Global modeling of cloudwater acidity, rainwater acidity, and acid inputs to ecosystems

Cloudwater acidity affects the atmospheric chemistry of sulfate and organic aerosol formation, halogen radical cycling, and trace metal speciation. Rainwater acidity including post-depositional inputs adversely affects soil and freshwater ecosystems. Here we use the GEOS-Chem model of atmospheric chemistry to simulate the global distributions of cloudand 10 rainwater acidity, and the total acid inputs to ecosystems from wet deposition. The model accounts for strong acids (H2SO4, HNO3, HCl), weak acids (HCOOH, CH3COOH, CO2, SO2), and weak bases (NH3, dust and sea salt aerosol alkalinity). We compile a global dataset of cloudwater pH measurements for comparison with the model. The global mean observed cloudwater pH is 5.2 ± 0.9, compared to 5.0 ± 0.8 in the model, with a range of 3 to 8 depending on region. The lowest values are over East Asia and the highest values are over deserts. Cloudwater pH over East Asia is low because of large acid inputs 15 (H2SO4, HNO3), despite NH3 and dust neutralizing 70% of these inputs. Cloudwater pH is typically 4–5 over the US and Europe. Carboxylic acids account for less than 25% of cloudwater H+ in the northern hemisphere on an annual basis, but 25– 50% in the southern hemisphere and over 50% in the southern tropical continents where they push the cloudwater pH below 4.5. Anthropogenic emissions of SO2 and NOx (precursors of H2SO4 and HNO3) are decreasing at northern mid-latitudes, but the effect on cloudwater pH is strongly buffered by NH4+ and carboxylic acids. The global mean rainwater pH is 5.5 in GEOS20 Chem, higher than the cloudwater pH because of dilution and below-cloud scavenging of NH3 and dust. GEOS-Chem successfully reproduces the rainwater pH observations in North America, Europe, and eastern Asia. Carboxylic acids, which are undetected in routine observations due to biodegradation, lower the annual mean rainwater pH in these areas by 0.2 units. The acid wet deposition flux to terrestrial ecosystems taking into account the acidifying potential of NO3and NH4+ in Nsaturated ecosystems exceeds 50 meq m-2 a-1 in East Asia and the Americas, which would affect sensitive ecosystems. NH4+ 25 is the dominant acidifying species in wet deposition, contributing 41% of the global acid flux to continents under N-saturated conditions.

oxidize dissolved organic compounds to less volatile forms leading to secondary organic aerosols (Ervens et al., 2011;Herrmann et al., 2015), and (3) convert halides into halogen radicals (von Glasow and Crutzen, 2003;Platt and Hönninger, 2003). It affects the solubility and bioavailability of iron in aerosol particles and thus the input of this micronutrient to marine ecosystems (Mahowald et al., 2005). Acidic deposition has a range of environmental effects on soil and freshwater ecosystems (Driscoll et al., 2001). Cloud-and rainwater acidity is affected in a complex way by natural and anthropogenic emissions, but 35 there has been little effort so far to evaluate the ability of global models to represent this. Here we present such an evaluation with the GEOS-Chem atmospheric chemistry model and go on to discuss the factors controlling cloud-and rainwater acidity on a global scale.
Cloud-and rainwater H + concentrations are determined by the balance between dissolved acids (H + donors) and bases (H + 40 acceptors). Sulfuric acid (H2SO4), nitric acid (HNO3), and hydrogen chloride (HCl) are the major strong acids in the atmosphere, and they dissociate completely in cloud-and rainwater. The major weak acids are CO2, SO2, and carboxylic acids including formic acid (HCOOH), and acetic acid (CH3COOH). Ammonia (NH3) and alkaline dust particles are the major bases.
