Quantifying daily NO x and CO 2 emissions from Wuhan using satellite observations from TROPOMI and OCO-2

. Quantification and control of NO x and CO 2 emissions are essential across the world to limit adverse climate change and improve air quality. We present a new top-down method, an improved superposition column model to estimate day-to-day NO x and CO 2 emissions from the large city of Wuhan, China, located in a polluted background. The latest released version 2.3.1 TROPOMI NO 2 columns and version 10r of the OCO-2 observed CO 2 mixing ratio are employed. We quantified daily 20 NO x and CO 2 emissions from Wuhan between September 2019 to October 2020 with an uncertainty of 31 % and 43 %, comparing to the 39% and 49% with the earlier v1.3 TROPOMI data, respectively. Our estimated NO x and CO 2 emissions are verified against bottom-up inventories with minor deviations (< 3 % for the 2019 mean, ranging from -20 % to 48 % on a daily basis). Based on the estimated CO 2 emissions, we also predicted daily CO 2 column mixing ratio enhancements, which match well with OCO-2 observations (< 5 % bias, within ±0.3 ppm). We capture the day-to-day variation of NO x and CO 2 emissions 25 from Wuhan in 2019–2020, which does not reveal a substantial ‘weekend reduction’ but does show a clear ‘holiday reduction’ in the NO x and CO 2 emissions. Our method also quantifies the abrupt decrease and slow NO x and CO 2 emissions rebound due to the Wuhan lockdown in early 2020. This work demonstrates the improved superposition model to be a promising new tool for the quantification of city NO x and CO 2 emissions, allowing policymakers to gain real-time information into spatial-temporal emission patterns and the effectiveness of carbon and nitrogen regulation in urban environments.


Introduction
Fossil fuel combustion by power plants, industrial activities, transportation and residential energy use sectors leads to the emission of nitrogen oxides (NO x = NO + NO 2 ) as well as carbon dioxide (CO 2 ).Traditional bottom-up NO x and CO 2 emission estimates have a time lag of several years because it takes time to access and compile accurate information on energy consumption and emission factors (Lamsal et al., 2011;F. Liu et al., 2020).
For decades, satellites have been continuously providing information on NO 2 distributions and trends with good quality, and satellite data are widely used to quantify NO x emissions and changes (Lamsal et al., 2010;Visser et al., 2019;Zhang et al., 2020Zhang et al., , 2021)).Based on satellite-retrieved NO 2 data, previous studies quantified long-term mean (monthly, yearly or multi-yearly) NO x emissions on global and regional scales (Lamsal et al., 2011;Visser et al., 2019).Beirle et al. (2011) analyzed plumes of satellite NO 2 columns downwind of strong sources averaged for each wind direction and then inferred NO x emissions from isolated significant point sources and megacities.Inspired by this idea, Lorente et al. (2019) analyzed the increase of NO 2 along with the wind over the extensive pollution source of Paris.The buildup of NO 2 over the city observed from space, in combination with wind speed and direction information, allows us to obtain day-by-day (sub)urban NO x emission estimates and lifetimes as long as the city is under a clear sky and winds are relatively constant in time.This approach does not need burdensome inverse modeling computations and opens possibilities for rapid and direct monitoring of NO x emissions from space.
In contrast to NO x , it is challenging to infer accurate localized anthropogenic CO 2 emissions from satellite CO 2 retrievals.One reason is that the background CO 2 concentration is orders of magnitude higher than the enhancement caused by anthropogenic emissions, reflecting the long atmospheric lifetime of CO 2 (Reuter et al., 2014(Reuter et al., , 2019)).Another reason is that the spatial and temporal coverage of current CO 2 sensors is too sparse to allow for substantial averaging of noisy signals by revisiting of scenes, precluding detailed CO 2 emission estimation (Zheng et al., 2020a;F. Liu et al., 2020).Using satellite NO 2 measurements to estimate anthropogenic NO x emissions as the basis to infer anthropogenic CO 2 emission has been proposed in several studies (Reuter et al., 2019;F. Liu et al., 2020;Berezin et al., 2013;Zheng et al., 2020a).However, to our knowledge, there is no method that estimates day-to-day top-down CO 2 emission estimation on a (sub-)city scale.
Here we revisit the method of Lorente et al. (2019) to improve our understanding of its potential and limitations and extend it to estimate city-scale daily NO x and CO 2 emissions.We present an improved superposition model that considers the buildup of pollution over a source area as in Lorente et al. (2019), as well as the decay of NO 2 down-wind of the source, but now also accounts for changes in the background NO 2 pollution along the wind direction.The background NO 2 pollution was considered to remain constant by Lorente et al. (2019) for Paris, which is not surrounded by significant surface sources of NO x pollution.Here we apply our improved method to a highly polluted urban area, the megacity of Wuhan in the Hubei Province of China, which, other than the relatively isolated city of Paris, is located in a polluted background with many surrounding surface pollution sources that potentially interfere with the buildup and decay of the NO 2 plume from Wuhan.Using this improved superposition model, together with bottom-up information on the CO 2 /NO x emission ratio, we infer NO x and CO 2 emissions on a day-by-day basis over a full year from September 2019 to August 2020 and analyze the variation in emissions and NO x chemical lifetime from day to day.Of particular interest are the reductions and subsequent rebound of NO x and CO 2 emissions associated with the COVID-19 lockdown measures in Wuhan, which have been reported in other studies and serve here as a useful check of the robustness of our method.

