Unraveling Pathways of Elevated Ozone Induced by the 2020 1 Lockdown in Europe by an Observationally Constrained Regional 2 Model : Non-Linear Joint Inversion of NOx and VOC Emissions 3 using TROPOMI 4

Abstract. Questions about how emissions are changing during the COVID-19 lockdown periods cannot be answered by observations of atmospheric trace gas concentrations alone, in part due to simultaneous changes in atmospheric transport, emissions, dynamics, photochemistry, and chemical feedback. A chemical transport model simulation benefiting from a multi-species inversion framework using well-characterized observations should differentiate those influences enabling to closely examine changes in emissions. This approach has another advantage in that we can, to a certain extent, disentangle the chemical and physical processes involved in the formation of ozone. Accordingly, we jointly constrain NOx and VOC emissions using well-characterized TROPOMI HCHO and NO2 columns during the months of March, April, and May 2020 (lockdown) and 2019 (baseline). We observe a noticeable decline in the magnitude of NOx emissions in March 2020 (14–31 %) in several major cities including Paris, London, Madrid, and Milan expanding further to Rome, Brussels, Frankfurt, Warsaw, Belgrade, Kyiv, and Moscow (34–51 %) in April. The large variability of changes in NOx emissions is indicative of different dates and the degree of restrictions enacted to prevent the spread of the virus. For instance, NOx emissions remain at somewhat similar values or even higher in northern Germany and Moscow in March 2020 compared to the baseline. Comparisons against surface monitoring stations indicate that the model estimate of the NO2 reduction is underestimated, a picture that correlates with the TROPOMI frequency impacted by cloudiness. During the month of April, when ample TROPOMI samples are present, the surface NO2 reductions occurring in polluted areas are described fairly well by the model (model: −21 ± 17 %, observation: −29 ± 21 %). Changes in VOC emissions are dominated by eastern European biomass burning activities and biogenic isoprene emissions. In March, however, TROPOMI HCHO sets an upper limit for HCHO changes such that the chemical feedback of NOx on HCHO constrained by TROPOMI NO2 reveals a non-negligible decline in anthropogenic VOC emissions in Paris (−9 %), Milan (−29 %), London (−5 %), and Rome (−5 %). Results support an increase in surface ozone during the lockdown. In April, the constrained model features a reasonable agreement with maximum daily 8 h average (MDA8) ozone changes observed at the surface (r = 0.43), specifically over central Europe where ozone enhancements prevail (model: +3.73 ± 3.94 %, +1.79 ppbv, observation: +7.35 ± 11.27 %, +3.76 ppbv). Results of integrated process rates of MDA8 surface ozone over central Europe in the same month suggest that physical processes (dry deposition, advection and diffusion) decrease ozone on average by −4.83 ppbv, while ozone production rates dampened by largely negative JNO2[NO2]-kNO+O3[NO][O3] become less negative, leading ozone to increase by +5.89 ppbv. Experiments involving fixed anthropogenic emissions suggest that meteorology (mainly as air temperature and photolysis) contributes to 42 % enhancement in MDA8 surface ozone over the same region with the remaining part (58 %) coming from changes in anthropogenic emissions. Results illustrate the capability of satellite data of major ozone precursors to help atmospheric models capture the essential character of ozone changes induced by abrupt emission anomalies.