Biomass burning emissions are from GFED v4 (van der Werf et al., 2017). Natural emissions include NOx from lightning (L. Murray et al., 2012) and soil , volcanic SO2 , marine dimethyl sulfide (DMS) (Breider 100 et al., 2017), and NH3 from oceans, natural soils, and human population (Bouwman et al., 1997). Sea salt aerosol emissions in two size classes (fine and coarse) follow Jaeglé et al. (2011). Dust emissions include desert and semi-desert sources (Fairlie et al., 2007;Ridley et al., 2013), and combustion and industrial sources (Philip et al., 2017) in four size classes (one fine and three coarse). Biogenic volatile organic compounds (VOC) emissions are from MEGAN (Guenther et al., 2012;Hu et al., 2015). 105 Sulfur chemistry in GEOS-Chem includes oxidation of DMS to SO2 and methanesulfonic acid (MSA), gas-phase oxidation of SO2 to H2SO4, and aqueous-phase oxidation of SO2 to H2SO4 in clouds, rain, and alkaline sea salt aerosols (Alexander et al., 2005(Alexander et al., , 2009Q. Chen et al., 2017). Nitrogen chemistry includes oxidation of NOx to HNO3 in the gas phase, and in the aqueous phase of aerosols and clouds (McDuffie et al., 2018;Holmes et al., 2019). Tropospheric HCl is mainly from acid displacement 110 reactions on sea salt aerosols (X. .
HNO3, HCl, and NH3 are semi-volatile and their gas-particle partitioning affects their scavenging efficiency in cloud-and rainwater . We calculate this partitioning at bulk thermodynamic equilibrium using ISORROPIA II for the H2SO4-HNO3-HCl-NH3-NVC metastable aqueous system, where NVC represents the non-volatile cations from fine-mode sea 115 salt aerosol (X. . The uptake of HNO3 and release of HCl (acid displacement) on coarse-mode sea salt aerosol is treated as a kinetic process (X. .

Simulation of HCOOH and CH3COOH
The most important carboxylic acids for cloud-and rainwater acidity are HCOOH (pKa = 3.8 at 298K) and CH3COOH (pKa = 4.8 at 298K) (Morgan, 1982;Keene et al., 1983). They are present in the atmosphere at comparable concentrations (Talbot et 120 al., 1997) but HCOOH is more important for contributing to acidity because of its higher Henry's law solubility and lower pKa. Sources of these acids include secondary production from VOC oxidation and direct emissions from biomass burning, fossil-fuels, soils, and vegetation (Khare et al., 1999), but these are poorly understood and models greatly underestimate atmospheric concentrations (Paulot et al., 2011;Stavrakou et al., 2012;Millet et al., 2015;Khan et al., 2018). Here we use the previous GEOS-Chem HCOOH simulation by Millet et al. (2015) which scales up the biogenic emissions from the MEGAN 125 inventory (Guenther et al., 2012) in order to fit atmospheric observations over the US. This yields a global HCOOH source of 1900 Gmol a -1 . Stavrakou et al. (2012) previously estimated a global HCOOH source of 2200-2600 Gmol a -1 from inversion of satellite data. In addition, we assume a minimum background mixing ratio of 100 pptv (50 pptv south of 60°S), based on https://doi.org/10.5194/acp-2020-485 Preprint. Discussion started: 22 June 2020 c Author(s) 2020. CC BY 4.0 License. measurements in the marine boundary layer and the free troposphere (Arlander et al., 1990;Talbot et al., 1990Talbot et al., , 1997Legrand et al., 2004) and satellite-derived free troposphere HCOOH columns over marine areas of 1-2×10 15 molecules cm -2 (Franco et 130 al., 2020).
