# New Gap-Filling Strategies for Long-Period Flux Data Gaps Using a Data-Driven Approach
## 4 Discussion
### How Large is the Uncertainty Related to the Long-Period Flux-Gap-Filling? The error in the long-period flux-gap-filling exhibited a double-exponential (Laplace) distribution, similarly to the random flux measurement error e.g., [34]. Figure 7 shows histograms of the SVR model (i.e., SVR-based model trained using all available data except for 2007, 2014, and the target year, hereafter called SVRall) error for the fluxes (= estimation using SVRall - gap-filled data using the marginal distribution sampling method) and the statistics that explain their distributions over the entire study period. The averages were close to 0, whereas the standard deviations ranged from 0.49 to 1.03. The distributions were slightly left-skewed. The excess kurtoses ranged from 2.65 to 4.83, indicating that the distributions were fitted to a double-exponential distribution (with excess kurtosis of 3) rather than a normal distribution (with excess kurtosis of 0). Figure 7: Histograms of the SVR model error for the fluxes, i.e., GPP (**a**), RE (**b**), NEE (**c**), and ET (**d**) over the entire study period. The solid red line represents a double-exponential distribution with the given average and standard deviation. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{3}{c}{**Support Vector Regression**} & \multicolumn{3}{c}{**Random Forest**} & \multicolumn{3}{c}{**Artificial Neural Network**} \\ \cline{2-13}  & **MBE** & **RMSE** & **Slope** & \(\mathbf{r^{2}}\) & **MBE** & **RMSE** & **Slope** & \(\mathbf{r^{2}}\) & **MBE** & **RMSE** & **Slope** & \(\mathbf{r^{2}}\) \\ \hline GPP & **0.335** & **0.925** & **1.045** & **0.896** & 0.412 & 0.940 & 1.046 & 0.885 & 0.338 & 0.938 & 1.050 & 0.895 \\ RE & **0.337** & **0.568** & **1.086** & 0.899 & 0.454 & 0.628 & 1.133 & **0.922** & 0.376 & 0.633 & 1.100 & 0.876 \\ NEE & **0.002** & 0.892 & **0.941** & 0.763 & 0.043 & **0.854** & 0.825 & 0.753 & 0.038 & 0.895 & 0.949 & 0.767 \\ ET & **0.229** & 0.477 & 1.105 & **0.854** & 0.252 & 0.474 & 1.096 & 0.831 & 0.240 & **0.477** & **1.095** & 0.833 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical parameters for error assessment of Experiment 3-6 using SVR, random forest (RF), and artificial neural network (ANN). MBE and RMSE indicate mean bias error and root-mean-square error, respectively (Units: g C m\({}^{-2}\) day\({}^{-1}\) for GPP, RE and NEE, mm day\({}^{-1}\) for ET). Slope and \(\mathbf{r^{2}}\) obtained from linear regression analysis. Numbers in bold indicate the best estimations based on each of the statistical parameters for error assessment. To quantify the uncertainties in the annual flux sums due to the long-period flux-gap-filling, we used a standard Monte Carlo approach [35]. First, we added artificial noise into the flux dataset to account for the SVR model errors. The noise was generated from a double-exponential distribution with a suitable standard deviation for each cultivation season (i.e., rice cultivation and non-rice cultivation), which was estimated similarly to Figure 7. We repeated this process 100 times, and then calculated the standard deviation of the annual sums (\(\sigma\)). The factor 2\(\sigma\) represents the uncertainty in the annual flux sum due to the long-period flux-gap-filling at approximate 95% confidence intervals. The values of 2\(\sigma\) were approximately 57 g C m\({}^{-2}\) year\({}^{-1}\) in GPP, 37 g C m\({}^{-2}\) year\({}^{-1}\) in RE, 52 g C m\({}^{-2}\) year\({}^{-1}\) in NEE, and 27 mm year\({}^{-1}\) in ET.