Global to local impacts on atmospheric CO₂ from the COVID-19 lockdown, biosphere and weather variabilities

A back-of-the-envelope calculation goes as following. The current fossil fuel emissions rate is 10 GtC y⁻¹ (Gigatonne carbon per year), of which approximately half is taken up by carbon sinks on land and in the ocean, with the remaining half left in the atmosphere, resulting in a CO₂ increase of 2.5 ppm per year, as observed in a worldwide network of CO₂ observatories such as the renowned Mauna Loa station in Hawaii [7]. Assuming a 7% reduction or 0.7 GtC for the whole year of 2020 (high estimate of [2]), it would cause a 0.18 ppm less increase in global atmospheric CO₂ at the end of year 2020 relative to 'business-as-usual' as of 2019.

In reality, the emissions reduction did not occur synchronously in different regions, for example, China in February and Europe, the US and India in March–April (figure S1 available online at stacks.iop.org/ERL/17/015003/mmedia). The estimated reduction of 8% in January–April 2020 [1] corresponds to a decrease of 0.26 GtC, a rather small quantity for atmospheric CO₂. However, we expect the COVID signal to largely stay in the Northern Hemisphere (NH) for these few months because atmosphere inter-hemispheric transport takes approximately 1 year. We further assume that the carbon sinks have not started because of dormant winter vegetation and sluggish ocean-atmosphere gas exchange. We therefore expect a 0.25 ppm less increase of NH CO₂ at the end of April, assuming that: (a) 2.16 GtC emissions equal to 1 ppm increase in atmospheric CO₂; (b) the reduced emissions was majorly located at the NH; (c) and thus COVID anomaly is limited to the NH within the timescale of a few months (e.g. Spring 2020). This magnitude of change is within the capability of today's high-accuracy CO₂ analyzers, but small for carbon satellites such as NASA's OCO-2 and the Japanese GOSAT with targeted precisions of ∼1 ppm and their ground calibrations of 0.4 ppm [8–10].

Challenges also arise from the fact that besides fossil fuel emissions, atmospheric CO₂ is also strongly influenced by the changes in the biosphere and atmospheric transport in association with weather variability. The growth and decay of the northern vegetation causes a seasonal CO₂ amplitude of 6 ppm, while interannual climate variability, such as the El Niño Southern Oscillation (ENSO), causes biogenic CO₂ changes of 1–3 ppm [11–14]. Thus, a key question is whether a 0.25 ppm COVID signal can be seen among other (natural) variabilities. The purpose of this study is to investigate the atmospheric CO₂ signals resulting from COVID-19 among other natural signals. We explored this question with carbon cycle models and a suite of space-borne and ground-based observations.

We first created a high spatial-temporal resolution fossil fuel emissions (${F_{{\text{FE}}}}$) dataset with daily emissions data from a near real time (NRT) product (updated from Liu et al [1]; see section 4). The daily country-level data were disaggregated to model grid resolution based on the Open source Data Inventory of Anthropogenic CO₂ (ODIAC) emissions database [15]. As seen in figure 1(a) (detailed temporal evolution in supplementary information figures S1–S2), the carbon emissions intensity decreased by more than 5 gC m⁻² mo⁻¹ during February–April 2020 in East Asia, Europe, the US and India, relative to the same period in 2019. While consistent with the temporal variations in the original country-level data [1], the spatially disaggregated data show further emissions reductions concentrated in industrialized regions and areas with high population densities, such as the North China Plain, India's Ganges Basin, and the US Northeast and Midwest, as well as isolated centers such as Sao Paolo.

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For terrestrial biosphere-atmosphere flux (${F_{{\text{TA}}}}$), we used a dynamic vegetation and terrestrial carbon cycle model VEGAS [11, 16], while ocean-atmospheric flux came from a multi-model product (see section 4). The biospheric fluxes (figure 1(b)) have regional variations with magnitude often larger than the ${F_{{\text{FE}}}}$ reduction, driven by climate variability. Overall, the terrestrial biosphere had widespread negative anomalies that were particularly strong in the Southern Hemisphere and in April, largely in response to a strong Indian Ocean Dipole event in the circum-Indian Ocean regions [17] (figure S3). As a result, the spatial pattern of net flux ${F_{{\text{net}}}}$ was dominated by biospheric fluxes.

