$$E_{NO_x}(\text{time, altitude, latitude, longitude}) = x(\text{day, altitude, latitude, longitude}) \times E_{NO_x,ref}(\text{time, altitude, latitude, longitude})$$

with $E_{NO_x,ref}$ the reference emissions from the bottom-up inventory. Thus, the values of $x_b$ are all set to 1 and the control covariance matrix $B$ is expressed in relative terms and not in emission covariances. The dimension of $x$ and $x_b$ is 24 × 16 × 64 × 60 and corresponds to the hours in a day, the level of altitude and the number of latitudinal and longitudinal grid cells in the domain, respectively. The dimension of $y$ is 1D (e.g., 780) and determined by the selection of the observations (selection criteria explained in the OMI observation section).

We use the CIF inversion system interfaced with the CHIMERE CTM and its adjoint and the OMI NO₂ columns to perform the inversion experiments. The CIF is an open-source unified system designed to allow the use of different atmospheric inversion approaches, atmospheric transport models, and observations with large flexibility (Berchet et al. 2021). It is designed to estimate the fluxes of various greenhouse gases and reactive species both at the global and regional scales. As we consider reactive species, the inversion problem is non-linear. We then use the M1QN3 limited-memory quasi-Newton minimization algorithm (Gilbert, Lemaréchal, and Simulator 2009) to minimize the cost function $J$ (Equation 29). It is worth noting that computing the uncertainties on the posterior emissions is very challenging when using variational approaches due to the dimensionality of the problem and constraints on time and computing sources (Berchet et al. 2021; Fortems-Cheiney et al. 2021; Rayner, Michalak, and Chevallier 2019). These uncertainties are then not estimated here.

### 3.2.1.2 HTAP v2.2 emission inventory

The Hemispheric Transport Atmospheric Pollution (HTAP) inventory, version 2.2 (Janssens-Maenhout et al. 2015) is used to prescribe anthropogenic emissions of pollutants to the CHIMERE model. For the country of China, HTAP v2.2 is constructed using regional emission inventories in collaboration with the MICS Asia Scientific Community (MICS-Asia) and REAS experts with a horizontal resolution of 0.25° × 0.25° converted to 0.1° × 0.1° (Galmarini et al. 2017). Emissions are estimated from seven main sectors of anthropogenic activities: air, ships, energy, industry, transport, residential, and agriculture. The HTAP v2.2 emissions correspond to the year 2010 and used as the prior in the inversion runs (Figure 39), whatever the considered year. In this study, emissions will be called Prior when they are used as a prior in the inversion. In parallel, they are also used as a reference for the emissions of the year 2010, the starting
point to evaluate the 12th and the 13th Five-Year Plans. In this study, they are called HTAP v2.2 when they are used as a reference in the simulations. In addition, the biogenic NOₓ emissions are given by the Model of Emissions of Gases and Aerosols from Nature version 2.1 (MEGAN v2.1) model (Guenther et al. 2012).

In this study, we set prior uncertainties B by taking diagonal terms as 70 % for the anthropogenic NOₓ emissions (Müller and Stavrakou 2005) and 100 % for the biogenic NOₓ emissions. We use horizontal correlations that decay exponentially with the correlation length scale derived from the model (CHIMERE) resolution. Noting that, in this study, NOₓ emissions are expressed as nitrogen oxides (NO₂ and NO) in kilotons (hereinafter, kt NOₓ or Tg NOₓ is referred to as kt or Tg).

### 3.2.1.3 OMI satellite observations

The Ozone Monitoring Instrument (OMI) is a nadir-viewing ultraviolet-visible spectrometer on National Aeronautics and Space Administration's (NASA) Earth Observing System (EOS) Aura polar satellite, launched in July 2004 (Schoeberl et al. 2006). The instrument is a result of the contribution of the Netherlands' Institute for Air and Space Development and the Finnish Meteorological Institute to the EOS Aura mission. It has been providing daily data since 9th August 2004 by making full global measurements of the solar radiation backscattered from the Earth's atmosphere and surface, along with measurements of the solar irradiance with a spatial resolution of 24 × 13 km² at nadir (across × along-track) with a local overpass time 13:40 LT (Levelt et al. 2006).

This study uses OMI NO₂ tropospheric columns from the European Quality Assurance for Essential Climate Variables (QA4ECV) project's NO₂ ECV precursor version 1.1 product (Boersma et al. 2018). This QA4ECV retrieval consists of an improved spectral fitting method and data assimilation scheme using the TM5-MP model in 1° × 1° degree horizontal resolution to estimate stratospheric background NO₂ and to reinforce the air mass factor (Zara et al. 2018; Lorente et al. 2017). OMI tropospheric NO₂ column data is defined as the vertical integrations of the NO₂ molecules between the surface and the tropopause. The data set is collected from the Tropospheric Emission Monitoring Internet Service (TEMIS https://www.temis.nl/airpollution/no2.php Last access: 26/09/2022). We first select OMI observation data of which; (i) the processing error flag equals 0 for a pixel, (ii) the solar zenith angle is lower than 80°, (iii) the snow ice flag is lower than 10 or equal to 255, (iv) the ratio of
tropospheric air mass factor (AMF) over geometric AMF is higher than 0.2 to avoid situations
in which the retrieval is based on very low (relative) tropospheric AMFs, and (v) the cloud
fraction is lower than 0.5. Second, we filter out these selected daily OMI observation data with
a maximum of 100 % error.

3.2.1.4 The regional CHIMERE CTM

CHIMERE is a state-of-the-art three-dimensional regional CTM that simulates hourly atmospheric concentrations of a number of pollutants of interest over a given domain (CHIMERE https://www.lmd.polytechnique.fr/chimere/ Last access:26/09/2022). External forcings are required to run a simulation, such as meteorological fields, primary pollutant emissions (anthropogenic and biogenic emissions), and initial and boundary conditions.

In this study, we use CHIMERE v2013 (Menut et al. 2013) with the following inputs to simulate NO₂ concentrations. Boundary conditions are given by a climatology from the global model LMDZ-INCA (Hauglustaine et al. 2004). Meteorological conditions come from the European Centre for Medium-Range Weather Forecasts (ECMWF) and are interpolated hourly. Biogenic emissions are estimated from the MEGAN v2.1 model (Guenther et al. 2012). Finally, anthropogenic emissions are those from the HTAP v2.2 bottom-up inventory (Janssens-Maenhout et al. 2015).

Our study configuration is based on a 0.5° × 0.5° horizontal resolution with 17 vertical layers from surface to 200 hPa and 8 layers within the first three kilometers. It includes 65 (longitude) × 61 (latitude) grid cells that correspond to 18°N – 50°N; 102°E – 132°E and covers eastern and southern China, seas and Korean Peninsula (Figure 40).

The gaseous chemical scheme used in CHIMERE is MELCHIOR-2 (Guenther et al. 2012; Menut et al. 2013). The aerosol module of CHIMERE is not considered in the simulations and inversions, as the adjoint of this module is not available (Fortems-Cheiney et al. 2021).

For the comparison between the observations and the model during the inversion process
(Figure 39), super-observations at the model resolution (0.5° × 0.5°) are considered. As the
number of OMI observations lying in the model grid-cell is generally small and will not allow
one to decrease observation errors by averaging, we choose to use the median of corresponding
OMI NO₂ columns. The averaging kernel *A* and the observation errors associated with the median columns are considered too. The observation errors are used to fill the *R* matrix.

<figure><img src="image_50.png" /><figcaption>Figure 40 Study domain. Selected locations presenting the most urbanized and industrialized regions (see section 3.3.3) are indicated by the rectangles.</figcaption></figure>

To compare with OMI super-observations, simulated NO₂ concentrations in the same grid cells as the super observations are selected. The hourly-simulated concentrations are interpolated in time and OMI's pressure levels. OMI averaging kernels are applied to these NO₂ vertical profiles using Equation 30 (Boersma et al. 2017).

$$y = \sum_{i=1}^{n} y_{i}^{s} A_{i} \qquad (\text{Eq. 30})$$

where; *y* is the model equivalent of the satellite data, *n* is the number of levels of the satellite observations, *y*ᵢₛ is the simulated concentration interpolated at the *i*-th level, *A*ᵢ is the averaging kernel of the *i*-th level. Finally, modelled NO₂ tropospheric columns are calculated and compared to OMI NO₂ columns (the 2nd term of the cost function *J*, Equation 29).

### 3.2.1.5 Inversion experiments

This study performs CIF-CHIMERE inversions with a daily assimilation window for 2015 and 2019. The inversion is considered convergent when the gradient norm of the *J* function is reduced by more than 95 % (Fortems-Cheiney et al. 2021). By this criterion, there are 267 and 296 convergent days per year, respectively. Due to the variability of the daily spatial coverage
of OMI observations, we consider monthly averaged corrections to build the final posterior emission inventories. Examples of monthly corrections are shown in the Figure 41 for the month August in 2015. Example of innovation and residue map for the same month is seen in Annex I: Innovation & Residue Map. It is seen that, the system goes towards to the observations where the simulations have higher monthly concentrations than OMI observations, in particular in the urbanized regions.

<figure><img src="image_51.png" /><figcaption>Figure 41 Monthly Corrections of NOₓ emissions for August 2015</figcaption></figure>

The main inversion run configurations made for 2015 and 2019 are summarized in Table 6.

Table 6 Summary of the inversions and simulations performed in this study. The output column gives the short names, which will be used in the following.

<table><thead><tr><th>Type</th><th>Target Year</th><th>Emission Inventory</th><th>Objective</th><th>Output</th></tr></thead><tbody><tr><td>Inversion</td><td>2015</td><td>HTAP v2.2 2010</td><td>Estimate monthly anthropogenic NO<sub>x</sub> Emissions</td><td>Emis Post15</td></tr><tr><td>Inversion</td><td>2019</td><td>HTAP v2.2 2010</td><td>Estimate monthly anthropogenic NO<sub>x</sub> Emissions</td><td>Emis Post19</td></tr><tr><td>Control</td><td>2015</td><td>HTAP v2.2 2010</td><td>Simulate hourly NO<sub>2</sub> Concentrations</td><td>Conc Prior15</td></tr><tr><td>Control</td><td>2019</td><td>HTAP v2.2 2010</td><td>Simulate hourly NO<sub>2</sub> Concentrations</td><td>Conc Prior19</td></tr><tr><td>Experiment</td><td>2015</td><td>Emis Post15</td><td>Simulate hourly NO<sub>2</sub> Concentrations</td><td>Conc Post15</td></tr><tr><td>Experiment</td><td>2019</td><td>Emis Post19</td><td>Simulate hourly NO<sub>2</sub> Concentrations</td><td>Conc Post19</td></tr><tr><td>Evaluation</td><td>2015</td><td>MEIC v1.3 for NO<sub>x</sub> + HTAP v2.2 for other species</td><td>Simulate hourly NO<sub>2</sub> Concentrations</td><td>Conc MEIC15</td></tr></tbody></table>
bilinearly interpolated at the location of the stations. The normalized mean biases (NMB), the root-mean-square error (RMSE), and the Pearson correlation coefficient (r) are the metrics used for the evaluation (Annex D: Statistical Indicators). The measured concentrations are taken as the reference. As already mentioned, it is also necessary to perform a control run based on the prior emissions to evaluate if the inversions help to better assess the emissions compared to the prior (for simplicity, we will use the term of improvement in the following). In addition, calculating the ratios of the statistical indicators between the experiment run and the control run for the same year allows one to quantify the improvement brought by the inversions (Annex E: Ratio Formulas). Indeed, when the ratios of the mean bias and of the RMSE are smaller than one and/or the correlation ratio is higher than one, we can consider that the new emission estimates are improved compared to the prior knowledge of these emissions. In addition, we also performed a run for 2015 where the emissions from HTAP v2.2 are replaced with the NOx emissions from MEIC version 1.3. This allows an evaluation of the emission estimates against an independent inventory.

It is worth noting that, for the comparison between models and surface stations, Lamsal et al., 2008 recommended to apply a correction factor to the measured NO₂ concentrations. Indeed, due to the measurement analyzer which catalyzes NO₂ into NO, other reactive oxidize nitrogen compounds (NOₓ) such as peroxyacetyl nitrate (PAN), and nitric acid (HNO₃) can be also converted to NO to a certain extent, which results in an overestimation of ambient NO₂ concentrations (Lamsal et al. 2008). For this reason, Lamsal et al. 2008 suggested using the following correction factor (CF) formula to alleviate and avoid this overestimation of NO₂.

$$CF = \frac{NO_2}{NO_2 + \sum AN + 0.95PAN + 0.35HNO_3} \quad (Eq.31)$$

We use CHIMEREv2013 to simulate NO₂, the sum of all alkyl nitrates (AN), PAN, and HNO₃ at a resolution of 0.5°×0.5° for 2015 and 2019, respectively. Calculated CFs are bilinearly interpolated according to the location of the stations (latitude, longitude) before being applied to the hourly measured ground-based NO₂ concentrations.

To avoid representativeness issues during the comparison of simulated concentrations at the coarse model resolution and the surface measurements, we first classify the stations according to their environment type. The types of the stations follow the classification done in Lachatre et al. 2020 using the method of Flemming, Stern, and Yamartino 2005. In the method they use
ozone and its diurnal variability to evaluate whether stations represent rural, suburban, urban, or traffic environments. In our analyses, we include stations in rural, suburban and urban environments and exclude stations in the traffic environment, as they are near sources and are not comparable to the coarse model resolution.

In addition to the evaluation of the emission estimates using surface measurements, we also analyze the emissions Emis_Pos15 and Emis_Pos19 in terms of annual, monthly, and regional emission budget. The emission budgets are calculated as the sum of emissions in each grid cell of the region / domain and over the time period considered. Comparison with the independent MEIC inventory for 2015 on an annual and monthly basis over Eastern China and selected urbanized locations are also performed and analyzed in Section 3.3.

## 3.3 Results and Discussion

### 3.3.1 Evaluation of the CIF-CHIMERE system and NOₓ emission estimates with ground-based measurements

The emission estimates evaluation is not direct and is based on the experiment and control runs described in Section 3.2. Then, we compared simulated surface NO₂ concentrations using prior (Conc_Prior), posterior (Conc_Pos), and MEIC (Conc_MEIC) NOₓ emissions for 2015 and 2019 with NO₂ ground-based measurements over Eastern China. Although the global north / south gradient observed by the ground-based measurements is rather well captured by the simulations using prior and MEIC inventories (Figures 42b and 42c), the model tends to overestimate concentrations in the North China Plain (NCP) and underestimate them in the western, northeastern, and southern regions except in the Pearl River Delta (PRD) (Figure 42d) for 2015. It is worth noting that this behavior is similar in simulations using posterior emissions (Annex F: Annual concentrations 2015).

In 2019, we observe the same north / south pattern with an underestimation in the south (except in the PRD) and an overestimation in the NCP region (Figure 43).

The statistics of the comparison between the simulations and the surface measurements are reported in Table 7.

For 2015, the annual mean of surface NO₂ concentrations calculated from hourly concentrations at the stations is 27.4 µg/m³ over East China. The annual mean value of NO₂ Conc_Prior15 and
NO₂ Conc_Post15 are higher than the stations' mean value, whereas NO₂ Conc_MEIC15 is smaller, suggesting that while NO₂ Conc_Prior15 and NO₂ Conc_Post15 tend to overestimate measured surface concentrations, NO₂ Conc_MEIC15 underestimates them. Note that, the annual mean value of NO₂ Conc_Post15 is slightly closer to the stations (~4.7%) than NO₂ Conc_Prior15 (~6.6%) and NO₂ Conc_MEIC15 (~7%). In 2019, the annual mean value of NO₂ Conc_Post19 (29.5 µg/m³) is also slightly closer to the stations (24.8 µg/m³) than NO₂ Conc_Prior19 is (30.3 µg/m³).