that the model estimate of the NO2 reduction is underestimated, a picture that correlates with the 32 TROPOMI frequency impacted by cloudiness. During the month of April, when ample TROPOMI 33 samples are present, the surface NO2 reductions occurring in polluted areas are anthropogenic emissions suggest that meteorology (mainly as air temperature and photolysis) 48 contributes to 42% enhancement in MDA8 surface ozone over the same region with the remaining 49 part (58%) coming from changes in anthropogenic emissions. Results illustrate the capability of 50 satellite data of major ozone precursors to help atmospheric models capture the essential character 51 of ozone changes induced by abrupt emission anomalies. 52

Introduction 53
Continuous monitoring of air pollution by satellites can help our understanding of both 54 anthropogenic and biogenic variability and change caused by rapid economic recession 55 [Castellanos and Boersma, 2012] and regulations [Krotkov et al., 2016;Souri et al., 2020a]. Earth's 56 atmosphere has exponentially become more polluted during previous decades because of rapid 57 industrialization increasing anthropogenic emissions [Li and Lin, 2015], thus any abrupt hiatus in 58 these emissions should result in an impulsive and sweeping impact on relatively short lifetime 59 pollutants such as nitrogen dioxide (NO2), formaldehyde (HCHO), and tropospheric ozone (O3). 60 The beginning of the global COVID-19 pandemic in early 2020 [Fauci et al., 2020] provided such 61 an abrupt change in human activities [Le Quéré et al., 2020]. A first step to fully understand how 62 The motivations of this study are to determine the capability of a regional model 82 constrained by satellite HCHO and NO2 columns to capture near-surface pollution, and if local 83 ozone production rates are the driving factors for heightening ozone pollution during the 2020 84 lockdown. In other words, what chemical and physical processes are associated with the elevated 85 ozone? How representative are satellite observations at capturing surface air quality through an 86 inversion context? Is meteorology the primary factor in shaping elevated ozone as suggested by 87 Ordóñez et al. [2020]? 88 To address these pivotal questions, it is desirable to constrain models using multi-species 89 observations because relationships between the atmospheric compounds such as HCHO and NO2 90 are importantly intertwined [Marais et al., 2012;Valin et al., 2016;Wolfe et al., 2016;Souri et al., 91 2020a,b]. Accordingly we build our inversion framework upon a non-linear joint analytical 92 inversion of NOx and VOCs proposed in Souri et al. [2020a] using TROPOMI HCHO and NO2 93 gas a priori profiles. We set the RMSE to 1.1×10 15 molec/cm 2 (<6×10 15 molec/cm 2 ) 156 in clear regions and 3.5×10 15 molec/cm 2 (>=6×10 15 molec/cm 2 ) in moderately to 157 highly polluted regions. (>=7.5×10 15 molec/cm 2 ) up in polluted areas. We set the magnitude-dependent 186 RMSE to be equal to 4% of HCHO total columns based on Vigouroux et al. [2020]. 187

MODIS AOD 188
To improve the simulation of total aerosol mass, we use the collection 6 189 MODIS aerosol optical depth (AOD) from both Aqua (~ 13:30 LT) and Terra (~ 190 10:30 LT) platforms over both land and ocean [Levy et al., 2013]  access June 2020). The NO2 chemiluminescence measurements are usually overestimated 207 due to interferences from the NOz family (PAN, organic nitrate, HNO3, etc.). We assume 208 that the interferences are not significantly different between the baseline and lockdown 209 mainly due to relatively low photochemistry in early spring [Lamsal et al., 2008] [Hoesly et al., 2018]. We also output 231 the CMAQ integrated process analysis quantifying the contribution of each process to the 232 amount of compounds. The physical setting of WRF includes the Lin microphysics scheme 233 [Lin et al., 1983], the Grell 3-D ensemble cumulus scheme [Grell and Dévényi, 2002], the 234 RRTMG radiation scheme, ACM2 planetary boundary layer parametrization [Pleim, 235 2007], and Pleim-Xu land-surface scheme [Xiu and Pleim, 2001]. We nudge moisture, 236 wind and temperature fields toward the reanalysis data used only outside of the PBL layer. 237 Moreover, leaf area index and the sea surface temperature are updated every 6 hours based 238 on satellite measurements included in the reanalysis data. Extensive model evaluations 239 based upon surface observations show a striking correspondence (Table S1, S2) which is 240 indicative of fair energy budget and transport in our model. 241

Inverse Modeling and Data Assimilation 242
