Evaluation of Ozone Formation Potential of Formaldehyde Using Smog Chamber Data

Formaldehyde (HCHO) is one of the important O 3 precursors in the atmospheric environment, but the mechanism for HCHO photochemical reactions is not very clear now. In the present study, the effects of relative humidity (RH) and initial VOC/NO x ratio ( R CN ) on the HCHO‒NO x photochemical reaction process are studied in terms of smog chamber experiments. The MCM mechanism of formaldehyde is evaluated based on the experimental results. The measured maximum ozone concentration (O 3-max ) increases first and then decreases with the increase of R CN , and the R CN at the inflection point is 4.0 and 4.8 in the low (RH = 7.8%‒11.5%) and high RH (RH = 71.9%‒84.0%) experiments, respectively. The RH has no obvious effect on the measured O 3-max values. The original MCM simulated O 3 concentration reaches the maximum value much earlier than the experimental result, but can well simulate the incremental reactivity (IR) values in the experiments. The simulated incremental reactivity of HCHO at 6 h (IR 6h ) by MCM is influenced by other VOCs, and the simulated maximum IR 6h is 1.9 ppb ppb –1 , demonstrating that the contribution of HCHO to ozone is comparable to that of acetaldehyde in the atmospheric environment.


INTRODUCTION
Ozone (O3) is one of the important pollutants in the tropospheric atmosphere, which can threaten the quality of atmospheric environment and human health (Biswas et al., 2019;Sahu et al., 2021).It was estimated that about 1.04-1.23 million respiratory global deaths in adults were attributable to ozone exposures in 2016, a remarkable increase due to the ozone increase in northern India, southeast China, and Pakistan (Malley et al., 2017).
In recent years, the issue of ozone pollution has worsened in some areas (Li et al., 2021a;Wang et al., 2020a;Wang et al., 2020b;Zhan et al., 2021).The surface ozone concentration in summer in Beijing showed an increase of 1.7 ppb yr -1 during the observation period of 2006-2016 (Chen et al., 2019).In the Yangtze River Delta of eastern China, the ozone concentration in 2018 increased by 19% over that in 2015 (Duan et al., 2021).The latest studies showed that the ozone pollution still occurred or even worsened in 2020 in some regions such as the Yangtze River Delta (Wang et al., 2021) and the North China Plain (Li et al., 2021b).Globally, not only China, but also other countries and regions, such as India, Germany, the USA, are also facing the dilemma of serious ozone pollution (Biswas et al., 2019;Ghahremanloo et al., 2021;Hashim et al., 2021;Hertig et al., 2019;Wyche et al., 2021).A statistically increasing trend of 0.71 µg m -3 yr -1 was observed for the surface ozone during 2008-2017 in Maltese Islands (Fenech and Aquilina, 2020).The ozone concentration in the south east of the UK during March-May 2020 also increased by 5-15% relative to the same period of 2015-2019 (Wyche et al., 2021).
Formaldehyde (HCHO) is one of the most important and abundant carbonyl compounds in the troposphere (Li et al., 2022;Ling et al., 2017;de Blas et al., 2019).In Fuzhou, China, the monthly average HCHO concentration in May 2018 was about 2.54 ppb (He et al., 2020), and in Shantou, it was about 4.12 ppb in October 2019 (Shen et al., 2021).In a background area in Northern Spain, the measured maximum concentration in July 2016 was about 9.82 ppb (de Blas et al., 2019).In a suburban area in Cairo, Egypt, the observed daily average HCHO concentration in summer in 2014 was about 32.9 ppb (Hassan et al., 2018).
Due to the high abundance and strong reactivity, HCHO plays a key role in the formation of O3 and radicals (de Blas et al., 2019;Wang et al., 2017;Yang et al., 2021;Zeng et al., 2019).The increase of HCHO and decrease of NO2 were considered to be the major reason for the increase of summer O3 in the Beijing-Tianjin-Hebei region during 2005-2018 (Li et al., 2020b).In the northern Colorado front range, USA, the contribution of HCHO to HO2 radicals was calculated about 20.7%-23.6%(Pfister et al., 2019).During the forest fire periods over the Southern Himalayan region, it was estimated that HCHO was the greatest contributor to ozone formation (Kumar et al., 2019).Unfortunately, the HCHO concentration has increased in some areas in recent years.The monthly average ground HCHO concentration in Beijing increased by about 1.71% yr -1 during 2005-2015 (Bai et al., 2018), the column HCHO concentration in the North China Plain showed an increase of 0.05 × 10 15 molecules cm -2 yr -1 during 2005-2016 (Zhou et al., 2019), and the HCHO concentration in the Yangtze River Delta also showed an obvious increase in the range of 2005-2016 (Shen et al., 2019).Similarly, in other country such as the major Indian metro cities, the HCHO concentration also had a high level in recent years (Pakkattil et al., 2021).
Model simulation is an effective method to study the ozone formation of VOCs.The Master Chemical Mechanism (MCM) (Jenkin et al., 1997(Jenkin et al., , 2003(Jenkin et al., , 2015) ) and Statewide Air Pollution Research Center (SAPRC) mechanism (Carter, 2016;Venecek et al., 2018) are widely used to study the ozone formation potential of various VOCs.A laboratory study also can study the ozone formation of VOCs directly, and it can be used to evaluate the simulation accuracy of the mechanisms and to further improve them (Carter and Heo, 2013;Chen et al., 2015;Hynes et al., 2005;Jia et al., 2012;Zhang et al., 2011;Zhang and Kamens, 2012).Carter (2010) has performed some smog chamber experiments to evaluate the simulation accuracy of the SAPRC mechanism regarding the HCHO-NOx photochemical reactions, although they mainly focused on the effect of light intensity under the conditions of low relative humidity (RH) (~15%) and room temperatures (T = 300-315 K).To the best of our knowledge, the influences of RH and precursor concentrations on the ozone formation of HCHO photochemical reactions have not been performed detailedly in the laboratory experiments, and the simulation accuracy of ozone formation from the HCHO-NOx system by the MCM mechanism is yet not evaluated.More importantly, HCHO is also an intermediate product of many oxidation processes, so the simulation accuracy of ozone formation by HCHO not only directly affects the estimate of ozone from HCHO, but also affects the simulation results of other VOCs's photochemical reactions, which highlights the necessity of detailed laboratory studies about the HCHO photochemical reaction.
The object of this study is focused on the ozone formation reactivity of formaldehyde under different reaction conditions (RH and precursor concentrations) in detail in terms of smog chamber experiments.These experimental results are also used to evaluate the simulation accuracy of the MCM mechanism (version 3.3.1).The contribution of HCHO to ozone concentration in the real atmospheric environment is further discussed.