<figure><img src="image_52.png" /><figcaption>Figure 42 Spatial distribution of annual mean surface NO₂ concentrations: (a) Stations; (b) CHIMERE using prior emissions (Conc_Prior15); (c) CHIMERE using MEIC emissions (Conc_MEIC); (d) Mean bias calculated by the mean differences between Conc_Prior15 and stations for 2015</figcaption></figure>
<figure><img src="image_53.png" /><figcaption>Figure 43 Spatial distribution of annual mean surface NO₂ concentrations: (a) Stations; (b) CHIMERE using prior emissions (Conc_Prior19); (c) Mean bias calculated by the mean differences between Conc_Prior19 and stations for 2019</figcaption></figure>

<table><caption>Table 7 Annual statistics for the comparison between simulated and measured NO₂ hourly surface concentrations for 2015 and 2019. Mean = Annual Mean, SD = Standard Deviation (SD), RMSE = Root Mean Square Error are in µg/m³. r = Pearson correlation coefficient. NMB = normalized mean bias in % (Formulas used here are given in the Annexes A and D), (SDs are calculated using annual means of the concentrations)</caption><thead><tr><th rowspan="2">Year</th><th colspan="2">Station</th><th colspan="4">Conc_Prior</th><th colspan="4">Conc_Post</th><th colspan="4">Conc_MEIC</th></tr><tr><th>Mean</th><th>SD</th><th>Mean</th><th>SD</th><th>r</th><th>NMB</th><th>RMSE</th><th>Mean</th><th>SD</th><th>r</th><th>NMB</th><th>RMSE</th><th>Mean</th><th>SD</th><th>r</th><th>NMB</th><th>RMSE</th></tr></thead><tbody><tr><td>2015</td><td>27.4</td><td>11.6</td><td>29.2</td><td>18.6</td><td>0.63</td><td>7</td><td>22.1</td><td>28.8</td><td>18.1</td><td>0.64</td><td>5</td><td>21.6</td><td>25.5</td><td>15.8</td><td>0.62</td><td>-7</td><td>20.6</td></tr><tr><td>2019</td><td>24.8</td><td>9.8</td><td>30.3</td><td>19.2</td><td>0.67</td><td>22</td><td>21.9</td><td>29.5</td><td>18.2</td><td>0.68</td><td>19</td><td>20.8</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

The other statistical indicators in Table 7 show also that they are globally slightly better for NO₂ Conc Post than for NO₂ Conc Prior for the two years and for NO₂ Conc MEIC for 2015. The larger impact of the use of the posterior emissions to simulate NO₂ concentrations is visible on the NMB, which decrease by about 30 % and 15 % compared to the prior in 2015 and 2019, respectively.

These first results suggest that the CIF-CHIMERE system constrained with OMI NO₂ observations behaves as expected, bringing the simulated NO₂ concentrations closer to the truth – given by the surface measurements – when the emissions estimates are used in a CTM. However, it is worth noting that the improvement remains small.

To complete this global evaluation of Chinese annual means, we also evaluated the statistics, station by station, to see how homogeneous they are over the domain and if spatial features appear. As described in section 3.2.2, we calculated the ratios of the experiment and control run statistical indicators (r ratios, mean bias ratios, and RMSE ratios) at each station (Figure 44 for 2019, Annex G: Statistical Indicators' Ratios for 2015). The r ratios are mainly larger than one
for most stations both in 2015 and 2019, showing a better agreement with the surface
measurements in terms of temporal correlation when the Emis_Post is used to simulate NO2
concentrations. The improvement is more significant in the south of the domain, especially in
the highly urbanized locations of the PRD and the Yangtze River Delta (YRD). The
improvement is relatively small, but it might be explained by the fact that the correlation
coefficient is calculated on hourly concentrations, whereas the emissions are corrected on a
monthly basis (Section 3.2.1). Concerning the mean bias and the RMSE, the situation is more
contrasted with ratios smaller than one (showing an improvement), mainly above the most
urbanized area of the PRD, Wuhan, and YRD. This is particularly the case in 2019. In these
regions, the reduction of the mean bias of the simulated NO2 concentrations compared to the
surface measurements can reach up to 30-40 % when the posterior emission estimates are used.

<figure><img src="image_54.png" /><figcaption>Figure 44 Ratios of the Conc_Prior19 and Conc Post19 statistical indicators: Correlation Coefficient, Mean Bias and RMSE, respectively (a-c), for 2019.</figcaption></figure>

As a result of these analyses, the inversions using OMI observations and CIF-CHIMERE seem
to correct NOₓ emissions towards the truth as the NO₂ concentrations simulated using these
emissions are closer to the surface measurements. The improvements compared to the surface
measurements remain small over the whole domain, but are much more significant in large
urbanized regions suggesting that the OMI NO₂ observations allow a better constrain on
polluted regions than on background regions.

Figure 45 show an example of the comparison of monthly averaged NO₂ surface concentrations
from simulations and stations for 2015 and 2019 for Wuhan, where the emission corrections
are the largest. The stations selected for this comparison correspond to grid cells in Wuhan with
minimum 60 kt emissions (Figure 46).
In both years, simulations using prior NOₓ emission inventory overestimate NO₂ surface concentrations compared to the stations. Using posterior NOₓ emission inventory decreases the differences between simulated NO₂ surface concentrations and measurements, especially from May to October 2015 and March to October 2019. In both years, the highest decrease is in the summer months (–22 % in August 2015 and –42 % in August 2019).

<figure><img src="image_55.png" /><figcaption>Figure 45 Monthly averaged NO₂ surface concentrations from stations and simulations for Wuhan in (top) 2015 and, (bottom) 2019.</figcaption></figure>
<figure><img src="image_56.png" /></figure>

Figure 46 (Left) Ground-Based Stations according to the selected locations, (Right) HTAP v2.2 NOx Emissions after applying the 60kt threshold (2010) to determine the selection of the locations. The remaining 0.5° × 0.5° grid cells correspond to the selected location.

### 3.3.2 Analysis of the estimated Chinese annual anthropogenic NOx emissions in 2015 and 2019

The annual NOx emission budget over East China and including other countries in the domain of Figure 40 are reported in Table 8 for several inventories. In 2015, the MEIC inventory gives NOx emissions 12.8% smaller than our estimation for East China. Liu et al. 2018 estimates NOx emissions for 2015 using the DECSO algorithm (Mijling and van der A 2012) also combining CHIMERE v2013b and OMI but a different version (DOMINO v2 (Boersma et al. 2011)), with a finer resolution (0.25° × 0.25°). According to this study, their annual anthropogenic NOx budget estimation (21.5 Tg) is calculated over the entire domain of Figure 40, also including e.g., the Korean Peninsula, a part of Japan, and is 5.2% larger than our calculations.
<table><caption>Table 8 The annual NOₓ emission budget (in Tg) over East China and the entire domain in the Figure 40 with respect to different inventories.</caption><thead><tr><th>Inventory</th><th>East China</th><th>Domain – Figure 40</th></tr></thead><tbody><tr><td>HTAP 2010</td><td>18.6</td><td>20.5</td></tr><tr><td>Emis Post15 (this study)</td><td>18.5</td><td>20.4</td></tr><tr><td>Emis Post19 (this study)</td><td>18.4</td><td>20.3</td></tr><tr><td>MEIC15</td><td>16.4</td><td>-</td></tr><tr><td>DECSO15 (Liu et al. 2018)</td><td>-</td><td>21.5</td></tr></tbody></table>

The different emission inventories are in rather good agreement, especially when comparing to the typical emission uncertainties (30-50 %). This is particularly the case for two based on top-down approaches involving OMI observations and the CHIMERE model.

The global annual NOₓ emission budget over Eastern China does not show significant changes from 2010 to 2019. However, significant spatial differences between HTAP v2.2 for 2010 and Emis Post15 and Emis Post19 inventories are visible as shown in Figure 47.

<figure><img src="image_57.png" /><figcaption>Figure 47 (a) NOₓ emissions at 0.5° × 0.5° resolution for 2010 from the HTAP v2.2 inventory in kt; Relative differences of NOₓ emissions for between 2010 and (b) 2015 and (c) 2019, respectively.</figcaption></figure>

In 2015 and 2019, a global increase compared to 2010 is estimated in the northern part of China and a decrease in the south and large urbanized and industrialized locations. When the emissions are reduced compared to 2010, this reduction remains moderate and varies from region to region. For some locations, such as PRD, the reduction can reach up to -12 % in 2015, which is in fairly good agreement with the 12th Five-Year Plan's nationwide target of a 10 % reduction for 2015 compared to 2010 (de Foy, Lu, and Streets 2016). In 2019, the estimated reduction is more confined around urbanized locations than in 2015, especially in the south.
To evaluate how important these reductions in NOₓ emissions are between 2015 and 2019, we analyzed the relative differences between the posterior emissions for 2019 and 2015 (Figure 48).

<figure><img src="image_58.png" /><figcaption>Figure 48 Relative differences between Emis_Pos19 and Emis_Pos15 NOₓ emissions.</figcaption></figure>

The differences between these two years range from ±8 % at the pixel scale. In the south, the emissions tend to increase slightly in 2019 compared to 2015; on the contrary, in the north and the locations such as Wuhan, YRD, and NCP, the emission reduction continues between 2015 and 2019 showing that the regulation effects are still ongoing. However, the reductions are smaller than 5 % below the expected levels in the 13th Five-Year Plan in which the emissions should decrease by 15 % compared to 2015 (“Notice of the State Council on Printing and Distributing the ‘13th Five-Year’ Ecological and Environmental Protection Plan_Government Information Disclosure Column” 2016). It is important to note that the changes in emissions inferred from our inversions as well as the target reductions of the 12th and 13th Five-Year Plans are smaller than the commonly assessed uncertainties on the emissions (30-50 %).

### 3.3.3 Analysis of the estimated annual anthropogenic NOₓ emissions at selected urbanized and industrialized locations

#### 3.3.3.1 Evaluation of the estimated annual anthropogenic NOₓ emissions in 2015 and 2019

As discussed in section 3.3.1, the inversions seem more relevant in polluted regions. We analyze emission changes focusing on the most urbanized and industrialized locations. For this, we select only the locations with a minimum of NOₓ emissions of 60 kt for 2010, which should
represent the most urbanized and industrialized locations, where we expect stronger emissions control (Figure 46). According to this selection, we have detected 15 locations reported from the north to the south, in Table 9. They are also reported in the Figure 40.

<table><caption>Table 9 Definition of the locations and their annual NOₓ budgets concerning the different emission inventories and years.</caption><thead><tr><th>Location</th><th>Latitude &amp; Longitude</th><th>HTAP v2.2 (kt)</th><th>Emis Post15 (kt)</th><th>MEIC15 (kt)</th><th>Emis Post19 (kt)</th></tr></thead><tbody><tr><td>Daqing</td><td>46-47°N, 124-125.5°E</td><td>78.9</td><td>71</td><td>72.5</td><td>70.1</td></tr><tr><td>Shenyang</td><td>41-44°N, 123-125°E</td><td>82.8</td><td>84.9</td><td>114.5</td><td>81.1</td></tr><tr><td>Baotou</td><td>40-42°N, 108-111°E</td><td>136.3</td><td>116.2</td><td>116.4</td><td>122.3</td></tr><tr><td>Beijing-Tianjin</td><td>38-41°N, 115-118.5°E</td><td>450.8</td><td>447.3</td><td>381.2</td><td>431.7</td></tr><tr><td>Dalian</td><td>38-41°N, 120-122°E</td><td>74.2</td><td>77.4</td><td>88.4</td><td>76.3</td></tr><tr><td>Shijiazhuang</td><td>37-39°N, 113-115°E</td><td>151.1</td><td>152.2</td><td>107.2</td><td>144.5</td></tr><tr><td>Shandong</td><td>35-38°N, 115-119°E</td><td>296.6</td><td>295.8</td><td>245.4</td><td>279.2</td></tr><tr><td>Henan</td><td>34-37°N, 112-114°E</td><td>145.5</td><td>136</td><td>84.2</td><td>132.2</td></tr><tr><td>Anhui</td><td>32-33°N, 116-118°E</td><td>76.4</td><td>71.8</td><td>39.8</td><td>70.1</td></tr><tr><td>Yangtze River Delta</td><td>29-32°N, 118-122°E</td><td>1229.4</td><td>1162.1</td><td>963.8</td><td>1129.8</td></tr><tr><td>Wuhan</td><td>29-32°N, 113-116°E</td><td>260.7</td><td>237.8</td><td>123.2</td><td>222</td></tr><tr><td>Chengdu</td><td>30-32°N, 103-105°E</td><td>79.9</td><td>76.7</td><td>109.2</td><td>77.9</td></tr><tr><td>Chongqing</td><td>29-30°N, 106-107°E</td><td>87.4</td><td>82.6</td><td>72.3</td><td>84.5</td></tr><tr><td>Hunan</td><td>27-28°N, 112-113°E</td><td>94.1</td><td>87.5</td><td>99.9</td><td>85.6</td></tr><tr><td>Pearl River Delta</td><td>22-24°N, 112-115°E</td><td>420.8</td><td>370.9</td><td>390</td><td>375</td></tr></tbody></table>
In 8 out of 15 locations (Daqing, Beijing-Tianjin (BT), Shandong, Henan, Anhui, YRD, Wuhan, and Hunan), there is a decrease in NOx annual emission budget between 2010, 2015, and 2019 (Table 10).

<table><caption>Table 10 Relative Differences of annual NOx emission budgets at the 15 selected locations.</caption><thead><tr><th>Location</th><th>Emis_Pos15 –<br>HTAP v2.2 (%)</th><th>Emis_Pos19 –<br>HTAP v2.2 (%)</th><th>MEIC15 – HTAP<br>v2.2 (%)</th><th>MEIC15 –<br>Emis_Pos15 (%)</th></tr></thead><tbody><tr><td>Daqing</td><td>-10</td><td>-11.1</td><td>-8</td><td>2.1</td></tr><tr><td>Shenyang</td><td>2.5</td><td>-2.1</td><td>38.3</td><td>34.9</td></tr><tr><td>Baotou</td><td>-14.8</td><td>-10.3</td><td>-14.6</td><td>0.2</td></tr><tr><td>Beijing-Tianjin</td><td>-0.8</td><td>-4.2</td><td>-15.4</td><td>-14.8</td></tr><tr><td>Dalian</td><td>4.4</td><td>2.8</td><td>19.2</td><td>14.2</td></tr><tr><td>Shijiazhuang</td><td>0.8</td><td>-4.3</td><td>-29.0</td><td>-29.5</td></tr><tr><td>Shandong</td><td>-0.3</td><td>-5.8</td><td>-17.2</td><td>-17</td></tr><tr><td>Henan</td><td>-6.6</td><td>-9.2</td><td>-42.2</td><td>-38.1</td></tr><tr><td>Anhui</td><td>-5.9</td><td>-8.2</td><td>-47.9</td><td>-44.6</td></tr><tr><td>Yangtze River<br>Delta</td><td>-5.5</td><td>-8.1</td><td>-21.6</td><td>-17.1</td></tr><tr><td>Wuhan</td><td>-8.8</td><td>-14.9</td><td>-52.7</td><td>-48.2</td></tr><tr><td>Chengdu</td><td>-4.1</td><td>-2.5</td><td>36.7</td><td>42.5</td></tr><tr><td>Chongqing</td><td>-5.5</td><td>-3.3</td><td>-17.2</td><td>-12.4</td></tr><tr><td>Hunan</td><td>-7</td><td>-9.0</td><td>6.2</td><td>14.2</td></tr><tr><td>Pearl River Delta</td><td>-11.9</td><td>-10.9</td><td>-7.3</td><td>5.2</td></tr></tbody></table>

The highest decrease is observed in Baotou in 2015, with a 14.8% decrease, and in Wuhan in 2019, with a 14.9% decrease. Four locations (Baotou, Chengdu, Chongqing, and PRD) show a reduction in 2015 compared to 2010 but an increase in 2019 compared to 2015. At two locations, Shenyang and Shijiazhuang, NOx emissions increase in 2015 but decrease in 2019 compared to 2010. Dalian is the only location where estimated NOx emissions for 2015 and 2019 are higher than HTAP v2.2 emissions in 2010, but a decrease is observed between 2015 and 2019. Finally, there are no locations that show a monotonic increase between 2010, 2015 and 2019.

The annual emission budgets derived from the independent MEIC inventory for each location are also reported in Table 10 for comparison. The estimated posterior NOx emissions for 2015 are closer to MEIC emissions at all locations, except for Shijiazhuang, Chengdu, and Hunan. Note that the correction of the emissions (Emis_Pos - HTAP v2.2) is relatively small in Shijiazhuang, with only 0.75% corrections. In Chengdu and Hunan, MEIC NOx emissions are higher than HTAP v2.2 emissions, whereas the inversion tends to decrease them. These results also suggest that the corrections made to the emissions during the inversion are consistent.
### 3.3.3.2 Monthly evaluation of the anthropogenic NOₓ emissions

Figure 49 shows the time series of monthly anthropogenic NOₓ emissions for the different emission inventories considered in this study. In terms of seasonal variations, NOₓ emissions are larger during wintertime, especially in December, at all the locations. However, a drop is observed for most of the locations in February, likely related to the Chinese New Year. This temporal evolution is consistent with the study of Ding et al. 2017 in which a 10% reduction in February is estimated because of the Spring Festival and a peak is observed in December.

<figure><img src="image_59.png" /><figcaption>Figure 49 NOₓ monthly budget comparisons at the selected locations.</figcaption></figure>

For the winter months, very few emissions changes between the years (2010, 2015 and 2019) are observed. These very small changes may be explained either because prior emissions do not need to be corrected or because the emissions remained stable between the years or because few or no observations are available to constrain the inverse modeling system (2010 being also used as prior emissions). For example, the latter is the case in Daqing for January and December 2015, where no OMI observation data are available over the location.
than in 2015. This is consistent with the results discussed in section 3.3.1, showing that the CIF-
CHIMERE system constrained by OMI observations performs as expected.

