Aerosol acidity and liquid water content regulate the dry deposition of inorganic reactive nitrogen

. Ecosystem productivity is strongly modulated by the atmospheric deposition of inorganic reactive nitrogen (the sum of ammonium and nitrate). The individual contributions of ammonium and nitrate vary considerably over space and time, giving rise to complex patterns of nitrogen deposition. In the absence of rain, much of this complexity is driven by the large difference between the dry deposition velocity of nitrogen-containing molecules in the gas or 25 condensed phase. Here we quantify how aerosol liquid water and acidity, through their impact on gas-to-particle partitioning, modulate the deposition velocity of total NH 3 and total HNO 3 individually, while simultaneously affecting the dry deposition of inorganic reactive nitrogen. Four regimes of deposition velocity emerge: i ) HNO 3 -fast, NH 3 -slow, ii ) HNO 3 -slow, NH 3 -fast, iii ) HNO 3 -fast, NH 3 -fast, and, iv ) HNO 3 -slow, NH 3 -slow. Conditions that favor partitioning of species 30 to the aerosol phase strongly reduce the local deposition of reactive nitrogen species and promote their accumulation in

under conditions of extreme acidity and/or low aerosol liquid water content. The dry deposition of total nitric acid, on the other hand, is quite variable, with maximum deposition velocities (close to gas-deposition rates) found in the Eastern US and minimum velocities in Northern Europe and China. In the latter case, the low deposition velocity leads to up to 10-fold increases in PM2.5 nitrate aerosol, thus contributing to the high PM2.5 levels observed during haze episodes. In this light, 5 aerosol pH and associated liquid water content can be considered as control parameters that drive dry deposition flux and can accelerate the accumulation of aerosol contributing to intense haze events throughout the globe. 10

Introduction
Human civilization and a high standard of living fundamentally depend on a sustainable food and energy supply (NAS, 2016). Both can be linked to the availability of reactive nitrogen (Nr) species in agricultural soils, which are key nutrients required by the biosphere for growth and crop production. Although fertilizers rich in Nr have ensured food security for most of the global 5 population, riverine outflow and atmospheric deposition of Nr to oceans and coastal zones has increased roughly three-fold compared to preindustrial levels (Duce et al., 2010;Kanakidou et al., 2016), with profound and diverse impacts on the Earth System (Ito et al., 2016;Jickells et al., 2017;Suntharalingam et al., 2019). Nr includes reduced nitrogen speciesthe main components of which are gas-phase ammonia (NH3) and its particulate-phase counterpart ammonium (NH4 + ). Oxidized 10 nitrogen also constitutes a significant fraction of Nr, and its deposition, being primarily in the form of nitric acid (HNO3) and particulate-phase nitrate (NO3 -) (Seinfeld and Pandis, 2016).
Reactive inorganic nitrogen species are major components of ambient particulate matter (Kanakidou et al., 2005;Sardar et al., 2005;Zhang et al., 2007), with important implications for human health (Pope et al., 2004;Lim et al., 2012;Lelieveld et al., 2015;Cohen et al., 2017), 15 ecosystem productivity (Fowler et al., 2013) and the climate system (Haywood and Boucher, 2000;Bellouin et al., 2011;IPCC, 2013). Ammonia reacts with sulfuric and nitric acids to form ammonium sulfate/bisulfate and nitrate aerosol, while gas-phase nitric acid can also react with non-volatile cations found in sea salt, mineral dust and biomass burning to form a variety of inorganic (soluble) salts. The acidity (pH) and liquid water content of aerosol in turn are central 20 parameters that govern the gas-particle partitioning of Nr species (Meskhidze et al., 2003;Guo et al., 2015;Guo et al., 2017a;Guo et al., 2018;Nenes et al., 2020). Given that species in the gas phase generally have a different atmospheric residence time than those in the aerosol phase (Seinfeld and Pandis, 2016), the degree of gas-particle partitioning can directly impact the atmospheric residence time of Nr species, with important implications for particulate matter levels 25 and dry deposition (e.g., Vayenas et al., 2005;Pinder et al., 2007Pinder et al., , 2008. It is therefore important to consider how aerosol acidity and liquid water content, through their effect on gas-to-particle partitioning, can affect the deposition fluxes of Nr species. Here we present a simple and thermodynamically consistent framework to address the links between deposition of Nr and aerosol acidity. We then demonstrate the power of this new framework with observational data to 30 understand the relevant "chemical regimes" that apply to select places around the world, and to understand the implications that changes in acidity have on deposition flux and PM levels. Nenes et al. (2020), based on the work of Meskhidze et al. (2003), Guo et al. (2016) and Guo et al. (2017a) developed a framework, where the sensitivity of PM to concentrations of 5 ammonia and nitrate is expressed in terms of aerosol pH and liquid water content. The basis of this approach lies in the realization that the magnitude of PM sensitivity to precursor emissions is driven by gas-to-particle partitioning, the latter of which is controlled by aerosol acidity and liquid water content. Given that the deposition velocity of ammonia and nitrate also is strongly modulated by the same partitioning, it should show similar sensitivity to the pH and liquid water content. 10