Smog Chamber Experiments
A self-made smog chamber system was used to perform the experiments in this study, which was also used and has been described in our previous studies (Jia and Xu, 2014, 2016, 2018, Jia et al., 2020;Zhang et al., 2021aZhang et al., , 2021b;;Yu et al., 2021).Hence, only a brief description is given here.The material of the pillow shape reactor was FEP (DuPont 500A, USA), and its volume was 1.2 m 3 .Two types of UV lamps, F40 BLB (GE, USA) and UVA-340 (Q-Lab Corporation, USA), were used to supply the light source, and the center wavelengths of them were 365 nm and 340 nm, respectively.The photolysis rate constant of NO2 was determined to be J[NO2] = 0.20 min -1 to represent the effective light intensity in the reactor.
The Zero Air Supply (Model 111 and Model 1150, Thermo Scientific, USA) was used to produce the zero air used as the background air in all experiments.The RH of background air was controlled by bubbling zero air through the highly purified water.The concentration of NO2 standard gas was 500 ppm (Diluted by N2, Beijing Huayuan Gas Co., Ltd., China).A 40 wt% formaldehyde solution in water was used to produce the HCHO gas in the reaction, and the concentration of HCHO gas was measured by acetylacetone spectrophotometry (Zhang et al., 2022).A 100 µg mL -1 standard solution of HCHO (J & K Scientific) was diluted to obtain the HCHO calibration curve of spectrophotometer.The concentrations of NOx (NO and NO2) and O3 were measured online by NOx analyzer (Model 42C, Thermo Scientific, USA) and O3 analyzer (Model 49C, Thermo Scientific, USA), respectively.The concentration of NO2 measured by the NOx analyzer includes all nitrogen-containing substances (NO2, HNO3, etc.) except NO, which is expressed as NOy below.The experimental procedure is similar to our previous one on the photochemical reaction of acetaldehyde (Zhang et al., 2021b).Experimental initial conditions are shown in Table 1.Seven experiments (Exps.1-7) were used to study the influence of the ratio of initial HCHO concentrations to NOx concentrations (NOx = NO + NO2) on ozone concentrations under low RHs (7.8%-11.5%),while Exps.8-14 were used for high-RH conditions (71.9%-84.0%).Hereafter, the ratio of the initial concentrations of HCHO to NOx is named RCN in the following description.The variation of RCN was mainly realized by changing the initial NOx concentrations under the relatively fixed initial HCHO concentrations.Based on the RCN value at the inflection point of O3-RCN curve, the reaction conditions were divided into high (RCN on the right of the inflection point) and low (RCN on the left of the inflection point) RCN scenarios.

