A comprehensive study about the in-cloud processing of nitrate through 1 coupled measurements of individual cloud residuals and cloud water 2

While the formation and evolution of nitrate in airborne particles are extensively investigated, little is known about the processing of nitrate in clouds. Here we present a 27 detailed investigation on the in-cloud formation of nitrate, based on the size-resolved mixing 28 state of nitrate in the individual cloud residual and cloud-free particles obtained by single 29 particle mass spectrometry, and also the mass concentrations of nitrate in the cloud water 30 and PM 2.5 at a mountain site (1690 m a.s.l.) in southern China. The results show a significant 31 enhancement of nitrate mass fraction and relative intensity of nitrate in cloud water and the 32 cloud residual particles, respectively, reflecting a critical role of in-cloud processing in the 33 formation of nitrate. We first exclude the gas phase scavenging of HNO 3 and the facilitated 34 activation of nitrate-containing particles as the major contribution for the enhanced nitrate, 35 according to the size distribution of nitrate in individual particles. Based on regression 36 analysis and theoretical calculations, we then highlight the N 2 O 5 hydrolysis for the in-cloud 37 formation of nitrate, even during the daytime, attributed to the diminished light in clouds. Nitrate is highly related (R 2 = ~0.6) to the variation of [NO x ][O 3 ], temperature and droplet 39 surface area in clouds. Accounting for droplet surface area greatly enhances the predictability of the observed nitrate, compared with using [NO x ][O 3 ] and temperature. The substantial contribution of N 2 O 5 hydrolysis to nitrate in clouds during the daytime was 42 reproduced by a multiphase chemical box model. Assuming a photolysis rate at 30% of the default setting, the overall contribution of N 2 O 5 hydrolysis pathway to nitrate formation 44 increases by ~20% in clouds. Given that N 2 O 5 hydrolysis acts as a major sink of NO x in the

