Effects of aerosol dynamics and gas–particle conversion on dry deposition of inorganic reactive nitrogen in a temperate forest

Dry deposition has an impact on nitrogen status in forest environments. However, the mechanism for the high dry-deposition rates of fine nitrate particles (NO−3 ) observed in forests remains unknown and is thus a potential source of error in chemical transport models (CTMs). Here, we modified and applied a multilayer land surface model coupled with dry-deposition and aerosol dynamic processes for a temperate mixed forest in Japan. This represents the first application of such a model to ammonium nitrate (NH4NO3) gas–particle conversion (gpc) and the aerosol water uptake of reactive nitrogen compounds. Thermodynamics, kinetics, and dry deposition for mixed inorganic particles are modeled by a triple-moment modal method. Data for inorganic mass and size-resolved total number concentrations measured by a filter pack and electrical low-pressure impactor in autumn were used for model inputs and subsequent numerical analysis. The model successfully reproduces turbulent fluxes observed above the canopy and vertical micrometeorological profiles noted in our previous studies. The sensitivity tests with and without gpc demonstrated clear changes in the inorganic mass and size-resolved total number concentrations within the canopy. The results also revealed that within-canopy evaporation of NH4NO3 under dry conditions significantly enhances the deposition flux of fine-NO−3 and fine-NH+4 particles, while reducing the deposition flux of nitric acid gas (HNO3). As a result of the evaporation of particulate NH4NO3, the calculated daytime mass flux of fine NO−3 over the canopy was 15 times higher in the scenario of “gpc” than in the scenario of “no gpc”. This increase caused high contributions from particle deposition flux (NO−3 and NH + 4 ) to total nitrogen flux over the forest ecosystem (∼ 39 %), although the contribution of NH3 was still considerable. A dry-deposition scheme coupled with aerosol dynamics may be required to improve the predictive accuracy of chemical transport models for the surface concentration of inorganic reactive nitrogen.

Abstract. Dry deposition has an impact on nitrogen status in forest environments. However, the mechanism for the high dry-deposition rates of fine nitrate particles (NO − 3 ) observed in forests remains unknown and is thus a potential source of error in chemical transport models (CTMs). Here, we modified and applied a multilayer land surface model coupled with dry-deposition and aerosol dynamic processes for a temperate mixed forest in Japan. This represents the first application of such a model to ammonium nitrate (NH 4 NO 3 ) gas-particle conversion (gpc) and the aerosol water uptake of reactive nitrogen compounds. Thermodynamics, kinetics, and dry deposition for mixed inorganic particles are modeled by a triple-moment modal method. Data for inorganic mass and size-resolved total number concentrations measured by a filter pack and electrical low-pressure impactor in autumn were used for model inputs and subsequent numerical analysis. The model successfully reproduces turbulent fluxes observed above the canopy and vertical micrometeorological profiles noted in our previous studies. The sensitivity tests with and without gpc demonstrated clear changes in the inorganic mass and size-resolved total number concentrations within the canopy. The results also revealed that within-canopy evaporation of NH 4 NO 3 under dry conditions significantly enhances the deposition flux of fine-NO − 3 and fine-NH + 4 particles, while reducing the deposition flux of nitric acid gas (HNO 3 ). As a result of the evaporation of particulate NH 4 NO 3 , the calculated daytime mass flux of fine NO − 3 over the canopy was 15 times higher in the scenario of "gpc" than in the scenario of "no gpc". This increase caused high contributions from particle deposition flux (NO − 3 and NH + 4 ) to total nitrogen flux over the forest ecosystem (∼ 39 %), although the contribution of NH 3 was still considerable. A dry-deposition scheme coupled with aerosol dynamics may be required to improve the predictive accuracy of chemical transport models for the surface concentration of inorganic reactive nitrogen. et al., 2019). Provided that physical deposition processes are dominant, the deposition velocities of SO 2− 4 and NO − 3 particles are expected to be similar because both species exist in the same submicrometer size range (e.g., Wolff et al., 2011). However, Sakamoto et al. (2018) observed a deposition velocity of NO − 3 as high as those of HNO 3 in temperate mixed forests, when using the relaxed eddy accumulation method . Nakahara et al. (2019) also observed a higher concentration gradient of fine NO − 3 than of fine SO 2− 4 in cool-temperate forests using a thermodynamic equilibrium model to explain this difference via the evaporation of NH 4 NO 3 particles in the NH 4 NO 3 -NH 3 -HNO 3 triad within the canopy. Numerical chemical transport models (CTMs) for eastern Asia have also demonstrated that models can overestimate the total (gas and particle) nitrate concentrations present in many locations (Kajino et al., 2013;Shimadera et al., 2018;Morino et al., 2015;Sakurai et al., 2015). Despite many uncertain factors (e.g., emission inventory, grid resolution, chemical and physical dynamics, and deposition modules), Shimadera et al. (2014) demonstrated that the surface concentration of total nitrate could be reproduced by increasing the dry-deposition velocity of HNO 3 by a factor of 20 with respect to previous studies. Hence, the deposition velocity of NO − 3 in fine particles and/or HNO 3 are among the major uncertainties in the CTMs.
