Heterogeneous Uptake of N 2 O 5 in Sand Dust and Urban Aerosols Observed during the Dry Season in Beijing

: The uptake of dinitrogen pentoxide (N 2 O 5 ) on aerosols a ﬀ ects the nocturnal removal of NO x and particulate nitrate formation in the atmosphere. This study investigates N 2 O 5 uptake processes using ﬁeld observations from an urban site in Beijing during April–May 2017, a period characterized by dry weather conditions. For the ﬁrst time, a very large N 2 O 5 uptake rate ( k (N 2 O 5 ) up to ~0.01 s − 1 ) was observed during a sand storm event, and the uptake coe ﬃ cient ( γ (N 2 O 5 )) was estimated to be 0.044. The γ (N 2 O 5 ) in urban air masses was also determined and exhibited moderate correlation (r = 0.68) with aerosol volume to surface ratio (V a / S a ), but little relation to aerosol water, nitrate, and chloride, a ﬁnding that contrasts with previous results. Several commonly used parameterizations of γ (N 2 O 5 ) underestimated the ﬁeld-derived γ (N 2 O 5 ). A new parameterization is suggested for dry conditions, which considers the e ﬀ ect of V a / S a , temperature, and relative humidity.


Introduction
Dinitrogen pentoxide (N 2 O 5 ) is an important nighttime reservoir of NO x which is a key precursor to photochemical production of ozone [1]. The loss of N 2 O 5 on aerosol surface, therefore, affects the lifetime of NO x and produces nitrate aerosol, contributing to particulate pollution (e.g., [2]). The formation of N 2 O 5 is initiated by the gas phase production of nitrate radical (NO 3 ), which is in rapid equilibrium with N 2 O 5 (R2) [3,4]. As (R2) is a second-order reaction, M in (R2) denotes the third body, i.e., ambient air.
γ(N 2 O 5 ) is highly variable (10 −4 to 0.2) and has complicated dependences on the chemical composition and physical properties of aerosols according to field studies (e.g., [2,10,11]). Laboratory studies have found that N 2 O 5 uptake is enhanced by chloride and aerosol water content ([H 2 O]) but suppressed by inorganic nitrate [12][13][14][15] and aerosol organic coating [16,17]. Sand dust has also been found to be an important interface for N 2 O 5 uptake [18,19], but differing results have been obtained even for the same dust type [19][20][21][22]. For example, different laboratory studies of Saharan dust reported γ(N 2 O 5 ) in the range 0.013~0.2 [20,21,23,24]. Although laboratory studies have suggested large γ(N 2 O 5 ) on mineral dust, there have been no reports on direct observations of N 2 O 5 uptake on ambient mineral dust.
Several parameterizations of γ(N 2 O 5 ) have been proposed to predict γ(N 2 O 5 ) based on laboratory results on the relation of γ(N 2 O 5 ) to temperature, relative humidity (RH), aerosol size, and aerosol inorganic and organic content (e.g., [14,16,25,26]). To evaluate the validity of these parameterizations in the real atmosphere, γ(N 2 O 5 ) was derived using field observations or direct measurements of N 2 O 5 reactivity [10,[27][28][29]. The enhancement effect of chloride and [H 2 O] and the inhibition effect of nitrate on γ(N 2 O 5 ) have been observed in the field [11,[30][31][32]. However, the parameterized γ(N 2 O 5 ) based on the observed physiochemical properties of aerosols has been found to be inconsistent with observed γ(N 2 O 5 ) [10,31]. For example, the widely adopted parameterization proposed by Bertram and Thornton (denoted γ(N 2 O 5 ) BT ) has often yielded higher values than the observed or directly measured γ(N 2 O 5 ) when the observed γ(N 2 O 5 ) is small (<0.02) [11,28,32,33]. The discrepancy may be due to overestimation of the enhancement effect of chloride, presence of organic aerosols, and unknown suppression effects on N 2 O 5 uptake [33]. More investigation of γ(N 2 O 5 ) in the real atmosphere is needed to improve the parametrization, while observation of N 2 O 5 uptake on ambient sand dust is also desirable.
The present study examines the heterogeneous uptake of N 2 O 5 based on field measurements in urban Beijing during April and May 2017, when RH was low (27 ± 18%, average ± standard deviation) and dust storms took place. We first introduce the meteorological conditions, chemical characteristics, and diurnal patterns of N 2 O 5 and related chemical species at the sampling site. The loss rate coefficients of N 2 O 5 are calculated to reveal the dominant removal pathways of N 2 O 5 . γ(N 2 O 5 ) is then estimated from the field measurements and compared to parameterized values. Meteorological and chemical factors that influence γ(N 2 O 5 ) are examined. A modified parameterization is proposed for relatively dry conditions.

