Heterogeneous Uptake of N₂O₅ in Sand Dust and Urban Aerosols Observed during the Dry Season in Beijing

Abstract

The uptake of dinitrogen pentoxide (N₂O₅) on aerosols affects the nocturnal removal of NO_x and particulate nitrate formation in the atmosphere. This study investigates N₂O₅ 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 N₂O₅ uptake rate (k(N₂O₅) up to ~0.01 s⁻¹) was observed during a sand storm event, and the uptake coefficient (γ(N₂O₅)) was estimated to be 0.044. The γ(N₂O₅) 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(N₂O₅) underestimated the field-derived γ(N₂O₅). A new parameterization is suggested for dry conditions, which considers the effect of V_a/S_a, temperature, and relative humidity.

1. Introduction

Dinitrogen pentoxide (N₂O₅) is an important nighttime reservoir of NO_x which is a key precursor to photochemical production of ozone [1]. The loss of N₂O₅ on aerosol surface, therefore, affects the lifetime of NO_x and produces nitrate aerosol, contributing to particulate pollution (e.g., [2]). The formation of N₂O₅ is initiated by the gas phase production of nitrate radical (NO₃), which is in rapid equilibrium with N₂O₅ (R2) [3,4]. As (R2) is a second-order reaction, M in (R2) denotes the third body, i.e., ambient air.

(R1)    NO₂(g) + O₃(g) → NO₃(g) + O₂(g)

(R2)   NO₃(g) + NO₂(g) + M ↔ N₂O₅(g) + M

NO₃ and N₂O₅ are partially removed via gas phase reactions of NO₃ with volatile organic compounds (VOCs) and NO [5]:

(R3)   NO₃(g) + VOCs → products

(R4)   NO₃(g) + NO(g) → 2NO₂(g)

N₂O₅ can undergo homogeneous hydrolysis with water vapor in the gas phase [6], producing nitric acid (R5) or heterogeneous hydrolysis of N₂O₅ on the aerosol surface forming nitryl chloride (ClNO₂) and particulate nitrate (NO₃⁻) (R6) [7,8]. ClNO₂ yield (φ(ClNO₂)) is used to describe the amount of ClNO₂ production from unit loss of N₂O₅ on aerosols [9].

(R5)   N₂O₅(g) + H₂O(g) → 2HNO₃(g)

(R6)   N₂O₅(g) + (H₂O or Cl⁻) (aq) → NO₃⁻(aq) + ClNO₂(g)

The rate of N₂O₅ uptake on aerosols (k(N₂O₅), s⁻¹) can be expressed as (Equation (1)), where c(N₂O₅) (m/s) is the mean molecular speed of N₂O₅, S_a (μm²/cm³) is the aerosol surface area density, and γ(N₂O₅) is the uptake probability of N₂O₅ on the aerosol surface.

$$k({\mathrm{N}}_2{\mathrm{O}}_5)=\frac{1}{4} \mathrm{c}({\mathrm{N}}_2{\mathrm{O}}_5){\mathrm{S}}_{\mathrm{a}}\mathsf{\gamma }({\mathrm{N}}_2{\mathrm{O}}_5)$$

(1)

γ(N₂O₅) 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 N₂O₅ uptake is enhanced by chloride and aerosol water content ([H₂O]) 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 N₂O₅ 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(N₂O₅) in the range 0.013~0.2 [20,21,23,24]. Although laboratory studies have suggested large γ(N₂O₅) on mineral dust, there have been no reports on direct observations of N₂O₅ uptake on ambient mineral dust.

Several parameterizations of γ(N₂O₅) have been proposed to predict γ(N₂O₅) based on laboratory results on the relation of γ(N₂O₅) 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(N₂O₅) was derived using field observations or direct measurements of N₂O₅ reactivity [10,27,28,29]. The enhancement effect of chloride and [H₂O] and the inhibition effect of nitrate on γ(N₂O₅) have been observed in the field [11,30,31,32]. However, the parameterized γ(N₂O₅) based on the observed physiochemical properties of aerosols has been found to be inconsistent with observed γ(N₂O₅) [10,31]. For example, the widely adopted parameterization proposed by Bertram and Thornton (denoted γ(N₂O₅)_BT) has often yielded higher values than the observed or directly measured γ(N₂O₅) when the observed γ(N₂O₅) 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 N₂O₅ uptake [33]. More investigation of γ(N₂O₅) in the real atmosphere is needed to improve the parametrization, while observation of N₂O₅ uptake on ambient sand dust is also desirable.