Our CH3COOH simulation follows the standard GEOS-Chem mechanism (Mao et al., 2013;Travis et al., 2016) without further improvement, except that the minimum background CH3COOH concentration is also taken to be 100 pptv (50 pptv south of 60°S), based on observations in the marine boundary layer and the free troposphere (Arlander et al., 1990;Talbot et al., 1990Talbot et al., , 135 1997Helas et al., 1992;Franco et al., 2020). The global simulated CH3COOH source is 1000 Gmol a -1 . Other modeling studies attempting to fit CH3COOH observations have estimated a source in the range 1700-3900 Gmol a -1 (Baboukas et al., 2000;Khan et al., 2018).  Vet et al. (2014) and Keene et al. (2015). We find that the mean GEOS-Chem HCOOH flux (7.5 mmol m -2 a -1 ) is consistent with the mean of the observations (6.9 mmol m -2 a -1 ). The model captures the high fluxes observed in the tropical continents where there are large biogenic sources, and the low fluxes observed at marine sites. GEOS-Chem underestimates the CH3COOH flux by a factor of 4. The observed patterns of HCOOH and CH3COOH fluxes are similar, suggesting that model CH3COOH could be corrected similarly to HCOOH in future work by scaling up biogenic emission. 145

Calculation of cloud-and rainwater composition and pH
Cloudwater composition is computed locally in each grid cell containing liquid cloudwater over 30-min time steps using the in-cloud liquid water content and cloud volume fraction from MERRA-2. Dissolution of gases in the cloud droplets follows the Henry's law constants of Table 1 and acid/base dissociation constants of Table 2. We assume that 70% of fine aerosol mass and 100% of coarse aerosol mass are partitioned into cloudwater (Hegg et al., 1984;Alexander et al., 2012). Sulfate-nitrate-150 ammonium and sea salt particles dissolve completely in cloudwater, and the alkaline component of the dust particles also dissolves. Freshly emitted sea salt particles contain an alkalinity of 0.07 eq kg -1 (Alexander et al., 2005), while freshly emitted dust particles contain an alkalinity of 4.5 eq kg -1 based on the assumption of 7.1% Ca 2+ and 1.1% Mg 2+ by dry mass (Engelbrecht et al., 2016) with CO3 2as anion. Sea salt NVCs are expressed as Na + equivalents, while dust NVCs are expressed as Ca 2+ equivalents. The upper limit of Ca 2+ concentration is set by formation of CaCO3(s). 155 The calculation of cloudwater composition in the cloudy fraction of each grid cell assumes a closed system where the summed concentrations of gas and cloudwater species in Table 3 are conserved, and the partitioning is then computed following the equilibria of Tables 1 and 2. The calculation is done by solving the electroneutrality equation iteratively using Newton's method (Moch et al., 2020). This improves on the original calculation of cloudwater composition in GEOS-Chem (Alexander 160 et al., 2012) through the inclusion of additional acidic and alkaline species (HCl, HCOOH, CH3COOH, NVCs) and using a more stable numerical solver.
We will present results as time averages (mainly annual) and spatial averages (vertical or zonal is a non-conservative quantity controlled by the other acidic and basic species in cloudwater (Liljestrand, 1985). Therefore, we calculate the average cloudwater [H + ] from the corresponding volume weighted average (VWA) concentrations of the cloudwater ions. We assume that all acids and bases except carbonates are conserved in the aqueous phase. For HCOOH and CH3COOH, the total (dissociated + undissociated) amounts are assumed to be conserved. Thus, the time-and space-averaged represents the VWA molar concentration in cloudwater of species A over the time period and spatial domain of interest. We calculate [A] from the concentration of the species, [A] !,# , and the cloud liquid water content, !,# , at each model time step i and grid cell j: where Ka is the HCOOH(aq)/HCOOacid dissociation constant from Table 2 computed at the average cloudwater temperature  180 for the time period and spatial domain. The same procedure is used for [CH 0 COO * ]. [HCO 0 * ] is calculated from equilibrium with atmospheric CO2 as follows: where 45 * and 67 are the Henry's law coefficient for CO2 and the CO2(aq)/HCO3acid dissociation constant, respectively, at the average cloudwater temperature for the period and domain (Tables 1 and 2 There is some arbitrariness in assuming that NH3, SO2, and carboxylic acids do not equilibrate with the gas phase during 190 averaging. We examined the sensitivity to this assumption by assuming alternatively that NH3T, SO2T, HCOOHT and CH3COOHT as defined in Table 3 (sum of gas-phase and aqueous-phase concentrations) are conserved and recalculating the gas-cloudwater equilibrium for the time-averaged conditions. We find no significant difference in the computed [H . ].
Calculation of rainwater VWA composition including [H . ] follows the same approach as for cloudwater. In that case we use 195 the model-archived wet deposition fluxes including contributions from in-cloud and below-cloud scavenging. We assume that SO2 is instantly oxidized by H2O2 (as available) in rainwater and is scavenged as SO4 2-. As with cloudwater, the maximum where [H . ] ; is the mean rainwater [H + ] and ; is the precipitation depth for month k. Figure 2 shows the global distribution of cloudwater pH as simulated by GEOS-Chem and as measured at mountain sites, coastal sites (marine fog), and from aircraft campaigns (Table A1) The global mean cloudwater pH in the observations is 5.2 ± 0.9, compared to 5.0 ± 0.8 in the model. Annual mean values in southern Europe, about 25% of the base cations are from Saharan dust. NH4 + is the main cation elsewhere in Europe. SO4 2is the dominant acidic component over the northern midlatitude oceans because of the oceanic source of SO4 2from the oxidation of DMS and because continental influence extends further for SO4 2than for NO3 - (Heald et al., 2006). Over the Arctic, the simulated pH is much lower (4-4.5) because of long-range transport of acidic species and less than 50% neutralization (Fisher 235 et al., 2011).

