Satellite observations from GOSAT and MODIS, model simulations from CarbonTracker, and ground-based measurements for validation from TCCON for 5 years from 1 June 2009 to 31 May 2014 were collected. The specifications of the used datasets are shown in Table 1. To highlight the differences of seasonal cycle over various land cover types, we selected nine different regions of interest where there are distinctive correlations of seasonal cycle between XCO₂ and terrestrial biosphere parameters. Figure 1 shows the locations of these regions overlapped with land cover map. Table 2 gives detailed specifications of these regions. In addition, XCO₂ data from 12 TCCON sites (shown in Figure 1) and model simulations are obtained to investigate the uncertainty of GM-XCO₂ datasets used in this study.

The SCA of XCO₂ is determined by CO₂ uptake and release by terrestrial biosphere. The temporal variation of XCO₂ can be divided into two components, long-term yearly increases mainly caused by anthropogenic emissions [3] and inherent seasonal cycle mainly resulted from photosynthesis and respiration by the terrestrial biosphere [23]. Fitting formulas for the XCO₂ seasonal cycle have been proposed in many different forms [13,14,20,54,55]. In this study, we use the typical one, adopted by Keeling et al. [54] and Thoning et al. [55], to statistically fit the seasonal cycle and yearly increases of XCO₂, which is given by the Equation (1) below, (1) x ( t ) = k 0 + k 1 × t + ∑ i = 1 2 ( a i cos ( 2 π i t ) + b i sin ( 2 π i t ) ) where k 0 is the XCO₂ at the start time, k 1 is the temporal growth rate of XCO₂, and the annual harmonic functions, ∑ i = 1 2 ( a i cos ( 2 π i t ) + b i sin ( 2 π i t ) ) , describe the seasonal variation of XCO₂. The harmonic functions include an annual seasonal cycle and semi-annual seasonal cycle [56]. We fit Equation (1) to the five-year time series of GM-XCO₂. However, the inter-annual variations in the seasonal cycle shape is not included in the fitted curves. In this study, the yearly increase of XCO₂ in each grid is removed to obtain the seasonal GM-XCO₂ data (hereafter referred to as dXCO₂), which are used in analyzing the seasonality in the following sections. The SCA is calculated as the difference between maximum and minimum value of dXCO₂ from five years GM-XCO₂ data from Jun 2009 to May 2014. An example of fitting GM-XCO₂ using Equation (1) in a selected grid (46.5°N, 111.5°E) is shown in Figure 2.

The seasonal variation of XCO₂ is driven by the seasonal imbalance between CO₂ uptake and release related to ecosystem photosynthesis and respiration [13], which are the outcomes of the underlying biosphere–atmospheric interactions. However, it is still not clear how much of the seasonal variation of XCO₂ can be explained by surface biosphere parameters at global scale with fine resolutions, especially from a data-driven perspective. We use the GM-XCO₂ dataset and terrestrial biosphere parameters, including NDVI, EVI, LAI, GPP, and LST data, and implement correlation analyses on their seasonal cycles. Pearson correlation coefficients (PCCs) in seasonal variation between XCO₂ and each of the parameters (NDVI, EVI, LAI, GPP, and LST) for the terrestrial biosphere are calculated for each grid using monthly mean values, respectively. XCO₂ data less than 350 ppm are excluded; NDVI and EVI larger than 0 and valid LST, GPP, and LAI were used. The spatial distribution of PCC between the monthly mean of dXCO₂ and the biosphere parameters was used to quantify the impact of biosphere activities on the seasonal cycle pattern of XCO₂.

XCO₂ SCA is an effective indicator of the strength of seasonal variation of XCO₂, which is related to the increase and drawdown of CO₂ in the atmosphere [13]. The spatial variation of SCA has been shown by Lindqvist et al. [14] using ground measurements from sparse TCCON stations. Further work by Kulawik et al. [15] using satellite retrievals has shown the global variation of SCA in 10° by 10° grids based on a traditional binning method, which, however, does not consider the detailed variation information within each grid. Based on our global land mapping data, Figure 3 shows the global land distribution of XCO₂ SCA derived from seasonal cycle of GM-XCO₂ from June 2009 to May 2014 using Equation (1). This is, to our knowledge, the first reported global map of CO₂ SCA at fine scale derived from real measurements. The goodness-of-fit evaluated by coefficient of determination (R²) between mapping and fitting XCO₂, as described in Section 2.2, is shown in Figure S1. We can see that R² for all fittings is larger than 0.9, indicating that the fittings well capture the seasonal cycle of GM-XCO₂. This global map of XCO₂ SCA clearly shows the latitude gradient decrease from north to south that is consistent with previous studies using ground measurements and binned satellite observations [15,35,57]. In the southern hemisphere (SH), the XCO₂ SCA are mostly lower than 4.0 ppm except some areas in Southern Africa, where the amplitude is above 4.0 ppm. It can be seen from this SCA map, moreover, that the range border of greater than 8 ppm extended over the high latitudes mostly with boreal forest in the NH. Moreover, the tropical and subtropical areas in India and Central Africa show abnormal SCA values larger than 8 ppm, which have not been seen previously and can be detected from our mapping dataset with fine spatial details.