Satellite data
In this study, we use the newly released level-2, version 2.3.1 of the S-5P TROPOMI (TROPOspheric Monitoring Instrument) data  between September 2019 and August 2020.The S-5P (Sentinel-5 Precursor) satellite was launched in October 2017, and the TROPOMI on board provides tropospheric NO 2 columns with an unprecedented horizontal resolution of up to 5.5 km × 3.5 km (as of 6 August 2019) and high signal-to-noise ratio (Griffin et al., 2019;van Geffen et al., 2020).The v2.3.1 dataset is provided by S5P-PAL (S5P Science and Technology Product Algorithm Laboratory) (Eskes et al., 2021).It is dedicated to supporting the research on the impact of the COVID lockdown on air quality.Improved (residual) cloud pressures correct the low bias of v1.x data compared to Ozone Monitoring Instrument (OMI) and ground-based measurements over east China (Wang et al., 2020;M. Liu et al., 2020).In addition, improved treatment for the surface albedo increases the columns for cloud-free scenes (van Geffen et al., 2022).Overall, compared to the earlier version, this dataset has 10-40 % higher tropospheric NO 2 columns over polluted scenes due to the improved cloud retrieval and other algorithm updates (van Geffen et al., 2022;Riess et al., 2022).Over Wuhan, we find an average increase (compared to the v1.3 data, from now on referred to as TROPOMI-v1.3) in tropospheric NO 2 column density of about 25 %.Still, there are also differences between the two versions in terms of spatial and temporal distribution (Fig. S1 in the Supplement).According to Fig. S1, the increase in v2.3.1 is much stronger over the polluted area (city center) and in the polluted period (9 September and 3 October 2019).Since the v1.xTROPOMI data are widely used in previous studies (e.g., Bauwens et al., 2020;Ding et al., 2020;Zhang et al., 2021), we also compared the estimated NO x lifetime and emissions from the TROPOMI-v2.3.1 data and the TROPOMI-v1.3 data, which will be discussed in Sect.3.1.For the record, when estimating the NO x emissions and lifetime over Wuhan, we scaled up the TROPOMI-v1.3NO 2 columns by a factor of 1.6 to correct for the known −40 % bias in TROPOMI NO 2 data as reported by M. Liu et al. (2020).
We sampled the TROPOMI NO 2 columns into 0.05 • latitude × 0.05 • longitude grid cells (∼ 6 × 6 km 2 ).To ensure good data quality, we filtered out the data with cloud radiance fractions greater than 0.5 (geometric cloud fraction less than 0.2) and obtained 81 clear-sky days with full TROPOMI NO 2 coverage over the Wuhan region in 1 full year.
The column-averaged dry-air mole fraction of CO 2 (XCO 2 ) data provided by the Orbiting Carbon Observatory-2 (OCO-2) is also employed to verify Wuhan's derived CO 2 emission inventory.We use version 10r of the bias-corrected XCO 2 product (Gunson and Eldering, 2020).The v10r OCO-2 XCO 2 product has high accuracy, with a single sounding precision of ∼ 0.8 ppm over land and ∼ 0.5 ppm over water and root-mean-square biases of 0.5-0.7 ppm over both land and water (O'Dell et al., 2021).

Bottom-up emission information
Bottom-up NO x and CO 2 emission inventories are used to provide the first guess of the NO x emission spatial pattern (for NO x , in the Supplement, Sect.S1 and Fig. S2) and to verify the top-down emissions.We use the Air Benefit and Attainment and Cost Assessment System Emission Inventory (ABACAS) (Zhao et al., 2013(Zhao et al., , 2018;;Zheng et al., 2019) to provide NO x and CO 2 emissions for the year 2019.The Multi-resolution Emission Inventory (MEIC) (Li et al., 2017) NO x emissions for 2017 are also employed.