Because the COVID signal is expected to be confined in the NH (figure S4), we focus our CO₂ analysis on the NH region from the equator to 45° N (hereafter NH45). Although the biospheric fluxes dominated both spatial and temporal variability (figure 2(a)), which can be seen that F_TA is highly consistent with the F_net variabilities, and when summed up over NH45, the magnitude of the 2020 ${F_{{\text{FE}}}}$ anomaly is larger than that of ${F_{{\text{TA}}}}$ (figure 2(a)). This is because fossil fuel emissions were reduced almost everywhere during the COVID-19 lockdown, whereas the positive and negative anomalies in ${F_{{\text{TA}}}}$ tend to cancel each other out. Consequently, the total flux anomaly F_net reached nearly −200 MtC mo⁻¹ in April 2020.

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Subsequently, these fluxes were used as boundary conditions for the community GEOS-Chem atmospheric transport model for the period of January 2008–May 2020 (see section 4). The output of the model is a four-dimensional depiction of spatial-temporal evolution of atmospheric CO₂ that can be compared to various types of CO₂ observations, as well as the expected COVID impact (figures S4–S7). Using a method termed DCA (Detrending, Climatology and Anomaly; see section 4), in which a CO₂ time series is detrended to remove the low-frequency signal and de-seasonalized to remove the climatological seasonal cycle, we calculated sub-annual anomalies of column CO₂, as shown in figure 2(b). After a positive anomaly in January 2020, the CO₂ anomaly trended downward, and was 0.21 ppm lower than the long-term climatology in March 2020, and 0.14 ppm lower on average during February–April (figure 2(b) shaded period). This anomaly is the largest for the same season while March 2020 is the lowest month in the last 10 years.

Launched in 2009, has collected column CO₂ (XCO₂) data for over 10 years. The spatial pattern of February–April 2020 GOSAT anomalies (figure 1(d)) is similar to the model over India, southern Africa, South America and the central US where large negative values are wide-spread, although the overall spatial correlation is weak (figures 1(c) and (d)). Detailed monthly evolution shows similar broad patterns of agreement, as well as larger detailed differences (figures S8 vs. S9). The time series of CO₂ anomalies averaged over NH45 (figure 2(b)) shows reasonable agreement, mostly within GOSAT's uncertainty range (see section 4 and figure S10), with a correlation coefficient of 0.43. The differences may originate from two main sources: (a) the satellite's sparse spatial-temporal sampling, particularly at higher latitudes and cloudy regions; and (b) errors in atmospheric transport model and simulated biospheric fluxes. The drop during February–April 2020 discussed above is also clear in GOSAT, although the signal is at the border of being statistically significant (figure 3(d)).

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To better appreciate how unusual year 2020 was, we plotted the CO₂ seasonal cycle from May 2019 to April 2020 (called Year 2020) against those of the previous 10 years (figure 3). The CO₂ anomaly for the model is outside the standard deviation of the previous 10 individual years, while it is just at the border of being statistically significant for GOSAT, which has almost twice as high a variance; this finding is not surprising given its sparse spatial-temporal coverage. Even though the COVID signal is small, the model-data consistency in the above analysis supports using both model and satellite column CO₂ for short-term anomaly detection.

In addition to the NH, we also conducted similar analyses at global and regional scales of interest. For the larger region of 45° S–45° N (G4545), both the model and GOSAT show somewhat clearer negative anomalies in 2020 (figures S11 and S12). The more robust 45° S–45° N signal captures the spatially more coherent biospheric anomalies in the Southern Hemisphere. In the other direction at the regional scale, a large decrease in Eastern China in February 2020 is seen (figure S13), which is consistent with the expectation of the large emissions reduction from China during the COVID lockdown. However, it is not statistically significant, and the spatial and temporal patterns are not consistent between the model and the observation.

We conducted two additional model sensitivity experiments to delineate these effects (see section 4). The monthly evolution of CO₂ anomalies from these experiments (figure 4) indicates that the roles of the biosphere, weather, and COVID vary from month to month. In February–April 2020, the biosphere in NH45 had positive but decreasing anomalies while the COVID effect steadily increased. The weather effect was large in February and March to drawdown CO₂, but small in April (all in comparison with 2019 by model design). Averaged over February–April, the biosphere contributed 0.042, weather contributed −0.086, and COVID contributed −0.096 ppm, leading to an average of −0.14 ppm CO₂ change (drawdown) while March alone was −0.21 ppm.