Modeling studies for dry deposition have demonstrated the importance of the volatilization of NH 4 NO 3 during the dry deposition of gaseous and particulate nitrates (Brost et al., 1988;van Oss et al., 1998;Kramm and Dlugi, 1994), although the process itself has been known in the atmosphericchemistry community for some time (Seinfeld and Pandis, 2006). Such modeling studies used the "big-leaf" concept to represent the forest canopy under steady-state and thermodynamic-equilibrium assumptions, with chemical reaction rates provided by observational data.  developed a more sophisticated model through the introduction of chemical timescales for a size-resolved particle and showed that the thermodynamic gas-particle conversion of NH 4 NO 3 (hereafter referred to as gpc) may explain the bidirectional fluxes observed above a Dutch heathland. However, several uncertainties remained in their modeled results, largely due to uncertainties in empirical treatments of particle deposition and thermodynamic processes and the assumption that gas concentrations are in equilibrium with the pure NH 4 NO 3 particle phase . Meanwhile, the equilibration of aerosols with surrounding liquid water is also important in determining their thermodynamic equilibrium (e.g., Fountoukis and Nenes, 2007). An accurate evaluation of the impact of NH 4 NO 3 -NH 3 -HNO 3 conversion within the canopy requires a processbased model that includes the thermodynamics of mixed inorganic aerosols linked to gas-phase chemistry, while ensuring that no equilibrium assumption is required (Nemitz, 2015).
We here propose a new multilayer land surface model coupled with dry deposition and aerosol dynamics (thermodynamics and kinetics of mixed inorganic aerosols) for forest environments. In aerosol dynamics modeling, the moment method is used to reduce computational costs and incorporates general processes, such as condensation, coagulation, below-cloud scavenging (e.g., Binkowski and Shankar, 1995), and dry deposition (Bae et al., 2009). These processes are implemented into a multilayer atmosphere-SOiL-VEGetation model (SOLVEG) including particle and fog droplet deposition and hygroscopic particle growth processes (Katata et al., 2014). We apply the model to a Japanese mixed forest for calibration and validation. Finally, we use numerical experiments to examine the impacts of two key processes on dry-deposition flux over the canopy: gas-particle conversion of inorganic nitrogen compounds and hygroscopic growth.
2 Model description

Model overview
A one-dimensional multilayer SOLVEG model consists of four submodels: atmosphere, soil, vegetation, and radiation within the vegetation canopy. A general description of gas and particle transport and dry deposition is given in Katata and Ota (2017). In the atmosphere submodel, onedimensional diffusion equations are solved between atmospheric layers for the horizontal wind speed, potential temperature, specific (relative) humidity, liquid water content of fog, turbulent kinetic energy and length scale (Katata, 2009), and gas and particle concentrations (Katata and Ota, 2017). Observational data are used to determine the upper boundary conditions. Bulk transfer equations are applied at the lowest layer using soil surface temperatures and specific humidity calculated by the soil submodel.
In the soil submodel, soil temperature, volumetric soil water content, and soil pore specific humidity are predicted from heat conduction, mass balance in liquid water, and water vapor diffusion equations, respectively (Katata, 2009). Root water uptake is calculated from the transpiration rate in the vegetation submodel. Mass conservation equations for the liquid and gas phases are solved to determine soil CO 2 (Nagai, 2004). Organic-matter dynamics are also considered (Ota et al., 2013): microbial decomposition and dissolved organic-carbon (DOC) leaching in the above-ground litter layer, the below-ground input of carbon from roots (root litter), and soil organic-carbon (SOC) turnover and DOC transport along water flows throughout the soil profile are determined for three SOC pools (active, slow, and passive) with different turnover times.
In the vegetation submodel, profiles for leaf temperature, leaf surface water, and vertical liquid water flux are predicted (Nagai, 2004). The heat budget equation at the leaf surface uses key variables from the atmosphere submodel combined with the radiation scheme to predict leaf temperature. At the upper boundary of the submodel, a given precipitation intensity is used to calculate the vertical liquid water flux within the canopy based on the surface water budget equation. The CO 2 assimilation rate due to photosynthesis is predicted using Farquhar's formulations (Farquhar et al., 1980) together with stomatal resistance. In the radiation submodel, direct and diffuse downward and upward fluxes of solar and longwave radiation are calculated to determine the radiation energy input at each canopy layer. Fractions of sunlit and shaded leaves at each canopy layer are used to calculate stomatal resistance and the total energy budget.