Measurement Site and Period
Field measurements were conducted in spring 2017 (April 24th to May 31st) at the Chinese Research Academy of Environmental Science (CRAES) (40.04 • N, 116.42 • E), which is situated in the northern part of the Beijing urban area (Figure 1). The surrounding areas are mainly residential, with some commercial buildings. For more information on the measurement site, the reader is referred to [34,35]. The Gobi Desert and Inner Mongolia lie to the northwest of Beijing, and sand dust from these regions can impact Beijing during the spring (e.g., [36]).

Measurement Site and Period
Field measurements were conducted in spring 2017 (April 24 th to May 31 st ) at the Chinese Research Academy of Environmental Science (CRAES) (40.04° N, 116.42° E), which is situated in the northern part of the Beijing urban area (Figure 1). The surrounding areas are mainly residential, with some commercial buildings. For more information on the measurement site, the reader is referred to [34,35]. The Gobi Desert and Inner Mongolia lie to the northwest of Beijing, and sand dust from these regions can impact Beijing during the spring (e.g., [36]).

Chemical Ionization Mass Spectrometry (CIMS) Setup
ClNO2 and N2O5 were simultaneously measured using a quadrupole CIMS. The same instrument was used in several previous field studies [32,[37][38][39]. The reader is referred to the earlier publications for detailed information on the principles, configuration, and calibration methods. Briefly, ClNO2 and N2O5 molecules are combined with the reagent I − (H2O) to generate I(ClNO2) -and I(N2O5) -in CIMS, which are detected at m/z 208 and m/z 235, respectively. In the present study, the detection limits were 3 pptv and 4 pptv (3σ, 1 min average) for N2O5 and ClNO2, respectively. The sensitivities of N2O5 and ClNO2 were determined to be 0.78 ± 0.05 Hz/pptv and 0.58 ± 0.04 Hz/pptv, respectively, based on daily calibrations. The dependency of N2O5 sensitivity on RH was measured on-site and used to correct ambient N2O5 data ( Figure S2). The indoor temperature was kept constant at ~296 K by air conditioners.
The sampling inlet of the CIMS system was installed ~1.5 m above the roof of a four-story building (~15 m a.s.l.). The sampling line was 3.5 m PFA tubing (1/4-inch O.D.), which was replaced daily with a new one that was washed to reduce the loss of N2O5 in the sample line. The total flow through the sample line was ~10 liters per minute (LPM), with 1.5 LPM being distributed to CIMS and 4.0 LPM to other instruments, while the remaining flow was discarded by a bypass pump. The loss of N2O5 in the sampling line was checked every two days, which was <10% after one day of use.

Chemical Ionization Mass Spectrometry (CIMS) Setup
ClNO 2 and N 2 O 5 were simultaneously measured using a quadrupole CIMS. The same instrument was used in several previous field studies [32,[37][38][39]. The reader is referred to the earlier publications for detailed information on the principles, configuration, and calibration methods. Briefly, ClNO 2 and N 2 O 5 molecules are combined with the reagent I − (H 2 O) to generate I(ClNO 2 ) − and I(N 2 O 5 ) − in CIMS, which are detected at m/z 208 and m/z 235, respectively. In the present study, the detection limits were 3 pptv and 4 pptv (3σ, 1 min average) for N 2 O 5 and ClNO 2 , respectively. The sensitivities of N 2 O 5 and ClNO 2 were determined to be 0.78 ± 0.05 Hz/pptv and 0.58 ± 0.04 Hz/pptv, respectively, based on daily calibrations. The dependency of N 2 O 5 sensitivity on RH was measured on-site and used to correct ambient N 2 O 5 data ( Figure S2). The indoor temperature was kept constant at~296 K by air conditioners.
The sampling inlet of the CIMS system was installed~1.5 m above the roof of a four-story building (~15 m a.s.l.). The sampling line was 3.5 m PFA tubing (1/4-inch O.D.), which was replaced daily with a new one that was washed to reduce the loss of N 2 O 5 in the sample line. The total flow through the sample line was~10 liters per minute (LPM), with 1.5 LPM being distributed to CIMS and 4.0 LPM to other instruments, while the remaining flow was discarded by a bypass pump. The loss of N 2 O 5 in the sampling line was checked every two days, which was <10% after one day of use. Overall uncertainty was 25% for N 2 O 5 and ClNO 2 [38]. The measurements were conducted at a time resolution of~10 s, and the data were later averaged to 1 min for further analysis.

