Using observed urban NO x sinks to constrain VOC reactivity and the ozone and radical budget in the Seoul Metropolitan Area

. Ozone (O 3 ) is an important secondary pollutant that impacts air quality and human health. Eastern Asia has high regional O 3 background due to the numerous sources and increasing and rapid industrial growth, which also impacts the Seoul Metropolitan Area (SMA). However, the SMA has also been experiencing increasing O 3 driven by decreasing NO x emissions, highlighting the role of the local in situ O 3 production on the SMA. Here, comprehensive gas-phase measurements collected on the NASA DC-8 during the National Institute of Environmental Research (NIER)/NASA Korea–United States Air Quality (KORUS-AQ) study are used to constrain the instantaneous O 3 production rate over the SMA. The observed NO x oxidized products support the importance of non-measured peroxy nitrates (PNs) in the O 3 chemistry in the SMA, as they accounted for ∼ 49 % of the total PNs. Using the total measured PNs ( (cid:54) PNs) and alkyl and multifunctional nitrates ( (cid:54) ANs), unmeasured volatile organic compound (VOC) reactivity (R(VOC)) is constrained and found to range from 1.4–2.1 s − 1 . Combining the observationally constrained R(VOC) with the other measurements on the DC-8, the instantaneous net O 3 production rate, which is as high as ∼ 10 ppbvh − 1 , along with the important sinks of O 3 and radical chemistry, is constrained. This analysis shows that (cid:54) PNs play an important role in both the sinks of O 3 and radical chemistry. Since (cid:54) PNs are assumed to be in a steady state, the results here highlight the role that (cid:54) PNs play in urban environments in altering the net O 3 production, but (cid:54) PNs can potentially lead to increased net O 3 production downwind due to their short lifetime ( ∼ 1 h). The results provide guidance for future measurements to identify the missing R(VOCs) and (cid:54) PN production.


S1. Analytical Equation for P(Ox)
The analytical description of P(Ox) and impacts from ΣANs chemistry has been described elsewhere (Farmer et al., 2011 and references therein).Briefly, P(Ox) can be described by combining the following equations (Eq.S1 -S8).These equations are assumed to describe P(Ox) for a single time during the day and is derived from the assumption that the HOx radicals (HOx = OH + HO2 + RO2) are in photostationary steady-state.The steady-state assumption for HOx means production and loss are equal. (Eq.S1) As described elsewhere, under the assumption of rapid P(Ox) and thus radical chain propagation dominates, every RO2 that is produced by the photooxidation of a VOC by OH will react with an NO molecule (R2, Sect.1), and some fraction of the time (e.g., 1 -α, the effective branching ratio), produce HO2 following the reaction of the alkoxy radical (RO) with O2.Therefore, it is assumed that, (1−) + 2 [NO] (Eq.S2) Combining Eq.S1 and S2 together with an assumed, constant P(HOx), [OH] can be calculated using the quadratic formula: where ) 2  (Eq.S4) (1−) + 2 (Eq.S5)  = −(  ) (Eq.S6) In the above equations, k is the rate constant for the described reaction in the subtext (e.g., HO2 + HO2), the term kOH+VOC[VOC] can be simplified to the VOC reactivity (R(VOC), s -1 ) for the ambient mixture of VOCs, α is the effective branching ratio for the ambient mixture of VOCs, and P(HOx) is the HOx production rate for the ambient mixture of gases.The rate constants for the two HOx self-reactions, HO2 (  2 + 2 ) and RO2 (  2 + 2 ), and the HO2-RO2 reaction (  2 + 2 ) were taken from Sander et al. (2011) for temperatures at 298 K and are 1.4×10 -12 , 6.8×10 -14 , and 8×10 -12 cm 3 molec. - s -1 , respectively.The OH and NO2 rate constant is also from Sander et al. (2011) for temperatures at 298 K and is 1.2×10 -11 cm 3 molec. - s -1 .For the base case used here, P(HOx) is assumed to be 1×10 7 molec.cm -3 s -1 , α is 0, and R(VOC) (kOH+VOC[VOC]) is 5.00 s -1 .