By comparison, the use of MEIC15 emissions to simulate NO₂ concentrations in 2015 gives better statistics for eight locations compared to the emission estimated in this study for 2015. The better performances when using MEIC emissions correspond to locations where the MEIC emissions are significantly smaller than the Emis_Pos15 and HTAP v2.2 (Beijing-Tianjin, Shijiazhuang, Shandong, Henan, Anhui, YRD, and Wuhan). This points out that the posterior emission corrections derived from OMI observations and the CIF-CHIMERE are likely underestimated. This might be partly explained by the limited daily spatial coverage of OMI measurements, which does not allow sufficient corrections of the emissions. TROPOMI satellite instrument observations with their better spatial resolution and coverage should help resolving this issue. On the contrary, when MEIC15 emissions are larger than Emis_Pos15 or HTAP v2.2, a degradation of the statistics is observed compared to Conc_Pos15 (Dalian, Chengdu, Hunan, PRD), suggesting that MEIC overestimate emissions at these locations. These results illustrate the complementariness of bottom-up and top-down approaches to assess NOₓ emissions and the need of robust ground-based measurement network to evaluate the emission inventories.

**3.4 Conclusions**

This chapter estimates anthropogenic NOₓ emissions over East China for 2015 and 2019 using the new inverse modeling system CIF-CHIMERE and OMI NO₂ satellite observations. One of the objectives was to evaluate if this new inversion system constrained by OMI observations can infer emissions closer to the truth. As true emissions are unknown, ground-based measurements of NO₂ surface concentrations are considered as the reference to evaluate the emission estimates indirectly. The analyses performed in this chapter show that using the NOₓ emissions estimates to simulate NO₂ surface concentrations improves the comparison with ground-based measurements, as is expected when atmospheric inversion approaches are applied. The results also suggest that the OMI observations provide a better constraint to the NOₓ emissions in the polluted areas compared to the background areas.

The annual anthropogenic NOₓ emission budgets estimated in this study for East China are in fairly good agreement with the annual emission budgets derived from independent inventories such as MEIC (~13 %) and DECSO (~5 %) when considering the un-certainties on NOₓ
emissions (30-50 %). Nevertheless, the analysis at the finer spatial scale of the most populated
and urbanized locations of East China shows situations more contrasted. In terms of the
evolution of the emissions between 2010, 2015, and 2019, according to our emissions'
estimates, some locations such as Baotou, PRD, and Wuhan show a reduction of emissions
between 2010 and 2015 close to the target reduction defined in the 12th Five-Year Plan. The
evolution of the emissions between 2015 and 2019 is rather small. Our estimates show very
slightly increased emissions, mainly in the southern locations, and a small decrease (<5 %) in
the NCP or locations such as Wuhan and the YRD. The comparison of our emission estimates
with MEIC emissions in 2015 stresses that our estimates likely underestimate the emission
reductions between 2010 and 2015 in the most polluted locations of East China. In parallel, our
emission estimates, when used to simulate NO₂ surface concentrations, lead to a better
agreement with surface measurements in regions where MEIC indicates an increase of the
emissions compared to 2010 – our estimates often suggest reduced or stable emissions. These
results illustrate the benefit of having a variety of inventories derived from different approaches
and of using their complementariness to assess NOₓ emissions better. They also stress the need
for a robust ground-based measurement network to evaluate the emission inventories.

In this chapter, we estimated NOₓ emissions using daily OMI observations, to do that, we
calculated emission corrections on a monthly basis due to the lack of daily coverage of OMI.
However, new satellite observations with higher spatial and temporal coverage on a daily basis,
such as TROPOMI on Sentinel 5p, could bring more information to the inversion system; and
thus lead to more accurate emission estimates.
# Chapter 4. NOₓ emissions in Europe derived from satellite observations

## 4.1 Context of the study

The work presented in this chapter has been done in the framework of the ARGONAUT ANR project. The ARGONAUT project (pollutAnts and gReenhouse Gases emissiOns monitoring from spAce at high resolUTion) has been devised to help address the question of coordinated monitoring and mitigation strategies to achieve optimal reduction policies for both air quality and climate change related emissions. One of the main objectives of the project was to develop the inverse modeling capabilities of the French community for highly reactive pollutants (e.g., NOₓ, NMVOCs), carbon monoxide, and GHG such as CO₂ at high resolution (0.1° × 0.1°) in France to exploit the new era of satellite observations at high resolution (the current TROPOMI and the future CO2M). These developments should help, in the end, to better take advantages of high resolution and co-emissions of species to constrain anthropogenic and biogenic sources separately. Considerations of the error statistics and the most adapted metrics, especially to solve the transport errors at a very high resolution of the point sources (2 km resolution), are also questions addressed in this project. One of the main outputs expected from the project is the provision of new estimates of French anthropogenic emissions of the primary air quality pollutants (NOₓ, CO and NMVOCs) and potentially CO₂ at high resolution (0.1° × 0.1°), based on the state-of-the-art atmospheric inversion CIF using CHIMERE and highly resolved TROPOMI products. A stepwise strategy has been developed in the project, starting from inversions at a moderate resolution over the European domain (0.5° × 0.5°) to inversions at a higher resolution over France (0.1° × 0.1°). Doing inversions over the European domain allows one to compare the performances of the inversions constrained by observations at medium resolution with OMI and high resolution with TROPOMI. Indeed, the OMI resolution is not adapted to do inverse at 0.1° resolution over France. In this framework, the PhD work was to perform the inversion tests with the new TROPOMI observations for the different domains and to ensure the consistencies of the inversions by evaluating them with surface NO₂ measurements. The tests were done for the COVID-19 lockdown period in the spring of 2020, where sudden changes in anthropogenic NOₓ emissions were expected and well reported from TROPOMI observations (Barré et al. 2021; Souri et al. 2021, and Figure 50). The tests presented in this chapter focus mainly on the first week of April 2020.
<figure><img src="image_60.png" /><figcaption>Figure 50 April 2020 and 2019 average NO₂ tropospheric column differences seen by TROPOMI (presented in EUMETSAT virtual conference in 2021)</figcaption></figure>

## 4.2 Comparison of inversions using OMI and TROPOMI over Europe

As seen previously (Chapters 2 and 3), the CIF-CHIMERE inverse modeling system using OMI NO₂ satellite observations allows the estimation of NOₓ emissions. We then use the set-up defined in Chapter 2 to perform emissions inversion using OMI and TROPOMI observations on a daily basis on the European domain (0.5° × 0.5°). We recall here that we use v1.3 data and super-observations at the model resolution calculated as the median of satellite pixels within the model grid-cell and the corresponding averaging kernel. In addition to the quality flags recommended by the respective user manuals of OMI and TROPOMI, we apply an additional filter based on the observation errors. Pixels with errors on the NO₂ tropospheric column larger than 100 % for OMI and 60 % for TROPOMI are filtered out. Figure 51 compares the NO₂ tropospheric columns observed by OMI and TROPOMI on April 1st, 2020. Despite using super-observations at 0.5° × 0.5° resolution, the best performances of TROPOMI, including a much higher spatial resolution, also lead to the significant difference in terms of sampling capabilities of the two instruments, TROPOMI leading to a much better spatial coverage capability. Note that our choice of filtering TROPOMI observations with 60% of observations errors rather than 100% like OMI is based on this better spatial coverage allowing one to be more restrictive in filtering the data while maintaining an improved coverage compared to OMI.
<figure><img src="image_61.png" /><figcaption>Figure 51 Comparison of NO₂ columns from OMI (QA4ECV) and TROPOMI (v1.3) and their coverage for the 01/04/2020</figcaption></figure>

Figure 52 shows the results of the inversions using OMI and TROPOMI for April 1st, 2020. Note that we had to reduce the errors on prior anthropogenic emissions in the **B** matrix to 35% to ensure the convergence of the system with TROPOMI. In this figure, the posterior (corrected by inversion) emissions are compared to the prior emissions corresponding to the year 2016 (the CAMS-REG 2016 inventory is used as prior, see Chapter 2). Here again, the impact of the improved coverage of TROPOMI compared to OMI is well illustrated. Using the TROPOMI observation allows correction of emissions over a larger area than when using OMI. The inversion with TROPOMI shows a large reduction of the NOₓ emissions compared to the prior. This reduction is much more limited when using OMI observations to constrain the inversion. Interestingly the patterns of increased emissions prescribed by the inversions (in red in the figure) are consistent between the two instruments.
<figure><img src="image_62.png" /><figcaption>Figure 52 NOₓ emission increments obtained by inversions using TROPOMI (left) and OMI (right) observations for 01/04/2020</figcaption></figure>

Figure 53 shows a comparison of the hourly NO₂ concentrations simulated with CHIMERE using either the prior emissions (light blue) or the posterior emissions obtained with OMI (blue) and TROPOMI (violet) with surface measurements in the Paris area (example of one urban background station with (48.5°N, 2°E)) for April 1st, 2020. The concentrations simulated using prior emissions largely overestimate the observed concentration all over the day. The concentrations simulated with posterior emissions derived from OMI observations are in quite good agreement with the surface measurements during the morning peak, but they still overestimate the measurement during the evening peak. It is worth noting that, as we use a daily assimilation window, the same correction factor is applied to each hourly emission of the day (see Chapter 2). However, OMI observations are performed in the early afternoon, and they may not well represent the emissions later in the day and are more convenient to constrain emissions before the measurement. Note also that we make the assumption in the inversion that the diurnal profile of the emissions is correct in the model, which is likely not the case, especially during the COVID-19 lockdown when the practices of the population in terms of transport were completely unusual. Concerning the concentrations simulated with the posterior emissions corrected with TROPOMI, they mainly underestimate the measured concentrations at the station, especially during the morning peak. This would suggest that the corrections of the emissions prescribed by TROPOMI are too large.
<figure><img src="image_63.png" /><figcaption>Figure 53 Comparison of the hourly NO₂ concentrations simulated with CHIMERE using prior and estimated emissions and observations at the Parisian background urban station</figcaption></figure>

## 4.3 Difficulties in using TROPOMI observations for inversions

The underestimation of NOₓ emissions obtained by inversion when TROPOMI observations are used is likely partly related to a systematic negative bias reported in TROPOMI observations. Indeed, the results presented in the previous subsection have been obtained with the TROPOMI observations v.1.3, available at the time of the study. Validation studies have shown that this version of the TROPOMI NO₂ product was biased negatively: around -51 % and -37 % in highly and slightly polluted areas, respectively (Verhoelst et al. 2021; Judd et al. 2020). This last negative bias was partly attributed to a degraded retrieval of the cloud pressure, which has been improved in the more recent version of the NO₂ TROPOMI product (van Geffen et al. 2022). Figure 54 shows an example of the differences between the product v1.3 and the PAL product v2.3, now available and used in the following (Pseftogkas et al. 2022).
<figure><img src="image_64.png" /><figcaption>Figure 54 Comparison of averaged TROPOMI tropospheric columns in December 2019 for the v1.3 (left) and PAL v2.3 (middle), absolute differences (right). (The figure is taken from Pseftogkas et al., 2022)</figcaption></figure>

Note that previous studies, such as, for example, Souri et al. 2021 chose to scale up TROPOMI NO₂ observations by 25% before including them in their inversion model to cope with this biases problem.

From our side, since CIF-CHIMERE is a new inversion system and TROPOMI is a quite new instrument (it is always a long process to get stabilized version of satellite products), using TROPOMI observations within the system was challenging throughout the PhD. In addition to this bias problem, we encounter strong convergence problems of the inversion system when using NO₂ TROPOMI observations. The inversions were convergent only for very few days. Applying a scaling factor to the NO₂ columns as Souri et al. 2021 did not help to solve the problem. The new TROPOMI PAL v2.3 product available since spring 2022 also did not solve our convergence problem. Several problems have been identified in the inversions process: (i) the inversion can lead to negative emissions, and (ii) the range of variations of the emissions and the NO₂ columns (several order of magnitude each) may give troubles to the inversion system to find an effective solution of the inverse problem. To solve these issues, new functionality has been included in the CIF by the developing team at LSCE, including the possibility of treating the control vector in a logarithmic scale. This allows one to solve our convergence problem during the inversion using TROPOMI as a constraint.

## 4.4 New set-up of the inversion

A new set-up of the inversion based on the use of the logarithm in the control vector has been defined for inversions over the European and France domains. The configurations used are based on the experience gained with the inversions performed with OMI (Chapters 2 and 3). They are detailed for the two domains.
### 4.4.1 Inversion over the European Domain

The configuration used for the European domain is close to the one we used for OMI inversion. To recall the configuration parameters:

* TROPOMI PAL v2.3 super observations (and their AKs) calculated by median were considered with quality flag higher than 0.75 and observations errors lower than 60 %.

* Anthropogenic and biogenic emission errors in **B** matrix were taken as 50 % and 100 %, respectively, with a 50 km horizontal correlation.

* Convergence criteria were taken as a 95 % reduction of the gradient norm.

* Daily inversions were performed for the week of 1-7 April 2020 (a week with the COVID-19 lockdown). The computation duration of one day of inversion was large (around 12 hours) and limits our capabilities to perform inversion over a longer period than a week, which would have been better to be more representative of the specific period of the lockdown and lead to more consolidated results.

* Daily inversions were also realized for the same week as above but for 2019. However, we only have two days of inversion. Changes in the super calculator (e.g., operating system changes in Très Grand Centre de Calcul du CEA (TGCC)) used to perform the inversions led to technical issues running the CIF-CHIMERE system, which could not have been solved by the time of this study. This prevents a meaningful comparison between emissions in 2019 and 2020 as initially planned.

### 4.4.2 Inversion over the France (ARGFR) Domain

To estimate NOₓ emissions for France at high resolutions (0.1° × 0.1°), the following configuration of the parameters was taken:

* TROPOMI PAL v2.3 super observations (and their AKs) calculated by median were considered with quality flag higher than 0.75 and observations errors lower than 60 %.

* Anthropogenic and biogenic emission errors in **B** matrix were taken as 30 % and 100 %, respectively, with no horizontal correlation (for simplicity).
* Convergence criteria were taken as a 95 % reduction of the gradient norm.

* ARGFR domain includes 121 lon × 165 lat grid cells and corresponds to -5°N – 10°N and 39.75°E – 54.25°E and covers France.

* Daily inversions were performed for more than 20 hours. This coupled with technical issues on the super calculator (see above) limits our testing capabilities over the domain. Only preliminary results are shown.

## 4.5 Evaluation of inversion coherence of log and linear scaled emissions: China + OMI case

Before applying the new set-up of the inversion, including the logarithmic scale of the control vector, we wanted to test the consistency of the inversion obtained when using or not using this logarithmic scale. This was also important to check that the results presented in Chapter 3 would not have been much affected by using this new control vector. To do this, we used our previous work, where convergent inversion was obtained using the OMI observations for Eastern China. For this comparison, the day 23/05/2019 was chosen because OMI observations have good spatial coverage over China (it was the best of all days in 2019). Figure 55 presents the comparisons of the NOₓ emission corrections in percentage using them as they are (left side) and in a logarithmic scale (right side). The negative and positive patterns of corrections of the emissions are similar for the two inversions. The magnitude of the corrections is mostly similar

<figure><img src="image_65.png" /><figcaption>Figure 55 Comparison of NOₓ emission corrections in % by performing inversion with the emissions in linear scale (left) and log scale (right) for the day 23/05/2019.</figcaption></figure>
for the negative corrections in the most urbanized regions but tends to be significantly larger
for the positive corrections. These positive corrections concern mostly moderated or low
emissions and should have less impact. It would be interesting to extend the study to a larger
period to correctly quantify the impact of using a logarithmic scale on emission inversion and
assess if it improves the performance.

## 4.6 European NOₓ emissions during April 2020 compared to 2016

### 4.6.1 Emission comparisons

Inversions covering the period April 1-7, 2020, were successfully performed using TROPOMI PAL v2.3 observations and prior emissions from 2016. Figure 56 shows the distribution of prior NOₓ emissions for the same week over Europe (1-7 April), where the total amount for this week is calculated as 164 kt.

<figure><img src="image_66.png" /><figcaption>Figure 56 Distribution of total NOₓ emissions for the week of 1-7 April from a prior inventory</figcaption></figure>

The inversions we have performed for 2020 estimate a NOₓ emission budget of 134 kt for this
period, 19% lower than for the prior, representative of 2016. Figure 57 shows the emission
corrections calculated by these inversions. According to this figure, the reduction of emissions
for the first week of April is mainly seen in the northern part of Western Europe: south of the
UK, north of France, Benelux, Germany, Poland, and north of Italy. The reduction against prior
(2016) emissions reaches up to 67% locally. In other countries and regions, reductions are
limited to major cities such as Barcelona and Madrid in Spain. Note that the system does not estimate any increase in NOₓ emissions. Table 11 compares NOₓ budgets from prior and estimated inventories by country. Accordingly, the highest reductions in emission budgets were achieved in Belgium and the Netherlands, with 48.2 % and 43.8 %, respectively.

<figure><img src="image_67.png" /><figcaption>Figure 57 Increment in NOₓ emissions (in %) for the week of 1-7 April</figcaption></figure>

Table 11 Prior and Estimated NOₓ emission budgets by some countries for the week of April 1-7, 2020, ordered from the highest to lowest difference in budget change.