To adjust the bottom-up emission inventories, we follow a non-linear joint 243 inversion method proposed in Souri et al. [2020a]. Briefly, a Gauss-Newton algorithm is 244 utilized to incrementally solve the Bayes' quadratic function in analytical fashion. The 245 posterior emissions are then derived by 246 (1) where y is bias-corrected TROPOMI NO2 and HCHO observations, xa (or x0) is the prior 247 emissions, xi is the posterior emission at the ith increment, F is the forward model (here 248 WRF-CMAQ) to project the emissions onto columns space, G is the Kalman gain, 249 = 2 " 3 4 " 2 " 3 + 5 6 7$ (2) and " (= ( " )) is the Jacobian matrix calculated explicitly from the model using the finite 250 difference method. So and Se are the error covariance matrices of the observations and 251 emissions. In terms of the prior errors, we use the numbers reported in Souri et al. [2020a]. 252 The instrument covariance matrices are populated with squared-sum of the aforementioned 253 RMSEs based on the compilation of the validation studies and precision errors provided 254 with the data. Both error matrices are diagonal. The inversion window is monthly. The 255 covariance matrix of the a posteriori is calculated by: 256 where : is the Jacobian from the ith iteration. Here we iterate Eq.1 three times. The 257 averaging kernels (A) are given by: 258 Not only does this method considers non-linear chemical feedback among NO2-259 HCHO-NOx-VOC by simultaneously incorporating the HCHO and NO2 in the inversion 260 framework, it also permits quantification of A that explicitly explains the amount of 261 information obtained from the observation. 262 We also correct total aerosol mass by daily assimilating the MODIS dark blue AOD 263 observations following the algorithm discussed in Jung et al. [2019]. Briefly, the 264 assimilation framework uses a modified optimal interpolation method adjusting uniformly 265 all relevant aerosol masses in a column as a function of a weighted-distance and appropriate 266 errors. 267

3.1.Variability of HCHO and NO2 columns seen by TROPOMI 269
We assess difference maps of TROPOMI HCHO and NO2 columns in 2020 with respect we observe a noticeable reduction in NO2 as we approach warmer months which can be explained 273 by increases in OH concentrations (higher water vapor content, solar radiation, and O3 levels), 274 faster vertical mixing due to larger sensible fluxes (more diluted columns due to stronger advection 275 in higher altitudes), and a reduction in temperature-dependent light-duty diesel NOx emissions 276 [Grange et al., 2019]. Two unintended consequences of this sequential decline, noted by Silvern 277 et al. [2019] and Souri et al. [2020a], are first the free-tropospheric region complications and 278 second a barrier to obtaining high amount of information from the sensor which manifests itself in 279 lower averaging kernels of emission estimates (shown later). The anomaly map in March indicates 280 pronounced decreases in tropospheric NO2 columns over several countries including France, 281 Spain, Italy, and Germany (box A). In contrast, we see negligible reductions in the magnitude of 282 the NO2 columns over some portions of the UK excluding London (box B), northern Germany 283 (box C), and Moscow, Russia (box D). A very recent study [Barré et al. 2020] observed roughly 284 the same tendency which was attributable to meteorological changes. While those changes are 285 indeed an important piece of information that will be investigated later in this study, we should 286 recognize that the degree of the enforced restrictions varies both spatially and temporally; 287 moreover changes in emission heavily rely on the dominant emission sector (e.g., mobile or 288 industry) and population. For instance, northern Germany is associated with less populated areas 289 and industrial areas which might be less impacted by the shutdown (see Figure 2 in Le Quéré et 290 al. [2020]), and as a result, we would expect a weaker signal in the reduction of NO2. According 291 to TASS press [https://tass.com/society/1144123, accessed Sep 2020], Russian governments did 292 not take significant measures to control the virus before April 15, immediately evident in the large 293 NO2 enhancement over Moscow in March (box D). During the next two months (April and May), 294 we observe a major turnaround over this city (box F and H). In May, the anomaly of the 295 tropospheric NO2 suggests an abrupt hiatus in the ongoing reduced NOx emissions in central 296 Europe (box G). However it is crucial to note that these maps are based upon sporadic clear-sky 297 pixels that might obscure the full portrayal of emissions changes happening throughout the period 298 (discussed later). 