) concentrations. On the average, the calculated HSO~ concentrations are less than the measured HSO~ concentrations by factors of 3500 and 2200 for the 1981 and 1982 data, respectively. As high concentrations of SO2(g) and H C H O are present in many of the 1981 and 1982 cases, it appears reasonable to assume that HMSA was formed and acted as a reservoir of S(IV) in solution because of its low decomposition rate. A possible scenario for the chemistry of S(IV) is as follows. Sulfur dioxide is emitted from a large source. The SO2 plume mixes into stratus clouds where SO2 reacts rapidly in cloud droplets with H 2 0 2 to form SO 2- and with H C H O to form HMSA. The SO2 concentration is then rapidly depleted through reaction with H202 and H C H O as well as through atmospheric dispersion. As the SO2 concentration decreases, HMSA starts to decompose back into its precursors HSO~ and HCHO; however, this rate is slow at the low pH values observed in the Los Angeles clouds and S(IV) is, therefore, trapped in the form of HMSA. Concentrations of H202(aq) exceed S(IV) but, because most S(IV) is, then, present as HMSA, no further reaction of H202 (aq) with S(IV) takes place in significant amount. This scenario was used by Richards et al. (1983) to explain their 1981 and 1982 data. The results of our equilibrium chemistry calculations are consistent with this hypothesis. This scenario will be simulated through a kinetic simulation as one of the sensitivity studies to confirm the hypothesis advanced here. 4.3. Equilibrium chemistry of aldehydes Measurements of formaldehyde and acetaldehyde were performed in both the interstitial gas phase and in the cloud droplet aqueous phase during the 1985

field programs. These measurements allow us to test the treatment of the equilibrium chemistry of aldehydes in the model. A comparison of measured and calculated aldehyde concentrations in the aqueous phase is presented in Table 3. The calculated concentrations were obtained by calculating the gas-phase/aqueous-phase equilibrium and hydration equilibrium using the total (gasphase and aqueous-phase) concentration as input to the model. It appears that the agreement is reasonably good for HCHO. The calculated aqueous HCHO concentration is consistently higher than the measured value. The calculated value ranges from 1.03 to 2.13 times the measured value with an average bias of 60% toward overprediction. Formaldehyde is primarily present (about 99.98%) in its hydrated form H2C(OH) 2. The comparison of measured and calculated acetaldehyde aqueous concentrations shows a large discrepancy. The calculated values are factors of 10 to 500 smaller than the measured values, with an average discrepancy of a factor of 40. This discrepancy could be due to measurement uncertainty or an improper treatment of chemical processes in the model. The same analytical measurement technique was used for the aldehyde collected in the gas phase and in the aqueous phase. Also, the same technique was used for both formaldehyde and acetaldehyde. The technique is aldehyde specific (i.e. no interference with other organic compounds appears likely) and the identification of the aldehydes through the gas chromatograph allows us to identify the various aldehydes (Grosjean, private communication, 1987). In addition, it should be noted that gas-phase aldehyde concentrations were near or below the detection limit. Therefore, the discrepancy between measured and calculated values could be larger if a lower detection limit was used. Therefore, it seems that the treatment of acetaldehyde equilibrium chemistry in the model is incorrect. The Henry's Law constant has been estimated by different groups and the various values are in close agreement. Betterton and Hoffmann (1988) reported an effective Henry's Law constant for acetaldehyde of 11.4 M atm-1 at 25°C. This value is commensurate

Table 3. Comparison of measured and calculated aldehyde concentrations Formaldehyde aqueous concentration (/,M)

Acetaldehyde aqueous concentration (/~M)

Tape/pass

Measured

Calculated

Measured

Calculated

434/3 434/4 435/2 435/3 435/4 436/2 436/3 436/4 440/3 440/4

21.9 31.0 38.2 53.6 42.3 37.7 41.7 46.4 24.8 33.6

29.4 31.9 81.5 84.2 84.6 62.5 66.2 67.2 48.1 47.5

5.2 4.0 5.8 4.7 4.2 5.2 7.4 6.7 3.9 7.5

0.058 0.052 0.302 0.43 0.30 0.023 0.023 0.025 0.009 0.012

Case Date 25/05/85 25/05/85 26/05/85 26/05/85 26/05/85 27/05/85 27/05/85 27/05/85 10/06/85 10/06/85

Mathematical modeling of cloud chemistry with the effective Henry's Law constant of 28.6 M a t m - ' which was used in our simulations. There is, therefore, some question remaining on the difference between the atmospheric measurements reported by Richards (1990) and the laboratory measurements of acetaldehyde solubility.

5. CHEMICALKINETICSAND TRANSPORT Richards (1990) suggested that vertical transport was important, based on the variation of inert species concentrations such as Pb and NH2. Therefore, it is necessary to consider vertical transport if one wants to provide a realistic description of the evolution of cloud species concentration. In this section, we present the results of two simulations conducted with cloud chemistry and vertical transport. The formulation and application of the model were depicted in Fig. 1. Richards (1990) collected cloud chemistry data in air parcels over periods of time ranging from 1½to 3 h. These data are, therefore, suitable for performance evaluation of the cloud chemistry model. Two case studies were selected to analyse the cloud chemistry and vertical transport processes. These two case studies are those of 25 and 26 May 1985. If one considers the NO3 and SO~- concentrations normalized with respect to chemically inert ion concentrations, there were some significant increases in NO3 concentrations with time on both of these days; on 26 May there was also a clear trend toward increasing SO~- concentrations. The flight of 25 May 1985 represents an air parcel trajectory that starts offshore at 0100 PST and moves inland over Long Beach and Los Angeles. The total period of simulation is 88 min. The flight of 26 May 1985 represents an air parcel trajectory that starts above Pomona at 0034 PST and moves eastward toward Ontario. The total period of simulation is 120 min. 5.1. Input data The input data for these simulations were prepared as follows. In the cloud layer, input data were similar to those described previously. Temperature, r.h. and liquid water content vertical profiles were available from the aircraft spirals and missed instrument land-

995

ing approaches. Aircraft data also provided concentrations of NO, NO2, 03 and SO2. No vertical profile data were available for HCs, aerosols, HNO3, NH3 and H202. No direct data were available on vertical transport variables such as updraft velocity and vertical diffusion coefficient. Concentrations of HCs were assumed to be proportional to NOx concentrations because automobiles are a major common source of these compounds. Concentrations of primary aerosols (Na, K, Mg, Ca, Fe, Mn and Pb) were assumed to be constant with height because these species are unreactive and no information on their vertical profile was available. The concentration of H202 was also assumed to be constant with height; the below-cloud H20 2 should be unreactive and its concentration should not therefore be less than the cloud H202 concentration. Concentrations of SO 2-, NO 3 (HNO 3 and aerosol NO~ ) and NH,~/NH 3 below the clouds were estimated as follows. For 25 May 1985, 24-h average concentrations of SO~- and NO~ PM-10 aerosols were available (ARB, 1987). These concentrations were assumed to be twice as much for 26 May 1985 because the measured aerosol scattering coefficient was about twice as much on 26 as on 25 May. The night-time concentrations of SO 2- and NO3 were estimated based on diurnal profiles reported by Grosjean (1988) for NO 3 aerosol and by John et al. (1985) for SO 2- aerosol. The HNO 3 and NH 3 concentrations were estimated based on the data of Russell and Cass (1984). The NH~ aerosol concentrations were estimated based on the thermodynamic analysis of Pilinis and Seinfeld (1987) for Na + and NH~ salts of SO 2- and NO 3 aerosols. The CI- aerosol concentration was calculated to provide electroneutrality between SO 2- , NO3, NH~, Na + , Mg 2+ , Ca 2+ , K ÷ , Pb, Fe and Mn. Concentrations of major species below and in the cloud at the beginning of the model simulations are presented in Table 4. The vertical resolution of the initial concentration was limited by the availability of data below the cloud (layers one and two) and in the cloud (layers three, four and five). Clearly, the vertical resolution consists of the five layers presented in Fig. 1 as the simulation proceeds. The vertical profile of the liquid water content was available from the aircraft forward scattering spectro-