MCM Simulation
MCM v3.3.1 (Jenkin et al., 2015) was used to simulate the smog chamber experiments in this study, which is a pure chemical model that does not contain the physical processes such as emission sources, transport.MCM has been widely used to simulate the reactions occurring in the laboratory experiments and actual environment in previous studies (Cheng et al., 2013;Jia and Xu, 2014;Xie et al., 2021).In the simulation of MCM v3.3.1, the wall loss rates of NOx, HNO3 and O3 were taken into account.In addition to the formation processes of HONO already included in the MCM, the formation of HONO from heterogeneous reaction of NO2 on the reactor surface was also considered in the simulation, and its reaction rate constant under different RH conditions proposed by Hu et al. (2011) was used.The HCHO wall loss experiments indicated that the effect of wall loss processes on the sink of HCHO was ignorable, so the wall loss process of HCHO was not taken into account in the simulations.In addition to these chamber-dependent reaction processes and species, the mechanism of the photochemical reaction of formaldehyde in MCM v3.3.1 includes 52 chemical reactions and 22 species (http://mcm.york.ac.uk).The chemical reactions were transferred into ordinary differential equations (ODEs) by the chemical reaction compiler (CRC; Jia, 2007) and integrated with MATLAB as described by Jia and Xu (2021).A MATLAB ode15s solver was used to solve the ordinary differential equations, and the timestep was adjusted according to the relative simulation error in the last step.In our simulation, the relative error tolerance was set to 10 -3 , which was considered to be sufficiently small compared to the experimental errors (Jia et al., 2009).After considering the measurement errors of initial HCHO concentrations (± 5%) and the wall loss rate constants (± 100%), the variation of the simulated ozone concentration during 6 h reactions was calculated to be less than 10%, which was much less than the differences between the measured and simulated O3 concentrations during reactions.Thus, it is considered that the incompleteness of the reaction mechanisms in MCM generated the largest uncertainty of simulation results.

Experimental Results
Fig. 1 shows the variations of O3 and NOy with reaction time from the experiments under different RCN.The growth rate of O3 concentrations was largest in the first 1-2 minutes from the beginning of the experiments (Fig. 1(a)), and then maintained a rapid increasing trend for a relatively long time, while the increase rate was decreased gradually, and the O3 concentrations tended to be stable and reached the maximum value (O3-max) when the O3 formation rate was equal to the wall loss rate at the end of the reactions.The NOy concentration dropped at first and then increased to reach the maximum at about 50-150 minutes, and finally decreased gradually.These variations are quite similar to those in the photochemical reaction of acetaldehyde (Zhang et al., 2021b).