<table><thead><tr><th>Country</th><th>Prior (kt)</th><th>Posterior (kt)</th><th>%</th><th>weekly coverage of TROPOMI (%)</th></tr></thead><tbody><tr><td>Belgium</td><td>2.7</td><td>1.4</td><td>-48.2</td><td>81</td></tr><tr><td>the Netherlands</td><td>3.2</td><td>1.8</td><td>-43.8</td><td>81</td></tr><tr><td>the UK</td><td>10.4</td><td>6.3</td><td>-39.4</td><td>30</td></tr><tr><td>Poland</td><td>9.2</td><td>5.7</td><td>-38</td><td>61</td></tr><tr><td>Germany</td><td>15.9</td><td>10.1</td><td>-36.5</td><td>79</td></tr><tr><td>France</td><td>11.6</td><td>9.1</td><td>-21.6</td><td>56</td></tr><tr><td>Italy</td><td>8</td><td>7</td><td>-12.5</td><td>62</td></tr><tr><td>Spain</td><td>7.1</td><td>6.5</td><td>-8.5</td><td>32</td></tr></tbody></table>

These results suggest that the emission reduction compared to the prior is larger in the northern European countries. However, it is important to check if the difference in emissions between the north and the south does not link with a sampling issue, as we consider only a limited number of days for this evaluation. Figure 58 shows the day-by-day TROPOMI observations for the studied week. The sampling of the northern countries is rather similar all over the week but more variable in the southern part of Europe, such as in Spain or Greece.
<figure><img src="image_68.png" /><figcaption>Figure 58 Day by day evolution of TROPOMI NO₂ columns (above figures are from the 1st to 3rd, below figures are from the 4th to 6th, and rightmost figure is for the 7th of April)</figcaption></figure>

In terms of daily corrections of the emissions, Figure 59 shows that the corrections are mostly concentrated in the countries and regions listed previously. These corrections are rather homogeneous and negative (around -50 % in the Paris area, -60% in southern England, -55% in Benelux ) from one day to another except for an increase of emissions prescribed in the south of Germany on April 2nd, and north of Italy on April 3rd. According to this sampling issue, the values of reductions (and the mean of weekly satellite coverage per country) given in Table 11 for Spain and Italy are likely, not representative.

<figure><img src="image_69.png" /><figcaption>Figure 59 Daily variation of NOₓ emission corrections from 1st to 7th of April 2020</figcaption></figure>
The comparison between the prior and the estimated emissions shows mainly a reduction of emissions during the first week of April when lockdowns were applied all over Europe and when one expects a significant drop in the NOₓ emissions due to these restrictions. However, it is important to note that the reason for this decline between prior and posterior is not only due to the COVID-19 lockdown but also integrates the downward trends in NOₓ in recent years as we compared with the prior emissions, which are representative of 2016 (e.g., -14% decrease in France, 12% decrease in the Netherlands in 2019 compared to 2016 (European Union Emission Inventory Report 2021)). Another explanation of the prescribed reductions may also arise from negative biases in the TROPOMI data, which may not be completely resolved in the PAL version of the TROPOMI product used. van Geffen et al. 2022 validated NO₂ PAL v2.2 data against ground-based instruments and found that using PAL v2.2 improves negative biases with the ground-based data compared to v1.3, but still, PAL v2.2 underestimates NO₂ concentrations. PAL v2.2 and PAL v2.3 have minor differences, which do not affect the column densities during retrieval or data quality.

### 4.6.2 Evaluation with surface measurements

As for the Chinese study in Chapter 3, we conducted an evaluation of the estimated emissions, comparing NO₂ surface measurements to NO₂ concentrations simulated with the prior emissions and with the estimated emissions. For this comparison, surface data are corrected with the factors explained in Section 2.4.

Figure 60 presents the spatial distribution of stations, as well as a comparison of the weekly average of NO₂ surface concentrations for stations, prior and posterior simulations.

<figure><img src="image_70.png" /><figcaption>Figure 60 Weekly mean of NO₂ surface concentrations from stations (left), and prior (middle) and posterior simulations (right).</figcaption></figure>
A total of 1927 stations are stated in the figures. The stations are rather well distributed all over Europe, with a larger number of stations in western and middle Europe, such as in Italy, Germany and Belgium/Netherlands. Averaged surface NO₂ concentrations calculated from hourly measurements from the stations and from prior and posterior simulations are 4.9 µg/m³, 7.9 µg/m³ and 5.9 µg/m³, respectively. NO₂ concentrations simulated with the prior emissions largely overestimate measured surface NO₂ concentrations (about 60% of bias, Table 12). This overestimation drops to 21 % when posterior emissions are used to simulate NO₂ concentrations. The RMSE is also improved when posterior emissions are used. Nevertheless, we did not observe any improvement in the correlation, as this might be understandable because daily corrections may not influence hourly correlations. A comparison showing the differences station by station between the prior simulations and stations and the posterior simulations and stations is presented in Figure 61. The overestimation of NO₂ concentrations is mainly localized in the most urbanized and industrialized regions: Belgium, the Netherlands, the Ruhr in Germany, Paris, north Italy, and Madrid. This overestimation is reduced when using the posterior emissions. On the other hand, an underestimation of the measured NO₂ surface concentrations by the simulations is observed mainly in the eastern part of Europe and slightly reinforced when posterior emissions are used. This may suggest that the reduction of emissions prescribed by TROPOMI could also be attributed to a residual negative bias in the data.

<figure><img src="image_71.png" /><figcaption>Figure 61 Differences between prior simulations and stations (left) and between posterior simulations and stations (right).</figcaption></figure>

<table><caption>Table 12 Statistics for the comparison between simulated and measured NO₂ hourly surface concentrations for 1-7 April 2020. Mean = annual mean, SD = standard deviation, RMSE = root mean square error are in µg/m³. r = Pearson correlation coefficient. NMB = normalized mean bias in % (Formulas used here are given in the Annexes A and D)</caption><thead><tr><th colspan="2">Station</th><th colspan="4">Prior</th><th colspan="4">Posterior</th></tr><tr><th>Mean</th><th>SD</th><th>Mean</th><th>SD</th><th>r</th><th>NMB</th><th>RMSE</th><th>Mean</th><th>SD</th><th>r</th><th>NMB</th><th>RMSE</th></tr></thead><tbody><tr><td>4.9</td><td>6.7</td><td>7.9</td><td>9.8</td><td>0.39</td><td>60.7</td><td>10</td><td>5.9</td><td>7.1</td><td>0.38</td><td>21.1</td><td>7.7</td></tr></tbody></table>
To push further the analysis, we also calculated the bias, RMSE and correlation ratios station by station as we did for the Chinese study (Annex E : Ratio Formulas). Figure 62 shows the ratios of these statistical indicators calculated for each station.

<figure><img src="image_72.png" /><figcaption>Figure 62 Ratios of the statistical indicators: correlation coefficient (left), mean bias (middle) and RMSE (right) of posterior and prior per station. (To recall, correlation ratios bigger than one and bias and RMSE ratios smaller than one meant to be an "improvement")</figcaption></figure>

According to the figure, posterior simulations show good improvement over Benelux, the UK, Ile-de-France and Northern Italy (with increased correlation coefficient ratio and decreased mean bias and RMSE ratio). The correlation and the RMSE are rarely or very slightly degraded with the posterior. On the contrary, the biases at the stations are more largely degraded in the south of Germany and Poland. To analyze if some specific features could arise from these results, the comparison has also been made, separating the type of stations (rural and urban). Figures 63 and 64 show the ratios of the different statistical indicators separately for the rural and urban stations. The simulations of the NO₂ concentrations at rural stations are improved systematically when posterior emissions are used. On the other hand, the simulations at urban stations show both improvement and degradation of the biases. The improvements seem to occur mostly in large cities or industrial areas.

<figure><img src="image_73.png" /><figcaption>Figure 63 Ratios of the statistical indicators (correlation coefficient (left), bias (middle), RMSE (right)) for rural type of stations</figcaption></figure>
<figure><img src="image_74.png" /><figcaption>Figure 64 Ratios of the statistical indicators (correlation coefficient (left), bias (middle), RMSE (right)) for urban type of stations</figcaption></figure>

These results suggest that when estimated emissions from CIF-CHIMERE system constrained by TROPOMI PAL v2.3 observations are used in a CTM, it brings simulated NO₂ concentrations closer to the “truth” given by the surface measurements and then we could state that the estimated NOₓ emissions are closer to the “truth”.

## 4.7 Preliminary emissions for April 2019 and open questions

As mentioned previously, the reduction observed between the prior and the estimated emissions during the first week of April corresponds to a potential reduction between 2016 (prior) and 2020 (posterior). It likely includes a reduction due to the restrictions applied during the COVID-19 lockdown but also continuous reductions of NOₓ emissions due to the mitigation. Residual negative biases in the TROPOMI product used for the inversion may also contribute to this prescribed reduction. To do a proper evaluation and assessment of the emission reductions induced by lockdowns, comparing with emissions inversed the year before is likely more relevant. To do so, we applied the CIF-CHIMERE to inverse emissions during the same period in April 2019 using TROPOMI observations. Unfortunately, technical issues on the CIF-CHIMERE after changes in the super calculator have limited these inversions to only two days and not the entire week as planned initially. The TROPOMI observations available for those two days are displayed in Figure 65. If the sampling of April 1st, 2019 covered, at least partly, similar regions to the ones mostly sampled during the first week of April 2020 (North of France, parts of Belgium and Germany, and North of Italy), the sampling of April 2nd, 2019 covers only the eastern part of Europe, quite differently from the regions sampled in 2020.
<figure><img src="image_75.png" /><figcaption>Figure 65 TROPOMI NO₂ observations for 1st of April in 2019 (left) and in 2020 (right)</figcaption></figure>

The emissions estimates based on these observations and compared to the same prior emissions than previously (2016) are shown in Figure 66 for the two days. Interestingly, one of the main features, which comes out of this comparison, is that the inversion also led to a reduction of emissions in 2019 compared to the prior. The prescribed reduction is of the same order of magnitude compared to 2020, especially in the northern part of western Europe (the UK, Benelux, the Netherlands) on April 1st, 2019 when the TROPOMI sampling is close to the one of 2020. Compared with April 2nd, 2019 is less meaningful due to the difference in sampling. On April 1st, 2019, the inversion system increased the emissions in the south of Germany and North of Italy, and a feature also presents for some days in the first week of April 2020. The observed reduction of emissions between 2019 test days and prior emissions representing 2016 are much larger than the expected decrease of emissions stated from the continuous NOₓ emissions regulations applied in Europe during this period (-15% decrease in Germany, 10% decrease in Italy in 2019 compared to 2016 (European Union Emission Inventory Report 2021). This might suggest that a residual negative bias remains in the last TROPOMI product used for this study and affect our inversions.
<figure><img src="image_76.png" /><figcaption>Figure 66 Increments in NOₓ emissions for 01/04/2019 (left), 02/04/2019 (right)</figcaption></figure>

We also compare the emissions estimates of April 1st and 2nd, 2019 to the corresponding emissions of 2020 (Figure 67). Suppose one assumes that these days are representative of the general situation and that we can compare April 1st, 2019 and 2020 in the regions where the sampling is similar (note that both days are weekdays). In that case, reductions of about 40%, and 30-50% for Ile-de-France and South of Germany and North of Italy, respectively, are deduced from the comparison and might be attributed to lockdown restrictions. Guevara et al. 2021 estimated a 50% reduction in the total budget of NOₓ emissions in Italy and France for the period March 23-April 26, 2021, which is consistent with our estimate. For Germany, it is lower than our estimate of 25%.

<figure><img src="image_77.png" /><figcaption>Figure 67 Differences between two estimated emissions for 2020 and 2019 for the days 1st (left) and 2nd (right) of April</figcaption></figure>
Note that the reduction observed between 2020 and 2019 emissions for April 2nd cannot be exploited because the TROPOMI sampling for that two days is very different. The differences observed in Figure 67 (right panel) over Eastern Europe represent only the difference between 2020 and the prior emissions and not between 2019 and 2020, as no emissions corrections were derived from the inversion for that day in this region due to sampling issue (Figure 66, right panel).

## 4.8 First tests of inversion at high resolution over France

As one of the objectives of the ARGONAUT project and of this PhD work was to set up inversions at high resolution over France, we tested the estimation of French emissions with a 10 km resolution inversion to take advantage of the high resolution TROPOMI observations using the PAL v2.3 product. For these inversions, we encountered the same problem of convergence of the system and using a logarithmic scale for the control vector was necessary. Due to the computational duration of the inversion (almost one day per inversion) and the technical issue encountered at the TGCC super calculator, only a few days of inversions have been performed with the configuration given in Section 4.4. Figure 68 shows an example of one test for the day of 01/04/2020. The gain in the spatial representation of the emission corrections is well visible in the figure. The correction is localized mainly along the main roads and the urban centers. Details on the changes in emissions on the ship tracks are also available. These preliminary results look promising. Analyzing the inversion on longer periods with a detailed evaluation at the station will be very interesting, especially to see if the high resolution allows improvements for both urban and rural stations.
<figure><img src="image_78.png" /><figcaption>Figure 68 Increments in NOₓ emissions over France for 01/04/2020</figcaption></figure>
General Conclusions and
Perspectives

In this study, we examined the capabilities of the newly developed inversion system, CIF,
coupled with the chemistry transport model, CHIMERE and its adjoint using observations from
different satellites at different resolutions for various urbanized regions in the Northern
Hemisphere. In particular, we focused on estimating NOₓ emissions to test the 4D-Var mode of
the CIF-CHIMERE system. NOₓ are primary air pollutants involved in the production of
secondary pollutants such as ozone and secondary aerosols. Governments or policymakers have
started introducing regulations to control and mitigate them during the last decades, with
successful reductions in Europe (-60 % since 1990) and China (-10 to -20 % since 2010). One
key issue is to monitor the emissions and their changes, independently from the official
declarations of the emitters. Satellite observations coupled with inverse modeling approaches
are one of the most promising tools to achieve this monitoring. Indeed, the strong development
of satellite observations with instruments providing highly resolved NO₂ tropospheric columns
with increased confidence in the data at a global scale once a day, such as TROPOMI, offers
new opportunities to monitor NOₓ emissions at a high spatial and temporal resolution when
used in the inverse modeling systems. Therefore, one of the objectives of this PhD work was to
test and prepare the daily inversion of NOₓ emissions using the new CIF-CHIMERE and
TROPOMI observations.

To start with, we set up the configuration of the new CIF-CHIMERE system and tested some
of its parameters that could be critical for our inversion applications. We performed a baseline
test with the configuration adapted from literature uses or based on expert knowledge to inverse
NOₓ emissions. We used as emission constraints NO₂ columns from the OMI satellite over the
domain of Europe at medium resolution (50 km). In each test, one parameter (from optimization
and variational parameters) of this baseline test was changed. Different parameters related to
the optimization were found to have less importance while estimating the emissions than
variational parameters. Indeed, the main drivers of the inversion are the error statistics
considered for the inversion, especially the errors on the background emissions and their
correlations. The different tests performed showed that the new CIF-CHIMERE system
responded well to error statistics prescribed in the background covariance matrix. These tests
allow us to define a configuration of use for the inversion system as well as a suited range of variations of the different parameters for the appropriate use of the system. This is helpful to define adapted configuration when other domains are considered. In addition, during the PhD, new functionality was implemented in the CIF-CHIMERE system by its developing team to overcome convergence problems we encountered when the variables were constrained and the constraints covered several orders of magnitude. We now have the possibility to use a logarithmic scale for the control vector, which helps the optimization and the convergence of the system. We tested the influence of using the logarithmic scale rather than the linear scale for the inversion. The test was made on only one day, but the results suggest that the patterns of correction of the emissions are not changed by changing the scale. The magnitude of the corrections is consistent for the largest emissions but can be significantly different in the background regions. This should not affect that much the result in terms of budget or air quality simulation performances. Nevertheless, this question should be addressed for a longer period in the future to be more representative.

