Recurrence Analysis of Eddy Covariance Fluxes

  • Milan Flach
  • Holger Lange
  • Thomas Foken
  • Michael Hauhs
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 180)


Measuring energy and matter fluxes between the atmosphere and vegetation using the Eddy Covariance (EC) technique is the state-of-the-art method to quantify carbon exchange between terrestrial ecosystems and their surrounding. The EC equipment is usually mounted onto a flux tower reaching higher than the local canopy. Today, more than 600 flux towers are in operation worldwide. The methodological requirements lead to high sampling frequency (20 Hz) and thus to the production of very long time series. These are related to temperature, wind components, water vapour, heat and gas exchange, and others. In this chapter, the potential of Recurrence Analysis (RA) to investigate the dynamics of this atmosphere-vegetation boundary system is elucidated. In particular, the effect of temporal resolution, the identification of periods particular suitable for reliable EC flux calculations, and the detection of transitions between dynamical regimes will be highlighted.


Temporal Resolution EddyEddy Covariance Method Covariance Average Path Length Singular Spectrum Analysis Recurrence Plot 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We would like to thank C.L. Webber, Jr. for the invitation to contribute a chapter to this book on Recurrence Analysis after one of us (H.L.) gave a presentation at the Recurrence Symposium in Grenoble, France. We would like to acknowledge the FLUXNET data providers and the organizers of the FLUXNET database as outcome of the La Thuile FLUXNET workshop 2007, which would not have been possible without the financial support provided by CarboEurope-IP, FAOGTOS-TCO, iLEAPS, Max Planck Institute for Biogeochemistry, the American National Science Foundation, University of Tuscia, and the U.S. Department of Energy. The Berkeley Water Center, Lawrence Berkeley National Laboratory, Microsoft Research eScience, Oak Ridge National Laboratory developed the database and supported technically. Two anonymous reviewers provided valuable hints for improvement.