Other Measurements
Trace gases, aerosol, and VOC composition related to N 2 O 5 and ClNO 2 were concurrently measured. NO and NO 2 were measured using a chemiluminescence analyzer equipped with a blue-light converter (model 42i-TL, Thermo Scientific Company, Waltham, MA, USA). NO y was measured using a total reactive nitrogen oxides analyzer with a MoO converter heated to 350 • C (model EC9843, Ecotech Company, Melbourne, Australia). O 3 and SO 2 were detected using UV photometry (model 49i, Thermo Scientific Company, Waltham, MA, USA) and pulsed-UV fluorescence (model 43C, Thermo Scientific Company, Waltham, MA, USA), respectively. All of the instruments were calibrated every two weeks. PM 2.5 mass concentration was measured using a beta attenuation monitor (model BAM 1020, Met One Instrument Inc., Grants Pass, WA, USA). Ionic compositions of PM 2.5 (Na + , NH 4 + , K + , Mg 2+ , Ca 2+ , Cl − , NO 3 − , SO 4 2− ) were measured on an hourly basis utilizing the Monitor for AeRosols and GAses in ambient air (MARGA, Metrohm Company, Herisau, Switzerland) [40,41]. An internal standard, bromide lithium, was used for regular calibration. VOCs were measured by an online gas chromatograph equipped with a flame ionization detector (GC-FID) (Chromatotec Group, Bordeaux, France) [42]. A list of measured species and reaction rate constants with NO 3 radical at 298K are shown in Table S1 [5]. Organic carbon (OC) and elemental carbon (EC) were measured by an OC-EC field analyzer (model-4, Sunset Laboratory Inc., Tigard, OR, USA). The dry-state particle size distribution was measured by a wide-range particle spectrometer (WPS Model 1000XP, MSP Corporation, Shoreview, MN, USA) covering the 10 nm~10 µm size ranges [43]. Aerosol surface area density (S a ) was estimated by assuming that particles were spherical. Hygroscopic growth of aerosols was estimated following the method in [44], and a growth factor for the diameter of particles, GF = 0.582 8.46 + 1 1−RH 1/3 was adopted for all the size ranges [45,46]. The growth factor for S a is the square of GF. Particles larger than 10 µm were significant in the heavy sand storm event, but they cannot be captured by the WPS instrument. Thus, the S a in such cases was estimated based on its relationship to PM 2.5 during the observation period ( Figure S6). For the same reason, the calculation of V a /S a is not applicable during heavy storm events. In other cases, it is assumed that particles larger than 10 µm contribute little to the total aerosol surface area.

Estimation of γ(N 2 O 5 ) and ϕ(ClNO 2 )
A modified steady state method was applied to estimate γ(N 2 O 5 ) and ϕ(ClNO 2 ) [3,39,42,47]. Due to rapid equilibrium between NO 3 and N 2 O 5 , these two species are regarded as a pair. The changing rate of the NO 3 and N 2 O 5 pair equals the production rate of NO 3 radial minus the total loss rate of NO 3 and N 2 O 5 (Equation (2)), assuming that transportation effect can be ignored.
where k 1 is the rate constant of (R1). k(NO 3 ), known as NO 3 reactivity, is expressed as follows: where k i is the rate constant of NO 3 + VOC reactions. The NO 3 radical concentration is estimated from the NO 3 and N 2 O 5 equilibrium: where K eq is the temperature-dependent equilibrium coefficient of the NO 3 -N 2 O 5 pair. Substitution of (Equation (3)) and (Equation (4)) into (Equation (2)) and rearrangement yields (Equation (5)) as follows,  [6,48].
When the surface area density (S a ) of aerosols and velocity of N 2 O 5 molecules (c(N 2 O 5 )) are available, γ(N 2 O 5 ) can be obtained following (Equation (1)). Then ϕ(ClNO 2 ) can be calculated using the below formula by integrating over the whole period of the selected case.
(Equation (11)) treats the N 2 O 5 uptake process as a net effect through the aqueous core (γ core ) and the organic coating (γ Org ). In this study, γ core adopts Bertram and Thornton's parameterization for easy comparison with previous studies [29,31]. γ Org is calculated using (Equation (12)), in which R c is the radius of the aqueous core, R p denotes the radius of the particle, and L means the depth of the organic coating. And R c , R p , and L are calculated following a previous study [50]. H org and D org are the Henry's law constant and the diffusion coefficient of N 2 O 5 in organic coating, which are calculated by assuming H org D org = 0.03H aq D aq [2,11]. H aq (5000 M/atm) and D aq (10 −9 m 2 /s) are the corresponding parameters of N 2 O 5 in the aqueous core [2].
The parameterized ClNO 2 yield is also calculated using the following equation [14].