Next, the new CIF-CHIMERE system is used to estimate Chinese NOₓ emissions for the years 2015 and 2019. The Chinese government first introduced regulations on NOₓ emissions in its 12th Five-Year Plan in 2011, followed by new ones in the 13th Five-Year Plan in 2016. Our target years were chosen as the last years of the two five-year plans, excluding 2020, due to the COVID-19 pandemic. To constrain Chinese NOₓ emissions, NO₂ column data from OMI satellite observations (13 km × 25 km) are used at 50 km resolution. Due to the low daily OMI coverage, monthly corrections of the NOₓ emissions were calculated. It is found that using these NOₓ emission estimates to simulate NO₂ surface concentrations slightly improves the comparison with ground-based measurements. The estimated annual budgets were in good agreement (within the uncertainties) with independent inventories such as MEIC and DECSO in 2015. Nevertheless, this agreement varies depending on the Chinese regions and the year period. The results suggest that OMI observations provide a better constraint to the NOₓ emissions in the polluted areas compared to the background areas. Polluted areas corresponding to the main urbanized regions in China satisfy the target of the 12th Five-Year Plan (-10 %). On the other hand, the evolution of estimated emissions from 2015 to 2019 remains small, suggesting that reduction targets of the 13th Five-Year Plan were not fulfilled. This statement is not supported by recent literature and needs further investigation.
This PhD work is a part of the ARGONAUT project. One of the aims of the project is to estimate French NOₓ emissions at high-resolution (10 km) using high-resolution satellite observations such as TROPOMI (5.5 km × 3.5 km). As OMI's moderate resolution is not suitable for inversions at 10 km over France, we first adapted the CIF-CHIMERE system to 50 km resolution covering a larger area, Europe, to be able to compare inversion performances of TROPOMI and OMI. Our results show the benefit of the high resolution and improved instrumental performances of TROPOMI to provide a larger daily coverage and improve the daily inversion capabilities. Due to the computation time, we first performed inversions at a moderate resolution over the European domain to evaluate the sudden changes in NOₓ emissions during the COVID-19 lockdown period. We focus on the first week of April 2020 and compare the new emission estimates to the prior emissions, which are representative of the year 2016. The evaluation of the inversion results by comparing the NO₂ concentrations simulated with these new emissions to surface concentration measurements from the air quality network shows that the new emission estimates improve the comparison statistics compared to the prior emissions. The bias is reduced from 60 % to 20 %, and the RMSE is decreased by about 25 %. We showed a systematic improvement in the comparison for rural stations. For urban stations, the improvement is larger for city clusters (e.g., Ile-de-France, North of Italy), but some degradation of the bias is observed in the south of Germany and in Poland mainly.

In terms of emissions changes compared to the prior for this first week of April 2020, a reduction of emissions is seen in the northwestern European countries with reductions up to 67 % at the grid-cell scale or around 35-45 % for countries such as Belgium, the Netherlands, UK, Germany or Poland. Countries in the South (France, Italy and Spain) show a minor reduction in their emissions during this week. The difference was attributed to the sampling of the observations, which is more constant and homogeneous from day to day in the north than in the south, instead to a difference in applying restrictions during the lockdown.

The methodology to assess the COVID-19 lockdown impact is usually to compare 2020 with 2019. However, due to the technical issue with the super calculator used to perform the inversion, only a few days have been inversed for April 2019. Nevertheless, the preliminary comparison we did for these days would suggest a reduction of 40 %, and 30-50 % for Ile-de-France, South of Germany and North of Italy respectively, but this needs to be confirmed on a larger time period to be representative. We also made the first inversion attempts at high
resolution for one day (April 1st, 2020) over France. The results look promising to assess and monitor emissions at high spatial resolution.

In general, except for China, our work has been done on limited time periods and days. An extension of the studied periods is needed to get results that are more representative and consolidated. Nevertheless, the results of this PhD work stress the promising possibilities offered by the new CIF-CHIMERE system and the TROPOMI data to monitor NOₓ emissions and their changes from moderate to high resolution. This work also raised some questions and perspectives, which could be addressed in the future.

From a methodological point of view, since the CIF-CHIMERE inversion system does not take aerosol into account (the adjoint of the CHIMERE- aerosol module is not coded in the adjoint model), limitations in the simulated NO₂ concentrations may arise due to the photochemical role of aerosols. Moreover, this work stresses several issues. One of them is the sampling impact of the observations on the inversion and the achievable temporal resolution. Despite improvements with TROPOMI, cloud coverage is still a limiting factor in some situations to achieve meaningful daily inversion. This raises the question of the temporal resolution to which the inversions can be done. Statistical evaluation of the coverage of TROPOMI per region and grid cell could help define this temporal resolution. Also, indicators of the coverage, which could represent the relevance and the confidence to the inversion, could be provided with the inversion results at higher resolution to allow a proper use of the results and avoid misinterpretation. Technically, this also raises the question of the best way to perform inversion at the suited resolution. If a weekly resolution is recommended, for example, is it more suitable to perform a 4D-Var inversion increasing the assimilation window to the week considering the individual observation day by day, or is it more suitable to aggregate the observations and treat them as an average over the week?

Another methodological issue that needs to be addressed in the future with the CIF-CHIMERE is the separation of the anthropogenic and biogenic emissions or the emissions by sectors. This implies technical developments in the CIF to adapt the control vector. Note that to do so, it is necessary to evaluate if enough information is given by the observations during the inversion. The high resolution of TROPOMI could help with this task. Also, co-assimilate pollutants having common and specific emission sources could help go further in our capabilities to separate the sources. This also leads to the creation of more complex B matrices instead of
simple homogeneous and isotropic **B** matrices, for example, correlations can be selected by the
type of sources.

From a scientific point of view, our study of China was a first step and raised the question about
the effectiveness of reducing the emissions during the 13th Five-Year Plan. Extending of study
to the entire decade would be interesting to evaluate if our findings are specific to 2019. Using
TROPOMI for recent years would also be interesting, but we need to ensure the consistency
between the OMI and TROPOMI observations to be able to calculate trends. In Europe and
France (and also other parts of the world), assessing the impacts of the pandemic on the NOx
emissions at high resolution, including all the lockdowns and restrictions, would be very
interesting too.

Note that one important concern in achieving these different developments and studies is to
ensure that the observations are not biased; however, TROPOMI data still consists of a residual
negative bias. Therefore, debiasing techniques could be considered to be applied before the
assimilation of the data in the inversion system. Furthermore, in addition to using observations
from low-orbit satellites in the inversion system, observations from geostationary satellite
instruments can also be used to provide high temporal resolution information to the inversion
system (e.g. TEMPO, Sentinel-4, GEMS).
# Annexes

## Annex A : Statistical formulas

The statistical formulas are recalled for the estimation and relation of the background and observations errors. Let $u$ and $v$ be a scalar variable with n dimension:

* Average:
$$ \bar{u} = \frac{1}{n} \sum_{i=1}^{n} u_i $$

* Variance
$$ \text{var}(u, v) = \frac{1}{n} \sum_{i=1}^{n} (u_i - \bar{u})^2 $$

* Standard Deviation:
$$ \sigma(u) = \sqrt{\text{var}(u)} $$

* Covariance:
$$ \text{cov}(u, v) = \frac{1}{n} \sum_{i=1}^{n} (u_i - \bar{u})(v_i - \bar{v}) $$

* Correlation:
$$ \rho(u, v) = \frac{\text{cov}(u, v)}{\sigma(u)\sigma(v)} $$
**Annex B : 4D-Var cost and the gradient evolution**

Let be the *J* cost function,

$$
J(\mathbf{x}) = \frac{1}{2} (\mathbf{x} - \mathbf{x}^b)^\mathrm{T} \mathbf{B}^{-1} (\mathbf{x} - \mathbf{x}^b) + \frac{1}{2} \sum_{i=0}^{n} (\mathbf{y}_i - \mathbf{H}_i(\mathbf{x}_i))^\mathrm{T} \mathbf{R}_i^{-1} (\mathbf{y}_i - \mathbf{H}_i(\mathbf{x}_i)) \quad (\text{Eq.21})
$$

where the state **x** at time *i* is obtained iteratively by the linear model **M**,

$$
\begin{align*}
\mathbf{x}_i &= \mathbf{M}_{0 \to i}(\mathbf{x}) \\
&= \mathbf{M}_{i-1,i} \left( \mathbf{M}_{i-2,i-1} \left( \dots \mathbf{M}_{1,2} \left( \mathbf{M}_{0,1}(\mathbf{x}) \right) \right) \right) \\
&= \mathbf{M}_i \left( \mathbf{M}_{i-1} \left( \dots \left( \mathbf{M}_2(\mathbf{M}_1(\mathbf{x})) \right) \right) \right) \\
&\quad \text{(to simplify)} \mathbf{M}_i \mathbf{M}_{i-1} \dots \mathbf{M}_2 \mathbf{M}_1(\mathbf{x}).
\end{align*}
$$

Then the cost function *J* can be written as a function of the model iteration as follows,

$$
J(\mathbf{x}) = J^b(\mathbf{x}) + \frac{1}{2} \sum_{i=0}^{n} (\mathbf{y}_i - \mathbf{H}_i \mathbf{M}_i \mathbf{M}_{i-1} \dots \mathbf{M}_2 \mathbf{M}_1(\mathbf{x}))^\mathrm{T} \mathbf{R}_i^{-1} (\mathbf{y}_i - \mathbf{H}_i \mathbf{M}_i \mathbf{M}_{i-1} \dots \mathbf{M}_2 \mathbf{M}_1(\mathbf{x})) \quad (\text{Eq.B1})
$$

The minimization of Eq.B1 requires its gradient as follows:

$$
\nabla J(\mathbf{x}) = \mathbf{B}^{-1}(\mathbf{x} - \mathbf{x}^b) - \sum_{i=0}^{n} \mathbf{M}_1^\mathrm{T} \mathbf{M}_2^\mathrm{T} \dots \mathbf{M}_{i-1}^\mathrm{T} \mathbf{M}_i^\mathrm{T} \mathbf{H}_i^\mathrm{T} \mathbf{R}_i^{-1} (\mathbf{y}_i - \mathbf{H}_i \mathbf{M}_i \mathbf{M}_{i-1} \dots \mathbf{M}_2 \mathbf{M}_1(\mathbf{x}))
$$

where innovation vector **d**<sub>*i*</sub> = **y**<sub>*i*</sub> − **H**<sub>*i*</sub>**M**<sub>*i*</sub>**M**<sub>*i*−1</sub> ... **M**<sub>1</sub>(**x**). Then the gradient of the *J*<sup>*o*</sup>(**x**),
$$ 
\begin{aligned}
-\nabla J^0(\mathbf{x}) &= \sum_{i=0}^{n} \mathbf{M}_1^T \mathbf{M}_2^T \cdots \mathbf{M}_{i-1}^T \mathbf{M}_i^T \mathbf{H}_i^T \mathbf{R}_i^{-1} \mathbf{d}_i \\
&= \mathbf{H}_0^T \mathbf{R}_0^{-1} \mathbf{d}_0 + \mathbf{M}_1^T \mathbf{H}_1^T \mathbf{R}_1^{-1} \mathbf{d}_1 + \mathbf{M}_1^T \mathbf{M}_2^T \mathbf{H}_2^T \mathbf{R}_2^{-1} \mathbf{d}_2 + \cdots + \mathbf{M}_1^T \cdots \mathbf{M}_{n-1}^T \mathbf{M}_n^T \mathbf{H}_n^T \mathbf{R}_n^{-1} \mathbf{d}_n \\
&= \mathbf{H}_0^T \mathbf{R}_0^{-1} \mathbf{d}_0 + \mathbf{M}_1^T (\mathbf{H}_1^T \mathbf{R}_1^{-1} \mathbf{d}_1 + \mathbf{M}_2^T (\mathbf{H}_2^T \mathbf{R}_2^{-1} \mathbf{d}_2 + \cdots + \mathbf{M}_n^T \mathbf{H}_n^T \mathbf{R}_n^{-1} \mathbf{d}_n)).
\end{aligned}
$$

So if we put it all together, we obtain the $\nabla J(\mathbf{x})$ as follows,

$$ \nabla J(\mathbf{x}) = \mathbf{B}^{-1}(\mathbf{x} - \mathbf{x}^b) - (\mathbf{H}_0^T \mathbf{R}_0^{-1} \mathbf{d}_0 + \mathbf{M}_1^T (\mathbf{H}_1^T \mathbf{R}_1^{-1} \mathbf{d}_1 + \mathbf{M}_2^T (\mathbf{H}_2^T \mathbf{R}_2^{-1} \mathbf{d}_2 + \cdots + \mathbf{M}_n^T \mathbf{H}_n^T \mathbf{R}_n^{-1} \mathbf{d}_n))) \quad (\text{Eq.B2}) $$

In the main text, Eq.B2 is the same as Eq.23 in which $\mathbf{d}_i$ is considered.

This factorization makes calculation of $J$ followed by $\nabla J$ defined by;

$$ \mathbf{x}_i^* = \mathbf{M}_{i+1}^T \mathbf{x}_{i+1}^* + \mathbf{H}_i^T \mathbf{R}_i^{-1} \mathbf{d}_i, \quad i = n-1, 0 \quad (\text{Eq.B3}) $$

$$ \mathbf{x}_n^* = \mathbf{H}_n^T \mathbf{R}_n^{-1} \mathbf{d}_n $$
# Annex C : Non-linear operators

In the case of the non-linearity of the model $\mathcal{M}$ and observation operator $\mathcal{H}$, thanks to the tangent linear hypothesis (TLH) and adjoint models (Lewis and Derber, 1985) these non-linear operators can be replaced with their tangent linear operators by using the below Equations. This procedure force cost function $J$ to be a convex function and 4D-Var algorithm can be used to calculate the result approximately.

$$ \mathcal{M}_{0 \to i}(\mathbf{x}_0) - \mathcal{M}_{0 \to i}(\mathbf{x}_0^b) \approx \mathbf{M}_{0 \to i}(\mathbf{x}_0 - \mathbf{x}^b) $$

$$ \mathcal{H}_i(\mathbf{x}_i) - \mathcal{H}_i(\mathbf{x}_i^b) \approx \mathbf{H}_i(\mathbf{x}_i - \mathbf{x}_i^b) $$
**Annex D : Statistical indicators**

Pearson's Correlation Coefficient (r), Normalized Mean Bias (NMB) and Root Mean Square Error (RMSE) Formulas from top to down (n = number of available hourly measurements in the relevant year, simulation and station are the averaged values of simulated concentrations and stations, respectively.)

$$r = \frac{\sum_{i}^{n}(\text{simulation}_i - \overline{\text{simulation}})(\text{station}_i - \overline{\text{station}})}{\sqrt{\sum_{i}^{n}(\text{simulation}_i - \overline{\text{simulation}})^2(\text{station}_i - \overline{\text{station}})^2}}$$

$$NMB(\%) = \frac{\sum_{i}^{n}(\text{simulation}_i - \text{station}_i)}{\sum_{i}^{n}\text{station}_i} \times 100$$

$$RMSE(\mu g/m^3) = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (\text{simulation}_i - \text{station}_i)^2}$$
# Annex E : Ratio formulas

$r$ ratios, MB ratios and RMSE ratios formulas are as follows:

$$r_{ratio} = \frac{r_{prior}}{r_{post}}$$

$$MB_{ratio} = \frac{MB_{prior}}{MB_{post}}$$

$$RMSE_{ratio} = \frac{RMSE_{prior}}{RMSE_{post}}$$
**Annex F : Annual concentrations 2015**

Spatial distribution of annual mean surface NO₂ concentrations: (a) CHIMERE using prior emissions (Conc_Prior15); (b) CHIMERE using posterior emissions (Conc_Post15)

<figure><img src="image_79.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_80.png" /></figure>
**Annex G : Statistical indicators' ratios 2015**

Ratios of the Conc_Prior and Conc Post's statistical indicators: Correlation Coefficient, Mean Bias and RMSE, respectively, for (a-c) 2015.

