## 4 Discussion
This is inconsistent with a previous finding that the Cubist method was not very sensitive to training sample size compared to other machine learning techniques [64]. Our results showed that the smaller sample sizes could mitigate the underestimation for high SIF values (like \(>\) 0.6 W m\({}^{-2}\) um\({}^{-1}\) sr\({}^{-1}\)) and increase the accumulated errors. Larger sample sizes could lead to lower accumulated errors, and the performance of the model became stable when the sample size was close to the million level. The very large sample used for developing the SIF model was more representative, and could encompass various climatic conditions and ecosystem types across the globe, and also sample the seasonal variations in each variable. The predicted SIF was possibly affected by the uncertainty of the gridded input data products. The global gridded input data products used in this study are widely used high-quality data. The EVI was calculated from the BRDF-corrected surface reflectance product [65], and previous studies have shown that the BRDF correction makes it possible to recover the real information on vegetation dynamics [66; 67; 39]. The high quality of MERRA-2 products and their effective applications in meteorology and hydrology were demonstrated by previous studies [53; 58; 68]. MERRA-2 data have coarse spatial resolution (0.5\({}^{\circ}\)\(\times\) 0.625\({}^{\circ}\)), and we resampled the data to 0.05\({}^{\circ}\) for the prediction of SIF. The accuracy of our SIF product could be further improved should high-quality meteorological data with finer spatial resolution be available. The comparison of spatial patterns and seasonal cycles between GOSIF and the coarse-resolution SIF directly aggregated from OCO-2 SIF soundings provides insight into the performance of our SIF product in the spatial and temporal domains. The seasonal cycles and annual averages of GOSIF captured the spatial variations presented in coarse-resolution OCO-2 SIF [69; 70], and were also generally consistent with those derived from previous coarse-resolution SIF products from GOSTAT [19; 20; 31] and GOME-2 [18; 71]. The comparison between our SIF product with current gridded GPP products may provide robust evidence on the potential of our new SIF in monitoring the terrestrial photosynthesis. We found that the spatial pattern of annual averaged new SIF agreed well with that from the MODIS GPP product [6]. However, the annual maximum magnitudes of the two products did not match well with each other. The highest values were observed in the U.S. Corn Belt region for our SIF product, while the MODIS GPP product had the highest values in the tropical regions. The high SIF signal in the U.S. Corn Belt region was also detected in previous studies based on GOME-2 SIF [33; 72]. This inconsistency between our SIF product and the MODIS GPP product may result from the underestimation of GPP by the MODIS GPP algorithm in high-productivity cropland regions mainly due to the low maximum LUE parameter value. A previous study [73] found that the mean annual MODIS GPP largely underestimated cropland GPP, and the optimization of the maximum LUE parameter significantly improved the accuracy of GPP. Another study [33] also found that the MODIS GPP model underestimated GPP at cropland sites with high fluxes. These studies suggested that reflectance-based indices usually underestimated 'greenness' for very dense crop canopies with high green biomass levels. Our new SIF product, GOSIF, is able to provide a reasonable diagnosis on the GPP over the largest crop belts worldwide as well as previous satellite SIF retrievals, but with much more spatial detail. The SIF had an increasing trend during 2001 to 2017 in many regions. The largest positive trends were observed in China and India, while large negative trends were found in parts of tropical regions (southern Amazon and eastern Brazil). The increasing trend in China benefited from China's afforestation efforts [74; 75] and improved agricultural management practices [76].