This study uses four satellite XCO2 Level 2 (L2) data products. An overview about these data sets is provided in Table 1. The first product listed in Table 1 is the latest version of the bias-corrected OCO-2 XCO2 product delivered to the Goddard Earth Science Data and Information Services Center (GES DISC) by the OCO-2 team (ACOS v10r Lite). The other three satellite XCO2 data sets are different versions of the GOSAT XCO2 product derived using retrieval algorithms developed by groups at the University of Leicester, UK (UoL-FP v7.3); the SRON Netherlands Institute for Space Research (RemoTeC v2.3.8); and the University of Bremen, Germany (FOCAL v1.0).

The XCO2 estimates derived from OCO-2 (e.g. O'Dell et al., 2018) and GOSAT (e.g. Kuze et al., 2016) observations are complementary because these two spacecraft use different sampling strategies. OCO-2 has been operating since September 2014. Its spectrometers collect about 85 000 cloud-free XCO2 soundings each day along a narrow (< 10 km) ground track as it orbits the Earth 14.5 times each day from its sun-synchronous 13:36 (local time) orbit. The OCO-2 soundings provide continuous measurements with relatively high spatial resolution (1.3 × 2.3 km2) along each track, but the individual ground tracks are separated by almost 25∘ longitudes in any given day. This spacing is reduced to approximately 1.5∘ longitude after a 16 d ground track repeat cycle. GOSAT has been returning 300 to 1000 cloud-free XCO2 soundings each day since April 2009. Its TANSO-FTS spectrometer collects soundings with 10.5 km diameter surface footprints, separated by approximately 250 km along and across its ground track at it orbits from north to south across the sunlit hemisphere.

We use data from NOAA's (National Oceanic and Atmospheric Administration) CO2 assimilation system, CarbonTracker (CT2019) (Jacobson et al., 2020; Peters et al., 2007), to define the relationship between XCO2 anomalies and fossil fuel emissions. CarbonTracker is a global atmospheric inverse model that assimilates atmospheric CO2 measurements to produce modelled fields of atmospheric CO2 mole fractions by adjusting land biosphere and ocean CO2 surface fluxes. An overview about CT2019 set is provided in Table 2, including references and access information. In short, CarbonTracker has a representation of atmospheric transport based on weather forecasts, as well as modules representing air–sea exchange of CO2, photosynthesis and respiration by the terrestrial biosphere, and release of CO2 to the atmosphere by fires and combustion of fossil fuels.

Satellite XCO2 retrievals contain information on anthropogenic CO2 emissions (e.g. Schneising et al., 2013; Reuter et al., 2014b, 2019; Nassar et al., 2017), but extracting this information requires appropriate data processing and analysis. For a strong (net) source region XCO2 is typically higher compared to its surrounding area. Our method is based on computing and subtracting XCO2 background values. The purpose of this background correction is to isolate the regional emission signal by removing large-scale spatial and day-to-day temporal XCO2 variations, which cannot be dealt with in our simple data-driven method to estimate emissions.

XCO2 varies temporally and spatially (e.g. Agustí-Panareda et al., 2019; Reuter et al., 2020; Gier et al., 2020), for example, due to quasi-regular uptake and release of CO2 by the terrestrial biosphere, which results in a strong seasonal cycle, especially over northern mid- and high latitudes. Compared to fluctuations originating from the interaction of the terrestrial biosphere and the atmosphere, the spatio-temporal XCO2 variations due to anthropogenic fossil fuel (FF) CO2 emissions are typically much smaller (e.g. 1 ppm compared to 10 ppm; Schneising et al., 2008, 2013, 2014; Agustí-Panareda et al., 2019).

A method used for background correction is the one described in Hakkarainen et al. (2019; see also Hakkarainen et al., 2016, for a first publication of that method). We use two different methods for background correction. We refer to these methods as “daily anomalies via (latitude band) medians” (DAM), which is essentially identical with the method described in Hakkarainen et al. (2019), and “target minus surrounding” (TmS).