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In summary, the three factors impacted CO₂ in intricate ways. In the period of February–April 2020, while the biosphere of the Southern Hemisphere had widespread CO₂ uptake, the NH had some uptake in South Asia and Siberia that was overridden by CO₂ release from other regions, partially in response to a warm winter (figure S3). In contrast, COVID emissions reduction was the most spatiotemporally consistent factor in the NH, contributing to majority of the CO₂ decrease. The weather impact on CO₂ fluctuated from month to month but contributed a significant portion of the CO₂ drawdown in the NH during February–March 2020. Its importance rises towards smaller scales to which we turn our attention now.

From the GLOBALVIEWplus dataset ObsPack [18] (see section 4). Figure 5 compares the model with surface observations at five marine boundary layer stations that span the remote Pacific region from north to south. Flask sampling at these sites is carefully conducted to represent atmospheric background concentrations on the scale of hundreds to thousands of kilometers.

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The anomalies at Kumukahi (KUM) are relatively small in February and March 2020, but decrease rapidly to lower than −1 ppm in April. The model and observations are broadly similar, in particular, the decrease in April. It is tempting to associate this drop with COVID reduction. However, a closer look at the model sensitivity experiments (figure S14) reveals large month-to-month fluctuations from the biosphere and weather, for example, a positive anomaly up to +1 ppm from the biosphere and a similarly large negative anomaly from weather in March. Of the total CO₂ drop by 1 ppm in April, 0.5 comes from the biosphere, 0.5 from the weather, and only 0.2 ppm from COVID.

Unlike a decrease in Hawaii, CO₂ at Barrow, Alaska (BRW) shows an increase in early 2020, while Midway Island in the North Pacific Ocean (MID) has a decrease in February–March and rebounds in April, both of which are attributable to the biosphere and/or weather (figure S14). Thus, while the sub-annual signal of 1–2 ppm at these marine surface stations is a few times larger than the global mean column anomalies seen by the satellite, the variability at a given station is dominated by the biosphere and weather. Nevertheless, the 0.1 ∼ 0.2 ppm decrease due to COVID-19, although smaller than the biospheric and weather effects, is separable using the model, and is consistent with the global-scale COVID induced drop discussed above. The overall consistency between the model and station observations suggests the ability of both the model and observation in capturing these sub-annual changes, regardless of the origin.

Because a major fraction of emissions comes from cities with high levels of human activities, one can expect a large COVID signal in urban CO₂ data. We analyzed CO₂ measurements in Beijing and Chengdu.

Surface observations in Beijing show CO₂ for the winter-spring (December 2019–April 2020) compared with the same period the year before (figure 6(a)). During the pre-COVID period of December–January, CO₂ was significantly higher in 2020 than in the year before, because this winter's atmosphere was more stable and less 'ventilated'. February was dominated by two high-CO₂ weather events, one in each year. We compared the wind speed of 2020 winter with 2019 based on the 0.25° × 0.3125° high resolution GEOS-FP modeling dataset. And the data showed that the mean daily wind speed is indeed much smaller around 1 February (1–3 m s⁻¹ in 2020 compared with those 3–8 m s⁻¹ in 2019), which contributed to the higher enhancement in 2020. The expected low CO₂ values due to COVID in January–February (figure 6(b)), as 'predicted' by the model, do not have a clear correspondence in the weather-dominated CO₂ observations. In general, the modeled magnitude of change is much smaller than the variability. During March–April, the difference between the 2 years decreases to much smaller values. We computed the enhancement for the shading period, and it is 30 ppm in 2020, compared with the 20 ppm in 2019. It is tempting to explain this difference as the result of emissions reduction, but it is mostly brought about by weather regime shifts in the spring season with dominantly northwesterly wind from the Mongolian Plateau. Thus, although the COVID-19 signal is large, it is 'buried' in even larger weather noise. Other cities are similarly dominated by weather, for example, a monthly drop of 1–2 ppm in New York City and Delhi, and an increase of 1–2 ppm in Washington DC and Paris (figure S15).

