The unprecedented world-wide lockdown in the first few months of year 2020 led to wide-spread reduced economic activities. As a result, fossil fuel CO2 emissions were reduced by 7.9% in the first 4 months of 2020 due to reduced transportation, industrial and power generation 2 and anticipated annual reduction of 4-7% 1 . This level of emissions reduction is on par with the annual target set out by the Paris climate agreement, but the COVID-19 induced reduction is short-lived as economic activities rebounds subsequently. While the lockdown increased activities such as tele-collaboration that benefit climate, other measures do not lead to transformation needed in energy systems. Monitoring and understanding such processes from global to local scales are of critical importance for achieving our climate goals. Over the last few decades, the scientific community has been developing world-wide carbon monitoring and information systems aiming at enabling the monitoring and verification of emissions reduction goals [4] [5] [6] [7] .
A back-of-the-envelope calculation goes as following. Current fossil fuel emissions rate is 10 GtC y -1 (Gigatonne carbon per year), of which about 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 world-wide network of CO2 observatories such as the renowned Mauna Loa station in Hawaii. Assuming 7% reduction or 0.7 GtC for the whole year of 2020 (high estimate of reference 1 ), it would cause a 0.18 ppm relative decrease in global atmospheric CO2 at the end of the year.
In reality, the emissions reduction does not occur uniformly throughout the year, for example, China in February and Europe, US and India in March-April (Fig. S1 ). The estimated reduction of 7.9% in January-April 2020 2 corresponds to a decrease of 0.26 GtC, a rather small quantity for atmospheric CO2. However, we expect the COVID signal to stay largely in the Northern Hemisphere (NH) for these few months because atmosphere inter-hemispheric transport takes approximately one year. We further assume that the carbon sinks have not kicked in because of dormant winter vegetation and sluggish ocean-atmosphere gas exchange. We therefore expect a 0.25 ppm decrease of Northern Hemisphere CO2 at the end of April. 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 precision of ~1 ppm and their ground calibration of 0.4 ppm 3,8,9 . 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 (weather). The growth and decay of the northern vegetation causes a seasonal CO2 amplitude of 6 ppm, while interannual climate variability such as ENSO causes biogenic CO2 changes of 1-3 ppm 10-13 . Thus, a key question is whether a 0.25 ppm COVID signal can be seen among other (natural) variabilities. We explored this question with carbon cycle models and a suite of space-borne and ground-based observations.
First, we created a high spatial-temporal resolution fossil fuel emissions ( !" ) dataset with daily emissions data from a near real time product (updated from Liu et al., (2020) 2 ; see Method). The daily country-level data was disaggregated to model grid resolution based on the ODIAC emissions database 14 . As seen in Fig. 1a (detailed temporal evolution in Fig. S1 -S2), carbon emissions intensity decreased by more than 5 gC m -2 mo -1 during February-April 2020 in East Asia, Europe, US and India, relative to the same period in 2019. While consistent with the temporal variations in the original country-level data 2 , the spatially disaggregated data here further shows emissions reductions concentrated in industrialized regions and areas with high population density such as the North China Plain, India's Ganges Basin, Northeast and Midwest US, as well as isolated centers such as Sao Paolo. For terrestrial biosphere-atmosphere flux ( #$ ), we used a dynamic vegetation and terrestrial carbon cycle model VEGAS 10, 15 , while ocean-atmospheric flux came from a multi-model product (see Method). The biospheric fluxes (Fig. 1b) have regional variations often larger than !" reduction, driven by climate variability. Overall, the terrestrial biosphere had wide-spread negative anomalies that was particularly strong in April (Fig. S3) . As a result, the spatial pattern of net flux %&' was dominated by biospheric fluxes.
Interestingly, when summed up globally, the magnitude of 2020 !" anomaly relative to 10-year climatology is comparable to that of #$ (Fig. 2a) , each about 50 MtC mo -1 decrease by April 2020. This is because fossil fuel emissions are reduced almost everywhere during COVID-19 lockdown, whereas the positive and negative anomalies in #$ tend to cancel out.
Consequently, the total flux anomaly Fnet reaches -100 MtC mo -1 .