The present study examines the heterogeneous uptake of N₂O₅ 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 N₂O₅ and related chemical species at the sampling site. The loss rate coefficients of N₂O₅ are calculated to reveal the dominant removal pathways of N₂O₅. γ(N₂O₅) is then estimated from the field measurements and compared to parameterized values. Meteorological and chemical factors that influence γ(N₂O₅) are examined. A modified parameterization is proposed for relatively dry conditions.

2. Methods

2.1. 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]).

2.2. Instruments

2.2.1. 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. Overall uncertainty was 25% for N₂O₅ and ClNO₂ [38]. The measurements were conducted at a time resolution of ~10 s, and the data were later averaged to 1 min for further analysis.

2.2.2. Other Measurements

Trace gases, aerosol, and VOC composition related to N₂O₅ and ClNO₂ were concurrently measured. NO and NO₂ 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). O₃ and SO₂ 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⁺, NH₄⁺, K⁺, Mg²⁺, Ca²⁺, Cl⁻, NO₃⁻, SO₄²⁻) 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 NO₃ 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, $\mathrm{GF}=0.582{\left(8.46+\frac{1}{1-\mathrm{RH}}\right)}^{1/3}$ 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.

2.3. Estimation of γ(N₂O₅) and φ(ClNO₂)

A modified steady state method was applied to estimate γ(N₂O₅) and φ(ClNO₂) [3,39,42,47]. Due to rapid equilibrium between NO₃ and N₂O₅, these two species are regarded as a pair. The changing rate of the NO₃ and N₂O₅ pair equals the production rate of NO₃ radial minus the total loss rate of NO₃ and N₂O₅ (Equation (2)), assuming that transportation effect can be ignored.

d([N₂O₅] + [NO₃])/dt = d[NO₃]/dt + d[N₂O₅]/dt
= k₁[NO₂][O₃] − k(NO₃)[NO₃] − k(N₂O₅)[N₂O₅]

(2)

where k₁ is the rate constant of (R1). k(NO₃), known as NO₃ reactivity, is expressed as follows:

$$k({\mathrm{NO}}_3)=k_{{\mathrm{NO}+\mathrm{NO}}_3}[\mathrm{NO}]+\sum k_{\mathrm{i}}[{\mathrm{VOC}}_{\mathrm{i}}]$$

(3)

where k_i is the rate constant of NO₃ + VOC reactions. The NO₃ radical concentration is estimated from the NO₃ and N₂O₅ equilibrium:

$$\left[{\mathrm{NO}}_3\right]=\frac{{[\mathrm{N}}_2{\mathrm{O}}_5]}{\left[{\mathrm{NO}}_2\right]K_{\mathrm{eq}}}$$

(4)

where K_eq is the temperature-dependent equilibrium coefficient of the NO₃–N₂O₅ pair. Substitution of (Equation (3)) and (Equation (4)) into (Equation (2)) and rearrangement yields (Equation (5)) as follows, where k(N₂O₅) is extracted.

k(N₂O₅) = (k₁[NO₂][O₃] − k(NO₃)[N₂O₅]/([NO₂]K_eq) − d[N₂O₅]/dt −
d[NO₃]/dt)/[N₂O₅].

(5)

d[N₂O₅]/dt and d[NO₃]/dt are approximated as the rate of increase of [N₂O₅] and [NO₃] over 5 min, and thus can be replaced by δ[N₂O₅]/ δt and δ[NO₃]/ δt with δt = 5 min. Then, the time series of k(N₂O₅) can be derived. The heterogeneous loss rate coefficient of N₂O₅ (k(N₂O₅)_het) is obtained when the homogeneous loss rate coefficient of N₂O₅ is subtracted [6,48].

k(N₂O₅)_het = k(N₂O₅) − k(N₂O₅)_homo

(6)

$$k({\mathrm{N}}_2{\mathrm{O}}_5{)}_{\mathrm{homo}}=k_{\mathrm{a}}{\times [\mathrm{H}}_2{\mathrm{O}]+k}_{\mathrm{b}}{\times [\mathrm{H}}_2{\mathrm{O}]}^2.$$

(7)

When the surface area density (S_a) of aerosols and velocity of N₂O₅ molecules (c(N₂O₅)) are available, γ(N₂O₅) can be obtained following (Equation (1)). Then φ(ClNO₂) can be calculated using the below formula by integrating over the whole period of the selected case.

$$\mathsf{\phi }\left({\mathrm{ClNO}}_2\right)=\frac{\Delta {[\mathrm{ClNO}}_2]}{\int {k(\mathrm{N}}_2{\mathrm{O}}_5{)}_{\mathrm{het}}\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]\mathrm{d}t}$$

(8)

2.4. Parameterizations of γ(N₂O₅) and φ(ClNO₂)

We evaluated three parameterizations of γ(N₂O₅). The first relates γ(N₂O₅) to RH and temperature (T) (denoted γ(N₂O₅)_EJ) [25] in which the dependences of γ(N₂O₅) on RH and T were separately derived on ammonium sulfate aerosol [12,13].

