In the first half of 2020, most countries in the world have imposed stringent policies to slow down the spread of Coronavirus disease 2019 (COVID- 19) , closing businesses and factories, restricting travel, and issuing stay-at-home orders. Such lockdown measures have helped to curb the spread of the virus (1) and meanwhile caused large reductions in global demand for fossil fuels (2) . In turn, levels of nitrogen dioxide (NO2) and other air pollutants have also fallen across the globe (3) (4) (5) , and global carbon dioxide (CO2) emissions declined by an estimated 8.6%, based on indicators of energy use between January and April of 2020 as compared to the same period in 2019 (6) . If history is a guide, though, such reductions in air pollution and CO2 emissions could be temporary: global CO2 emissions have rebounded and resumed their former rates of growth after every financial crisis in the fossil fuel era (7, 8) . Indeed, economic activities are already increasing in many places, and governments and central banks have already passed or proposed large economic stimulus packages to spur recovery (9) without any climate mitigation co-objective.
Yet the COVID-19 pandemic has come at an important moment in the centuries-long timeline of fossil energy use, and for that reason as well as the pandemic's outsized disturbance to social and economic systems (10) , it may mark a turning point in the world's energy and economic structure-one with lasting influence on the trajectory of global CO2 emissions.
However, annual, country-level inventories of CO 2 emissions (11) are plainly insufficient to monitor variations in the sources and dynamics of CO 2 emissions during fast-evolving periods like the COVID-19 pandemic. Nor can such annual estimates support adaptive and agile climate and energy policies going forward, as countries and other jurisdictions seek to finetune such policies to achieve environmental goals in a rapidly evolving technological and economic context.
Increasing the frequency and resolution of data on CO2 emissions is thus a research priority.
Unfortunately, the data streams required to conduct continuous carbon monitoring with the high temporal and spatial resolution are yet very limited. Bottom-up approaches to estimate daily CO2 emissions at the country level using activity data and energy use indicators have recently emerged (6, 12, 13) , but gaining access to reliable daily statistics of sector-specific fossil fuel consumption is a challenge, and activity proxies such as traffic congestion indices and heating degree days must be used in those recent studies to empirically analyze the relative changes of emissions. Moreover, such bottom-up estimates lack independent validation. Near real-time observations from ground-and space-based platforms thus represent an attractive means of supplementing and validating bottom-up estimates with direct measurements (14) (15) (16) (17) (18) . However, CO2 concentrations are sparsely sampled in time and space, even for the carbon satellites (14, 15) , and natural variability in ecosystem carbon fluxes and atmospheric transport prevents unambiguous detection of fossil fuel CO2 emissions over time scales of weeks to months.
Moreover, the current generation of carbon monitoring satellites often returns significant errors in single soundings data (14, 15) . Satellite observations of NO2, a species co-emitted with CO2 during the combustion of fuels, have broader coverage than CO2 observations, especially from the recently launched TROPOspheric Monitoring Instrument (TROPOMI) onboard the Copernicus Sentinel-5 Precursor satellite (19) . Due to the relatively short lifetime in NOx, the satellite is capable of detecting the short-term variability in NO2 columns (3, 5) . Satellite NO2 columns have been widely used to retrieve the spatial patterns or temporal trends of NOx emissions (e.g., [20] [21] [22] [23] .
There are also attempts to infer CO2 emissions from satellite-based NO2 observations (24) (25) (26) , however, such a method requires good knowledge of CO2 to NOx emission ratios that are regiondependent, sector-specific, and dynamically changing (27) .