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Interestingly, CO₂ measured in the city of Chengdu shows a stepwise drop on January 24, the day before the traditional Chinese Lunar New Year, followed by a city-wide lockdown with little urban activity for the next 1–2 months (figure 7). The difference between the month before and after the lockdown is more than 20 ppm, and the abrupt change on the time scale of one day is consistent with a COVID signal, and there is no other known mechanism to explain this result. Concurrent particulate matter (PM2.5) measurements support this interpretation because the short-lived PM2.5 has a similar pattern on timescales shorter than a few days, but it has much less monthly and longer timescale variations compared to CO₂.

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Why is the COVID signal clear in Chengdu, but not in Beijing? The answer lies in the differences in weather. Chengdu, which is situated within the Sichuan Basin in southwestern China, is surrounded by great mountain ranges including the Tibetan Plateau and has generally very calm weather with a famously known atmospheric inversion layer that is rarely broken [19], whereas Beijing, which is at the edge of the North China Plain, is subject to large weather fluctuations, frontal passages and seasonal shifts. Thus, weather variation is relatively small in Chengdu to allow COVID signal to be revealed. And the simulations in Chengdu also confirmed a 1–10 ppm reduction resulted from COVID-19 during the lock-down period (compared with the observed 30 ppm), despite of the coarse resolution and fossil fuel emissions data. And the smaller modeled signal can be attributed to two potential reasons: (a) Lacked of local emissions reductions data for model input, which is substituted by national average value of −18.4% in February, and this was likely to be underestimated through communications with local inhabitants; (b) The spatial mismatch. Considering the instrument is deployed on the rooftop of a 6th floor building that is near a traffic line, and thus the observed signal reflected more of the traffic emissions reductions.

Have been conducted in Beijing periodically since 2017 using mobile platforms [20, 21] (see section 4). Some of these 'CO₂-tracking' trips took advantage of light-weight low-cost CO₂ sensors [22]. Three trips were selected from before, during, and after the COVID-19 lockdown while minimizing differences in other factors such as weather conditions, rush hours, and weekend effects. The average CO₂ is 513 ppm before, 455 ppm during, and 501 ppm after the height of lockdown (figure 8). To further remove the confounding effect of still somewhat different weather conditions, we subtracted the CO₂ concentration measured at the Institute of Atmospheric Physics (IAP) tower station. This difference can be thought as a traffic-induced on-road 'CO₂ enhancement' relative to a 'city background'. This 'traffic enhancement' is 65, 30 and 50 ppm respectively for the three periods. The more than 30 ppm less traffic CO₂ during COVID, and still somewhat low value during recovery, is consistent with direct traffic data, which is not surprising, because the reduced transportation is the largest contributor of CO₂ reduction during lockdowns in cities.

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To simulate the atmospheric CO₂, the model solves the carbon mass balance equation as follows:

$$\begin{equation}\frac{{d{\text{C}}{{\text{O}}_{\text{2}}}}}{{dt}} = {F_{{\text{net}}}} \equiv {F_{{\text{FE}}}} + {F_{{\text{TA}}}} + {F_{{\text{OA}}}}\end{equation} \tag{ 1 }$$

where $\frac{{d{\text{C}}{{\text{O}}_{\text{2}}}}}{{dt}}$ is the atmospheric CO₂ growth rate, ${F_{{\text{FE}}}}$ is fossil fuel emissions, ${F_{{\text{TA}}}}$ is terrestrial to atmosphere flux, ${F_{{\text{OA}}}}$ is ocean to atmosphere flux, and ${F_{{\text{net}}}}$ is net surface to atmosphere flux. The model is run in a 'forward' fashion for each three-dimensional model grid point (location), forced by the three fluxes, as well as meteorological variables for atmospheric transport and mixing. Here we use the GEOS-Chem atmosphere transport model v12.5.0 (http://acmg.seas.harvard.edu/geos/) at a horizontal resolution of 4° × 5° with 47 vertical levels. The fluxes (below) at different resolutions are re-gridded to 4° × 5°. The model is driven by the meteorology field MERRA2 from the NASA Global Modeling and Assimilation Office. Details of the setup and evaluation were described previously [27, 28]. The simulation period was from 1 January 2008 to 31 May 2020, and data after January 2010 were used for analysis.

