*2.6. Statistical Analyses and Model Evaluation*

We firstly calculated the daily values of EC-based GPP and then aggregated to the eight-day and annually values for seasonal and yearly GPP validation. To evaluate the performance of the MOD17A2H GPP model, we compared the modeled GPP with the flux tower-estimated GPP both in 8-day and annual time steps. We extracted the eight-day composite MODIS C6 GPP product (MOD17A2H) and the other MODIS products (e.g., MOD15A2H and MOD09A1 products) from the pixels centered on the flux towers, and compared the MODIS GPP product with the EC-based GPP observations.

The model performance (i.e., differences between simulated and tower-based GPP) were quantified by using the coefficient of determination (R2), root mean squared error (RMSE), and relative RMSE (rRMSE):

$$\text{RMSE} = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} (Y\_{sim,t} - Y\_{obs,t})^2} \tag{4}$$

$$\text{rRMSE} = \frac{1}{\overline{Y\_{obs,t}}} \times \sqrt{\frac{1}{n} \sum\_{i=1}^{n} \left(Y\_{sim,t} - Y\_{obs,t}\right)^2} \times 100 \tag{5}$$

where, *Y*sim and *Y*obs represent the simulated and observed GPP data, respectively, and *n* is the total number of samples. All the statistical analyses and results presentation are performed in Matlab R2016b software (Mathworks, Natick, MA, USA).

## **3. Results**

#### *3.1. Evaluation of MODIS GPP Products and MOD17 Algorithm in the Arid Region*
