# New Gap-Filling Strategies for Long-Period Flux Data Gaps Using a Data-Driven Approach
## 2 Materials and Methods
### Data-Driven Approach Using Support Vector Regression and Its Modification  
In this study, we used a data-driven methodology using remote-sensing data and support vector regression (SVR) [8], which has been demonstrated in the estimation of terrestrial CO\({}_{2}\) fluxes in Asia. SVR is a machine learning technique that transforms nonlinear regressions into linear regressions. It includes a data classification process that maps the original low-dimensional input space to a higher-dimensional feature space for classifying the data linearly e.g., [20]. This method first sets up an empirical model using site observational data and explanatory variables, and then applies the established model to generate extensive spatial data for continental-scale applications. Similarly, we were able to set up a model using one site's observational data, and then predict time-series data to fill long gaps using the model. Detailed information about SVR can be found in [PERSON] et al. [21]. LIB-SVM software was used to implement the SVR [22] ([[http://www.csie.ntu.edu.tw/~](http://www.csie.ntu.edu.tw/~)]([http://www.csie.ntu.edu.tw/~](http://www.csie.ntu.edu.tw/~))|cjlin/libsvm/). To apply the data-driven approach to the filling of long gaps in flux data, we modified the methodology as follows. First, we set the temporal scale of interest from days to multi-year. The target \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multicolumn{2}{c}{**Data Retrieval**} & \multicolumn{2}{c}{**Length of the 1 st**} & \multicolumn{2}{c}{**Length of the 2 nd**} & \multicolumn{2}{c}{**Total Length of the**} \\  & \multicolumn{2}{c}{**Rate (\%)**} & \multicolumn{2}{c}{**Longest Gap (Day)**} & \multicolumn{2}{c}{**Longest Gap (Day)**} & \multicolumn{2}{c}{**Long Gaps (Day)**} \\ \cline{2-9}  & \(F_{\text{CO}_{2}}\) & **ET** & \(F_{\text{CO}_{2}}\) & **ET** & \(F_{\text{CO}_{2}}\) & **ET** & \(F_{\text{CO}_{2}}\) & **ET** \\ \hline
2003 & 52.3 & 55.9 & 34.3 & 34.3 & 23.0 & 23.0 & 34.3 & 34.3 \\
2004 & 68.1 & 69.4 & 13.1 & 13.0 & 1.4 & 1.5 & 0.0 & 0.0 \\
2005 & 69.8 & 72.0 & 13.4 & 13.4 & 1.5 & 2.2 & 0.0 & 0.0 \\
2006 & 60.7 & 62.4 & 35.3 & 35.3 & 20.5 & 20.5 & 35.3 & 35.3 \\
2007 & 34.6 & 35.7 & 82.5 & 81.5 & 61.4 & 61.4 & 143.9 & 142.9 \\
2008 & 62.5 & 67.1 & 13.9 & 13.8 & 4.8 & 4.7 & 0.0 & 0.0 \\
2009 & 61.9 & 63.0 & 4.8 & 4.8 & 2.9 & 2.9 & 0.0 & 0.0 \\
2010 & 64.5 & 67.2 & 4.1 & 3.9 & 3.3 & 3.2 & 0.0 & 0.0 \\
2011 & 71.1 & 70.6 & 2.6 & 2.7 & 2.4 & 2.4 & 0.0 & 0.0 \\
2012 & 65.1 & 67.3 & 7.6 & 7.5 & 2.9 & 2.1 & 0.0 & 0.0 \\
2013 & 63.3 & 65.5 & 31.3 & 31.2 & 1.7 & 1.7 & 31.3 & 31.2 \\
2014 & 35.5 & 36.2 & 123.1 & 123.1 & 41.1 & 41.1 & 164.1 & 164.1 \\
2015 & 63.4 & 63.4 & 12.4 & 12.4 & 3.1 & 3.1 & 0.0 & 0.0 \\ \hline AVG [2] & 59.4 & 61.2 & 29.1 & 29.0 & 13.1 & 13.1 & 31.5 & 31.4 \\ STD & 11.8 & 11.9 & 35.5 & 35.4 & 18.8 & 18.8 & 56.4 & 56.4 \\ \hline \hline \end{tabular}  
* Longer than 30 days; 2 The average values (%) of \(F_{\text{CO}_{2}}\) and ET were 63.9 and 65.8, respectively, for the study period except 2007 and 2014, and were 35.1 and 35.9 for 2007 and 2014, respectively.  
\end{table} 
Table 1: Annual data retrieval rates, lengths of the first and second longest gaps, and total lengths of the long gaps 1 for CO\({}_{2}\) flux (\(F_{\text{CO}_{2}}\)) and evapotranspiration (ET) from 2003 to 2015 for the study site. AVG denotes average; STD denotes standard deviation.