${F_{FE}}$ combines a number of sources, including the Global Carbon Project (GCP) annual country-level carbon budget for 1959–2018 [29] with updates for 2019 by Le Quere et al [2], daily data for 2019–2020 from Liu et al [1], the TIMES hourly scaling factor of Nassar et al [30], and the spatial information of the ODIAC database of Oda et al [15].

Recently, a daily resolution, country-level data became available [1]. This novel dataset achieved daily resolution by taking advantage of a variety of sector-based energy and economic activity statistics, including real-time traffic data and daily electricity generation data of major power suppliers. However, the Liu et al [1] data were available only for early 2019 and 2020, and for this work, it was updated to cover the period of January 2019 through May 2020. For the years 2008–2018 when we do not have daily resolution data, we use the 2019's daily variation as a surrogate but retain their annual total. Because the emissions of Liu et al [1] for 2019–2020 are slightly different from GCP, in order to maintain the consistency of ${F_{{\text{FE}}}}$ from 2018 to 2019–2020, we use the country-level GCP fossil fuel values as a constraint to rescale the yearly total ${F_{{\text{FE}}}}$ from 2008 to 2020, and the same scaling factor for 2019 is used for 2020 to obtain a harmonized time series. Furthermore, we combine the diurnal scaling factor from the TIMES method of Nassar et al [30] and the daily national CO₂ emissions of 2019 of Liu et al [1] to obtain hourly country-level CO₂ emissions in 2019 and 2020.

The gridded spatial information comes from the ODIAC emissions [15]. ODIAC uses the annual country-level fuel consumption based on CO₂ emissions estimates [31] and disaggregates to a 1 km or 1 degree resolution using satellite night light observations and point source data. The annual data were disaggregated to monthly based on a climatological seasonal cycle. Here we simply disaggregated the country-level hourly data above to 1° × 1° with the spatial information of ODIAC. Since COVID-19 reductions are more concentrated in cities with a major reduction in transportation [1, 32], this disaggregation in proportion to ODIAC's spatial pattern may underestimate the reduction in metropolitan regions.

Altogether, the method can be summarized in the following equation for 2008 ∼ 2018:

$$\begin{align*}{F_{{\text{FE}}}}^{c,i,j,y,{t_{\text{h}}}} &= {\text{ ODIA}}{{\text{C}}^{c,i,j,y}} \times \frac{{{\text{GC}}{{\text{P}}_{{\text{tot}}}}^{c,y}}}{{{\text{ODIA}}{{\text{C}}_{{\text{tot}}}}^{c,y}}} \nonumber\\ &\quad\times \frac{{{\text{L}}{{\text{Z}}^{c,2019,{t_{\text{d}}}}}}}{{{\text{L}}{{\text{Z}}_{{\text{tot}}}}^{c,2019}}} \times {\text{TIME}}{{\text{S}}^{i,j,{t_{{\text{diurnal}}}}}}\end{align*}$$

and for 2019 ∼ 2020:

$$\begin{align*}{F_{{\text{FE}}}}^{c,i,j,y,{t_{\text{h}}}} &= {\text{ ODIA}}{{\text{C}}^{c,i,j,2018}} \times \frac{{{\text{GC}}{{\text{P}}_{{\text{tot}}}}^{c,2019}}}{{{\text{ODIA}}{{\text{C}}_{{\text{tot}}}}^{c,2018}}} \nonumber\\ &\quad\times \frac{{{\text{L}}{{\text{Z}}^{c,y,{t_{\text{d}}}}}}}{{{\text{L}}{{\text{Z}}_{{\text{tot}}}}^{c,2019}}} \times {\text{TIME}}{{\text{S}}^{i,j,{t_{{\text{diurnal}}}}}}\end{align*}$$

where y is the year, t_h is the hour, t_d is the day, t_diurnal is the diurnal cycle. c is country, i is longitude, j is latitude, and tot is the yearly total value. ${ }F_{{\text{FE}}}^{\,c,i,j,y,{t_{\text{h}}}}$ is the emission of country c at location i, j at time t_h of the year i. The four datasets used to obtain this harmonized labeled ODIAC, GCP, TIMES and LZ, where LZ is the updated Liu et al [1] dataset.

