# Increasing Ecosystem Fluxes Observed from Eddy Covariance and Solar-Induced Fluorescence Data
## 2 Materials and Methods
### Machine Learning Algorithms  
We used two ML algorithms, eXtreme Gradient Boosting (XGB) and Random Forest (RF), to develop data-driven models. The XGB algorithm is an updated version of the Gradient Boosted Decision Tree (GBDT) algorithm [49] and can build augmented trees to handle complex nonlinear relationships between inputs and outputs. In addition, the XGB algorithm adds regularization terms to the loss function, effectively preventing overfitting during the training process [50]. The RF is an integrative algorithm that randomly samples features during the training of each tree, rather than using all features. This randomness increases model diversity and reduces over-reliance on the same features for each tree [51]. Both the XGB and RF algorithms are based on decision tree models and can offer excellent accuracy and efficient operation on large datasets without overfitting [52; 53; 54]. Due to the feature selection process, decision trees are inherently resistant to the covariance between input variables. Specifically, when two input features are highly correlated, the decision tree model will select only one of them as a splitting feature during the decision process [55]. Recently, the XGB model has been used to identify the main climatic drivers of GPP variability at global FLUXNET sites and to quantify reasonable responses of GPP to various climatic factors such as VPD [56]. Similarly, RF models have been used to estimate regional GPP for rice-wheat rotation croplands, showing better performance than traditional methods [57; 58].  
We constructed site-level ML models for each PFT using available observations (Figure 1), including nine inputs (SIF and climatic drivers) and two outputs (GPP or ET). For each output (GPP or ET), a total of sixty models were built using one of the two ML algorithms (XGB or RF) by combining one out of three SIF products (CSIF, GOSIF, or RTSIF) with site-level observations across ten PFTs. Observations from all sites within each PFT were randomly divided into training (80%) and validation (20%) datasets to develop PFT-dependent models. During the training process, we optimized model hyperparameters using cross-validation and hyperparameter tuning to identify the optimal parameter combinations. Specifically, the hyperparameters were set to several candidate values, and different combinations were sequentially tested using five-fold cross-validation. The optimal combination of hyperparameters was then selected based on the results of the cross-validation. For validation, we used the remaining 20% of site-level observations to evaluate the performance of our data-driven models in deriving GPP and ET. Thereafter, based on year-to-year dominant PFTs from MODIS for each grid cell, we extended data-driven models from site level to global scales using gridded meteorology from the MERRA-2 reanalysis and the three SIF products by applying the corresponding PFT-specific ML models at individual grids. Thus, we generated six GPP, ET, and WUE products (2 ML algorithms \(\times\) 3 SIF datasets) at a spatial resolution of 0.05\({}^{\circ}\) and 8-day temporal resolution during 2001-2020 on the global scale.