## 6 Conclusions  
In this study, a light-use-efficiency-based model (EF-LUE) was developed and applied to estimate global cropland GPP from 2001 to 2019. The water availability variable (i.e., indicating moisture stress), expressed by evaporative fraction (EF), was integrated in the EF-LUE model to consider the impact of water availability on GPP. Three key model parameters (\(\epsilon_{max}\), \(T_{opt}\), and \(VPD_{0}\)) in the developed EF-LUE model were optimized based on ground flux observations, and the optimized parameters were further extrapolated spatially according to climate zone classifications for global GPP estimation. The proposed EF-LUE model performed well in simulating spatial and temporal variations of global cropland GPP. It showed overall the highest R\({}^{2}\), KGE, and NSE and the lowest RMSE over the four existing GPP datasets (i.e., MOD17 GPP, revised EC-LUE GPP, GOSIF GPP, and PML-V2 GPP), when compared with the ground measurements of GPP from flux towers across crop sites globally. The accuracy of the EF-LUE GPP was also close to or even better than that of the PML-V2 GPP and GOSIF GPP, which highlighted the ability and potential of the LUE-based model for global GPP estimation, provided that the LUE model is well structured and calibrated, as with the EF-LUE model developed in this study. This study demonstrated the reliability of the EF-LUE model for estimating global cropland GPP by integrating EF as the indicator of soil water availability. It revealed that the EF-LUE GPP could track the impact of drought and heat-wave events on cropland productivity. This study provided a valuable dataset of cropland GPP at the global scale for the past two decades and could be further used for crop yield estimation.  
Conceptualization, D.D. and L.J.; methodology, D.D., L.J., Q.C. and C.Z.; software, D.D., C.Z. and M.J.; validation, D.D.; formal analysis, D.D., L.J., Q.C., C.Z., G.H., M.J. and J.L.; investigation, D.D., L.J., C.Z. and Q.C.; resources, L.J.; data curation, D.D., L.J. and C.Z.; writing--original draft preparation, D.D.; writing--review and editing, L.J. and C.Z.; visualization, D.D.; supervision, L.J., C.Z. and Q.C.; project administration, L.J.; funding acquisition, L.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA19030203), the National Key Research and Development Program of China (Grant No. 2017 YFE0119100), and the National Natural Science Foundation of China (Grant Nos. 42001092, 42171039).  
Authors thank data providers and platforms for GPP products from MOD17, the revised EC-LUE method, GOSIF method, NIRv method, and PML-V2; FAPAR data from the Copernicus Global Land Service System (CGLS) GEOV2 dataset; ERA5 reanalysis data, ESA CCI landcover dataset; Koppen-Geiger climate classification data; and eddy covariance flux data from the communities including FLUXNET, ChinaFlux, AmeriFlux, AsiaFlux, and European Fluxes Database. We are grateful to everyone who contributed to these data. We thank the anonymous reviewers for their constructive comments.  
The authors declare no conflict of interest.