A multilayer snow module is unique in its ability to include the gravitational and capillary liquid water flows in the unsaturated snow layer based on van Genuchten's concept of water flow in the unsaturated zone (cf. Hirashima et al., 2010;Katata et al., 2020). In the soil module, freeze-thaw processes based on the freezing-point depression equation are considered in equations of heat conduction and liquid water flow. Winter-related processes for grassland phenology, such as leaf development and senescence due to cold stresses, are also implemented in the vegetation submodel. Carbon gain, both from photosynthesis and remobilized reserves, is allocated to sinks according to changing sink priorities and strengths. Sink strengths are calculated based on the dynamics of leaves and stems and their acclimation to low temperatures. The removal of tillers and leaves by cutting can also be simulated during the growing season, as can subsequent regrowth of the sward. The regrowth rate after cutting is calculated at each phenological stage. The natural turnover of leaves and roots is modeled using typical life spans in years. Rooting depth and the fraction of roots in soil layers are modeled as functions of root biomass. The daily amount of dead root biomass (root litter) is used as the input to SOC in SOLVEG's soil submodel.

Dry deposition
Since full descriptions for the dry-deposition process of gases and particles are available in Katata et al. (2013Katata et al. ( , 2014 and Katata and Ota (2017), this subsection presents only the key equations.
Using compensation points for trace gases in the substomatal cavity, χ s (nmol m −3 ), and above the leaf water surface, χ d (nmol m −3 ), we model bidirectional gas exchange fluxes with stomata, F gs (nmol m −2 s −1 ), and with leaf water surfaces, F gd (nmol m −2 s −1 ), for each canopy layer following the approach presented in Katata et al. (2013): where a is the leaf area density (m 2 m −3 ), D gas and D w are the diffusivities (m 2 s −1 ) of trace gas and water vapor, respectively, r b , r s , and r d are the resistances (s m −1 ) for the leaf boundary layer, stomata, and evaporation (cuticular), χ a is the ambient gas concentration (nmol m −3 ) in the canopy layer, and R = (r b r s + r b r d + r s r d ). The total gas exchange flux over the leaves can be calculated as the sum of F gs and F gd for all canopy layers. In accordance with a number of observations (e.g., Huebert and Robert, 1985), all χ s , r d , and r s values are set to zero for highly reactive and water-soluble gas species of HNO 3 and HCl; i.e., we assume perfect absorption by plant canopies. For both species, parameterization specific to a deciduous forest by Meyers et al. (1989) is used to calculate r b . For NH 3 , χ s is calculated based on the thermodynamic equilibrium between NH 3 in the liquid and gas phases (Nemitz et al., 2000;Sutton et al., 1994) as follows: where T c is the canopy temperature ( • C) and s is the stomatal emission potential (also known as the apoplastic ratio) at 1013 hPa . NH 3 concentrations in leaf surface water (χ d ) are calculated by assuming Henry's law and dissociation equilibria with atmospheric concentrations of NH 3 at each canopy layer. To calculate the exchange flux of SO 2 and NH 3 over the wet canopy, an empirical formula for r d is applied (Massad et al., 2010) as follows: where b is the constant, RH is the relative humidity (%), and AR is the ratio of total acid/NH 3 , represented as (2[SO 2 ] in each atmospheric layer. The value of AR is determined from the gaseous inorganic concentration. Since the affinity (such as solubility in water) of SO 2 at the leaf surface is approximately twice that of NH 3 ( van Hove et al., 1989), a half value of r d calculated by Eq. (4) is applied to SO 2 deposition. The RH value could be affected by leaf surface water content at each canopy layer as a function of water balance due to the leaf surface water evaporation, interception of precipitation by leaves, capture of fog water by leaves, and drip from leaves (Katata et al., 2008(Katata et al., , 2013). Since our model is not a dynamic modeling approach (e.g., Sutton et al., 1998;Flechard et al., 1999), uncertainties in Eq. (4) could affect the simulation of the charging and discharging of NH 3 in the cuticle due to the wet canopy being in equilibrium with non-zero leaf surface concentrations of NH 3 .

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G. Katata et al.: Aerosol dynamics and gas-particle conversion in dry deposition The gas exchange flux over the ground F g0 (nmol m −2 s −1 ) was described with compensation points at the ground χ g (nmol m −3 ) as follows: T s0 exp 10 378 where c H 0 is the surface exchange coefficient for heat, |u r | and χ a0 are the horizontal wind speed (m s −1 ) and gas concentration at the bottom of the atmospheric layer (nmol m −3 ), respectively, T s0 is the soil surface temperature ( • C), and g is the ground level emission potential for NH 3 at 1013 hPa. As explained in Katata et al. (2014), the particle deposition rate of each inorganic species in each canopy layer, F p (µg m −2 s −1 or no. m −2 s −1 ), is represented as follows: where E p is the particle capture by leaves (µg m −3 s −1 or no. m −3 s −1 ) and ε is the total particle capture efficiency by leaves as a result of inertial impaction (Peters and Eiden, 1992), gravitational settling, Brownian diffusion (Kirsch and Fuchs, 1968), and interception (Fuchs, 1964;Petroff et al., 2009). F f is the shielding coefficient for particles in the horizontal direction, |u| is the horizontal wind speed (m s −1 ) at each canopy layer, and c p is the particle mass or number concentration (µg m −3 or no. m −3 ). E p , ε, and c p are integration values of given size bins with particle diameters (D p ; µm).