Aerosol nitrate originates from the oxidation of NOx, which refers to gas phase 60 oxidation of NO2 by the hydroxyl radical (OH) followed by condensation (daytime 61 chemistry) and the hydrolysis of N2O5 (nighttime chemistry) to nitrate in aqueous particles, 62 initiated by the oxidation of NO2 by ozone (O3) to produce the NO3 radical (Seinfeld and 63 Figure 1 shows the statistical results of the nitrate mass fractions in cloud water and 208 PM2.5 and the hourly average relative intensity of nitrate (represented by the RPA) in the 209 cloud-free, cloud residual, and cloud interstitial particles. The results clearly indicate the 210 enhancement of nitrate in clouds. It can be seen that the mass fraction of nitrate in cloud 211 water (~20% on average) is obviously higher than those in PM2.5 (< 15% on average) during 212 the cloud-free periods and cloud events, for both the 2018 spring and 2020 winter periods. 213 Consistently, the relative intensity of nitrate was substantially enhanced in the cloud 214 interstitial particles and particularly cloud residues, relative to the cloud-free particles. The 215 influence of air mass on the enhanced nitrate can be ruled out for the 2018 spring period, as 216 they similarly originated from southern areas over the whole campaign period (Fig. S2). 217 While the air masses originated from different regions during the 2020 winter period, they 218 did not show the difference between the cloud-free periods and cloud events, with the 219 shifting of air masses and/or wind direction after 27 Nov (Figs. S1 and S2). Thus, the 220 influence of air mass on the enhanced nitrate in 2020 winter should also be limited. 221 There are several pathways that might contribute to the enhanced nitrate in cloud 222 droplets, including (1) the scavenging of gas-phase HNO3, (2) the preferential activation of 223 nitrate-rich particles, and (3) in-cloud aqueous production of nitrate via reaction of NO3 224 radicals or hydrolysis of N2O5. The mechanism via the dissolution of NO2 and its aqueous 225 phase oxidation is relatively slow and unlikely to be a significant source of cloud water 226 nitrate (Seinfeld and Pandis, 2006). 227 We first exclude the scavenging of gas-phase HNO3 as a major pathway through the 228 analysis of size distribution of nitrate RPA and RPA ratio (nitrate / sulfate), although all the 229 gas phase HNO3 could be efficiently scavenged and present in the aqueous phase in a typical 230 cloud with LWC > 0.1 g m -3 (Seinfeld and Pandis, 2006). As can be seen in Fig. 2 nitrate in smaller size, rather than sulfate in larger size. And their pattern could be well 238 explained by the model calculation assuming that all of the cloud nitrate comes from the 239 uptake of HNO3. Therefore, our pattern at least indicates a limited contribution of gas-phase 240 scavenging of HNO3 to the observed nitrate in the cloud RES particles. As also discussed in 241 the following section, the formation of HNO3 would be certainly suppressed by the presence 242 of cloud. 243 We also indicate that the contribution of preferential activation of the nitrate-rich 244 particles should be limited since such a process would lead to the depletion of nitrate in the 245 cloud interstitial particles relative to the cloud-free particles. But this is not the case, as the 246 RPA of nitrate and RPA ratios of nitrate to sulfate in the cloud interstitial particles are 247 considerably higher than those in the cloud-free particles (Fig. 2). Both the enhanced nitrate 248 in the cloud residual and interstitial particles suggest the in-cloud formation of nitrate, 249 although the variation of nitrate RPA cannot provide a quantitative view. The enhancement 250 of nitrate in the cloud interstitial particles may also indicate that the significant role of RH 251 in the formation of nitrate, even in the inactivated particles. Similar results have also been 252 observed in our previous study for oxalate (Zhang et al., 2017). Consistently, the formation 253 of nitrate in the cloud interstitial particles also grows their size towards the larger mode, 254 compared with the cloud-free particles (Fig. S4). 255 256 3.2. In-cloud nitrate formation 257 14 A theoretical estimation of nitrate production for 2020 winter is performed based on the 258 well-established kinetic characteristic of reactions between NO2 and O3 and uptake of N2O5 259 onto aerosol/droplet surfaces that formed HNO3 (SI text S1), corresponding to the nighttime 260 chemistry. It is reasonable since the heterogeneous hydrolysis of N2O5 within aerosol 261 particles, fog, or cloud droplets has been shown to be much faster than homogeneous In the present study, the average LWC of cloud droplets is at a level of ~10 5 μg m −3 , 3-4 289 magnitude higher than those for urban haze conditions. As previously reported, high aerosol The theoretical estimate indicates that the hydrolysis of N2O5 may substantially 295 contribute to the in-cloud production of nitrate even during the daytime, consistent with the 296 observation results as discussed in Section 3.1. The theoretically predicted nitrate (NO -3 ) 297 production from the hydrolysis of N2O5 represents ~5-15% of the measured nitrate (Fig. 3) 298 based on our assumption. It could roughly explain ~10% increase of the nitrate mass fraction 299 16 in clouds (Fig. 1). There are some factors that may contribute to the uncertainties in the 300 estimation. One is that the assumed γ = 0.06 might not be representative for N2O5 uptake in 301 cloud droplets, since the previously reported γ varies in a wide range, depending on various 302 factors (e.g., droplet compositions, pH, temperature) (Bertram and Thornton, 2009 (Burkholder et al., 2015). Another is that the SA 305 estimated by the size distribution data of cloud residues obtained by the GCVI-SMPS only 306 represents part (< 50%) of the cloud droplets, as GCVI was set to collect droplets larger than 307 7.5 μm in the present study. In addition, the scavenging of HNO3 may still contribute to 308 the in-cloud nitrate production, as estimated in section 3.3, although N2O5 hydrolysis still 309 represents the dominant pathway. and temperature as inputs, separated for the cloud RES and cloud-free particles, as detailed 313 in SI text S2. Note that the concentration of NOx is used here to represent that of NO2, since 314 most of NO data were not available for the 2018 spring. The effect should be limited since 315 NO could be negligible when the air masses are dominantly attributed to long range transport, 316 which could also be supported by the data (NO, ~0.1 μg m -3 , < 2% of NO2 concentration) in 317 2020 winter. As expected, the nitrate RPA in the cloud residual particles is highly correlated 318 to the predicted ones (R 2 = 0.75 and 0.71 with p < 0.01 for the daytime and nighttime, 319 respectively), even during the daytime (Fig. 4). An inclusion of temperature and SA in the 320 17 model substantially improves the correlation coefficient R 2 , which is originally 0. 16