Table 4. Initial concentrations of major chemicalspecies below and in the cloud Species

Simulation of 25 May 1985

Simulation of 26 May 1985

(ppb)

B e l o w - c l o u d In-cloud

Below-cloud

NO NO 2 03 SO 2

SO~NO~ NH2

0.0 12.0 68.0 0.0 1.3 1.9 5.7

0.0 1.1 80.0 0.2 3.8 7.4 2.6

0.0 8.0 45.0 1.0 2.6 3.8 12.0

In-cloud 0.0 7.1 57.7 0.9 4.1 15.8 8.7

996

CHRISTIAN SEIGNEUR and

seopic probe (FSSP). However, the King probe data were assumed to be more reliable and were used where available in the cloud layer. Consequently, the FSSP data were used to obtain the liquid water contents as a function of height but were scaled to match the available King probe data. Vertical profiles of temperature, pressure and water mixing ratio are presented in Figs 3 and 4 for the 25 and 26 May 1985 simulations, respectively. The vertical diffusion coefficient was assumed to be constant with height with a value of 20 m 2 s - z, a typical value for stratus clouds (Qin and Chameides, 1986). The updraft velocity was not measured; it is, however, a critical parameter because it defines the rate of upward transport of pollutants from below the cloud into the cloud. The updraft velocity was estimated by means of the cloud microphysics model. The inputs to this cloud microphysics model are the updraft velocity, the vertical temperature and pressure profiles, and the r.h. below the cloud. The outputs of the model include the liquid water content of the cloud and precipitation rate. The cloud model was used with a variety of updraft velocities to determine which updraft velocity led to a cloud water content and a precipitation rate that corresponded to the observations. Updraft velocities of 0.065 and 0.077 m s - t

ANTHONY M. WEGRECKI

were selected in this manner for the 25 and 26 May 1985 simulations, respectively. No precipitation occurred on 25 May 1985 but a light drizzle occurred on 26 May 1985 (0.0075 mm h- 1 in the model simulation). We assumed that species present in coarse aerosols such as Na, K, Ca, Mg, Fe, Mn, Pb and C1 were totally present in the droplet phase; i.e. the scavenging efficiency of the rain was 1. For SO 2 - , NO3 and NH2 aerosols which are present mostly in the sub-pm range, we assumed that the scavenging efficiency of rain drops was 0.1. This assumption is based on the fact that sub-/~m aerosols are not scavenged efficiently by rain drops (e.g. Seigneur and Barnes, 1986). 5.2. Simulation of 25 May 1985 The results of the simulation of 25 May 1985 are presented in Table 5 for the concentrations of major species. It appears that calculated concentrations of SO2, - and NO3 decrease steadily because concentrations of these species are lower below cloud than in the cloud at the initial time, and chemical formation of these species is not sufficient to compensate for the decrease in concentration due to vertical transport. The measured SO 2- concentration first increases, then decreases below its initial value. The measured

1200" 1100" SO0

1000.

700

900" S00'

600

Height (m)

Height (m) soo

700" 600' SO0"

400

400" S00

3O0" 200"

200 100

"

"

0.99

0.0

0.91

0,92

0,93

0.94

0,95

1

0.99 0.97

0.9s

I

100 0.86

~ :

0.99

O.S8

0.9

Pressure (AtmOspheres)

ooOO°°° ..........i 600 '

.e- t - 60

Hei0ht (m) so0. 400

0.99

0.0g

1

1100, 1000" 900. 000.

Height (m)

rain

0.94

1200,

min

~ - 1 • lO4

0.92

Pressure (Atmospheres)

700.

•a - t .

154

so0.

'

94 rain

go0.

rain

400. 300

300.

20O

200. 100

100

10

10 10,5 11 11.5 12 13.5 13 13.5 14 14.5

11

12

13

14

15

Temperature (Degrees Celsius)

Temperature (Degrees Celsius) 1200,

.... oo go

.........

600'

.t-

t . 60

Height (m) s0o,

.o-

I . 104 rain

400 '

Height

(m)

800 700 900

-e- t - 34 t = 94

500

300 '

t = 154

400 300

200. lOO. -

1000 000

i min

: 2

:

i

i

i

i

4

6

8

10

12

Liquid Water Content (Kg/Kg x 10 "=)

Fig. 3. Vertical profiles of temperature, pressure and water mixing ratio on 25 May 1985.

rain

rain min

I

2O0 t 0 0 I' O

I

2

I

4

I

6

I

9

110

112

Liquid Water Content (Kg/KG x 1 0 4 )

Fig. 4. Vertical profiles of temperature, pressure and water mixing ratio on 26 May 1985.

Mathematical modeling of cloud chemistry Table 5. Comparison of measured and calculated cloud concentrations of major chemical species. Simulation of 25 May 1985 Simulation time (min)

SO42 (ppb) Measured Calculated NO3(ppb) Measured Calculated NH,~ (ppb) Measured Calculated pH Measured Calculated NOa(ppb) Measured Calculated O3(ppb) Measured Calculated

0

44

88

3.76 3.76

5.15 3.34

3.01 2.55

7.37 7.37

11.70 6.36

11.20 5.92

2.64 2.64

4.82 3.35

4.63 4.24

3.26 3.31

3.33 3.60

3.36 3.74

1.1 1.1

9.2 3.2

10.4 5.2

80.4 80.4

61.6 77.0

66.0 72.2

997

showed that 0 3 concentrations are not significantly affected by cloud chemistry. Therefore, the variations observed by Richards (1990) in 0 3 concentrations inside and outside of clouds must correspond to the sampling of different air parcels. Sampling outside of clouds may have corresponded to air entrained from aloft where 0 3 concentrations were typically higher. The comparison of measured and calculated concentrations with transport and chemistry shows some discrepancies which suggest that (1) emissions from tall stacks into elevated cloud layers may contribute significantly to NOx concentrations in coastal clouds and (2) the below-cloud concentrations of SO42- and NO3 may not have been estimated accurately and actual measurements would be necessary for further model evaluation. The major pathways for NO3 formation include the aqueous reduction of NO 3 radicals (59% in the cloud layer) and the heterogeneous hydrolysis of N 2 0 5 (38%). The major pathways for SO~ formation include the aqueous oxidation of SO2 by H 2 0 2 (95%), by 02(3%) and by OH radicals (2%). 5.3. Simulation of 26 May 1985

