# 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
variables were daily integrated GPP (g C m\({}^{-2}\) day\({}^{-1}\)), RE (g C m\({}^{-2}\) day\({}^{-1}\)), NEE (g C m\({}^{-2}\) day\({}^{-1}\)), and ET (mm day\({}^{-1}\)), whereas the input variables were the daily downward shortwave radiation (\(R_{sdt}\), MJ m\({}^{-2}\) day\({}^{-1}\)), daytime air temperature (\(T_{\rm air}\), \({}^{\circ}\)C), daytime vapor pressure deficit (VPD, hPa) and precipitation (\(P\), mm day\({}^{-1}\)) at the flux tower, and the leaf area index (LAI, m\({}^{2}\) m\({}^{-2}\); [23]), enhanced vegetation index (EVI, unitless; [24]), and land-surface water index (LSWI, unitless; [25]) from the eight-day moderate resolution imaging spectroradiometer (MODIS) data products (MOD15A2 and MCD43A4 version 6; [26][[https://daac.ornl.gov/LAND_VAL/guides/MODIS_Web_Service_C6.html](https://daac.ornl.gov/LAND_VAL/guides/MODIS_Web_Service_C6.html)]([https://daac.ornl.gov/LAND_VAL/guides/MODIS_Web_Service_C6.html](https://daac.ornl.gov/LAND_VAL/guides/MODIS_Web_Service_C6.html))). The LAI, EVI, and LSWI data had a grid size of 1.5 km (i.e., 3 x 3 pixels) and were linearly interpolated to daily values under the assumption that day-to-day fluctuations of these indices were small. Additionally, a fuzzy transform was applied to the cultivation, assigning fuzzy values of 0-1 to barley, rice, and fallow, to distinguish each ecosystem state; this was similar to the procedure used by [PERSON] and [PERSON] [27] (Figure 3). From the perspective of ecological processes, NEE was not directly estimated using machine learning, but was instead calculated by subtracting the estimated GPP from the estimated RE. To understand the microclimatology and ecosystem state of the study site, we briefly examined the seasonality and annual sums (or means) of the input variables (Figures S1 and S2, Table 2). A feature worth noting was a mid-season depression in \(R_{sdtn}\) due to \"_changma_\", i.e., an intensive rainy spell that occurs during the summer [10; 15]. The highest \(T_{\rm air}\) was \(\sim\)30 \({}^{\circ}\)C in early August, while the lowest \(T_{\rm air}\) was \(\sim\)-3 \({}^{\circ}\)C in January. The VPD seasonally changed with \(T_{\rm air}\) and \(P\), and there was also a mid-season depression, similarly to \(R_{sdtn}\). The variations of LAI, EVI, and LSWI were related to the cultivation (i.e., two-crop rotation). The averages of annual sums (or means) during the study period were \(5075\pm 176\) (average \(\pm\) one standard deviation) MJ m\({}^{-2}\) year\({}^{-1}\) for \(R_{sdtn}\), \(15.7\pm 0.5\)\({}^{\circ}\)C for \(T_{\rm air}\), \(6.7\pm 0.8\) hPa for VPD, \(1254\pm 229\) mm year\({}^{-1}\) for \(P\), \(0.91\pm 0.06\) m\({}^{2}\) m\({}^{-2}\) for LAI, \(0.29\pm 0.01\) for EVI, and \(0.09\pm 0.01\) for LSWI. Note that the lowest annually-averaged \(T_{\rm air}\) and LAI (14.8 \({}^{\circ}\)C and 0.78 m\({}^{2}\) m\({}^{-2}\), respectively) occurred simultaneously in 2012, while both were the highest (16.5 \({}^{\circ}\)C and 0.99 m\({}^{2}\) m\({}^{-2}\), respectively) in 2004. To determine appropriate gap-filling strategies, we tested the following three hypotheses: (1) Estimation using in situ meteorological measurement data as input data to SVR is more reasonable than that using remote-sensing (or modeling) data; (2) A closer (to gaps) training dataset for machine learning results in better estimation; and (3) A longer training dataset for machine learning results in better estimation. To test these hypotheses, we designed experiments to target the flux data in 2009 because it was the middle of the database (Table 3). All the SVR-based models estimated the fluxes in 2009, and the original gap-filled data in 2009 from the marginal distribution sampling method were used for their validation.