Global distribution of cloudwater pH and composition 205
The carboxylate ions HCOOand CH3COOaccount for less than 25% of H + throughout the extratropical northern hemisphere (Fig. 3). The carboxylic acids are more important relative contributors to H + in the tropics and in the southern hemisphere, exceeding 50% in some areas of the tropical continents and southern midlatitudes. Ayers and Gillett (1988) found that 240 carboxylic acids were responsible for observed cloudwater pH below 4 over tropical Australia, but GEOS-Chem underestimates carboxylic acids in that region (Fig. 1). Carboxylates were not measured in the Ecuador cloudwater measurements (Makowski Giannoni et al., 2016), but we find from the model that the carboxylic acids contribute about 50% of the H + . GEOS-Chem shows similar pH values as observed at Cape Grim (mean of 5.5), reflecting the low concentrations of acidic and basic species from continental sources. Cloudwater pH sampled on the Antarctic coast also has a mean pH of 5.5 245 (Saxena and Lin, 1990) but the model is much lower over the Antarctic coast because of SO4 2from oxidation of DMS. This may be because of sea salt alkalinity from blowing snow that is not accounted for in the model .
Alkaline cloudwater (pH > 5.6) is found in the observations over western India, Tibet, and Morocco, consistent with the model where the alkalinity is mainly from dust. GEOS-Chem simulates pH of 6-8 over the area extending from the Sahara to the 250 Gobi Desert. The transport of dust alkalinity from North Africa raises the cloudwater pH in the Caribbean to above 5.5, both in the observations (Gioda et al., 2011) and in the model. Figure 4 shows the zonal mean distributions of cloudwater pH and cloud liquid water content (contour lines). In addition to the latitudinal variations described previously, cloudwater pH increases as the cloud liquid water content increases because of 255 the effect of dilution. Liquid water content peaks at about 900 hPa, and decreases at higher altitudes, and this largely explains the mean variation of pH with altitude. Pye et al. (2020) showed in their review the annual mean tropospheric-column cloudwater pH from three models: CMAQ (northern hemisphere only), TM4-ECPL, and GEOS-Chem. They calculated the annual mean pH using VWA [H + ] rather than 260 Eq. (1). We find that their calculation method underestimates the pH over alkaline regions by 1-3 units but has little error for Emissions of SO2 and NOx in the northern mid-latitude continents are decreasing rapidly because of air quality concerns (Hoesly et al., 2018;Zheng et al., 2018). Considering that NH3 and dust neutralize presently balance over 50% of the acidic anions over these continents (Fig. 3), one might expect large increases in cloudwater pH as SO2 and NOx emissions decrease.
There is however a large buffering effect from the semi-volatile carboxylic acids and NH3. Consider the case of the US. Figure  275 5 shows the mean simulated cloudwater composition for 2013 over the continental US, and the change in composition resulting from a factor of two decrease in strong acidity (SO4 2-, NO3 -). The total concentrations of carboxylic acids (RCOOHT = HCOOHT + CH3COOHT) and ammonia (NH3T) are held at 2013 levels and the gas-cloudwater equilibrium is recalculated. For 2013, the mean cloudwater pH is 4.7, a level at which only one-fourth of RCOOHT is present as carboxylate ions, and most of the NH3T is present as NH4 + . Decreasing the strong acidity by half triples the dissociated fraction of RCOOHT and volatilizes 280 a significant fraction of NH4 + , which limits the increase in cloudwater pH to 5.7. Without this buffering effect, the pH would have increased by 2.1 units to 6.8. NH4 + volatilization exerts a stronger buffering effect than carboxylic acid dissolution because NH3T concentrations are much larger. rainwater pH is 5.5 and varies from 4.5 over industrialized areas and the tropical forests to 8 over deserts, showing the same spatial patterns as cloudwater pH but with lower acidity because of dilution. Figure 7 shows the simulated concentrations of rainwater ions, except for Na + and Clwhich again do not contribute significantly to net acidity. Rainwater ion concentrations are on average 4 times more dilute than cloudwater concentrations (Fig. 3). The relative contribution of SO4 2in industrialized 290 regions is higher than for cloudwater because of additional SO4 2from below-cloud scavenging of SO2. The NO3contribution in central Africa is higher than for cloudwater because of high-altitude convective scavenging of HNO3 produced from lightning NOx. In Amazonia and tropical Africa, HCOOand CH3COOcontribute a larger fraction of rainwater acidity compared to cloudwater because of below-cloud scavenging, and as a result the rainwater pH is similar to that of cloudwater.

