A multiphase chemistry model coupled with a quasi-spectral microphysical model has been applied to measurements from the European Cloud Ice Mountain Experiment campaign to quantify the formation of the strong acids nitrate and sulfate and to evaluate the role of microphysical processes in redistributing reactive species among the different phases (gas versus cloud and/or rain). Significant formation of nitrate and sulfate are found to be due to the reaction of pernitric acid with the sulfite ion. Moreover, pernitric acid, because of its equilibrium in the gas phase and its high solubility, is always available both in cloud water and in rainwater via mass transfer from the gas phase. The sulfite ion comes from the mass transfer from the gas phase of sulfur dioxide in cloud water. When rain formation begins, it is efficiently transferred to the rainwater by collision/coalescence processes. This leads to an enhancement in strong acid production when microphysics is activated in the model. Modeled results have been compared with experimental data in an effort to retrieve a behavior law related to the partitioning between the gas and aqueous phases of the cloud. In particular, when collision/coalescence processes are considered, an improvement in retrieving the partitioning of soluble species and especially nitrate is observed. A higher production in sulfate could help interpret the discrepancy of global model calculations with observed sulfate concentrations in Europe in wintertime.
 For several years, significant efforts have been made by the scientific community to understand atmospheric chemistry. However, these efforts have concentrated mainly on atmospheric chemistry in the homogeneous gas phase, which currently begins to be well documented [Atkinson et al., 1996; Intergovernmental Panel on Climate Control (IPCC), 2001]. The role of clouds in the chemical composition of the atmosphere is significant in two aspects of planetary evolution: the atmospheric oxidizing capacity and the greenhouse effect linked to the role of aerosols (direct and indirect) in radiative forcing. Even if some modeling studies have tried to understand the overall role of cloud chemistry in global climate studies [Jacob, 1986; Lelieveld and Crutzen, 1990; Dentener et al., 2002], our knowledge is still at a rudimentary stage when looking at the details of cloud processes [Facchini, 2002].
 Recently, the reaction pathway of pernitric acid with the sulfite ion in aqueous phase has been proposed to play an important role in tropospheric chemistry [Warneck, 2000; Leriche et al., 2000]. Furthermore, recent studies by Warneck , Dentener et al. , and Williams et al.  have also suggested the potential role of aqueous phase pernitric acid reactivity in tropospheric chemistry. The kinetic constant of this reaction has been measured by Amels et al. . Because of its thermal decomposition in the gas phase, its impact on tropospheric chemistry via cloud chemistry could be important in winter and/or at high latitudes. The reaction of pernitric acid with the sulfite ion produces both sulfate and nitrate and is the only reaction pathway, which links N chemistry and S chemistry. This reaction could have an impact on the amounts of nitrate and sulfate in aerosols for nonprecipitating clouds and on the wet acid deposition when clouds are precipitating. Also, this reaction could have an effect on NOx levels because pernitric acid is a NOx reservoir species [see Leriche et al., 2001]. Finally, pernitric acid can lead to a release of nitrous acid by the cloud droplets at moderate pH in moderately polluted conditions [Williams et al., 2002]. The possible role of this reaction in the production of sulfate aerosol could be a first hypothesis to explain the systematic underestimation of sulfate in winter in Europe by global models as described, for example, by Feichter et al. , by Chin et al. , and by Barrie et al. . Global models, however, often do not contain a very good description of cloud processes. Many models exclude the explicit implementation of intermediate chemical reactions, and have resolution too coarse to provide a detailed comparison with measurements in polluted regions.
 The present modeling study aims at:
 • quantifying the formation of strong acids like nitrate and sulfate when considering multiphase chemistry during an observed cloud event,
 • verifying the importance of intermediate species such as HNO4 in this strong acid production and
 • evaluating the role of microphysical processes in redistributing reactive species among the different phases (gas versus cloud and/or rain).