Here, we develop a novel approach to infer a ten-day moving average of anthropogenic (28) and near-real-time statistics and proxies in 2020. Based on the high-quality NO2 column observations from TROPOMI, we then separate the meteorological effects and model the local sensitivity of NO2 column to surface NOx emission changes (29) with the nested-grid GEOS-Chem chemical transport model (30) , to assess NOx emission changes in 2020 compared to those in 2019. Next, we use the top-down estimates to correct the sectoral distribution in the preliminary bottom-up emissions, based on the emission differences revealed by the grid cells dominated by a single source sector. Finally, the TROPOMIconstrained NOx emissions and the spatiotemporal heterogeneity of emission sectoral information are combined with the spatially-explicit, sector-specific ratio maps of CO2 to NOx emissions to infer ten-day moving average CO2 emissions from specific sectors. We use this integrated satellitebased emissions monitoring approach to track NOx and CO2 emissions in mainland China over the period from January to April 2020 as the coronavirus lockdown was imposed and relaxed. Figures 1B and 1D ) from January to April in 2019 and 2020. The 2019 emissions are directly derived from the MEIC inventory, which is also the base for estimating the NOx and CO2 emissions in 2020 constrained by TROPOMI observations. The 2019 emissions data show a reduction in the daily NOx and CO2 by 30% and 38%, respectively, from 1st January to the Chinese New Year 2019 (5th February) and a rebound in emissions twenty days later when the holiday ended and people returned to work. The larger decrease in CO2 than in NOx is because the major driver of emissions decrease is the reduced activities in the power and industry sectors (where emissions ratios of CO2 to NOx are large), while transport emissions (with low CO2 to NOx emission ratios) decreased much less because travel demand was still high during the holiday.
The 2020 daily emissions constrained by TROPOMI observations, however, show much faster decreases than those in 2019. During the period from 1st January to the Chinese New Year 2020 (25th January), NOx and CO2 emissions are estimated to have dropped by 58% and 51%, respectively. The larger decrease in NOx emissions than in CO2 is due to a much larger decline in the transport emissions than power and industrial emissions during the COVID-19 lockdown as we will show in the following analysis. The daily emissions of NOx and CO2 in 2020 are estimated up to be 50% and 40%, respectively, lower than those in 2019, and they did not return to the preholiday levels until two months later.
The divergence of the daily emissions between 2020 and 2019 corresponds to the timeline of the virus control measures. The sharper emission declines in 2020 started on 20th January 2020, when the most stringent control measures were activated by the National Health Commission. The Wuhan lockdown began three days later on 23rd January 2020, which was followed by similar measures in the other Chinese cities within the next few days. These lockdown measures did not ease until about one month later when the lowest-risk regions and cities slowly reopened some of the less exposed industries and businesses. About two months after the Chinese New Year 2020, most of China's cities had lifted the control measures including Wuhan that reopened on 8th April after a 76-day lockdown. During the Wuhan lockdown period (grey shades in Figure 1 ), China's emissions were lower than the 2019 emissions by a cumulative of 892 kt NOx (21.9% net reduction, green shades in Figure 1 ) and 348 Mt CO2 (16.2% net reduction, blue shades in Figure 1 ). 6 The total reduction in China's CO2 emissions over January-April 2020 is equivalent to a −11.5% decrease over the corresponding period of 2019, a bit higher than the estimate of −7.8% (−3.6% to −12.9%) from (6) . The largest emission reductions occurred in February, while the emissions rapidly rebouned in March and April (Table S1) , and the CO2 emissions in April 2020 is estimated +2.7% higher than that in 2019. The emission reductions over January-March 2020 are −15.6% compared to the the same period of 2019, which is higher than the the bottom-up estimate of −10.3% from (13) . Overall, our TROPOMI-constrained emission estimates present larger emission reductions during January-April than the bottom-up estimates (6, 13) .
We also used the bottom-up approach (see Methods) to estimate daily NOx and CO2 emissions in 2020 (dashed curves in Figures 2A and 2B) , which are broadly comparable to the TROPOMI constrained inversions but still reveal large discrepancies. The differences in the NOx emissions mainly occur over the regions dominated by the emissions from transport (blue curve in Figure 2C ) and industry (yellow curve in Figure 2C ), while the power sector also contributes to the discrepancy in the CO2 emissions (red curve in Figure 2D ). The bottom-up inventory tends to overestimate industrial and transport emissions during the lockdown period, especially at the beginning of lockdown, while tends to underestimate emissions for the power sector when lockdown gradually lifted in March. Since the complete statistics of daily fuel combustion are not available for the bottom-up inventory (see Methods), which relies instead on the daily data for 12% of China's power plants and some proxies such as the daily traffic congestion indices and monthly industrial Gross Domestic Product (GDP) combined with the daily coal use in the power sector to represent the relative changes of daily emissions, which is inevitably associated with uncertainties.
