Kinetics of the OH + NO2 reaction: effect of water vapour and new parameterization for global modelling

The effect of water vapour on the rate coefficient for the atmospherically important, termolecular reaction between OH and NO2 was determined in He–H2O (277, 291, and 332 K) and N2–H2O bath gases (292 K). Combining pulsed-laser photolytic generation of OH and its detection by laser-induced fluorescence (PLP-LIF) with in situ, optical measurement of both NO2 and H2O, we were able to show that (in contrast to previous investigations) the presence of H2O increases the rate coefficient significantly. We derive a rate coefficient for H2O bath gas at the low-pressure limit (k2 0 ) of 15.9× 10 −30 cm6 molecule−2 s−1. This indicates that H2O is a more efficient collisional quencher (by a factor of ≈ 6) of the initially formed HO–NO2 association complex than N2, and it is a factor of ≈ 8 more efficient than O2. Ignoring the effect of water vapour will lead to an underestimation of the rate coefficient by up to 15 %, e.g. in the tropical boundary layer. Combining the new experimental results from this study with those from our previous paper in which we report rate coefficients obtained in N2 and O2 bath gases (Amedro et al., 2019), we derive a new parameterization for atmospheric modelling of the OH+NO2 reaction and use this in a chemical transport model (EMAC) to examine the impact of the new data on the global distribution of NO2, HNO3, and OH. Use of the new parameters (rather than those given in the IUPAC and NASA evaluations) results in significant changes in the HNO3/NO2 ratio and NOx concentrations (the sign of which depends on which evaluation is used as reference). The model predicts the presence of HOONO (formed along with HNO3 in the title reaction) in concentrations similar to those of HO2NO2 at the tropical tropopause.


Introduction
In our recent study of the title reaction (Amedro et al., 2019), we reported extensive measurements of the rate constant (k 1 ) for the termolecular reaction between OH and NO 2 (Reaction R1) in N 2 and O 2 bath gas over a large range of temperatures and pressures.
Reaction (R1) converts NO 2 to nitric acid (HNO 3 ) and peroxynitrous acid (HOONO), and its rate strongly influences the relative abundance of atmospheric NO x (NO 2 + NO) and longer-lived "reservoirs" of NO x , which include, for example, HNO 3 and organic nitrates. It also converts OH (the main initiator of atmospheric oxidation) to a long-lived reservoir (HNO 3 ). As the abundances of OH and NO x directly impact on photochemical ozone formation and the lifetimes of greenhouse gases, Reaction (R1) may be considered one of the most important gas-phase processes in atmospheric science (Newsome and Evans, 2017). As outlined by Amedro et al. (2019), the rate coefficients and product branching for this reaction are dependent on pressure and temperature and also on the bath-gas identity, i.e. the identity of the collision partner (M in Reaction R1). The efficiency per collision of energy transfer from the initially "hot" association complex to bath gas can vary considerably, with more complex bath gases possessing more degrees of freedom and bonds with similar vibrational frequencies to those in the association complex being generally more efficient. In this sense, we may expect H 2 O to be better than N 2 or O 2 in quenching [HO-NO 2 ] # .
In this second part of our study of the reaction between OH and NO 2 , we extend the experiments to H 2 O and He bath gases. After N 2 (≈ 78 %) and O 2 (≈ 21 %), water vapour is the third most abundant gaseous species in the lower atmosphere. Its concentration is highly variable in time and space, varying in mixing ratio from a few percent at sea level to parts-per-million levels in the stratosphere. Most of the atmosphere's water vapour is present in the planetary boundary layer where its average mixing ratio on the global scale is ≈ 1 % but which may exceed 5 % in tropical regions.
The effect of water vapour on gas-phase radical reactions has been the subject of numerous studies (Buszek et al., 2011) and is sometimes interpreted in terms of formation of H 2 O-radical complexes leading, via a chaperone-type mechanism, to an increase in the rate constant. An important example of this is the HO 2 self-reaction for which the rate constant increases by a factor of up to 2 in the presence of water vapour due to formation of an HO 2 -H 2 O complex (Lii et al., 1981;Kircher and Sander, 1984). Theoretical calculations (Allodi et al., 2006;Sadanaga et al., 2006;Thomsen et al., 2012) suggest that, under our experimental conditions, the fraction of OH and NO 2 clustered with H 2 O is < 0.1 %, which is insufficient to significantly impact on k 1 .
On the other hand, the role of H 2 O as a collision partner in termolecular, atmospheric reactions has rarely been reported though its potential impact has been highlighted (Troe, 2003). Indeed, water vapour is known to be a more efficient third-body collider, by up to an order of magnitude, compared to N 2 in termolecular reactions such as H + H + M, H + OH + M, and H + O 2 + M (Getzinger and Blair, 1969;Michael et al., 2002;Fernandes et al., 2008;Shao et al., 2019).
The conclusions of three previous experiments examining the role of H 2 O in kinetic studies of Reaction (R1) are highly divergent, with the addition of H 2 O found to (1) increase the rate coefficient (Simonaitis and Heicklen, 1972), (2) have no measurable effect (D'Ottone et al., 2001), or (3) even reduce it (Sadanaga et al., 2006). The overall aim of this research was to clarify these differences and provide quantitative data on the third-body efficiency of H 2 O for the title reaction. Based on the kinetic data for the water-vapour effect reported in this paper and in N 2 and O 2 presented in the first part of this study (Amedro et al., 2019), we have generated a new parameterization for the overall rate coefficient, k 1 , and examined its impact on atmospheric OH, NO x , and NO y in a global chemical transport model.