Aerosol dynamics
In order to simulate changes in particle size due to condensation, evaporation, and water uptake, a triple-moment modal method (Kajino et al., 2012) is employed at each atmospheric layer in SOLVEG. Particles are grouped into fine (accumulation) and Aitken modes with size distributions prescribed by a lognormal function; the coarse mode is not considered in the simulation. The lognormal function is identified by three parameters: number concentration (N; no. m −3 ), geometric mean diameter (D g ; µm), and geometric standard deviation (σ g ). The triple-moment method predicts spatiotemporal changes in three moments (k) in order to identify changes in the shape of the lognormal size distribution of each mode.
The selected three moments are 0th, 2nd, and 3rd (M 0 , M 2 , and M 3 ), which are respectively number (N), surface area (m 2 m −3 ), and volume concentrations (m 3 m −3 ). D g values for each moment are named D g0 , D g2 , and D g3 . The relationships of the above lognormal parameters with the three moments for each atmospheric layer are as follows: Particle growth is dynamically solved following the method of Kajino et al. (2012). Gas-to-particle mass transfer is driven by the difference between the current state and the thermodynamic equilibrium state, as simulated by the ISORROPIA2 model (Fountoukis and Nenes, 2007) for semivolatile inorganic components such as NO − 3 , NH + 4 , Cl − , and liquid water (H 2 O). The gas-phase chemical production of HNO 3 could further affect simulated HNO 3 concentration and flux, and this parameter should therefore be implemented to this model in the future. In the present, the gas-particle conversion of organics is not considered because the required observational speciation data were not available. Thus, both organics and other components of the total mass were assumed to be hydrophobic aerosols in the present simulation. Since the current study focuses on mass gain or loss specific to accumulation mode aerosols, coagulation processes are also not included. Brownian coagulation, while critically important for predicting the number concentration of Aitken mode particles, is not important in the prediction of accumulation mode particle mass (e.g., Kajino et al., 2013).

Study site and observational data
We used measurements from an observation tower in a mixed forest, namely the Field Museum Tamakyuryo (FM Tama) of the Tokyo University of Agriculture and Technology, located in a western suburb of Tokyo, Japan (35 • 38 N, 139 • 23 E). Deciduous trees (Quercus spp.) are dominant around the meteorological tower together with Japanese cedar trees (Cryptomeria japonica). The canopy height around the tower is approximately 20 m. The growth period of deciduous trees is typically from April to December. Further detailed descriptions of this site are provided by Matsuda et al. (2015) and Yamazaki et al. (2015).
Simulations were carried out over two experimental periods: the first in early autumn (26 September to 11 October 2016) and the second in late autumn (7 November to 7 December 2016). In the early-autumn period, daytime (08:00-17:00 local time) and nighttime (17:00-08:00 local time) mean concentrations of inorganic gases were available at five heights (1,8,16,23, and 30 m), with fine-particle mass concentrations observed using a four-stage filter-pack sampling system. System specifications were identical to those used in Nakahara et al. (2019), except for the particle filter material. This study used a glass fiber filter coated with Teflon for collecting fine and coarse particles. For the earlyautumn period, filter-pack sampling was continuously performed during the day and night except during periods of rain. As a result, five daytime reading datasets and six nighttime reading datasets were collected. The gaps between data in rain days of the early-autumn period were linearly interpolated for simulations. Since this interpolation could cause unrealistic effects on the results, we used only the calculations and measurements in the periods of no rain for comparisons of inorganic mass concentration. For the late-autumn period, the time resolution was relatively low, as weekly continuous measurements were used. After the samples were collected, inorganic ions in each filter were extracted into deionized water by ultrasonic extraction and then analyzed using ion chromatography (Dionex ICS-1100, Thermo Scientific).
In the late-autumn period, measurements of particle number concentrations were taken during the daytime (10:00-16:00) for 7 d without rainfall. Airborne particle number concentrations were measured by an electrical low-pressure impactor (ELPI+, Dekati Ltd.). This involves sampled particles being charged by corona discharge and later separated by size using the principle of inertial classification through a 13-stage cascade low-pressure (40 hPa) impactor combined with a backup filter stage. During collection, charged particles produce a current proportional to their respective number concentrations. The broad particle size distribution measured by the ELPI+ ranges from 6 nm to 10 µm. More details on the ELPI+ system used are provided in Järvinen et al. (2014). The ELPI+ particle sample inlets were placed at heights of 30, 23, 17, 8, and 1 m at the tower through Tygon intake tubing with an inner diameter of 7.94 mm and respective lengths of 6, 5, 10, 20, and 25 m. Each sampling line for the five measuring heights was manually switched every 2 min. The transit times for particle samples in the tubing at each height ranged between 2 and 12 s. Results of the first minute of concentration measurement were rejected in order to avoid the mixing of air samples from different heights. Data were stored at a sampling rate of 1 s −1 . Raw data were averaged over intervals of 60 s and were later used for calculating 600 s mean vertical profiles. Particle penetration efficiencies were estimated using the indoor particles in the laboratory by changing the lengths of the sampling tubes accordingly (30, 20, 15, 10, and 5 m). Based on these results, raw concentrations were corrected prior to postprocessing. Furthermore, the data were further screened out according to several selection criteria to ensure their credibility with respect to three uncertainties: uncertainty in the number concentration measurements, signal-to-noise ratio (Deventer et al., 2015), and variation in background current (the signal obtained from particle-free air through a HEPA -highefficiency particulate air -filter for each particle stage) before and after the measurements.