Linking deposition flux with partitioning fraction
For a given air mass with total nitrate NO3 T (i.e., the amount of aerosol and gas-phase nitrate), the equilibrium aerosol nitrate concentration, 3 − , is given by where (NO 3 − ) is the fraction of NO3 T that partitions to the particle phase. The deposition flux of NO3 T , 3 , is then given by the contribution from the gas and particle phases (Seinfeld and Pandis, 15 2016): where 3 has units of moles N per unit area and time, , are the gas-and particulate-phase deposition velocities, respectively and = / (of order 10 for NH 3 T and NO3 T ; Duyzer, 1994;Seinfeld and Pandis, 2016).
Similarly, equilibrium partitioning of NH 3 T to the aerosol is given by NH 4 + = (NH 4 + ) NH 3 T , 20 where (NH 4 + ) is the fraction of NH 3 T (i.e., the amount of aerosol ammonium and gas-phase ammonia) that partitions to the particle phase: where

The acidity and liquid water content link: deposition velocity "regimes"
From equations (1) and (2), it becomes apparent that the (NH 4 + ) and (NO 3 − ) are modulators of the deposition fluxes. Depending on their value, both 3 and 3 vary by a factor of 10 with the highest values corresponding to partitioning fractions close to zero. Through their effects on gas-particle partitioning, aerosol acidity and liquid water content can impact the 5 deposition flux, which we quantify as follows.
The partitioning fractions can be expressed as functions of the liquid water content, Wi: where Ψ = Equations (3) yields "sigmoidal" functions, with the partitioning fraction ranging from zero to unity over a characteristic pH range. The same equation can then be used to define a "characteristic 10 pH" that determines when the deposition of ammonia or nitrate is "fast" (i.e., effective deposition velocity approaching that of the gas phase) or "slow" (i.e., approaching the particle-phase deposition velocity). Following Nenes et al. (2020), we define characteristic thresholds being α for (NO 3 − ) and β for (NH 4 + ), which separate the corresponding deposition velocity regimes ( Figure   1). When (NO 3 − ) is below α (or (NH 4 + ) is below β), a sufficient amount of NO 3 T (or NH 3 T ) is in 15 the gas phase so that the effective deposition velocity is approximately equal to the gas-phase limit ("fast" for NO3 T or NH3 T , respectively). The transition between "fast" and "slow" velocity can occur over a range of ε, but α=β=0.9 is selected to define the thresholds so that in the map areas with slow-fast pairs (slow NH3/Fast HNO3 and vice-versa) deposition conditions most closely approach the gas-particle deposition velocity limits. Equations (5) and (6)  Based on the values of ′ , " and its relation to the aerosol pH, we can then determine whether the deposition NO 3 T (or NH 3 T ) is "slow" or "fast"; Nr deposition can belong to one of four 25 distinct chemical regimes: • Regime 1: pH > " and pH < ′ : "NH3 fast, HNO3 fast". • Regime 2: pH > " and pH > ′ : "NH3 fast, HNO3 slow".
• Regime 4: pH< " and pH < ′ : "NH3 slow, HNO3 fast". Figure 2 indicates these four regions. Observation or modeling data, based on their value of acidity 5 and liquid water, will belong to one of these four "chemical regimes" of deposition velocity for NH 3 T and/or NO 3 T .
Following Nenes et al. (2020), the characteristic point (defined by a characteristic acidity * and liquid water content * ) on the chemical regime map where the two lines "crossover", thus separating Regime 1 from Regime 3, and Regime 2 from Regime 4 corresponds to a * = 10 − 1 2 ( Ψ Φ ) ~2.2, and * ~ 300 μg m -3 for 298K. Therefore, for moderately acidic aerosol (pH*~2) and sufficiently high amounts of waterthe aerosol levels can considerably increase because the deposition velocity changes by about 10-fold for both NH 3 T and NO 3 T . For higher (or lower) pH levels, the aerosol transitions between regions 2 (or 4). For liquid water above * , there is a "transition pH" from a NH3-slow, HNO3-fast deposition scheme to a NH3-fast, HNO3-slow 15 deposition rates (Fig. 2). Similarly, there is also another "transition pH" that defines when both NH 3 T and NO 3 T change from "fast" to "slow" deposition. Given the combined complexity of deposition velocity and aerosol thermodynamics, it is remarkable that deposition velocity patterns for NH 3 T and NO 3 T can be unraveled simply using pH and liquid water. This is illustrated in the following section. 20

