## 2 Materials and Methods
### Estimation of GPP Based on Machine Learning Algorithms  
The Random forest (RF) algorithm is an ensemble learning approach for classification or regression that integrates many decision trees [63]. The number of decision trees, the number of features to select for each split, and the minimum number of observations per leaf are hyper-parameters that need to be modified. The RF algorithm subsamples features according to the user's settings before growing each tree, which can reduce the correlation among individual decision trees and thus improve model accuracy. Furthermore, its ability to handle high-dimensional information helps us analyze climatic and environmental factors [64]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Category** & **Variable** & **Description** & **Source** \\ \hline Vegetation Indices & SIF & Solar-induced chlorophyll fluorescence & [47] \\  & NIR\({}_{\mathrm{V}}\) & Near-infrared reflectance of vegetation & MCD43C4 \\  & LAI & Leaf Area Index & [48] \\ Plant Traits & HC & Canopy height & [55] \\  & SLA & Specific leaf area & [54] \\  & Nm & Foliar nitrogen concentration per unit dry mass & [54] \\ Climatic Factors & Tmp & Air temperature & [11] \\  & Tmax & Maximum air temperature & [11] \\  & Tmin & Minimum air temperature & [11] \\  & DTR & Diurnal temperature range & [11] \\  & Prec & Precipitation & [11] \\  & SRAD & Downward shortwave radiation flux at the surface & [11] \\  & SWC & Soil water content & [11] \\  & VPD & Vapor Pressure Deficit & [11] \\ Other Factors & PFT & Plant functional type & MCD12Q1 \\  & CO\({}_{2}\) & Atmospheric carbon dioxide concentration & [60] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of the datasets used in the data-driven models. Artificial neural networks (ANNs) are a type of machine learning algorithm inspired by the structure and function of biological neural networks [65]. A typical ANN usually consists of input, output, and hidden layers, each containing several artificial neurons. The back propagation neural network (BPNN) is one of the most popular and proven ANN algorithms being used for ecological studies [66; 67; 68]. During the model training process, signals flow from the input layer to the output layer, perhaps after passing through several hidden layers. Errors in the output layer propagate backward to the previous layers until they meet the user-defined threshold. The network attempts to minimize the discrepancies between observations and predictions. We used the RF model to identify the factors with the most powerful explanation of GPP and to explore the importance of these predictors. We trained six RF models to select features using the 'TreeBagger' function of MATLAB 2021b, i.e., two types of models (PFT-specific and universal) for each vegetation index (SIF, \(\mathrm{NIR_{v}}\), and LAI). RF was chosen due to the robustness of ranking feature importance under different hyperparameters and high interpretability. For each of the six models, one vegetation index as well as all environmental factors (plant functional type [PFT] and atmospheric carbon dioxide concentration [CO2]), climatic constraints (air temperature [Tmp], maximum air temperature [Tmax], minimum air temperature [Tmin], diurnal temperature range [DTR], precipitation [Prec], downward shortwave radiation flux at the surface [SRAD], soil water content [SWC], and vapor pressure deficit [VPD] for the current month, the previous month, and the previous two months), and plant traits (canopy height [Hc], specific leaf area [SLA], and foliar nitrogen concentration per unit dry mass [Nm]) were initially selected for training (Table 1). Each model comprised 100 decision trees, was sampled without replacement, and was trained using 70% of the data. Model performance was evaluated using out-of-bag (OOB) R-squared (R\({}^{2}\)) and root mean square error (RMSE) values. The predictor with the lowest importance score in the iteration was removed and the whole procedure was then repeated until only the vegetation index, CO2, and PFTs were left.