Other input data
Besides the satellite data and bottom-up emission inventories, a set of other parameters is input into our improved superposition model.They include the hydroxyl radical (OH) concentration, the loss rate (k) of NO x in the atmosphere, the NO x /NO 2 ratio and the wind field.We use version 12.1 of the GEOS-Chem model with a horizontal resolution of 0.25 • × 0.3125 • (∼ 30 × 37.5 km 2 ) to provide the a priori guesses for chemical parameters relevant to daytime NO x .The wind field is from ERA5 (ECMWF Reanalysis v5), the fifth-generation ECMWF (European Centre for Medium-Range Weather Forecasts) atmospheric reanalysis of the global climate (Hersbach et al., 2020).Detailed information on these data can be found in Sect.S2.Considering that the wind field strongly influences the distribution of NO 2 col-umn patterns, and thus on the NO x emission estimation, we filter the TROPOMI NO 2 data based on the wind fields.After excluding the days with fluctuating wind direction (if the wind direction changes more than 45 • in the hours before the TROPOMI overpass) within the study domain, we finally obtained 50 d out of the ensemble of 81 valid satellite days between 1 September 2019 and 31 August 2020 to estimate NO x and CO 2 emissions from Wuhan.The fraction of useful days is comparable to what Lorente et al. (2019) obtained for Paris, which is 27 d in 5 months.

NO 2 pattern fits: estimation of lifetime and emission
To ensure that the whole area of Wuhan is included, we determine our study domain as a circular region centered at 114 • E, 30.7 • N, with a diameter of ∼ 186 km.It includes the whole area of Wuhan and the small city of Ezhou to the east of Wuhan, the southwest part of Huanggang and the east part of Xiaogan (Fig. S4, red circle).We also do a sensitivity test to narrow the study area down to within the Third Ring Road of Wuhan to check the robustness of our model to the area size of the study domain (Fig. S4, the blue circle).For each day, we converted the two-dimensional NO 2 column map over the domain to a one-dimensional line density along the wind direction (Sect.S3) (Beirle et al., 2011;Lorente et al., 2019).NO x emissions and lifetimes can be estimated by fitting the NO 2 line density over the domain.Lorente et al. (2019) presented a superposition column model based on a simple column model (Jacob, 1999) to simulate NO 2 line density over Paris.They considered the buildup of NO 2 caused by spatially varying NO x emissions from each cell and used the NO 2 line density value at the upwind end of the city to represent the background value, which they assumed to be constant over the city.This appears plausible if the background value were to mostly represent free-tropospheric NO 2 , which has a longer lifetime than NO 2 in the oxidizing polluted boundary layer and varies smoothly according to models.Our method to simulate the NO 2 line density over the city is also based on the column model (Jacob, 1999) but differs from that of Lorente et al. (2019) in considering the background NO 2 value.Each cell along the wind direction is treated separately as a column model.Since the satellite has an overpass time of around 13:30 LT (local time), NO x is removed in the atmosphere dominantly through the first-order reaction with OH.NO x emissions from the current cell contribute to the total line density through the buildup of NO 2 density within the cell and exponential decay of NO 2 downwind of the cell (Eq.1).It does not contribute to the upwind cells (Eq.2).
where N i represents the NO 2 line density (molec.cm −1 ) contributed from E i in cell i; L is the length of each cell, ; and u denotes the NO 2 -density-weighted mean wind speed in units of centimeters per second (cm s −1 ) within the planetary boundary layer.We add up the contributions from each cell and the background value to model the overall NO 2 line density: (3) Here, b represents the starting background value, equivalent to the mean NO 2 line density within the 5 (for summer, spring and autumn) or 10 (for winter) cells upwind of x = 0. α denotes the linear change of background value with distance along the wind and represents the chemical decay of background NO 2 flowing into the polluted boundary layer over the city.
We fit the terms that drive N(x) (i.e., E i , k and α) with the fixed L, u and [NO x ]/[NO 2 ] from external data, via a leastsquares minimization to the TROPOMI observed line density N TROPOMI (x).For each day, we run the model 20 times, randomly choosing OH concentration within the ±20 % interval of the GEOS-Chem-simulated OH concentration.The set of parameters E i , k and α that best explain the observations over the city is the answer we are seeking.The parameter that describes the decay of upwind NO 2 over the city, the α value, is determined by the difference of NO 2 line density between the end and start point of the study domain, α = (N 31 −N 1 ) 30L , and we allow it to change between ±α in the fitting procedure.For the 50 d on average, the α value is (−0.006±0.008)×10−22 molec.cm −2 .The α value being negative reflects the decay of upwind NO 2 pollution along the wind.
The assumption of a linearly decreasing NO 2 background is relevant under conditions when the city is in a polluted background.It accounts for decay of upwind NO 2 pollution arriving at the city when transported over and downwind of the city.In reality, upwind NO 2 pollution mixes in with the freshly emitted NO x and is then subject to chemical decay (with non-linearities due to turbulent mixing and spatial heterogeneity in emissions).We acknowledge that our linear decrease of background NO 2 pollution is a severe simplification.Still, as shown in Fig. 1, compared to fitting results with a constant background value, we obtain a better correlation (up to 25 %) and lower bias (nearly 50 % lower) between fitted and observed NO 2 line densities when fitting with a linearly changing background value.