Impacts of initial concentration ratios and RH on O3
RCN has an obvious impact on the formation rate of O3 concentrations in the experiments.For examples, under the condition of RCN = 2.2 in Exp. 1 (Fig. 1(a)), the maximum formation rate of O3 was about 0.3 ppb min -1 after 10 minutes of the start of the experiment, while it was 0.7 and 0.8 ppb min -1 under the conditions of RCN = 3.9 (Exp.5) and 11.5 (Exp.7), respectively.In the VOC-NOx photochemical reactions, the ozone formation terminates once NOx is consumed to sufficiently low levels.This is because NOx is removed more rapidly than VOCs (Carter, 1994), and so the NOx availability limits the O3 formation at the end of the reaction.
The effect of RCN on the formation rate of O3 is intuitively reflected in its effect on O3-max.It can be seen that with the increase of RCN, the time required to have O3-max generally decreased (Fig. 2(a)).This is because the initial NOx concentration gradually decreased with the increase in RCN, which led to that the NOx in the experiments with higher RCN was consumed more quickly.In addition, the RCN also can affect the O3-max value in the experiments.As shown in Fig. 2 concentration increased first and then decreased with the increase of RCN under low RH conditions, and the RCN at the inflection point of the curve that describes the variation of O3-max concentration with RCN was estimated to be about 4.0.Similarly, the O3 formation rate was influenced by the RCN under high RH conditions, and the O3-max values also increased first and then decreased with the increase of RCN, while the RCN at the inflection point was estimated about 4.8.RH also has a significant effect on the time required to have O3-max.Overall, the time required to have O3-max under high RH conditions was smaller than that under low RH conditions, and this effect increased gradually with the increase of RCN.The effect of RH on the O3-max concentration was relatively small.According to the variation pattern of O3-max concentrations with RCN, the largest difference in O3-max concentrations between low and high RHs appeared in the range of RCN = 2.2-3.2,where the O3-max under low RHs was about 10% larger than that under high RHs, while for RCN > 3.8, this difference was smaller than 7%.
Similar to the variation of O3-max values with RCN, the variation of O3 concentration at 6 h (O3-6h) with RCN also has an inflection point.The RCN value at the inflection point of O3-6h is close to that in the O3-max curve.A similar variation pattern of O3-6h with RCN has also been observed in the acetaldehyde photochemical reactions (Zhang et al., 2021b), but the RCN at the inflection point of the O3-6h-RCN curve was about 3.2 and 2.8 under low and high RHs, respectively, which is smaller than that in this study.Furthermore, in the acetaldehyde photochemical reactions, under high RCN (RCN on the right side of the O3-6h inflection point), the O3-6h concentration under high RHs was lower than that under low RHs, which is the opposite of formaldehyde photochemical reactions, implying that there must be some differences in photochemical mechanisms between acetaldehyde and formaldehyde.

Ozone production yield of HCHO
The ozone production yield (yO3) of HCHO is calculated by the following formula: where [O3]t is the measured O3 concentration at time t from the start of an experiment, [HCHO]0 and [HCHO]t is the HCHO concentration at the beginning and time t, respectively.The initial O3 concentration was measured by the O3 analyzer to be below detection limitation (1 ppb), so the concentration of O3 at the beginning of experiments was considered as zero in Eq. ( 1).Variation of the ozone yield at the time of O3-max (yO3-max) with RCN is shown in Fig. 3. Similar to the variation of O3-max with RCN, the yO3-max also increased first and then decreased with RCN as a whole.Under low RHs, the yO3-max was in the range of 0.6-1.1 ppb ppb -1 , while it was in the range of 1.2-1.7 ppb ppb -1 under high RHs.It was found that the formation rate of HONO from NO2 on the reactor surface under high RHs was smaller than that under low RHs (Hu et al., 2011), which may be one of the important reasons for the larger yO3-max value under high RHs than that under low RHs.According to the mechanism of HCHO-NOx photochemical reaction in MCM, the main consumption of HCHO is its photolysis and reaction with OH radicals, which are also the main source of HO2 radical.The low HONO formation rate under high RHs weakens the generation of OH, leading to the reduction of proportion of HCHO consumed by OH radicals.The larger HO2 radical concentrations under low RHs convert a larger proportion of NOx to HNO3, HONO, and HO2NO2, leading to a lower O3 concentration.It is estimated from the MCM described in a later section (Section 3.2) that the OH radical concentration at time = 400 min at 75% RH is 20% smaller than that at 10% RH, whereas the NO2 concentration at 75% RH is 39% larger than that at 10% RH.

Ozone incremental reactivity of HCHO
The incremental reactivity (IR) can well exclude the influence of background conditions on the O3 formation from VOC, which is calculated using the following formula (Carter, 1995): where ( ) experiment where the HCHO is added, ( ) is the corresponding value where the HCHO is not present, and [HCHO]0 is the amount of HCHO added.Fig. 4(a) shows that IR had an obvious increasing trend with the increase of reaction time, and then tended to be stable at the end of the experiments, which was similar to the variation pattern of O3 concentrations with reaction time (Fig. 1(a)).According to the comparison of Exp. 1 (RCN = 2.2) and Exp.7 (RCN = 11.5), it was found that the RCN has an effect on IR during the experiments.The time required to have the maximum IR (IRmax) in Exp.7 was about 250 minutes earlier than that in Exp. 1, and the IRmax in Exp. 1 was about 17% larger than that in Exp. 7. Similarly, for Exps.8 and 14, the RCN generated a 45% difference in IRmax values and a 260 min difference in the appearance time of IRmax.The IRmax under low RCN was larger than that under high RCN, and the IRmax under high RHs was lower than that under low RHs as a whole (Fig. 4(b)).In the acetaldehyde photochemical reactions, during 60-360 minutes, the IR at low RCN was larger than that at high RCN both under low-and high RHs (Zhang et al., 2021b).For example, the IR at 6h (IR6h) with RCN = 2.0 (RH = 10.9%) was 1.8 times larger than that with RCN = 13.7 (RH = 11.4%) in acetaldehyde photochemical reaction.However, the IR6h in Exp. 1 (RCN = 2.2, RH = 12.6%) was 17.6% smaller than that in Exp.7 (RCN = 11.5, RH = 11.5%),whereas the IRmax in Exp. 1 was 1.1 times larger than that in Exp.7 in the formaldehyde photochemical reaction.Furthermore, the IR under low RHs in the acetaldehyde photochemical reaction during 120-360 minutes was slightly larger than that under high RHs, while it was the opposite for formaldehyde.Therefore, the RCN and RH have different effects on the IR values between acetaldehyde and formaldehyde photochemical reactions.