Overall Observations
Measurement results for N 2 O 5 , ClNO 2 , and related chemical and meteorological parameters are shown in Figure 2 for the period from 24th April to 31st May. The weather conditions were mainly sunny, except for a little rain on 23rd May. Wind speeds were mostly below 3 m/s (Figure 1c). A prominent feature of the field study was dry weather, with an average relative humidity (RH) of 27 ± 18% during the whole campaign. Both N 2 O 5 and ClNO 2 exhibited typical diurnal variations, increasing during the night and decreasing during the day ( Figure S3).
Atmosphere 2019, 10, x FOR PEER REVIEW 6 of 16 organic coating. And Rc, Rp, and L are calculated following a previous study [50]. Horg and Dorg are the Henry's law constant and the diffusion coefficient of N2O5 in organic coating, which are calculated by assuming HorgDorg = 0.03HaqDaq [2,11]. Haq (5000 M/atm) and Daq (10 −9 m 2 /s) are the corresponding parameters of N2O5 in the aqueous core [2]. The parameterized ClNO2 yield is also calculated using the following equation [14].

Overall Observations
Measurement results for N2O5, ClNO2, and related chemical and meteorological parameters are shown in Figure 2 for the period from 24 th April to 31 st May. The weather conditions were mainly sunny, except for a little rain on 23 rd May. Wind speeds were mostly below 3 m/s (Figure 1c). A prominent feature of the field study was dry weather, with an average relative humidity (RH) of 27 ± 18% during the whole campaign. Both N2O5 and ClNO2 exhibited typical diurnal variations, increasing during the night and decreasing during the day ( Figure S3). The early part of the study (24 th April to 2 nd May) was influenced by dry air masses mainly from the northwest, as indicated by the backward trajectories ( Figure S1) calculated using the online hybrid single-particle lagrangian integrated trajectory (HYSPLIT) model [51]. N2O5 levels were higher than those of ClNO2 from 24 th April to 1 st May with low aerosol loadings, suggesting low N2O5 uptake or ClNO2 yield. This period was influenced by light dust, as indicated by abundant Ca 2+ (10-40 μg/m 3 ) and moderate PM2.5 (20-100 μg/m 3 ) mixed with fresh urban emissions. The night of May 2 nd was an The early part of the study (24th April to 2nd May) was influenced by dry air masses mainly from the northwest, as indicated by the backward trajectories ( Figure S1) calculated using the online hybrid single-particle lagrangian integrated trajectory (HYSPLIT) model [51]. N 2 O 5 levels were higher than those of ClNO 2 from 24th April to 1st May with low aerosol loadings, suggesting low N 2 O 5 uptake or ClNO 2 yield. This period was influenced by light dust, as indicated by abundant Ca 2+ (10-40 µg/m 3 ) and moderate PM 2.5 (20-100 µg/m 3 ) mixed with fresh urban emissions. The night of May 2nd was an exception as the air mass originated from the southeast, bringing humid air and higher ClNO 2 to N 2 O 5 ratios. Overall, this period is referred to as "light dust" in the subsequent discussion.
A heavy sand storm impacted Beijing on the night of 3rd and 4th May, with PM 2.5 reaching 700 µg/m 3 (Figure 2). The sand storm event is displayed separately for clarity ( Figure 3). ClNO 2 mixing ratios of up to 0.82 ppbv and much lower N 2 O 5 levels (10-20 pptv) were observed, indicating rapid N 2 O 5 loss on sand dust. To our knowledge, this is the first observation of N 2 O 5 and ClNO 2 during a heavy dust event. This period is denoted as a "sand storm." In the later period of observation (14 th May to 31 st May, Figure S3), air masses arrived from the south or east ( Figure S1), with a mean RH in the range 20~60%. Daytime ozone levels were 80-120 ppbv, indicating moderately high photochemical pollution. This period is named "urban air." During this period, ClNO2 levels were generally higher than those of N2O5. The levels of N2O5 (up to 0.7 ppbv) and ClNO2 (up to 3.0 ppbv) were slightly higher than or comparable to values previously reported in polluted North China and urban/industrial regions of the US and EU [32,38,[52][53][54][55][56][57][58], but lower than our previous observations in southern China [37,39].