 This model has been used for the modeling of a cloud event [Voisin et al., 2000] during the European Cloud Ice Mountain Experiment (CIME) (CIME Special Issue, Atmos. Res., 58(4), 229–230, 2001), which is a typical polluted wintertime event. The simulation is described in detail by Leriche et al. . This paper is the continuation of Leriche et al.  paper and focuses on the formation pathway of strong acids, sulfate and nitrate for a precipitating and nonprecipitating cloud. We also compare measurements of the partitioning between the gas and aqueous phase with model calculations. Of particular focus on is the very soluble and reactive species nitric acid which is found to be more efficiently produced when microphysical processes are considered.
 The chemistry included in the chemical module is explicit and describes a rural environment. The gas-phase mechanism includes the oxidation of methane, and the chemistry of NOy and ammonia, which is derived and updated after Madronich and Calvert . The exchange of chemical species between the gas and aqueous phase is parameterized by the mass transfer kinetic formulation developed by Schwartz . The thermodynamical data involved in mass transfer are listed in Table 1 with accommodation coefficients and Henry's law constants, and in Table 2, for aqueous phase equilibrium, only new references for updated values after Leriche et al.  are given. The aqueous phase chemistry includes the detailed chemistry of HOx (Table 3), chlorine (Table 4), carbonates (Table 5), NOy (Table 6), and sulfur (Table 7) and the oxidation of organic volatile compounds (VOCs) with one carbon atom (Table 8). These aqueous phase chemical mechanisms have been updated and only new references for updated values are indicated in Tables 3–8. The pH of the droplets is calculated at each time step by solving a simplified ionic balance equation.
Table 1. Values of Mass Accommodation Coefficients and Henry's Law Constantsa
 The microphysical module takes into account two categories of liquid water, cloud water and the rainwater, which is distributed according to a lognormal spectrum defined by the median size diameter D0 and the standard geometric deviation σ. The microphysical processes taken into account are collision/coalescence represented by autoconversion, accretion and self-collection, and evaporation and sedimentation. The time step of this module is ten seconds. The chemical and microphysical processes act together to redistribute the chemical species concentrations as described in Figure 1.
 This model can be used with two different options. In one case, the microphysical processes are not taken into account, which means that only cloud water is considered varying with time but with a constant radius for the droplets. In the other case, the microphysics is considered, and because of the quasi-spectral nature of the Berry and Reinhardt parameterization, allows for partitioning of the liquid phase among the two water categories (cloud and rain) and for varying mean raindrop diameter. The first case simulates a nonprecipitating cloud while the second case corresponds to a precipitating cloud with maritime parameters (defined through the median size diameter and the standard geometric deviation for the lognormal distribution of cloud droplets).
3. Results and Discussion
3.1. Description of the Simulation
 The conditions of the simulation are described in detail by Leriche et al. . We only briefly summarized these conditions below. To initialize the model, we used data from the CIME campaign. CIME was a European experiment, which took place during winters 97 and 98 at the top of The Puy de Dme mountain in the center of France. During December 1997, chemical measurements were performed in both gas and aqueous phases by Voisin et al.  in the presence of clouds. We chose to simulate the 13 December because there was a stable meteorological situation which produced drizzle without either ice or rain. The air mass was polluted coming from the north-northeast. In the simulation, the chemical measurements used to initialize the chemistry are typical of a wintertime-polluted air mass with high NOx (7.1 ppbv) and high formaldehyde (6 ppbv) concentrations.
 Meteorological parameters are prescribed by the time change of the temperature, which simulates the temperature variation in an orographic cloud at the top of the Puy de Dme mountain, the site of the CIME experiment. The simulation begins at noon and its duration is half an hour. The liquid water content of the cloud initialized with 0.3 g m−3, further evolves as a function of time and temperature through microphysical conversions, providing the partitioning between cloud and rainwater, and the change in raindrop diameter. At the end of the simulation, the cloud evaporates as the temperature increases. The maximum in the cloud water and rainwater content are respectively found at 12.07 p.m. and at 12.12 p.m. If the microphysical processes are not considered (when autoconversion is turned off), the liquid water content of the cloud only evolves through the effect of varying the temperature across the simulation (which describes a nonprecipitating case). In this case, the maximum in the liquid water content arises at 12.15 p.m.
