Modelling random uncertainty of eddy covariance flux measurements

  • Domenico VitaleEmail author
  • Massimo Bilancia
  • Dario Papale
Original Paper


The eddy-covariance (EC) technique is considered the most direct and reliable method to calculate flux exchanges of the main greenhouse gases over natural ecosystems and agricultural fields. The resulting measurements are extremely important to characterize ecosystem exchanges of carbon, water, energy and other trace gases, and are widely used to validate or constrain parameter of land surface models via data assimilation techniques. For this purpose, the availability of both complete half-hourly flux time series and its associated uncertainty is mandatory. However, uncertainty estimation for EC data is challenging because the standard procedures based on repeated sampling are not suitable for this kind of measurements, and the presence of missing data makes it difficult to build any sensible time series model with time-varying second-order moments that can provide estimates of total random uncertainty. To overcome such limitations, this paper describes a new method in the context of the strategy based on the model residual approach proposed by Richardson et al. (Agric For Meteorol 148(1): 38–50, 2008). The proposed approach consists in (1) estimating the conditional mean process as representative of the true signal underlying observed data and (2) estimating the conditional variance process as representative of the total random uncertainty affecting EC data. The conditional mean process is estimated through the multiple imputation algorithm recently proposed by Vitale et al. (J Environ Inform, 2018). The conditional variance process is estimated through the stochastic volatility model introduced by Beltratti and Morana (Econ Notes 30(2): 205–234, 2001). This strategy is applied to ten sites that are part of FLUXNET2015 dataset, selected in such a way to cover various ecosystem types under different climatic regimes around the world. The estimated uncertainty is compared with estimates by other well-established methods, and it is demonstrated that the scaling relationship between uncertainty and flux magnitude is preserved. Additionally, the proposed strategy allows obtaining a complete half-hourly time series of uncertainty estimates, which are expected to be useful for many users of EC flux data.


Eddy covariance Net ecosystem exchange Global warming Uncertainty Conditional heteroskedasticity Time series Ecology 



Domenico Vitale (DV), Massimo Bilancia (MB), Dario Papale (DP). This paper has been started in the context of the ICOS-INWIRE Research Project funded by the European Community’s 7th Framework Program (FP7 / 2007-2013) under the Agreement \(\hbox {n}^{\circ }\) 313169 and continued and finalized under the ENVRIPLUS H2020 European Project (Grant Agreement 654182), that the authors thank for the support. DV conceived the study; DV and DP contributed to the study design; DV, MB and DP wrote the first draft of the manuscript. All authors equally contributed to the writing of Sect. 1. DV wrote Sects. 3.3456.3 and cared about the overall paper structure; MB wrote Sects.; Sects. 2 and 7 were written jointly by DV, MB and DP. All authors reviewed and revised the manuscript, approved the final version, and agreed to submit the manuscript for publication. This work used eddy covariance data acquired and shared by the FLUXNET community, including these networks: AmeriFlux, AfriFlux, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, ChinaFlux, Fluxnet Canada, GreenGrass, ICOS, KoFlux, LBA, NECC, OzFlux TERN, TCOS Siberia, and USCCC. The ERA-Interim reanalysis data are provided by ECMWF and processed by LSCE. The FLUXNET eddy covariance data processing and harmonization was carried out by the European Fluxes Database Cluster, AmeriFlux Management Project, and Fluxdata project of FLUXNET, with the support of CDIAC and ICOS Ecosystem Thematic Center, and the OzFlux, ChinaFlux and AsiaFlux offices. The authors thank in particular the PIs that shared the data used in the study.

Supplementary material

477_2019_1664_MOESM1_ESM.pdf (23.3 mb)
Supplementary material 1 (pdf 23813 KB)


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Authors and Affiliations

  1. 1.Department for Innovation in Biological, Agro-Food and Forest Systems (DIBAF)University of TusciaViterboItaly
  2. 2.Ionian Department of Law, Economics and EnvironmentUniversity of Bari Aldo MoroTarantoItaly

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