Evaluation of MCM v3.3.1 with experimental results
The numerical simulation of HCHO photochemical reactions with MCM is compared with the experimental results.Taking Exp. 1 as an example (Fig. 5(a)), we see that the simulated O3-max concentration is 27.4% larger than the measured result.Moreover, the simulated O3 concentration reached the maximum value much earlier than the experimental result.The simulated average O3 formation rate was about 1.0 ppb min -1 during the 0-200 minutes, whereas it was measured only about 0.3 ppb min -1 .Similarly, the simulated O3 concentrations in Exps.7 and 9 (Figs.5(b) and 5(c)) also reached the maximum values much earlier than the experimental results.Nevertheless, the simulated and measured O3 concentrations both reached the maximum values at about 300 min after the start of the reaction in Exp. 14 (Fig. 5(d)).Meanwhile, the simulated O3-max was only 3.1% lower than the measured result, and this difference was much smaller than that in the other experiments.In acetaldehyde photochemical reactions (Zhang et al., 2021b), the original MCMsimulated O3 formation rates were much smaller than the measured results after about 20 minutes from the start of the reactions, whereas the simulated O3 formation rates in formaldehyde photochemical reactions were much larger than the measured values during the early stage, indicating that the causes of the differences between the simulated and measured results are different in these two reaction systems.
The differences between the simulated and measured O3 concentrations were well reflected at 3 h of the reactions.The ratios of the simulated O3 concentration at 3 h (O3-3h) to the measured result (RO3-3h) are shown in Fig. 6.It can be seen that the simulated O3-3h values are much larger than the measured values under low-RH experiments (Exps.1-7), and that the differences between the simulated and measured O3-3h decrease greatly with the increase of RCN.Similarly, the MCM-simulated O3-3h levels in high-RH experiments (Exps.8-14) are also overestimated relative to the measured values, and the RO3-3h values decrease with the increase of RCN.Nevertheless, the differences between simulated and measured O3-3h are much smaller than those under low RHs, indicating that the low RHs may worsen the simulation accuracy of O3-3h concentrations.
Furthermore, the ratios of simulated O3 concentrations at 6 h to the measured results (RO3-6h) are calculated and shown in Fig. 7.Under low-RH conditions, RO3-6h values are in the range of 1.1-2.5, which are smaller than the RO3-3h values (1.6-3.8).Similarly, under high RHs the RO3-6h (0.9-1.5) is also smaller than the RO3-3h (1.0-2.3).The overestimation of the O3 formation rate under both low and high RH conditions by MCM in the early stages is also accompanied by an obvious overestimation of the consumption rate of precursors compared with the measured results (Fig. 5), which leads to that the simulated concentrations of precursors in the latter stages are much smaller than the measured results.As a result, the O3 formation rate is overestimated by MCM at early stages, but it is underestimated at latter stages compared with the measured results.Therefore, the ratios of simulated O3 concentrations to measured results at 6 h (RO3-6h) are smaller than those at 3 h (RO3-3h) under both low and high RH conditions as a whole.In the photochemical reaction of acetaldehyde, the original MCM underestimated the O3-6h by 24%-35% and 17%-49% under low-and high-RH conditions, respectively, and the differences between the simulated and measured results increased with reaction time in the range of 0-360 minutes, which are contrary to formaldehyde.This further demonstrates the differences of MCM simulation accuracy for the photochemical reactions of these two aldehydes.
The differences between the simulated and measured O3-max are further compared and shown in Fig. 8.Although the variation of the ratios of simulated and measured O3-max concentrations decreases with reaction time, which is the same as RO3-6h and RO3-3h, the differences between the simulated and measured O3-max are relatively smaller to those for O3 concentrations at 3 h and 6 h.Under low-RH experiments (Exps.1-7), compared with the measured O3-max values, MCM-simulated results vary from overestimation to underestimation as RCN rises.Under high-RH experiments (Exps.8-14), the simulated O3-max in Exps.9 (RCN = 3.1) and 10 (RCN = 3.2) are slightly larger (0.4% and 6.8%) than the measured results, while in other experiments, the simulated O3-max are slightly smaller than the measured results.Nevertheless, MCM well simulates the variation patterns of O3-max values with RCN, and the simulated RCN values at the inflection points of the O3-max-RCN curves are generally consistent with the measured results.
Overestimate of the O3 formation rate in the early stage of formaldehyde photochemical reactions also exists in the SAPRC mechanism (Carter, 2016).For example, in one of their experiments named "ETC470" (RH ≈ 15%) by Carter (2016), the SAPRC-16 simulated ∆(O3 -NO) was about 50% larger than the measured value at 3 h, while there was no great difference at 6 h between the simulation and experiment.Therefore, the larger simulation error at the early reaction stage of formaldehyde photochemical reactions is probably a common problem in these two widely used mechanisms.At the early stage, the simulated O3 formation rate is much larger than the measured one, which leads to faster consumption rates of HCHO and NOx.With the increase in reaction time, the limitation effect of low precursor concentrations in the simulation is larger than that in the experiments at the latter stage, which can offset the overestimation of the simulation in the early stage.Actually, the mechanism in the simulation at the latter stage of the reaction may still be much different from that in the actual reaction.In the real environment where the emissions and consumptions of precursors exist simultaneously, it is expected that the original MCM will significantly overestimate the O3 concentration in the HCHO photochemical reaction.
The differences between the simulated and measured NOy concentrations are different under different experiments.In Exp. 1 (RH = 12.6%, RCN = 2.2), MCM overestimates the measured NOy concentration during the 10-150 minutes stage, but underestimates the measured level during the later reaction.The difference between the measured and simulated NOy increases significantly with reaction time (Fig. 5(a)).In Exp. 7 (RH = 11.5%,RCN = 11.5),MCM well simulates the variation pattern of the experimental NOy concentrations, but the simulated concentrations are larger than the measured values (2.4%-14.9%) in the first 30 min of reaction, and then smaller than the ones (1.3%-27.9%)during later 30-570 minutes of reaction (Fig. 5(b)).In Exp. 9 with a high RH and a low RCN (RH = 72.1%,RCN = 3.1), MCM also well simulates the variation of experimental NOy concentration as a whole, and the largest difference occurs at t = 58 minutes, when the simulated result overestimates the measured value by 22%.In Exp. 14 (RH = 73.7%,RCN = 10.7),MCM overestimates the measured NOy concentration during entire course of a 6-hour experiment.
The rate of decrease in NO concentrations simulated by MCM in the early stage is much larger than the measured value (Fig. 5), so the simulated NO concentration reaches below 1 ppb earlier than the measured result, which is consistent with the overestimation of O3 formation rate by simulation.Compared with the measured HCHO concentration after the start of the reaction, the simulated results are much smaller as a whole (Fig. 5).For example, in Exp. 1, the measured HCHO concentration at t = 750 minutes was 152 ppb, while the simulated one was 18 ppb, implying that the simulated results may overestimate the consumption of HCHO in the reaction by about 30%.Since the simulated results overestimate the O3 formation rate in Exp. 1 by about 20% at the same time, they might underestimate the ozone production yield of HCHO according to Eq. ( 1) as a whole.