 As discussed before, two options are available for considering cloud chemistry: either the liquid water content is in the only one form of cloud with no conversion allowed for rain production (nonprecipitating case) or liquid water is shared out between cloud phase and rain phase with varying raindrop diameter (precipitating case).
3.2. Formation Pathway of Strong Acids: Sulfuric and Nitric Acids
3.2.1. Simulation Results: Precipitating Versus Nonprecipitating Cloud
 We now examine the formation pathway of strong acids (sulfate and nitrate) in the gas phase, in cloud and in rain. We present results for two simulations, with and without microphysical conversions. Results for the formation of nitric acid and sulfate through chemical reactions are presented in Figure 2 for both cases. Only the main production pathways are indicated in both gas and aqueous phases. First, total production of both nitric acid and sulfate (gas plus liquid phases) are higher in the case where microphysics is activated, a factor of 1.2 more important for nitric acid and a factor 1.45 more important for sulfate than for the case without microphysics. The production pathway of pernitric acid (reaction (A69)) is an important contribution to the formation of both nitric acid and sulfate. This pathway accounts for 58% of the total sulfate production for the case with microphysics considering cloud plus rain contributions, and 53% for the case without microphysics. For nitric acid formation, it accounts for 37% of the total production for the case with microphysics considering cloud plus rain contributions, and 28% for the case without microphysics. The budget of HNO4 indicates that the reaction with the sulfite ion contributes 82% to the total pernitric acid destruction (gas and liquid phases) in the case with microphysics considering cloud plus rain contributions. The other predominant destruction pathways of HNO4 are reactions (A66) and (A68) (around 7% and 10%, respectively, in the case with microphysics considering cloud plus rain contributions). For nitric acid, the main production pathway arises via the gas phase production from reaction of NO2 with OH (58% for the case with microphysics and 68% for the case without microphysics). This could be expected in our run conditions describing a high NOx regime. The contribution of hydrolysis of N2O5 (reaction (A74)) to the production of nitric acid is less significant with 5% contribution to the total production for the case with microphysics considering cloud plus rain contributions and 4% for the case without microphysics. The sulfate formation in the gas phase is negligible and the formation in the aqueous phase by oxidation of sulfur dioxide by hydrogen peroxide (reaction (A117)) contributes 39% to the total production for the case with microphysics considering cloud plus rain contributions and 46% for the case without microphysics. If we examine the formation pathway in the aqueous phase for the case with microphysics, we observe that the contribution of one reaction is the same in cloud and in the rain phase. This fact explains the more important total production of nitric acid and sulfate when microphysics is considered.
 These results underline the efficient production of nitrate and sulfate by the pernitric acid pathway in the aqueous phase, which enhances total production of sulfate and nitrate in aerosols for a nonprecipitating cloud and leads to an acidification of rain for a precipitating cloud. This aqueous production pathway of both nitrate and sulfate is not taken into account in global models such as the GOCART model for example [Chin et al., 2000]. As suggested by Dentener et al. , the production of sulfate aerosols by pernitric acid in cloud could improve the comparison between sulfate concentrations simulated by global models with observations. In fact, global models tend to underestimate sulfate concentrations over Europe in winter.
3.2.2. Sensitivity Tests
 We have made some sensitivity tests on this simulation on microphysical processes or on initial chemical conditions to understand their relative contribution to the observed behavior of the strong acid formation. A first test on sedimentation shows that sedimentation acts as a sink for soluble species but has no significant role on chemical pathways. Second, to test how the contribution of pernitric acid in nitric acid and sulfate formation is linked to NOx levels, we have performed a sensitivity test in which we have reduced the initial NOx concentration by a factor of 50. Results of this new run are presented in Figure 3, which is directly comparable to Figure 2, except that total nitric acid production is 6 to 9 times smaller when reducing NOx by 50 and total sulfate production is 1.2 to 1.16 times smaller. As expected, when diminishing the initial NOx concentration, the contribution to total nitric acid production of gas phase pathway becomes less important and represents 10% and 16% of the total nitric acid production respectively, when microphysics is considered, or not.