299 We further investigate potential changes in HCHO total columns shown in Figure 3 in the 300 same context as we discussed for NO2. Various VOCs with different sources contribute to the 301 formation of HCHO (see Figure 2 in Chan Miller et al. [2016]) leading to striking HCHO column 302 patterns with large variations. In theory, we have a higher chance to single out anthropogenic-303 derived HCHO concentration by looking at wintertime measurements, although temperature and 304 photochemistry are always key influencers of oxidizing/photolyzing all types of VOCs. The 305 inevitable trade-off for this is dealing with a weaker signal that is near to instrument detection 306 limit. Encouragingly, the TROPOMI HCHO retrieval offers a very low detection limit for 307 individual pixels (7×10 15 molec/cm 2 ) that can be further lowered down by co-adding 308 measurements (roughly a factor of 1/√n). Accordingly, we observe a promising signal in March 309 over eastern European countries that is not explainable by biogenic emissions; but the magnitudes 310 of the difference over these areas (<1.5 ×10 15 molec/cm 2 ) are below the detection limit (~ 2.4×10 15 311 molec/cm 2 given the co-added measurements over time) to relate them to the lockdown in a robust 312 manner; nonetheless TROPOMI sets an upper limit for these changes. In April, results show 313 elevated HCHO concentrations in high latitudes in 2019 (box I), mainly a result of biomass burning 314 activities in eastern Europe [e.g., Karlsson et al. 2013]. As temperature rises in May, the footprint 315 of biogenic emissions become more visible. This signal is not only induced by the inherent 316 temperature-dependency of biogenic isoprene emissions, but also stems from the fact that isoprene 317 reactivity significantly increases by rising temperature [Pusede et al. 2015]. The dipole anomaly 318 of HCHO columns suggested by TROPOMI (box J and K) pertains largely to variations in ambient 319 surface air temperature (shown later). 320

3.2.Top-Down estimates of NOx and VOC emissions 321
Following the inversion and the data assimilation frameworks, we adjust the total amounts 322 of VOC, NOx emissions, and aerosols mass using the well-characterized TROPOMI HCHO, NO2 323 and MODIS AOD observations for the study time period. We focus on the topic of gas phase 324 chemistry (i.e., ozone and its precursors) implying that the aerosol data assimilation is carried out 325 to partially remove errors associated with radiation [e.g., Jung et al., 2019] or heterogenous 326 chemistry [Jacob, 2000], therefore, the aspect of aerosol changes induced by the lockdown will be 327 examined elsewhere. The spatial distributions of magnitude of the top-down NOx and VOC 328 emissions (i.e., constrained by the observations), their corresponding changes and averaging 329 kernels are shown in Figure 4 and Figure 5, respectively. It is worth emphasizing that we use 330 identical prior values in terms of anthropogenic emissions in both years; therefore, the differences 331 in the top-down emissions are primarily dictated by the observations used in the inversion. 332 According to Figure 4, large averaging kernels associated with NOx emissions are confined in 333 high-emitting regions suggesting that the most valid estimates can be found in areas undergoing 334 strong TROPOMI NO2 signals. We observe a large reduction (31-45%) in the bias associated with 335 simulated surface NO2 using the posterior emissions compared to the surface measurements in 336 Europe, although improvements in correlation were minimal (not shown). Similarly, as expected, 337 the discrepancies between the simulated tropospheric NO2 columns versus TROPOMI are largely 338 mitigated by the inversion (Figure S3 and S4). Immediately apparent in Figure 4 is a strong 339 correlation between anomaly maps of TROPOMI tropospheric NO2 ( Figure 2) and those of top-340 down emissions. However, in practical terms, the magnitude of these anomalies is not as drastic 341 as the ratio of observation to model ratio because of the consideration of observational errors and 342 chemical feedback [Souri et al., 2020a], which always leaves some doubt about the practicality of 343 direct mass balance methods. We observe reductions in NOx emissions in March (14-31%) in 344 several major cities including Paris, London, Madrid, and Milan; the reductions further expand to 345 Rome, Brussels, Frankfurt, Warsaw, Kyiv, Moscow, and Belgrade with higher magnitudes (34-346 51%) in April. Table 2  As to VOC emissions, we observe a significant improvement in the magnitude and spatial 358 distribution of simulated HCHO columns after the inversion with respect to TROPOMI data 359 ( Figure S5 and S6). It is very evident that the magnitudes of the emissions primarily follow 360 anthropogenic sources in March; expectedly, very low averaging kernels over major European 361 cities in this month are indicative of