Application of the framework
The above framework requires knowledge of aerosol pH and liquid water content, which can be routinely simulated by state-of-the-art atmospheric chemical transport models (e.g., CMAQ, CAMx). Thermodynamic analysis of ambient aerosol and gas-phase measurements also provides aerosol pH and liquid water content. Therefore, the above framework can be used to characterize 25 the chemical domain of both ambient and simulated aerosol.
Application of the chemical domain approach is demonstrated for ambient data representing select locations over the world. For this purpose, we use the same datasets as in Nenes et al. (2020), which were obtained from observations over 5 locations worldwide: Cabauw, Netherlands (CBW), Tianjin, China (TJN), California, USA (CNX), SE US (SAS), and a wintertime NE USA (WIN) study. This dataset covers a wide range of atmospheric acidity, temperature, relative humidity and liquid water levels. Figure 3 presents the chemical domain classifications for each location, with characteristic curves being calculated from the average temperature of the dataset. Cabauw is characterized by high deposition velocity for NH 3 T , while 5 NO 3 T alternates between fast and slow deposition, with most of the time being in the slow deposition regime (Figure 3a). The California dataset (Figure 3b) is quite interesting, as both NH 3 T and NO 3 T deposit rapidly, which means that they are less subject to long-range transport and are rapidly lost from the boundary layer. Tianjin displays similar behavior to Cabauw (Figure 3c). The Southeast US (SAS) is considerably more acidic; for this reason, NH 3 T exhibits variability in its 10 deposition velocity (alternating between slow and fast), while NO 3 T always maintains a high deposition velocity. The wintertime eastern US dataset (WIN) corresponds to a broad region (aircraft data set), hence the data naturally occupies multiple domains. There are no locations in this dataset characterized by low deposition velocities for both NH 3 T and NO 3 T .

Implications for deposition flux of Nr at selection locations worldwide 15
To understand the implications of acidity and liquid variations on the reactive nitrogen flux (moles m -2 s -1 ), we first sum the contributions from NO3 T and NH3 T . Summing Equations 1 and 2 yields the reactive nitrogen flux, , expressed as mols N per area and unit time: T (fraction of Nr that is NH 3 T ) and substituting into Equation 4 gives: Further dividing Equation (5) with N gives the non-dimensional Nr flux, * : (6) * expresses how rapid is, compared to if the flux of Nr occurred with the particle deposition velocity. Equation 6 embodies the effect of acidity and liquid water content (through their effect on (NH 4 + ), and (NO 3 − )) on the Nr deposition velocity and flux. * ranges between 1 and k; when it is equal to k, deposition is most efficient and occurs with the gas-phase deposition velocity for both NO 3 T and NH 3 T (Regime 1). Under such conditions, reactive nitrogen is rapidly lost from 5 the atmosphere. When * is unity, all the reactive nitrogen is in particulate form and the dry deposition is at its slowest possible rate (Regime 4)allowing its transport over larger distances and resulting in an increase of its lifetime in the boundary layer (considering only dry removal) by a factor of k.
We apply Equation 6 on observations that span a wide range of atmospheric acidity and 10 liquid water content, to explore the degree to which atmospheric acidity can modulate * . The observations analyzed (Table 1) are for characteristic conditions found in the US, Europe and China (refer to the Table caption for more information on the data). US and European sites cited tend to be more acidic than the Asian sites (although Cabauw, clearly is similar to the latter, Figure   3a). To understand the deposition rate trends, we first examine the patterns for ammonia and nitrate 15 separately, and then the combined Nr flux.
For ammonia, given that the pH is mostly above 1 (Table 1) Greece, and ~1 for the Asian sites. The immediate implication for its deposition patterns is that at the more acidic sites, NO 3 T remains close to the production region, while for less acidic conditions it can be transported away with a 10-fold increase in its boundary layer lifetime.
To understand the impact of both NH 3 T and NO 3 T pattern variability on the deposition flux of total reactive nitrogen, we first note that NH 3 T constitutes the majority of the Nr in all sites considered (i.e., Γ~0.5-0.96; Table 1). Given this, and considering that the acidity levels usually do not approach low enough levels to ensure that (NH 4 + ) → 1 (Figure 3a), does not substantially vary from location to location, and, it closely follows that of NH3 (Figure 4b). 5 Because of the opposite trends of normalized deposition flux between NH 3 T .and NO 3 T (Figure 4b), the shifts in ammonia deposition flux are partially mitigated when included in * . The implication is that, although nitrate exhibits large variability in dry deposition flux rate, ammonia should exhibit less variabilityand therefore total reactive nitrogen should also have lower variability. 10