NO 3 concentration shows a significant increase after 44 min, then, remains about constant for the next 44 min. This increase cannot be explained with our present knowledge of NO 3 chemistry and is not consistent with the lower below-cloud concentrations assumed for this simulation. The calculated and measured NH,~ concentrations are in reasonable agreement with an increase that results from the entrainment of higher NH~ concentrations from below the cloud into the cloud. The measured pH shows a slight increase whereas the calculated pH shows a more significant increase due to the decrease in SO42 and NO 3 concentrations. The concentration of NO 2 increases in both the simulation and the measurements. However, the increase is significantly less in the simulation than in the measurements. This result suggests that the actual NOx concentrations transported into the cloud were greater than in the simulation. Emissions of NO x from tall stacks located along the coast were not considered in our simulation and may be the cause of the discrepancy between measured and calculated NOx concentrations. The 03 concentration follows a pattern related to that of NO2. Concentrations of NO2 inland are much higher than offshore due to NO and NO2 emissions from automobiles and other sources; conversely, 03 concentrations are lower inland due to reaction with NO emissions. Therefore, 03 concentrations are lower below-cloud than in-cloud and 0 3 concentrations decrease in the cloud as the updraft entrains lower 0 3 concentrations into the cloud. Richards (1990) reported that 0 3 concentrations along a flight orbit were higher outside of clouds than inside clouds. Seigneur and Saxena (1985) simulated the effect of clouds on 03 chemistry and their results

The results of the simulation of 26 May 1985 are presented in Table 6 for the concentrations of major species.There is good agreement between the measured and calculated SO42- concentrations with a slight decrease over the 2-h period. The NO 3 concentrations also show a decrease over the 2-h period although the decrease is larger in the calculated concentrations than in the measured concentrations. The largest discrepancy between measured and calculated concentrations appears for the NH~ concentrations. The simulation shows first an increase due to the entrainment of higher concentrations from below the cloud, then a decrease due to the rainout of Table 6. Comparison of measured and calculated cloud concentrations of major chemical species. Simulation of 26 May 1985 Simulation time (min)

SO~- (ppb) Measured Calculated NO~- (ppb) Measured Calculated NH,~ (ppb) Measured Calculated pH Measured Calculated NO2(ppb) Measured Calculated O 3(ppb) Measured Calculated

0

60

120

4.06 4.06

4.35 3.61

2.47 2.53

15.80 15.80

17.50 10.75

10.70 7.0

8.68 8.68

8.72 8.92

11.20 7.06

3.35 3.40

3.31 3.61

3.65 3.73

7.10 7.10

7.50 6.59

6.40 6.0

57.7 57.7

58.3 53.5

57.9 51.0

998

CHRISTIAN SEIGNEURand ANTHONYM. WEGRECKI

NH~. The measured values show an increase in NH~ concentration over the 2-h period. The pH increases in both the calculations and the measurements. The increases in pH are quite commensurate: 0.30 in the measurements and 0.33 in the simulation. The concentration of NO 2 shows a slight decrease in both measurements and calculations, which results from the conversion of NOz to NO~. The calculated 0 3 concentration decreases as lower 0 3 concentrations are entrained from below the cloud. Little variation appears in the measured 03 concentrations. The concentrations of inert species such as Na, K, Ca, Mg, Fe and Mn decreased, on average, by 43 and 78% from the initial concentrations after 1 and 2 h, respectively. The calculated decreases in these concentrations were 63 and 82% after 1 and 2 h, respectively. This good agreement between measured and calculated inert species concentrations suggests that the major vertical transport processes (updraft and rain) are treated satisfactorily in this simulation. The major pathways leading to acid formation are similar to those of the previous simulations. Aqueous reduction of NO 3 radicals (61%) and heterogeneous hydrolysis of N 2 0 5 (39%) lead to NO 3 formation. Aqueous oxidation of SOz by HzO 2 (83 %), 0 2 (12%) and OH radicals (5%) leads to S O ] - formation. Overall, there is good agreement between the results of the model simulation of transport and chemistry for the case study of 26 May 1985 and the measured values of cloud species concentrations. Consequently, this case study was selected for further analysis of the physical and chemical processes that affect acid formation in clouds. 6. SENSITIVITY ANALYSIS STUDIES

The simulation of the atmospheric physical and chemical processes of air pollution is particularly useful to investigate the relative importance of these processes which govern air pollution levels and the effect in changes in precursor levels on air pollution levels. The study of the physical and chemical processes that govern the formation of air pollutants allows one to determine the parameters to which the model is the most sensitive and, therefore, which parameters need to be known with accuracy to obtain satisfactory model performance. The effect of changes in precursor levels on air pollution levels provides some useful information for the development of air pollution control strategies. Because satisfactory model performance was obtained for the simulation of 26 May 1985, we used this simulation as the base case for these sensitivity analysis studies. Nineteen sensitivity study simulations were performed. Eight simulations pertain to changes in precursor levels. Six simulations address the sensitivity of the model to physical and chemical parameters. Five simulations consider the effect of different environmental conditions on the model simulation results.

6.1. Sensitivity to precursor levels A key issue in the chemistry of atmospheric acidity is the response of the concentration of major chemical species to the concentrations of precursors. Previous work has demonstrated that the responses of SO 2- to SO2, N O r to NOx, and SO 2- and NO~ to HC concentrations can be highly non-linear (Seigneur et al., 1984, 1985; Saxena and Seigneur, 1986). It is therefore of particular interest to investigate the sensitivity of the cloud concentrations of major chemical species, i.e. SO~-, N O ~ , NH~, and H + , to the levels of precursors. The precursors considered in this analysis were SO2, nitrogen oxides (NOx), reactive HCs (RHC) and N H 3. The base case concentrations of SO2 were very low (i.e. below or equal to the detection limit of 1 ppb) and, for the sensitivity study, we varied the SO2 initial concentrations from 0 to 4 ppb. For the other sensitivity studies, the initial concentrations of NOx, RHC and NH 3 were individually divided by a factor of two. These changes in initial concentrations affected both below and in-cloud concentrations. The SO~- cloud concentration and the SO~- wet deposition after 2 h of simulation are presented in Fig. 5 as function of the initial SO2 concentration. These two curves show that the SO2/SO~- relationship is non-linear. The response of SO~- concentration or wet deposition to the initial SO2 concentration decreases as the initial SO2 concentration increases. This result is due to the fact that the SO2/SO~- system is oxidant limited at high SO2 concentrations. In these simulations, the aqueous oxidation of SO2 by H202 accounts for about 90% of total SO~formation whereas the aqueous oxidation of SO2 by 02 accounts for about 10%. The change in the NOx initial concentrations affects solely the N O 3 and H ÷ concentrations. The amount of NO3 present in the cloud, which was formed during the 2-h simulation, has been reduced from 1.24 to 0.58 ppb. The aqueous reduction of NO 3 radicals is the dominant pathway (74% versus 61% in the base case) and the heterogenous hydrolysis of N 2 0 s accounts for the rest of NO3 formation (26 vs 39% in the base case). As expected, the NO 3 aqueous reduction becomes a relatively more important pathway as the NOx concentration decreases. The response of NO 3 formation to a reduction in NOx is nearly linear with a reduction 0f53% in NO~ formation for a reduction of 50% in NO~ initial concentrations. The pH increases slightly from 3.75 to 3.78. The reduction in RHC initial concentrations has no effect on SO42- and NO3 concentrations. This result is not too surprising as this sensitivity study addresses a night-time simulation where no, or little, oxidant formation takes place. Therefore, the oxidation of SO2 and NO2 takes place through reaction with oxidants which were formed during daytime and are present at the beginning of the simulation. Reactive hydrocarbons, however, would have some effect on the oxidant levels produced during daytime. Three-dimensional simulations of oxidant and acid species formation