N2O5 Reactivity and Loss Pathways
This section examines the relative importance of the three N2O5 loss reactions, i.e., VOC oxidation, homogeneous loss, and heterogeneous loss. The lifetime of N2O5 (τ(N2O5)) is a measure of its total reactivity and was estimated using (Equation (14)). P(NO3) is the production rate of NO3 radical from the NO2 and O3 reaction. We selected nighttime periods with abundant N2O5 or ClNO2 and low NO levels (NO < 0.1 ppbv). A total of nine cases were selected (see Figure 4), including two "light dust" (30 th April and 1 st May), two "sand storm" (3 rd May and 4 th May), and five "urban air." Results show that the τ(N2O5) ranged from 1 min to 45 min (Figure 4a). The shortest τ(N2O5) was found in the sand storm on May 4 th night, which is attributable to the rapid heterogeneous loss rate coefficient of N2O5 (up to 0.01 s −1 , Figure 4b).
The loss rate coefficients of N2O5 uptake were calculated and compared with other loss pathways In the later period of observation (14th May to 31st May, Figure S3), air masses arrived from the south or east (Figure S1), with a mean RH in the range 20~60%. Daytime ozone levels were 80-120 ppbv, indicating moderately high photochemical pollution. This period is named "urban air." During this period, ClNO 2 levels were generally higher than those of N 2 O 5 . The levels of N 2 O 5 (up to 0.7 ppbv) and ClNO 2 (up to 3.0 ppbv) were slightly higher than or comparable to values previously reported in polluted North China and urban/industrial regions of the US and EU [32,38,[52][53][54][55][56][57][58], but lower than our previous observations in southern China [37,39].

N 2 O 5 Reactivity and Loss Pathways
This section examines the relative importance of the three N 2 O 5 loss reactions, i.e., VOC oxidation, homogeneous loss, and heterogeneous loss. The lifetime of N 2 O 5 (τ(N 2 O 5 )) is a measure of its total reactivity and was estimated using (Equation (14)). P(NO 3 ) is the production rate of NO 3 radical from the NO 2 and O 3 reaction. We selected nighttime periods with abundant N 2 O 5 or ClNO 2 and low NO levels (NO < 0.1 ppbv). A total of nine cases were selected (see Figure 4), including two "light dust" (30th April and 1st May), two "sand storm" (3rd May and 4th May), and five "urban air." Results show that the τ(N 2 O 5 ) ranged from 1 min to 45 min (Figure 4a). The shortest τ(N 2 O 5 ) was found in the sand storm on May 4th night, which is attributable to the rapid heterogeneous loss rate coefficient of N 2 O 5 (up to 0.01 s −1 , Figure 4b).
The loss rate coefficients of N 2 O 5 uptake were calculated and compared with other loss pathways (Figure 4b). The indirect loss through gas-phase reactions of NO 3 radical with VOCs contributed 1.9%~30.2% of total N 2 O 5 loss. Biogenic VOCs dominated the nocturnal NO 3 + VOCs reaction (67.2% of NO 3 loss), while aromatic hydrocarbons (20.1%) and alkenes (12.5%) also made significant contributions. The homogeneous loss of N 2 O 5 by H 2 O(g) contributed 1.2%-20.6% of N 2 O 5 loss. These values may be the upper limit if the rate constant of the homogeneous N 2 O 5 hydrolysis adopted from [6] is overestimated as suggested by [10,59]. The most important removal pathway of N 2 O 5 was heterogeneous uptake on aerosols, contributing 58.1%-96.9% of total N 2 O 5 loss. The heterogeneous loss rate coefficient of N 2 O 5 (k(N 2 O 5 ) het ) was most prominent in the sand storm on the nights of 3rd May and 4th May.
It is worth noting that other potential NO 3 loss pathways which were not considered in our analysis may give rise to uncertainties in our result. For example, NO 3 + VOCs reactions can produce HO x and RO x radicals, which consume NO 3 radical [60]. In addition, NO 3 is subject to heterogeneous loss [61]. Due to a lack of measurements of RO x , and HO x , and limited knowledge on the NO 3 uptake coefficient, these NO 3 loss pathways are not included here. HOx and ROx radicals, which consume NO3 radical [60]. In addition, NO3 is subject to heterogeneous loss [61]. Due to a lack of measurements of ROx, and HOx, and limited knowledge on the NO3 uptake coefficient, these NO3 loss pathways are not included here.