inadequacies of one-month averaged TROPOMI HCHO data. 362 However, we surprisingly observe a noticeable decline in the amount of VOC emissions (majorly 363 anthropogenic) in Paris (-9%), Milan (-29%), London (-5%), and Rome (-5%). All of these cities 364 emit considerable amounts of VOCs during wintertime [Schneidemesser et al., 2011;Possanzini 365 et al., 2002;Baudic et al., 2016]. This tendency, which is striking, mainly stems from the indirect 366 impacts of the reduced NOx emissions on HCHO formation [Marais et al., 2012;Valin et al., 2016;367 Wolfe et al., 2016;Souri et al., 2020b]. The sensitivity of HCHO levels to VOC emissions is 368 controlled by the availability of OH that is impacted by NOx. A decrease in NOx emissions in NOx-369 saturated areas frees up more OH to faster oxide VOCs [Souri et al., 2020b] resulting in a steeper 370 gradient of HCHO with respect to its sources. Likewise we observe larger Jacobians of HCHO 371 with respect to VOC emissions in 2020 over the cities mentioned (not shown). If we assume the 372 relative changes in HCHO levels between the two years to be insignificant, which are suggested 373 by TROPOMI HCHO (considering the errors in the retrieval), the steeper gradient of HCHO 374 concentrations with respect to VOC emissions should normally lead to a reduction in the VOC 375 emissions in 2020. In other words, it would require a smaller VOC emission rate to reach to the 376 same amount of HCHO. We note that the TROPOMI HCHO observations provide an upper limit 377 of the changes so that we can make this assumption. Table 3 summarizes the amount of VOCs 378 changing in the cities mentioned. The inversion partly corrects for the large underrepresentation 379 of biomass burning emissions in high latitudes occurring in April 2019 but due to large 380 uncertainties of the retrieval over this area, averaging kernels are low. We revisit the pronounced 381 dipole anomaly of dominantly biogenic VOC emissions in May. It is readily evident from the 382 averaging kernels that more realistic information from TROPOMI HCHO is attainable in warmer 383 months, contrary to the NO2 case. 384

Disparities and rationale behind the differences in near-surface concentrations 385
suggested by the constrained model versus those by in-situ measurements 386

NO2 and HCHO 387
We further investigate the effect of the lockdown on the surface HCHO and NO2 388 concentrations based on the constrained simulations. Figure 6 gives the difference maps (lockdown 389 minus baseline) of daily-averaged surface NO2 and HCHO overplotted with the differences of 390 surface wind vectors, planetary boundary layer heights (PBLHs), surface air temperature, and the 391 ratio of photolysis rates below clouds (Jbelow) to those in clear-sky conditions (Jclear) following 392 Madronich [1987]. The anomaly of emissions is on par with those of surface NO2 and HCHO 393 surface concentrations, this is perhaps not surprising, since the emissions are mostly located near 394 the surface. Horizontal transport (shown as wind vectors) plays a critical role in explaining the 395 spatial variations in emissions downwind. 396 PBLH describes the level of vertical diffusion of air parcels [Jacobson, 2005]. The increase 397 (decrease) in the PBLH is an indication of more (less) diluted air, subject to assuming that the 398 pollutant concentration (in mixing ratio) would exponentially decrease aloft. The extent to which 399 PBLH can impact air pollution relative to advection is strongly dependent upon the wind speed 400 (see Figure 8 in Su et al., [2018]). The stronger the wind, the more likely PBLHs are going to be 401 of secondary importance. We subjectively identify calm conditions by assuming that wind speeds 402 should be below 1 m/s. We overlay the calm conditions as black dots over the PBLH contour. 403 Although model uncertainties exist, the less pronounced NO2 reduction over UK and northern 404 Germany in March is unlikely to be resulting from shallower PBLHs in 2020 given how strong the 405 predominant winds are. A strong expansion of PBL over the central Europe in April and May 2020 406 relative to 2019 possibly contributes to a larger reduction of NO2 concentration. 407 Because of relatively colder air and less photochemistry in March, VOCs become naturally 408 less reactive. This in turn will provide an opportunity for the volume of air to become dispersed. 