# Effect of the Partitioning of Diffuse and Direct APAR on GPP Estimation
## 3 Results
### Half-Hourly GPP Estimation by Diffuse and Direct APAR (DDA)-Based Method  
In order to explore the effects of partitioning the diffuse and direct APAR on the half-hourly GPP estimation, site GPPs were collected from the FLUXNET2015 data sets. Meanwhile, the total APAR-based method was used as a comparison method. Figure 4 shows the validation of half-hourly GPP estimated by the diffuse and direct APAR-based model (GPP_DDA) and the total APAR-based GPP (GPP_TA) against the FLUXNET GPP (observed GPP) in six sites covering different vegetation types during the entire year. The results showed that GPP estimated using the DDA method presented higher R\({}^{2}\) and lower RMSE values (R\({}^{2}\) varied from 0.565 to 0.682, RMSE values were within the range of 3.219 to 12.405) against observed GPP than GPP_TA (R\({}^{2}\) varied from 0.558 to 0.653, RMSE values ranged from 3.407 to 13.081), which indicated that the partition of diffuse and direct APAR in the GPP estimation can reduce the uncertainties when using big leaf models. In addition, a corrected RMSE value (see Section 2.7) was calculated for removing the scale difference between the satellite data and in-situ data as well as the systematic error of the big leaf-based model. Table 6 summarized the statistic metrics of DDA-based GPP and TA-based GPP with the observed GPP, concluding R\({}^{2}\), RMSE, RMSE* and the variation coefficient of RMSE* values. From the result of the RMSE* values, obvious decrease of RMSE* values of the DDA-based GPP can be found in all vegetation types (the variation coefficient of RMSE* is varied between \(-\)11.224% and \(-\)23.015%). Moreover, a test between these two models was used to indicate the difference between the DDA method and the total APAR-based method. The \(p\)-values were all less than 0.05 under a significance level of 0.05, which showed a significant difference in partitioning diffuse and direct APAR in the GPP estimation compared to the total APAR-based method. Besides, for a more intuitive validation of the DDA-based method, different levels of diffuse fraction are distinguished for calculating RMSE values between the DDA-based GPP and the observed GPP. Similarly to Figure 2, diffuse fraction was firstly divided in to ten groups, ranging from 0 to 1 with 0.1 intervals and the levels of diffuse fraction corresponds to 1 to 10 accordingly. Next, RMSE values between the DDA-based GPP and the observed GPP were calculated under different levels. Figure 5 shows the RMSE variation under different levels of diffuse fraction in different vegetation types over six FLUXNET sites. A \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Vegetation** & \multicolumn{2}{c}{**R\({}^{2}\)**} & \multicolumn{2}{c}{**RMSE (umolC/m\({}^{2}\)/s)**} & \multicolumn{2}{c}{**RMSE\({}^{*}\) (umolC/m\({}^{2}\)/s)**} & \multicolumn{2}{c}{**Variation Coefficient of**} \\ \cline{2-7}
**Types/Metrics** & **DDA** & **TA** & **DDA** & **TA** & **DDA** & **TA** & **RMSE* (\%)** \\ \hline EBF & 0.565 & 0.558 & 3.219 & 3.407 & 2.785 & 3.321 & \(-\)16.140 \\ ENF & 0.651 & 0.635 & 5.470 & 5.814 & 4.722 & 5.319 & \(-\)11.224 \\ DBF & 0.682 & 0.653 & 12.405 & 13.081 & 7.120 & 8.358 & \(-\)14.512 \\ SAV & 0.645 & 0.622 & 11.528 & 11.903 & 6.302 & 7.468 & \(-\)15.513 \\ GRA & 0.635 & 0.619 & 10.076 & 11.016 & 8.395 & 9.625 & \(-\)12.779 \\ CRO & 0.627 & 0.608 & 7.292 & 7.315 & 5.362 & 6.965 & \(-\)23.015 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The statistic metrics of DDA-based GPP (left side) and TA-based GPP (right side) with observed GPP.