These fluxes were then used to drive the community GEOS-Chem atmospheric transport model for the period of January 2008-May 2020 (see Method). The output of the model is a 4-dimensional depiction of spatial-temporal evolution of atmospheric CO2 that can be compared to various types of CO2 observations, as well as expected COVID impact ( Fig. S4-S7 ). Using a method termed DCA (Detrended Climatology and Anomaly; see Method), in which a CO2 time series is detrended to remove the low-frequency signal and climatological seasonal cycle, we calculated sub-annual anomalies of column CO2, shown in Fig.  2b . After a large positive anomaly in Jan 2020, the CO2 anomaly trended downward, and was 0.19 ppm lower than long-term climatology in March-April 2020, and 0.36 ppm lower in May ( Fig. 2b shaded period) . This anomaly is twice the second lowest monthly value in July 2016 and stands out among the past 10 years, and particularly so for the same season.
The Japanese GOSAT carbon satellite, launched in 2009, has collected column CO2 (XCO2) data for over 10 years. The spatial pattern of February-April 2020 GOSAT anomalies (Fig. 1d) are similar to the model over India, southern Africa, South America and central US where large negative values are wide-spread, though the overall spatial correlation is modest and significant sign differences exist near the northern edge in Eurasia ( Fig. 1 c and d ). Detailed monthly evolution shows similar broad patterns of agreement as well as larger detailed differences ( Fig.  S8 vs. S9). In a sense, the differences are expected because of satellite's sparse spatial-temporal sampling, particularly at higher latitudes and cloudy regions. However, the signal-to-noise ratio is enhanced via spatial-temporal averaging: the time series of CO2 anomalies averaged over 50S-50N ( Fig. 2b) shows reasonable agreement. Most encouragingly, the drop in 2020 stands out both in model and GOSAT.
To better appreciate how unusual year 2020 was, we plotted the CO2 seasonal cycle from May 2019 to April 2020 against those of the previous 10 years (Fig. 3) . The 50S-50N land average CO2 for especially March-April is outside the standard deviation as well as the envelope of the previous 10 individual years for both model and GOSAT. Such agreement lends confidence in using both model and satellite column CO2 for short-term anomaly detection. We also analyzed data at smaller scales including the NH 0-50N where strongest COVID-signal is expected. The model shows clear negative anomaly but the corresponding GOSAT signal is not as statistically significant as in 50S-50N (Fig. S10) , likely due to increase in noise towards smaller scales. The more robust 50S-50N signal has contribution from GOSAT's ability to capture the anomalies in the Southern Hemisphere which is largely a biospheric signal. Similarly, a large decrease in GOSAT anomaly for Eastern China in February 2020 (Fig. S11 ), though may be partly related to COVID reduction, is not statistically robust. 
We conducted two additional model sensitivity experiments to delineate the effects of biosphere, atmospheric transport (weather), and COVID reduction in !" (See Method and aspects of the detailed result in Fig. S4-S7) . The monthly evolution of CO2 anomalies from these experiments (Fig. 4) indicate that the roles of the biosphere, weather, and COVID vary from month to month. In February 2020, biosphere has a near zero but positive anomaly, while COVID effect steadily increases from February to May. The weather effect was large in March and May to drawdown CO2, but small in both February and April, all in comparison with 2019 by model design. Averaged over February-April, the biosphere contributed 0.030, weather 0.029, and COVID 0.069 ppm, leading to a February-April average of 0.128 ppm CO2 drawdown with March and April both about 0.18 ppm. By percentage, the biosphere, weather, and COVID contributed 23%, 23%, and 54%, respectively. In May 2020, all three factors contributed to CO2 drawdown, leading to a rapid decrease to 0.36 ppm.
In summary, the three factors impacted CO2 in an intricate way. In the period February-May 2020, the biosphere was recovering from a large carbon loss (relative to climatology) from year 2019, mostly in South America, Africa, and Australia in response to a moderate El Nino 10 , with additional CO2 uptake from Northern Hemisphere including South Asia and Siberia (Fig. S3 ). COVID emissions reduction was the most spatiotemporally consistent factor, contributing to majority of the CO2 decrease. The weather impact on CO2 fluctuated from month to month. The weather effect is not predominant because its variability tends to be averaged out on global scales. Its importance rises at smaller scales to which we turn our attention now.
Similar to the global-scale analysis above, we also analyzed data from atmospheric background CO2 stations from the NOAA global reference network ObsPack 16 (see Method). 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. Among these stations is Cape Kumukahi, Hawaii (KUM), a site downslope of the Mauna Loa observatory, but is better than Mauna Loa at capturing large-scale atmosphere background signal and more comparable with model which does not resolve the island.