S2. Comparison of NO2 Measurements
There were three different measurements of NO2 on the DC-8 during KORUS-AQ: (1) by chemiluminescence (Weinheimer et al., 1994), (2) by laser induced fluorescence (Thornton et al., 2000), and (3) by cavity enhanced absorption spectroscopy (Min et al., 2016).Here, only chemiluminescence and laser induced fluorescence are considered.Comparison of the NO2 mixing ratios by these two measurements are shown in Figure S2.Though the correlation is high (R 2 = 1.00), the laser induced fluorescence NO2 is ~16% higher than the chemiluminescence NO2.To determine which NO2 to use for the study, the NO2-to-NO ratio was compared, as this ratio can be calculated with the observations on the DC-8.This ratio is defined by Eq.S9: 2 (Eq.S9) Note, though steady-state RO2 is used throughout the paper and can provide some uncertainty in the calculated NO2-to-NO ratio in Eq.S9, at high NO mixing ratios where both HO2 and RO2 concentrations are low, the O3 + NO reaction dominates the term.It was found that the NO2-to-NO ratio using the University of California, Berkeley, NO2 generally agreed better with the calculated NO2-to-NO ratio from Eq. S9.However, both NO2-to-NO ratios 1σ spread of observations overlap with the calculated NO2-to-NO ratio from Eq. S9.Thus, the University of California, Berkeley, NO2 measurements are used throughout the manuscript.The use of the NCAR NO2 had small changes but does not change the main conclusions and trends discussed throughout the paper.
Finally, photostationary steady-state (PSS) NO2, calculated through rearrangement of Eq.S9, is compared against the measured NO2 by chemiluminescence (CL) and laser induced fluorescence (LIF) in Fig. S4.The measured NO2,LIF versus NO2,PSS is closer to the one-to-one line (slope = 1.06) compared to the measured NO2,CL versus NO2,PSS (slope = 1.23).This further supports the results in Fig. S3, showing that the NO2,LIF (NO2 UCB in Fig. S3) is closer to the predicted PSS NO2.

Figure S3
. Binned NO2-to-NO ratio, where NO is from NCAR chemiluminescence and NO2 is either from NO2 chemiluminescence (black) or University of California, Berkeley, laser induced fluorescence (dark red), versus NO.Shading is ±1σ spread in the observations for both observed ratios.The NO2-to-NO ratio in blue is calculated using observations (Table 2) and Eq.S9. Figure S4.Scatter plot of predicted NO2 PSS, from Eq. S9, and measured NO2, from laser induced fluorescence (LIF) or chemiluminescence (CL).The PSS vs CL slope is 1.23, the PSS vs LIF slope is 1.06, and the 1:1 line is red.