γ(N₂O₅)_EJ = (2.79 × 10⁻⁴ + 1.3 × 10⁻⁴ × RH − 3.43 × 10⁻⁶ × RH² + 7.52 ×
10⁻⁸ × RH³) × 10^{(0.04 × (T − 294)}

(9)

The second parameterization of γ(N₂O₅) (denoted γ(N₂O₅)_BT) considers the bulk concentration of chloride [Cl⁻], nitrate [NO₃⁻], and aerosol water content ([H₂O]) [14]. Three important assumptions are adopted to establish this parameterization: (1) the whole particle is in an aqueous phase; (2) aerosols can be supersaturated; and (3) the accommodated N₂O₅ can react within the whole particle volume. Then γ(N₂O₅)_BT is expressed as (Equation (10)).

$$\mathsf{\gamma }({\mathrm{N}}_2{\mathrm{O}}_5{)}_{\mathrm{BT}}=Ak(1-\frac{1}{1+\frac{k_{\mathrm{R}3}{[\mathrm{H}}_2\mathrm{O}]}{k_{\mathrm{R}2\mathrm{b}}{[\mathrm{NO}}_3^{-}]}+\frac{k_{\mathrm{R}4}{[\mathrm{Cl}}^{-}]}{k_{\mathrm{R}2\mathrm{b}}{[\mathrm{NO}}_3^{-}]}})$$

(10)

where [H₂O], [Cl⁻], and [NO₃⁻] are derived from the extended aerosol inorganics model (E-AIM) (Text S1) [49]. Organic aerosols were not considered in the E-AIM model. k_R2b, k_R3, and k_R4 are reaction rate constants: k_R4/k_R2b = 29 ± 6; k_R3/k_R2b = 0.06 ± 0.01 [14]. A is proportional to V_a/S_a. k is an empirical pre-factor in which k = β(1 − exp(−δ[H₂O])) with β = (11.5 ± 3) × 10⁵ and δ = 0.13 ± 0.05.

The third parameterization (denoted γ(N₂O₅)_A) adds the inhibition effect of the organic coating on γ(N₂O₅) [16].

$$\frac{1}{{\mathsf{\gamma }(\mathrm{N}}_2{\mathrm{O}}_5{)}_{\mathrm{A}}}=\frac{1}{{\mathsf{\gamma }}_{\mathrm{core}}}+\frac{1}{{\mathsf{\gamma }}_{\mathrm{Org}}}$$

(11)

$${\mathsf{\gamma }}_{\mathrm{Org}}=\frac{{4\mathrm{RT}H}_{\mathrm{org}}{D}_{\mathrm{org}}{R}_{\mathrm{c}}}{{\mathrm{c}(\mathrm{N}}_2{\mathrm{O}}_5){LR}_{\mathrm{p}}}$$

(12)

(Equation (11)) treats the N₂O₅ 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 N₂O₅ in organic coating, which are calculated by assuming H_orgD_org = 0.03H_aqD_aq [2,11]. H_aq (5000 M/atm) and D_aq (10⁻⁹ m²/s) are the corresponding parameters of N₂O₅ in the aqueous core [2].

The parameterized ClNO₂ yield is also calculated using the following equation [14].

$$\mathsf{\phi }({\mathrm{ClNO}}_2{)}_{\mathrm{BT}}=(1+\frac{\left[{\mathrm{H}}_2\mathrm{O}\right]}{483\left[{\mathrm{Cl}}^{-}\right]}{)}^{-1}$$

(13)

3. Results and Discussion

3.1. Overall Observations

Measurement results for N₂O₅, ClNO₂, 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 N₂O₅ and ClNO₂ exhibited typical diurnal variations, increasing during the night and decreasing during the day (Figure S3).