The anomalies at Kumukahi are relatively small in February and March, 2020, but decrease rapidly to lower than -1 ppm in April. Model and observation are broadly similar, in particular, the decrease in April. It is tempting to associate this drop with COVID reduction. However, a closer look at model sensitivity experiments (Fig. S12 ) reveals large month-to-month fluctuations from 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 of 1 ppm in April, 0.5 comes from biosphere, 0.5 from 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 rebound in April, both attributable to the biosphere and/or weather (Fig. S12) . Thus, while the sub-annual signal of 1-2 ppm at these marine surface stations is a few times larger than 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, though smaller than biospheric and weather effect, are separable using model, and is consistent with the global-scale COVID induced drop discussed above. The overall consistency between model and station observations suggests the ability of both model and observation in capturing these subannual changes, regardless of the origin, thus lending support for interpreting the signal using model experiments.
Because major fraction of emissions comes from cities with high human activities, one can expect large COVID signal in urban CO2 data. Thus, we analyzed CO2 measurements in Beijing and Chengdu.
Surface observations in Beijing shows CO2 for the winter-spring (December 2019-April 2020) compared to the same period the year before (Fig. 6a) . During the pre-COVID period of December-January, CO2 is significantly higher in 2020 than the year before, because this winter's atmosphere was less 'ventilated'. February was dominated by two high-CO2 weather events, one in each year. The expected low CO2 values due to COVID in January-February (Fig. 6b) 'predicted' by the model do not have a clear correspondence in the weather-dominated CO2 fluctuations, and in general, the modeled magnitude of change is much smaller than the variability. During March-April, the difference between the two years decreases to much smaller values. It is tempting to explain this difference as the result of emissions reduction, but it is mostly brought about by weather regime shift in the spring season with dominantly northwesterly wind from Mongolian Plateau. Thus, although COVID-19 signal is large, it is 'buried' in even larger weather noise. Other cities are similarly dominated by weather (Fig. S13) , for example, a monthly drop of 1-2 ppm at New York City and Delhi, an increase of 1-2 ppm in Washington DC and Paris.
Interestingly, CO2 measured at the city of Chengdu shows a stepwise drop on January 24, the day before traditional Chinese Lunar New Year, followed by city-wide lockdown with little urban activity for the next 1-2 months (Fig. 7) . The difference between the month before and after the lockdown is 20-30 ppm and the temporal characteristics is consistent with a COVID signal. Concurrent particulate matter (PM2.5) measurements support this interpretation because the short-lived PM2.5 has similar pattern on timescales shorter than a few days, but it has much less monthly and longer timescale variations compared to CO2.
Why is the COVID signal relatively clear in Chengdu, but not in Beijing? The answer lies in the differences in weather. Chengdu, 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 17 , whereas Beijing, being at the edge of the North China Plain is subject to large weather fluctuations, frontal passages and seasonal shifts. Thus, while weather tends to dominate in Beijing, its variation is sufficiently small in Chengdu to allow COVID signal to be revealed.
Direct observation of on-road CO2 concentration has been conducted in Beijing periodically since 2017 using mobile platforms 18, 19 (See Method). Some of these 'CO2-tracking' trips took advantage of light-weight low-cost CO2 sensors 20 . Three trips were selected from before, during, and after the COVID-19 lockdown while minimizing differences in other factors such as weather condition, rush hour, and weekend effects. The average CO2 is 513 ppm before, 455 ppm during, and 501 after the height of lockdown (Fig. 8) . To further remove the compounding effect of still somewhat differing weather conditions, we subtracted CO2 concentration measured at the 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 depressed value during recovery is consistent with direct traffic data, not surprisingly, because the reduced transportation is the largest source of CO2 reduction during lockdown in cities.