S3. Error Analysis in Calculation of αeff and R(VOC)
In Sect.3.3, Eq. 8 -11 assumes that L(Ox) and L(∑ANs) is negligible.However, L(Ox) is approximately 25% of the P(Ox) over SMA (e.g., Figure 6).An analysis of how much unmeasured R(VOC) and the αeff is impacted by neglecting these two terms is calculated using Eq.S9.
Here, γ is the effective Ox produced per VOC reacted (1.53), α is the effective branching ratio to form ∑ANs, R(VOC) is the VOC and CO reactivity, and LOx and L∑ANs are the loss terms for Ox and ∑ANs.
One limit in these equations is if L(∑ANs) is near 0 and L(Ox) is important.At this limit, assuming all R(VOC) is captured by observations, this would lead to an αeff of ~0.02.This is equivalent to the calculated αeff using the observed VOCs and calculated secondary VOCs from F0AM and would indicate no missing R(VOCs).
However, there are multiple reasons to assume this limit in that L(∑ANs) is 0 is incorrect and that the observations do not capture αeff and R(VOC).2023) showed that even for long-lived ANs, the lifetime is ~50 hours.However, for multifunctional ANs, this lifetime drops down to 2 -16 hours.Note, however these multifunctional ANs are mainly from biogenic VOCs and not anthropogenic VOCs.Yet, as predicted in MCM (Jenkin et al., 2015), ANs from anthropogenic VOCs are expected to have similar lifetimes as ANs from biogenic VOCs.
To investigate the role of L(∑ANs) and L(Ox) on unmeasured R(VOC) and α, Eq.S9 instead of Eq. 11 is used.The results are summarized in Figure S4.If the ANs lifetime of 16 hours is assumed, which may be a lower limit, the average unmeasured R(VOC) decreases from 1. 7 −0.4 +1.1 s - 1 to 1.4 s -1 , and the unmeasured α would be 0.09, leading to an αeff of 0.032.Note, both of these values are very close to the values calculated assuming losses were negligible.For the unmeasured R(VOC) and α shown in Fig. 4, the ∑ANs lifetime would be equivalent to 11.5 hrs.This is in the range of lifetime for multifunctional ANs, but a lower limit (González-Sánchez et al., 2023).If the typical ANs lifetime shown in González-Sánchez et al. ( 2023), ~6 hrs, is assumed, the average unmeasured RVOC increases from 1. 7 −0.4 +1.1 s -1 to 2.2 s -1 .This would lead to an αeff of 0.045.Note this is still with the uncertainty of R(VOC) found with the Penn State observations at low NOx.
Thus, though uncertainty in both ∑ANs lifetime and the unmeasured α impact the calculated unmeasured RVOC, (a) inclusion of the loss terms of both Ox and ∑ANs lies within the spread in observed RVOC at low NOx mixing ratios and the associated calculated RVOC assuming the loss terms were negligible, (b) if the L(Ox) term is considered, the L(∑ANs) term must also be included as it is non-negligible in environments with freshly-produced, multifunctional ANs.
There are two potential other sources of uncertainty in the calculated, unmeasured RVOC-(1) assumed α for the F0AM secondary species and (2) α for aromatics.First, for α ranging from 0.00 -0.10 for F0AM species, the unmeasured RVOC falls within the spread of observations and calculated unmeasured RVOC assuming F0AM α is 0.05.Thus, the calculated unmeasured is insensitive to the F0AM α until the F0AM α is greater than 0.10.Though the α values for secondary, oxygenated species is unconstrained (Orlando and Tyndall, 2012), α being greater than 0.10 is currently unexpected with what is currently known about chemistry of these secondary species.Second, the α for aromatic compounds was changed from the values found in MCM (Jenkin et al., 2015) and Perring et al. (2013) to all being 0.01.This is due to recent a recent study finding that α is potentially lower for aromatic compounds (Xu et al., 2020).Even with this low α value for the aromatics, the average unmeasured RVOC is not greatly impacted, increasing from 1.7 to 1.8 s -1 .This is due to the aromatics accounting for a small fraction of the total α and ∑ANs.
Thus, though there are numerous assumptions and sources of uncertainty associated with constraining the unmeasured RVOC with the observations, the overall results of, on average, 1.7 s -1 unmeasured RVOC is robust.As these various sensitivity investigations minimally impact the calculated unmeasured RVOCs using the assumptions in the main text, the unmeasured RVOCs associated with α = 0.10 and assuming the loss terms are negligible are used.
As described in Sect.S1 and Eq. 1 (and S7), HO2 is important in the next Ox production.
However, an intercomparison of measured and F0AM modeled HO2 shows that the two values diverge from the one-to-one line at high NOx mixing ratios (Figure S6a), where the measured HO2 is higher compared to F0AM modeled HO2.As this is at high NOx mixing ratios, this impacts the calculated P(Ox), where the measured HO2 would suggest high P(Ox) with increasing NOx, whereas F0AM HO2 shows decreasing P(Ox) with increasing NOx (Figures S6b).The latter, decreasing P(Ox) with increasing NOx, more closely aligns with theory (e.g., Sect.S1 and (Seinfeld. and Pandis, 2006)).Further, the latter more closely aligns with observations in that P(Ox) increases with decreasing NOx, e.g., the "NOx penalty" (Jhun et al., 2015;Pusede and Cohen, 2012).Though calculations using observed HO2 have suggested that P(Ox) either remains constant and/or decreases wit the decreasing NOx (e.g., Whalley et al., 2018Whalley et al., , 2021)), this does not align with both theory and the "NOx penalty" observed, suggesting potential uncertainties for HO2 at low HO2 and high NOx mixing ratios.Thus, to be consistent with theory and "NOx penalty" 184 observations, F0AM calculated HO2 is used throughout the study.185