Relative importance of N 2 O 5 hydrolysis pathway to nitrate in clouds 333
The relative contribution of nitrate formation in the cloud droplets and cloud-free 334 particles is also assessed using the CAPRAM model, as shown in Fig. 5. The relative 335 contribution difference between the cloud droplets and cloud-free particles is primarily 336 attributed to the different LWC setting, which is tightly linked to the cloud droplets' SA. 337 Furthermore, the comparison between cloud scenarios with different LWC setting (0.05 g m -338 3 versus 0.15 g m -3 ) also shows an enhanced contribution of N2O5 hydrolysis to nitrate with 339 increasing LWC. 340 Nitrate is known to form predominantly by the hydrolysis of N2O5 (> 80%) for both the 341 18 cloud droplets and cloud-free particles for the nighttime. However, both Fig. 3 and Fig. 4  342 indicate the potential importance of the heterogeneous N2O5 hydrolysis to nitrate formation 343 during the daytime. This is likely attributed to the substantial attenuation of the incident solar 344 radiation by clouds, in which the visibility was as low as < 0.1 km over this study. Previous events and cloud-free periods (Fig. S5), we indicate that the cloud events did not have much 356 effect on the variation of O3 during our observation. 357 The model results in Fig. 5 with the consideration of photolysis rate are, to some extent, 358 consistent with our observations. The overall contribution of N2O5 hydrolysis pathways 359 increases by ~20% (from ~50-60% to ~70-80%) when the photolysis rate is reduced to 30% 360 of the default setting. For daytime only, the contribution of this pathway also increases from 361 nearly 0 to ~20% during the noon hours and ~40% for the morning hours. A similar model 362 19 study also indicates that N2O5 hydrolysis contributed to 30% of daytime nitrate formation at 363 Mt. Tai (Zhu et al., 2020). Attributed to the substantial attenuation of incident solar radiation 364 by clouds and high loading of PM2.5, the daytime N2O5 hydrolysis has also been observed to 365 be an important formation pathway for nitrate in the haze episodes in Xi'an (China), and the 366 contribution increases from 8.2% to 20.5% of the total nitrate over 14:00-16:00 by model

Conclusions and atmospheric implications 376
The presented results provide direct evidence that in-cloud aqueous processing, in 377 particular, the hydrolysis of N2O5 significantly contributes to the enhanced nitrate in cloud 378 residues. We highlight that the hydrolysis of N2O5 serves as the critical route for the in-cloud 379 Enhanced aerosol nitrate is expected to have higher hygroscopicity after cloud evaporation 398 (Sun et al., 2018;Hodas et al., 2014), and therefore, an increase of the particles' ability to act 399 as cloud condensation nuclei after their cloud passage (Roth et al., 2016). This is different 400 from that observed in California coast that the nitrate-to-sulfate mass ratio decreases rapidly 401 with cloud height, due to the volatilization during drop evaporation pushes NO3 to the gas 402 phase (Prabhakar et al., 2014). In addition, vertical turbulent mixing of the residual aerosols 403 from evaporating cloud droplets may contribute to the nitrate aerosol loading during the 404 22

Competing interests 406
The authors declare that they have no conflict of interest. 407

Data availability 408
All the data can be obtained by contacting the corresponding author.