To investigate how biosphere activities drive the spatial pattern of XCO₂, we correlated the XCO₂ SCA, as shown in Figure 3, with NDVI SCA, an indicator of the strength of vegetation photosynthesis and its resulting carbon uptake. Corresponding to Figure 3, Figure 4 presents the NDVI SCA overlapped with amplitude contour lines of GM-XCO₂ shown in Figure 3, which is derived in the same way as XCO₂ SCA for the same period. Comparing Figure 3 with Figure 4, it can be seen that the overall spatial distribution of XCO₂ SCA shows a very similar pattern as that of NDVI, with a high correlation coefficient of 0.69 for global land and 0.74 for the NH land. Both the SCAs of XCO₂ and NDVI generally decrease with latitude from north to south. Especially, the amplitude of XCO₂ has the largest value ranging from 8.0 ppm up to 12 ppm over high latitude in the NH, corresponding well to the highest amplitude of NDVI in these areas, which is likely caused by the strong CO₂ uptake during the growing season by boreal forest (Figure 1) [13,58]. The SCA of XCO₂ changes mostly from 4.0 ppm to 8.0 ppm over the mid-latitude area in the NH. It is remarkable to find that large amplitudes up to 8 ppm are presented over the Northern Indian area (8.68 ± 0.49 ppm) and some hotspots in Central Africa (8.33 ± 0.25 ppm), whereas the NDVI SCAs in these areas are relatively low. These areas, partly shown as CnI and GcA in Figure 1, are probably due to the CO₂ release from soil respiration of terrestrial biosphere in Northern India region or the large wild fires in the central Africa area. In addition, the temporal variation of anthropogenic emissions on the XCO₂ SCA in Northern India may partly contribute to these SCA anomalies. Further discussion is presented in Section 4.3.

In this section, correlation analyses are conducted, respectively, between seasonal variations of GM-XCO₂ data and several biophysical parameters associated with biosphere activities, including NDVI, EVI, LAI and GPP, to explore the underlying biosphere–atmospheric coupling process that drives the XCO₂ seasonality. Figure 5 shows the global distribution of the Pearson Correlation Coefficients (PCCs) with a significant level (p-value < 0.01) between monthly-averaged dXCO₂ and NDVI, EVI, LAI, and GPP, respectively, from June 2009 to May 2014 in each grid. Due to the lack of available data, the tropical forests in Amazon and Southeast Asia and the Tibetan Plateau are not considered here.

All of the PCCs between seasonal cycles of XCO₂ and seasonal variations of NDVI, EVI, LAI, and GPP, shown in Figure 5, present similar spatial patterns and are mostly negatively correlated, except for the bare land areas (shown in Figure 1). Especially, the seasonal cycle of XCO₂ show stronger and significant negative correlations with the biosphere parameters over Northeast Asia around 45°N than those over the other areas. Among the indices of NDVI, EVI, LAI, and GPP, XCO₂ shows stronger negative correlation with NDVI and EVI than those with LAI and GPP globally. In the NH high-latitude region, the correlation coefficients are −0.69, −0.68, −0.66, and −0.59 for NDVI, EVI, LAI, and GPP, respectively. They are −0.74, −0.69, −0.64, and −0.67 in the NH low-latitude region. It is known that LAI and GPP are the vegetation parameters derived from semi-empirical biophysical models, which likely induce more uncertainty than NDVI and EVI that are directly retrieved from MODIS-observed radiance. Moreover, it can be seen that the PCCs between XCO₂ and LAI are slightly weaker than those from other indices in the low latitudes, which is likely because LAI is an indicator of vegetation biophysical structure rather than biochemical activities [59,60]. The PCCs from EVI, moreover, are slightly higher than that from NDVI over Northeast China. This difference may be related to the saturation effect of NDVI in high biomass regions, while EVI data does not become saturated as easily as NDVI by using the non-saturated NIR band for high biomass regions [61].