Evaluation of MCM v3.3.1 with IR in HCHO photochemical reaction
The variations of the ratios of simulated IRmax to the measured values (RIR-max) under different RHs and RCN are shown in Fig. 9.In the low RH experiments (Exps.1-7), except Exps. 1 and 2, the RIR-max in the other experiments is in the range of 0.96-0.85,indicating that the simulated IRmax in these experiments by original MCM underestimates the experimental-based IRmax by about 4%-15%.Similarly, in the high-RH experiments (Exps.8-14), except Exp. 10, the MCM also underestimates the experiment-based IRmax by 2%-12% in these experiments.It should be pointed out that although the differences between the simulated and measured IRmax are relatively small, the time required to have IRmax is much different from the measured value.For example, in Exp. 1, the simulated IRmax appeared at about time = 653 minutes, while it was measured at about 750 minutes.Therefore, compared with the experimental results under different RHs and low RCN, the original MCM may overestimate the contribution of HCHO to ozone in the real environment because of its overestimation of ozone formation rates.
In short, the differences in the photochemical reactions of HCHO between the original MCM and measured results are apparent, especially the much larger ozone formation rates at the early stage of the reaction from MCM.Therefore, the improvement of description of the mechanism of the photochemistry of HCHO in MCM v3.3.1 is required.