 Surprisingly, however, when diminishing the initial NOx concentration, the production of strong acids by the pathway involving pernitric acid is still important.
 For nitric acid, pernitric acid pathway contributes 90% to the total production for the case with microphysics considering cloud plus rain contributions and 84% for the case without microphysics. For sulfate, it represents 28% of the total production for the case with microphysics considering cloud plus rain contributions and 21% in case without microphysics. The most important production pathway for sulfate production is now the oxidation of the sulfite ion by hydrogen peroxide because the diminution of NOx involves a new chemical regime of peroxides production. This can explain the smaller diminution of total sulfate production in comparison to the diminution of total nitric acid production.
 The differences observed in the low NOx regime (Figure 3) between the two cases with and without microphysics are still remaining the same as in the high NOx regime (Figure 2). The productions via aqueous phase are also equivalent in the cloud and rain phases and contribute equally to the total production for both nitric acid and sulfate. This has to be directly related to the indirect effect of microphysical conversion. To understand this equal production in cloud and rain phases, we have examined the sources of the precursors of nitric acid and sulfate in the aqueous phase. We only focus on the reaction with pernitric acid since the source of hydrogen peroxide in the aqueous phase is the same as pernitric acid.
 On the one hand, nitric acid and sulfate are produced in the aqueous phase through the oxidation of the sulfite ion by pernitric acid continuously formed in the gas phase and very soluble. On the other hand, the sulfur dioxide is transferred from the gas phase to the cloud phase through mass transfer, before rain production and produces the sulfite ion that leads to nitric acid and sulfate production. A schematic diagram is drawn in Figure 4 to investigate the origin of those chemical precursors of nitric acid and sulfate in aqueous phase. The pernitric acid, available in the gas phase, is efficiently transferred to the aqueous phase through mass transfer with a relative contribution of pernitric acid production in the cloud phase of 90% and a relative contribution of pernitric acid production in the rain phase of 87%. The other production pathways of pernitric acid in the aqueous phase are reactions (A64) and (A65), which contribute respectively 8% and 2% to total pernitric acid production in the cloud phase and 8.5% and 2% in total pernitric acid production in the rain phase. The remaining production in the rain phase comes from conversion of cloud water into rainwater by collision/coalescence processes. Although the kinetic constant of reaction (A65) is greater than that of reaction (A64), reaction (A65) has a more important contribution in HNO4 production because HO2 prevails on O2− for simulated low pH values (pKa of HO2 4.8 and simulated pH 3.7). For sulfite ion production in the aqueous phase, the pattern is slightly different. The sulfite ion already exists in cloud phase from the mass transfer of sulfur dioxide, and as the rain appears, it is transferred through collision/coalescence processes to the rain phase. This source of the sulfite ion in the rain phase represents 99% of the total production in the rain phase (chemical and microphysical processes). Moreover, the destruction of the sulfite ion in the cloud phase by collision/coalescence processes is only 1% of the total destruction (chemical and microphysical processes). The resulting effect of this precursor production is an increase in the production of nitric acid and sulfate equally shared among the cloud and the rain phases.