Hakkarainen et al. (2019) applied their method to the OCO-2 Level 2 XCO2 data product to filter out trends and seasonal variations in order to isolate CO2 source/sink signals. For background correction, Hakkarainen et al. (2019) calculate daily medians for 10∘ latitude bands and linearly interpolate the resulting values to each OCO-2 data point. Instead of interpolation, we compute the median around each latitude (running median) using a latitude band width of ±15∘. We use a larger width compared to Hakkarainen et al. (2019), as we also apply our method to GOSAT data, which are much sparser than OCO-2 data. Our investigations showed that the width of the latitude band is not critical. The band needs to be wide enough to contain a statistically significant sample but narrow enough to resolve large latitudinal gradients in CO2. We subtract the corresponding median from each single XCO2 observation in the original Level 2 XCO2 data product files to obtain a data set of XCO2 anomalies, ΔXCO2DAM.

In order to verify that our results do not critically depend on the details of one method, we also use the second TmS method. Here we obtain the background by averaging XCO2 in a region surrounding the target region (see Table 3 for the latitude and longitude corner coordinates of the target and its surrounding region).

We call these background-corrected XCO2 retrievals XCO2 anomalies, and satellite-derived maps and time series of these XCO2 anomalies are presented and discussed in Sect. 4.1. These XCO2 anomalies are then used to compute East China FF CO2 emission estimates, CO2FF, as described in the following subsection.

To determine whether satellite XCO2 retrievals can provide information on relative changes of anthropogenic CO2 emissions for the East China target region, we must establish a relationship between the XCO2 anomalies (see Sect. 3.1) and the desired estimates of the target region fossil fuel (FF) emissions. To develop a method to convert the XCO2 anomalies, ΔXCO2, to FF emission estimates, CO2FF, we use an existing model data set, the CarbonTracker CT2019 data set described in Sect. 2.2, which contains atmospheric CO2 fields and corresponding CO2 surface fluxes during 2015–2018.

Figure 1 shows CT2019 XCO2 maps (left) and corresponding surface CO2 flux maps (right) for selected days in the January-to-May-2018 period. The XCO2 has been computed by vertically integrating the CT2019 CO2 vertical profiles (weighted with the surface pressure normalized pressure change over each layer). The model data are sampled at local noon, which is close to the overpass time of the satellite data sets used here. The spatio-temporal sampling of a specific satellite XCO2 data product is not considered here; i.e. we use the CT2019 data set independent of any satellite data product apart for the sampling at local noon. As can be seen from Fig. 1, XCO2 is clearly elevated over the East China target region (red rectangle) relative to its surrounding region on 15 January 2018 (Fig. 1a) and on 15 March 2018 (Fig. 1c). On 15 May 2018 (Fig. 1e) the target region and parts of the surrounding region contain large areas of lower-than-average XCO2, a pattern which primarily results from carbon uptake by vegetation during the growing season, which starts in eastern China around May each year. The CO2 fluxes, which are shown on the right-hand side panels of Fig. 1, show similar spatial pattern as the XCO2 maps, but due to atmospheric transport and the long lifetime of atmospheric CO2 there is no one-to-one correspondence between atmospheric XCO2 and surface emissions. The CO2 fluxes are the sum of several contributing fluxes including FF emissions, biogenic fluxes and other fluxes (fires, oceans).

Figure 2a shows time series obtained by applying the DAM method to CT2019 XCO2 for the East China target region. The CT2019 data set not only contains atmospheric CO2 concentrations but also its components due to fossil fuel (FF) emissions and biogenic (BIO) and other fluxes. From the CT2019 data set we computed total XCO2 (TOT) and its FF and BIO components. From these components we subtracted the background using the DAM method, and the corresponding monthly ΔXCO2DAM time series are shown in Fig. 2a. As can be seen from Fig. 2a, total ΔXCO2DAM (black line) is dominated by its FF (red line) and BIO (green line) components (their sum, i.e. FF + BIO (grey line), is close to TOT (black line)). As can also be seen, FF emissions for East China (red line) are larger than the BIO fluxes (green line) at least during October to April. During May to September the BIO fluxes are negative due to uptake of atmospheric CO2 by the terrestrial biosphere, and their absolute value is on the same order or may even significantly exceed the FF emissions. As a consequence, total ΔXCO2DAM (black line) gets negative. During these months, the total anomaly (black line) is closer to BIO (green line) than to FF (red line).