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]. N₂O₅ levels were higher than those of ClNO₂ from 24th April to 1st May with low aerosol loadings, suggesting low N₂O₅ uptake or ClNO₂ yield. This period was influenced by light dust, as indicated by abundant Ca²⁺ (10–40 μg/m³) and moderate PM_2.5 (20–100 μg/m³) 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 ClNO₂ to N₂O₅ 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/m³ (Figure 2). The sand storm event is displayed separately for clarity (Figure 3). ClNO₂ mixing ratios of up to 0.82 ppbv and much lower N₂O₅ levels (10–20 pptv) were observed, indicating rapid N₂O₅ loss on sand dust. To our knowledge, this is the first observation of N₂O₅ and ClNO₂ during a heavy dust event. This period is denoted as a “sand storm.”

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, 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].

3.2. 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” (30th April and 1st May), two “sand storm” (3rd May and 4th 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 4th night, which is attributable to the rapid heterogeneous loss rate coefficient of N₂O₅ (up to 0.01 s⁻¹, Figure 4b).

$${\mathsf{\tau }(\mathrm{N}}_2{\mathrm{O}}_5)=\frac{{\mathrm{N}}_2{\mathrm{O}}_5\mathrm{concentration}}{{\mathrm{N}}_2{\mathrm{O}}_5\mathrm{loss}\mathrm{rate}}=\frac{{[\mathrm{N}}_2{\mathrm{O}}_5]}{\mathrm{P}\left({\mathrm{NO}}_3\right){-\mathsf{\delta }[\mathrm{N}}_2{\mathrm{O}}_5{]/\mathsf{\delta }t-\mathsf{\delta }[\mathrm{NO}}_3]/\mathsf{\delta }t}$$

(14)

The loss rate coefficients of N₂O₅ uptake were calculated and compared with other loss pathways (Figure 4b). The indirect loss through gas-phase reactions of NO₃ radical with VOCs contributed 1.9%~30.2% of total N₂O₅ loss. Biogenic VOCs dominated the nocturnal NO₃ + VOCs reaction (67.2% of NO₃ loss), while aromatic hydrocarbons (20.1%) and alkenes (12.5%) also made significant contributions. The homogeneous loss of N₂O₅ by H₂O(g) contributed 1.2%–20.6% of N₂O₅ loss. These values may be the upper limit if the rate constant of the homogeneous N₂O₅ hydrolysis adopted from [6] is overestimated as suggested by [10,59]. The most important removal pathway of N₂O₅ was heterogeneous uptake on aerosols, contributing 58.1%–96.9% of total N₂O₅ loss. The heterogeneous loss rate coefficient of N₂O₅ (k(N₂O₅)_het) was most prominent in the sand storm on the nights of 3rd May and 4th May.

It is worth noting that other potential NO₃ loss pathways which were not considered in our analysis may give rise to uncertainties in our result. For example, NO₃ + VOCs reactions can produce HO_x and RO_x radicals, which consume NO₃ radical [60]. In addition, NO₃ is subject to heterogeneous loss [61]. Due to a lack of measurements of RO_x, and HO_x, and limited knowledge on the NO₃ uptake coefficient, these NO₃ loss pathways are not included here.

3.3. 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].

• 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.
• Ambient NO should be below 0.1 ppbv. Otherwise, little production of N₂O₅ would occur.
• ClNO₂ should exhibit an increasing trend, indicating considerable uptake of N₂O₅. In cases with decreasing or fluctuating ClNO₂, physical processes or changes of air mass may invalidate the method for the estimation of γ(N₂O₅).
• S_a should be above 200 μm²/cm³ to facilitate significant N₂O₅ uptake. In cases with S_a below 200 μm²/cm³, we found that the derived γ(N₂O₅) 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(N₂O₅) and φ(ClNO₂) were calculated following the method in Section 2.3, as summarized in

Table 1. Field-derived N₂O₅ uptake coefficient (average ± standard deviation) and ClNO₂ production yield estimated for the selected periods. The time periods are all local time (LT). Since only one φ(ClNO₂) value was derived for each time period, no standard deviation was obtained for φ(ClNO₂).

Category	Periods		γ(N2O5)	φ(ClNO2)	Notes
	From	To
Urban air masses	16th May 23:00	17th May 04:00	0.022 ± 0.005	0.065
	17th May 21:00	18th May 01:00	0.013 ± 0.006	0.048
	18th May 21:00	19th May 04:00	0.030 ± 0.009	0.055 (21:26~22:41)	ClNO2 yield changed
				0.117 (01:06~03:31)
	20th May 21:00	21st May 04:00	0.032 ± 0.007	0.082
	22nd May 0:00	22nd May 04:00	0.035 ± 0.010	0.312
	27th May 20:00	28th May 04:00	0.042 ± 0.008	0.084 (20:01~21:36)	ClNO2 yield changed
				0.319 (01:36~03:01)
	28th May 20:00	28th May 23:00	0.023 ± 0.007	0.142
Heavy sand storm events	4th May 04:00	4th May 06:00	0.019 ± 0.012	0.677	Sand storm arrived
	4th May 23:00	5th May 05:00	0.044 ± 0.002	0.129	Sand storm continued

. γ(N₂O₅) ranged from 0.013 to 0.042 in urban air masses. The γ(N₂O₅) 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(ClNO₂) (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 ClNO₂ yield in the current parameterization or an unknown suppression effect on ClNO₂ yield [32,62].