Half-hourly meteorological data for horizontal wind speed, air temperature, and humidity at heights of 30, 25, 20, 10, 6, and 1 m at the tower were used for model in-put and validation. Incoming shortwave and longwave radiation values at 30 m were used for the model input, while incoming longwave radiation was estimated by the parameterization method of Duarte et al. (2006). Net radiation was measured using a net radiometer (Q7, REBS) and stored as half-hourly means by a data logger (CR10X, Campbell Scientific). A sonic anemometer (81000, Young) was used to measure three-dimensional wind velocities and air temperatures, and an enclosed infrared CO 2 /H 2 O gas analyzer (LI-7200, LI-COR) was used to measure the molar fraction of CO 2 and H 2 O. These data were sampled at a frequency of 10 Hz using an interface unit (LI-7550, LI-COR). Halfhourly CO 2 , heat, and momentum fluxes were calculated using Eddy Pro software (version 4.2.0, LI-COR), where double rotation (Kaimal and Finnigan, 1994) and block averaging were applied to fluctuation data in order to calculate covariance. We then corrected the effect of air density fluctuations on the flux values (Burba et al., 2012). Corrections were made for low-frequency losses (Moncrieff et al., 2004) and high-frequency losses for low-pass filtering (Ibrom et al., 2007) and sensor separation (Horst and Lenschow, 2009). All raw flux data were checked following the quality control program of Vickers and Mahrt (1997). Finally, we applied the quality check system proposed by Mauder and Foken (2006) and excluded data judged to be low quality (quality control flag of 2).
The total (one-sided) leaf area index (LAI) measured with a plant canopy analyzer (LAI-2200, LI-COR) was 4.3 and 3.6 m 2 m −2 for October and November 2016, respectively. Vertical profiles of leaf area density (LAD) were provided in order to obtain the above values of total LAI after gamma function interpolation, with a maximum at a height of 15 m following Katata et al. (2013). LAI of the understory vegetation with 0.5 m height was given a typical value of 2.0 m 2 m −2 in a Japanese forest (e.g., Sakai et al., 2006) due to a lack of observational data.

Boundary and initial conditions
The boundaries of each vegetation layer were set at heights of 0.05, 0.1, 0.2, 0.3, and 0.5 m (understory vegetation) and from 1 to 20 m (forest canopy) with an increment of 1 m. Atmospheric layers were extended from the 20 m canopy to 30 m with an increment of 1 m. Half-hourly data for precipitation, atmospheric pressure, horizontal wind speed, air temperature and humidity, and incoming longwave and shortwave radiation were applied to the top atmospheric layer. Inorganic mass concentrations of gases (SO 2 , NH 3 , HNO 3 , and HCl) and PM 2.5 particles (SO 2− 4 , NO − 3 , NH + 4 , Na + , Cl − , Ca 2+ , K + , and Mg 2+ ) measured by a filter pack were linearly interpolated at half-hourly timescales. For the Aitken mode, inorganic mass concentrations were assumed to be one tenth of those of the fine mode, based on size-resolved number concentrations from ELPI+ observations (not shown). The boundaries of the soil layers were at depths of 0.02, 0.05,  Supplement Table S1.
The boundary conditions and input data used in the setup of the simulation are summarized in Table 1. Lognormal parameter sets of (D g3 , σ g ) for fine and Aitken modes at the upper boundary condition were respectively set at (0.089 µm, 2.1) and (0.26 µm, 2.0) based on manual fitting of ELPI+ measurements at a height of 30 m (Fig. 1a). These parameter sets were applied to the early-and late-autumn periods. In order to simulate the vertical profiles of the total number concentration within the canopy, the volume fraction of inorganic compounds, f io , was given by the data of total inorganic mass and total number concentration. For the late-autumn period, temporal changes in weekly f io values in both the fine and Aitken modes was shown by data from filter-pack and ELPI+ measurements. However, for the early-autumn period, ELPI+ measurements were unavailable as described above. Consequently, temporal changes in f io (Fig. 1b) were set based on both filter-pack data at the study site and total PM 2.5 mass concentrations observed at the nearest air quality monitoring station at Hachioji (3 km westnorthwest of the study site). For both periods, f io values for the Aitken mode were assumed to be equal to the fine mode, since no observational data were available.
Since no data were available at the study site for emission potentials of NH 3 at the ground surface (χ g ) and stomata (χ s ), we used typical values of g = 300 (Massad et al., 2010) and s = 2000 (Neirynck and Ceulemans, 2008).