Mathematical modeling of cloud chemistry

999 .06

.......~::~:;~:;i:;i:;:~:~;-:.-

Sulfate Cloud Concentration

~3

.05 e-

• :.::i:i~.~i~~:~:~:'~::::

p-

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F--

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Sulfate Wet Deposition

8_

8 .04

t9

1

I

I

I

1

2

3

4

.03

Initial SO2 Concentration (ppb)

Fig. 5. Sulfatecloud concentration and wet deposition after 2 h as a function of the initial SO 2 concentration. need to be carried out to address this problem. It should be noted also that NOx emission reductions would also affect oxidant levels and, consequently, affect NO3 formation in this manner. The effect of NOx levels on oxidant levels does not appear in our 2-h nocturnal simulation but should be kept in mind when designing emission control strategies. A reduction in NH 3 initial concentrations has a direct effect on NH~ concentrations which are reduced proportionally. As a result, the pH decreases slightly from 3.73 to 3.47 because the cloud droplets become more acidic as NH 2 concentrations decrease. 6.2. Sensitivity to physico-chemical parameters There are some uncertainties associated with some key parameters of the cloud model and it is of particular interest to assess the sensitivity of the model output to these uncertainties. The parameters that were investigated here included the following: (i) the rate of N205 heterogeneous hydrolysis; (if) the rate of NO3 gas/droplet mass transfer; (iii) the updraft velocity and (iv) the liquid water content. The heterogeneous hydrolysis of N205 and the aqueous reduction of NO 3 are the two dominant pathways for the rate of formation of NO 3 under the simulation conditions considered. Therefore, the first two parameters are critical to the accuracy of the model for NO3 concentration predictions. The chemistry of the cloud is likely to be affected by two major parameters: the amount of liquid water aqueous chemistry and the rate of entrainment of chemical species into the cloud.

The last two parametric sensitivity studies address these two questions. In the base case, the N20 ~ heterogeneous hydrolysis was calculated according to the kinetics reported by Harker and Strauss (1981). In the first sensitivity study, it was assumed that the heterogeneous hydrolysis of N20 5 would take place every time that a molecule of N 2 0 5 would hit a water droplet. Therefore, the kinetics of N2Os heterogeneous hydrolysis is limited by the gas-phase diffusion o f N 2 0 s and should be an upper limit to the actual rate. It appears that the amount of NO3 formed increases by 0.4 ppb which corresponds to a 30% increase from the base case. The N205 hydrolysis pathway accounts for 81% of NO3 formation (vs 39% in the base case) whereas the NO 3 aqueous reduction pathway accounts for only 19% (vs 61% in the base case). The formation of NO3 from the aqueous reduction of NO 3 radicals depends, in part, on the rate of mass transfer of NO 3 radicals from the gas phase to the aqueous phase. There is presently some uncertainty regarding the accommodation coefficient of NO 3 radicals on water droplets. In the base case, this accommodation coefficient has a value of 0.2 based on the data reported for HO 2 by Mozurkewich et al. (1987). We investigated the sensitivity of NO 3 formation to the value of the NO 3 accommodation coefficient. This parameter was varied from 10 -6 to 1. The amount of NO3 formed through NO 3 aqueous reactions is not very sensitive to the NO 3 accommodation coefficient except at very low values of the coefficient. It is interesting to note that as the accommodation coefficient of NO 3 decreases, the amount of NO3 formed increases. As N O 3 radicals are not scavenged by

1000

CHRISTIAN SEIGNEURand ANTHONYM. WEGRECKI

droplets, they react with NO 2 to form N 2 0 5. Hydrolysis of N205 leads to two NO3 ions whereas aqueous reduction of NO 3 leads to only one N O 3 ion. Therefore, more NO~- (7.3 vs 7.0 ppb) is formed when the gas-phase conversion of NO3 to N 2 0 5 dominates the gas/droplet mass transfer of NO 3 radicals. The sensitivity of the cloud chemistry calculations to two cloud physics parameters, the updraft velocity and the cloud water content, was investigated. The results of these two sensitivity studies are reported in Table 7 for the SO 2 - , N O 3 , NH~ and H ÷ ion concentrations. An increase in the updraft velocity by a factor of two leads to a larger contribution of species entrained from below the cloud to the total cloud chemical composition. Because below-cloud initial concentrations are less than in-cloud initial concentrations, the cloud species concentrations are lower after 2h of simulation when the updraft velocity is higher. The pH increases from 3.73 to 4.00 as the acid species concentrations decrease. The increase in cloud water content has no effect on chemically inert species such as NH2 ions. The concentrations (expressed in ppb) of SO,2- and NO3 ions have increased slightly because of the larger volume of water available for chemical reactions. For example, reactions of SO2 with 02 and OH increase by factors of about two when the cloud water content increases by a factor of two. The total amount of SO~- formed increases from 0.42 to 0.50 ppb. It should be noted that the oxidation of SO2 by H 2 0 2 is not affected by the liquid water content because it is a fast reaction which is limited by the initial amount of either SO2 or H202. The relative contribution of the major pathways to SO 2- formation were 68% for the H202 aqueous reaction (vs 83% in the base case), 21% for the 02 aqueous reaction (vs 12% in the base case), 10% for the OH aqueous reaction (vs 5% in the base case) and 1% for minor pathways. The NO~ formation increases from 1.24 to 1.26 ppb as the cloud water content increases. There is a slight increase in the NO 3 aqueous reduction pathway due to the larger amount of water as this pathway accounts for 66% of NO3 formation vs 61% in the base

case. Because of the parallel decrease in N O 3 gasphase radical concentration, the N205 pathway decreases slightly, thereby compensating the increase in the NO 3 pathway. 6.3. Sensitivity to environmental conditions The base case simulation of 26 May 1985 pertains to the night-time chemistry and transport of stratus clouds. It is of interest to study the variations in the chemical reactions that would occur as the environmental conditions change. Five different cases were considered: (i) daytime conditions;

(ii) night-time non-raining cloud; (iii) night-time cloud free conditions (i.e. gas-phase chemistry only;)

(iv) night-time ground-level fog conditions and (v) night-time plume dispersed in a stratus cloud. The results of these simulations are summarized in Table 7 for SO 2 - , NO~, NH~ and H + concentrations. For the daytime simulation, photolysis rates typical of midday for 26 May were used. These rates were halved to account for light attenuation due to cloud cover. The daytime simulation shows a slight increase in SO 2- concentrations (0.17 ppb) which is due to an increase in the aqueous oxidation of SO2 by OH(aq) and other minor SO2 oxidation pathways. The increase in NO~ concentrations is more significant because it amounts to 0.62 ppb, i.e. about 9%. There is also a significant change in the major chemical pathways leading to NO~ formation. During daytime, high concentrations of OH radicals lead to a predominance of the gas-phase reaction of NO 2 with OH radicals (86% of NO~ formation vs a negligible amount at night-time). The NO 3 aqueous reduction pathway decreased from 61% (night-time) to 10% (daytime). The N 2 0 5 hydrolysis pathway also decreased from 39% (night-time) to 4% (daytime). These decreases in the relative importance of the NO3 and N 2 0 5 pathways result from the fact that NO 3 photolysis and reaction with N O lead to lower NOa concentrations during daytime than at night. During daytime, concentrations of phenoxy compounds increase

