# New Gap-Filling Strategies for Long-Period Flux Data Gaps Using a Data-Driven Approach
## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Variables**} & \multicolumn{4}{c}{**Experiment No. 1-1**} & \multicolumn{4}{c}{**Experiment No. 1-2**} \\ \cline{2-9}  & **MBE** & **RMSE** & **Slope** & \(\mathbf{r^{2}}\) & **MBE** & **RMSE** & **Slope** & \(\mathbf{r^{2}}\) \\ \hline GPP (g C m\({}^{-2}\) day\({}^{-1}\)) & **0.441** & **1.204** & 1.070 & **0.841** & 0.518 & 1.545 & **1.028** & 0.679 \\ RE (g C m\({}^{-2}\) day\({}^{-1}\)) & **0.373** & 0.717 & **1.086** & 0.819 & 0.376 & **0.655** & 1.100 & **0.875** \\ NEE (g C m\({}^{-2}\) day\({}^{-1}\)) & **-0.068** & **1.156** & **0.948** & **0.653** & \(-\)0.142 & 1.463 & 0.585 & 0.294 \\ ET (mm day\({}^{-1}\)) & **0.225** & **0.457** & 1.081 & **0.832** & 0.228 & 0.761 & **0.997** & 0.328 \\ \hline \end{tabular}  
* We performed linear regression analysis instead of orthogonal (or major axis) regression analysis even though the observational data from 2009 (the target year) also had uncertainties. For error assessment, we implicitly assumed that the uncertainties of measured data were negligible when we set up a support vector regression (SVR)-based model using the observational data.  
\end{table} 
Table 4: Statistical parameters for error assessment of Experiments 1-1 and 1-2. MBE and RMSE indicate mean bias error and root-mean-square error, respectively. Slope and \(r^{2}\) were obtained from linear regression analysis1. GPP, RE, NEE, and ET represent the daily gross primary production, ecosystem respiration, net ecosystem exchange, and evapotranspiration, respectively. Numbers in bold indicate the best estimations based on each of the statistical parameters for error assessment. Figure 4: Time series of the daily gross primary production (GPP) (**a**), ecosystem respiration (RE) (**b**), net ecosystem exchange (NEE) (**c**), and evapotranspiration (ET) (**d**) at the study site in 2009 from the observations (Obs) and the SVR-based model from Experiments 1-1 (SVR\({}_{1-1}\)) and 1-2 (SVR\({}_{1-2}\)). Based on the results of Experiments 2-1 to 2-5 (Figure 5), we rejected Hypothesis 2, that is, that a training dataset for machine learning closer to the gaps would result in better estimation. We expected that using the closest training dataset would give the best results for Experiment 2-1, because the ecosystem state of the target year might be similar to that of the training years. Contrary to this expectation, the results of Experiment 2-1 were not the best except the RMSE for ET, and there were no increasing (decreasing) trends of the RMSE (\(r^{2}\)) with the amount of time elapsed between the target year and the training year. On the basis of the results for Experiments 3-1 to 3-6 (Figure 6), we accepted Hypothesis 3, that is, that a longer training dataset for machine learning would result in better estimation. We expected the experimental results to improve as the training datasets became longer. Considering that extrapolation (interpolation) involves predicting a value outside (inside) the domain of the data, extrapolation is more uncertain than interpolation. If the domain is extended with the length of the training dataset, the gap-filling is closer to interpolation (with less uncertainty) than extrapolation. As expected, using longer datasets for training produced better estimations (i.e., lower RMSE and higher \(r^{2}\)) by gradually reducing the discrepancies between the observations and the SVR-based model (Figures S3 and S4). It is worth noting that GPP improved quite a lot with Experiment 3-4 (Experiment 3-5), probably because the model included the data in 2012 and 2004, when the lowest and highest annually-averaged \(T_{\text{air}}\) and LAI occurred simultaneously, respectively (see Table 2). Figure 5: Statistical parameters for error assessment of Experiments 2-1, 2-2, 2-3, 2-4, and 2-5. MBE (**a**) and RMSE (**b**) indicate mean bias error and root-mean-square error, respectively. Slope (**c**) and \(r^{2}\) (**d**) obtained from linear regression analysis.