## 2 Study Area, Data and Methods
### Methods  
RF is a fast and flexible machine learning algorithm, which is often used for analyzing the classification and regression tasks [42]. This model can successfully process highly dimensional and multicollinear data, being insensitive to overfitting [43]. The RF model provides a feature-selection tool to identify the importance of the predictor. Feature importance is defined as the contribution of each variable to the model, with important variables showing a greater impact on the model evaluation results [44]. In this section, a GPP prediction model based on RF framework was proposed. The flowchart of estimating and upscaling GPP and calibrating the MOD17A2H GPP product with the RF model is shown in Figure 3, including four steps as follows:  
1. Variable selection and data matching. Crop photosynthesis is a complicated process affected by shortwave radiation, air temperature, vapor pressure deficit, soil edapholicating and fertilization at the canopy scale, etc. Meanwhile, at the ecosystem level, GPP is closely related to light, water and canopy phenology [23; 45]. Based on the previous literature as well as our current available data, nine input explanatory variables, NDVI, LAI, FPAR, DSR, daily maximum air temperature (\(T_{\text{max}}\)), daily minimum air temperature (\(T_{\text{min}}\)), daily mean air temperature (\(T_{\text{mean}}\)), VPD, and RH, were chosen for predicting the GPP dynamics in the NYRD region. As RF model training requires a large number of samples, MODIS data were linearly interpolated from 8-day/16-day to daily values to match the input parameters, following a previous study by [PERSON] et al. [19]. 2. RF model construction, training and testing. In this paper, 90% (the rest 10%) of the EC data at Shouxian and Dongtai during the entire observation period were employed to train (validate) the RF model, and 100% of the EC data at Dafeng were applied to validate the model. The Shouxian and the Dafeng sites were independent of each other with a negligible autocorrelation between them, as these sites are about 300-400 km far away from each other (Figure 1). Here, a 10-fold cross-validation (CV) algorithm was applied to weaken the overfitting [20]. In 10-fold CV experiments, all the training data at the Shouxian and Dongtai sites during the entire observation period were randomly partitioned into ten equal-sized subsamples. Of the ten subsamples, nine subsamples were used as the training data and the remaining one was the testing data. This CV process was repeated ten times, with all ten subsamples used exactly once as the testing data. The ten results from the folds were averaged to produce a single estimation. To select the best model, we adjusted the four hyperparameters of the RF model based on Bayesian optimization [46; 47]: the number of trees to grow (n_estimators), the minimum sample number placed in a node prior to the node being split (msplit), maximum number of features considers to split a node (Mfeatures), and the maximum number of levels in each decision tree (Mdepth). Three statistical metrics--the index of agreement (IA) [48], the coefficient of determination (\(R^{2}\)), and the root mean square error (RMSE)--were used to examine the simulated performance of the 10-fold CV results. The range of IA is 0-1, and a better correspondence between the observed and modeled results often occurs when it approaches 1 [49]. Therefore, n_estimators = 219, msplit = 2, Mfeatures = 9, and Mdepth = 32 were set for the final RF model. 3. GPP upscaling. The general relationships between GPPRF and explanatory data were first trained at site level, and then applied regionally by using regional surface meteorological stations of explanatory variables as follows: GPPRFVS\(f\) (\(T_{\text{max}}\), \(T_{\text{min}}\), \(T_{\text{mean}}\), VPD, RH, NDVI, LAI, FPAR, DSR). * 4 MOD17A2H GPP product calibration. Based on the upscaled results of GPPRF and GPPMOD at the station scale, a relationship between GPPRF and GPPMOD was built.