Hypothetical scenarios of lifting the restrictions can therefore be estimated after SEIR is parameterized. These methods are, however, difficulty to applied globally because: 1) human travel records obtained from a personal tracking system do not exist in most countries, 2) the announcement of control policies and the practical implementation and public compliance can be inconsistent, and 3) a process model like SEIR requires many regionally heterogeneous epidemic parameters 11, 12 which are unavailable globally. Furthermore, validating the model only by the records from a strictly controlled region or country (e.g. Wuhan or China) might bias the estimation of an extreme scenario with no controls. Without using the global data, it is also difficult to assess the seasonal effects.
We build a panel regression model (Methods) to quantify contribution of SA, climate, and MOC to the transmissibility of COVID-19 over the globe during the community spread period. We estimate the daily reproductive number, R0 , of COVID-19, following a widely adopted statistical approach 8, 16 which only requires the daily confirmed number of infectees 1 . R0 is an indicator of the transmissibility of a virus, representing average number of secondary infectees generated by a primary infector 17 . For R0 > 1, the number infected is likely to multiply, and for R0 < 1, transmission is likely to die out 18 . We proxy daily SA by the satellite concentration of NO2 (Sentinel-5P level-2 pollutant product) 19 because it is significanlty negatively associated with SA and available globally. The weather data are from the meteorologcial reanalysis 20 . We quantify MOC through regionalized time fixed effects. Depening on the infectee records availability, we estimate 6,386 daily R0 values from 3,315,748 confirmed cases of 213 countries or provinces/states from late January to mid April. Besides the overall contribution, we also compare the regional difference of the contribution, and the MOC evolvement. We finally estimate that compared to a hypothetical scenario with no restriction of SA, the global R0 reduction contributed by the limiting SA from late January to mid April, and the consequent spared number of infectees.
Quantifying the overall contribution of SA and climateUsing all global records, we find that SA, Ultraviolet (UV), temperature (T), windspeed (u), and relative humidity (RH) significant affect R0 (R 2 =0.51 and all p<0.001, Table 2 , Extended Data). Esimated by the product of the dependent-variable coefficient and value range over the response-variable value range, Table 1 (a) shows strongly positive contribution of SA, moderately positive and negative contribution of temperature and UV, and weakly negative contribution of windspeed and RH. Therefore, SA restriction, UV illumination, high wind and high humidity could reduce the transmission. SA has a leading contribution of 18.3%±2.0% (95% Confidence Interval, CI). Sunlight kills the virus directly, increases cell cytotoxicity and modulates the biosynthesis of vitamin D which are essential to promote immune responses 21 . Higher relative humidity prevents viral particles traveling as far as it could in drier air 22 .
We further control the regions to only include data in China and developed countries to confirm the contribution of SA and weather. The R 2 is increased to 0.61 and the SA contribution is increased to 23.2%±3.0% (95% CI), 4.9% higher than the global scale, whereas UV, wind, and RH become insignificant ( Table 3 , Extended Data). The result might be explained by the fact that in more developed areas, people tend to stay indoors with a controlled climate most of the time 21 . This suggests that simply depending on favorable weather conditions, such as warm weather and high UV, has strong limitations in stopping the virus transmission in these areas.
We suspect a nonmonotonic contribution of temperature by restricting temperature to low or high (T<25°C or T≥25°C) in the regresion because the coefficient of temperature changes from weakly positive to strongly negative ( Table 4 vs. Table 5 , Extended Data). We hypothesize that the virus might have a viable temperature range. This finding agrees with a few previous studies on coronavirus 23 and COVID-19 24, 25 , but disagrees with most studies claiming temperature has a decreasing 26, 27 , increasing 22 or no effect 28 on the transmissibility. However, we note that the sample size, with only 747 samples, is relatively small when restricting tempeture to high (T≥25°). More data in the incoming season are needed to confirm the temperature effects because most regions in the globe have not experienced a COVID-19 pandemic with high temperature.
We estimate the global decrease of R0 due to the SA restriction as half monthly mean in Figure 1 . Because China has the earliest outbreak since late January, earlier than the rest of the world, we provide the R0 reduction from late January to Feburary only in China in Figure 1 (a)-(c) and the R0 reduction of the world from March to mid April in Figure 1 (d)-(f). China imposed the strongest policy on restricting SA at an early stage, from Feburary to the first half of March, and saw the largest reduction of R0. The major outbreak provinces of China had a R0 reduction from 0.08 to 0.18 in the first half of Feburary, and from 0.02 to 0.12 in the latter half of Feburary and first half of March. China graduately lifted the restriction of SA since the latter half of March ( Figure 1 e and f) . The SA restriction in Europe came in the latter half of March, and the R0 reduction was from 0.02 to 0.06 in the latter half of March and from 0.04 to 0.06 in the first half of April. The western US started SA strictions in the latter half of March, earlier than the rest of the US. The western US saw a reduction of R0 from 0.02 to 0.08 from later March to April, and the eastern saw R0 reduction from 0.04 to 0.10 in April.