S4. Sensitivity in F0AM Results with Missing R(VOC)
We add to the model a test of whether the estimated additional OH reactivity of ~1.7 s -1 would degrade model performance in simulating formaldehyde or OH.We add approximately 800 pptv of C4H9CHO (pentanal), on average, as a proxy for unmeasured aldehydes, such as octanal, nonanal, decanal, etc.The concentration of pentanal varies according to the calculated missing OH reactivity.The average OH reactivity from this species is ~0.5 s -1 .Total OH reactivity goes up by 1.2 s -1 after including all the products produced from the oxidation of pentanal.Therefore, the added primary species (pentanal) results in over twice as much reactivity from secondary oxidation products.The largest secondary oxidation products are smaller aldehydes (HOC3H6CHO, HOC2H4CHO, C3H7CHO), which have OH reactivity of 0.1 to 0.2 s -1 each.With the inclusion of ~0.5 s -1 pentanal to F0AM as a surrogate for missing R(VOC), OH is reduced by ~25% compared to the base model (Figure S9).We attribute this OH reduction to the build-up of the peroxynitrate (C5H9NO5) from pentanal to approximately 500 pptv.This pentanal peroxynitrate is likely overestimated given the rapid exposure of PN species to warmer temperatures through mixing, as discussed by Crawford et al. (2021).Model formaldehyde change with the inclusion of ~0.5 s -1 pentanal to F0AM by < 5% (Figure S10).This is attributed to the balance of increased production of formaldehyde and RO2 to convert NO to NO2 by pentanal, but the decreased OH which then reduces production/conversion.

S5. Aerosol Contamination of the CAFS Downwelling Optic
During KORUS-AQ ambient aerosols deposits were regularly evident on all leading edges of the aircraft, particularly during low altitude spirals near Seoul.The deposits collected on the leading edge of the downwelling CAFS optic (Figure S12), resulting in optical reductions in the actinic flux of up to 20%.The precise reductions depended on the aerosol coating efficiency and cleaning by precipitation.The optic was centered above the DC-8 fuselage in the zenith 1 port, just aft of the forward cabin exit door.The upwelling optic was unaffected, likely due to the larger aircraft boundary layer near its location under the aft fuselage.
Extensive analysis was required to correct the downwelling data.This involved identification of contaminated periods, characterization of the angular impact, optical thickness and time evolution.Corrections were applied to the direct beam only.Corrections to diffuse light were estimated to be small (<3%) and the corrective skill insufficient for application to the data.Such aerosol coating had not been detected during numerous high aerosol encounters on previous campaigns.They appear to result from unprecedented aerosol combinations in the SMA.
The final CAFS dataset includes a flagging scheme (Table S3) to tag the contaminated periods.For any quality flag > 0 the photolysis frequency uncertainties should be increased by 20% to account for the low bias during contamination.For quality flag 0 the uncertainty should be conservatively increased by 10% due to the uncertainty in the aerosol cleaning efficiency during the remainder of the flights.