Experimental details
The details of the experimental set-up have been published previously (Wollenhaupt et al., 2000;Amedro et al., 2019), and only a brief description is given here.

PLP-LIF technique
The experiments were carried out in a quartz reactor of 500 cm 3 volume, which was thermostatted to the desired temperature by circulating a 60 : 40 mixture of ethylene glycol-water. The pressure in the reactor was monitored with 100 and 1000 Torr capacitance manometers. Flow rates were chosen so that a fresh gas sample was available for photolysis at each laser pulse (laser frequency, 10 Hz), thus preventing build-up of products. Pulses of 248 nm laser light (≈ 20 ns) for OH generation from HNO 3 , H 2 O 2 , and O 3 /H 2 O precursors were provided by an excimer laser (Compex 205 F, Coherent) operated using KrF.
OH concentrations (10 11 to 10 12 molecule cm −3 ) were similar to those reported by Amedro et al. (2019) and the same arguments, which rule out a significant influence of secondary reactions, apply. The concentration ranges of the H 2 O 2 , HNO 3 , and O 3 precursors are listed in the notes to Tables 1 and 2. OH was detected following excitation of the OH A 2 (v = 1) ← X 2 (v = 0) transition (Q11(1) at 281.997 nm using a YAG-pumped dye laser (Quantel Brilliant B and Lambda-Physik Scanmate)). OH fluorescence was detected by a photomultiplier tube (PMT) screened by a 309 nm interference filter and a BG 26 glass cut-off filter.

Online absorption measurement of NO 2 and H 2 O concentration
As discussed by Amedro et al. (2019), the determination of the NO 2 concentration is critical for accurate measurement of k 1 . We therefore deployed in situ, broadband (405-440 nm), and single-wavelength (365 nm) optical absorption spectroscopy techniques. The former was located prior (in flow) to the quartz reactor; the latter was located behind the quartz reactor. Using the broadband cell, the NO 2 concentration was retrieved by least square fitting from 405 to 440 nm to a reference spectrum (Vandaele et al., 2002) and de-graded to the resolution of our spectrometer. Simultaneously, we measured NO 2 at 365 nm using the absorption cross section of 5.89 × 10 −19 cm 2 molecule −1 , which was determined previously by Amedro et al. (2019), who give a detailed description of the NO 2 concentration measurements and the choice of reference spectrum. For the temperatures used in this study, corrections to the NO 2 concentration due to formation of the N 2 O 4 dimer were not necessary. For the present experiments, a third absorption cell (l = 40 cm) was placed downstream of the quartz reactor to measure the H 2 O concentration at 184.95 nm. This set-up used a low-pressure mercury Pen-Ray lamp isolated with a 185 nm interference filter as light source. Optical extinction was converted to concentrations using a cross section of 7.14 × 10 −20 cm 2 molecule −1 (Cantrell et al., 1997).

Chemicals
N 2 and He (Westfalen, 99.999 %) were used without further purification. H 2 O 2 (AppliChem, 50 wt %) was concentrated to > 90 wt % by vacuum distillation. Anhydrous nitric acid was prepared by mixing KNO 3 (Sigma Aldrich, 99 %) and H 2 SO 4 (Roth, 98 %) and condensing HNO 3 vapour into a liquid-nitrogen trap. NO (Air Liquide, 3.5) was purified of other nitrogen oxides by fractional vacuum distillation and then converted to NO 2 via reaction with a large excess of O 2 . The NO 2 thus made was trapped in liquid N 2 , and the excess O 2 was pumped out. The resulting NO 2 was stored as a mixture of ∼ 0.5 % NO 2 in N 2 or ∼ 5.5 % NO 2 in He. Distilled H 2 O (Merck, liquid chromatography grade) was degassed before use and kept at constant temperature. (1)-(2) describe the decay of OH and the derivation of the bimolecular rate coefficient k 1 .
where [OH] t is the concentration (molecule cm −3 ) at time t after the laser pulse. k is the pseudo-first-order rate coefficient and is defined as where k d (s −1 ) accounts for OH loss due to diffusion out of the reaction zone and reaction with its photolytic precursors such as HNO 3 or H 2 O 2 . Figure 1. Values of k 1 from this study (black squares) as a function of He concentration at 292 K. Errors are 2σ statistical only. The solid line is a fit to our data using Eq. (4) with k 0 = 1.4 × 10 −30 cm 6 molecule −2 s −1 , k ∞ = 6.3 × 10 −11 cm 3 molecule −1 s −1 , F c = 0.32, m = 3.1, and n = 0. Previous datasets at room temperature (Wine et al., 1979;D'Ottone et al., 2001;Anastasi and Smith;1976;Morley and Smith, 1972) are displayed for comparison.
An exemplary dataset illustrating OH decays and a plot of k versus [NO 2 ] is given in Fig. S1 of the Supplement.
Values of k 1 obtained in He bath gas (25-690 Torr, 292 K) are summarized in Figs. 1 and 2 and listed in Table 1. The kinetics of termolecular reactions can be described by the Lindemann-Hinshelwood mechanism, whereby the rate constant at the low-pressure limit (k 0 , units of cm 6 molecule −2 s −1 ) is proportional to the pressure, and at the high-pressure limit (k ∞ , units of cm 3 molecule −1 s −1 ) is independent of pressure. In the intermediate pressure range, the fall-off regime, the rate coefficient is a function of both low-pressure (k 0 ) and high-pressure (k ∞ ) rate coefficients and the (reaction-partner-dependent) broadening factor F , which accounts for the lower rate constant measured in the fall-off regime than predicted by the Lindemann-Hinshelwood mechanism reactions (Troe, 1983). Under the conditions of temperature and pressure relevant for atmospheric chemistry, the title reaction is in the fall-off regime.
