# Improving the Gross Primary Production Estimate by Merging and Downscaling Based on Deep Learning
## Results  
### Quality Evaluation of Merging Results  
The trained merging model has been tested. The results of comparing GLASS GPP, CMIP6 DL GPP, and multi-model ensemble mean with fluxnet data in China are shown in Figure 3. However, the results only represent the accuracy of the ten sites, as there are only ten unevenly distributed flux towers in China. As can be seen from the figure, all three datasets have a wide distribution range in the four indicators. The distribution range in MAE, RMSD and \(r^{2}\) of the multi-model ensemble mean is wider than that of the other two datasets, indicating that it has a higher uncertainty. Although the distribution range is relatively small on ubRMSD, many outliers exist in the multi-model ensemble mean. The  
Figure 2: Loss function curves for the training and the validation dataset. uncertainty of CMIP6\({}_{\text{DL}}\) GPP is lower compared with the multi-model ensemble mean, while the median performs the best in MAE, RMSD, and ubRMSD. The merged data have improved overall (Figure 3a-c), indicating that data are closer to the actual value than the multi-model ensemble mean. Table 2 shows the model's performance on the test dataset taking GLASS GPP as the benchmark, with the results showing that the merged GPP has improved in the aspect of the four indices and has a higher accuracy in China as a whole compared with the multi-model ensemble mean. The normalized Taylor diagram obtained by calculating correlation coefficients, ubRMSD, and standard deviation ratios is used to evaluate further the CMIP6\({}_{\text{DL}}\) GPP, CMIP6 GPP, and muti-model ensemble mean. GLASS GPP has been used as the reference due to its relatively low uncertainties. Figure 4 shows the distribution of correlation coefficient, ubRMSD, and standard deviation ratio between 25 datasets (including CMIP6\({}_{\text{DL}}\) GPP, the multi-model ensemble mean, and 23 CMIP6 datasets) and the reference data in 2013-2014. As shown in Figure 4, the red dot represents GLASS GPP. Since it is used as reference data, the correlation coefficient and standard deviation ratio are equal to 1, and ubRMSD is 0. The black dot represents CMIP6\({}_{\text{DL}}\) GPP data, which is the closest to the red dot in the figure, indicating that the overall performance of CMIP6\({}_{\text{DL}}\) GPP data is better than that of all datasets simulated by other models. The correlation coefficient of all CMIP6 GPP is less than 0.82, and ubRMSD is greater than 0.5. There are significant differences among the 23 model data, of which CAS-ESM2-0 performs the best, even better than the multi-model ensemble mean. The multi-model ensemble mean is still superior to most single CMIP6 data, though it is affected by the high error of model data. In general, CMIP6\({}_{\text{DL}}\) GPP data perform \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **MAE** & **RMSD** & **ubRMSD** & \(\mathbf{r^{2}}\) \\ \hline CMIP6\({}_{\text{DL}}\) GPP & 0.3575 & 0.7691 & 0.7668 & 0.8556 \\ Ensemble mean & 1.2378 & 1.7664 & 1.5137 & 0.6632 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean absolute error (MAE), root mean square deviation (RMSD), unbiased root mean square difference (ubRMSD), and coefficient of determination (r\({}^{2}\)) between merged GPP, the multi-model ensemble mean, and GLASS GPP. Figure 3: (a) MAE (b) RMSD (c) ubRMSD (d) r\({}^{2}\) between GLASS GPP, CMIP6\({}_{\text{DL}}\) GPP, the multi-model ensemble mean, and observations over China. Blue “+” represents outlier of CMIP6 DL, orange “+” represents outlier of Ensemble Mean. To evaluate the spatial accuracy of the merged data, the spatial absolute error distributions of CMIP6\({}_{\text{DL}}\) GPP, the multi-model ensemble mean, and GLASS GPP are plotted, respectively. Figure 5a shows the MAE between CMIP6\({}_{\text{DL}}\) GPP and GLASS GPP in the test dataset, with the results showing that the regions with MAE less than 0.5 account for 73.91%. The errors in Northwest, Northeast, and North China are generally minor, less than 0.21 gCm\({}^{-2}\)d\({}^{-1}\).