Derivation of γ(N2O5) and Evaluation of Parameterizations
To estimate γ(N2O5) from the measurement data, the following selection criteria were adopted; the procedures were similar to those used in previous studies with minor modifications [11,47].
1. The air mass should be stable without dramatic changes in temperature, RH, and wind direction.
Wind speed should be less than 3 m/s to minimize the effect of air mass transport. 2. Ambient NO should be below 0.1 ppbv. Otherwise, little production of N2O5 would occur. 3. ClNO2 should exhibit an increasing trend, indicating considerable uptake of N2O5. In cases with

Derivation of γ(N 2 O 5 ) and Evaluation of Parameterizations
To estimate γ(N 2 O 5 ) from the measurement data, the following selection criteria were adopted; the procedures were similar to those used in previous studies with minor modifications [11,47].

1.
The air mass should be stable without dramatic changes in temperature, RH, and wind direction. Wind speed should be less than 3 m/s to minimize the effect of air mass transport.

2.
Ambient NO should be below 0.1 ppbv. Otherwise, little production of N 2 O 5 would occur.

3.
ClNO 2 should exhibit an increasing trend, indicating considerable uptake of N 2 O 5 . In cases with decreasing or fluctuating ClNO 2 , physical processes or changes of air mass may invalidate the method for the estimation of γ(N 2 O 5 ). 4.
S a should be above 200 µm 2 /cm 3 to facilitate significant N 2 O 5 uptake. In cases with S a below 200 µm 2 /cm 3 , we found that the derived γ(N 2 O 5 ) was either abnormally high (for example, above 0.1), or even negative. This phenomenon indicates that the method we adopted may be invalid in low aerosol loadings.
Two examples that satisfy the criteria are shown in Figure S4. In total, nine cases were selected, with durations of 2 to 7 h, and γ(N 2 O 5 ) and ϕ(ClNO 2 ) were calculated following the method in Section 2.3, as summarized in Table 1. γ(N 2 O 5 ) ranged from 0.013 to 0.042 in urban air masses. The γ(N 2 O 5 ) range is comparable to the results of one previous study in urban Beijing (0.012~0.055) [57] and higher than those obtained in some places in the US and Europe [27,59], but lower than other results obtained over the North China Plain [32,44]. The field-derived ϕ(ClNO 2 ) (0.218 ± 0.247) was much lower than parameterized values using (Equation (13)) (0.796 ± 0.056) in all cases, which is consistent with the findings in previous studies, suggesting an overestimation of ClNO 2 yield in the current parameterization or an unknown suppression effect on ClNO 2 yield [32,62]. Table 1. Field-derived N 2 O 5 uptake coefficient (average ± standard deviation) and ClNO 2 production yield estimated for the selected periods. The time periods are all local time (LT). Since only one ϕ(ClNO 2 ) value was derived for each time period, no standard deviation was obtained for ϕ(ClNO 2 ).