The solid lines in Figs. 1 and 2 are fits according to the Troe formalism for termolecular reactions (Troe, 1983) as adopted by the IUPAC panel in their evaluation of atmospheric reactions: Figure 2. Comparison between the present dataset; the highpressure measurements by Hippler et al. (2006); and the lowpressure measurements by Anderson et al. (1974), Westenberg and Dehaas (1972), Anderson (1980), and Erler et al. (1977). All measurements were made at room temperature. The black line is our pa- where T is the temperature in kelvin, [M] is the bath-gas concentration (molecule cm −3 ), and m and n are dimensionless temperature exponents. The broadening factor, F , is where N = (0.75-1.27 log F c ) and F c is the broadening factor at the centre of the fall-off curve.
As discussed in some detail in the first part of our studies of the title reaction (Amedro et al., 2019), the low-or high-pressure rate constants for the title reaction (k 0 and k ∞ ) are not well defined by existing datasets, which do not deliver sufficiently accurate rate coefficient at very low pressures (< 1 mbar) or at very high pressures (> 500 bar). Studies in which k ∞ has been derived from rates of vibrational relaxation of OH (Smith and Williams, 1985;D'Ottone et al., 2005) return values of k ∞ that provide some constraint on its value, but the associated uncertainty is too large to consider this parameter well defined.
In our previous paper, Amedro et al. (2019) describe highly accurate measurements of k 1 over a wide range of temperatures and pressures in the fall-off regime. From measurements of k 1 in N 2 bath gas, we retrieved values for k 0 and k ∞ of 2.6 × 10 −30 cm 6 molecule −2 s −1 and 6.3 × 10 −11 cm 3 molecule −1 s −1 , respectively, by fixing F c to a value of 0.39, which has a theoretical basis (Cobos and Troe, 2003). The reasons for choosing this value of F c are dis-cussed in Amedro et al. (2019). Note that whereas k 0 is dependent on the bath gas used, at the high-pressure limit, k ∞ should be the same in N 2 , O 2 , He, or H 2 O bath gases.
In Fig. 1 we display pressure-dependent rate coefficients (solid, black squares) obtained in He bath gas at 292 K. The black line is a fit (Eq. 4) to our data with k ∞ fixed to 6.3 × 10 −11 cm 3 molecule −1 s −1 and n = 0 as derived from an extensive dataset obtained using N 2 bath gas (Amedro et al., 2019). For this dataset, the best fit is obtained with F c = 0.32, and k He 0 = 1.4 × 10 −30 cm 6 molecule −2 s −1 . When using F c = 0.39 (i.e. same value as that obtained in N 2 bath gas), the fit slightly overestimates (∼ 5 %) the measurements at pressures above ∼ 300 Torr, whereas it underestimates by 10 % at lower pressures (Fig. S2). We note that using a higher F c = 0.39 resulted in a lower value of k He 0 equal to 1.0 × 10 −30 cm 6 molecule −2 s −1 . The T -dependence factor in He, m(He), was determined to be 3.1 over the temperature range from 277 to 332 K (Table 1 and Fig. S6).
The high precision of our measurements in He and N 2 indicates that different broadening factors (F c ) are required to interpret the pressure dependence of k 1 obtained in N 2 and He. This can be rationalized by considering that F c is the product of strong-collision (F SC c ) and weak-collision (F WC c ) components (Eqs. 6-8) (Gilbert et al., 1983;Troe, 1983;Troe and Ushakov, 2011): F WC c ≈ β 0.14 c .
Here, S K is the Kassel parameter, r is the total number of external rotational modes of the reactants (equal to 5 in the reaction between OH and NO 2 ), and β c is the collision efficiency. While the strong collision component is independent of bath gas (F SC c ≈ 0.46 for the title reaction) a change in F WC c due to a lower collision efficiency (β c ) of He relative to N 2 is likely.
The collision efficiency for N 2 , which was used to calculate F c = 0.39, was β c (N 2 ) ≈ 0.3 (Troe, 2001). The value of F c = 0.32 from our He data implies β c (He) ≈ 0.08, a factor of 3.7 times lower than β c (N 2 ). A large difference in collision efficiency between N 2 and He is consistent with theoretical calculations (Glänzer and Troe, 1974;Troe, 2001;Golden et al., 2003).