Table 7. Major species concentrations after 2 h for various cloud physics parameters and environmental conditions Environmental conditions

SO2(ppb)

NO~ (ppb)

NH 2 (ppb)

pH

Initial conditions Base case Updraft velocity ( x 2) Cloud water content ( x 2) Daytime cloud Night-time non-raining cloud Night-time cloud free conditions Night-time fog Night-time plume in cloud

4.06 2.53 1.76 2.60 2.70 3.80 3.15 4.9 10.1

15.80 7.0 4.36 7.02 7.62 9.70 8.60 16.1 15.8

8.68 7.06 5.51 7.06 7.02 10.6 10.6 8.7 8.7

3.35 3.73 4.0 4.01 3.70 3.59 -3.2 3.0

Mathematical modeling of cloud chemistry (0.3 ppb in the cloud after 2 h) and the reaction of N O 3 radicals with phenoxy compounds is a small but nonnegligible pathway for NO 3 formation (4% of the total NO 3 formed). Because of higher concentrations of SO 2- and N O ~ , the pH of the cloud droplets is slightly lower at the end of the daytime simulation than at the end of the night-time simulation. The non-raining cloud simulation differs from the base case only by the lack of precipitation. As a result, concentrations of soluble species are higher in the cloud because rain does not deplete these concentrations. The SO 2 - , N O j and NH~ concentrations are higher by 50, 40 and 50%, respectively. The difference in NO~- concentration is less because NO~ is formed toward the end of the simulation and is not depleted by rainout as much as other species that are depleted throughout the 2-h simulation. The pH at the end of the non-raining cloud simulation is lower because of the presence of higher concentrations of SO~- and NO 3 . The night-time cloud free simulation is best compared to the night-time non-raining cloud simulations as there are no removal processes in both simulations. (The base case simulation involves rainout of soluble species which makes the comparison more difficult.) It appears that no SO 2- formation takes place in the night-time cloud free simulations. This result is consistent with the previous results that showed that the dominant pathways for SO 2- formation in the nighttime simulation were aqueous reactions. Little NO~ formation takes place (0.24 ppb over the 2-h simulation); the N20~ hydrolysis reaction is the dominant pathway. For the night-time fog simulation, a single layer extending from ground level up to 100 m was used. All species' initial concentrations were identical to those of the fourth layer of the base case cloud simulation (i.e. the layer corresponding to the aircraft measurements) except for NO, NO2 and 03 initial concentrations which were 40, 10 and 20 ppb, based on groundlevel data (ARB, 1987). PAN concentrations were assumed to be 5 ppb. The results after 2 h of simulation show high SO 2 - , NO 3 and NH,~ concentra, ions because there is no entrainment of lower concentrations and rainout of soluble species via droplet ~¢.~imentation was not considered. The amount of SO~- and NO3 formed are 0.9 and 0.3 ppb, respectively. Sulfate formation is limited by the initial amount of SO2 present. It takes place primarily through aqueous reaction of SO2 with H202 (90%). For NO3 formation, the gas-phase reaction of NO2 with OH radicals is the dominant, yet limited, pathway. Concentrations of OH radicals are not negligible in fog, about 3 x 10 -6 ppb, because of the reaction of PAN in presence of NO (Seigneur and Saxena, 1984). Concentrations of NO 3 radicals, on the other hand, are small because NO emissions at ground level deplete 0 3 rapidly at night and the reaction of NO2 with 03, therefore, does not take place to produce NO 3 •

1001

The plume simulation was conducted by assuming that the initial NOx and SO2 concentrations were 100 ppb each. The NOx concentration consisted of 90 ppb of NO and 10 ppb of NO2. These concentrations are consistent with measurements reported by Richards (1990) in the vicinity of the Fontana area in 1981-1982. About 11 ppb of SO42- are formed during the 2-h plume simulation. The aqueous oxidation of SO2 by 02 accounts for 90% of SO 2- formation whereas the remaining 10% result from the oxidation of SO 2 by H20 2. The importance of the 0 2 pathway for SO2 oxidation results from the fact that the SO2 concentration is very high, the concentration of Fe which act as a catalyst is significant (0.3 to 6/~M for Fe) and the pH which reaches 4.4 toward the end of the simulation is favorable to this catalyzed reaction. A negligible amount of NO 3 was formed. Concentrations of NO 3 were small because, in the simulation, 0 3 was depleted by NO and no NO 3 was, therefore, formed. Formation of OH radicals at night can result from reaction of NO with PAN and NO 3 with aldehydes or phenoxy compounds. Nitrate concentrations are low in a NO plume and PAN concentrations were below the detection limit of I ppb. Therefore, no major pathway was available for NO3 formation. It is particularly interesting to note that in a plume, HMSA formation takes place rapidly. After 1 h, the HMSA concentration is equal to 1 x 10 -6 M, which is commensurate with values observed in clouds (Richards et al., 1983). As diffusion takes place, the HMSA concentration decreases to 0.02× 10 -6 M. This value of HMSA concentration is higher than the value expected from equilibrium between SO 2 and HCHO because the HMSA dissociation reaction is slower than the formation reaction. This simulation confirms that S(IV) concentrations that were observed in 1981-1982 could be explained as being HMSA resulting from the reaction of SO 2 with HCHO in cloudwater in plumes.

7. CONCLUSIONS A mathematical model of cloud physics and chemistry was evaluated with the cloud chemistry data collected in stratus clouds in the Los Angeles Basin from 1981 to 1985 by Richards (1990). This mathematical model simulates transport, diffusion and rainfall as well as atmospheric chemistry. The treatment of chemistry includes gas-phase chemistry, gas/droplet mass transfer and aqueous-phase chemistry. First, the equilibrium chemistry of the model was evaluated. A total of 52 case studies was used to assess model performance. The average normalized bias and absolute error in the H + concentration are - 3 and 20%, respectively. If it is assumed that hydroxymethane sulfonic acid (HMSA), a species resulting from the reaction of SO2 with H C H O in solution, was present in cloud droplets, the bias becomes 0.2% and the absolute error remains

