The natural CO2 cycle is affected by factors related to climate and vegetation aspects [6, 31, 32]. Due to the VIF analysis, we were able to summarize three main factors for São Paulo state: Global Radiation (Qg), Relative Humidity (RH) and Sun-Induced chlorophyll Fluoresce at 757 nm (SIF 757). Several studies have already been conducted using this method to identify which variables select for ecological studies , computational studies , and remote sensing studies .
Except for wind speed, all variables studied correlated negatively with Xco2 (Figure 1), hence, related to the sink of atmospheric CO2. In general, the highest concentrations of Xco2 are observed in the months corresponding to the Brazilian autumn and winter (April to August) and lowest in the summer, from December to February. Studies such as by Siabi et al. (2019)  and Falahatkar et al. (2017)  reported how the different seasons affect the average CO2 concentration in the atmosphere
Recently, researches were conducted at regional scales in Brazil such as by Morais Filho et al. (2021)  and da Costa et al. (2021) , indicating negative correlations between Xco2 and SIF over agricultural areas, approximately -0.5 and -0.8 respectively. SIF is a variable directly related to the photosynthesis of plants, laboratory-scale experiments have demonstrated this relation , and remote sensing studies at the canopy and global level reported positive relations between SIF and Gross Primary Production, also a negative correlation between SIF and the Xco2 [5, 39, 40, 41].
As a result of photosynthesis, it is expected that SIF increases during summer [7, 36], as in this season, higher precipitation events and higher temperatures are observed . Our results show higher SIF average values in the months where summer occurs in São Paulo state, and an inverse relationship between SIF and Xco2. The lowest average values of Xco2 usually occur during the summer period in the study region. This is due to plant CO2 assimilation , printing a quasi-periodical Xco2 and SIF time changes as well as observed in other studies [5, 6, 36, 44].
Most of São Paulo's state has a wet summer and dry winter  resulting in a positive correlation between precipitation and SIF (Pearson’s correlation = 0.61 and p < 0.05), while negative with Xco2 (r = −0.49, p < 0.05) (Figure 1a). Precipitation is a photosynthetic control factor, so the greater availability of water that exists in the summer at São Paulo’s state induces plants to perform more photosynthesis through primary productivity, which leads to a reduction of atmospheric CO2. The opposite is observed in the dry winter because water availability is lower resulting in less photosynthesis, or less CO2 assimilation by plants, either in natural or agricultural areas [7, 28, 45].
Another effect observed during summer in the region is the increase of relative humidity (RH), which reduces the water transfer between soil or plant to the atmosphere , inducing plants to keep their stomata open, where CO2 assimilation occurs . Studies have already shown the relationship of stomata opening in periods with good water availability is related to plant growth [48, 49]. Thus, establishing the negative relationship between RH and Xco2, also previously observed by Golkar et al. (2020) .
In the same way, another requirement for photosynthesis occurs is sunlight which is the source of energy to carry out the biochemical processes of this phenomenon. Therefore, as the amount of radiation (Qg) is absorbed by the plant, photosynthesis tends to increase, and consequently higher assimilation of CO2 and decreasing the concentration of this greenhouse gas on the atmosphere [7, 30]. We can observe these relationships in our results (Figure 3b), Qg correlates positively with SIF, and those variables relate negatively with Xco2.
Since we are dealing with the natural cycle of CO2 the main factor of the higher concentrations of this gas in the atmosphere is due to the lowest photosynthetic absorption by plants. The autumn and winter have low available water and sunlight for plants, leading to a decrease in photosynthesis, also another important factor is that the annual calendar for agriculture in the state of São Paulo have harvest periods between these seasons , and as consequence decreasing the cover area by vegetation. Shekhar et al. (2020)  show how the crop’s grown in summer decrease the values of Xco2 over Nile Delta and when the harvest starts the values of Xco2 are higher, also, they found that SIF values are higher in the grown season.
Our model was based on Qg and RH, which are two variables related to the CO2 assimilation process, or CO2 sink. The model has lower RMSE values than have been reported in previous studies, such as by Guo et al. (2012)  where the values of this metric ranged from 0.7 to 1.1 ppm. In a more recent study by Taylor et al (2020)  when evaluating initial OCO-3 data results from the globe and model-related errors, they found an RMSE between 1 and 2 ppm. Another important measure is the MAPE, which shows in percentage how much we are getting wrong, studies with remote sensing have already demonstrated errors below 10% as being considered extremely low for predicting various plant and climate aspects [54, 55]. With this, we can evaluate that the performance of the model proposed in this work presents a very low error.
The coefficient of determination (R2) was 0.44, an increment of almost 20% from the simple linear fit with Qg alone with a higher importance in the model. Although the R2 is moderate, studies using other orbital sensors such as MODIS to model the average CO2 concentration in the atmosphere have reported similar results (Guo et al., 2015) . In addition, we should consider that although OCO-2 and NASA-POWER are two high quality and validated databases [8, 9, 56], the difference between grids and spatial resolution (see Table 2 in methods) cannot be disregarded, as it is an aspect that can influence these results, leading us to consider the coefficient of determination observed in this study as being high.
These differences between the databases can be suppressed by the greater temporal coverage of NASA-POWER, being able to estimate the daily temporal variability of the natural CO2 cycle in the atmosphere for the state of São Paulo, besides reducing in the future the spatial scale of Xco2 obtained from OCO-2 and gaining greater spatial resolution cover. Other vegetation index-based models aimed at reducing the spatial sampling of OCO-2 data, but focused on SIF, as is the case of Zhang et al. (2018)  and Yu et al. (2019) .
Despite the errors associated with the model and the uncertainty measures due to the difference in satellite resolution, an advantage of using models similar to the one proposed here is being able to have a daily measure of the variability of atmospheric CO2 and how the climate parameters affect this dynamic, also serving as an indirect indicator of how is the daily assimilation capacity of this gas in a region.