<figure><img src="image_81.png" /></figure>

(a)

<figure><img src="image_82.png" /></figure>

(b)

<figure><img src="image_83.png" /></figure>

(c)
# Annex H : In situ comparison

<table><caption>Table H : NO₂ Annual Mean surface concentrations and statistics of the 15 selected locations for (top) 2015 and, (bottom) 2019.</caption><thead><tr><th rowspan="2">Location</th><th colspan="4">Annual Mean (µg/m³)</th><th colspan="3">r</th><th colspan="3">NMB (%)</th><th colspan="3">RMSE (µg/m³)</th></tr><tr><th>Station</th><th>Prior</th><th>Post</th><th>MEIC</th><th>Prior</th><th>Post</th><th>MEIC</th><th>Prior</th><th>Post</th><th>MEIC</th><th>Prior</th><th>Post</th><th>MEIC</th></tr></thead><tbody><tr><td>Daqing</td><td>24.9</td><td>25.4</td><td>23.9</td><td>24.4</td><td>0.68</td><td>0.69</td><td>0.66</td><td>2.1</td><td>-3.9</td><td>-1.8</td><td>12.8</td><td>12.6</td><td>13.6</td></tr><tr><td>Shenyang</td><td>41.8</td><td>41</td><td>41.7</td><td>41.4</td><td>0.65</td><td>0.65</td><td>0.59</td><td>-1.9</td><td>-0.2</td><td>-0.9</td><td>21.3</td><td>21.4</td><td>23.1</td></tr><tr><td>Baotou</td><td>36.7</td><td>33.4</td><td>30.3</td><td>26.4</td><td>0.55</td><td>0.54</td><td>0.55</td><td>-9</td><td>-18</td><td>-28</td><td>22.2</td><td>23</td><td>23.9</td></tr><tr><td>Beijing-Tianjin (M*)</td><td>46.7</td><td>66.2</td><td>67</td><td>55.9</td><td>0.66</td><td>0.67</td><td>0.65</td><td>41.9</td><td>43.6</td><td>19.7</td><td>36</td><td>36.4</td><td>28.8</td></tr><tr><td>Dalian (P)</td><td>28.3</td><td>27.6</td><td>28.4</td><td>29.5</td><td>0.58</td><td>0.59</td><td>0.53</td><td>-2.7</td><td>0.4</td><td>4.1</td><td>17.6</td><td>17.5</td><td>19.1</td></tr><tr><td>Shijiazhuang (M*)</td><td>39.1</td><td>65</td><td>65.8</td><td>56.3</td><td>0.58</td><td>0.58</td><td>0.57</td><td>66</td><td>68.5</td><td>44.1</td><td>40.1</td><td>40.6</td><td>34</td></tr><tr><td>Shandong (M*)</td><td>42.3</td><td>52.9</td><td>53.4</td><td>41.4</td><td>0.65</td><td>0.66</td><td>0.63</td><td>25</td><td>26.4</td><td>-2</td><td>25.4</td><td>25.6</td><td>22.3</td></tr><tr><td>Henan (P, M)</td><td>38.8</td><td>52.7</td><td>50.7</td><td>38</td><td>0.59</td><td>0.59</td><td>0.59</td><td>35.8</td><td>30.8</td><td>-2.1</td><td>28.3</td><td>27</td><td>22.7</td></tr><tr><td>Anhui (P*, M*)</td><td>25</td><td>35.8</td><td>34.8</td><td>29.1</td><td>0.44</td><td>0.43</td><td>0.43</td><td>43.4</td><td>39.4</td><td>16.4</td><td>24.5</td><td>24.2</td><td>21.5</td></tr><tr><td>Yangtze River Delta (P, M)</td><td>37.9</td><td>62.5</td><td>59.7</td><td>50.7</td><td>0.58</td><td>0.6</td><td>0.58</td><td>65.2</td><td>57.8</td><td>33.8</td><td>37</td><td>34.5</td><td>28.5</td></tr><tr><td>Wuhan (P, M*)</td><td>47.1</td><td>69.5</td><td>64.9</td><td>49.8</td><td>0.62</td><td>0.63</td><td>0.57</td><td>47.7</td><td>37.9</td><td>5.8</td><td>34.5</td><td>31.4</td><td>26.7</td></tr><tr><td>Chengdu (P*)</td><td>43.2</td><td>49.4</td><td>47.9</td><td>62.9</td><td>0.5</td><td>0.49</td><td>0.54</td><td>14.3</td><td>11</td><td>45.8</td><td>24.8</td><td>24.4</td><td>31</td></tr><tr><td>Chongqing (P*, M)</td><td>38.5</td><td>59.1</td><td>56.8</td><td>50.9</td><td>0.4</td><td>0.39</td><td>0.41</td><td>53.4</td><td>47.6</td><td>32.3</td><td>34.1</td><td>32.8</td><td>27.5</td></tr><tr><td>Hunan (P)</td><td>33.5</td><td>46.4</td><td>44</td><td>49.2</td><td>0.54</td><td>0.55</td><td>0.55</td><td>38.8</td><td>31.6</td><td>47</td><td>24.2</td><td>22.5</td><td>26.3</td></tr><tr><td>Pearl River Delta (P)</td><td>30.1</td><td>33.9</td><td>30.5</td><td>35.3</td><td>0.54</td><td>0.55</td><td>0.59</td><td>12.5</td><td>1.3</td><td>17.3</td><td>20.6</td><td>19.5</td><td>20.8</td></tr></tbody></table>

<table><thead><tr><th rowspan="2">Location</th><th colspan="3">Annual Mean (µg/m³)</th><th colspan="2">r</th><th colspan="2">NMB (%)</th><th colspan="2">RMSE (µg/m³)</th></tr><tr><th>Station</th><th>Prior</th><th>Post</th><th>Prior</th><th>Post</th><th>Prior</th><th>Post</th><th>Prior</th><th>Post</th></tr></thead><tbody><tr><td>Daqing (P*)</td><td>19</td><td>23.7</td><td>22.1</td><td>0.72</td><td>0.71</td><td>24.6</td><td>16.3</td><td>12.2</td><td>11.7</td></tr><tr><td>Shenyang (P*)</td><td>33</td><td>41.5</td><td>41.3</td><td>0.74</td><td>0.73</td><td>25.7</td><td>25</td><td>19.6</td><td>19.5</td></tr><tr><td>Baotou</td><td>36.7</td><td>35.5</td><td>33.5</td><td>0.6</td><td>0.61</td><td>-3.2</td><td>-8.6</td><td>21.8</td><td>21.7</td></tr><tr><td>Beijing-Tianjin (P)</td><td>38</td><td>67.5</td><td>66.7</td><td>0.65</td><td>0.65</td><td>77.9</td><td>75.5</td><td>42.7</td><td>41.8</td></tr><tr><td>Dalian</td><td>21.3</td><td>27.5</td><td>28.1</td><td>0.68</td><td>0.68</td><td>29.2</td><td>31.9</td><td>15.6</td><td>15.9</td></tr><tr><td>Shijiazhuang (P)</td><td>29</td><td>67.8</td><td>66.7</td><td>0.62</td><td>0.63</td><td>134.2</td><td>130.3</td><td>47.5</td><td>46.5</td></tr><tr><td>Shandong (P)</td><td>38.3</td><td>57.2</td><td>55.6</td><td>0.73</td><td>0.74</td><td>49.2</td><td>45</td><td>28.7</td><td>27.6</td></tr><tr><td>Henan (P)</td><td>34</td><td>57.1</td><td>54</td><td>0.69</td><td>0.69</td><td>67.9</td><td>59</td><td>32.1</td><td>29.7</td></tr><tr><td>Anhui (P)</td><td>23.9</td><td>37.1</td><td>35.6</td><td>0.69</td><td>0.69</td><td>55.5</td><td>49.1</td><td>20.6</td><td>19.5</td></tr><tr><td>Yangtze River Delta (P)</td><td>34.4</td><td>62.3</td><td>58.4</td><td>0.62</td><td>0.65</td><td>81.2</td><td>69.6</td><td>38.3</td><td>34.3</td></tr><tr><td>Wuhan (P)</td><td>39.3</td><td>72.5</td><td>64.7</td><td>0.66</td><td>0.67</td><td>84.8</td><td>64.8</td><td>41</td><td>34.8</td></tr><tr><td>Chengdu (P)</td><td>39.5</td><td>54</td><td>53.2</td><td>0.6</td><td>0.6</td><td>36.8</td><td>34.8</td><td>26</td><td>25.5</td></tr><tr><td>Chongqing (P)</td><td>35.5</td><td>60.9</td><td>59.7</td><td>0.52</td><td>0.52</td><td>71.5</td><td>68.3</td><td>35.1</td><td>34.3</td></tr><tr><td>Hunan (P)</td><td>27</td><td>48.5</td><td>45.7</td><td>0.67</td><td>0.67</td><td>79.5</td><td>69.4</td><td>27.5</td><td>25.4</td></tr><tr><td>Pearl River Delta (P)</td><td>25.7</td><td>35.3</td><td>31.9</td><td>0.57</td><td>0.61</td><td>37.1</td><td>23.8</td><td>21.9</td><td>19.1</td></tr></tbody></table>

P : Posterior better than Prior ; P*: Posterior better than Prior when excluding *r*

M : MEIC is better than Prior ; M*: MEIC is better than Prior when excluding *r*

(Note that; “better” means lower NMB and RMSE, and higher *r*)
**Annex I : Innovation & Residue Map**

NO₂ monthly mean columns differences between Prior and OMI observations (below) and Posterior and OMI observations (bottom) for 2015.

<figure><img src="image_84.png" /></figure>

<figure><img src="image_85.png" /></figure>
# Annex J : Résumé substantiel en français

L'Organisation mondiale de la Santé estime que l'exposition à la pollution de l'air ambiant provoque 4,2 millions de décès prématurés dans le monde chaque année. Ce problème environnemental est apparu au 20ème siècle en raison d'une intense industrialisation et urbanisation, incitant les gouvernements à mettre en place des politiques pour réduire les émissions anthropiques de polluants atmosphériques. Depuis 1990, les pays industrialisés, en particulier en Europe, ont pris des initiatives pour réduire les émissions de polluants grâce à des stratégies d'atténuation. Les pays en développement, comme la Chine, ont également commencé à mettre en place des politiques d'atténuation plus récemment.

Les oxydes d'azote ($NO_x$) sont l'un des principaux polluants, causant des impacts sanitaires directs tels que des infections respiratoires, de l'asthme et des maladies pulmonaires chroniques, et endommageant les écosystèmes. Les $NO_x$ sont des précurseurs d'autres polluants atmosphériques tels que l'ozone et les aérosols secondaires, contribuant également au changement climatique en tant que forceurs climatiques à courte durée de vie. Lorsqu'ils se dissolvent dans l'eau, ils créent des acides qui nuisent à la végétation, aux bâtiments et aux matériaux, et contribuent à l'acidification et à l'eutrophisation des écosystèmes. Par conséquent, les $NO_x$, en particulier le $NO_2$, sont des polluants hautement réglementés.

En Europe, selon l'Agence européenne pour l'environnement, les émissions de $NO_x$ ont été réduites de près de 60 % entre 1990 et 2019, le transport routier et l'énergie étant les principaux secteurs émetteurs. En Chine, la production d'électricité et l'industrialisation, fortement dépendantes de la consommation de charbon, sont les principaux contributeurs aux émissions de $NO_x$, suivis des véhicules routiers. Un développement économique rapide a entraîné une augmentation significative des émissions de $NO_x$ entre les années 90 et la fin des années 2000. Pour lutter contre ce problème, la Chine a mis en place des réductions d'émissions de $NO_x$ avec des objectifs de réduction de 10 % en 2015 et de 15 % en 2020 dans leurs 12ème et 13ème plans quinquennaux gouvernementaux, respectivement.

Les capacités d'observation des polluants, en particulier les concentrations de $NO_2$, ont augmenté au cours des trois dernières décennies avec le développement de réseaux de mesure de la qualité de l'air. Dans le même temps, les observations par satellite des colonnes troposphériques de $NO_2$ ont montré des améliorations sans précédent : depuis l'instrument
satellite GOME avec une résolution spatiale de quelques centaines de kilomètres au milieu des années 90 jusqu'à OMI et GOME-2 (résolution de quelques dizaines de kilomètres) au milieu des années 2000 et TROPOMI (résolution de quelques kilomètres) depuis 2018. Les capacités de modélisation atmosphérique ont également progressé, permettant aux modèles de transport chimique de simuler les distributions tridimensionnelles des concentrations de polluants à des échelles locales à globales avec une haute résolution spatiale et temporelle. Des systèmes opérationnels tels que le Service de surveillance de l'atmosphère Copernicus (CAMS pour Copernicus Atmospheric Monitoring Service en anglais) en Europe et la plateforme nationale Prev'Air en France, ont fourni des estimations des polluants atmosphériques à différentes échelles en exploitant la complémentarité de la modélisation et des observations et le développement de puissants systèmes d'assimilation de données.

Un problème clé est d'évaluer la réalité et l'efficacité des politiques de réduction des émissions. Les méthodes d'évaluation traditionnelles sont souvent basées sur des inventaires d'émissions officiels dérivés des déclarations d'activités des émetteurs et des données statistiques, appelées approche "bottom-up". Ces inventaires impliquent de fortes incertitudes et ne prennent pas en compte la variabilité spatiotemporelle élevée des flux d'émissions. En revanche, l'approche d'inversion atmosphérique, ou approche "top-down", utilise des observations atmosphériques disponibles, telles que des observations satellitaires, pour contraindre les émissions à travers la modélisation atmosphérique et un système d'inversion (assimilation de données). Cette approche estime les émissions tout en exploitant la variabilité spatiotemporelle élevée des observations satellitaires et la puissance de calcul avec une capacité de mise à jour rapide, apportant des informations complémentaires aux inventaires "bottom-up".

Au début de ce travail de thèse, le nouvel instrument satellitaire TROPOMI commençait tout juste à fournir des colonnes troposphériques de NO₂ à une résolution spatiale sans précédent de quelques kilomètres. Au niveau français, un nouveau système d'inversion était en cours de développement, le Community Inversion Framework (CIF) (Berchet et al. 2021) basé sur une version précédente moins polyvalente, PYVAR (Fortems-Cheiney et al. 2021), qui était d'abord dédiée à l'inversion et à la surveillance des gaz à effet de serre (CO₂, CH₄) à l'échelle mondiale. Ses capacités à appliquer des approches "top-down" aux espèces hautement réactives à l'échelle régionale et à haute résolution étaient limitées. Par conséquent, dans le cadre du projet ANR ARGONAUT, cette thèse visait à développer la modélisation inverse régionale des espèces réactives en France en utilisant le CIF, le modèle régional national CHIMERE et les nouvelles
observations TROPOMI. Pour ce faire, nous avons concentré nos tests sur l'outil CIF-CHIMERE pour les émissions de NOₓ en raison de la maturité des produits satellitaires de NO₂ et de leur bonne résolution temporelle. Nous avons considéré comme zones d'étude l'Europe, la France et la Chine. L'Europe et la Chine sont traitées à résolution moyenne (50 km) et la France à haute résolution (10 km). Les inversions sont contraintes soit en utilisant les données de OMI (13 km x 25 km) pour la Chine et l'Europe ou de TROPOMI (5,5 km x 3,5 km) pour l'Europe et la France.

Comme il s'agit d'un nouveau système, nous avons d'abord testé les capacités de l'outil CIF couplé au modèle CHIMERE. Les premiers tests du système CIF-CHIMERE ont été effectués pour tester la configuration du nouveau système et déterminer ses paramètres critiques pour l'inversion. Pour ce faire, un test de base, incluant une configuration adaptée des données de la littérature ou basées sur des connaissances d'experts, a été défini pour inverser les émissions de NOₓ sur le domaine de l'Europe à résolution moyenne (50 km) en utilisant les colonnes NO₂ du satellite OMI. Le système a été testé en modifiant un paramètre à la fois, et il a été constaté que les paramètres variationnels, liés aux statistiques d'erreurs des émissions a priori, étaient plus significatifs que les paramètres d'optimisation dans l'estimation des émissions. Les statistiques d'erreur, en particulier celles sur les émissions de fond et leurs corrélations, sont ainsi des éléments déterminants pour l'inversion. L'étude a permis de définir une configuration et une plage de variations des différents paramètres adaptées au système d'inversion et qui permettent de définir rapidement une configuration adaptée à d'autres domaines d'étude.

Dans un second temps, le système CIF-CHIMERE a été utilisé pour estimer les émissions de NOₓ chinoises pour 2015 et 2019, en utilisant les données de colonne de NO₂ des observations satellites OMI pour quantifier les réductions des émissions de NOₓ chinoises en lien avec les stratégies d'atténuation du gouvernement chinois mises en place. Les années cibles 2015 et 2019 ont été choisies car elles correspondent aux dernières années des deux plans quinquennaux. Nous n'avons pas considéré 2020 en raison de la pandémie de COVID-19 qui aurait pu fausser les conclusions. La faible couverture quotidienne de OMI ne permet pas de dériver des émissions journalières, des corrections mensuelles des émissions de NOₓ ont donc été calculées. Nous avons pu constater que les observations de OMI fournissent une meilleure contrainte sur les émissions de NOₓ dans les zones polluées par rapport aux zones de fond. L'utilisation de ces estimations d'émissions de NOₓ pour simuler les concentrations de NO₂ en surface avec un modèle améliore légèrement la comparaison des simulations avec les mesures au sol. Les
budgets annuels estimés sont en bon accord (dans les incertitudes) avec les inventaires indépendants tels que l'inventaire MEIC ou DECSO en 2015. Les résultats suggèrent que l'objectif du douzième plan quinquennal a été atteint (-10 %) dans les zones polluées correspondant aux principales régions urbanisées de Chine. En revanche, l'évolution des émissions estimées de 2015 à 2019 reste faible, et les objectifs de réduction du treizième plan quinquennal n'ont pas été atteints. Ces derniers résultats ne semblent pas complètement cohérents avec la littérature récente et nécessitent des investigations supplémentaires.

Pendant la thèse, une nouvelle fonctionnalité a été implémentée dans le système CIF-CHIMERE par l'équipe de développement pour surmonter les problèmes de convergence des inversions que nous avons rencontrés. Nous avons maintenant la possibilité d'utiliser une échelle logarithmique pour le vecteur de contrôle, ce qui facilite l'optimisation et la convergence du système. Nous avons testé l'influence de l'utilisation de l'échelle logarithmique plutôt que de l'échelle linéaire pour l'inversion sur une seule journée, les résultats suggèrent que les distributions spatiales des corrections des émissions obtenues par inversion ne sont pas modifiées en changeant d'échelle. L'amplitude des corrections est cohérente pour les plus grandes émissions, mais peut être significativement différente dans les régions de fond. Cela ne devrait pas affecter beaucoup le résultat en termes de budget ou de performances de simulation de la qualité de l'air. Néanmoins, cette question devrait être abordée pour une période plus longue à l'avenir pour être plus représentative.

