## 3 Results
### Flux Data Modeling, Uncertainty Analysis, and Benchmarking  
For NEE gap-filling, the overall performance of SVM-based models outcompeted all others (Table 1). The R\({}^{2}\) values of the regression between ANN-predicted NEE and the original NEE were satisfactory based on a 10-fold CV and a 7-day FW settings. However, a big reduction in performance was found when 14-day FW setting was used (R\({}^{2}\) = 0.02), which was unexpected. Meanwhile, the 7-day FW setting appeared to be a better setting compared with others. Likewise, SVM-based models yielded the optimal performance across all partition settings with an average R\({}^{2}\) value of 0.89 and an average RMSE value of 78.2. Both ANN-based models and the REddyProc software produced very similar results. The LSLM-based models generally provided the worst performance indices across all partitioning settings, and 10-fold CV generally provided the best performance for linear models. Interestingly, no performance plunge was detected under ANN-based LE models. Obviously, REddyProc gap-filling algorithms could provide reliable predictions for LE, but its performance on NEE prediction appeared to be limited. In general, the regressions between REddyProc-based predictions and original values explained more variation as more features were included in the models (from none to all three variables). Interestingly, Rg-only models appeared to be the best model (R\({}^{2}\) = 0.64) for NEE gap-filling. Finally, Figures 8 and 9 depict the performance of the best gap-filling machine learning models for NEE and LE, respectively. The best results generated by REddyProc-based models were also included in both figures for comparison purposes. The optimal results of NEE and LE gap-filling were both provided by SVM-based models using 7-day FW setting. concentration from April to August within the 2017 and 2018 growing seasons of a grass-dominated grassland ecosystem located in Middle Tennessee. A one-time hay harvest was conducted around each mid-July. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Target Variable** & **Algorithm** & \multicolumn{2}{c}{**Training/Testing Partition Setting**} & **Average** \\ \hline \hline \multirow{8}{*}{NEE} & \multicolumn{2}{c}{**10-Fold CV**} & \multicolumn{2}{c}{**7-Day FW**} & \multicolumn{2}{c}{**14-Day FW**} \\ \cline{2-5}  & LSLM & 0.57 & 0.33 & 0.42 & 0.44 \\  & LSLM & (7.8) & (17.7) & (13.9) & (13.3) \\  & ANN & 0.64 & 0.69 & 0.02 & 0.45 \\  & (13.4) & (13.4) & (153.6) & (60.1) \\  & SVM & 0.71 & 0.77 & 0.77 & 0.75 \\  & (12.7) & (11.8) & (11.8) & (12.1) \\ \cline{2-5}  & \multicolumn{2}{c}{**None**} & \multicolumn{2}{c}{**Reature Setting**} & \multicolumn{2}{c}{**Rg + Tair + VPD**} \\ \cline{2-5}  & REddyProc & 0.21 & 0.64 & 0.56 & 0.47 \\  & (40.9) & (15.7) & (19.6) & (25.4) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Benchmarking performance of gap-filling artificially created missing net ecosystem exchange (NEE) or latent heat flux (LE) data points. Results were evaluated as R\({}^{2}\) and root mean square error (RMSE) values (in parenthesis) based on a simple linear regression between predicted and eddy covariance-measured values. Particularly, last-square linear models (LSLM), artificial neural network (ANN), and support vector machine (SVM) algorithms were used and evaluated based on different cross validation settings (10-fold CV, 7/14 day flaking windows). Three different variable settings used by REddyProc were compared, including: global radiation, ambient air temperature, and vapor pressure deficit are all available (Rg + Tair + VPD); both Tair and VPD are missing but Rg is available (Rg); and all three variables are missing (None). Figure 7: Above-ground biomass yield versus cumulative gross primary production (GPP) from April to August within the 2017 and 2018 growing seasons of a grass-dominated grassland ecosystem located in Middle Tennessee.