Category
Periods γ (N  The γ(N 2 O 5 ) derived on the night of 3rd May (4th May 04:00~06:00) and 4th May (4th May 23:00 to 5th May 05:00) represents the N 2 O 5 uptake in the early and later stage of the sand storm event. Five-minute average γ(N 2 O 5 ) was low (0.008) at the beginning of the dust storm at~04:00 on 4th May (see Figure 3), but γ(N 2 O 5 ) increased gradually to 0.039 at 06:00 when aerosols reached high levels. The γ(N 2 O 5 ) continued to increase and remained at~0.044 on the following night, with sustained high levels of aerosols. This stable value can be considered the γ(N 2 O 5 ) on ambient dust particles in the region, and this field-derived value compares well with the laboratory-determined γ(N 2 O 5 ) ((5 ± 2) × 10 −2 ) on bulk CaCO 3 dust [21]. The γ(N 2 O 5 ) on May 5th was higher than in urban air masses (see Table 1), although the aerosol water content ([H 2 O]) was relatively low (14~21 M) during the dust storm, according to E-AIM ( Figure S5). Assuming a volume-limited mechanism, larger particle size in the sand dust plumes might be responsible for the high γ(N 2 O 5 ) on 5th May. Another possibility is that E-AIM (model III), which is used in the present work, underestimates the [H 2 O] adsorbed by sand dust particles because it does not consider the significant enhancement of hygroscopicity in the conversion of CaCO 3 to deliquescent Ca 2+ [63].
To evaluate the applicability of the commonly used parameterizations, the field-determined 5-min average γ(N 2 O 5 ) values were averaged to hourly values and compared with three parameterized γ(N 2 O 5 ) values ( Figure 5), calculated according to the approaches introduced in Section 2.4 and based on the hourly average of the input parameters. We also calculated and showed propagated errors of three parameterized γ(N 2 O 5 ) by taking partial differentials of the variables in the parameterization formula and the measurement uncertainty for each variable. Because the measured V a /S a is invalid for the heavy sand storm event (method Section 2.2), parameterized γ(N 2 O 5 ) was not calculated in that case. Overall, the parameterized γ(N 2 O 5 ) BT (0.026 ± 0.003) was lower than the field-observed γ(N 2 O 5 ) (0.032 ± 0.010) and had much less variability. This result contrasts with previous studies, which usually indicated higher parameterized γ(N 2 O 5 ) BT [11,30,31,33]. The parameterization that considered only T and RH (γ(N 2 O 5 ) EJ ) was systematically lower than the field-observed γ(N 2 O 5 ), which differs from the good fit of γ(N 2 O 5 ) EJ at Wangdu in the humid summer period [11]. When the organic coating effect was considered and combined with γ(N 2 O 5 ) BT , the parameterized γ(N 2 O 5 ) A using (Equation (11)) was even lower. The significant underestimation of γ(N 2 O 5 ) when organic coatings were considered is similar to the findings of previous studies (e.g., [11]).
Atmosphere 2019, 10, x FOR PEER REVIEW 10 of 16 organic coating effect was considered and combined with γ(N2O5)BT, the parameterized γ(N2O5)A using (Equation (11)) was even lower. The significant underestimation of γ(N2O5) when organic coatings were considered is similar to the findings of previous studies (e.g., [11]).