${F_{TA}}$ is simulated by a dynamic vegetation and terrestrial carbon cycle model VEGAS [11, 16]. The model is forced by observed climate variables including monthly precipitation, hourly temperature and radiation, and historical land use patterns, as well as atmospheric CO₂. The model was run at hourly time step and 0.5° × 0.5° resolution from 1901 to April 2020. This version 2.6 of VEGA largely S follows the simulation protocol of the TRENDY [33] and the MsTMIP [34] terrestrial model intercomparison projects with some model and NRT forcing data updates. Carbon cycle models have been extensively applied to long-term, interannual and seasonal variations, but rarely in sub-annual changes of interest here. VEGAS has been shown to be among the models better at simulating such short-term changes [35, 36].

${F_{{\text{OA}}}}$ uses the spatial pattern of pCO₂ observation derived fluxes from Takahashi et al [37]. To obtain the temporal variation, we rescaled the Takahashi spatial pattern for the year 2013 with the temporal evolution of ${F_{{\text{OA}}}}$ from the GCP annual carbon budget analysis which is based on estimates from multiple ocean carbon cycle models [29]. The carbon budget was only available up to 2018. For the year of 2019 and 2020, the GCP ocean values were linearly extrapolated using the values from the previous 10 years. The annual carbon budget thus does not contain a possible sub-annual contribution from the ocean, which is generally believed to be small compared with land and fossil flux anomalies.

To delineate the contribution to CO₂ changes from fossil fuel emissions ${F_{{\text{FE}}}}$, biospheric flux ${F_{{\text{TA}}}}$, and weather, we designed three sets of experiments:

• (a)  
  BWC (biosphere + weather + COVID): the full experiment described above with realistically varying biospheric fluxes ${F_{{\text{TA}}}}$, weather, and ${F_{{\text{FE}}}}$ including COVID-induced emissions reduction.
• (b)  
  BW (biosphere + weather, no COVID): same as in BWC, but replacing ${F_{{\text{FE}}}}$ of 2020 with that of 2019.
• (c)  
  B (biosphere only): same as in BW, but replacing all years' meteorology values (wind, etc) with that of 2019.

Thus, compared with BWC, experiment BW removes the effect of COVID emissions, while Experiment B further removes the weather effect. The differences among these experiments show the effect on CO₂ of each individual factor. In figure 4, the anomaly for experiment B is calculated as a detrended anomaly, while those of BW and BWC represent the differences between 2020 and 2019, following the experimental design.

The satellite column CO₂ data are Level-3 products from the National Institute for Environmental Studies (NIES) [24] (www.gosat.nies.go.jp/en/about_5_products.html). The L3 data were derived from the L2 data with spatial interpolation using the Kriging technique. The data is at 2.5^o × 2.5^o resolution and available from August 2009 to April 2020, and these data were gap-filled with the spline method. There are known biases in oceanic glint data, so we only used land data in our analysis. For this reason, regional average analyses in such as figure 2(b) are over land only for both the model and GOSAT to facilitate comparison. Additional uncertainty comes from missing GOSAT data in regions such as the core of the Amazon due to persistent cloud cover and the northern boundaries where a large solar zenith angle may lead to larger uncertainty (e.g. figure 15 in [24]). Thus, we excluded grid points with data coverage less than 63% and applied a spline fit to fill the gaps for the remaining data.

The surface station data are from the GLOBALVIEWplus ObsPack framework [18] that collects a great variety and numbers of in-situ, flask sampling, aircraft and other CO₂ measurements. The five stations data used in our analysis are all flask sampling data. These are baseline stations managed by NOAA that have been in operation for several decades. Great care is taken to sample air representative of large-scale atmospheric background conditions. The data product used here is GLOBALVIEWplus 5.0, with the most recent update ObsPack NRT (obspack_co2_1_NRT_v5.2_2020-06-03) provided by NOAA's CarbonTracker team [38, 39]. The most recent year's data have been quality-controlled by an automated procedure, and they may still be subject to modifications from further manual quality control.