We decompose the difference in the ten-day moving average of CO2 emissions between 2020 and 2019 into power, industry, transport, and residential sectors ( Figures 3A and 3B ). The industry sector was the major driver of the CO2 emissions changes. During the Wuhan lockdown period (grey shades in Figure 3 ), the cumulative CO2 emissions from the industry sector declined by 24.3% compared to those in 2019, accounting for 72% of the total reduction in CO2 emissions for that period. The transport and power sectors are estimated to have experienced cumulative CO2 emissions reductions by 31.1% and 5.0%, respectively, contributing 18% and 10% of the total CO2 reduction. The emissions decline in the power sector was possibly driven by the lower demand by industry that consumes more than two-thirds of the total electricity in China. Residential emissions increased by 1%. The population-weighted heating degree day in 2020 winter was estimated 3% lower than that in 2019 due to the high air temperature, therefore the larger residential emissions in 2020 are mainly due to the more energy consumed when people were forced to stay at home, especially at the beginning of the lockdown period. After the lockdown measures lifted, the recovery of the industry and transport sectors rapidly pushed CO2 emissions back to pre-lockdown levels.
The regional decomposition ( Figure 3C and 3D) also confirms a CO2 emission dynamics that was dominated by industry. China's provinces were classified into three categories distinguished by its increasing share of industrial GDP in the provincial total GDP and the length of lockdown. The provinces dominated by the industrial economy were more sensitive to the lockdown measures, with both a deeper drop and a faster recovery in emissions. The CO2 emissions declined by 8.2% in the provinces where industrial GDP contributes less than 34%
(median value of all the provinces) of the provincial total GDP (pink bars in Figure 3C and 3D).
However, the emission decreases were more than twice higher in provinces where the share of industrial GDP is larger than 34%. The industrial provinces with a lockdown longer than 40 days (dark blue bars in Figures 3C and 3D) show comparable reductions of CO2 emissions (−20.2%) than those (−21.2%) with a shorter lockdown period (light blue bars in Figure 3C and 3D).
Half of China's provinces are estimated to have reduced their cumulative CO2 emissions by more than 15% from 23rd January 2020 to 7th April 2020 compared to the same period in 2019 ( Figures 4A and 4B ). Since the industrial sector was the major driver of this emission decline, provinces with larger shares of the industrial economy experienced more CO2 emission reductions than others ( Figure 4B ). The provinces of Jiangsu and Anhui that have the largest industrial economies both reduced their CO2 emissions by more than 30%. We also observe large CO2 reductions in the Hubei Province whose capital is Wuhan and in Beijing and Shanghai, significantly higher than the other provinces with similar economic structures due to the stringent virus control measures in these provinces. It should also be noted that the CO2 emissions from Guangxi Province located in the southwest of China are estimated to have increased by 5% during the lockdown period. This is because the generation of hydroelectric power from Jan to March in 2020 was 27% lower than that in 2019 due to the severe drought in this region, which has caused an increase in the generation of thermal power by 16% (http://www.stats.gov.cn/). The droughtinduced increased fossil fuel use in power plants offset the emissions decrease due to lockdown.
With China's industry slowly recovering from the coronavirus, CO2 emissions from most of China's eastern provinces have returned to their pre-COVID-19 levels by April 2020, which are higher than the emissions in the same period of 2019 ( Figures 4C and 4D ). The provinces whose economy is dominated by industry restarted emissions rapidly, mirroring their larger drop during the lockdown. The provinces that had experienced stringent lockdown did not rebound their CO2 emissions significantly, such as Hubei, Hebei, and Tianjin, although these provinces were dominated by the industrial economy. These provinces stayed at the highest emergency response levels against the coronavirus for more than 90 days. The emissions from Beijing and Shanghai were 17% and 22%, respectively, lower than that in 2019 at this period, which exhibited comparable and even larger reductions in CO2 emissions compared to the previous two months.
The Guangxi province, still suffering from the drought in April 2020, increased CO2 emissions by 29% compared to those in 2019, corresponding to the 30% increase in thermal power generation.