409 Thus the reduced VOC emissions over several major cities influence larger areas and become less 410 distinctive. The temperature dependency of HCHO concentration progressively becomes more 411 pronounced with increasing temperature. Both photochemistry and biogenic derived emissions are 412 a function of shortwave solar radiation [Madronich, 1987;Guenther et al., 2012;Stavrakou et al., 413 2014] that can vary significantly with cloud transmissivity and the solar zenith angle. The ratio of 414 Jbelow/Jclear well describes such a relationship; positive (negative) differences in the ratio suggest 415 more (less) photochemistry. The strongly positive ratio of Jbelow/Jclear over the central Europe in 416 April potentially overrides the fluctuations associated with surface temperature leading HCHO 417 levels to rise. 418 Clearly, with the help of the CMAQ process analysis, more quantitative work on relevant 419 physical/chemical processes pertaining to NO2 and HCHO surface concentrations can be done 420 here, but before proceeding it is necessary to examine whether the constrained model can 421 adequately represent the changes observed by surface measurements. Unfortunately we limit the 422 analysis to NO2 due to the lack of routinely measured HCHO observations. Several factors can 423 complicate this analysis: i) having overconfidence in the constrained model where the satellite 424 observations used were uncertain; this problem can be safely addressed by considering grid cells 425 whose averaging kernels are above a threshold (here 0.5), ii) ignoring spatial representivity 426 function to directly compare point measurements to the model grids; a statistical construction of 427 the spatial representivity function [Janic et al., 2016] requires a dense observational network so 428 that we can build a semivariogram; instead, we only consider model grid cells having more than 429 two stations; those observations then are then averaged, iii) interferences of NOz family on NO2 430 chemiluminescence measurements [Dickerson et al., 2019] which can be partly discounted when 431 calculating differences, iv) model uncertainties, especially with respect to turbulent and convective 432 fluxes that are heavily determined by representing local heterogenicity of forces and non-433 hydrostatic dynamics [Emanuel, 1994] TROPOMI was able to sample on. There is a strong degree of correlation between the frequency 447 of the data and the discrepancy between the model versus the surface observations. This is 448 especially the case for May when we see too few days to be able to realistically reproduce NO2 449 changes. Given the reasonable performance of our model at reproducing the changes observed 450 over the surface in April, a result of abundant samples from TROPOMI, we only focus on this 451 month for the subsequent analysis. where NOx emissions drastically decreased such as Germany, Italy, France, UK, Switzerland, and 457 Belgium (shown as box L). This tendency potentially is driven by ozone chemistry [Sicard et al., 458 2020a;Shi and Brasseur, 2020;Grange et al. 2020;Salma et al., 2020;Lee et al., 2020] and/or 459 meteorology [Lee et al., 2020;Wyche et al., 2021;Ordóñez et al., 2020] has drawn much attention. 460 The challenge is to simulate a model that is the characteristic of such a complex tendency [e.g., Regarding the horizontal transport, the values mostly follow the transport pattern and are 478 dependent on whether the advected air mass is more or less polluted. The vertical transport 479 correlates with the PBLH which is an indicator of the atmospheric stability and turbulence, 480 although we should not rule out the impact of the subgrid convective transport that can occur 481 sporadically. Low PBLHs are usually associated with more stable (or sometimes capping 482 inversion) and weaker vertical mixing [e.g., Nevius and Evans, 2018]. Vertical transport which is 483 majorly dictated by the vertical diffusion is by far the most influential factor in the magnitude of 484 ozone [e.g., Cuchiara et al., 2014]. In contrast to NO2 and HCHO, a stronger vertical diffusion 485 increases surface ozone due to positive gradients of ozone with respect to altitude. However, the 486 aerodynamic resistance controlling dry deposition velocity [Seinfield and Pandis, 2006] is also a 487 function of turbulent transport. For example, during daytime, intensified turbulence exposes more 488 pollution to surface deposition. It is because of this reason that we see the dry deposition process 489 largely counteracting vertical transport. This will leave the chemistry process the major driver of 490 the ozone changes. 491 We separately sum the quantities of the physical processes and PO3 contributing to MDA8 492 surface ozone changes binned to box L. The physical processes lead to -4.83 ppbv changes in the 493 MDA8 ozone mainly due to a relatively larger dry deposition in 2020, whereas P(O3) contributes 494 to +5.89 ppbv. The net effect is +1.01 ppbv which is slightly smaller than the simulated changes 495 in MDA8 ozone in this region (+1.79 ppbv). This apparent discrepancy is caused by the differences 496 in boundary and initial conditions which are not quantifiable by the process analysis and would 497 require additional sensitivity test. Nonetheless, we believe these numbers should provide 498 convincing evidence on the fact that chemistry has promoted the enhancements of surface ozone 499 during the lockdown. 