Our simulation used basic and less time-resolved datasets for a first application of the model to the NH 4 NO 3 gasparticle conversion and aerosol water uptake of reactive ni-trogen compounds. The uncertainties associated with input data described above, such as number concentration and particle size distribution, should be improved in the future.

Simulation scenarios
To reveal the impacts of NH 4 NO 3 gas-particle conversion and hygroscopic growth, the following four simulation scenarios were adopted: (1) NH 4 NO 3 gas-particle conversion and aerosol water uptake ("gpc" scenario); (2) aerosol water uptake but no NH 4 NO 3 gas-particle conversion ("no gpc" scenario); (3) NH 4 NO 3 gas-particle conversion but no aerosol water uptake ("gpc dry" scenario); and (4) no NH 4 NO 3 gas-particle conversion and no aerosol water uptake ("no gpc dry" scenario). Calculations in all scenarios were compared with observations of vertical profiles of the total number and inorganic mass concentrations within and above the canopy.

Micrometeorology during autumn 2016
Temporal changes in friction velocity (u * ), net radiation (R net ), and sensible (H ) and latent heat (LE), and CO 2 fluxes over the canopy for the early-autumn and the late-autumn periods are shown in Figs. 2 and 3, respectively. Overall, the modeled momentum and heat fluxes agreed with observed values, although observed high friction velocities in November and December 2016 were slightly underestimated (Fig. 3a). Water vapor and CO 2 exchange processes determining the level of stomatal uptake of gases were also reproduced well by the model (Figs. 2c, e and 3c, e).
Figures 4 and 5 illustrate time series of horizontal wind speed, air temperature, and relative humidity under the canopy in both simulation periods. Wind speed was underestimated within the forest, as was friction velocity (Fig. 3a and d), probably due to horizontal advection over hilly terrain . For calculated air temperature and humidity, the primary determinants of ambient conditions of gas-particle conversion and aerosol hygroscopic growth, calculated temporal changes were similar to observations within the canopy (Figs. 3b, c and 4b, c). These features were also noted in mean vertical profiles during both daytime and nighttime in the early-autumn period (Fig. S1).

Inorganic mass concentration and flux in early autumn 2016
Figure 6a and b shows time series for observed and calculated major inorganic nitrogen compounds (HNO 3 and NH 3 gases and NO − 3 and NH + 4 fine particles) under the canopy in the early-autumn period. Substantial differences were observed between the scenarios of gpc and no gpc for HNO 3 and fine-NO − 3 concentrations during the daytime on  28 September. In the gpc scenario, HNO 3 concentrations were increased due to the evaporation of NH 4 NO 3 during the daytime, whereas NO − 3 concentrations were decreased. Consequently, strong variations in NO − 3 mass concentration were reproduced in the gpc scenario. A lesser impact of evaporation due to NH 4 NO 3 on both NH 3 and fine-NH + 4 concentrations was observed.  The calculated fine-mode mass-based wet diameter (D g3 ) and RH are shown in Fig. 6c. Hygroscopic growth has a significant impact, reflecting in particle size distribution differences between the scenarios of no gpc and no gpc dry; e.g., D g3 values in the latter were 1.4 µm higher than those in the former at 0.4 µm during the nighttime on 29 September 2016. Although this process also influences size distribution during the daytime, a competing shrinkage mechanism, NH 4 NO 3 evaporation, appeared in the gpc scenario. As a result, the difference in daytime D g3 between the scenarios of gpc and no gpc was up to 0.12 µm on 28 September. Figure 7 depicts vertical profiles of normalized gaseous and particulate mass concentrations in the early-autumn period. The profiles averaged for the sampling periods were compared with observed profiles. In the scenario of no gpc (Fig. 7b), vertical gradients in fine-particle compounds (SO 2− 4 , NO − 3 , and NH + 4 ) were similar, since the same equation for collection efficiency (Eq. 8) was used for all inorganic particle compounds. In contrast, vertical gradients of NO − 3 and NH + 4 concentrations drastically increased due to NH 4 NO 3 evaporation in the gpc scenario ( Fig. 7c and f), producing gradients similar to those observed ( Fig. 7a and d). This feature was also visible in vertical profiles of mass flux for all inorganic nitrogen components during the daytime (Fig. S2). The impact of NH 4 NO 3 evaporation was smaller during nighttime (Fig. 7c) than daytime (Fig. 7f), which also aligns with observed diurnal patterns ( Fig. 7a and d). High values of observed fine-SO 2− 4 concentration were calculated in both scenarios (Fig. 7a-c). Figure 8 shows the time series for the calculated apparent mass flux of HNO 3 , NH 3 , and fine NO − 3 and NH + 4 over the  . Temporal changes in observed and calculated mass concentrations of (a) HNO 3 and NH 3 gases and (b) NO − 3 and NH + 4 fine particles and mass-equivalent geometric mean wet diameter (D g3 ) at 8 m height from 27 September to 11 October 2016. Calculations for three scenarios (gpc, no gpc, and no gpc dry; see main text for details) are plotted in the figure. The relative humidity (RH) calculated at 6 m height in Fig. 3c also appears in (c). Grey-shaded areas represent periods of rainfalls during which no filter-pack data are available. Please note that the date is given on the x axis in the month/day format. canopy in both the scenarios of gpc and no gpc. The actual deposition flux of each component (ecosystem flux) is shown for comparison with apparent flux. The impact of NH 4 NO 3 evaporation on fluxes was the