CO 2 emission estimation
City-scale CO 2 emissions are estimated through Eq. ( 4): (4) The anthropogenic CO 2 /NO x emission ratio is provided by the ABACAS inventory and amounts to ∼ 591 g CO 2 per g NO x emitted from our study domain for the year 2019.
In 2020, emissions from the transport sector had substantially decreased due to the lockdown measurements (Huang et al., 2021;Zheng et al., 2020b).The more substantial decrease in transport NO x emissions relative to declines from other sectors is predicted to have led to an increase in the CO 2 /NO x emission ratio, for this ratio is lowest in the transport sector (Zheng et al., 2020b).The monthly CO 2 /NO x emission ratio for Wuhan was calculated based on recent reports on sectoral NO x emissions in 2020 from Hubei Province (Zheng et al., 2021a).We further calculated the daily CO 2 /NO x emission ratio based on the monthly, daily, and diurnal variations of CO 2 and NO x emissions (Fig. S5).The final daily CO 2 /NO x emission ratio for the study period displayed in Table S1 in the Supplement indeed shows increases in the CO 2 /NO x emission ratio of up to 20 % during the lockdown period in 2020 due to the reduced contribution from the transport sector.

Uncertainty in NO x and CO 2 emission estimation
Uncertainties in quantifying NO x and CO 2 emissions contain the systematic error in the TROPOMI NO 2 retrieval, bias in the assumed a priori OH concentration, NO x /NO 2 ratio, CO 2 /NO x emission ratio, uncertainties in wind fields and the area of the study domain.The v2.3.1 NO 2 column dataset corrected the low bias in TROPOMI (v1.x) tropospheric NO 2 column over eastern China by 15 %-100 % (van Geffen et al., 2022), but there remains an uncertainty of ∼ ±20 %.The chemical transport models (CTMs) have difficulty simulating accurate OH concentration, but for > 90 % of the days, our fitted OH concentrations fall in the ±20 % range around GEOS-Chem simulation, so the uncertainty in OH concentration is likely on the order of ±20 %.The difference between the model-simulated and observed NO x /NO 2 ratio is less than 10 %, so we give an uncertainty in NO x /NO 2 ratio of ±10 %.Uncertainty in the CO 2 /NO x emission ratio comes from the errors in sectoral NO x and CO 2 emissions, and we calculated that the corresponding uncertainty is ±30 %.We use the NO 2 -column-weighted mean instead of the arithmetic mean value to get the boundary layer mean wind speed to minimize the error in the wind field, but there may remain ±20 % uncertainty in the ERA5 reanalysis data.We ran a test by randomly choosing parameter values within their uncertainty ranges 20 times to predict an ensemble of NO x and CO 2 emission outcomes.Then the ratio of the standard deviation to the mean value of the 20 emission outcomes is regarded as the uncertainty on NO x and CO 2 emission caused by uncertainties in the corresponding parameters, which are displayed in Table S2.The uncertainty caused by the domain size is determined by narrowing down our study domain to the Wuhan city center (see Sect.S4 and Fig. S6).The results demonstrate that when the study domain is narrowed down to 84 km diameter, as expected, it turns out to be structurally different from that with the 186 km diam- eter domain.This is because the mean OH concentration is lower in the city center, leading to longer fitted NO x lifetime.However, the change in fitted NO x lifetime and NO x emission is within ±15 %.So, we apply a 15 % uncertainty in NO x emissions and lifetime estimation caused by the area size of the study domain.Finally, considering that all these parameters are independent of each other, we use the rootmean-square sum of the contributions to represent the overall uncertainty estimation, which we quantify for NO x emission on a single day at ∼ 31 % and for CO 2 emission at ∼ 43 %.