500 Chemistry is also a function of meteorology, specifically solar radiation and temperature. 501 A typical scenario to isolate emissions from meteorology is by running the model with fixed 502 anthropogenic emissions (and boundary conditions) and subtracting the outputs from the variable 503 emission output. Figure 11 shows the contribution of anthropogenic emissions (VOCs and NOx) 504 to the changes seen over the surface. The anthropogenic emissions make up roughly 58% of the 505 changes. The map is strongly in line with the changes in NOx emissions constrained by TROPOMI. 506 The impact of meteorology plus biogenic changes (the former is dominant) highly correlates with 507 anomalies in both surface air temperature and photolysis rate ( Figure 6). We observe negligible 508 ozone changes due to emissions over Iberian Peninsula reinforcing the significance of the 509 meteorological impacts [Ordóñez et al., 2020]. 510 Figure 12 shows the numerically-solved ozone production rates (PO3) simulated by the 512 constrained model during the MDA8 hours period. We observe positive PO3 in less polluted areas 513 and eastern Europe where biomass burning activities occurred in 2019, while negative PO3 in 514 major cities. Negative values in PO3 are indicative of either loss in O3 or O3-NO-NO2 partitioning. 515

3.4.Ozone chemistry 511
The difference in PO3 between the two years suggests that the ozone enhancement in box L is 516 caused by a reduction in negative PO3 in 2020 over major cities compared to 2019. To examine 517 which pathways are contributing to this pattern, we attempt to analytically reproduce the 518 numerically-solved PO3 (Figure 12) through two different equations: the first equation widely 519 applied in photochemically active environments follows [Kleinman et al., 2002]: 520 This equation yields negative values only if the O3 loss pathways including NO2+OH, HOx+O3 , 521 O 1 D+H2O and O3+VOCs dominate over the first two terms. The second equation which is 522 independent of RO2 and HO2 concentrations [Thornton et al., 2002], is: 523 In summer, this equation tends to be positive during early afternoon, almost zero during afternoon 524 (steady-state), and negative in early morning (or night) in which the second term (O3 titration) is 525 leading. Any abrupt changes in NOx and VOC, and photolysis can directly affect equation 6 526 moving PO3 out of the diel steady-state. The assumption of the steady-state (PO3 from equation 6 527 equals to zero) is also not valid if an air parcel is in the vicinity of high-emitting NOx sources 528 [Thornton et al., 2002]. 529 well with the changes in NOx and prevailing chemical conditions regimes (NOx-sensitive vs VOC-532 sensitive). Souri et al. [2020a] found the reaction of RO2+NO to be primarily dependent on VOCs. 533 Likewise, we observe a strong degree of correlation between the anomaly of RO2+NO and that of 534 VOCs (Figure 3). Figure 13 indicates that the chemical pathways of ozone loss are rather constant 535 between the two years; therefore the largely negative PO3 over urban areas shown previously in 536 Figure 12 is not reproducible using this equation. Figure 14 shows the reactions rates of JNO2[NO2], 537 kNO+O3[NO][O3], and the difference during the MDA8 hours. The difference maps replicate the 538 largely negative PO3 over cities suggesting that we are not in the diel steady-state, and O3 titration 539 is prevailing due to relatively low photochemistry in the springtime. Table 4 lists the averaged 540 reactions rates involved in equation 5 and 6 along with the numerically-solved PO3 shown in 541 Figure 12 over box L. These numbers suggest that the major chemical pathways of enhanced ozone 542 are through JNO2[NO2] and kNO+O3 [NO][O3], implying that O3-NO-NO2 partitioning is more 543 consequential than other chemical pathways. This analysis strongly coincides with Lee et al. 544 [2020] and Wyche et al. [2021] who observed roughly constant O3+NO2 concentrations over the 545 UK before and during the lockdown 2020. 546

Summary 547