1002

CHRISTIANSEIGNEURand ANTHONYM. WEGRECKI

20%. The most recent data set, which was collected in 1985, shows a clear trend toward underprediction of H +. Analysis of the chemistry of S(IV) shows that the aqueous concentrations of S(IV) that were measured can only be explained if HMSA was present. Comparison of measured and calculated formaldehyde and acetaldehyde concentrations shows that the equilibrium chemistry of formaldehyde is simulated correctly but that a large discrepancy exists between the calculated and measured gas/liquid distributions of acetaldehyde. The calculated aqueous concentration of HCHO is, on average, about 60% higher than the measured concentration. The calculated aqueous concentration of acetaldehyde is, on average, about 40 times smaller than the measured concentration. Two cases were selected to analyze the cloud chemistry and vertical transport processes: 25 and 26 May 1985. These two case studies were selected because they show significant increases in NO3 concentrations. A cloud microphysics model was used to estimate the updraft velocities which were not otherwise available. The simulation of 25 May 1985 does not predict correctly the measured cloud species concentrations, which suggests that NOx emissions from tall stacks may contribute significantly to NOx concentrations in coastal clouds and that the below-cloud concentrations of SO~- and N O r may not have been estimated accurately. The simulation of 26 May 1985 shows very good agreement between calculated and measured values. There was some light drizzle observed on that day and the good agreement between the calculated and measured concentrations of inert species suggests that the model simulates well the updraft and rainfall processes. Calculated and measured concentrations of SO 2- and NO 3 and acidity (pH) are in good agreement. It seems that the model treats satisfactorily the major physical and chemical processes for this case study. The two major pathways leading to nitrate formation are the heterogeneous hydrolysis o f N 2 0 s and the aqueous reduction of NO 3 radicals. The major pathway for SO42- formation is the aqueous oxidation of SO2 by H202. The aqueous catalyzed oxidation of SO 2 by 02 and the aqueous oxidation of SO 2 by OH radicals also contribute noticeably to SO~- formation. Several sensitivity analyses were conducted using the simulation of 26 May 1985 as base case. The sensitivity of SO 2- and NO 3 concentrations and pH to precursor levels, chemical kinetic parameters, meteorological parameters and environmental conditions were discussed. Based on the results of this study, the following recommendations can be made: (i) Future cloud chemistry measurement programs should include measurements below the cloud in addition to the in-cloud measurements because vertical transport is a major process

governing cloud chemical composition, even in stratiform clouds. (ii) Tracer experiments would be extremely useful to help understand transport phenomena occurring in clouds. These transport phenomena may be more complicated than a simple onedimensional updraft, even for stratiform clouds. (iii) Measurements and mathematical modeling of organic acids in clouds and fogs would be useful to assess the contribution of organic acids to cloud acidity. (iv) The gas/liquid equilibrium of acetaldehyde needs to be studied in the laboratory, as theoretical calculations and measurements are in disagreement by about a factor of 40. (v) The effect of precursor concentrations (particularly NOx and RHC) on acid concentrations should be studied by means of three-dimensional one-day or multi-day simulations, because of the effect of these precursors on the daytime chemistry of oxidant formation. (vi) The heterogeneous hydrolysis of N 2 0 5 needs to be studied in more detail because it is a major pathway for nocturnal formation of NO 3 . Acknowledgements--The authors gratefullyacknowledgethe continuous support of the Project Officers, Mr Eric M. Fujita, Dr Praveen K. Amar and Mr Bart E. Croes of the California Air Resources Board. Thanks are also due to Dr L. Willard Richards of Sonoma Technology, Inc. for helpful advice regarding the use of the experimental data and Mr Vince A. Mirabella of the Southern California Edison Company for allowing us to use the PLMSTAR air quality model for this study. This study was performed under Contract No. A732-042, Modeling of Cloudwater Chemistry in the South Coast Air Basin,by Bechtel Environmental, Inc. and Sonoma Technology,Inc. under the sponsorship of the California Air Resources Board. REFERENCES

ARB (1987) Air Quality Data Report. California Air Resources Board, Sacramento, California. Bell R. P. (1966) The reversible hydration of carbonyl compounds. Adv. Phys. org. Chem. 4, 1-29. Betterton E. A. and Hoffmann M. R. (1988) Henry's law constants of some environmentally important aldehydes. Envir. Sci. Technol. 22, 1415-1418. Grosjean D. (1988) Aldehydes, carboxylic acids and inorganic nitrate during NSMCS. Atmospheric Environment 22, 1637-1648. Harker A. B. and Strauss D. R. (1981) Kinetics of the heterogeneous hydrolysis of dinitrogen pentoxide over the temperature range 214--263K, Rockwell International Science Center, Federal Aviation Administration Publication FAA-EE-81-3. Huie R. E. and Neta P. (1987) Rate constants for some oxidations of S(IV) by radicals in aqueous solutions, Atmospheric Environment 21, 1743-1747. John W., Wall S. M. and Ondo J. L. (1985) Dry acid deposition on materials and vegetation:Concentrations in ambient air, Report to California Air Resources Board, Sacramento, California. Kessler E. (1969) On the distribution and continuity of water substance in atmospheric circulations. Met. Monographs 10, 85. Koenig L. R. and Murray F. W. (1976) Ice bearing cumulus

Mathematical modeling of cloud chemistry cloud evolution: Numerical simulation and general comparison against observation. J. appl. Met. 15, 747-762. Martin L. R. and Hill M. W. (1987a) The ion-catalyzed oxidation of sulfur: Reconciliation of the literature rates. Atmospheric Environment 21, 1487-1490. Martin L. R. and Hill M. W. (1987b) The effect of ionic strength on the manganese catalyzed oxidation of sulfur (IV): Atmospheric Environment 21, 2267-2270. Mozurkewich M., McMurry P. H., Gupta A. and Calvert J. G. (1987) Mass accomodation coefficient for HO2 radicals on aqueous particles, J. geophys. Res. 92, 4163--4170. Pilinis C. and Seinfeld J. H. (1987) Continued development of a general equilibrium model for inorganic multicomponent atmospheric aerosols. Atmospheric Environment 21, 2453 2466. Qin Y. and Chameides W. L. (1986) The removal of soluble species by warm stratiform clouds. Tellus 38B, 285-299. Richards L. W. (1990) Airborne chemical measurements in night-time stratus clouds in the Los Angeles basin. Atmospheric Environment (submitted). Richards L. W., Anderson J. A., Blumenthal D. J., McDonald J. A., Kok G. L. and Lazrus A. L. (1983) Hydrogen peroxide and sulfur (IV) in Los Angeles cloud water. Atmospheric Environment 17, 911-914. Russell A. G. and Cass G. R. (1984) Acquisition of regional air quality model validation data for nitrate, sulfate, ammonium ions and their precursors. Atmospheric Environment 18, 1815-1827. Saxena P. and SeignEur C. (1986) The extent of nonlinearity in the atmospheric chemistry of sulfate formation. J. Air Pollut. Control Assoc. 36, 1151-1154. Seigneur C. and Barnes H. M. (1986) Technical considerations in regional aerosol modeling. In Air Pollution Modeling and Its Application (edited by C. de Wispelaere) Vol. 5, pp. 343 369. Plenum Press, New York. Seigneur C, and Saxena P. (1984) A study of atmospheric acid formation in different environments. Atmospheric Environment 18, 2109-2124. Seigneur C. and Saxena P. (1985) The impact of cloud chemistry on photochemical oxidant formation. Wat. Air Soil Pollut. 24, 419-429. Seigneur C. and Saxena P. (1988) A theoretical investigation of sulfate formation in clouds. Atmospheric Environment 22, 101--115. Seigneur C., Saxena P. and Mirabella V. A. (1985) Diffusion and reaction of pollutants in stratus clouds Application to nocturnal acid formation in plumes. Environ. Sci. Technol. 19, 821-828. Seigneur C., Saxena P. and Roth P. M. (1984) Computer simulations of the atmospheric chemistry of sulfate and nitrate formation. Science 225, 1028-1030. Snider J. R. and Dawson G. A. (1985) Tropospheric light alcohols, carbonyls, and acetonitrile: Concentrations in the southwestern United States and Henry's law data. d. geophys. Res. 90, 3797-3805. Sverdrup G., Spicer C. W. and Ward G. F. (1987) Investigation of the gas phase reaction of dinitrogen pentoxide with water vapor. Int. J. Chem. Kinet 19, 191-205. Whitten G. Z. and Gery M. W. (1986) Development of CBMX Mechanisms for Urban and Regional AQSMs. EPA600/3-86-012, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina. Wobus H. B. (1971) Calculation of the terminal velocity of water drops. J. appl. Met. 10, 751-754.