In Fig. 1, we also compare our measurements of k 1 in He with data collected in the same pressure range using similar techniques. The three first measurements (Morley and Smith, 1972;Anastasi and Smith, 1976;Wine et al., 1979) used flash photolysis of H 2 O as a OH precursor with detection of OH by resonance fluorescence. Morley and Smith (1972) reported rate coefficients at pressures of 20 to 280 Torr at room temperature with the NO 2 concentration calculated manometrically. Our parametrization agrees within the combined uncertainty of both measurements (Fig. S3). Anastasi and Smith (1976) reported one value of k 1 at 25 Torr of He, which is ≈ 20 % lower than our measurement. Wine et al. (1979) presented values of k 1 at three pressures of He. The agreement with our parameterization at the lowest two pressures is excellent but a deviation of ≈ 20 % is observed at the highest pressure (Fig. S4). As both studies measured NO 2 concentrations using optical absorption at 365 nm, the ≈ 20 % difference is significant. Most recently, D'Ottone et al. (2001) reported rate coefficients from 30 to 600 Torr of He using a very similar approach to ours, i.e. PLP-LIF technique with in situ measurements of NO 2 by absorption at 365 nm. The disagreement (up to 40 %) between our measurements and theirs exceed the combined reported uncertainty (Fig. S5). While it is unclear what could have caused the discrepancy, we note that the data of D' Ottone et al. (2001) are significantly more scattered and do not describe a smooth increase in rate coefficient with pressure as expected from termolecular reactions in the fall-off regime. This would appear to indicate an underestimation of the total uncertainty in their study. Figure 2 extends the pressure range to additionally display data obtained in low-pressure flow tubes (Westenberg and Dehaas, 1972;Anderson et al., 1974;Erler et al., 1977;Anderson, 1980) and the high-pressure measurements by Hippler et al. (2006). At low pressures our data are in excellent agreement (within 10 %) with the data of Erler et al. (1977), but they predict values ≈ 40 % lower than those reported by Westenberg and Dehaas (1972) and Anderson (1980). The data of Anderson et al. (1974) display a large intercept (4.9 × 10 −14 cm 3 molecule −1 s −1 ) at zero pressure, which is attributed to a second-order heterogeneous removal rate constant. As indicated in a critical assessment of the lowpressure data by Amedro et al. (2019), it is unclear whether one can simply subtract a constant value equal to the intercept (obtained from a linear fit) to each data point. If we were to do so, the work by Anderson et al. (1974) would be in very good agreement with the low-pressure study by Erler et al. (1977) as well as with our parameterization extended to low pressures. Additionally, Amedro et al. (2019) demonstrated that, owing to the large asymmetric broadening of fall-off for this reaction, the assumption that the rate coefficient is in the low-pressure limit at N 2 pressures of 0.5 Torr < p < 10 Torr is invalid and leads to underestimation of k 0 . This observation is still true of datasets obtained at low pressures of He, so that while very good agreement is observed between our parameterization and individual rate coefficients obtained between 3 and 8 Torr of He, reported values of k He 0 are 40 % lower than our values obtained from the fall-off analysis. As indicated in Fig. 2, our parameterization of k 1 in He is in very good agreement with the highpressure data reported by Hippler et al. (2006).

Influence of H 2 O on k 1
As mentioned above, the effect of water vapour on k 1 was determined in mixtures of H 2 O with both N 2 and He. This O] = 0.9-4.5 × 10 17 molecule cm −3 ) while keeping the total pressure constant at 50 Torr. Under these conditions, the addition of H 2 O resulted in an increase in k 1 up to a factor of 2 as illustrated by the datasets of Fig. 3 in which the increase in slope as more water vapour is added is proportional to the increase in k 1 (Eq. 2). At the highest concentration of water vapour (4.5×10 17 molecule cm −3 ) the rate coefficient in He-H 2 O increased by a factor of > 3 compared to that obtained in pure He (see Table 1).
In order to determine the temperature dependence of the enhancement in k 1 caused by the presence of water, the experiments in He were carried out at three different temperatures (277, 291, and 332 K). The values of k 1 obtained from these experiments are plotted versus the mole fraction of H 2 O in Fig. 4b. At the pressures used in our experiments, k 1 displays fall-off, precluding a direct measurement of k H 2 O 0 .
The total rate constant measured in, for example, a H 2 O-N 2 bath gas is not equal to the sum of the individual rate constants calculated from the mixing ratios of N 2 and H 2 O; i.e. k N 2 −H 2 O = k N 2 + k H 2 O ; k N 2 −H 2 O is only equal to the sum of k N 2 and k H 2 O at the low-pressure limit ( 1 Torr in the case of the OH reaction with NO 2 ) and under certain conditions where gas mixtures are composed of strong colliders and/or have similar collision efficiencies (Troe, 1980;Burke and Song, 2017). Additionally, at the high-pressure end of the fall-off curve, the rate coefficient is independent of bath gas composition. To be able to make a reasonable prediction of this effect under atmospheric conditions, where the mole fraction of water vapour (x H 2 O ) can be as large as 0.05, we analysed our measurements using two different approaches to determine k H 2 O 0 . In the first case, the low-pressure rate constant in a N 2 -H 2 O mixture is defined as the sum of two individual low-pressure-limit rate constants, where x N 2 and x H 2 O are the mixing ratio for N 2 and H 2 O, respectively; k N 2 0 and k H 2 O 0 are low-pressure-limiting rate constants (units of cm 6 molecule −2 s −1 ) for pure N 2 and H 2 O; k ∞ is the high-pressure limit rate constant (units of cm 3 molecule −1 s −1 ); T is the temperature in kelvin; [M] is The broadening factor, F , is where N = (0.75-1.27log F c ) and F c is the broadening factor at the centre of the fall-off curve.
In the second approach, we follow Burke and Song (2017), where, in addition to the low-pressure limiting rate coefficients, the broadening factors for each bath gas are also mixed linearly and log F N 2 −H 2 O is defined as where , where F N 2 c and F H 2 O c are the broadening factors at the centre of the fall-off curve for N 2 and H 2 O.