Implications of modified deposition flux for boundary-layer PM2.5 levels
The immediate consequence of modulating deposition velocities is that the atmospheric residence time of aerosol precursors is changed. When the deposition velocity of Nr species is low, then the precursor is given an opportunity to accumulatewhen it also corresponds to a compound 15 that PM2.5 levels are sensitive to, aerosol levels can increase considerably. Based on the discussion in Section 4, aerosol nitrate accumulates (i.e., "slow deposition"), exactly when aerosol is most sensitive to changes in its concentration. To illustrate this effect, we estimate how the concentration of aerosol nitrate and ammonium would change in response to changes in deposition velocity. Following the approach of Weber et al. (2016), the steady-state boundary layer 20 concentration of nitrate can be written as: where h is the height of the boundary layer, E is the emission rate including transport from outside the boundary layer, and P is the photochemical production rate. Assuming that partitioning of total nitrate changes from a value (NO 3 − ) (1) to (NO 3 − ) (2) , the steady-state NO 3 T (with all other factors being equal) changes according to: 25 Equation 8 suggests that if the pH (through its impact on (NO 3 − )) varies sufficiently, the change in total nitrate in the boundary layer will approach a factor of k~10 (Figure 4a). Assuming that this occurs, we can then show PM would drop considerably in regions where nitrate constitutes a significant fraction of PM levels (Figure 4a, difference between solid lines and dotted lines).
Given that aerosol nitrate is often a significant constituent of PM in regions where the aerosol 5 exhibits a mildly acidic pH (e.g., Cabauw, China), this constitutes an important and overlooked positive feedback (i.e., one that magnifies the response in particle mass or deposition rates) between acidity, nitric acid production, ammonium and PM buildup that is a consequence of aerosol thermodynamic partitioning and deposition velocity. These processes are summarized in Figure 5. A time varying mixing layer, along with storage of both NH 3 T and NO 3 T aloft, complicate 10 the dynamics, but the implications are the same: pH and liquid water content are integral to the deposition of reactive nitrogen.

Conclusions
Here we present a simple framework to understand how aerosol acidity and liquid water 15 content can modulate the dry deposition flux of inorganic reactive nitrogen species, and assessment of factors that cause variability in Nr deposition and the implications. Our analysis identifies four deposition velocity regimes: i) HNO3-fast, NH3-slow, ii) HNO3-slow, NH3-fast, iii) HNO3-fast, NH3-fast, and, iv) HNO3-slow, NH3-slow. When this framework is applied to ambient measurements or predictions of PM and gaseous precursors, the "chemical regime" of deposition 20 velocity is directly determined. Generally, conditions that favor strong partitioning of species to the aerosol phase strongly impact the deposition flux of Nr species and their potential for longrange transport. Applying this framework to select locations around the world reveals important implications: i) ammonia deposition rates display little sensitivity to pH and liquid water variations, except under conditions of extreme acidity or aerosol liquid water content, ii) for the examples 25 considered dry deposition of total Nr is 50-85% (by mol) total ammonia, which means that modest modulations of Nr flux are seen from acidity changes. There are regions, however, (e.g., coastal areas, dust) where total nitrate may constitute a much larger fraction of the Nrand for which acidity would drive fluctuations thereof. Total nitrate deposition flux is close to the maximum levels (approximately equal to the corresponding gas-deposition rates) in the Eastern US and has minimum rates for North Europe and China. When the latter occurs, the low deposition velocity can promote considerable accumulation of nitrate aerosol in the boundary layerincreasing up to 10-fold the PM2.5 nitrate, eventually causing the extremely high levels observed. If liquid water 5 content is high enough (e.g., close to fog conditions) both total ammonia and nitrate deposit slowly and are allowed to accumulate, which create the potential for the most intense haze episodes.
Nighttime conditions tend to be characterized by lower temperatures and higher humidityboth of which favor partitioning to the aerosol phase, which slows down deposition for both types of reduced nitrogen. This diurnal-deposition cycle exacerbates the daytime-nighttime contrast in 10 boundary layer aerosol concentration.
The above also point to the effect that model prediction biases in pH could have when it comes to prediction of reactive nitrogen deposition fluxes and PM levels in the boundary layer.
For example, in the case of PM2.5 nitrate, not only the aerosol levels will be directly affected owing to partitioning ratio biases (Vasilakos et al., 2018) but too much accumulation (if pH is predicted 15 too high) or accelerated loss (if pH is predicted too low) may magnify nitrate prediction biases through the discussed feedback from deposition velocity. A similar situation can also arise for aerosol ammonium, only that the trends of bias with respect to pH are reversed. Identical biases also can arise for semi-volatile species that are sensitive to aerosol pH, such as chloride, amines and organic acids. 20 Although ammonium almost exclusively resides in the fine modewhere the equilibrium analysis carried out here is most applicable -nitrate can also reside partially in the coarse mode in the presence of dust and/or sea salt particles (e.g., Karydis et al., 2016) because the latter tend to have a high enough pH to favor partitioning (Vasilakos et al., 2018;Fang et al., 2017). The same principle and trends also apply in such situations, as acidity and liquid water content drive gas-to-25 aerosol partitioning and modulate the deposition velocity (the analysis can also be extended to separately consider coarse and fine mode particles), though larger particles have a higher deposition velocity than submicron particles. The effect of organic aerosol and its associated liquid water content may also affect the partitioning, although such effects are most likely limited to low relative humidity (below 40%) and temperatures low enough for strong diffusivity limitations to 30 limit the applicability of equilibrium considerations (Battaglia Jr. et al., 2019;Pye et al., 2020).
The "fast" region at higher temperatures suggests that deposition would be slower and long-range transport becomes more prevalent in winter. Furthermore, nitrate forms largely from oxidation of NOx emissions; nonlinearities in gas-phase oxidation complicate the relationship between the thermodynamic framework and precursor emissions. Despite these limitations, the new understanding presented here applies throughout most of the atmosphere close to the surface 5 demonstrating that aerosol pH and its associated liquid water content naturally emerge as parameters that drive dry deposition flux and atmospheric lifetime of reactive nitrogen, and can initiate feedbacks that promote heavy PM2.5 pollution episodes.