Consequently, compared to a hypothetical scenario with no SA restriction during the community spread, we estimate in Figure 1 The number of spared infectees is a compound result of R0 reduction and timing. Athough the R0 reduction in Europe and US is significantly smaller than that in China, it spared significantly more infectees because of their higher number of infectors when the restriction of SA started. Error! Reference source not found. shows the regional spared infectees through SA restrictions in half-month intevals. Only China Mainland, Taiwan, South Korea, and Australia show a diminshed trend, as a result of early restrictions of SA, whereas the Europe and the US continue to see large number of spared infectees growing exponentially by the end of this analysis. The rest of the world, though having fewer number of spared infectees than Europe and US, show rapid growth. Maintaining restricted SA might still be a safer option for them. We suspect the lifting of SA restritions to reopen the economy in these countries might pose great risk.
In Figure 3 , the MOC is descreased the fastest in Australia and China to a value lower than or close to -1 eventually, indicating a resillient medical system or more effective control policy. The effectivness of the MOC in Australia might be explained by the adoption of additional control measures including mandatory quarantine of overseas arrivals and travel bans outside of Australia, and the relative small number of infectors in the beginning of the outbreak 29 . Although China was hit much harder in the begining, it survived the stress by imposing more strict control policies including the lockdown of the Hubei province, large-scale demobilization and mandatory quarantine of returning migrants (domestic) workers 29 , and by promptly increasing medical facilities including temporary hospitals 30 and reinforced medical crews from other provinces to the outbreak center 31 . The MOC of Europe, US, and arctic countries starts from a high value and decreases rapidly, but has not reached a low value at the end of our analyses (above or close to zero), indicating that their medical facility capacity and control polices (other than restricting SA) is evolving rapidly while still under stress of the large number of infectees accumlated during an earlier phase of the outbreak. The MOC of Africa and Latin America, though started with a low number, does not decrease as rapidly as the rest of the world.
Our study has the following limitations. First, R0 , the reproductive number, is estimated from confirmed infectee records which can be inaccurate due to the lack of tested cases especially in the beginning of the outbreak and in regions with less testing capacity. Without globally distributed epidemic parameters of COVID-19 other than the confirmed cases, the adopted statistical estimation seems to be the only practical global solution (Method). Second, although the weather impacts are significant and are within expectation, the contribution of temperature, is subjected to revisitation after more countries experience the warmer weather. Finally, because the MOC is not parameterized but merely quantified, we cannot project MOC into the future. Therefore, our result should only be used to assess the contribution of each predictor, especially the restriction of socioeconomic activities, instead of predicting the total number of infectees in the future climate, or the end of the COVID-19 pandemic. 
Since except for the number of infectees and deaths, epidemic parameters of COVID-19 are not globally available, we employ the stochastic approach by 8, 16 to estimate the reproductive number, R0. R0 of a given country or state/province at day t, R0t, can be estimated from daily confirmed number of infectees (C), via an intermediate variable, daily number of new infectors (I). The conversion from to is given by equation (1),
where is probability of an infectee to get clinical confirmation t days since being infected 16 . The conversion from to 0 is given by equation (2),
where is the probability of an infector to infect other people after t days since being infected 8 .
We fit a panel regression model with region-by-time fixed effects 3 (MOC) to quantify the contribution of SA and weather conditions to R0, using the REGHDFE module in Stata software 4,32 , 0 , = + 1 ln( 2 ) , + 2 T , + 3 ln( ) , + 4 , + 5 , + ,
where 2 T, , , stand for the total column of Nitrogen Dioxide concentration(mol/m 2 ), air temperature (°C ), ultraviolet intensity (W/m 2 ), relative humidity (%), and windspeed (m/s), and , is the region-by-time fixed effects, with subscripts i and r standing for the response unit and region. A response unit is either a country or a province/state depending on the availability of COVID-19 records. For example, records are available in China, US, Canada, and Australia at province/state level while only available at country level in most other regions. t stands for the days after community spread (Ct>30). The world is divided into 10 regions depending on the geographic proximity and data availability. They are, China, United States, Europe, Africa, Latin America, Australia (Australia and New Zealand), West Asia, South Asia, East Asia and Arctic (Canada and Russia).
The reduction of 0 , by restricting SA can be estimated by the product of 1 and the difference of between the ln( 2 ) , under restriction and the ln( 2 ) with no restriction which is averaged from the same period of the last year, i.e., 2019. Note that we only averaged the same period using the year of 2019 because Sentinel-5P data is only available after June 2018. Substituting the hypothetical 0 , back to equation (2), we can estimate the number of infectees with no restricted SA.
R0 is estimated from daily clinical confirmation of COVID-19 infectees assembled at Johns Hopkins University 1 in excel tables. The 2 concentration is retrieved from Sentinel-5P level 2 product 19 at daily intervals of 3.5 km ×7.5 km nadir resolution in netcdf4 format. Climate predictors are extracted from the ERA 5 atmospheric reanalyses 20 at hourly intervals and 0.25°× 0.25° grids in GRIB format. All climate predictors are averaged to daily mean and then averaged to the country or state/province weighted by population density from Gridded Population of the World (GPW) 33 in GeoTiff format. The 2 concentration is first spatially averaged to sub-level administrative areas of the response unit then weighted averaged by population density to the response unit.
In this section, we provide the regression results mentioned in the main text to show the significance and value range each predictor. 