# New Gap-Filling Strategies for Long-Period Flux Data Gaps Using a Data-Driven Approach
## 1 Introduction  
Continuous flux measurements using the eddy covariance (EC) technique are challenging because it is costly and labor-intensive to maintain and repair the instruments and facilities required for theselong-term measurements. A long-term database for continuous flux measurement will contain a considerable number of data gaps, since flux gaps are unavoidable due to system failures such as power cuts, rain, lighting, wrong calibration, lens/filter/transducer contamination, and data quality filtering, such as steady-state testing and developed turbulent condition testing. Gap-filling is typically conducted before analyzing data, such as by quantifying seasonal/annual/decadal budgets and comparing them with modeling or remote-sensing results at a long timescale. There are various gap-filling techniques with different approaches, but essentially, most predict fluxes for gaps using measured data around the gaps [1; 2; 3; 4; 5]. In the Korea Flux Monitoring Network (KoFlux), the Haenam Farmland (HFK) site has the longest record (from July 2002 to present) of carbon/water/energy flux measurements produced using the EC technique. Over the period of its activity, various institutions, including Yonsei University, the National Institute of Meteorological Sciences, Seoul National University, and the National Center for AgroMeteorology of Korea have operated the HFK site. The HFK site is located in typical Korean farmland, which is characterized by mosaic patches of various agricultural lands including rice (and barley) paddy, beans, and sesame fields. The long-term database at HFK is vital in enabling better understanding of how the farmland has adapted and been managed to cope with natural and/or human disturbances over various time and spatial scales. Unfortunately, there are long gaps (i.e., gaps longer than 30 days) in the data, particularly in 2007 and 2014 (Figure 1). These gaps occurred during transfers of the flux tower management, primarily due to a lack of funding. Such long gaps hinder attempts to analyze the decade-long time-series data. General gap-filling approaches (e.g., marginal distribution sampling [1], mean diurnal variation, and look-up tables methods [2; 3]) are impractical for such long gaps. For example, the marginal distribution sampling method, which is one of the standard gap-filling methods in global/regional flux networks such as FLUXNET and KoFlux, would perform poorly because marginally distributed data rarely exist around gaps. It is also challenging to apply other methods such as the mean diurnal variation and nonlinear regression [2; 3; 4]. During long gaps of more than a month, the ecosystem state may change. Such changes can affect the relationships between the fluxes and their controlling factors (i.e., drivers), resulting in large gap-filling uncertainties [4; 5]. Figure 1: Time series of daily net ecosystem exchange (NEE) of CO\({}_{2}\) (**a**) and evapotranspiration (**c**) for the HFK site. The daily fluxes were calculated by averaging all available data in a day (not gap-filling). Shaded areas indicate the long gaps (i.e., gaps longer than 30 days) over the study period. If we have multiple-year data, we can fill long-period gaps using a machine learning algorithm and data from other years, e.g., the data from 2003 to 2015 except 2007 and 2014 [5]. Recently, a data-driven approach using machine learning and remote-sensing or reanalysis data (i.e., interpolating/extrapolating EC measurements via available networks temporally/spatially) has been used to estimate terrestrial CO\({}_{2}\)/H\({}_{2}\)O fluxes at the regional/global scale e.g., [6; 7; 8]. As the challenging issues for long-period-gap-filling are similar to those for inter-/extrapolation of EC measurements using the data-driven approach, this method can be applied to the gaps in the HFK data after appropriate modifications. [PERSON] et al. [4] tested artificial-neural-network-based gap-filling techniques for 12 day gaps and showed them to be generally superior to other techniques for these long gaps.