highest from 26 to 29 September. The calculated NO − 3 flux above the canopy was positive during the nighttime for several days (Fig. 8c) due to the condensation of HNO 3 (Fig. 8a). As for in-canopy NH 3 concentrations (Figs. 6 and 7), NH 4 NO 3 evaporation has less impact on NH 3 flux than on other species (Fig. 8b). Figure 9 shows the time series for number concentration within the canopy in the late-autumn period, together with parameters for the lognormal size distribution of the fine mode. Initial number concentration values on 7 November (Fig. 9a) were tuned via adjustments of the ratio of inorganic compounds (f io ) for each mode. Below-canopy D g3 and σ g were smaller in gpc dry than in no gpc dry due to NH 4 NO 3 evaporation ( Fig. 9b and d), whereas below-canopy D g0 was larger in gpc dry than in no gpc dry (Fig. 9c). For the scenarios of gpc and no gpc in which aerosol water was considered, D g3 increased due to hygroscopic growth, although the influence of NH 4 NO 3 gas-particle conversion on D g3 was still apparent (Fig. 9b). Some discrepancies between observations and calculations were found after 25 November 2016 with respect to temporal changes in number concentration (Fig. 9a). Figure 10 shows vertical profiles of parameters for the lognormal size distribution and normalized NO − 3 mass concentration in the scenarios of no gpc and gpc. For fine particles, the values of D g3 and normalized NO − 3 concentrations at 8 m were respectively 5.1 % and 8.9 % smaller in the scenario of gpc than in the scenario of no gpc due to the evaporation of NH 4 NO 3 (Fig. 10b and d), and the calculated σ g was also 1.2 % smaller (Fig. 10c). In contrast, calculated D g0 slightly increased by 0.3 % at the same height (Fig. 10a). Almost no effect of NH 4 NO 3 gas-particle conversion was found in the Aitken mode ( Fig. 10e-h). Figure 11 shows differences in the total number concentration for the regions above, within, and below the canopy during the daytime in the late-autumn period, with particular reference to the differences among these concentrations. In the submicrometer size range (0.1-0.4 µm), differences between height pairs were strongest between 8 and 1 m (below), between 30 and 24 m (above), and between 24 and 8 m (within the canopy). In the scenario of no gpc dry, the difference in number concentration between height pairs was minimal in the submicrometer size range, as determined by modeled size-resolved dry-deposition velocity (Fig. 11e). Similar results have been demonstrated by past numerical studies of size-resolved particle number flux (Ryder, 2010); for a particle diameter around 0.15 µm, the apparent flux switches from deposition to emission within the canopy and approximately reflects the peak in number size distribution. Furthermore, apparent emission fluxes were represented as more particles shrink into a given size bin from the next larger size bin than leave to the next smaller size bin, whereas more particles shrink out of a given size bin than shrink into it from the next larger size bin, resulting in apparent fast deposition (Ryder, 2010). In the gpc scenario ( Fig. 11a-d), particles in the fine mode shrunk in this size range due to in-canopy NH 4 NO 3 evaporation, resulting in an apparent tendency to emit from the canopy to the air above (Fig. 11d). Meanwhile, differences in number concentrations between 24 and 8 m (within the canopy) for large particles (> 0.3 µm) were excessively high in the gpc scenario compared to observational data. In the scenario of no gpc, in which only aerosol water uptake was considered (Fig. 11c), fine-particle sizes increased due to hygroscopic growth (Fig. 10), and the concentration differences between height pairs always remained positive in this range. Finally, in the gpc scenario where both NH 4 NO 3 evaporation and hygroscopic growth processes are considered (Fig. 11b), calculated negative gradients of number concentration appeared between 24 and 8 m (within the canopy) for the submicrometer range of 0.1-0.4 µm, again similar to observed patterns (Fig. 11a).

Uncertainties in observation and model results
SOLVEG reproduced the general features of gas concentration, fine-particle mass, and fine-particle number concentration observed within the canopy. Several uncertainties (e.g., low time resolution of weekly filter-pack data in the lateautumn period, initialization of measurement uncertainty, and complex topography of the study site) may cause un-derestimations in calculated wind speed (Figs. 3a and 4a) and overestimations in total number concentration within the canopy after 25 November 2016 (Fig. 9a). In Fig. 8, the conditions for NH 4 NO 3 condensation were calculated for the studied forest, although these conditions are normally found over strong sources of NH 3 (e.g., Nemitz et al., 2009). Thus, the results of this study should be considered a first test of the model to the NH 4 NO 3 gas-particle conversion and aerosol water uptake of reactive nitrogen compounds, rather than a conclusive assessment of its capability. Another uncertainty in the results could be associated with the assumption of the same composition in size at the initial and boundary conditions. Variations of chemical composition in size cause variations in equilibrium vapor pressure at the particle surface due to Kelvin and Raoult effects, due to uncertainty in the simulation of the swelling and shrinking of particles. Since we used a modal aerosol dynamics method, the differences of these effects within each mode cannot be resolved. It is necessary to revisit this issue in the future using size-resolved composition measurements and size-resolved aerosol models, as done by Ryder (2010), to assess this uncertainty.
