## 3 Results and Analyses
### Downscaled Results  
To evaluate the quality of the downscaled GPP, a pixel-by-pixel comparison between the MODIS GPP at 500 m and the downscaled GPP results was implemented during Julian days 169-209 (Figure 4b). From Julian day 169 to 209, the downscaled GPP for all pixels could be explained between 85% and 91% of 500 m MODIS GPP, with RMSEs varying between 0.71 and 1.30 gC m\({}^{-2}\)d\({}^{-1}\). The points in the scatterplots clustered around the 1:1 lines (R\({}^{2}\) = 0.89, RMSE = 1.03), and the downscaled GPP were slightly higher than MODIS GPP at high GPP values. In general, the downscaled GPP showed a strong consistency with the MODIS GPP at 500 m.  
Figure 6 illustrates the absolute differences of GPP values between the 500 m MODIS GPP and the downscaled GPP results. During Julian days 169-209, the percentages of absolute differences in ranges of [0, 1], [1, 2], [2, 3], [3, 4], [4, 5] and [5, 6] were 70.78%, 23.02%, 3.47%, 1.61%, 0.89% and 0.23%, respectively. The pixels whose absolute GPP differences between the 500 m MODIS GPP and the downscaled GPP results were in the range of [0, 2], accounting for 93.80% of the total pixels in the study area, showing that the downscaling method proposed in this study could be effectively used to obtain the GPP at 500 m resolution. Figure 7 shows the density distributions concerning the GPP differences between the 500 m MODIS GPP and the downscaled GPP results. The mean values of differences between downscaled GPP and 500 m MODIS GPP varied between 0.60 and 1.03 gC m\({}^{-2}\)d\({}^{-1}\), with standard deviations changing between 0.47 and 1.10 gC m\({}^{-2}\)d\({}^{-1}\), which were smaller than those between MODIS GPP at 500 m and 1 km (mean = 1.36, std. = 1.34). It was worthwhile to note that, the proposed downscaling method could effectively solve the GPP underestimation of 1 km MODIS GPP.  
Figure 5: Relationships between topographic factors and inconsistency in the MODIS GPP at 500 m and 1 km during Julian days 169–209.  
Figure 6: The spatial distribution of absolute GPP differences between the 500 m MODIS GPP and the downscaled GPP results for Julian days 169–209. Figures (**a**–**f**) indicate Julian days 169–209, respectively.  
Figure 7: The density distributions concerning the GPP differences between the 500 m MODIS GPP and the downscaled GPP results for Julian days 169–209. Figures (**a**–**f**) indicate Julian days 169–209, respectively.  
To illustrate the advantages and benefits of the proposed downscaling method, the downscaled results in this work, along with the kriging downscaled results, spline downscaled results and IDW downscaled results, were compared against the MODIS GPP at 500 m (Figure 4). In general, the proposed downscaled results (R\({}^{2}\) = 0.89, RMSE = 1.03) had a stronger consistency with the 500 m MODIS GPP than the kriging downscaled results (R\({}^{2}\) = 0.43, RMSE = 1.36), the spline downscaled results (R\({}^{2}\) = 0.40, RMSE = 1.50) and the IDW downscaled results (R\({}^{2}\) = 0.42, RMSE = 1.10) for all Julian days. Hence, it can be concluded that the proposed downscaling method has a potential application for GPP downscaling to obtain 500 m GPP distributions, especially in mountainous areas. The results also illustrated that vegetation heterogeneity factors and topographic factors were effective for downscaling land surface fluxes, showing good matches with other related studies [7; 8; 38].