Global distribution of rainwater pH and composition
Similarly, below-cloud scavenging of desert-generated dust results in alkaline rainwater over a much larger area compared to 295 cloudwater.
The right panel in Fig. 6 shows the change in rainwater pH when the contribution from carboxylic acids is excluded. These acids biodegrade quickly, and thus their acidity is not generally captured by rainwater pH measurements. We find that rainwater pH increases by 0.4-1 unit in the Amazon, tropical Africa, and southeast Asia, consistent with observations (Andreae et al., 300 1990;Sanhueza et al., 1992;Sigha-Nkamdjou et al., 2003;Yoboué et al., 2005). Over the US, Europe, and eastern China the increase in pH is 0.1-0.4 units, which is similar to the observed contribution of carboxylic acids to rainwater H + (10-60%) in these areas (Keene and Galloway, 1984;Kawamura et al., 1996;Peña et al., 2002;Xu et al., 2010;Niu et al., 2018). Over the oceans, the change in pH from HCOOH and CH3COOH is small (~0.15 units) and in agreement with marine observations (Keene et al., 2015). 305 Our global distribution of rainwater pH can be compared to previous model simulations by Rodhe et al. (2002) and Tost et al. (2007). Neither included carboxylic acids and thus they overestimated pH values over tropical continents. Tost et al. (2007) did not include dust alkalinity either, resulting in large pH underestimates over desert regions. The pH values over eastern 330 North America and Europe in these previous studies are about 0.5 units lower than in our simulation, reflecting the more recent decreases in SO2 and NOx emissions (Hoesly et al., 2018).

Soil and freshwater acidification by wet deposition
Acidification of soil and freshwater is one of the major adverse effects of wet deposition fluxes on ecosystems because it causes the leaching of nutrients, mobilizes toxic metals, and directly damages biota (Driscoll et al., 2001). Quantifying this 335 effect requires accounting for post-depositional processes. The H + flux associated with carboxylates and HCO3is not relevant because carboxylic acids are readily consumed by bacteria, and the amount of HCO3in ecosystems is controlled by the ambient CO2 concentrations (Reuss and Johnson, 1986). The acidifying effects of NO3and NH4 + depend on the biotic demand for nitrogen (N) (Reuss and Johnson, 1986). In ecosystems with high N demand (so-called N-limited ecosystems), NO3and NH4 + are readily assimilated by plants and microbes. Uptake of NO3is accompanied by the uptake of H + (or release of OH -), 340 cancelling the acidic effect of NO3deposition. NH4 + uptake is accompanied by the release of H + , reversing the neutralizing effect of NH4 + . Therefore, in N-limited ecosystems the acidic flux is calculated as follows (Rodhe et al., 2002): where F denotes the wet deposition flux in equivalents. However, in many industrialized regions, N deposition greatly exceeds the biotic demand and results in N-saturated conditions (Aber et al., 1989;Watmough et al., 2005;Gundersen et al., 2006;345 Duan et al., 2016). In such conditions, only a small fraction of the deposited NO3and NH4 + is assimilated. The excess NO3causes H + accumulation, while the excess NH4 + can be converted by microbes to NO3 -(nitrification), which releases 2H + for every NH4 + converted and also results in net H + formation. Considering the full acidifying potential of NO3and NH4 + , we calculate the acidic flux in N-saturated conditions as follows (Galloway, 1995;Rodhe et al., 2002):

8) 350
H + (N-sat) can be viewed as the upper limit of acidic inputs through wet deposition as some of the accumulated NO3can denitrify to N2. Figure 9 shows H + (N-lim) and H + (N-sat) , along with the free H + flux which represents the direct acid input to ecosystems excluding carboxylic acids. The global mean H + (N-lim) over continents (4.1 meq m -2 a -1 ) is higher than the mean free H + flux 355 (3.1 meq m -2 a -1 ). The free H + flux is higher than H + (N-lim) over central Africa and Amazonia because of H + associated with NO3and HCO3 -, respectively. H + (N-lim) is highest over the eastern US, Central and South America, and East Asia, reflecting high SO4 2fluxes. The global mean H + (N-sat) over continents (18 meq m -2 a -1 ) is much larger than H + (N-lim) and the free H + flux because of acidity generated from NH4 + nitrification. Over eastern India, East and Southeast Asia, the eastern US, and Central and South America, H + (N-sat) is more than 50 meq m -2 a -1 , which exceeds the critical load for acidification of highly 360 sensitive ecosystems with low acid buffering capacity (Kuylenstierna et al., 2001;Bouwman et al., 2002).

