# New Gap-Filling Strategies for Long-Period Flux Data Gaps Using a Data-Driven Approach
## 2 Materials and Methods  
### Site and Data Description  
The HFK site is located near the southwestern coast of the Korean Peninsula (34\({}^{\circ}\)33\({}^{\prime}\)14\({}^{\prime\prime}\) N, 127\({}^{\circ}\)34\({}^{\prime}\)12\({}^{\prime\prime}\) E, 12 m a.s.l. ; Figure 2). The major vegetation near the tower (within \(\sim\)300 m) is seasonally cultivated crops such as beans, sweet potatoes, Indian millet, and sesame. Beyond this area, rice paddies prevail, except in the northern area. The HFK site practices two-crop rotation in the same area in sequential seasons (i.e., rice for summer and fall and barley for spring). A detailed description of the HFK site has been given previously by [PERSON] et al. [9]. The EC technique is used to measure the CO\({}_{2}\)/H\({}_{2}\)O/energy fluxes from a 20 m tower at the site. Vertical and horizontal wind speeds and temperature are measured with a three-dimensional sonic anemometer and thermometer (SAT; Model CSAT3, Campbell Scientific Inc., Logan, UT, USA) at 10 Hz. An open-path infrared gas analyzer (IRGA; Model LI-7500, LI-COR Inc., Lincoln, NE, USA) is used to measure CO\({}_{2}\) and H\({}_{2}\)O concentrations. Half-hourly ECs and the associated statistics are calculated online from the 10 Hz raw data and stored in a datalogger (Model CR5000, Campbell Scientific Inc., Logan, UT, USA). The ECs are corrected in the post-processing phase (a sector-wise planar fit rotation producing eight tilt planes every 28 days [11; 12; 13] and Webb-Pearman-Leuning correction [14]). Other measurements such as net radiation, air temperature, humidity, soil temperature, ground heat fluxes, and soil water content are sampled every 10 s, averaged over 30 min, and logged in the datalogger. More information about EC and these meteorological measurements can be found in [PERSON] et al. [15]. To improve the data quality by eliminating data that is physiologically and physically implausible, the collected data are examined by a quality control procedure based on the KoFlux data-processing protocol [16; 17]. This procedure includes storage term calculation [18], spike detection [18], gap-filling (by marginal distribution sampling method that is appropriate for gaps of less than a month [1]), and nighttime CO\({}_{2}\) flux correction [19]. For gap-filling of meteorological data (e.g., downward shortwave radiation, air temperature, humidity, and precipitation), linear interpolation is applied for short (<4 h) gaps and linear regression is performed using data from the automated synoptic observing system operated by the Korea Meteorological Administration, which is located about 100 m from the flux tower. The distribution of long gaps in the meteorological data was similar to that in the flux data. After quality control (and before gap-filling), the final percentage of data retrieval was \(59\pm 12\%\) for CO\({}_{2}\) flux and \(61\pm 12\%\) for ET over the study period from 2003 to 2015 (Table 1). The data retrieval rates for CO\({}_{2}\) flux and ET were relatively low because the open-path IRGA measurements were  
Figure 2: Location of the study site. The shaded area around the tower indicates the effective flux footprint measured by the eddy covariance system (adapted from [PERSON] et al. [10]). frequently impaired by sea fog (the site is located near the sea). The data retrieval rates were \(\sim\)35% in 2007 and 2014, somewhat lower than in other years (\(\sim\)65%). The first and second longest gaps in 2007 and 2014 lasted 82 and 61, and 123 and 41 days, respectively. The total lengths of the long gaps (i.e., longer than 30 days) were 143 days in 2007 and 164 days in 2014. The CO\({}_{2}\) flux manifested bimodal peaks that occurred first in May (the most vigorous growing period of barley) and later in August (the most vigorous growing period of rice) for the other years (see Figure 1). It is hard to reliably quantify the seasonal variation and annual budgets of CO\({}_{2}\) in 2007 and 2014.