In the case where two bath gases have identical (or very similar) values of F c , the two approaches result in identical predictions and the first approach will be preferred for its simplicity. This is the case for N 2 and H 2 O bath gases. However, when two bath gases have significantly different values of F c (as is the case for He-H 2 O mixtures; see below) the second approach provides a more accurate parameterization. as variable and all other parameters fixed with k ∞ = 6.3×10 −11 cm 3 molecule −1 s −1 , k N 2 0 = 2.6 × 10 −30 cm 6 molecule −2 s −1 , and m = 3.6 as derived in Amedro et al. (2019); o was fixed to 3.4 (see below) and F c was held at 0.39, making the assumption that the broadening factors at the centre of the fall-off curve for H 2 O and N 2 were identical. The fit to the data returned k H 2 O 0 = (15.9 ± 0.7) × 10 −30 cm 6 molecule −2 s −1 where the uncertainty is 2σ (statistical only). The solid black line in Fig. 4a represents the parameterization for a varying fraction of H 2 O in N 2 at a total pressure of 50 Torr using the parameters given above. Equating www.atmos-chem-phys.net/20/3091/2020/ efficiency (β c ) is likely to be larger for H 2 O than for N 2 . We found that the He-H 2 O data cannot be modelled by assuming the same F c for both He and H 2 O bath gas, and the approach of Burke and Song (2017) was therefore preferred. In order to analyse the data, we fixed the following parameters: k H 2 O 0 = 15.9×10 −30 cm 6 molecule −2 s −1 , F H 2 O c = 0.39, F He c = 0.32, k He 0 = 1.4 × 10 −30 cm 6 molecule −2 s −1 , and m = 3.1 to derive o = 3.4 ± 0.8 (2σ , statistical only), which describes the temperature dependence of the lowpressure limit in H 2 O as depicted in Fig. 4b.

Parameterization of k 1 from data obtained in N 2 -H 2 O and He-H 2 O bath gases
There is clearly some uncertainty related to the arbitrary use of A potential explanation for the very divergent observations of the effect of H 2 O is the heterogeneous loss of NO 2 when adding H 2 O. We tested for NO 2 loss in a set of experiments in which NO 2 and H 2 O were monitored simultaneously while systematically varying the amount of H 2 O. Our results indicated a reduction in the concentration of NO 2 by up to ≈ 20 % as we increased the concentration of H 2 O up to 4.5 × 10 17 molecule cm −3 . Unless NO 2 is monitored in situ (as in our experiments), 20 % loss of NO 2 would lead to a similar size reduction in the OH decay constant and thus an underestimation of the rate coefficient. A fractional loss of NO 2 of this magnitude would explain why Sadanaga et al. (2006) found an apparent reduction in k 1 when adding H 2 O.
However, the situation becomes more complex if NO 2 is converted to trace gases that are reactive towards OH. For this reason, we performed an additional experiment to investigate whether NO 2 was converted via reaction with H 2 O on surfaces to HONO and/or HNO 3 . Note that conversion of NO 2 to HONO at low pressures (e.g. 50 Torr) would result in an increase in the OH decay constant (k OH+HONO > k OH+NO 2 ), whereas conversion of NO 2 to HNO 3 would result in a decrease (k OH+HNO 3 < k OH+NO 2 ).
In order to test for the presence of HONO, we modified the broadband absorption set-up by replacing the halogen lamp with a deuterium lamp, allowing us to detect HONO around 350 nm as well as NO 2 . The optical absorption of NO 2 and HONO (340-380 nm) was monitored in a flow of NO 2 (1.7 × 10 15 cm −3 ) at 50 Torr of He in the absence and presence of H 2 O ([H 2 O] = 4.5 × 10 17 molecule cm −3 , the maximum concentration used in this work). A depletion in NO 2 of 21 % (3.7 × 10 14 molecule cm −3 ) was observed when H 2 O was added. An analysis of the spectra with and without H 2 O (Fig. S7) enabled us to establish an upper limit to the HONO concentration of ≈ 1 × 10 13 molecule cm −3 , which would correspond to just 3 % of the NO 2 lost. At this concentration, HONO does not significantly increase the loss rate of OH (< 3 % using a rate coefficient for reaction of OH with HONO of 6.0 × 10 −12 cm 3 molecule −1 s −1 (IU-PAC, 2019). In the same experiment, we also recorded the optical density at 185 nm, where H 2 O, NO 2 , and HNO 3 all absorb. Despite the large HNO 3 absorption cross section at this wavelength (1.6 × 10 −17 cm 2 molecule −1 ; Dulitz et al., 2018) we found no evidence for HNO 3 formation, indicating that the NO 2 lost was not converted to gas-phase HNO 3 . Given its great affinity for glass in the presence of H 2 O, we expect that any HNO 3 formed is strongly partitioned to the walls of the reactor. The tests indicate that, on the timescales of our experiments, NO 2 is lost irreversibly on the humidified walls of our experiment. The maximum concentration of H 2 O used in this experiment, 4.5 × 10 17 molecule cm −3 , corresponds to a relative humidity of 80 % (at 292 K) so that H 2 O condensation is not expected.
It is difficult to establish whether our observations of significant NO 2 loss can explain the result of D'Ottone et al. (2001), who did not observe an enhancement in k 1 . D' Ottone et al. (2001) did not state whether, in their experiments, NO 2 and H 2 O were monitored simultaneously. Also, our observed loss of NO 2 is not necessarily transferable to other studies as the heterogeneous loss of NO 2 will vary from one experimental set-up to the next, as residence times and surface areas may vary substantially.
A very simple calculation serves to illustrate the role of water vapour as a third-body quencher for the title reaction. We consider, for example, the tropical boundary layer with a temperature of 30 • C and a relative humidity of 80 % at a total pressure of 1 bar. The pressure of water vapour is 34 mbar, and those of O 2 and N 2 are then 210 and 756 mbar, respectively. A rough contribution of each quenching gas to the overall rate coefficient can be calculated from the respective low-pressure rate coefficients. For N 2 , O 2 , and H 2 O these are (in units of 10 −30 cm 3 molecule −1 s −1 ) 2.6, 2.0, and 15.9. Water vapour is therefore a factor of ≈ 8 more efficient than O 2 , and a factor of ≈ 6 more efficient than N 2 as a quencher of the HO-NO 2 intermediate, which is qualitatively consistent with known strong binding (40 kJ mol −1 ) in the HNO 3 -H 2 O complex (Tao et al., 1996).