We evaluated the impact of measurement uncertainty on our results, as shown in figure 2(b) (satellite) and figure 5 (ground stations). For GOSAT, we first took its location-specific measurement uncertainty produced by the GOSAT team (figure S10(a)). We then used a Monte Carlo method to generate an ensemble of spatially correlated uncertainty maps using the statistical method of joint multivariate Gaussian distribution. For each ensemble member, each location (model grid point) was assigned a random error drawn from a Gaussian distribution with the standard deviation from the GOSAT measurement uncertainty map. A spatial correlation scale of 1000 km was assumed in the multivariate covariance matrix. Sensitivity experiments using correlation scale of 2000 and 5000 km showed similar final results. The errors were then added to the CO₂ value at the corresponding locations. A total of 100 such maps (realizations) for any given month were generated, with 8 shown in figure S10(b). An uncertainty range was computed for any given regional mean CO₂ (figure S10(c) and figure 2 of main text). This task is simpler for a ground station, where we just used the within-month standard deviation as the uncertainty because it does not involve spatial correlation.

A network of six tower stations using high accuracy Picarro CO₂ analyzers has been running since 2018 as part of the Beijing-Tianjin-Hebei (JJJ) carbon monitoring project [21], run by the Chinese Meteorological Administration and the IAP of the Chinese Academy of Sciences. The CO₂ analyzers were calibrated four times a day, with calibration gas tracing to the World Meteorological Organization standard. The data have a nominal accuracy of 0.1 ppm. A network of low-cost CO₂ sensors has been running in various stages of development since 2016, as a collaborative effort among the IAP, the University of Maryland, and the US National Institute for Standards and Technology. These sensors were found to be able to achieve an accuracy of ∼5 ppm after calibration and environmental correction [22]. The data used in this paper for Beijing stations were measured with Picarros while the data in Chengdu were from a low-cost sensor node with three individual CO₂ sensors.

We conducted several on-road CO₂ measurements in Beijing and the surrounding area using mobile platforms before, during and after the COVID-19 lockdown. Because urban CO₂ concentrations are strongly influenced by weather, we selected three trips with the closest weather as possible for the days of 20 February 2019, 21 February 2020, and 9 May 2020. Additionally, we calculated the on-road CO₂ enhancement relative to a city 'background' measured at the IAP tower station. We used CO₂ sensors of different accuracies, including Picarro and LI-COR LI-7810, both mounted inside a car with an air inlet from above roof [20]. We also used low-cost sensors mounted on windshields, and these sensors were calibrated before and after each trip [21]. Some of the sensors were in the same car as Picarro and their agreement was within 5 ppm. A detailed analysis of these trips and methodology are described in D. Liu et al [40].

Atmospheric CO₂ data contain variabilities on a variety of time scales, from long-term increasing trends driven by fossil fuel emissions and carbon sinks [41], decadal variations [42], and interannual variability dominated by ENSO [11], to a prominent seasonal cycle [16, 43] in response to the annual growth and decay of the biosphere. The possible COVID-19 signal of interest here lasts for a few months on sub-annual (month to intra-seasonal) timescales. Monthly-scale high-frequency variabilities are generally less well studied and are often filtered out so as to focus on seasonal and longer-term changes [44].

Here, we calculate sub-annual anomalies using a four-step 'detrended anomaly' approach termed DCA:

• (a)  
  A 12 month running mean is applied to the original CO₂ data. The running mean mostly contains signals longer than a year, including long-term trends, and interannual to decadal variations (figure 9(a)).
• (b)  
  This running mean is then subtracted from the original CO₂ data. The result is considered 'detrended' and is dominated by seasonal cycles (figure 9(b) black line).
• (c)  
  A climatology is then calculated as the mean seasonal cycle (figure 9(b) red line).
• (d)  
  The sub-annual anomalies (detrended anomalies) are the differences between the detrended CO₂ and its climatology.

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The approach using running mean or other filtering techniques to obtain low-frequency signals has been widely used to study CO₂ variability [16, 33, 44, 45]. The last two steps consist of a standard definition of climatology and anomaly. The final sub-annual signal is thus detrended (low-frequency removed) and de-seasonalized (climatological seasonal cycle removed). In comparison with the DCA method, the standard climatology/anomaly method (simply called the CA method here) does not involve detrending, and it retains a low-frequency signal. Therefore, the DCA method is suitable for finding CO₂ sub-annual anomalies, while the CA method is used for flux analysis, such as in figure 2(a), which contains both interannual and sub-seasonal information.