NO x lifetimes and emissions
We display the estimated NO x lifetime and NO x emissions for each clear-sky day during the study period in Table S1.
The estimated planetary boundary layer mean OH concentration over the region for each day is presented in Fig. 2  2.8 ± 1.3 h for spring, 1.4 ± 0.3 h for summer and 1.9 ± 0.5 h for autumn.The results are lower than those calculated from the GEOS-Chem simulation by Shah et al. ( 2020), with ∼ 6 h in summer and > 20 h in winter.This is because they calculated the 24 h mean NO x lifetime, while the loss rate of NO x is much higher around noon.NO x lifetime for Wuhan is also shorter than for Paris (Lorente et al., 2019), especially during winter, reflecting the higher radiation levels and temperature in Wuhan than in Paris.It should be noted that Liu et al. ( 2016) fitted a NO x lifetime of 2.6 h for Wuhan in the warm season (May to September) for the 2005-2013 mean, and our result for 2019-2020 is 1.7 ± 0.4 h.One reason is that they calculated NO x lifetime based on a long-term mean NO 2 distribution and the coarser resolution of OMI data, both of which lead to spatial smoothing of NO 2 gradients and thus longer apparent NO x lifetimes (Qu, 2020).Another explanation is the increasing ozone concentrations in China in recent years (Li et al., 2020) promote OH formation and thereby NO x loss reactions, which shorten NO x lifetime (Zara et al., 2021).The estimated NO x lifetime and emissions from the two TROPOMI datasets for the whole study period are presented in Fig. S7.On average, the TROPOMI-v1.3 data result in 13 % lower NO x emissions from Wuhan than the TROPOMI-v2.3.1 data.NO x lifetime estimated from TROPOMI-v1.3 data is 5 % shorter than that from TROPOMI-v2.3.1, which may be attributed to the fact that the TROPOMI-v2.3.1 data have a higher gradient between the city center and the background.Uncertainties in NO x emissions and lifetime estimation are 33 % higher in the TROPOMI-v1.3 data (39 %) for the higher uncertainty in the NO 2 column data (here we use 30 %).
We further verified the estimated NO x emissions from the two TROPOMI datasets in 2019 with the bottom-up emission inventories.We obtained 14 d (including 9 weekdays, 3 weekend days, and 2 holiday days) between September and November 2019 for the top-down NO x emission estimation and compared them with those from the ABA-CAS (2019) and MEIC (2017) inventories.Overall, as presented in Fig. 3a, compared to the bottom-up emission inventories, TROPOMI-v1.Unlike the bottom-up inventories, our daily TROPOMI NO x emissions do not indicate the existence of a so-called "weekend reduction effect" but do point out a distinct "holiday reduction effect" in Wuhan NO x emissions.The bottomup inventories suggest that weekend NO x emissions are 30 % reduced relative to weekdays.The TROPOMI-v2.3.1 estimation shows reductions in weekend NO x emission of < 3 %, while on the 2 d (1 and 3 October) of the National Holiday, NO x emissions are 8 % lower than the workday mean.Surface NO 2 and O 3 observations from Beijing do not show a weekend effect (Zhao et al., 2019;Hua et al., 2021) either.Our TROPOMI top-down NO x emissions show a similar spatial pattern as in the ABACAS and MEIC (Fig. S2), with the highest emissions located in the city center of Wuhan.However, the TROPOMI NO x emission pattern appears more smeared out than from ABACAS due to the strong dependence of the bottom-up spatial distribution on population density, the difference in spatial resolution and the decrease in NO x emissions in early 2020, mainly occurring in the high-emission region.