For our tropical boundary layer case study, in which the O 2 pressure is only a factor of 6 greater than that of H 2 O, we calculate that H 2 O contributes more to the rate coefficient of the title reaction than O 2 does. Clearly, the neglect of including the quenching effect of H 2 O leads to an underestimation (in the boundary layer) of the rate coefficient for this centrally important atmospheric reaction.
In order to assess both the effect of H 2 O (this work) and the new parameterization for k 1 in N 2 and O 2 bath gases presented in the first part of this study (Amedro et al., 2019), we have used a 3-D chemical transport model (EMAC; see below) to explore the impact on a global scale.

Atmospheric modelling of the OH + NO 2 reaction including the effect of water vapour
The EMAC (ECHAM/MESSy Atmospheric Chemistry) model employed is a numerical chemistry and climate simulation system (Jöckel et al., 2006 using the fifthgeneration ECMWF Hamburg general circulation model (ECHAM5; Roeckner et al., 2006) as core atmospheric general circulation model. For the present study, we applied EMAC (ECHAM5 version 5.3.02, MESSy version 2.53.0) in the T42L47MA resolution, i.e. with a spherical truncation of T42 (corresponding to a quadratic Gaussian grid of approx. 2.8 • by 2.8 • in latitude and longitude) with 47 vertical hybrid pressure levels up to 0.01 hPa. The model has been weakly nudged in spectral space, nudging temperature, vorticity, divergence, and surface pressure (Jeuken et al., 1996). The chemical mechanism scheme adopted (MOM; Mainz Organic Mechanism) includes oxidation of isoprene and saturated and unsaturated hydrocarbons, including terpenes and aromatics . Further, tracer emissions and model set-up are similar to the one presented in Lelieveld et al. (2016). EMAC model predictions have been evaluated against observations on several occasions de Meij et al., 2012;Elshorbany et al., 2014;Yoon and Pozzer, 2014): for additional references, see http://www. messy-interface.org (last access: November 2019). For this study, EMAC was used in a chemical transport model (CTM mode) (Deckert et al., 2011), i.e. by disabling feedbacks from photochemistry on radiation and dynamics. Two years were simulated (2009)(2010), with the first year used as spin-up time. Table 3. Parameters for calculating k 1 using Eqs. (15) and (16).
The following parameterization of k 1 was implemented in EMAC; values of each parameter are listed in Table 3.
The broadening factor, log F , is As described in Sect. 1, the reaction between OH and NO 2 forms not only HNO 3 but also HOONO. HOONO decomposes rapidly at typical boundary layer temperatures, but it is long lived with respect to thermal dissociation at the temperatures found in the upper troposphere and lower stratosphere (UTLS).
The rate constant (k 6 ) for thermal decomposition of HOONO was calculated from the channel-specific rate coefficient for its formation (k 1 α) and an equilibrium coefficient: k 6 = k 1 α/K eq , where K eq = 3.5 × 10 −27 exp(10135/T ) (Burkholder et al., 2015;IUPAC, 2019) based on the analysis of Golden et al. (2003). The branching ratio to HOONO formation (α) was adapted from the present IUPAC recommendations for k 1a and k 1b , which were derived from experimental work (Hippler et al., 2006;Mollner et al., 2010) and theoretical analysis (Troe, 2012). The IUPAC recommendations were augmented with a pressure-independent HOONO yield of 0.035 to better represent the dataset of Mollner et al. (2010), who detected HOONO directly at room temperature. We assume α is independent of water vapour. The expression used and a plot of α at different temperatures and pressures is given in Fig. S8.
In the absence of experimental data on the reactions of HOONO with OH or on its photolysis, we follow the approach of Golden and Smith (2000) and set these equal to those for HO 2 NO 2 : HOONO + hν → HO + NO 2 .
In Fig. 5, we illustrate the global impact (annual average) of H 2 O vapour on the rate coefficient. We plot the fractional reduction in k 1 at the Earth's surface when setting x H 2 O to zero rather than using the EMAC global water-vapour fields. We focus on the boundary layer as the H 2 O concentration is largest here and decreases rapidly with altitude. As expected, the greatest effect is found in warm, tropical regions where neglecting the impact of water vapour results in an average underestimation of the rate coefficient by up to ≈ 8 %. At higher or lower latitudes the effect is diminished and water vapour accounts for only 3 %-4 % of the overall rate coefficient at 40 • N or S. The presence of water vapour does not impact on values of k 1 above the boundary layer.
Our experimental data do not give insight into whether the H 2 O-induced enhancement in k 1 is accompanied by a change in the branching ratio to favour either HNO 3 or HOONO. However, as the formation of HOONO is favoured at high pressures (more effective collisional deactivation), it is possible that the HOONO yield may be enhanced relative to HNO 3 in the presence of H 2 O. If this is the case, the increase in rate coefficient at high water-vapour levels (e.g. in the tropical lower troposphere) may be to some extent offset by the subsequent thermal dissociation of HOONO in these warm regions.
