# Comparison of Machine Learning Methods to Up-Scale Gross Primary Production
## 3 Results
### Cross Comparison with MODIS Products  
We compared the averaged up-scaled GPP in the growing season (from May to September 2014) with corresponding MODIS GPP products, pixel by pixel, as shown in  
Figure 8: Validation of up-scaled GPP using **(a)** Cubist, **(b)** RF, **(c)** ANN, **(d)** SVM, **(e)** DBN at footprint scale. These figures demonstrate the relationship between 8-day weighted average GPP at flux tower sites in the footprint and 8-day average up-scaled GPP from May to September in 2014 using five machine learning methods. The solid line is the fit line between GPP at flux tower sites in the footprint and up-scaled GPP, and the dashed line is the 1:1 line. Accuracy of up-scaled GPP using RF were the highest.  
Figure 7: Changes in climate footprint distance of GPP at flux tower sites with the changes in measurement height. This figure shows the changes in GPP footprint distance when the measurement heights increase 50% or decrease 50%.  
Figure 9. In general, a good linear relationship existed between the up-scaled GPP and MODIS GPP (R\({}^{2}\) ranged from 0.81 to 0.84, and RMSE ranged from 0.68 g C m\({}^{-2}\) d\({}^{-1}\) to 0.89 g C m\({}^{-2}\) d\({}^{-1}\)). The up-scaled GPP using RF had the strongest relationships with MODIS GPP (R\({}^{2}\) was 0.83 and RMSE was 0.68 g C m\({}^{-2}\) d\({}^{-1}\)). However, we could also found that most the plots in Figure 9 were distributed above the 1:1 line, which indicated that up-scaled GPP using machine learning methods were higher than MODIS GPP products in most cases. To illustrate this, we compared the MODIS GPP with GPP at flux tower sites, as shown in Figure 10. Although a good linear relationship existed between the MODIS GPP and GPP at flux tower sites, most the plots were distributed under the 1:1 line, which demonstrated that the MODIS GPP products were underestimated in the study area, and lead to a high error (RMSE = 3.66 g C m\({}^{-2}\) d\({}^{-1}\)). Previous studies [30] have also shown that in the Heihe River Basin, MODIS GPP products were underestimated. Therefore, in this paper, up-scaled GPP using machine learning methods were higher than MODIS GPP in most cases.  
Figure 11 demonstrated the difference of up-scaled GPP and MODIS GPP. We found that spatial distribution of up-scaled GPP was consistent with MODIS GPP. The difference of up-scaled GPP with MODIS GPP ranged from 2.00 g C m\({}^{-2}\) d\({}^{-1}\) to 4.00 g C m\({}^{-2}\) d\({}^{-1}\) in most of the upstream study area. We also studied the Pearson coefficients between the 8-day up-scaled GPP and 8-day MODIS GPP products from May to September in 2014 (Figure 12). The absolute values of Pearson coefficients were higher than 0.60 in most of the upstream study area.  
Figure 9: Comparison of up-scaled GPP using **(a)** Cubist, **(b)** RF, **(c)** ANN, **(d)** SVM, **(e)** DBN with MODIS GPP pixel by pixel. These figures demonstrate the relationship between MODIS GPP (8-day, 1000 m) and 8-day average up-scaled GPP from May to September in 2014 using five machine learning methods. The solid line is the fit line between MODIS GPP and up-scaled GPP, and the dashed line is the 1:1 line. The number of pixels is 23268 (n = 23268). Due to the underestimation of MODIS GPP products, up-scaled GPP using machine learning methods were higher than MODIS GPP products in most cases.  
Figure 11: Difference in up-scaled GPP using (**a**) Cubist, (**b**) RF, (**c**) ANN, (**d**) SVM, (**e**) DBN with MODIS GPP. Up-scaled GPP were higher than MODIS GPP in most areas.  
Figure 10: Validation of MODIS GPP against GPP at flux tower sites. MODIS GPP products were underestimated compared with GPP at flux tower sites. The solid line is the fit line between GPP at flux tower sites and MODIS GPP, and the dashed line is the 1:1 line.