## 2 Materials and Methods
### Data-Driven SIF Prediction Model Using the Random Forest Algorithm
#### 2.3.2 Random Forest Approach for SIF Modeling  
Random forest has been widely applied in remote sensing applications such as classification, and the estimation of high-density wetland biomass [60; 61; 62; 63]. Random forest (RF) was first proposed by [PERSON] [64] and is a classifier that uses multiple decision trees to train and predict samples. Compared with other widely used non-parametric algorithms, RF is insensitive to unbalanced distributions and the problem of missing data. Because of the random way it selects data for splitting each tree node, it is also less sensitive to the over-fitting problem [60; 64]. It performs better for large, high-dimensional data sets and is more robust to noise and feature selection [65; 61; 62; 63; 64]. Additionally, the prediction ability of Random Forest is resistant to the multicollinearity of the driven variables [66; 67; 68], so all the all the variables in Equation (2) were used to predict the spatially continuous TanSat SIF. The main parameters used in RF are the numbers of input prediction variables and decision trees. [PERSON] et al. [69] found that there was no obvious relationship between the accuracy and the number of selected prediction variables, and so used the default value of the square root of the total number of variables [62; 70]. For the number of decision trees, [PERSON] et al. [71] found by developing 10 to 200 trees (at intervals of 10) that the accuracy was insensitive to the number of trees. In this study,100 trees and six variables (three prediction variables were selected) were used in RF. The importance of each predictor was calculated by calculating the percentage increase in the mean-squared error when the value of a particular variable was changed (while keeping the other values unchanged): this allowed us to determine which were the important variables [64].  
Here, a Random Forest (RF) approach was employed to model the normalized SIF, as in Equation (6): the flowchart for the corresponding procedure is illustrated in Figure 1. The input variables used were MCD43C4, and the vegetation index, air temperature and cos (SZA\({}_{0}\)) datasets. Since the spatial resolution of MCD43C4 is 0.05\({}^{\circ}\), to maintain consistency with MCD43C4, the TanSat SIF needed to be aggregated to a resolution of 0.05\({}^{\circ}\). The SIF training samples were eliminated if there were less than 20 samples in each 0.05\({}^{\circ}\) cell between 10\({}^{\circ}\)S and 60\({}^{\circ}\)N. However, due to the low vegetation coverage in some areas, there were few valid data. Therefore, in order to keep the integrity of the global coverage of the samples, we relaxed these restrictions and only eliminated samples which had less than 5 samples in each grid cell. The final results were that there were 118,722 SIF grid cells for 2017, 187,077 cells for 2018, and 173,153 cells for 2019. The air temperature data were also resampled to 0.05 degrees using polynomial interpolation.  
To validate the RF model, we randomly took 70% of the data as the training set and 30% as the validation set for each year. Three accuracy metrics, the coefficient of determination (R\({}^{2}\)), Relative Deviation (RD) and Root Mean Square Error (RMSE) were used to evaluate the performance of the RF model.