We selected six regions of interest with a PCC higher than 0.5 distributed across multiple latitudes as shown in Figure 6 to investigate the correlation of seasonal variations of XCO₂ and NDVI from June 2009 to May 2014. These six regions of interest are shown in Figure 1, including FnC: forest in Northern Canada covered by 63% of forest, FeR: forest in Eastern Russia covered by 86% of forest, CwR: crop in Western Russia covered by 70% of cropland, CnC: crop in Northern China covered by 58% of cropland with mixed 18% grassland and shrub-land, GcA: grass in Central Africa covered by 36% of grassland mixed with 30% of forest, and CnI: crop in Northern India covered by 89% of cropland.

It can be seen from Figure 6 that XCO₂ decreases sharply when NDVI increases quickly during the growing season in summer. A stronger negative correlation in the forest region (−0.68 in FeR) compared to the cropland region (−0.50 in CwR) at the same latitude zone can be found. PCCs between seasonal variations of XCO₂ and NDVI is up to 0.8 over GcA, CnI, and CnC. The rainy season over GcA boosts the grass growth and promote the CO₂ uptake. Strong correlation presented in CnI and CnC, imply that the seasonal crop farming from planting, growing to harvesting may have a large impact on the seasonal variation of CO₂ uptake and release. Moreover, from Figure 6, we can see that there is an offset between the time of XCO₂ troughs and NDVI peaks. The time delay, as lags of month, over the six regions of interest are also indicated in Figure 6. Comparing with phase of NDVI, the phase of XCO₂ is generally delayed by a lag of about 0–2 months, which generally agrees with results from Table 3 in [62] by Olsen et al., which shows the delayed time between seasonal amplitudes of XCO₂ and boundary layer CO₂ to be within 2 months [62], with generally a greater difference in high latitude regions compared to low ones in NH. This offset is probably due to the time delay in XCO₂ response to terrestrial biosphere activities associated with the mass of CO₂ in the column and vertical mixing and convection of CO₂ from the surface to the column profile [58,62,63]. In this study, we define the time delay to be the lags of months between XCO₂ and NDVI that make their negative correlation the strongest. We can see the delayed time over the three regions (FnC, FeR, and CwR) in high latitude regions are over one month, and larger than the other three regions at low latitudes (CnC, GcA, and CnI), probably indicating a relatively slow vertical mixing due to very large changes of the CO₂ mass at high latitudes with strong biosphere absorption. The global pattern of this phase delay effect is elaborated in Section 3.3.

While almost impossible for surface measurements, the GM-XCO₂ and NDVI data in this study allow us to investigate the global distribution of phase delay effect in terms of lags of months. The results are shown in Figure 7a, which is the averaged phase lag for five years of GM-XCO₂ and NDVI data. This map of phase delay effect, to our knowledge, is the first such map derived from a completely data-driven approach using satellite observations.

Generally, the phase delay in southern hemisphere is either zero or one, probably due to the much smaller change of CO₂ mass in the column that needs time to be well mixed in column. In the NH mid- and high-latitude regions, interestingly, the pattern of the phase delay is similar to the seasonal cycle pattern derived from GM-XCO₂ shown in Figure 3 and from NDVI shown in Figure 4. The larger amplitudes, such as North America and North Eurasia boreal forest regions, correspond to a smaller time delay, suggesting that the strength of vertical mixing is much stronger in these areas, even though the biosphere–atmosphere exchange in these areas is also large. As shown in [64] by Huang et al., the strength of vertical mixing in boreal and arctic regions is not as strong as that in the tropics, which may lead to stronger phase delay effect in high latitude regions. Moreover, XCO₂ has a large footprint, which is supposed to have contributions from different oceanic and land regions. However, satellite observations of XCO₂, such as from ACOS-GOSAT, are more sensitive to CO₂ variations within the boundary layer [65], which allows us to explore the biosphere–atmosphere interactions by correlating seasonal cycles of satellite-observed XCO₂ and surface biosphere parameters.