S6. Comparison in Calculating P(Ox)
Two different equations to calculate P(Ox) are introduced in the main text -Eq. 1 and Eq. 9. Eq. 1 is more explicit as it is tracking the number of Ox molecules formed from all reactions of RO2 and HO2 molecules with NO (and accounting for the fraction of reactions where RO2 and NO form ANs); whereas, Eq. 9 is simplified version and takes the reactivity averaged α and γ for the environment and fold HO2 into the R(VOC).Comparing the P(Ox) from the two equations is shown in Figure S13.Since Eq. 1 is more explicit, it is approximately 24% higher than Eq. 9, as Eq. 9 does not directly account for RO2 concentrations and assumes the total amount of HO2 molecules formed.Eq. 1 is more accurate as it is not assuming the total amount of HO2 formed and thus used when directly calculating P(Ox) (e.g., Fig. 6).Eq. 9 thus may lead to an under-estimation in unmeasured R(VOC); however, due to the number of unknowns and uncertainties, it cannot be evaluated at this time.

Figure S1 .
Figure S1.Example analytical solutions to instantaneous P(Ox), assuming different scenarios with changes in total VOC reactivity (R(VOC)) (a), changes in HOx radical production (P(HOx)) (b), or changes in the alkyl and multi-functional nitrate effective branching ratio (α) (c).See Sect.S1 and Eq.S1 -S8 for the analytical equations.Note, for all scenarios/panels here, R(VOC), P(HOx), and α are constants, as discussed above and shown in Eq.S1 -S8.

Figure S2 .
Figure S2.Scatter plot of the NO2 measured by University of California, Berkeley, laser induced fluorescence and the NCAR chemiluminescence.The one-to-one line is shown in blue and the ODR fit for the data is shown in red.
First, the total OH reactivity measured by Penn State indicates missing reactivity at low NOx mixing ratios, as discussed in Sect.3.3 and shown in Fig. 4. Second, the comparison of speciated and measured ∑PNs as well as the comparison of the F0AM calculated and measured ∑PNs indicates missing R(VOC) to account for the unmeasured PNs, as discussed in Sect.3.1 and 3.4 and Fig. 2 and 5. Finally, González-Sánchez et al. (

Figure S5 .
Figure S5.Same as Figure 4, but with the sensitivities discussed in Sect.S3, including inclusion of Ox and ANs loss terms, range of α for F0AM secondary species, and lowering the aromatic α value.

Figure S6 .
Figure S6.(a) Scatter plot of HO2 predicted from F0AM vs measured HO2, colored by measured NOx mixing ratios.One-to-one line represented by the grey line.(b) Calculated P(Ox), using Eq. 1, for HO2 predicted by F0AM (black) or HO2 measured (blue).

Figure S7 .
Figure S7.The difference in the isoprene mixing ratio measured by University of Oslo PTR-MS and University of California, Irvine WAS, versus the observed NOx.All data are shown in grey and equally sized bins are shown in black for observations collected over the SMA.

Figure S8 .
Figure S8.Same as FigureS7, but for monoterpenes.Lower amount of data is associated with the measurements being below detection limit for WAS.

Figure S10 .
Figure S10.Evaluation of the F0AM model performance versus gases measured on DC-8 over the SMA and not used to constrain the model.(a) Scatter plot of F0AM predicted NO2 versus observed NO2 from UC Berkeley.(b) Scatter plot of F0AM predicted OH versus Penn State observed OH.(c) Scatter plot of F0AM predicted CH2O versus CAMS observed CH2O.

Figure S11 .
Figure S11.Comparison of F0AM predicted OH versus observed OH for the base F0AM model (top) and sensitivity F0AM model that included ~0.5 s -1 pentanal to account for missing R(VOC).

Figure S13 .
Figure S13.Strong aerosol contamination of the optic following the flight on 19 May, 2016.

Figure S14 .
Figure S14.Fractional contribution for different sources of HOx predicted from F0AM.282

Table S2 .
The higher PNs lumping based on their primary precursor species from F0AM.

Table S3 .
CAFS data quality flag summary