CO 2 emissions and X CO 2 enhancements
We estimate noontime top-down (technically representing a merger of top-down and bottom-up information, but we define it as top-down for simplicity) CO 2 emissions from Wuhan between September and November 2019 to be 6.32± 2.74 s −1 (the errors represent the uncertainty of the emission estimation), comparable to ABACAS-2019, of 6.40 ± 2.78 t s −1 (Fig. 3b).Based on the estimated daily CO 2 emissions, we further use the superposition column model to simulate daily XCO 2 enhancements and evaluate them with OCO-2 observations.We successfully obtained 2 d between May 2018 (start time of TROPOMI-v2.3.1 NO 2 product) and December 2021 with simultaneous (both overpass at around 13:00-13:30 LT), co-located TROPOMI NO 2 and OCO-2 CO 2 observations over Wuhan on 15 September 2018 and 13 April 2020.We inferred total top-down CO 2 emissions from Wuhan based on our TROPOMI-inferred NO x emissions and the ABACAS-predicted CO 2 /NO x emission ratios on 15 September 2018 and 13 April 2020 to be 7.92 ± 3.44 and 4.44±1.93t s −1 , respectively.Then they are used to predict the XCO 2 enhancements with the superposition column model.To compare with the sparse distributed OCO-2 observations, we apply the superposition model on the CO 2 line density with a width of 1 km, while a width of 186 km is used for NO 2 .The column model does not take the diffusion of NO 2 or CO 2 into account, but it can be assumed that all diffusion is encapsulated within the domain for a line density covering a cross-section as wide as 186 km.However, when the line density is only 1 km wide, the diffusion will move some CO 2 out of this line, and this will influence the CO 2 enhancement prediction.We will discuss this influence further below.
Neglecting chemical production and loss of CO 2 in the atmosphere, the superposition column model of CO 2 (Eq.5) is simpler than that of NO x :  where N CO 2 is CO 2 density in units of grams per square meter (g m −2 ), E CO 2 denotes our estimated CO 2 emission (g s −1 ), and u and L are the wind speed (m s −1 ) and length of grid cell (6000 m).Then N CO 2 (g m −2 ) is converted to the dry-air column mixing ratio XCO 2 (ppm) for comparison with the OCO-2 observation (Zheng et al., 2020a): in which M air and M CO 2 are air and CO 2 molar mass of air and CO 2 (g mol −1 ), g is the gravitational acceleration (9.8 m s −2 ), and p (Pa) and w (kg m −2 ) are surface pressure and total column water vapor, respectively.We calculate the XCO 2 enhancement due to the top-down CO 2 emissions on 15 September 2018 and 13 April 2020 and compare these with the enhancements observed by OCO-2.As shown in the right panels of Fig. 4, the superposition model captures the spatial pattern of observed XCO 2 along the OCO-2 orbit on both days.The predicted amplitudes of the XCO 2 enhancements are also comparable to those in the OCO-2 observation with a small bias (less than 5 % for both days).For comparison, we also use the 2019 bottom-up CO 2 emissions to predict the XCO 2 enhancement on the 2 d (blue lines in Fig. 4, the right panel).XCO 2 enhancements predicted by bottom-up CO 2 emissions deviate more from the OCO-2 observed enhancements than those predicted by the top-down CO 2 emissions.On 13 April 2020 in particular, the bottom-up enhancement differs by +41 %, while the topdown enhancement differs only within ±5 % compared to the observed XCO 2 enhancement.At the beginning of Wuhan's reopening, CO 2 emission from the city (our top-down estimation) is expected to be far lower than the pre-lockdown level (bottom-up estimation).
We see that the predicted XCO 2 enhancements on 13 April 2020, both from the bottom-up and top-down emissions, are much "narrower" compared to the OCO-2 observation.On this day, the OCO-2 orbit passes over the city center, and the diffusion plays an important role, which is neglected in the column model.In contrast, on 15 September 2018, the OCO-2 orbit passed downwind of the city cen-ter, and the widths of the predicted and observed XCO 2 enhancements are more comparable.For comparison, we also ran a Gaussian plume model to simulate the XCO 2 enhancement (Sect.S5 and Fig. S8).On 13 April 2020, the result from Gaussian model agrees better with the OCO-2 observation, and on 15 September 2018, results from the two models (Gaussian model and the superposition column model) are close to each other and match well with the observation.
We also display XCO 2 enhancement line densities along the wind direction with uncertainty on both days (Fig. 5).The line density shows a substantial increase of XCO 2 along the wind direction over the region with strong CO 2 emissions (Fig. 5a and b, the inset maps).Where lines cross the OCO-2 orbit, the observed XCO 2 enhancement (as box plots in Fig. 5a and b) is shown, and its values agree with the predicted XCO 2 lines within ±0.3 ppm.It is remarkable that the XCO 2 enhancement is lower on 15 September 2018 than on 13 April 2020, despite CO 2 emission on 15 September 2018 being nearly 65 % higher than those on 13 April 2020.The main reason for this is the lower wind speed on 13 April 2020, which accumulates pollutants over the city, and the fact that the OCO-2 ground track passed over the city center of Wuhan on this day.On 15 September 2018, higher wind speeds and the OCO-2 track being situated over the outskirts of the city imply that a lower enhancement of CO 2 is observed.
We use an "indirect" method to estimate daily city anthropogenic CO 2 emissions and then predict XCO 2 enhancements, which may induce uncertainties from the NO x emission estimation, the assumption of CO 2 /NO x emission ratio and the model to predict XCO 2 enhancements.Despite all these uncertainties, we still generate daily Wuhan CO 2 emissions and XCO 2 enhancements that agree well with the bottom-up inventory and OCO-2 observation, respectively.