The task for the satellite inversion is to obtain estimates of East China FF CO2 emissions from the satellite-derived (total) XCO2 anomalies, ΔXCO2DAM (black line in Fig. 2a). To determine to what extent this is possible, we fitted CT2019 ΔXCO2DAM (i.e. the quantity that we can also obtain from satellites) to the East China CT2019 FF CO2 emissions (which are the known true emissions in this model data assessment exercise). The results are shown in Fig. 2b for October-to-May periods. The estimated emissions (black crosses) have been obtained via a linear fit of ΔXCO2DAM to the CT2019 FF emissions (red dots). The two parameters of the linear fit are also shown in Fig. 2b: scaling factor A (= 0.90) and offset B (= 7.41). As can be seen, the estimated emissions agree reasonably well with the true emissions. The linear correlation coefficient R is 0.83 (see Fig. 2c), and the relative difference in terms of mean and standard deviation is 0.2 % ± 5 % (see Fig. 2d). However, for individual months the error can be as large as 10 %. From this we conclude that the (approximately 2σ) uncertainty of our method is approximately 10 %.

A similar figure but generated using the TmS method is shown in Appendix A as Fig. A1. As can be seen, the results shown in Fig. A1b to d are similar to the ones shown in Fig. 2b to d, but the linear correlation is slightly worse and the errors are slightly larger. In contrast, the time series shown in panel (a) differ significantly. This is because of the different background corrections used for the two methods. But despite these significant differences the quality of the derived emissions is similar (the standard deviation of the monthly biases is 5.5 % for TmS and 4.8 % for DAM; see panel d). Nevertheless, the DAM method gives slightly better results compared to the TmS method, and this is also confirmed by applying both methods to the satellite data (see Sect. 4). Therefore, the DAM method is our baseline method, and we focus on results obtained with the DAM method.

It is perhaps surprising that the offset (fit parameter B; see above) is so large (7.41 for DAM and 7.63 for TmS). Probably one would assume that the XCO2 anomalies ΔXCO2 are directly proportional to the target region fossil fuel emissions, i.e. one would assume that FF is (approximately) equal to a constant multiplied by ΔXCO2 (no offset added) (for example, for FF = 8 Gt CO2 yr-1 and ΔXCO2 = 2 ppm one would have expected that the conversion factor is 4 Gt CO2 yr-1 ppm-1). In that case, as we are only interested in relative changes in emissions, we would not need to know the exact value of the scaling factor. However, when analysing the satellite data, we found that ΔXCO2 is around 2 ppm for January but decreases in subsequent months, nearly approaching zero in May (which is consistent with the CT2019 results shown in Fig. 2a). As anthropogenic emissions are not expected to change that much within a few months (and zero emissions around May are not realistic at all), we concluded that the simple proportionality assumption does not hold. To investigate this we used the CT2019 data set to test and improve our method, and the results are reported in this section. We applied our method to CT2019 XCO2 (as shown in Fig. 2) and compared the retrieved FF values with the (true) CT2019 FF values. We found large differences, which could be significantly reduced by adding an offset to the linear fit as discussed above. The reason for the large offset is the influence of the biosphere. Around May the uptake of atmospheric CO2 due to the biosphere is so large that ΔXCO2 is close to zero – but the FF emissions are not – and the East China target region is essentially carbon neutral or even a net sink (see also Fig. 1).

As explained, scaling factor A and offset B are obtained empirically via a linear fit using CT2019 data (Fig. 2b) and used for the conversion of the satellite XCO2 anomalies during the entire time period January 2015 to May 2020 (as will be shown in Sect. 4). As can be seen from Fig. 2b and c, the retrieval biases are within ±10 % during 2015–2018. We assume in our study that the same conversion is also appropriate for 2019 and 2020. However, it cannot be ruled out that 2019 or 2020 were significantly different compared to previous years with respect to aspects relevant for our study. To address this, we compare the period October 2019 to May 2020 results with the corresponding results from previous October-to-December periods to find out to what extent the period of interest, i.e. October 2019 to May 2020, is significantly different, taking into account the year-to-year variability, which we use to obtain uncertainty estimates.

The methods described in this section have been applied to convert satellite-derived target region XCO2 anomalies, ΔXCO2, into estimated target region FF CO2 emissions, CO2FF. How this has been done using the DAM method for background correction is explained in the following Sect. 4, where we refer for the corresponding TmS method results to Appendix A.