As described by Amedro et al. (2019) (Fig. 1 of that paper), two expert panels (IUPAC, NASA) evaluating kinetic data for use in atmospheric modelling fail to reach consensus for the title reaction, with the preferred rate coefficients differing by as much as 50 % in the cold UTLS. For this reason, we have calculated values of k NASA comparison with the rate coefficient derived from the IUPAC parameterization shows that k IUPAC 1 k this work 1 varies from ≈ 0.9 at the surface to ≈ 1.1 at the tropopause but increases to > 1.3 at the low pressures and temperatures that reign at 30 km and above. At high altitudes (low pressure and temperature) the rate coefficients that the evaluation panels recommend are strongly biased by choice of the rate coefficient (and its temperature dependence) at the low-pressure limit. As discussed by Amedro et al. (2019) the available experimental data at low pressures and temperatures are not of sufficient accuracy to use as basis for recommendation of k 0 , and this is reflected in the highly divergent values of k 1 under these conditions.
As mentioned above, the atmospheric HNO 3 /NO 2 ratio is expected to be highly sensitive to the rate coefficient k 1 , with an increase in k 1 resulting in an increase in the HNO 3 /NO 2 ratio and vice versa. The HNO 3 /NO 2 ratio also depends on the concentration of OH, and thus the effect of using different values of k 1 will be most apparent in regions where the greatest OH concentrations are found, i.e. at low latitudes. At higher latitudes, especially in winter months where solar insolation is weak and OH levels are relatively low, the HNO 3 /NO 2 ratio will also be impacted by night-time conversion of NO 2 to N 2 O 5 and finally, via heterogeneous hydrolysis, to HNO 3 . In Fig. 7 we plot zonally and yearly averaged model values of HNO 3 NO 2 (IUPAC)/ HNO 3 NO 2 (this work) in the upper panel (Fig. 7a) and HNO 3 NO 2 (NASA)/ HNO 3 NO 2 (this work) in the lower panel (Fig. 7b). Compared to the present parameterization of k 1 , the IUPAC evaluation returns HNO 3 /NO 2 ratios that are between 0.9 and 1 throughout most of the lower and free troposphere (up to ≈ 5 km) and larger HNO 3 /NO 2 ratios (factor of 1.1 to 1.15) above ≈ 10 km especially at the tropical tropopause. The divergence between the HNO 3 /NO 2 ratios increases as we move further into the stratosphere with HNO 3 NO 2 (IUPAC)/ HNO 3 NO 2 (this work) values as large as 1.2 to 1.3 above 25 km. At the same time, NO x levels (NO x = NO + NO 2 ) decrease by a factor of ≈ 0.95 (see Fig. S9). When we compare our parameterization with that of the NASA panel, the picture is largely reversed (lower panel, Fig. 7b). Again, we find reasonable agreement in the HNO 3 /NO 2 ratio in the lowermost atmosphere, but in this case lower values (0.8 to 0.9) in the lower stratosphere, which are accompanied by a factor of 1.06 change in NO x concentrations (Fig. S9). For both the NASA and IUPAC parameterizations, the largest differences in the HNO 3 /NO 2 ratio compared to the present study are found higher in the atmosphere. The modelling studies confirm the simple calculation of Amedro et al. (2019;see Fig. 1 of their paper), showing that the IUPAC and NASA parameterizations result in very different values of k 1 in some parts of the atmosphere, and they will result in divergent predictions of partitioning of reactive nitrogen between NO x and NO y . Use of the parameterization based on the present dataset lies roughly between the two evaluations, with best agreement observed with NASA for the lower atmosphere. However, as previous laboratory studies had not identified the important role of H 2 O in the title reaction, which could therefore not be incorporated in either of the previous parameterizations, any agreement at better than the 10 % level is fortuitous, reflecting random cancelling of systematic bias.
As reaction with OH is the predominant sink for most atmospheric trace gases, its concentration largely defines the oxidizing power of the atmosphere (Lelieveld et al., 2004(Lelieveld et al., , 2008(Lelieveld et al., , 2016 and even changes of a few percent in its concentration are significant. An increase in the rate coefficient of the title reaction will reduce the atmospheric abundance of this centrally important radical. In Fig. S10 we illustrate the impact of using the parameterization of k 1 from the present study compared to the IUPAC and NASA recommendations. The upper panel in Fig. S10 plots the ratio of OH concentrations obtained when using the IUPAC parameterization and that from the present study, OH(IUPAC)/OH(this work). Throughout the troposphere OH(IUPAC)/OH(this work) deviates by only a few percent, with a value of 1.02 at the surface and 0.96 at the tropical tropopause. OH(NASA)/OH(this work) is also 1.02 at the surface but increases to 1.04 at the tropical tropopause as the NASA-derived value of k 1 is lower at the temperatures and pressures encountered in this part of the atmosphere. The weak effect of changing k 1 on OH at the surface reflects the fact that many reactions apart from that with NO 2 contribute to the overall sink term for OH in the lower troposphere.