The slowdown in human activities due to the COVID-19 pandemic had an immediate and 548 sweeping impact on air pollution over Europe [Barré et al. 2020;Siccard et al., 2020]. Satellite 549 monitoring systems with large spatial coverage help shed light on the spatial and temporal extent 550 of those impacts. The relationships between satellite-derived HCHO and NO2 columns and near-551 surface emissions have proven difficult to fully establish without using realistic models, capable 552 of providing insights on the convoluted processes involving chemistry, dynamics, transport, and 553 photochemistry and therefore help with deciphering what anomaly maps of satellite concentrations 554 are suggesting [e.g., Goldberg et al., 2020]. To address these challenges, we jointly constrained 555 NOx and VOC emissions using TROPOMI HCHO and NO2 columns following a non-linear Gauss 556 Newton method developed in Souri et al. [2020a], in addition to assimilating MODIS AOD 557 observations based on Jung et al. [2019]. The constrained emissions also permitted investigating 558 the simultaneous effects of physical and chemical processes contributing to ozone formation, 559 illuminating the complexities associated with non-linear chemistry, 560 Several implications of the derived emissions for the months of March, April, and May 561 2020 (lockdown) relative to those in 2019 (baseline) were investigated. First, as previously 562 reported [Sicard et al., 2020;Barré et al. 2020], we observed a significant reduction in NOx in 563 March (14-31%) in several major polluted regions including Paris, London,Madrid,and Milan. 564 The reductions were further seen in other cities such as Rome,Brussels,Frankfurt,Warsaw,565 Belgrade, Kyiv, and Moscow (34-51%) in April. Second, a large spatial and temporal variability 566 associated with the reduction in NOx was evident, as each country might have different level and 567 timeline of restrictions. For instance, NOx emissions decreased drastically in April rather than 568 March in some portions of UK, northern Germany, Moscow, and Poland. Third, we showed that 569 anthropogenic VOC emissions over Paris (-9%), Milan (-29%), London (-5%), and Rome (-5%) 570 decreased in March, a picture that was achievable through jointly using NO2 and HCHO 571 observations. The reduced anthropogenic VOC emissions were a result of two key assumptions: 572 the reduced NOx emissions in NOx-rich areas increased HCHO made from VOCs (evident in larger 573 Jacobians derived from the regional model), and TROPOMI HCHO suggested a negligible 574 difference in HCHO concentration between the two years. This striking result emphasizes the 575 importance of building a multi-specie framework into inverse modeling studies, as the intertwined 576 chemical feedback between HCHO and NO2 is quite important and shown in proof of concept by 577 Marais et al. [2012], Valin et al. [2016], Wolfe et al. [2016], and Souri et al. [2020b]. [2020] and Wyche et al. [2021]. We found negligible differences in ozone production from 597 [HO2+RO2][NO] and ozone loss from O 1 D+H2O and O3+HOx between the two years suggesting 598 photochemistry was rather low in the springtime over Europe. 599 We further quantified the contributions of physical processes (transport, diffusion and dry 600 deposition) and chemistry to the formation/loss of ozone using the integrated process rates. The 601 physical processes decreased MDA8 ozone by -4.83 ppbv resulting from relatively larger dry 602 deposition in 2020, whereas chemistry (ozone production) augmented ozone levels by +5.89 ppbv, 603 indicating that rising ozone was primarily impacted by changes in chemistry. Enhanced air 604 temperature and photolysis in 2020, both of which were well captured in our model, also affected 605 chemistry. Experiments with fixed anthropogenic emissions underwent significant enhancement 606 in surface MDA8 ozone over central Europe, but those only contribute to 42% of the total 607 enhancement indicating that anthropogenic emissions were the major factor. 608 The results shown here reveal previously unquantified characteristics of ozone and its 609 precursors emission changes during the lockdown 2020 in Europe. We have been able to measure 610 the amount of changes along with the level of confidence in NOx and VOC emissions using a state-611 of-the-art inversion technique by leveraging well-characterized satellite observations, which in 612 turn, allowed us to unravel the chemical and physical processes contributing to increased ozone in 613 Europe. Unless a comprehensive air quality campaign targeting COVID-19 related lockdown is 614 available, we recommend that the impact of lockdown on air pollution should be examined through 615 the lens of well-established models constrained by publicly available data, especially those from 616 space in less cloudy environments. 617 with implementing the AOD assimilation framework. KC, JM, and XL guided the discussion. All 623 authors contributed to discussion and edited the paper. 624

Data availability 625
The atmospheric inversion data are publicly available from Souri et al. [2021]