3.2.3. Potential Uncertainties in the Chemical Mechanism
 The above discussion on the formation of strong acids in cloud and rain strongly depends on the value of the reaction constant of the oxidation of sulfite ion by pernitric acid (reaction (A69)). This constant has only been measured once by Amels et al.  study, which is part of the PhD work of Götz  and this value can be a source of potential error. Despite the lack of data on the reaction constant of reaction (A69), the reactivity of peroxo compounds R-OOH toward the sulfur(IV) has been investigated in details by Drexler et al. . In this study, looking at the reactivity of hydrogen peroxide (R = H), peroxonitrous acid (R = NO) and peroxoacetic acid (R = Ac), a general relationship for the rates of oxidation of sulfur(IV) by peroxo compounds following a three-term rates law was established including available data for reactivity of peroxomonosulfuric acid (R = SO3−) and methyl hydroperoxide (R = CH3). These three-term rates are proton catalysis, general acid catalysis and water catalysis. For hydrogen peroxide, only the proton catalysis is significant for atmospheric chemistry. An interesting result of this study is the relationship correlating the rate constant for water catalysis (independent of pH value) with the pKa of the peroxo compounds. Using this relationship to estimate the reaction constant of reaction (A69) gives a value of 2.2 × 105 M−1 s−1, which is in the same order of magnitude than the value measured by Amels et al. .
 However, as the main conclusion about strong acids formation depends on the value of reaction constant of reaction (A69), additional sensitivity tests have been performed on this reaction constant taking into account the maximal potential error: the constant is divided or multiplied by a factor 10. Figure 5 shows the relative contribution of each production pathway to the total production of (a) nitric acid and (b) sulfate for three cases: the reaction constant of reaction (A69) is divided by 10, the reference simulation (using reaction (A69) constant) is corresponding to Figure 2 and the reaction constant of reaction (A69) is multiplied by 10. For each case, the total production in ppbv h−1 is indicated. The most important result from this test is that the contribution of reaction (A69) is still significant even if the reaction constant is divided by 10 for both production of nitric acid and sulfate. The relative contribution of this reaction is respectively 16.9% and 33% of the total production of nitric acid and sulfate when the reaction constant is divided by 10, is respectively 36.6% and 59% of the total production of nitric acid and sulfate for the reference simulation and is respectively 40% and 64% of the total production of nitric acid and sulfate when the reaction constant is multiplied by 10. For both nitric acid and sulfate, we can notice that the increase of the contribution of reaction (A69) as well as the increase of the value of the total production is more important between the simulation where the reaction constant is divided by 10 and the reference simulation than between the reference simulation and the simulation where the reaction constant is multiplied by 10. This is due to the nonlinearity of the chemistry. In conclusion, this test shows that, despite the potential error on the reaction constant of reaction (A69), it is clearly demonstrated that this reaction significantly contributes to the production of both nitric acid and sulfate in winter.
3.3. Partitioning of Chemical Species Between Phases
 In this paper, we are also interested in investigating the effect of microphysical conversions on the partitioning of chemical species as described by Voisin et al. . This partitioning was represented by the q factor, defined as:
where Cgi and Cwi are respectively the gaseous and aqueous concentrations of the species i in molec cm−3, L is the liquid water content in vol/vol, H* is the Henry law effective constant of the species i in M atm−1 and R = 0,08206 atm M−1 K−1. This factor indicates whether the species i is at Henry's law equilibrium (q = 1), undersaturated in the aqueous phase (q < 1) or oversaturated in the aqueous phase (q > 1).
 An important point is that, while measuring q, the liquid water content involved in the partitioning includes both cloud water and drizzle. In order to adequately compare the measurements with model calculations, we introduce a bulk q factor defined as:
with , and H*total is the effective Henry's law constant that includes possible dissociation and hydration, using the bulk pH.
 The bulk pH, calculated from resolving the ionic balance equation in the mixed solution of cloud water and rainwater, has a mean value of 3.7 whereas the bulk pH measured during the cloud event is more acidic with a value of 3.3. The difference between the experimental and simulated pH values is first due to the precision of the experimental pH value, around 0.1 units. Second, we use chemical measurements from bulk samples to initialize the model, which may not be representative of the initial chemical composition of cloud droplets determined by aerosol nucleation and not known in detail in the measurements.
Figure 6 shows the partitioning factor between the gas and condensed phase through a comparison between experimental results versus two model results (without and with microphysics) for several chemical species ordered by increasing solubility. Experimental results correspond to values for the simulated cloud event of 13 December. The values of the q factor for the radical HO2 has been indicated as an example of the partitioning of a very reactive radical but no measurements were available for this species.