Comparison of photochemical reaction mechanisms between formaldehyde and acetaldehyde
As discussed above, RH and RCN have different effects on the photochemical reactions between HCHO and CH3CHO, demonstrating that there exist some differences in photochemical reaction mechanisms between them.Based on the MCM simulated results, the main differences are further compared as follows.
Under 298 K conditions, the reaction rate constant of HCHO with OH radicals is 8.49 × 10 -12 cm 3 molecule -1 s -1 , which is about 43% smaller than the reaction rate constant of CH3CHO and OH radicals (1.50 × 10 -11 cm 3 molecule -1 s -1 ).The relatively lower reactivity of HCHO with OH radicals than CH3CHO is the main reason for HCHO with the larger RCN at the inflection points of the variations of O3 concentrations with RCN.Meanwhile, the photolysis rate constant of HCHO (~7.91 × 10 -5 s -1 , J[NO2] = 0.56 min -1 ) is about 17.5 times larger than that in CH3CHO (~ 4.53 × 10 -6 s -1 ).Thus, the proportion of HCHO consumed by photolysis will be much larger than that of CH3CHO.Without considering the chamber-dependent reactions, the variations of consumed HCHO and CH3CHO with reaction time under a typical reaction condition (T = 298 K, [NO2]initial = 100 ppb, J[NO2] = 0.20 min -1 , RH = 70%) are shown in Fig. 10.It can be seen that the consumed HCHO concentration is about 4.6 times larger than that of CH3CHO after 6 h reaction, which is mainly due to the larger photolysis rate constant of HCHO than CH3CHO.Though the rate constant of OH with HCHO is over 2 times larger than CH3CHO (43%, 298 K), due to the much larger photolysis rate of HCHO than CH3CHO, the OH consumed HCHO is about 4 times larger than the corresponding value of CH3CHO.HO2 radicals from photolysis can evaluate the amount of OH radicals in the photochemical reactions of aldehydes.The amount of consumed HCHO by OH radicals is 2.6 times larger than that by photolysis, while it is about 4.9 times for CH3CHO.Since in the smog chamber experiments RH can significantly affect the formation rate of HONO, which is the important source of OH radicals, the larger proportion of consumed CH3CHO by OH radicals relative to HCHO may be the main reason for the larger effects of RH on the O3 concentrations from CH3CHO than from HCHO.
The reactions between different radicals and NO are the main causes of O3 accumulation.In the photochemical reactions of HCHO, the radicals generated by its photolysis and reaction with OH radicals only include HO2 radicals, while the mechanism of the photochemical reactions of CH3CHO contains CH3O2, HO2, HCOCH2O2 and CH3CO3 radicals.HO2 radicals contribute the most to the conversion of NO to NO2 among those radicals.The HO2 radicals are mainly generated directly from the HCHO photolysis in the mechanism of photochemistry of HCHO, whereas they convert from other radicals in the photochemical reaction of CH3CHO, thus, the content of HO2 radicals produced in the photochemistry of HCHO are much larger than those in photochemistry of CH3CHO, which lead to the simulated O3 formation concentration after 6 h reaction in former (294 ppb) is about 1.8 times larger than that in the latter as discussed above.