The γ(N₂O₅) 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 N₂O₅ uptake in the early and later stage of the sand storm event. Five-minute average γ(N₂O₅) was low (0.008) at the beginning of the dust storm at ~04:00 on 4th May (see Figure 3), but γ(N₂O₅) increased gradually to 0.039 at 06:00 when aerosols reached high levels. The γ(N₂O₅) 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(N₂O₅) on ambient dust particles in the region, and this field-derived value compares well with the laboratory-determined γ(N₂O₅) ((5 ± 2) × 10⁻²) on bulk CaCO₃ dust [21]. The γ(N₂O₅) on May 5th was higher than in urban air masses (see Table 1), although the aerosol water content ([H₂O]) 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(N₂O₅) on 5th May. Another possibility is that E-AIM (model III), which is used in the present work, underestimates the [H₂O] adsorbed by sand dust particles because it does not consider the significant enhancement of hygroscopicity in the conversion of CaCO₃ to deliquescent Ca²⁺ [63].

To evaluate the applicability of the commonly used parameterizations, the field-determined 5-min average γ(N₂O₅) values were averaged to hourly values and compared with three parameterized γ(N₂O₅) 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(N₂O₅) 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(N₂O₅) was not calculated in that case. Overall, the parameterized γ(N₂O₅)_BT (0.026 ± 0.003) was lower than the field-observed γ(N₂O₅) (0.032 ± 0.010) and had much less variability. This result contrasts with previous studies, which usually indicated higher parameterized γ(N₂O₅)_BT [11,30,31,33]. The parameterization that considered only T and RH (γ(N₂O₅)_EJ) was systematically lower than the field-observed γ(N₂O₅), which differs from the good fit of γ(N₂O₅)_EJ at Wangdu in the humid summer period [11]. When the 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]).

3.4. 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 (V_a/S_a), water content ([H₂O]), and ratio of chloride to nitrate ([Cl⁻]/[NO₃⁻]). The observed γ(N₂O₅) shows moderate correlation with V_a/S_a (R = 0.68, Figure 6a) but does not exhibit a clear relationship with [H₂O] and [Cl⁻]/[NO₃⁻] (Figure 6b,c). It seems that the parameter V_a/S_a 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 γ(N₂O₅) and [H₂O]/[NO₃⁻] were reported in Seattle, California, and over the eastern United States [10,28,33]. Our studies in China observed the enhancement effects of [Cl⁻] and [H₂O] and the suppression effect of [NO₃⁻] [11,32]. No correlation between γ(N₂O₅) and aerosol size (R² = 0.025) was found in the northeastern US [10].

The finding that γ(N₂O₅) 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 (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 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(N₂O₅) and NO_x/NO_y 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 V_a/S_a, it was desirable to have a parameterization without [NO₃⁻], [H₂O], or [Cl⁻] but containing V_a/S_a. It turned out that multiplying γ(N₂O₅)_EJ with V_a/S_a 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].

Therefore, we propose the following parameterization for dry conditions based on γ(N₂O₅)_EJ:

$$\begin{gathered} \mathsf{\gamma }({\mathrm{N}}_2{\mathrm{O}}_5{)}_{\mathrm{dry}}=0.958\times \frac{{\mathrm{V}}_{\mathrm{a}}}{{\mathrm{S}}_{\mathrm{a}}}\times \mathsf{\gamma }({\mathrm{N}}_2{\mathrm{O}}_5{)}_{\mathrm{EJ}} \\ =0.958\times \frac{{\mathrm{V}}_{\mathrm{a}}}{{\mathrm{S}}_{\mathrm{a}}}\times (2.79\times {10}^{-4}+1.3\times {10}^{-4}\times \mathrm{RH}-3.43\times {10}^{-6}\times {\mathrm{RH}}^2+7.52 \\ \times {10}^{-8}\times {\mathrm{RH}}^3)\times {10}^{(0.04\times (\mathrm{T}-294)} \end{gathered}$$

(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 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(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.

4. 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 NO_x 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.