This study presents the first-ever estimates of the ten-day moving average CO2 emissions from satellite observations, derived from the near real-time and high spatial-temporal resolution NO2 retrievals from TROPOMI, state-of-the-art chemical transport model GEOS-Chem, and CO2
to NOx source emission ratios from a detailed inventory of Chinese emissions, MEIC. The substantial short-term variability in emissions due to the COVID-19 lockdown creates an unmistakable signal despite known model uncertainties and satellite observation errors, providing a unique opportunity to develop and validate satellite-based carbon emissions monitoring.
The uncertainties in our results lie in satellite observations of NO2 column densities, determination of the NO2 column response to surface NOx emission changes by the GEOS-Chem model, differentiating sectoral NOx emissions from satellite-constrained estimates, as well as CO2
to NOx emission ratios. Using spatial-temporal average and the relative difference of TROPOMI data is expected to cancel a major part of the systematic errors in satellite observations. The robustness of the response factor between NO2 column and anthropogenic NOx emissions is proved by a series of sensitivity runs of the GEOS-Chem model. Corrections on sectoral emissions are also tested through different definitions of the grid-cell dominant source sector and the inversion results of ten-day mean CO2 emissions are found to be stable (Fig. S12 ). The influence of CO2 to NOx ratios on the estimates of CO2 relative reductions from the 2019 MEIC data to the 2020 inversions is marginal as we use the consistent sector-specific ratio maps with MEIC. The robustness of our estimates could also be demonstrated by the broad consistency of our estimates with previous studies (6, 13) and with independent economic and industrial statistics data collected on the monthly scales (Fig. S14 ). More details about the uncertainty analysis could be found in 
The authors acknowledge the free use of tropospheric NO2 column data from the TROPOMI sensor from www.temis.nl. Funding: This work was supported by the National Natural Science 
Figures S1-S14 Table S1 References (1-33) The emissions difference is split into power, industry, residential, and transport sectors in (A), and split into three regional categories in (C), including 1) the provinces with the share of industrial GDP in provincial total 5 GDP lower than 34%, 2) the provinces with a share of industrial GDP higher than 34% and a lockdown shorter than 40 days, and 3) the provinces with the industrial GDP share higher than 34% and a lockdown longer than 40 days. The cumulative CO2 emissions during Wuhan lockdown (grey shades in (A) and (C)) are presented by source sector in (B) and by source region in (D). 
Materials and Methods Figs. S1 to S14 Table S1 Integrated modeling framework
This work integrates a detailed bottom-up inventory, high-quality spaceborne constraints, and a chemical transport model to estimate 10-day mean dynamic changes in China's NOx and CO2 emissions from January to April in 2020, as depicted in Figure S1 . has an accurate representation of emission spatial distributions (11, 12) and emission annual trends (13, 14) , evaluated by satellite observations.
The MEIC model uses monthly and daily temporal profiles including electricity generation, industry factory operating rate, traffic volume index, and heating degree day to disaggregate the annual emission estimates to daily emissions. The daily sectoral NOx emissions from January to April in 2019 are shown in Figure S2a . to be made to make the emission estimates in 2020 possible. First, the statistics data for January and February were combined together, so we assume that the activity changes in these two months are the same. Second, the growth rate in the electricity generation is only available for all of the thermal electricity, which includes coal-, oil-, and natural gas-fired electricity that cannot be further split. We assume that the activity data of all of the thermal power plants (Fig. S3a) , which causes uncertainties in the daily emission estimates of the industry sector. The monthly emissions from the residential and transport sectors of each city are split into daily emissions based on the daily variation of the population-weighted HDD (Fig. S4 ) and the Baidu index (Fig. S5) in each city.
Relative changes in NO2 TVCDs between 2019 and 2020 from TROPOMI (19) . Only pixels with quality assurance value above 0.5 and cloud fraction below 30% are kept to reduce the retrieval errors.
NO2 measurements are then aggregated to a spatial resolution of 0.5° × 0.625° to match the grid of GEOS-Chem ( Fig. S6a and S6b) . During the first four months of 2020, the satellite NO2
TVCDs decreased in most places over China, especially in Wuhan and the surrounding area Figure S7 shows the distribution of the valid sample days in each grid cell for each 10-day period. Note that grid cells dominated by natural sources (defined as NO2 TVCDs below 1×10 15 molec/cm 2 in this study), which are more than half of all grid cells in China, are excluded in the following analysis because we mainly focus on anthropogenic emissions (22) .