Application to the environment
In the atmospheric environment, the HCHO concentration is typically in the range of 0-10 ppb (Pang and Mu, 2006;Sheng et al., 2019).Thus, the IR6h in the typical atmospheric environment is calculated under the conditions of RH = 70%, J[NO2] = 0.56 min -1 , [NO2]initial = 0-100 ppb, T = 300 K, [HCHO]initial = 10 ppb.Without considering the effects of other VOCs, it can be seen that IR6h first increases rapidly and then decreases slowly with the increase of NO2, and the NO2 concentration at the inflection point is about 3 ppb.The maximum IR6h is about 1.0 ppb ppb -1 , indicating that 10 ppb HCHO can contribute about 10 ppb O3 after 6-h photochemical reaction under this condition.Similarly, the IR6h of CH3CHO is also simulated, which is much larger than that for HCHO.For example, under NO2 = 7.0 ppb, the IR6h of CH3CHO is about 4.0 times larger than that of HCHO, indicating that CH3CHO has a larger ozone formation potential than HCHO under this condition.In this simulation, under NO2 = 7 ppb, 99.8% of HCHO (CH3CHO) has been consumed after 6 h of the reaction due to the large photolysis rate and low initial precursor concentrations.In the photochemical reaction of CH3CHO, one of the photolysis products, CH3CO3, not only can react with NO, but its reaction product, CH3CO2 radicals, can further react with NO.Thus, when the consumed amount of HCHO and CH3CHO is the same, CH3CHO can generate a larger amount of O3 than HCHO.
In the actual environment, there are many kinds of VOCs precursors of ozone that can affect the photochemical reaction of formaldehyde.To illustrate the effect of other VOCs on the ozone formation potential of formaldehyde, we added 2 ppb of ethylene, propylene and isoprene to the simulation as the background condition (Fig. 11).These typical concentrations are from the measured concentration ranges in Beijing (Li et al., 2020a).Since different regions have different concentrations of VOCs in the atmosphere, the simulated ozone formation potential of formaldehyde will be different in other scenarios.Under NO2 < 7 ppb, the other VOCs decrease the IR6h of HCHO, while under NO2 > 7 ppb it is opposite.Meanwhile, the maximum IR6h increases to 1.9 ppb ppb -1 after adding other VOCs to the background.Similarly, the other VOCs have the same effects on the O3 formation from CH3CHO.Under low-NO2 concentration conditions, the background reaction is mainly located in the NO2 -limited scenario, so the added HCHO can further increase the limitation effects of NO2 on the reactions, and only part of HCHO can be consumed under this condition.With the increase of NO2, the limitation effects of NO2 on the reactions decrease, and the consumption of HCHO increases due to the increase of OH radicals.For example, when the initial concentration of NO2 is 30 ppb, compared with the simulated results without other VOCs in the background, the OH and NO3 radicals at 6 h respectively increase by about 100% and 197% after addition of other VOCs, which leads to an increase in the consumed amount of HCHO in the reaction, and further increases the contribution of HCHO to the O3 formation.
In Beijing, a typical ozone-polluted city in the North China Plain, the mean NOx concentration was measured about 20-30 ppb (Liu et al., 2020;Mousavinezhad et al., 2021), it is calculated that the IR6h of CH3CHO is about 1-2 times larger than that of HCHO in Fig. 11 under this condition.Nevertheless, the concentration of HCHO was measured about 1-2 times larger than that of CH3CHO (Pang and Mu, 2006;Sheng et al., 2019).Therefore, the contribution of HCHO to O3 formation is comparable to that of CH3CHO in Beijing.

CONCLUTION
The photochemical processes of the HCHO-NOx system have been studied in detail by smog chamber experiments and simulated by MCM mechanism.In the low-RH experiments (RH = 7.8%-11.5%),for the condition of RCN < 4.0 the O3-max increased with the increase of RCN, while it decreased with increasing RCN under RCN > 4.0.Similarly, the O3-max has the same variation with RCN in the high-RH experiments (RH = 71.9%-84.0%).Nevertheless, the RCN at the inflection point of the O3-max-RCN curve is 4.8.The RH has no significant effect on the O3-max values for HCHO photochemical reactions.The original MCM can well simulate the O3-max value in the experiments as a whole, whereas the simulated O3 formation rates during the early stage are much larger than the experimental results.The MCM-simulated IR of HCHO is affected by other VOCs.The contribution of HCHO to ozone formation in the atmospheric environment is comparable to that of CH3CHO.

Fig. 5 .Fig. 6 .
Fig. 5. Variations of simulated and measured concentrations of NO, NOy, O3 and HCHO (Symbols in figures represent experimental observation values, and solid lines represent MCM-simulated values, the pink lines represent NOy, the green lines represent HCHO, the bule lines represent O3, and the dark lines represent NO, respectively.)

Fig. 7 .Fig. 8 .
Fig. 7. Comparisons of the ratios of simulated O3 concentrations at 6 h to the measured results (RO3-6h) under different RHs and RCN from different cases.

Fig. 9 .
Fig. 9. Comparisons of the ratios of simulated IRmax to the measured values (RIR-max) under different RHs and RCN from different cases.

Table 1 .
Initial conditions in the HCHO-NOx photochemical reaction experiments.