 We notice a rather good agreement between experimental and numerical results, except for nitric acid and sulfur dioxide when microphysics is not considered. For sulfur dioxide, the discrepancy between model and measurements comes from an overestimation of measured sulfur dioxide concentrations in cloud because of HMSA conversion into S(IV) due to some experimental biases. However, coupling chemistry and microphysics improves considerably the comparison for almost all the soluble species, and more particularly for nitric acid. The remaining difference between numerical and experimental results for nitric acid comes from the discrepancy between pH values that are measured and simulated with an experimental value more acidic. In fact, Voisin et al.  show that the q factor for nitric acid decreases when the pH increases.
 The undersaturation of nitric acid in the aqueous phase comes from its high solubility in connection with its production in the gas phase, which is faster than its production in the aqueous phase. In fact, the rate of nitric acid production in the gas phase is greater than the rate of transfer to aqueous phase. This means that the equilibrium time of phase exchange is greater than the characteristic time of nitric acid production in the gas phase. When microphysics is considered, the gaseous nitric acid must pass two aqueous frontiers corresponding to cloud and rain phases. Nitric acid is more undersaturated in the aqueous phase when microphysics is taken into account. Finally, coupling chemistry and microphysics allows for a more realistic nitric acid partitioning between the gas and aqueous phases, closer to the measurements.
 A coupled model of multiphase chemistry [Leriche et al., 2001] has been applied to a cloud event taken from the European CIME experiment [Voisin et al., 2000] during a polluted chemical situation. First, the production pathways of the strong acids, nitric and sulfuric acid are examined. The results show a significant contribution of the reaction between pernitric acid and the sulfite ion in the production of both acids. Moreover, the comparison between a case without microphysics corresponding to a nonprecipitating cloud and a case with microphysics corresponding to a precipitating cloud shows a greater production of strong acids when microphysics is considered. This is due to an equivalent production in cloud and rain phases, which arise from interaction between microphysics and chemistry. The study of the main sources of strong acids precursors highlights the role of collision/coalescence processes in the enhancement of strong acids production.
 Second, modeling results have been compared with data, based upon a behavior law that relates the partitioning among gas/aqueous phases and species solubility. Coupling multiphase detailed chemistry with microphysics allows for retrieving this behavior law that could be possibly used as a parameterization in global models.
 The numerical results and their comparisons with observational data demonstrate the interest of such a modeling approach in linking laboratory kinetics with in situ measurements. It also represents a potential tool for sensitivity analysis on chemical species reactivity and partitioning among various phases of the cloud, which can now be assessed using new instruments such as a counter virtual impactor [Noone et al., 1988]. In that sense, if completed by some aerosol chemistry and microphysics, it could help to interpret data from such an instrumentation platform. More generally, this modeling study has put evidence on the importance of intermediate compounds such as pernitric acid, which is often neglected in models and leads to sulfuric and nitric acid production in clouds [Herrmann et al., 2001]. Further laboratory investigations in the conditions of a real atmosphere (temperature, pressure, concentration) for aqueous phase pernitric acid reactivity are needed. However, considering the actual knowledge, the linkage between sulfur and nitrogen chemistry through pernitric reactivity in aqueous phase can bring a possible explanation of the discrepancy between models and observations that is found in winter in sulfate aerosol concentrations, which are actually underestimated in global models [IPCC, 2001].
 This work was supported by the “Programme National de Chimie Atmosphérique” (PNCA) of the INSU (Institut des Sciences de l'Univers). Computer resources were provided by I.D.R.I.S (Institut du Développement et des Ressources en Informatique Scientifique), project n°000187. The first author is very grateful to Agence de l'Environnement et de la Matrise de l'Energie (ADEME) and to Electricité de France (EDF), who financed this work. The authors would like to thank Professor Horst Elias for his help on the reactivity of pernitric acid with the sulfite ion measured by his team.