Nous avons également effectué des tests préliminaires pour appliquer le système CIF-CHIMERE en Europe et en France, principalement pour évaluer les changements soudains dans les émissions de NOₓ pendant la période de confinement due au COVID-19. Ce travail fait partie du projet ARGONAUT, qui vise à estimer les émissions de NOₓ en France à haute résolution (10 km) en utilisant des observations par satellite à haute résolution telles que TROPOMI. Dans un premier temps, le système CIF-CHIMERE a été adapté à une résolution de 50 km, couvrant une zone plus grande que la France, l'Europe, pour comparer les performances d'inversion de TROPOMI et d'OMI. L'accent a été mis sur la première semaine d'avril 2020, et les nouvelles estimations d'émissions ont été comparées aux émissions a priori correspondant à l'année 2016. L'évaluation des résultats d'inversion a montré que les nouvelles estimations d'émissions ont amélioré les statistiques de comparaison par rapport aux émissions a priori, réduisant le biais de 60 % à 20 % et diminuant le RMSE d'environ 25 %. L'amélioration est systématique pour les stations rurales et significative pour les stations urbaines dans les
grandes régions urbanisées, mais une dégradation du biais est observée pour certaines stations urbaines, notamment dans le sud de l'Allemagne et en Pologne. En ce qui concerne les changements d'émissions par rapport au prior pour la première semaine d'avril 2020, une réduction des émissions a été observée dans les pays d'Europe du Nord-Ouest, avec des réductions allant jusqu'à 67 % à l'échelle du point de grille du modèle ou environ 35-45 % pour des pays tels que la Belgique, les Pays-Bas, le Royaume-Uni, l'Allemagne ou la Pologne. Les pays du Sud (France, Italie et Espagne) ont montré une réduction de leurs émissions plus faible au cours de cette semaine, ce qui est attribué à l'échantillonnage des observations, qui est plus constant et homogène de jour en jour dans le nord que dans le sud, plutôt qu'à une différence dans l'application de restrictions pendant le confinement. Bien que la méthodologie pour évaluer l'impact du confinement consiste généralement à comparer 2020 avec 2019, des problèmes techniques avec le supercalculateur utilisé pour effectuer l'inversion ont entraîné l'inversion de seulement quelques jours pour avril 2019 ne permettant pas de présenter des résultats totalement représentatifs. Néanmoins, une comparaison préliminaire suggère une réduction de 40 % pour l'Ile-de-France et de 30 à 50 % pour le sud de l'Allemagne et le nord de l'Italie. Une étude élargie sur une période plus longue est nécessaire pour confirmer ces premiers résultats. Ces résultats montrent toutefois que la haute résolution de TROPOMI et ses meilleures performances instrumentales fournissent une plus grande couverture quotidienne et donc des capacités d'inversion des émissions à l'échelle journalière améliorées.

Enfin, les premières tentatives d'inversion à haute résolution pour une journée (1er avril 2020) sur la France semblent prometteuses pour évaluer et surveiller les émissions à haute résolution spatiale.

Cette thèse de doctorat a permis de discuter le potentiel du nouveau système CIF-CHIMERE et des données TROPOMI pour surveiller les émissions de NOₓ à différentes résolutions, de modérées à élevées. Cependant, le travail a été réalisé sur des périodes de temps et un nombre de jours limités, une perspective à court terme de ce travail serait d'étendre la durée des périodes étudiées pour obtenir des résultats plus représentatifs et consolidés. A plus long terme, d'autres questions se posent suite à ce travail. Par exemple, nous avons noté que, malgré les améliorations apportées par TROPOMI, la couverture nuageuse restait un facteur limitant dans certaines situations, la question de la résolution temporelle à laquelle les inversions peuvent être effectuées doit donc être encore approfondie. La question de la séparation des émissions anthropiques et biogéniques ou des émissions par secteur reste également une question ouverte
pour laquelle la haute résolution spatiale apportée par TROPOMI pourrait aidée mais cela nécessite des développements techniques dans le CIF pour adapter le vecteur de contrôle.
D'autre part, l'étude sur la Chine a soulevé la question de l'efficacité de la réduction des émissions au cours du 13e plan quinquennal, une extension de l'étude à l'ensemble de la décennie serait intéressante pour évaluer si les résultats que nous avons obtenus sont spécifiques à l'année 2019 ou généralisables. L'utilisation de TROPOMI pour les années récentes serait également intéressante, mais la cohérence entre les observations OMI et TROPOMI doit être vérifiée pour pouvoir calculer des tendances. En Europe et en France, il serait également très intéressant d'évaluer l'impact de la pandémie sur les émissions de NOx à haute résolution, en incluant tous les confinements et les restrictions qui ont eu lieu pendant la durée de la pandémie.
A noter que pour réaliser ces différents développements et études, il est important de s'assurer que les observations ne sont pas biaisées; cependant, les données TROPOMI semblent encore présenter un biais négatif résiduel. Par conséquent, des techniques de débiaisage pourraient être envisagées avant d'assimiler les données dans le système d'inversion.
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# Table of Contents

ACKNOWLEDGEMENTS.................................................................................................................. 7

ABBREVIATIONS.................................................................................................................... 11

INTRODUCTION.................................................................................................................... 17

FIRST PART : CONTEXT........................................................................................................ 21

CHAPTER 1 : NITROGEN OXIDES IN THE ATMOSPHERE ................................................................ 21

1.1 EARTH'S ATMOSPHERIC COMPOSITION AND STRUCTURE................................................................ 21

1.2 ATMOSPHERIC LIFETIME ........................................................................................................ 23

1.3 NOₓ CHEMISTRY (MAINLY TROPOSPHERIC)........................................................................ 25

1.4 NOₓ AS AN AIR POLLUTANT : DISCOVERY AND IMPACTS ................................................................ 28

1.5 NO₂ MONITORING TOOLS........................................................................................................ 29

1.6 NO₂ CONCENTRATION LEVELS IN THE ATMOSPHERE ................................................................ 30

1.7 NOₓ EMISSIONS .................................................................................................................... 35

1.7.1 NOₓ emission sources ........................................................................................................ 35

1.7.1 NOₓ emission inventories.................................................................................................... 37

1.7.1.1 Bottom-up approach.................................................................................................... 37

1.7.1.2 Top-down approach .................................................................................................... 38

1.7.1.3 Examples and comparison of two approaches.................................................... 38

1.8 OBJECTIVES OF THE THESIS.................................................................................................... 41

SECOND PART : METHODOLOGY AND INSTRUMENTS ................................................................ 43

CHAPTER 2 : INVERSE MODELING AND ITS TOOLS ................................................................ 43

2.1 THE CONCEPT AND THEORY.................................................................................................... 43

2.1.1 What is an inverse problem? .................................................................................... 43

2.1.2 Overview of data assimilation: past to present ............................................................ 44

2.1.2.1 Assimilation as an inverse problem ........................................................................ 44

2.1.2.2 First usages of data assimilation in atmospheric science ................................. 45

2.1.2.3 Sequential approach: the Kalman filter and its variants .................................... 46

2.1.2.4 Variational approach .................................................................................................... 47

2.1.3 General notations of data assimilation ........................................................................ 49

2.1.3.1 The state vector, control variable and observations........................................ 50

2.1.3.1.1 The state vector.................................................................................................... 50

2.1.3.1.2 Control variable.................................................................................................... 50

2.1.3.1.3 Observations ........................................................................................................ 51

2.1.3.2 Analysis, innovation and residuals ........................................................................ 51
<table>
  <tbody>
    <tr>
      <td>2.1.3.3 Errors</td>
      <td>52</td>
    </tr>
    <tr>
      <td>2.1.3.4 Hypotheses</td>
      <td>53</td>
    </tr>
    <tr>
      <td>2.1.4 Assimilation techniques</td>
      <td>54</td>
    </tr>
    <tr>
      <td>2.1.4.1 Statistical data assimilation</td>
      <td>54</td>
    </tr>
    <tr>
      <td>2.1.4.2 Variational data assimilation</td>
      <td>55</td>
    </tr>
    <tr>
      <td>2.1.4.2.1 Formulation of variational data assimilation</td>
      <td>55</td>
    </tr>
    <tr>
      <td>2.1.4.2.2 4D-Var and its pioneering 3D-Var</td>
      <td>56</td>
    </tr>
    <tr>
      <td>2.1.4.2.3 4D-Var algorithm</td>
      <td>59</td>
    </tr>
    <tr>
      <td>2.1.4.2.4 Limitations of 4D-Var</td>
      <td>60</td>
    </tr>
    <tr>
      <td>2.2 CIF INVERSE MODELING SYSTEM</td>
      <td>61</td>
    </tr>
    <tr>
      <td>2.2.1 Development of CIF in this study</td>
      <td>61</td>
    </tr>
    <tr>
      <td>2.2.1.1 The control vector (x)</td>
      <td>61</td>
    </tr>
    <tr>
      <td>2.2.1.2 The background vector (xb)</td>
      <td>62</td>
    </tr>
    <tr>
      <td>2.2.1.3 The background error covariance matrix (B)</td>
      <td>62</td>
    </tr>
    <tr>
      <td>2.2.1.4 The observation operator (H(x))</td>
      <td>62</td>
    </tr>
    <tr>
      <td>2.2.1.5 The observation vector (y)</td>
      <td>63</td>
    </tr>
    <tr>
      <td>2.2.1.6 The observation error covariance matrix (R)</td>
      <td>63</td>
    </tr>
    <tr>
      <td>2.2.1.7 The minimizer M1QN3</td>
      <td>63</td>
    </tr>
    <tr>
      <td>2.2.1.8 Analysis (xa)</td>
      <td>64</td>
    </tr>
    <tr>
      <td>2.3 ATMOSPHERIC MODELING</td>
      <td>65</td>
    </tr>
    <tr>
      <td>2.3.1 CHIMERE Regional CTM</td>
      <td>68</td>
    </tr>
    <tr>
      <td>2.3.1.1 Setup of the CHIMERE Simulations</td>
      <td>69</td>
    </tr>
    <tr>
      <td>2.3.1.1.1 Domain : Eastern China</td>
      <td>70</td>
    </tr>
    <tr>
      <td>2.3.1.1.2 Domain : Europe</td>
      <td>73</td>
    </tr>
    <tr>
      <td>2.4 ATMOSPHERIC OBSERVATIONS</td>
      <td>74</td>
    </tr>
    <tr>
      <td>2.4.1 Satellite observations</td>
      <td>75</td>
    </tr>
    <tr>
      <td>2.4.1.1 OMI</td>
      <td>75</td>
    </tr>
    <tr>
      <td>2.4.1.1.1 Data selection and processing</td>
      <td>78</td>
    </tr>
    <tr>
      <td>2.4.1.2 TROPOMI</td>
      <td>79</td>
    </tr>
    <tr>
      <td>2.4.1.2.1 Data selection and processing</td>
      <td>82</td>
    </tr>
    <tr>
      <td>2.4.2 Surface observations</td>
      <td>82</td>
    </tr>
    <tr>
      <td>2.4.2.1 Chinese in-situ network</td>
      <td>83</td>
    </tr>
    <tr>
      <td>2.4.2.1.1 Data selection and processing</td>
      <td>83</td>
    </tr>
    <tr>
      <td>2.4.2.2 European in-situ network</td>
      <td>85</td>
    </tr>
    <tr>
      <td>2.5 SENSITIVITY ANALYSIS OF THE CIF INVERSE MODELING SYSTEM</td>
      <td>86</td>
    </tr>
    <tr>
      <td>2.5.1 Parameters definition</td>
      <td>87</td>
    </tr>
    <tr>
      <td>2.5.1.1 Optimization parameters</td>
      <td>87</td>
    </tr>
    <tr>
      <td>2.5.2 Variational parameters</td>
      <td>88</td>
    </tr>
  </tbody>
</table>
2.5.2 Sensitivity to optimization parameters.................................................................................. 89

2.5.3 Sensitivity to variational parameters.................................................................................. 90

2.5.3.1 B variances.................................................................................................................. 90

2.5.3.2 B covariances .................................................................................................................. 92

2.5.3.3 Biogenic emission error .................................................................................................. 94

### THIRD PART : SCIENTIFIC APPLICATIONS.................................................................................. 96

### CHAPTER 3. INVERSE MODELING OF NOₓ EMISSIONS OVER CHINA .................................................. 96

SUMMARY .................................................................................................................................................. 96

3.1 INTRODUCTION .......................................................................................................................... 97

3.2 MATERIALS AND METHODS ........................................................................................................ 100

3.2.1 Inversion-related tools and data .................................................................................. 100

3.2.1.1 Inverse modeling and the CIF system.................................................................. 100

3.2.1.2 HTAP v2.2 emission inventory .................................................................................. 102

3.2.1.3 OMI satellite observations.......................................................................................... 103

3.2.1.4 The regional CHIMERE CTM .................................................................................... 104

3.2.1.5 Inversion experiments.................................................................................................. 105

3.2.2 Evaluation data and the method .................................................................................. 107

3.2.2.1 MEIC bottom-up emission inventory.................................................................. 107

3.2.2.2 CNEMC ground-based observations.................................................................. 107

3.2.2.3 Evaluation and analysis methodology .................................................................. 107

3.3 RESULTS AND DISCUSSION ........................................................................................................ 109

3.3.1 Evaluation of the CIF-CHIMERE system and NOₓ emission estimates with ground-based measurements.................................................................................................................. 109

3.3.2 Analysis of the estimated Chinese annual anthropogenic NOₓ emissions in 2015 and 2019 .................................................................................................................. 114

3.3.3 Analysis of the estimated annual anthropogenic NOₓ emissions at selected urbanized and industrialized locations.................................................................................. 116

3.3.3.1 Evaluation of the estimated annual anthropogenic NOₓ emissions in 2015 and 2019 .................................................................................................................. 116

3.3.3.2 Monthly evaluation of the anthropogenic NOₓ emissions.................................. 119

3.3.3.3 Comparison with in-situ measurements .................................................................. 120

3.4 CONCLUSIONS .................................................................................................................................. 121

### CHAPTER 4. NOₓ EMISSIONS IN EUROPE DERIVED FROM SATELLITE OBSERVATIONS .................................................. 123

4.1 CONTEXT OF THE STUDY ........................................................................................................ 123

4.2 COMPARISON OF INVERSIONS USING OMI AND TROPOMI OVER EUROPE ........................................ 124

4.3 DIFFICULTIES IN USING TROPOMI OBSERVATIONS FOR INVERSIONS ........................................ 127

4.4 NEW SET-UP OF THE INVERSION.......................................................................................... 128

4.4.1 Inversion over the European Domain........................................................................ 129

4.4.2 Inversion over the France (ARGFR) Domain.................................................................. 129
<table><tr><td>4.5 EVALUATION OF INVERSION COHERENCE OF LOG AND LINEAR SCALED EMISSIONS: CHINA + OMI CASE</td><td>130</td></tr><tr><td>4.6 EUROPEAN NO<sub>x</sub> EMISSIONS DURING APRIL 2020 COMPARED TO 2016</td><td>131</td></tr><tr><td>4.6.1 Emission comparisons</td><td>131</td></tr><tr><td>4.6.2 Evaluation with surface measurements</td><td>134</td></tr><tr><td>4.7 PRELIMINARY EMISSIONS FOR APRIL 2019 AND OPEN QUESTIONS</td><td>137</td></tr><tr><td>4.8 FIRST TESTS OF INVERSION AT HIGH RESOLUTION OVER FRANCE</td><td>140</td></tr><tr><td><strong>GENERAL CONCLUSIONS AND PERSPECTIVES</strong></td><td><strong>142</strong></td></tr><tr><td><strong>ANNEXES</strong></td><td><strong>147</strong></td></tr><tr><td>ANNEX A: STATISTICAL FORMULAS</td><td>147</td></tr><tr><td>ANNEX B: 4D-VAR COST AND THE GRADIENT EVOLUTION</td><td>148</td></tr><tr><td>ANNEX C: NON-LINEAR OPERATORS</td><td>150</td></tr><tr><td>ANNEX D: STATISTICAL INDICATORS</td><td>151</td></tr><tr><td>ANNEX E: RATIO FORMULAS</td><td>152</td></tr><tr><td>ANNEX F: ANNUAL CONCENTRATIONS 2015</td><td>153</td></tr><tr><td>ANNEX G: STATISTICAL INDICATORS' RATIOS 2015</td><td>154</td></tr><tr><td>ANNEX H: IN SITU COMPARISON</td><td>155</td></tr><tr><td>ANNEX I: INNOVATION &amp; RESIDUE MAP</td><td>156</td></tr><tr><td>ANNEX J: RÉSUMÉ SUBSTANTIEL EN FRANÇAIS</td><td>157</td></tr><tr><td><strong>BIBLIOGRAPHY</strong></td><td><strong>163</strong></td></tr><tr><td><strong>TABLE OF CONTENTS</strong></td><td><strong>185</strong></td></tr><tr><td><strong>TABLE OF FIGURES</strong></td><td><strong>189</strong></td></tr><tr><td><strong>LIST OF TABLES</strong></td><td><strong>193</strong></td></tr></table>
Table of figures