Variation of NO x and CO 2 emissions in Wuhan from
September 2019 to August 2020 Figure 6 displays the day-to-day variation of NO x and CO 2 emissions in Wuhan between September 2019 and August 2020.Before the pandemic of COVID-19, NO x emissions stayed at a stable level of 11.53 ± 1.08 kg s −1 , and CO 2 stayed at 6.32 ± 0.66 t s −1 (the errors denote the standard deviation), as indicated by the dashed red lines.From January 2020 onwards, strict lockdown measurements were implemented to combat the COVID-19 pandemic, which led to lower industry production and less traffic on the road and a sharp drop in NO x and CO 2 emissions (Ding et al., 2020;Zhang et al., 2020Zhang et al., , 2021;;Zheng et al., 2021b;Feng et al., 2020).Our method closely captures the timing and magnitude of these well-known sharp reductions in emissions.
Wuhan NO x emissions on 30 January 2020 were 3.65 ± 1.59 kg s −1 , nearly 70 % lower than pre-lockdown levels, and decreased further and came to the lowest level in early February 2020, in accordance with Feng et al. ( 2020), who es- timated similar reductions based on surface NO 2 observations.The day with our lowest NO x emission from Wuhan of 2.55 ± 1.11 kg s −1 , only ∼ 22 % of the normal level, was 5 February.CO 2 emissions have a similar temporal pattern to NO x emissions, but the reduction relative to pre-lockdown level is smaller.The lowest CO 2 emission is at ∼ 27 % of the pre-lockdown level (also on 5 February 2020), and the mean emission rate during the lockdown period (23 January to 8 April 2020) is 60 % lower than pre-lockdown level, while it is 67 % for NO x .That CO 2 emission reductions are more modest than NO x reductions reflects the fact that the transportation sector had the strongest reductions during the lockdown, but since this sector also has the lowest CO 2 /NO x ratios, the relative reduction in CO 2 remains somewhat smaller than in NO x emissions.This finding is similar to that of Zheng et al. (2020b), who estimated the NO x and CO 2 emission variations for the whole China.
From early February 2020 onwards, emissions increased slowly throughout the lockdown period.Wuhan NO x emissions intensity in February 2020 was no more than https://doi.org/10.5194/acp-23-551-2023Atmos.Chem.Phys., 23, 551-563, 2023  2020) reported 4.8 % higher CO 2 emissions for the whole of China in August 2020 compared to August 2019.For the city of Wuhan, however, we calculate here some 20 % lower CO 2 emissions in August 2020 compared to the pre-lockdown level.Wuhan experienced a much more strict and longer period of lockdown than other regions of China, and therefore a slower rebound of NO x and CO 2 emissions should be expected.
As we have stated above, to ensure the performance of the model, we must filter out the days when the cloud fraction is greater than 0.2 and the days when the wind direction shows substantial spatial or temporal variation within the study domain.Finally, we obtain 50 out of the 365 d with reliable NO x and CO 2 emissions estimation.However, these 50 d cover at least 2 d for each month (except for December 2019).For 2019, it includes 9 workdays, 3 weekend days, and 2 holiday days, which are enough to investigate the weekend reduction effect and holiday reduction effect in NO x emissions.It also covers 12 d across the lockdown period and 24 d after that, allowing us to monitor the large reduction and recovery of NO x and CO 2 emissions from Wuhan due to the COVID lockdown.Therefore, these 50 d provide useful information to investigate the temporal emission patterns of NO x and CO 2 from Wuhan and help to monitor the effectiveness of emission reductions in large urban centers.

Conclusion
In this study, we introduced an improved superposition column model to estimate daily NO x and CO 2 emissions from a Chinese megacity of Wuhan based on the latest released version 2.3.1 of TROPOMI NO 2 column data and OCO-2 XCO 2 observation.Our estimated daily NO x and CO 2 emissions agree well with bottom-up emissions with a small bias of < 3 %.Predicted XCO 2 enhancements based on our CO 2 emissions estimates are proved to be in good agreement (within ±5 %) with OCO-2 observations over Wuhan.Compared to previous studies, our work shows that satellite measurements can provide detailed information on sub-city-scale NO x and CO 2 emissions on a daily basis.We achieved the day-to-day variation of NO x and CO 2 emissions from Wuhan between September 2019 and August 2020.We pointed out that the weekend reduction effect is small, but a holiday reduction effect in Wuhan NO x and CO 2 emissions can be clearly detected.We also captured the abrupt decrease in NO x and CO 2 emissions as the lockdown for COVID began on 23 January 2020 and the slow rebound as Wuhan reopened on 9 April 2020.Daily updates of city-scale NO x and CO 2 emissions provide policymakers with emission and policy control data on NO x and CO 2 emission control in urban environments.
In the future, following the launch of the Carbon Dioxide Monitoring mission (CO2M) (Sierk et al., 2021), our improved superposition column method may be explored further to constrain city-scale CO 2 and NO x emissions to assess the effectiveness of emission control measures.CO2M provides simultaneous and co-located CO 2 and NO 2 observations with a wider swath than OCO-2, providing better opportunities to verify and improve CO 2 and NO x emissions from space.

