## 2 Methodology
### Methodology  
The schematic representation of the estimated GPP based on GOSIF SIF products and auxiliary data is shown in Figure 1.  
The first step comprised data pre-processing. The data sources used in this study were not identical, and they featured different spatial and temporal resolutions. Therefore, to reduce the uncertainty caused by geographic location, all remote sensing data were converted to the same geographical projection (WGS84), and the data were resampled to the same spatial resolution as GOSIF (0.05\({}^{\circ}\)) using the bilinear interpolation method. In addition, to ensure the accuracy of machine learning methods during modeling, GPP ground observations should be used as the input variable in the training set of the machine learning model. However, the data volume derived from flux towers is small, the spatial scale of flux towers is small, the underlying ground surface is complex, and the vegetation types are diverse. As they are affected by spatial heterogeneity, it is difficult to directly apply the observations from the GPP flux towers to the regional scale. Therefore, we have calibrated the GPP products (MODIS GPP and GLASS GPP) through multiple linear regression methods, using flux observations from sites with different vegetation types. Thus, we have obtained new GPP datasets as \"reference values\" for the training set of the machine learning model.  
The second step entailed building the model. In recent years, SIF and NIRv provide alternative approaches to estimate global GPP [45; 70; 73]. Meanwhile, precipitation and temperature are important for plant photosynthesis. Thus, we added SIF, DEM, land cover, NIRv, month, latitude, and longitude as explanatory variables. To ensure the robustness of the model, we randomly sampled the calibrated GPP datasets in 2001, 2004, 2007, 2010, and 2013, and added the explanatory variables. Then, the generated dataset was divided into a training dataset (70% of the generated dataset) and a validation dataset (30% of the generated dataset). Random forest (RF) is an integrated machine learning algorithm that integrates multiple weak classifiers (decision trees) [79]. Multivariate adaptive regression splines (MARS) is an automatic and adaptive nonparametric regression algorithm, which attempts to build a nonlinear regression model by fitting the weighted sum of multivariate spline basis functions [80]. The gradient boosting regression trees (GBRT) method proposed by [PERSON] is an iterative decision tree, which combines several weak classifiers in different proportions to form a strong classifier by additive model and forward distribution algorithm, and has been applied in remote sensing [81; 82]. Light gradient boosting machine (LightTGBM) uses a decision tree-based learning algorithm that enables fast, efficient, parallel learning and large-scale data processing [83]. Long short-term memory (LSTM), a kind of neural network used for processing sequence data, is a special kind of recurrent neural network (RNN) [84]. In this study, global GPP estimation models were established using random forest (RF), MARS, GBRT, LightGBM, and LSTM algorithms using a training dataset.  
Figure 1: Flowchart of the global GPP estimation from GOSIF SIF data.  
Subsequently, the validation dataset was used to validate these five models. The accuracies of models established by these algorithms were compared, and the optimal model and explanatory variables were selected to estimate the long-term global GPP.  
Based on the five model results for the RF, MARS, GBRT, LightGBM, and LSTM algorithms, we compared two statistical indicators: coefficient of determination (R\({}^{2}\)) and root-mean-square error (RMSE) (see Appendix A for details). By comparing the accuracy of the model training dataset with the validation dataset and the efficiency of the model, we found that the GBRT model was more suitable for estimating global GPP based on GOSIF, and so we used this model to estimate global GPP from 2001 to 2017.