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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
© Author(s) 2016. This work is distributed
under the Creative Commons Attribution 3.0 License.
Model evaluation paper
01 Jun 2016
Review status
This discussion paper has been under review for the journal Geoscientific Model Development (GMD). The revised manuscript was not accepted.
A robust gap-filling method for Net Ecosystem Exchange based on Cahn–Hilliard inpainting
Yufeng He and Mark Rayment School of Environment, Natural Resources and Geography, Bangor University, UK
Abstract. Traditional gap-filling approaches adopt a temporally linear perspective on data; whether synthesizing data statistically within a moving window, or using complex functions based on a “best-guess” understanding of the processes driving exchange. The former approach is limited in its ability to capture non-linear trends, and the latter is limited in situations where the flux response to driving variables is poorly understood or unknown (e.g. the response of gas exchange to water table depth in wetlands). Rearranging time-averaged half-hourly net ecosystem exchange (NEE) into a 48*N matrix has been used to visualize NEE as a “flux fingerprint” and suggests a different way of filling data gaps. In this paper, we introduce an image processing technique known as image inpainting to fill gaps in this two-dimensional representation of a one-dimensional data. This has the advantage that any short-term structure can be accommodated without expressly implying any particular functional response to driving environmental variables, and medium-term temporal structure (i.e. day-to-day covariance) can be incorporated into gaps in the flux signal. In this way, data gaps are filled solely using information contained in robust, primary data. This new method compares favorably with the marginal distribution sampling (MDS), when tested on twelve European-Flux datasets with four types of artificial gaps. Furthermore, we show that how random structures or noise embedded in the signal affect the gap-filling performance, which can simply be improved through a de-noising procedure by using a Fourier transform algorithm. The inpainting-based gap-filling approach is more effective than MDS on the de-noised data.

Citation: He, Y. and Rayment, M.: A robust gap-filling method for Net Ecosystem Exchange based on Cahn–Hilliard inpainting, Geosci. Model Dev. Discuss., doi:10.5194/gmd-2016-108, 2016.
Yufeng He and Mark Rayment
Yufeng He and Mark Rayment


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Short summary
We introduce a new method based on image inpainting to gap-filling the signal of Net Ecosystem Exchange.It is more intuitive, compact and highly comparable with a commonly-used method. Results showed a similar level of gap-filling errors between the two methods across twelve datasets. The gap-filling performance was improved from both methods when the original datasets were de-noised, implying that the noise or random structures embedded in signal determines the uncertainty level of gap-filling.
We introduce a new method based on image inpainting to gap-filling the signal of Net Ecosystem...