Influencing Factors of γ(N2O5) and Implications
To further investigate the discrepancy between the observed γ(N2O5) and related parameterizations, various influencing factors of γ(N2O5) were examined, namely aerosol volume to surface ratio ( (Figure 6b,c). It seems that the parameter Va/Sa alone can explain the variation of γ(N2O5) in the present study. Including the chemical composition (NO3 − , H2O, and Cl − ) worsens the result of parameterizations. This result contrasts with those of previous studies, which were conducted in conditions with higher relative humidity. Positive correlations between   [11,32]. No correlation between γ(N 2 O 5 ) and aerosol size (R 2 = 0.025) was found in the northeastern US [10]. The finding that γ(N2O5) is dependent on Va/Sa but not chemical composition may be explained by the dry conditions encountered in this study. The deliquescence relative humidities (DRH) of (NH4)2SO4, NH4Cl, and NH4NO3 at 298 K are 79.9%, 80%, and 61.8% [64], respectively, which is much higher than the RH in this study. Thus, the inorganic components of aerosols (Cl − and NO3 − ) observed during our study may not be in the aqueous phase, making aqueous chemical reactions irrelevant to N2O5 uptake. Another interesting observation is the negative correlation between γ(N2O5) and the NOx/NOy ratio (R = 0.64) (Figure 6d). Because NOx/NOy is a measure of the chemical aging of air masses, the negative correlation between γ(N2O5) and NOx/NOy may imply a chemical enhancement effect of unknown secondary products on N2O5 uptake or be explained by the larger particle size as the air masses age.
We then attempted to explore other forms of parameterizations that would better fit the observed γ(N2O5). As the field-derived γ(N2O5) did not show dependence on chemical compositions (i.e., NO3 − , H2O, and Cl − ) but exhibited positive correlation with Va/Sa, it was desirable to have a parameterization without [NO3 − ], [H2O], or [Cl − ] but containing Va/Sa. It turned out that multiplying γ(N2O5)EJ with Va/Sa yielded a good representation of the observed γ(N2O5), with a slope of 1.044, an intercept of 0.0009, and a correlation coefficient of 0.73 as shown in Figure 7 (RMA regression) [25]. (d) ratio of NO x to NO y (NO x /NO y ). The error bars of γ(N 2 O 5 ) have the same meaning as in Figure 5.
The finding that γ(N 2 O 5 ) is dependent on V a /S a but not chemical composition may be explained by the dry conditions encountered in this study. The deliquescence relative humidities (DRH) of (NH 4 ) 2 SO 4 , NH 4 Cl, and NH 4 NO 3 at 298 K are 79.9%, 80%, and 61.8% [64], respectively, which is much higher than the RH in this study. Thus, the inorganic components of aerosols (Cl − and NO 3 − ) observed during our study may not be in the aqueous phase, making aqueous chemical reactions irrelevant to N 2 O 5 uptake. Another interesting observation is the negative correlation between γ(N 2 O 5 ) and the NO x /NO y ratio (R = 0.64) (Figure 6d). Because NO x /NO y is a measure of the chemical aging of air masses, the negative correlation between γ(N 2 O 5 ) and NO x /NO y may imply a chemical enhancement effect of unknown secondary products on N 2 O 5 uptake or be explained by the larger particle size as the air masses age.
We then attempted to explore other forms of parameterizations that would better fit the observed γ(N 2 O 5 ). As the field-derived γ(N 2 O 5 ) did not show dependence on chemical compositions (i.e., NO Figure 7 (RMA regression) [25].   (15) where the factor 0.958 is the inverse of the slope 1.044; the units of RH and T are the same as in (Equation (9)), and the unit of Va/Sa is 10 −8 m. For example, the value 1.0 is used for Va/Sa in (Equation (15)) when Va/Sa = 10 nm. This parameterization (γ(N2O5)dry) is valid for the observed RH range (20%-56%) and temperature above 282 K which are the conditions encountered in the present study. It is highly desirable to test its applicability in other regions/periods with low humidity.

Concluding Remark
This work presents new observational insights into N2O5 uptake on sand dust and urban aerosols under low-humidity conditions. The results reveal a dependence of γ(N2O5) on aerosol properties that differs from those obtained in previous investigations under humid conditions and suggest the important role of the aerosol volume to area ratio (i.e. aerosol diameter). The proposed new parameterization can be used in air quality models to improve simulations of the nighttime fate of NOx and formation of nitrate aerosol in dry and dusty seasons. More investigation is needed to reappraise the controlling factors in N2O5 uptake in dry environments.
where the factor 0.958 is the inverse of the slope 1.044; the units of RH and T are the same as in (Equation (9)), and the unit of V a /S a is 10 −8 m. For example, the value 1.0 is used for V a /S a in (Equation (15)) when V a /S a = 10 nm. This parameterization (γ(N 2 O 5 ) dry ) is valid for the observed RH range (20%-56%) and temperature above 282 K which are the conditions encountered in the present study. It is highly desirable to test its applicability in other regions/periods with low humidity.

Concluding Remark
This work presents new observational insights into N 2 O 5 uptake on sand dust and urban aerosols under low-humidity conditions. The results reveal a dependence of γ(N 2 O 5 ) on aerosol properties that differs from those obtained in previous investigations under humid conditions and suggest the important role of the aerosol volume to area ratio (i.e., aerosol diameter). The proposed new parameterization can be used in air quality models to improve simulations of the nighttime fate of NO x and formation of nitrate aerosol in dry and dusty seasons. More investigation is needed to reappraise the controlling factors in N 2 O 5 uptake in dry environments.