In the remaining valid grid cells, the average share of grid cells with more than 5 valid sample days could reach 87%, and they cover 81% of national anthropogenic NOx emissions over China (Fig. S7c) , indicating that the 10-day moving average value used in this work are representative for the emission estimates over China. Southeast Asia at a spatial resolution of 0.5° × 0.625° (3, 4) , with boundary conditions adopted from a 2° × 2.5° global simulation. We use the "tropchem" mechanism that simulates full chemistry in the troposphere. Vertical mixing in the planetary boundary layer is simulated using a nonlocal mixing scheme (28) . (S1)
where subscript perturbed and base represent the perturbation scenario and the baseline, respectively and t represents each 10-day period. Ω , , ,2019 and Ω , , ,2019 are model simulated NO2 TVCDs on 10-day period t over grid cell i in 2019. ∆E is the 40% emission perturbation. , is a unitless factor that represents the local sensitivity of changes in NO2 columns to changes in NOx on 10-day period t in grid cell i. Figure S9a shows the spatial variation of four-month averaged β coincidently sampled with the TROPOMI data. Generally, β tends to be less than one in polluted regions such as the North China Plain, the Yangtze River Delta, and the Pearl River Delta, because an increase in NOx emissions consumes OH and increases the NOx lifetime. While in clean areas where an increase in NOx emissions decreases the NOx lifetime, β tends to be greater than one. Figure   S9b shows the 10-day moving average of national β over China. β is smaller in winter when the concentrations of OH and RO2 radicals are lower, and increases in spring, which reflects longer NOx lifetime in winter time.
Error in β is one of the sources of uncertainty in our overall approach. Therefore, sensitivity tests are conducted to test the robustness of β obtained from the model simulation.
Lamsal et al. (23) used the global GEOS-Chem model to perform several tests and proved the stability of β. For example, they find that a perturbation of 30% NOx emissions instead of 15% changes global averaged β by <2%. Increasing anthropogenic VOCs and CO by 15%
increases the global value of β by 2.8% and 1.0%, respectively. When NOx emissions are only perturbed for a single grid cell in Ohio, β in neighboring grids is affected by 2-6%, which indicates that β is barely influenced by the transport of NO2 from other grid cells at the resolution of 2° × 2.5°.
In this study, we use the nested-grid model with higher resolution than the global model used in Lamsal et al. (23) , which are believed to better resolve the nonlinear NOx chemistry and heterogeneous emission sources. However, β obtained from smaller grid cells might be more affected by the transport of NO2 from neighboring grids or background area, especially during winter time when the NO2 lifetime is longer. We therefore conduct a sensitivity test We also find that perturbing NOx emissions by 30% or 50% instead of 40% only changes β by -0.7% and 0.8%. We also conduct sensitivity scenarios with an additional 20% decrease in CO and a 40% decrease in VOCs, which increase β by 2.5% nationally. The results of the sensitivity tests show that the β value is quite robust. Here we emphasize again that we limit our calculations only to grid cells dominated by anthropogenic emission sources, which is defined as tropospheric NO2 columns above 1×10 15 molec/cm 2 .
Since the CO2 to NOx emission ratio depends on the source sector, it is important to know sectoral NOx emissions to convert TROPOMI-constrained NOx emissions to CO2 emissions.
Our bottom-up emission estimates in 2020 provide sectoral emissions at the daily scales, while the imperfect daily statistics data we used leave uncertainties in the sectoral emissions, which show discrepancies in total NOx emissions compared to the TROPOMI-constrained estimates (Fig. S10a) . Here, we use the TROPOMI-constrained NOx emissions to correct the biases in the sectoral emission distributions from the bottom-up inventory in 2020, which finally makes the bottom-up emissions data match top-down estimates (Fig. S10a ). Our method is described as follows. Next, we classify grid cells based on the dominant emission source sector in each grid cell. Before the COVID-19 lockdown (23rd January 2020), we assume that the dominant sector in each grid cell in 2020 is consistent with that in the same period of 2019. We calculate the average percentages of emissions from power, industry, residential, and transport sectors in each grid cell using the MEIC emissions in January 2019. The dominant emission source sector in each grid cell is defined as the source sector that accounts for more than 50% of emissions in that grid. Figure S11 shows the examples of the grid cells dominated by power, industry, and transport sectors, where the TROPOMI can observe large NO2 column enhancement at the locations of point sources and road networks. We also try the threshold values of 60%, 70%, and 80% to test the sensitivity, which will be discussed later. Then we calculate the differences in national emissions estimated for each source sector in 2020 (Fig. S10b) .