1003

velocity which entrains water vapor, cloud water and rain water, and precipitation of rain water. The microphysical processes governing the conversion of water between the three different phases are depicted in Fig. 2. The governing equations of the cloud microphysics model are as follows:

u Oq~(z,t) + Oqv(z,t)

Oqv(z,t) c~t

Oz

t3q,(z,t)

Ot

uOq¢(z't) ~z

c~t

dqr(Z't)

+ dqv(Z't)

~q,(z,t) ~t

~t

~Jo.d

+cqc(z't) cnoud

c~t

(u_w) Oq~(c~z,t) Oq,(z,t)

c3t

(A.1) rai.

Ot

(A.2) r~i,

Oq~(z,t) r~

~t

(A.31

Irain'

where

qv(z,t) = mixing ratio of water vapor q¢(z,t) = mixing ratio of cloud water qr(Z,t)=mixing ratio of rain water u = vertical updraft velocity w = vertical raindrop fall velocity z = height above ground level t = time. The conversion of water between its different phases is governed by the following equations (Kessler, 1969).

=]

~q,(z,t)

e,Cp~ 7"~Z)

LI~2 J cSp

(A.4)

~t ,o,ood Lq~(z)(q,~(z)+~)+Rv~Z) ~z) c3qv(z't)ot r,i, = 1.72 X 10 -4 N07/20 [qsl(2)--qv(z,t)] x [pd(Z)qr(Z,t)] 13/20 Oqc(Z,t)

~t

(A.5)

= _ lO-3[q¢(z,t)-Al/pa(z)]

rain - A 2EiNo vs q¢(z,t)]

x [pd(z)q,(z,t)] 7Is

(A.6)

where

p(z) q~t(z) e L~ R~ T(z) Cvw

= pressure in atm = saturation mixing ratio with respect to liquid = ratio of mol. wt of water vapor to that of dry air =0.622 =latent heat of condensation =2.489 × 106j kg-1 =specific gas constant for water vapor=461.51 J k g - I K-1 = temperature (K) =weighted specific heat of cloudy air at constant pressure which is given by:

Cpw

= Cpd + qv(z,t)Cp~ + (qc(z, t) + qr(Z, t))C~

Cpd

=specific heat of dry air = 1005 J kg-~ K =specific heat of water vapor= 1846.4 J kg 1 K = specific heat of liquid water =4190 J kg- ~K = Marshall-Palmer distribution curve intercept at zero radius = 107 m - 4 = density of dry air (kg m - 3) =5.0× 10 -4 =0.2935 -collection efficiency = 1.

APPENDIX A: CLOUD MICROPHYSICS MODEL

Cp~ C~ -No

The cloud microphysics model treats the vertical motion of water vapor, cloud water and rain water as well as the conversion of water between these three different phases. The vertical motion of water consists of an updraft with constant

Pd A1 A2 Ej

(A.7)

1004

CHRISTIAN SEIGNEUR and ANTHONY M. WEGRECK1

The raindrop fall velocity (w) is calculated according to Wobus et al. (1971) and is a function of the raindrop radius (r) as follows: w= -1.197 x 10-4r2+8.64 x 10-air s + 1.44 x 10-13r6; for r~< 50 ,am w= -9x

(A.8)

10-3r+0.18; for 50/~m
(A.9)

w = - 0 . 0 0 8 r - 0 . 0 7 + B ; for 2 3 0 / t m < r ~ < 4 5 0 g m

(A.10)

w = 5.545/D - 9.215 + B; for r > 450 ~m

(A.11)

where r(~m) = 0.244618 × [No] - l/,~[pd(gjqr(Z, t)] 1/4 106 (Koenig and Murray, 1976)

(A.12)

B=O.4/(r-210), x = r - 4 5 0

(A.13)

and

q,(z)=fv[u, T(z), p(z), qv(0)] qdz) = fc[u, T(z), p(z), qv(0)]

(A.15)

qr(Z) = fr[u, T(Z), p(Z), qv(0)].

(A.17)

(A.16)

Therefore, if u, T(z), p(z) and q,(0) are known, it is possible to calculate qv(z), qc(z) and q,(z). However, the updraft velocity, u, is not typically available and meteorological data consist generally of the vertical temperature profile [T(z)], pressure [_p(z)], r.h. below cloud [(q,(0)], total liquid water content in cloud [qc(z)+ q,(z)] and precipitation rate [(2 = (w-u)qr(0)]. Equations (A.15-17) can be rewritten as follows:

qv(z) =L [u, 7Iz), p(z), qv(0)] LWC(z)=f~[u, T(z), p(z), qv (0)] +fr[U, T(z), p(z), q,(0)]

(A.15) '

2 = (w [q,(0)] - U)qr(0 )

D = 2.036791 × 10- i s;(5 _ 3.815343 x 10- a2 X,~

(A.18) CA.19)

This system of equations can be solved to obtain the value of the updraft velocity, u, knowing qv(0), LWC(z) and 2.

+ 4.516634 x 10- 9 X3 _ 8.020389 x 10- 7Z2 +1.44274121 x 1 0 - 3 X + 1.

velocity and relative humidity at ground level (i.e. lower boundary condition).

(A.14) APPENDIX B: GAS-PHASE CHEMICAL MECHANISM

Equations (A. 1-3) are solved for their steady-state solution and the mixing ratios of water vapor, cloud water and rain water are thus function of temperature, pressure, updraft

Table B.1 presents the Carbon-Bond Mechanism IV (Whitten and Gery, 1986) that simulates the gas-phase chemistry.

Table B.1. The Carbon-Bond Mechanism IV Rate constant*

Reaction 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

NO z O 0 3+ NO O+NO 2 O+NO 2 O+NO NO 2+O 3 0 3 O3 O3+OH O3+HO 2 NO3+NO NO3+NO 2 NO 3+ NO 2 N20 5 N20 5 NO+NO 2 HNO2+HNO 2 HNO 2 NO2+OH NO + OH HO2 + N O NO+NO H20 2 OH + H20 2 OH +HNO z OH+HNO 3 NO 3 HOz+HO 2 HO2+HO 2 OH+CO FORM+OH FORM FORM FORM+O FORM +NO 3 ALD2 + O

=NO+O =O 3 = NO 2 =NO =NO 3 =NO2 =NO 3 =0.205 O H + 0 . 8 9 7 O O =HO 2 =OH =2.NO 2 =NO+NO 2 =N20 5 =2.HNO 3 =NO3+NO 2 =2'HNO2 =NO+NO 2 =NO+OH =HNO 3 = HNO2 =OH+NO 2 =2.NO 2 =2.OH = HO2 =NO 2 =NO 3 =0.85NO2 +0.85 O + 0 . 1 5 N O =H20 2 =HzO 2 =HO2 =HO2+CO =2"HO2+CO =CO =OH+HO2+CO =HNOa +HO2+CO =C203 +OH =

variable 4.65 × 10 +6 26.6 13,800.0 2320.0 3120.0 0.0474 variable 0.042 x kl 100.0 3.0 28,100.0 0.59 1780.0 0.0285 3.12 2.4x 10 -~ 1.5x 10 -5 0.18xkl 16,300.0 9770.0 12,300.0 1.52 x 10 -4 0.0014 x kl 2520.0 9770.0 192.0 30.6 × kl 4144.0 3270.0 400.0 15,000.0 variable variable 237.0 0.93 636.0

Activation energyt

-690.0 1430.0 -600.0 -411.0 2450.0

940.0 580.0 -250.0 1230.0 60.0 10,840.0

-560.0 -427.0 -240.0 -530.0 187.0 -778.0 -1150.0 -5800.0

1550.0 986.0

Mathematical modeling of cloud chemistry Table B.1.