Figure 1 .
Figure 1.Tropospheric NO 2 columns over Wuhan on 29 September 2019, 30 January 2020 and 2 May 2020 (left panels, from top to bottom); the red circle inside each map defines the study domain.The corresponding NO 2 line densities along wind within the study domain are given in the right panel.For each day, the correlation coefficient (R) between the observed (black line) and fitted (grey and red lines) NO 2 line density is given.The fitted mean bias (MB), NO x emissions (E) and NO x lifetime (τ ) are also displayed.

Figure 2 .
Figure 2. Daily boundary layer mean OH concentration over our study domain.The OH concentration estimated from our improved superposition column model is given with the red line.The grey shade represents 0.8-1.2times the GEOS-Chem-simulated OH concentration, and the grey line represents CMAQ model simulation results.
3-2019 NO x emissions are 21 % and 23 % lower than ABACAS-2019 and MEIC-2017, respectively.On the other hand, TROPOMI-v2.3.1-2019NO x emissions are comparable to those from ABACAS-2019 (2 % difference) and ∼ 5 % lower than MEIC-2017.That NO x emissions estimated from TROPOMI-v2.3.1 in 2019 are lower than MEIC-2017 likely reflects the fact that NO x emissions decreased in 2019 relative to 2017 in response to Chinese emission controls.According to the Wuhan Bureau of Statistics, NO x emissions reduced by 6 % between 2017 and 2019 (Wuhan Bureau of Statistics, 2019; Bauwens et al., 2020), close to the difference between TROPOMI-v2.3.1-2019 and MEIC-2017.Through the comparison with the bottom-up emissions, we find that the TROPOMI-v2.3.1 NO 2 data generate more reliable NO x emissions from Wuhan in 2019 than the v1.3 data, even when the low bias in TROPOMI-v1.3 data is corrected by a factor of 1.6.

Figure 3 .
Figure 3. Daily noontime (a) NO x and (b) CO 2 emissions in Wuhan estimated from TROPOMI (red and blue bars; the error bars represent the uncertainty in the emission estimations) and the bottom-up emission inventories ABACAS (black bars) for the year 2019 and MEIC (silver bars) for the year 2017.The dark-and light-grey shades represent weekends and holidays, respectively.The mean levels of each dataset are given as dashed lines with corresponding colors.

Figure 4 .
Figure 4. Simultaneous, co-located TROPOMI NO 2 and OCO-2 CO 2 observations over Wuhan (the left panel) on 15 September 2018 (top panels) and 13 April 2020 (bottom panels), the wind speed and direction on each day are shown.The dry-air mole fraction of CO 2 (XCO 2 ) enhancements along the OCO-2 orbit are given for the corresponding day (the right panel).The grey crosses and black lines represent the OCO-2 observation.The blue lines denote XCO 2 enhancement predicted with bottom-up emissions, and the red lines (shading represents the uncertainty interval) denote that predicted with top-down CO 2 emission, estimated in this study.

Figure 5 .
Figure 5. Two presentative predicted XCO 2 enhancement lines (red and blue) with uncertainty (grey shades) on (a) 15 September 2018 and (b) 13 April 2020.When the XCO 2 enhancement lines pass through the OCO-2 orbit, the observed XCO 2 enhancements are shown with box plots.The mean values are shown as green triangles, and the outliers beyond the 5 %-95 % interval are shown as circles.The predicted XCO 2 enhancement line density maps overlaid with OCO-2 observed XCO 2 enhancement on each day are shown inside, with the position of the presentative lines and the wind direction.

Figure 6 .
Figure 6.The 50 d (a) NO x and (b) CO 2 emissions in Wuhan estimated from TROPOMI between 1 September 2019 and 31 August 2020.The error bars denote the uncertainty in emission estimations, and the weekends, holidays and lockdown period are shaded with dark-grey, light-grey and green colors, respectively.The mean pre-lockdown emission levels are given as dashed red lines.
. For 90 % of the days, our model-fitted OH concentrations fall into the intervals of 0.8-1.2times the GEOS-Chem model values.There are only 5 d on which we had to impose a change in OH concentrations of more than 30 % relative to the GEOS-Chem simulation to obtain realistic fitting results.We estimate that the seasonal mean noontime NO x lifetime over Wuhan and adjacent region is 4.8±0.8h for winter, https://doi.org/10.5194/acp-23-551-2023Atmos.Chem.Phys., 23, 551-563, 2023