where t is the time before 23rd January 2020, s is the source sector (power, industry, residential, The corrections described above are made day by day for the period before 23rd January 2020. After 23rd January 2020, the lockdown has influenced the emissions from each source sector differently, therefore the method to determine the dominant emission source sector in each grid cell cannot be performed based on the 2019 emissions anymore. Therefore for each day, we use the corrected sectoral emission maps on its prior day before we identify the dominant source sector on that day. And using the same method described above to constrain sectoral emission maps for each day. We compare the ten-day moving average CO2 to NOx emission ratios between 2019 and 2020 for the whole country (Fig. S13) . The largest difference is that the CO2 to NOx emission ratio slightly decreased during the Spring Festival holiday in 2019 while increased over the same period in 2020. This is because the transport emissions decreased substantially during the Spring Festival holiday in 2020 due to the stringent lockdown measures. The CO2 to NOx emission ratios are much lower in the transport sector than the other sectors, so the average First, the satellite retrievals of NO2 TVCDs usually suffer from uncertainties in the radiative transfer model and in the ancillary data utilized for calculating the stratospheric NO2 background and the air mass factors. For example, the TROPOMI single-pixel errors are typically ~40-60% in winter time (32) . We use spatial and temporal averaging in our analysis to reduce the random errors. Meanwhile, TROPOMI NO2 is found to be systematically underestimated over China (33) , especially over polluted regions. However, relative differences between 2019 and 2020 are used to derive NOx emission changes, which could cancel out a major part of the systematic errors.
Second, the β value simulated by GEOS-Chem model reflects the feedback of NOx emissions on NOx chemistry, which could be affected by a lot of factors, such as the model representation of chemical and physical processes (e.g. transport and deposition), the model resolution, and changes in emissions of other species involved in the NOx chemistry. We evaluate the model simulation against satellite data to prove the model's ability to capture the characteristics of NO2 columns. We also conduct several sensitivity scenarios to show the robustness of β value, as discussed in previous sections. The variations of β when considering different perturbation magnitude of NOx emissions, influences from other species and different model resolutions are small and β is proved to be quite robust.
Third, since the CO2-to-NOx ratio is sector-specific, we need to capture the dynamic sectoral distribution of NOx emissions from Jan to Apr in 2020 for the conversion from CO2 to NOx. We use the TROPOMI-constrained NOx emissions to correct the sectoral emissions from the bottom-up estimates, based on the grid cells dominated by one single emission source, as discussed above. The thresholds used for the determination of dominant source sector in each grid could be the largest error source here. Sensitivity tests using threshold values from 0.5 to 0.8 obtain similar CO2 emission estimations (Fig. S12) , reflecting the robustness of our method.
Finally, the sector-specific CO2-to-NOx ratio maps we achieved from the MEIC emission model also include some uncertainties, which could influence the absolute magnitude of the CO2 emissions estimates. The uncertainties in NOx emission inventories are typically higher than those in CO2 emissions inventories, while the MEIC NOx inventory we used in this study has revealed a good performance when modeling with the GEOS-Chem model and comparing it to the TROPOMI NO2 column observations (Fig. S8) . Besides, the influence of the potential uncertainties in the CO2-to-NOx ratios on the estimates of CO2 emissions reductions from 2019 to 2020 is relatively marginal, because we use consistent sector-specific CO2-to-NOx ratio maps with the MEIC model and the comparison is also performed with the MEIC emissions.
We also compare the CO2 emissions estimated from the TROPOMI-constrained NOx emissions with the economic and industrial statistics data collected on the monthly scales (Fig.   S14 ). The relative changes in the 2020 CO2 emissions compared to those in 2019 are consistent with those indicators of the industry in China, which independently evaluate our estimates of the CO2 emission changes. 