Although our experiments do not give insight into the branching between formation of HOONO and HNO 3 in the title reaction, previous work predicts a significant yield of HOONO especially at low temperatures (see Fig. S8). As the lifetime of HOONO with respect to re-dissociation to reactants is short at, for example, boundary layer temperatures (≈ 1 s at 298 K and 1 bar pressure), its formation may be seen as an effective reduction in the rate coefficient for OH + NO 2 (Golden and Smith, 2000). However, its lifetime increases to several days at temperature and pressure conditions typical of the tropical tropopause (100 mbar, 220 K). As HOONO formation and loss are now parameterized (see above) in EMAC, we can explore its potential contribution to odd-nitrogen species in the atmosphere. The reaction between OH and NO 2 to form HOONO converts short-lived HO x (HO x = OH + HO 2 ) and NO x (NO x = NO + NO 2 ) into a longer-lived "reservoir" species, and in this sense it is similar to the reaction between HO 2 and NO 2 to form HO 2 NO 2 : which is also thermally unstable, dissociating to reform HO 2 and NO 2 . Unlike HOONO, for which there are no atmospheric measurements, much effort has been made to measure concentrations of HO 2 NO 2 in colder regions of the atmosphere, and it is considered an important component of the NO y budget at high altitudes (Nault et al., 2016). We therefore compared EMAC predictions of HOONO concentrations with those of HO 2 NO 2 . The results are displayed in Fig. 8, in which we plot the zonally averaged HOONO/HO 2 NO 2 ratio. Immediately apparent from Fig. 8 is that, compared to HO 2 NO 2 , HOONO is a minor component of NO y in the warm, lower atmosphere. This reflects the difference in the thermal decomposition rate constant of the two trace gases, i.e. that of HO 2 NO 2 being ≈ 4 × 10 −5 s −1 in, for example, the middle troposphere at 400 mbar and 250 K, whereas HOONO decomposes a 10 times faster so that its lifetime is only ≈ 1000 s. In the UTLS region, the ratio increases further (HO 2 NO 2 is a factor of 50 more long lived with respect to thermal decomposition at 100 mbar and 220 K), but the lifetimes of both gases under these conditions are sufficiently long that their concentrations are largely determined by their production rates and their losses due to photolysis and reaction with OH. The maximum ratio of HOONO to HO 2 NO 2 is found at the tropical tropopause, where concentrations become comparable. As the modelled loss processes of HOONO and HO 2 NO 2 (rate constants for photolysis and reaction with OH) are assumed to be identical, the occurrence of the maximum HOONO to HO 2 NO 2 ratio at the tropical tropopause is related to the ratio of the (temperature-dependent) rate coefficients responsible for their formation (at 220 K and 100 mbar this favours HOONO formation by a factor of ≈ 2) and the model OH/HO 2 ratio. Whilst this result indicates that HOONO could be an important reservoir of NO x under certain conditions, we must bear in mind that there is great uncertainty associated not only with the branching ratio to HOONO formation in Reaction (R1b) but also with its loss processes (reaction with OH, photolysis), which remain unexplored experimentally. OH reacts with HO 2 NO 2 via H abstraction from the H−OO group (IUPAC, 2019), and a similar mechanism is likely for HOONO. As the H−OO bond strength is likely to be greater in HOONO than in HO 2 NO 2 (larger electron density around the peroxy bond), we may expect the rate coefficient to be lower for HOONO. A significantly lower rate coefficient for reaction with OH (or photolysis rate constant) could greatly increase the abundance of HOONO. If this were the case, airborne instruments that measure NO x would likely also measure some fraction of HOONO following its rapid decomposition in warm inlet lines, as has been observed for HO 2 NO 2 and CH 3 O 2 NO 2 (Nault et al., 2015;Silvern et al., 2018). Clearly, more experimental or theoretical data that better constrain the yield of HOONO and its atmospheric loss processes as well as atmospheric measurements are necessary in order to improve our understanding of the role of the reaction between OH and NO 2 throughout the atmosphere.

Conclusions
We have made very precise and accurate measurements for the overall rate coefficient, k 1 , of the reaction between OH and NO 2 , which is of critical importance in atmospheric chemistry. Our experiments demonstrate clearly that the presence of H 2 O increases significantly the overall rate coefficient (k 1 ) of the reaction between OH and NO 2 . H 2 O is found to be a more efficient collisional quencher (by a factor of ≈ 6) of the initially formed HO-NO 2 association complex than N 2 and a factor of ≈ 8 more efficient than O 2 . A new parameterization of the rate coefficient for the title reaction that considers the roles of N 2 , O 2 , and H 2 O as third-body quenchers (also using data from our previous paper; Amedro et al., 2019) has been incorporated into a global chemistry transport model to assess its impact on, for example, the HNO 3 /NO 2 ratio as well as NO x and OH levels. Compared to existing evaluations of the kinetic data, use of the new parameters will result in significant changes (5 %-10 %) Figure 8. Model (EMAC) ratio of HOONO (formed in the reaction of NO 2 with OH) to HO 2 NO 2 (formed in the reaction of NO 2 with HO 2 ) calculated using the present parameterization of k 1 and equating the (unknown) rate coefficients for loss of HOONO via reaction with OH or photolysis to those of HO 2 NO 2 . The black line represents the model tropopause.
in the partitioning of NO x and NO y , the direction of the bias depending on which evaluation is used as reference and on region of the atmosphere. This work highlights the continuing importance of obtaining accurate laboratory kinetic data for those reactions that are central to our understanding of atmospheric chemistry and which provide anchor-points in chemical transport models. Though the result is associated with great uncertainty owing to missing kinetic parameters for HOONO, the global model predicts the presence of HOONO in concentrations similar to those of HO 2 NO 2 at the tropical tropopause. The present dataset addresses only the overall rate coefficient (k 1 ). Detailed experimental studies of the formation of HOONO (e.g. its yield at various temperatures and in the presence of H 2 O) and on the fate of HOONO (OH kinetics, photolysis) are required to better assess its role as an NO x and HO x reservoir in cold parts of the atmosphere.
Data availability. The rate coefficients measured during this experimental study are listed in Table 1.
Author contributions. The experiments were carried out by DA, AJCB, and MB. The data analysis and preparation of the paper were performed by DA, with assistance from JL and JNC. The global modelling was performed by AP.
Competing interests. The authors declare that they have no conflict of interest.
Financial support. The article processing charges for this openaccess publication were covered by the Max Planck Society.
Review statement. This paper was edited by Rainer Volkamer and reviewed by three anonymous referees.