Conclusions 370
We used the GEOS-Chem global model of atmospheric chemistry to simulate the global distributions of cloudwater and rainwater acidity, and the total acid inputs from wet deposition to terrestrial ecosystems. This involved an improved pH calculation in GEOS-Chem including contributions from dust alkalinity, sea salt aerosol alkalinity, and carboxylic acids (HCOOH and CH3COOH). Our prime motivation was to better understand and evaluate the global cloudwater pH distribution in the model for future simulations of sulfate, organic, and halogen chemistry. Extending the analysis to rainwater pH provided 375 further opportunity for model evaluation and allowed us to quantify post-depositional effects in acid inputs to ecosystems on a global scale.
We compiled cloudwater pH measurements worldwide from the literature and compared them to the GEOS-Chem simulation.
The global mean cloudwater pH is 5.2 ± 0.9 in the observations, and 5.0 ± 0.8 in GEOS-Chem sampled at the same locations. 380 The lowest pH values of 3-4 are over East Asia because of high acid inputs and despite an average 70% neutralization by NH3 and dust cations. Low pH values extend across the North Pacific because of weak neutralization. Cloudwater pH is 4-5 over the US and Europe with dominant acid input from HNO3 and over 50% neutralization from NH3. Alkaline cloudwater with pH as high as 8 is found over the northern subtropical desert belt extending from the Atlantic Ocean to Mongolia, including western India. Carboxylic acids account for less than 25% of the cloudwater H + in the northern hemisphere, but 25-50% in 385 the southern hemisphere and over 50% in the southern tropical continents where they drive the pH to below 4.5. We find little dependence of cloudwater pH on altitude other than dilution from changes in liquid water content.
Anthropogenic emissions of SO2 and NOx are decreasing rapidly in the developed world, and this together with the large fraction of neutralized acidity might be expected to lead to large increases in cloudwater pH. However, there is a strong 390 buffering effect because of the semi-volatility of NH4 + and carboxylates. We find that a factor of 2 decrease in SO4 2and NO3inputs over the US increases the cloudwater pH by 1 unit, compared to an increase of 2.1 units in the absence of buffering.

Equilibrium reactions
CaCO3(s) « Ca 2+ + CO3 2-3.3 × 10 -9 -1200 Table 3: Species included in the cloudwater pH calculation a a The calculation assumes a closed system for the cloudy fraction of the model grid cell where concentration totals (T) are conserved and are partitioned between species using the Henry's law and acid-base dissociation equilibria of Tables 1 and 2, and the local cloudwater liquid water content and temperature. b H2SO4 has sufficiently low vapor pressure to be completely in the cloudwater phase, and H2SO4(aq) and HSO4concentrations are negligible at typical cloudwater pH (> 3). c CO2(g) mixing ratio is taken to be 390 ppm as representative of 2013.   (Table A1). See Sect. 2.3 for the procedure to compute average pH in the model. White color denotes areas where the topographic elevation is higher than 700 hPa. The maximum modeled and observed pH values are 8.2 and 7.3, respectively. The bottom panel shows the observations grouped by regions (Table A1), with means ± standard deviations calculated from the ensemble of data sets for the region, and the corresponding GEOS-Chem mean values sampled at the location and month of the measurements. The global mean ± standard deviation pH values computed from the regional mean observed and modeled values are inset in the bottom panel.