The DAM method has been applied to the OCO-2 and GOSAT satellite XCO2 data products listed in Table 1. Figure 3 shows a global OCO-2 DAM XCO2 anomaly map at 1∘ × 1∘ resolution for the period 2015–2019. A similar map is shown in Hakkarainen et al. (2019; see their Fig. 3, top panel). The degree of agreement confirms the finding reported in Sect. 3.1 that the generation of these anomaly maps does not critically depend on how exactly the median is computed and used to subtract the background. Hakkarainen et al. (2019) discuss their OCO-2-derived maps in quite some detail also in terms of seasonal averages and comparisons with model simulations. They show that positive anomalies correspond to fossil fuel combustion over major industrial areas including China. Their seasonal maps (see their Fig. 4) show a strong positive anomaly over East China (similar to that shown here in Fig. 3) except for the June–August (JJA) summer season, where the XCO2 anomaly can be negative. This is consistent with the CT2019 results presented in Sect. 3.2.

A zoom into Fig. 3 is presented in Fig. 4, which shows more details for China and its surrounding area. As can be seen from Fig. 4, ΔXCO2DAM is positive especially in the region between Beijing, Wuhan and Hong Kong, with the highest values in the area between Beijing and Shanghai. This positive anomaly indicates that this region is a strong CO2 source region as also discussed in Hakkarainen et al. (2019). As already explained, there is no one-to-one correspondence (especially not for every grid cell) between local XCO2 anomalies and local CO2 emissions (or uptake) because the emitted CO2 is transported and mixed in the atmosphere. Furthermore, the satellite data are typically sparse due to strict quality filtering to avoid potential XCO2 biases, for example, due to the presence of clouds. Cloud-contaminated ground scenes are identified to the extent possible via the corresponding retrieval algorithm (see references listed in Table 1) and flagged to be bad and are therefore not used for this analysis. The sparseness of the satellite data set is obvious from Fig. 5, which shows OCO-2 DAM XCO2 anomaly maps for February during the 6 years 2015 to 2020.

A key difference between the OCO-2 and the GOSAT data products is the different sampling of the target region, with GOSAT having much sparser coverage compared to OCO-2. This is illustrated in Fig. 6, which shows February-to-March-2020 averages of the OCO-2 XCO2 data product (Fig. 6a) and the three GOSAT data products (Fig. 6b–d) at 1∘ × 1∘ resolution. The OCO-2 product shown in Fig. 6a is NASA's OCO-2 operational Atmospheric CO2 Observations from Space (ACOS) algorithm version 10r bias-corrected XCO2 product (the so-called Lite product), which is referred to in this publication via the product identifier (ID) CO2_OC2_ACOS. The three GOSAT XCO2 products are (see details and references as given in Table 1) the University of Leicester's GOSAT product (ID CO2_GOS_OCFP; Fig. 6b), SRON Netherlands Institute for Space Research GOSAT product (CO2_GOS_SRFP; Fig. 6c), and University of Bremen's GOSAT product (CO2_GOS_FOCA; Fig. 6d) as retrieved with the Fast atmOspheric traCe gAs retrievaL (FOCAL) retrieval algorithm initially developed for OCO-2 (Reuter et al., 2017a, b). As can be seen from Fig. 6, the spatial sampling of the target region is different for each product as only quality-filtered (i.e. good) data are shown and the quality filtering is algorithm specific (see references listed in Table 1).

Figure 6 also shows as red rectangle the East China target region as defined for this study (the geographical coordinates are listed in Table 3). The fossil fuel (FF) CO2 emissions of this target region are approximately 8 Gt CO2 yr-1; i.e. the selected target region covers approximately 80 % of the FF emissions of all of China, which are approximately 10 Gt CO2 yr-1 (Le Quéré et al., 2018; Friedlingstein et al., 2019). In the following section we present East China FF emission estimates as derived from the satellite XCO2 anomalies during and before the COVID-19 period.

Carbon dioxide fossil fuel emission estimates, CO2FF, have been derived from the XCO2 anomalies, ΔXCO2, computed for each of the four satellite XCO2 data products listed in Table 1. In this section the emission results are presented and discussed. We focus on results based on ΔXCO2 derived with the DAM method and refer to Appendix A for results based on the TmS method.