The detectability of COVID-19 CO2 signal depends strongly on spatial and temporal scales. Our results show that the carbon satellite GOSAT is able to detect a short-term global mean CO2 anomaly decrease of 0.2-0.3 ppm, a number below the satellite instrument's targeted accuracy of individual measurements. This somewhat surprising result is made possible by spatial and temporal averaging to compensate for the sampling sparsity, and importantly also by the cancellation of biosphere and weather variability at large-scale. As a result, the drop in globalscale CO2 anomalies was dominated by the spatially coherent COVID emissions reduction, followed by a biospheric recovery from previous year's relative carbon loss, which became more important in the spring season, while weather impact fluctuated. One implication for detection is the need for meticulous approaches in enhancing signal-to-noise ratio and maximizing spatialtemporal data coverage 21, 22 . A critical perspective here is the focus on sub-annual time scale which has received little attention in the past compared to the much larger CO2 seasonal cycle and interannual variability. Our results suggest that current observation and modeling capabilities can depict sub-annual variations with some consistency, and the COVID period has the largest sub-annual CO2 anomaly in the last 10 years.
Surface observations of the atmospheric background CO2 concentration have variabilities up to 1-2 ppm, substantially larger than the ~0.2 ppm COVID fossil signal. However, the modeling results are sufficiently realistic in capturing sub-annual variabilities consistent with station observations, lending support in using model experiments to separate the COVID effect from the larger weather and biospheric variability.
At urban scale in many cities such as Beijing, New York City and Paris, atmospheric variability dominates the signal. Seasonal variations in weather patterns prevented us from discerning the COVID signal with confidence despite of the large fossil fuel emissions changes expected there. A major caveat is that the model resolution is too coarse to resolve the cities properly and the real signal is likely stronger than seen here and it would be better simulated by meso-scale models. Moreover, where weather variability is modest such as in Chengdu, the lockdown caused a clear CO2 reduction. Additionally, decrease in on-road CO2 enhancement larger than 20 ppm in Beijing was observed which is perhaps the most direct observation of localized emissions reduction.
Despite of the dramatic reduction in economic activities during 2020 COVID-19 worldwide lockdown, the short-duration of the event has left only a small signature in the atmospheric CO2 which results from fossil fuel emissions accumulated over two hundred years due to CO2's long life-time in the atmosphere. Nevertheless, our analysis demonstrates that its global-to-local impacts are already detectable, albeit still imprecisely, by current carbon monitoring systems using a variety of approaches, and that meaningful causality attribution to fossil fuel, biosphere and weather can be made by combining model and observations. Continued improvement and expansion of such capabilities can play a critical role in monitoring and verification of fossil fuel emissions reduction target at local, country, and global scales. They can also facilitate climate mitigation efforts from governments, cities, institutions and citizens. The gridded spatial information comes from the Open source Data Inventory of Anthropogenic 38 CO2 emission (ODIAC) 14 . ODIAC uses the annual country-level fuel consumption bases CO2 39 emissions estimates 27 and disaggregate to 1 km or 1 degree resolution using satellite night light 40 observations and point source data. The annual data was disaggregated to monthly based on a 41 climatological seasonal cycle. Here we simply disaggregated the country-level hourly data above 42 to 1 o ×1 o with the spatial information of ODIAC. Since COVID-19 reduction is more 43 concentrated in cities with major reduction in transportation 2,28 , this disaggregation in proportion 44
to ODIAC's spatial pattern may underestimate the reduction in metropolitan regions. 45 46
Altogether, the method can be summarized in the following equation for 2008~2018: 47 where y is year, th is hour, td is day, tdiurnal is the diurnal cycle. c is country, i is longitude, j is 51 latitude, tot is the yearly total value. Carbon cycle models have been applied to long-term, interannual and seasonal variations 63 extensively, but rarely in sub-annual changes of interest here. VEGAS has been shown to be 64 among the models better at simulating such short-term changes 31,32 . 65 66
The ocean-atmosphere carbon flux 67 *$ uses the spatial pattern of pCO2 observation derived fluxes of Takahashi et al. (2009) 33 . To 68 obtain the temporal variation, we rescaled the Takahashi spatial pattern for the year 2013 with 69 the temporal evolution of *$ from the GCP annual carbon budget analysis which is based on 70 estimates from multiple ocean carbon cycle models 25 . The carbon budget was up to only 2018. 71
For the year of 2019 and 2020, the GCP ocean values are linearly extrapolated using the values 72 from the previous 10 years. The annual carbon budget thus does not contain possible sub-annual 73 contribution from ocean, which is generally believed to be small compared to land and fossil flux 74
anomalies. 75 76
Model sensitivity experiments 77 
The approach using running mean 161 to remove low-frequency signals 162 has been used by various authors, 163 e.g., to study the CO2 seasonal 164 amplitude change 15 