<table>
  <tbody>
    <tr>
      <td>Figure 1 Parisian Sunset at the top of the Montparnasse tower (December 2021).</td>
      <td>21</td>
    </tr>
    <tr>
      <td>Figure 2 Atmospheric layers (Image taken from Seinfeld and Pandis, 2016)</td>
      <td>22</td>
    </tr>
    <tr>
      <td>Figure 3 Atmospheric lifetime of different species from short-lived to long-lived species (Image taken from Seinfeld and Pandis, 2016)</td>
      <td>24</td>
    </tr>
    <tr>
      <td>Figure 4 Long-range transportation of NO<sub>x</sub> from PAN. (Taken from Solène Turquety's "Atmospheric chemistry and air quality" course slides, 05/10/2020).</td>
      <td>28</td>
    </tr>
    <tr>
      <td>Figure 5 Global map of mean tropospheric NO<sub>2</sub> concentrations from 2005 to 2018 as observed by the OMI satellite instrument. Figure is taken from Jamali, Klingmyr, and Tagesson 2020.</td>
      <td>31</td>
    </tr>
    <tr>
      <td>Figure 6 Ambient annual mean of surface NO<sub>2</sub> Concentrations for 2019 (in µg/m<sup>3</sup>), extracted from https://www.eea.europa.eu/data-and-maps/dashboards/air-quality-statistics.</td>
      <td>32</td>
    </tr>
    <tr>
      <td>Figure 7 Spatial distribution of annual mean surface NO<sub>2</sub> concentration in 2019 for China (Visualized by using data of the CNEMC network).</td>
      <td>33</td>
    </tr>
    <tr>
      <td>Figure 8 Inter-annual monthly averages of NO<sub>2</sub> tropospheric vertical columns over East Central China measured by GOME and SCIAMACHY satellite instruments. Figure taken from Richter et al., 2005 (Shaded areas show the standard deviation).</td>
      <td>33</td>
    </tr>
    <tr>
      <td>Figure 9 Time series of annual mean of tropospheric NO<sub>2</sub> concentration using DBEST (Jamali et al., 2015) trend analysis method and OMI satellite measurements for the Globe, Europe and China. Figures are taken from Jamali, Klingmyr, and Tagesson 2020.</td>
      <td>34</td>
    </tr>
    <tr>
      <td>Figure 10 EU Anthropogenic NO<sub>x</sub> emission sources by sectors for 2019 (Taken from EU emission inventory report, 2021)</td>
      <td>37</td>
    </tr>
    <tr>
      <td>Figure 11 Compilation of regional MIX Asia bottom-up emission inventory with local bottom-up inventories (Figure is taken from Li M. et al. 2017)</td>
      <td>39</td>
    </tr>
    <tr>
      <td>Figure 12 Compilation of several regional bottom-up emission inventories to build a global HTAP v2.2 emission inventory (Figure is taken from Janssens-Maenhout et al., 2015).</td>
      <td>39</td>
    </tr>
    <tr>
      <td>Figure 13 Annual time series of NO<sub>x</sub> emissions from different emission inventories over mainland China. (Figure taken from Ding et al., 2017)</td>
      <td>40</td>
    </tr>
    <tr>
      <td>Figure 14 Illustration of 3D-Var & 4D-Var (Taken from Lahoz and Schneider, 2014).</td>
      <td>58</td>
    </tr>
    <tr>
      <td>Figure 15 Visualization of gradient descent minimization for the state x in 2D. J is a quadratic convex cost function. Its minimum is obtained x<sup>a</sup>. The image taken from, Bouttier and Courtier, ECMWF, 1999.</td>
      <td>59</td>
    </tr>
    <tr>
      <td>Figure 16 Scheme of the CIF</td>
      <td>64</td>
    </tr>
    <tr>
      <td>Figure 17 Illustration of simplified mass balance processes represented in each grid cell of a 3D CTM</td>
      <td>67</td>
    </tr>
    <tr>
      <td>Figure 18 Eastern China domain visualization</td>
      <td>70</td>
    </tr>
    <tr>
      <td>Figure 19 Main inputs and their sources for CTM CHIMERE simulations over Eastern China</td>
      <td>71</td>
    </tr>
    <tr>
      <td>Figure 20 European domain visualization.</td>
      <td>73</td>
    </tr>
    <tr>
      <td>Figure 21 Main inputs and their sources for CTM CHIMERE simulations over Europe.</td>
      <td>74</td>
    </tr>
    <tr>
      <td>Figure 22 Visualization and illustration of the Aura Spacecraft (images credit: Northrop Grumman Space Technology NGST)</td>
      <td>75</td>
    </tr>
    <tr>
      <td>Figure 23 OMI measurement geometry (Taken from Levelt et al., 2006).</td>
      <td>76</td>
    </tr>
    <tr>
      <td>Figure 24 Solar irradiance and the Earth's radiance spectrum measured by OMI over the Netherlands. The image taken from Levelt et al., 2006</td>
      <td>77</td>
    </tr>
    <tr>
      <td>Figure 25 TROPOMI measurement geometry (Taken from TROPOMI user's manual, 2019)</td>
      <td>79</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>Figure 26 Spatial resolution comparison of satellite instruments. Note that TROPOMI pixel size further decreased now (Taken from BIRA-IASB, www.aeronomie.be/en/news/2021/three-years-tropomi-measurements)</td>
      <td>80</td>
    </tr>
    <tr>
      <td>Figure 27 OMI (left) and TROPOMI (right) NO<sub>2</sub> tropospheric column comparison for 17/04/2018 (Taken from Lorente et al., 2019)</td>
      <td>80</td>
    </tr>
    <tr>
      <td>Figure 28 Spectral Coverage of TROPOMI (Image credits: ESA)</td>
      <td>81</td>
    </tr>
    <tr>
      <td>Figure 29 Example of a spectral analysis of a TROPOMI NO<sub>2</sub> measurement spectrum (black line is the best fit while red line is noise) (taken from Borger et al., 2020)</td>
      <td>81</td>
    </tr>
    <tr>
      <td>Figure 30 Spatial distribution of the CNEMC Network sites for Eastern China</td>
      <td>83</td>
    </tr>
    <tr>
      <td>Figure 31 Correction factor examples winter (left) vs summer (right) for 1 day</td>
      <td>85</td>
    </tr>
    <tr>
      <td>Figure 32 Spatial distribution of the EEA sites for Europe (the image is produced in https://www.eea.europa.eu/data-and-maps/explore-interactive-maps/up-to-date-air-quality-data, accessed on 30/03/2023)</td>
      <td>86</td>
    </tr>
    <tr>
      <td>Figure 33 OMI tropospheric column for the reference day (08/02/2020)</td>
      <td>87</td>
    </tr>
    <tr>
      <td>Figure 34 NO<sub>x</sub> emission corrections obtained by Test A (left), Test E (middle), Test F (right). Note that, the corrections are the same.</td>
      <td>90</td>
    </tr>
    <tr>
      <td>Figure 35 Increments according to the different errors in prior NO<sub>x</sub> emissions (From left to bottom left, test A and tests J to M, respectively) (differences&lt;1% is neglected).</td>
      <td>92</td>
    </tr>
    <tr>
      <td>Figure 36 Anthropogenic NO<sub>x</sub> emissions increments (in %) provided by inversions test from left to right; with no correlation (Test H), sigma=50 (Test A, reference test) and sigma=100 (Test G), respectively (differences&lt;1% is neglected).</td>
      <td>93</td>
    </tr>
    <tr>
      <td>Figure 37 Increments according to the 100% (Test N, left) and 200% (Test O, right) errors in biogenic NO<sub>x</sub> emissions (differences&lt;1e-5% is neglected).</td>
      <td>95</td>
    </tr>
    <tr>
      <td>Figure 38 Increments using 100% biogenic error emissions in a winter day (Test N, left) and in a summer day (Test P, right) (differences&lt;1e-5% is neglected).</td>
      <td>95</td>
    </tr>
    <tr>
      <td>Figure 39 Schematic view of the atmospheric inversion and evaluation.</td>
      <td>101</td>
    </tr>
    <tr>
      <td>Figure 40 Study domain. Selected locations presenting the most urbanized and industrialized regions (see section 3.3.3) are indicated by the rectangles.</td>
      <td>105</td>
    </tr>
    <tr>
      <td>Figure 41 Monthly Corrections of NO<sub>x</sub> emissions for August 2015</td>
      <td>106</td>
    </tr>
    <tr>
      <td>Figure 42 Spatial distribution of annual mean surface NO<sub>2</sub> concentrations: (a) Stations; (b) CHIMERE using prior emissions (Conc_Prior15); (c) CHIMERE using MEIC emissions (Conc_MEIC); (d) Mean bias calculated by the mean differences between Conc_Prior15 and stations for 2015</td>
      <td>110</td>
    </tr>
    <tr>
      <td>Figure 43 Spatial distribution of annual mean surface NO<sub>2</sub> concentrations: (a) Stations; (b) CHIMERE using prior emissions (Conc_Prior19); (c) Mean bias calculated by the mean differences between Conc_Prior19 and stations for 2019</td>
      <td>111</td>
    </tr>
    <tr>
      <td>Figure 44 Ratios of the Conc_Prior19 and Conc Posts statistical indicators: Correlation Coefficient, Mean Bias and RMSE, respectively (a-c), for 2019.</td>
      <td>112</td>
    </tr>
    <tr>
      <td>Figure 45 Monthly averaged NO<sub>2</sub> surface concentrations from stations and simulations for Wuhan in (top) 2015 and, (bottom) 2019</td>
      <td>113</td>
    </tr>
    <tr>
      <td>Figure 46 (Left) Ground-Based Stations according to the selected locations, (Right) HTAP v2.2 NO<sub>x</sub> Emissions after applying the 60kt threshold (2010) to determine the selection of the locations. The remaining 0.5° × 0.5° grid cells correspond to the selected location.</td>
      <td>114</td>
    </tr>
    <tr>
      <td>Figure 47 (a) NO<sub>x</sub> emissions at 0.5° × 0.5° resolution for 2010 from the HTAP v2.2 inventory in kt; Relative differences of NO<sub>x</sub> emissions for between 2010 and (b) 2015 and (c) 2019, respectively</td>
      <td>115</td>
    </tr>
    <tr>
      <td>Figure 48 Relative differences between Emis Posts and Emis Posts NO<sub>x</sub> emissions</td>
      <td>116</td>
    </tr>
    <tr>
      <td>Figure 49 NO<sub>x</sub> monthly budget comparisons at the selected locations</td>
      <td>119</td>
    </tr>
    <tr>
      <td>Figure 50 April 2020 and 2019 average NO<sub>2</sub> tropospheric column differences seen by TROPOMI (presented in EUMETSAT virtual conference in 2021)</td>
      <td>124</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>Figure 51 Comparison of NO<sub>2</sub> columns from OMI (QA4ECV) and TROPOMI (v1.3) and their coverage for the 01/04/2020</td>
      <td>125</td>
    </tr>
    <tr>
      <td>Figure 52 NO<sub>x</sub> emission increments obtained by inversions using TROPOMI (left) and OMI (right) observations for 01/04/2020</td>
      <td>126</td>
    </tr>
    <tr>
      <td>Figure 53 Comparison of the hourly NO<sub>2</sub> concentrations simulated with CHIMERE using prior and estimated emissions and observations at the Parisian background urban station</td>
      <td>127</td>
    </tr>
    <tr>
      <td>Figure 54 Comparison of averaged TROPOMI tropospheric columns in December 2019 for the v1.3 (left) and PAL v2.3 (middle), absolute differences (right). (The figure is taken from Pseftogkas et al., 2022)</td>
      <td>128</td>
    </tr>
    <tr>
      <td>Figure 55 Comparison of NO<sub>x</sub> emission corrections in % by performing inversion with the emissions in linear scale (left) and log scale (right) for the day 23/05/2019</td>
      <td>130</td>
    </tr>
    <tr>
      <td>Figure 56 Distribution of total NO<sub>x</sub> emissions for the week of 1-7 April from a prior inventory</td>
      <td>131</td>
    </tr>
    <tr>
      <td>Figure 57 Increment in NO<sub>x</sub> emissions (in %) for the week of 1-7 April</td>
      <td>132</td>
    </tr>
    <tr>
      <td>Figure 58 Day by day evolution of TROPOMI NO<sub>2</sub> columns (above figures are from the 1st to 3rd, below figures are from the 4th to 6th, and rightmost figure is for the 7th of April)</td>
      <td>133</td>
    </tr>
    <tr>
      <td>Figure 59 Daily variation of NO<sub>x</sub> emission corrections from 1<sup>st</sup> to 7<sup>th</sup> of April 2020</td>
      <td>133</td>
    </tr>
    <tr>
      <td>Figure 60 Weekly mean of NO<sub>2</sub> surface concentrations from stations (left), and prior (middle) and posterior simulations (right)</td>
      <td>134</td>
    </tr>
    <tr>
      <td>Figure 61 Differences between prior simulations and stations (left) and between posterior simulations and stations (right)</td>
      <td>135</td>
    </tr>
    <tr>
      <td>Figure 62 Ratios of the statistical indicators: correlation coefficient (left), mean bias (middle) and RMSE (right) of posterior and prior per station. (To recall, correlation ratios bigger than one and bias and RMSE ratios smaller than one meant to be an “improvement”)</td>
      <td>136</td>
    </tr>
    <tr>
      <td>Figure 63 Ratios of the statistical indicators (correlation coefficient (left), bias (middle), RMSE (right)) for rural type of stations</td>
      <td>136</td>
    </tr>
    <tr>
      <td>Figure 64 Ratios of the statistical indicators (correlation coefficient (left), bias (middle), RMSE (right)) for urban type of stations</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Figure 65 TROPOMI NO<sub>2</sub> observations for 1<sup>st</sup> of April in 2019 (left) and in 2020 (right)</td>
      <td>138</td>
    </tr>
    <tr>
      <td>Figure 66 Increments in NO<sub>x</sub> emissions for 01/04/2019 (left), 02/04/2019 (right)</td>
      <td>139</td>
    </tr>
    <tr>
      <td>Figure 67 Differences between two estimated emissions for 2020 and 2019 for the days 1st (left) and 2nd (right) of April</td>
      <td>139</td>
    </tr>
    <tr>
      <td>Figure 68 Increments in NO<sub>x</sub> emissions over France for 01/04/2020</td>
      <td>141</td>
    </tr>
  </tbody>
</table>
# List of Tables

<table><tbody><tr><td>Table 1 Overview of global NO<sub>x</sub> emission budgets and their uncertainties in parenthesis for selected sources and sectors</td><td>36</td></tr><tr><td>Table 2 Inversion tests with changed optimization parameters for the day of 08-02-2020</td><td>90</td></tr><tr><td>Table 3 Inversions tests with different errors in anthropogenic NO<sub>x</sub> emissions for the day of 08-02-2020</td><td>91</td></tr><tr><td>Table 4. Inversions tests with different spatial correlations for the day of 08-02-2020</td><td>93</td></tr><tr><td>Table 5 Inversions tests with different errors in biogenic NO<sub>x</sub> emissions for two days 08-02-2020 and 28-08-2019</td><td>94</td></tr><tr><td>Table 6 Summary of the inversions and simulations performed in this study. The output column gives the short names, which will be used in the following</td><td>106</td></tr><tr><td>Table 7 Annual statistics for the comparison between simulated and measured NO<sub>2</sub> hourly surface concentrations for 2015 and 2019. Mean = Annual Mean, SD = Standard Deviation (SD), RMSE = Root Mean Square Error are in µg/m<sup>3</sup>. r = Pearson correlation coefficient. NMB = normalized mean bias in % (Formulas used here are given in the Annexes A and D), (SDs are calculated using annual means of the concentrations)</td><td>111</td></tr><tr><td>Table 8 The annual NO<sub>x</sub> emission budget (in Tg) over East China and the entire domain in the Figure 40 with respect to different inventories</td><td>115</td></tr><tr><td>Table 9 Definition of the locations and their annual NO<sub>x</sub> budgets concerning the different emission inventories and years</td><td>117</td></tr><tr><td>Table 10 Relative Differences of annual NO<sub>x</sub> emission budgets at the 15 selected locations</td><td>118</td></tr><tr><td>Table 11 Prior and Estimated NO<sub>x</sub> emission budgets by some countries for the week of April 1-7, 2020, ordered from the highest to lowest difference in budget change</td><td>132</td></tr><tr><td>Table 12 Statistics for the comparison between simulated and measured NO<sub>2</sub> hourly surface concentrations for 1-7 April 2020. Mean = annual mean, SD = standard deviation, RMSE = root mean square error are in µg/m<sup>3</sup>. r = Pearson correlation coefficient. NMB = normalized mean bias in % (Formulas used here are given in the Annexes A and D)</td><td>135</td></tr></tbody></table>