Figure 7b shows the PCC between seasonal variation of XCO₂ and NDVI if the phase delay effect is excluded. We can see that, over most of the regions, the PCC is stronger than −0.8, particularly for most areas in North America where PCCs are around −0.6 before excluding the effect. In addition, the negative correlation over some area of boreal forest, most areas of grassland and forest in Central Africa have been increased to stronger than −0.9. These results show that the correlation between seasonal cycles of XCO₂ and NDVI may be underestimated if this phase lag effect is not removed. Furthermore, it suggests that this phase lag effect associated with atmospheric transport should be considered when assessing the impact of biosphere–atmosphere interactions on seasonal cycle patterns of XCO₂.

As shown in Figure 10, there are large gaps of satellite XCO₂ retrievals in high latitude regions, especially during the winter season due to snow cover in these regions and very small signal noise ratio in observation. For analyzing the XCO₂ SCA, the availability of retrievals around the peak and trough of the cycle is important. Fortunately, the ACOS-GOSAT XCO₂ retrievals cover the peak and trough of the XCO₂ cycle, as indicated by CT2015 simulations, suggesting that our data-driven mapping method can generally reproduce the SCAs in these regions from the satellite retrievals. However, at high latitude boreal regions, the ACOS-GOSAT retrievals may also be affected by systematic retrieval errors [14,68], so the SCA values at these high latitude regions, as shown in Figure 3, should be interpreted with caution. Further validations should be carried out with more TCCON data available in the future.

Abnormal results are shown over some regions (e.g., CnI, GcA, FsA, and CeB) in the tropical area (30°N–30°S), where large XCO₂ SCA can be seen from both GM-XCO₂ and CT-XCO₂, even the former is slightly larger than the latter, and high PCCs exist for NDVI and EVI, as shown in Figure 5. These regions are covered by vegetation, such as grass, forest, and crop mixed with bare land, where the interaction between CO₂ uptake and release from vegetation and soil respiration likely has impact on the seasonal cycle of CO₂. As indicated from previous studies on CO₂ emission from soils, the soil respiration in the tropic and subtropical areas is much larger than high latitudes [72,73] and, therefore, likely has non-negligible impact on the XCO₂ seasonal pattern. LST, a remotely sensed terrestrial parameter, is effective in depicting the land surface temperature distribution at the global scale with long time-series. LST has been used as one of the critical parameters in estimating seasonal soil respiration over forests in the Midwest USA [74]. Higher surface temperature is associated with stronger soil and plant respiration rates, but also possibly enhanced photosynthesis [33]. However, the net effect of increasing LST in the tropical areas has been shown to result in increasing atmospheric CO₂ [34]. In tropical areas, soil and plant respiration contribute a very important part to the seasonal variation of atmospheric CO₂. The tropical carbon storage is very vulnerable to temperature change [34]. Therefore, an investigation of the correlation between XCO₂ from satellite observation and LST can indicate the possible impact of LST on the seasonal variation of XCO₂ in the tropical areas, where the carbon storage has been shown to be sensitive to future temperature variabilities [34].

Figure 11 shows the correlation between seasonal XCO₂ and LST variation over the tropical areas. The results interestingly show the seasonal cycle of XCO₂ is highly positive correlated with seasonal variation of LST, which is opposite to the negative correlation with NDVI, as shown in Figure 5a. Especially, over Central Africa and Southern Asia, the PCC is generally larger than 0.70, indicating the possible impact of LST on the seasonal cycle of XCO₂. Additionally, Figure 12 shows the detailed time series of the selected five regions of interest shown in Figure 1. The seasonal variation of XCO₂ is generally consistent with the variation of LST; especially, the variation around peak XCO₂ matches well with the variation around peak LST. Coincident with the maximum LST, terrestrial respiration and weakened photosynthesis could contribute to the maximum XCO₂. As is shown in Sreenivas et al. [75], XCO₂ showed a positive correlation with temperature, and soil respiration and biomass burning may be an important terrestrial carbon source contributing to the CO₂ concentration in India. To further investigate the possible influence from anthropogenic emissions on the SCA anomaly, we found that the fossil fuel emission from bottom-up estimation in CnI [76,77] (shown in Figure S4) does show a seasonal cycle, which, however, has much less consistency than LST with XCO₂ around the peaks of the XCO₂ cycle. This may suggest that the SCA anomaly observed in CnI is partly contributed from fossil fuel emissions but dominantly contributed from LST variations around the spring period. The effect of terrestrial respiration in these regions need to be further investigated and directly observed LST could be an alternative parameter to its further investigation for lack of surface measurements.