## 4 Results
### Spatiotemporal Patterns of Global Cropland GPP  
We compared the mean annual GPP estimated by the EF-LUE, MOD17 product, the revised EC-LUE GPP product, GOSIF GPP product, PML-V2 GPP product, and NIRv GPP product in the common available years of the six data sets (2002-2018). Spatial patterns of global cropland GPP estimated by the six data sets were similar (Figure 7). The  
Figure 6: Boxplot for comparisons of 8-d mean GPP between the EF-LUE GPP, MOD17 GPP, revised EC-LUE (rEC-LUE in the figures) GPP, GOSIF GPP, and PML-V2 GPP with the GPP measurements at cropland flux tower sites in 2002–2018.  
highest cropland GPP (>1500 g C m\({}^{-2}\) yr\({}^{-1}\)) was mainly distributed in tropical regions (e.g., Southeast Asia, and Brazil), due to sufficient hydrothermal conditions. The lowest crop GPP regions occurred in Russia and South of the Sahara Desert (<500 g C m\({}^{-2}\) yr\({}^{-1}\)) where climate and edaphic conditions were rigid, and the level of agricultural development was relatively low.  
The global mean annual GPP (2002-2018) for cropland simulated by our EF-LUE model is 1054.8 g C m\({}^{-2}\) yr\({}^{-1}\), very similar to the values of 1094.6 g C m\({}^{-2}\) yr\({}^{-1}\) from previous studies which is the median value of ground measurements and various diagnostic models (1998-2005) [74]. In general, our result of global mean annual GPP averaged over 2002-2018 was lower than that of the GOSIF and the PML-V2 GPP, and higher than that of the MOD17, the revised EC-LUE, and the NIRv GPP products.  
Figure 8 showed the difference in mean annual GPP (2002-2018) between the EF-LUE model and the five GPP datasets listed in Table 4. The MOD17 GPP showed generally low values (this was consistent with the site-level assessment where MOD17 gave the largest negative bias as shown in Figure 6), especially in Western Europe, East Asia, Southeast Asia, and some high-productivity regions in Africa and South America, whereas it was higher than the EF-LUE GPP in Central Europe, and Western Russia. This might be attributed to the constant \(\varepsilon_{max}\) value for all cropland used in the MOD17 method. Another reason for the large deviation in arid and semi-arid regions might be the insufficient expression of soil moisture constraints in the LUE model of the MOD17 GPP method. The EF-LUE GPP was significantly higher than the other two LUE GPP products and close to GOSIF GPP, NIRv GPP and PML-V2 GPP in Western Europe. However, in Eastern Europe and Russia, our model results seemed lower than GOSIF GPP, NIRv GPP, and PML-V2 GPP,  
Figure 7: Spatial pattern of global mean annual GPP of cropland (average over 2002–2018) estimated by (**a**) EF-LUE, (**b**) MOD17, (**c**) revised EC-LUE, (**d**) GOSIF GPP, (**e**) PML-V2 GPP, and (**f**) NIRv GPP.  
the PML-V2 GPP showed the highest values in this region. Both the MOD17 GPP and the revised EC-LUE GPP used the VPD function to constrain actual LUE without explicit consideration of soil moisture condition. The values from the revised EC-LUE GPP were generally higher than that of MOD17 GPP in the local high-productivity regions of southern China, Brazil, and Africa, which may be due to the consideration of diffuse radiation in estimation of LUE in the revised EC-LUE method. PML-V2 also used VPD to regulate canopy conductance and GPP. Although SIF is sensitive to drought, uncertainty might be introduced due to the fact that the long-term GOSIF GPP product was generated based on coarse-resolution SIF observations and re-produced at high spatial resolution using the relationship between SIF and other explanatory variables such as EVI, temperature, PAR, and VPD, rather than directly using SIF observations at higher spatial resolution. The NIRv GPP, based only on reflectance from red and near-infrared wavelength, might have missed subtle changes in photosynthetic activity caused by physiological processes associated with pigmentation [6,9].