## 2 Materials and Methods
### SIFc-GPP Relationship Analysis  
All analyses were performed using programming environments in R language version 3.6.1 [39]. All significance tests were performed with an alpha of 0.05 by default unless specified otherwise. All mean values presented in the paper were accompanied by corresponding Standard Error (SE) values unless otherwise stated. This study covered 12 vegetated biomes according to IGBP [40; 41] classification: croplands (CRO), closed  
Figure 1: The spatial distribution of all the 212 eddy-covariance (EC) flux tower sites from the FLUXNET 2015 Tier 1 dataset, depicted by black triangles. Biomes in the legend are from a static land cover map (MCD12C1 Land Cover Type 1: IGBP global vegetation classification scheme for 2007) retrieved from Friedl and McIver [38]. Biomes are: croplands (CRO), closed shrulands (CSH), deciduous broadleaf forest (DBF), deciduous needleleaf forest (DNF), evergreen broadleaf forest (EBF), evergreen needleleaf forest (ENF), grasslands (GRA), mixed forests (MF), open shrulands (OSH), savannas (SAV), permanent wetlands (WET), and woody savannas (WSA).  
shrublands (CSH), deciduous broadleaf forests (DBF), deciduous needleleaf forests (DNF), evergreen broadleaf forests (EBF), evergreen needleleaf forests (ENF), grasslands (GRA), mixed Forests (MF), open shrublands (OSH), savannas (SAV), permanent wetlands (WET), and woody savannas (WSA) (see Table S3 for more details).  
First, the correlation and differences between the SIFc and GPP dataset have been analyzed. Specifically, the differences between two SIFc datasets (CSIF and GOSIF) and the differences between two GPP datasets (GPP_D and GPP_N) were tested based on daily (8-day temporal resolution based on GPP data; all the daily GPP/SIF data were extracted at 8-day intervals) data using the confidence interval (CI) approach. Second, the relationships between two reconstructed SIFc products and GPP_M were investigated across six combinations of temporal scales (i.e., daily: mean of half-hour GPP data for each day, yearly: mean of daily GPP and SIF for each year, and multi-yearly: mean of the whole observation period) and spatial scales (i.e., site and biome), using major axis regression in the _smatt_ package [42] to account for data uncertainties in both x and y in the analysis of the SIFc-GPP relationship. In the analysis of the SIFc-GPP relationship, we forced trend lines to pass through the origin by setting intercept to zero based on the logic that zero SIF would suggest zero photosynthesis or GPP approximately [2; 43]. Whether significant differences existed among biomes in the SIFc-GPP conversion coefficients at site-yearly and site-multi-yearly scales were evaluated using _wilcox.test()_ in _ggsignif_ package. Third, the SIFc-GPP relationships at six spatial (site and biome) and temporal (daily, yearly, and multi-yearly) scales were analyzed to examine the change of the SIFc-GPP relationship with scales.  
The abovementioned analyses led to the conclusion that it is necessary to synopsize the inter-biome variability of GPP/SIFc slopes using a two-slope scheme. To develop the two-slope scheme, we first reclassified all sites into ENF and Non-ENF biomes, and then analyzed and compared the site-scale GPP/SIFc slopes within the ENF and Non-ENF groups. The mean and standard error (SE) were calculated from site-scale GPP/SIFc slopes within the ENF and Non-ENF biomes, respectively, to represent the two GPP/SIFc slopes and their uncertainty of the two-slope scheme. Similarly, the adequacy of using median and median absolute deviation (MAD) of site-scale GPP/SIFc slopes within the ENF and Non-ENF biomes to represent the two-slope scheme was also investigated. The two-sided Students t-test, the _t.test (two.sided)_ function in R was applied to test the difference between ENF and Non-ENF groups. The performance of two-slope scheme was measured with correlation coefficient (r), standard deviation (SD), root mean square error (RMSE), and percentage bias (PB) between flux GPP and SIFc_GPP.