1005

(Contd.) Rate constant*

Reaction 38 39 40 41 42 43 44 45 46 47 48 49 50

ALD2 + O H ALD2 + N O 3 ALD: ALD2~+ HO 2 C203 + NO C203+NO 2 PAN CzO3 + C 2 0 3 C203 + HOz MGLY MGLY+OH OH PAR + O H

51

O+OLE

52 53

OH + O L E O3 + O L E

54 N O 3 + O L E 55 O + E T H 56 OH + E T H 57 O 3 + E T H 58 T O L + O H

59 60 61

PHEN + N O 3 PHO + NO 2 XYL+OH

62 63

TLA + O H ISOP+O

64

ISOP+OH

65

ISOP+O 3

66 67 68 69 70 71

ISOP+ NO 3 XO2N+NO XO2 + N O XO2 + HO: XO2 + C20 3 SO2 + OH

=C20 3 24,000.0 =CzOa + H N O 3 3.7 =XO2 +2"HO2 + C O + FORM variable =XOz + 2 . F O R M + H O 2 5.0 =NO2 + X O 2 + F O R M + H O 2 16,500.0 =PAN 9000.0 =C203 +NO2 0.0222 = 2 . X O z + 2 . F O R M + 2 . HO2 3700.0 = PAA++ 9600.0 =C203 +HO2 + C O 0.02 × kl =XO2+C20 3 26,000.0 = X O 2 + FORM + H O 2 21.0 = 1.49XO2+0.06XOzN+0.93 HO 2 +0.45 ALD 2 -0.75 PAR 1150.0 =0.95 ALD2 +0.35 HOz + 0.20 XO 2 +0.15 C O + 0.05 FORM +0.05 CzO 3 + -0.35 PAR 5920.0 = FORM +ALDz + XO2 + H O 2 - PAR 42,000.0 =0.5 ~kLD2 +0.66 FORM + 0.212 CO +0.28 HOE+ 0.144 XO 2 + 0.08 OH - PAR 0.018 =0.91 XO2+0.91 HO2+0.09XO2N 11.4 = FORM +XO2 + C O + 2 . H O z 1080.0 =XO2 + 2 . F O R M + H O 2 12,000.0 = F O R M + 0 . 3 7 CO+0.13 HO: 0.0027 = HO2 +0.64 XO2 + 1.13 FORM + 0.56 MGLY +0.36 P H E N + 0.36 PAR + 1.13 CO 9750.0 = PHO+HNO 3 14,000.0 = 20,000.0 = H O : + 0 . 7 2 X O 2 + 0 . 6 7 C O + 1 . 3 3 MGLY +0.28 PHEN+0.56 PAR +0.06 TLA +0.67 FORM 36,000.0 =XOz + P H O + 2 . P A R 20,000.0 = HO2 +0.8 ALD2 +0.55 OLE+0.5 XO2 +0.5 CO +0.45 E T H - 0 . 1 PAR 28,000.0 =0.87 XO 2 +0.87 FORM +0.87 HO 2 +0.29 PAR +0.29 OLE+0.58 ETH +0.29 ALD 2 126,000.0 = FORM +0.45 ALD2 + 0.55 ETH +0.98 HO2+ 0.10 OLE+0.60 CO -0.25 PAR 0.018 =XO2N 165.0 = 1000.0 =NO 2 12,000.0 = MHP~ 5000.0 = XO 2 + HO 2 + FORM 2400.0 = H2SO4 + HO2 1500.0

* All rate constants are in appropriate ppm and min units at 298 K and 1 atm photolysis reactions (+hv) are in units of m i n - t ; all bimolecular reactions are termolecular reactions are in units of p p m - 2 min i Rate constants designated as Gery (1986). f The numbers listed are Arrhenius temperature coefficients in degrees

kr=k29sex p B x

--

Activation energy$ -250.0

-250.0 -250.0 14,000.0

324.0 -537.0

1897.0 800.0 -382.0 2840.0

- 1300.0

of air. That is all unimolecular and in units of p p m - t m i n - l ; and all variable are defined in Whitten and Kelvin for B in the expression

.

+These species were added to provide upper estimates of peroxy acetic acid and methyl hydroperoxide concentrations which are needed in the aqueous chemical mechanism. List of nomenclature for organic chemical groups: FORM, formaldehyde; ALD2, carbonyl groups of other aldehydes; C203, peroxyacyl radical; XO2, peroxyalkyl radical; PAN, peroxyacetyl nitrate; MGLY, methylglyoxal; PAR, paraffinic carbons; OLE, olefinic carbon bond; ETH, ethylene; TOL, toluene; PHEN, phenolic compound; PHO, phenoxy radical; XYL, xylenes; ISOP, isoprene; PAA, peroxyacetic acid and MHP, methylhydroperoxide.

~(A)

24:5-B

1006

CHRISTIAN SEIGNEURand ANTHONY M. WEGRECKI

APPENDIX C: AQUEOUS PHASE CHEMICAL MECHANISM The aqueous-phase chemical mechanism is presented in Seigneur and Saxena (1988). Changes to this mechanism are presented in Tables C.1 and C.2.

Table C.1. Equilibrium reactions of acetaldehyde Equilibrium reaction

K29 a

-AH

Reference

R

CH3CHO(g)~CH3CHO(aq)

13 M a t m - ~

5.5 K

CH3CHO(aq)~CH3CH(OH)2(aq)

1.2

2.5 K

Snider and Damson (1985) Bell (1966)

Table C.2. Modified aqueous kinetic reactions Reaction

Rate expression (M min - 1)

S(IV)(+ 1/202)M"2+,S(VI)

S(IV)> 10 -4 M 4 x 104. 10 -4'°7~/t/(1+,/l)[Mn2 + ]2 S(IV)< 10 -4 M 6 x 104 x 10 -'*'07"/1/~1+41)[Mn2+ ] IS(IV)]

S(IV) ( + 1/2 O2)F*~+,S(IV)

360

HSO3 + O H ( + H S O 3 + 0 2 ) ---,SO~.- + SO,~ + H+ + H20

2.1 x 10tt[OH] [HSO~-]+3.1 x 10It [OH] [SO~ - ]

Reference Martin and Hill (1987b)

10-2,/1/~1+41) [Fe 3+] [S(IV)] 1 + 150[S(IV)] 2/3

[H + ]

Martin and Hill (1987a) Huie and Neta (1987)