  1. 1.
    A. Serafimovich, F. Eder, J. Hübner, E. Falge, L. Voß, M. Sörgel, A. Held, Q. Liu, R. Eigenmann, K. Huber, H. F. Duarte, P. Werle, E. Gast, S. Cieslik, L. Heping, T. Foken, in ExchanGE Processes in Mountainous Regions (EGER): Documentation of the Intensive Observation Period (IOP3) June, 13th to July, 26th 2011 (Arbeitsergebn, Univ Bayreuth, Abt Mikrometeorol, 2011), pp. 47–135. ISSN 1614-8916Google Scholar
  2. 2.
    P. Gerstberger, T. Foken, K. Kalbitz, in The Lehstenbach and Steinkreuz Catchments in NE Bavaria, Germany, ed. by E. Matzner. Ecological Studies, vol. 172 (Springer, 2004), pp.15–41Google Scholar
  3. 3.
    M. Aubinet, T. Vesala, D. Papale, Eddy Covariance: A Practical Guide to Measurement and Data Analysis (Springer, Dordrecht Heidelberg London New York, 2012)CrossRefGoogle Scholar
  4. 4.
    D. Papale, M. Reichstein, M. Aubinet, E. Canfora, C. Bernhofer, W. Kutsch, B. Longdoz, S. Rambal, R. Valentini, T. Vesala, D. Yakir, Towards a standardized processing of Net Ecosystem Exchange measured with eddy covariance technique: algorithms and uncertainty estimation. Biogeosciences 3, 571–583 (2006)Google Scholar
  5. 5.
    M. Reichstein, E. Falge, D. Baldocchi, D Papale, M. Aubinet, P. Berbigier, C. Bernhofer, N. Buchmann, T. Gilmanov, A. Granier, T. Grünwald, K. Havrankova, H. Ilvesniemi, D. Janous, A. Knohl, T. Laurila, A. Lohila, D. Loustau, G. Matteucci, T. Meyers, F. Miglietta, J.-M. Ourcival, J. Pumpanen, S. Rambal, E. Rotenberg, M. Sanz, J. Tenhunen, G. Seufert, F. Vaccari, T. Vesala, D. Yakir, R. Valentini, On the separation of net ecosystem exchange into assimilation and ecosystem respiration: review and improved algorithm. Glob. Change Biol. 11(9), 1424–1439 (2005)Google Scholar
  6. 6.
    A.M. Moffat, D. Papale, M. Reichstein, D.Y. Hollinger, A.D. Richardson, A.G. Barr, C. Beckstein, B.H. Braswell, G. Churkina, A.R. Desai, E. Falge, J.H. Gove, M. Heimann, D. Hui, A.J. Jarvis, J. Kattge, A. Noormets, V.J. Stauch, Comprehensive comparison of gap-filling techniques for eddy covariance net carbon fluxes. Agricul. Forest Meteorol. 147(3–4), 209–232 (2007)Google Scholar
  7. 7.
    F. Takens, Detecting strange attractors in turbulence, in Dynamical Systems and Turbulence, ed. by D.A. Rand, L.-S. Young, Lecture Notes in Mathematics, vol. 898 (Springer, 1981), pp. 366–381Google Scholar
  8. 8.
    M.B. Kennel, R. Brown, H.D.I. Abarbanel, Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45(6), 3403–3411 (1992)Google Scholar
  9. 9.
    C.L. Webber Jr., N. Marwan (eds.), Recurrence Quantification Analysis (Springer, Understanding Complex Systems. Cham Heidelberg New York Dordrecht London, 2015)Google Scholar
  10. 10.
    K.W. Hipel, A.I. McLeod, Time Series Modelling of Water Resources and Environmental Systems (Elsevier, Amsterdam, 1994)Google Scholar
  11. 11.
    L. Cao, Practical method for determining the minimum embedding dimension of a scalar time series. Physica D 110(1), 43–50 (1997)Google Scholar
  12. 12.
    A.M. Fraser, H.L. Swinney, Independent coordinates for strange attractors from mutual information. Phys. Rev. A 33, 1–7 (1986)Google Scholar
  13. 13.
    H. Lange, Are Ecosystems dynamical systems? Int. J. Comput. Anticipatory Syst. 3, 169–186 (1998)Google Scholar
  14. 14.
    J.P. Zbilut, C.L. Webber Jr., Embedding and delays as derived from quantification of recurrence plots. Phys. Let. A 171, 199–203 (1992)Google Scholar
  15. 15.
    C.L. Webber Jr., J.P. Zbilut, J. Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76, 965–973 (1994)Google Scholar
  16. 16.
    N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, Recurrence-plot-based measures of complexity and their application to heartrate—variability data. Phys. Rev. E 66(2), 026702 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    N. Marwan, M. Carmen Romano, M. Thiel, J. Kurths, Recurrence plots for the analysis of complex systems. Phys. Rep. 438(5–6), 237–329 (2007)Google Scholar
  18. 18.
    R.V. Donner, Y. Zou, J.F. Donges, N. Marwan, J. Kurths, Recurrence networks—a novel paradigm for nonlinear time series analysis. New J. Phys. 12(3), 033025 (2010)Google Scholar
  19. 19.
    R.V. Donner, J.F. Donges, Y. Zhou, J.H. Feldhoff, Complex network analysis of recurrences, in Recurrence Quantification Analysis, ed. by C.L. Webber Jr., N. Marwan (Springer, Understanding Complex Systems. Cham Heidelberg New York Dordrecht London, 2015), pp. 101–163Google Scholar
  20. 20.
    N. Golyandina, A. Zhigljavsky, Singular Spectrum Analysis for Time Series (Springer, Springer Briefs in Statistics. Heidelberg New York Dordrecht London, 2013)CrossRefzbMATHGoogle Scholar
  21. 21.
    H. Lange, Recurrence quantification analysis in watershed ecosystem research. Int. J. Bifurcat. Chaos 21(04), 1113–1125 (2011)Google Scholar
  22. 22.
    H. Lange, S. Boese, Recurrence quantification and recurrence network analysis of global photosynthetic activity, in Recurrence Quantification Analysis, ed. by C.L. Webber Jr., N. Marwan (Springer, Understanding Complex Systems. Cham Heidelberg New York Dordrecht London, 2015), pp. 349–374Google Scholar
  23. 23.
    G. Fratini, M. Mauder, Towards a consistent eddy-covariance processing: an intercomparison of EddyPro and TK3. Atmos. Meas. Tech. 7(7), 2273–2281 (2014)Google Scholar
  24. 24.
    D.H. Lenschow, J. Mann, I. Kristensen, How long is long enough when measuring fluxes and other turbulence statistics. J Atm Oceanic Techn 11, 661–673 (1993)Google Scholar
  25. 25.
    H.J.I. Rinne, A.C. Delany, J.P. Greenberg, A.B. Guenther, A true eddy accumulation system for trace gas fluxes using disjunct eddy sampling method. J. Geophys. Res. 105(24), 791–798 (2000)Google Scholar
  26. 26.
    J. Rinne, C. Ammann, Disjunct eddy covariance method, in Eddy Covariance: A Practical Guide to Measurement and Data Analysis, ed. by M.Aubinet, T. Vesala, D. Papale (Springer, Dordrecht Heidelberg London New York, 2012), pp. 291–307Google Scholar
  27. 27.
    J.C. Kaimal, J.C. Wyngaard, Y. Izumi, O.R. Cot, Spectral characteristics of surface-layer turbulence. Q. J.Royal Meteorol Soc. 98, 563–589 (1972)Google Scholar
  28. 28.
    U. Ligges, S. Krey, O. Mersmann, S. Schnackenberg, tuneR: analysis of music (2014),
  29. 29.
    N. Marwan, J.F. Donges, Y. Zou, R.V. Donner, J. Kurths, Complex network approach for recurrence analysis of time series. Phys. Let. A. 373(46), 4246–4254 (2009)Google Scholar
  30. 30.
    T. Foken, B. Wichura, Tools for quality assessment of surface-based flux measurements.Agric. For. Meteorol. 78, 83–105 (1996)Google Scholar
  31. 31.
    N. Marwan, S. Schinkel, J. Kurths, Recurrence plots 25 years later—gaining confidence in dynamical transitions. EPL (Europhysics Letters) 101(2), 20007 (2013)Google Scholar
  32. 32.
    S. Haapanala, H. Hakola, H. Hellén, M. Vestenius, J. Levula, J., Rinne, Is forest management a significant source of monoterpenes into the boreal atmosphere?’ Biogeosciences 9(4), 1291–1300 (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Milan Flach
    • 1
  • Holger Lange
    • 2
  • Thomas Foken
    • 3
  • Michael Hauhs
    • 3
  1. 1.Max-Planck-Institute for BiogeochemistryJenaGermany
  2. 2.Norwegian Institute of Bioeconomy ResearchÅsNorway
  3. 3.University of Bayreuth, Bayreuth Center of Ecology and Environmental Research (BayCEER)BayreuthGermany

Personalised recommendations