Code and Data availability
User access to data used in this manuscript is described in the citations referenced for each 25 dataset, and can also be accessed from the compiled dataset of Pye et al. (2019). The ISORROPIA-II thermodynamic equilibrium code is available at isorropia.epfl.ch. Relevant spreadsheets and mapping templates are provided upon request. Table 1. Aerosol composition and meteorological conditions for flux deposition calculations, and aerosol composition changes from modifications to the deposition velocity. The reported aerosol precursor concentrations, LWC and RH, T are obtained from table S1 of Guo et al., (2017b) but original references from which the data was obtained is also shown in row 6. Data for Finokalia,Greece was obtained from Bougiatioti et al., (2016), assuming that the Total NO3is 5 equal to the aerosol nitrate, and Total NH4 + is equal to the aerosol ammonium (0.81μg m -3 ) plus 0.5μg m -3 gas-phase NH3.The data in rows 7-17 are input to ISORROPIA-II (metastable, forward) and the output is then presented in rows 17-21. This data and the equations presented in the text is utilized to compute the quantities remaining rows (22-29).
Guo et al.,   Particle phase fraction of total nitrate, ε(NO3 -) (blue curve) and total ammonium, ε(NH4 + ) (red curve) versus pH for a temperature of 288 K and an aerosol liquid water content of (a) 10 g m -3 , and, (b) 250 g m -3 . A combination of moderate acidity and low liquid water content creates conditions for rapid dry deposition of both total ammonium and nitrate (panel a) and vice versa for 5 moderate acidity and high liquid water content (panel b). In defining the sensitivity domains, we have assumed that a partitioning fraction of 90% (black dotted lines), and its corresponding "characteristic" pH, defines where the aerosol deposition velocity dominates the total dry deposition rate of each nitrogen-containing species.    ammonium and nitrate (a) aerosol pH is low and LWC is moderate, as is characteristic of the SE US. Here the partitioning of ammonium is mostly in the aerosol phase, and the relevant dry deposition velocity is low. The concentration of total ammonium is dictated by the aerosol deposition velocity limit; ammonia export to the free troposphere is favored, and vice versa for total nitrate. (b) aerosol pH is high and LWC is moderate (as is characteristic of N.Europe in the 25 winter and China). Here the partitioning of total ammonia is shifted to the gas phase, and the relevant dry deposition velocity is rapid, total ammonia does not accumulate considerably in the boundary layer and export to the free troposphere is minimal. Nitrate partitions to the aerosol phase, desposits slowly and accumulates rapidly in the boundary layer. These conditions favor haze events and export to the free troposphere.