Concerning potential shortcomings in the modeling aspect, particle growth due to biogenic secondary organics was not considered and might increase uncertainty in model results. Although this effect might not be important for the dry-deposition and evaporation processes that formed the main focus of this study, this effect certainly influences particle mass flux in the forest itself. Nevertheless, the order of the magnitude of observed normalized inorganic mass concentration within the canopy during the daytime, i.e., SO 2− 4 > NH 3 > NH + 4 > NO − 3 > HNO 3 (Fig. 7a), was well reproduced by the gpc scenario of the model (Fig. 7c). For the late-autumn period, while there is no direct measurement of aerosol water content, the ambient RH profile to determine hygroscopic aerosol growth was reproduced (Figs. 4c and 5c). As a result, the observed in-canopy negative gradient in number concentration (i.e., apparent emission of particles) in the 0.1-0.4 µm size range was simulated in the gpc scenario ( Fig. 11a and b). These results indicate that the model developed can be effectively used to address the impact of aerosol dynamics on dry-deposition processes. (apparent) particle deposition due to NH 4 NO 3 evaporation may be important in chemical transport modeling.
Theoretical values of deposition velocity for submicrometer particles, typically ranging from 0.1-1 cm s −1 , may have no substantial impact on surface concentrations in CTMs. However, as discussed above, a high deposition velocity of fine NO − 3 due to evaporation in the forest (up to 40 times the above values) may effectively remove nitrate particles from the atmosphere over the forest and leeward. If aerosol dynamics and gas-particle conversion processes can be incorporated into the dry-deposition scheme of CTMs, we may improve upon or even eliminate prior studies' overestimates of the surface concentration of fine NO − 3 (Kajino et al., 2013;Shimadera et al., 2014Shimadera et al., , 2018Morino et al., 2015;Sakurai et al., 2015). Hicks et al. (2016) found that, when modeling particle deposition velocities, the greatest uncertainty manifested in the range 0.1-1.0 µm. The cause of this uncertainty has not yet been convincingly established, although differing treatments of key particle deposition processes (e.g., turbulent diffusion) have been suggested by prior studies (Petroff and Zhang, 2010;Zhang and Shao, 2014). As demonstrated in Fig. 12b and c, the evaporation of NH 4 NO 3 under less humid conditions may play an important role in the dry deposition of submicrometer particles.

Conclusions
A new multilayer land surface model fully coupled with dry deposition and aerosol dynamics was developed to evaluate the impact of NH 4 NO 3 -NH 3 -HNO 3 conversion in temperate forests. The model was applied to field studies of mass and number concentration profiles in a Japanese mixed forest during autumn 2016. Four model scenarios with and without NH 4 NO 3 gas-particle conversion and/or aerosol water uptake were tested to quantify the impact of these parameters on processes of dry deposition. Overall, the model successfully reproduced micrometeorological conditions (in particular, relative humidity) within and above the canopy. When NH 4 NO 3 gas-particle conversion processes were included in the simulation, the vertical gradients of normalized mass concentrations of nitrogen gases (HNO 3 and NH 3 ) and fine particles (NO − 3 and NH + 4 ) within the canopy were clearly higher than those of SO 2− 4 . For particle size distribution, the observed emission tendency of total number concentration from the canopy to the atmosphere was explained by a larger effect of within-canopy evaporation of NH 4 NO 3 than due to hygroscopic growth. As a result, the removal flux of calculated fine NO − 3 from the air above the forest to the forest can increase by up to 40 times under the DRH of pure NH 4 NO 3 . Similarly, the removal flux of calculated fine NH + 4 can increase up to ∼ 10 times, although calculations for fine NH + 4 fluctuate strongly with RH. Conversely, HNO 3 flux over the forest can decrease by 50 % or more due to NH 4 NO 3 evaporation, supporting the findings of previous studies. Processes of aerosol dynamics and NH 4 NO 3 -NH 3 -HNO 3 conversion play a crucial role in the dry deposition of inorganic nitrogen particles in temperate forests. These processes can and should be incorporated into chemical transport models (CTMs) in order to improve the accuracy of total nitrate surface concentrations. An aerosol-dynamics-dry-deposition scheme simplified from that present in this study could therefore be implemented in CTMs.
Data availability. The output data in this study are publicly accessible via contacting the authors.
Author contributions. GK developed the model with support from MK and performed the simulations using the data collected by KM, AS, and KT. GK prepared the paper with contributions from all coauthors.