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On the estimation of persistence in geophysical time series

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Abstract

The estimation of persistence (or: self-correlation) is necessary to evaluate the effective degree of freedom (or: the number of statistically independent samples) of a geophysical time series. The application of textbook definitions may result in problems when the time series contains periodic signals. This is demonstrated with analytical solutions for a given auto-correlation function. On physical grounds, in this paper we estimate the persistence time as the integral over the absolute value of the auto-correlation function. This procedure has been proposed by Stratonovich and is shown to work for slow and fast oscillations involved. In the practical part of the paper, a 42-year long time series of phase height measurements at Kühlungsborn (54 ∘N, 12 ∘E) is studied. In the period band between 2.7 and 27 years, it shows a persistence time of about 12 years and an effective degree of freedom of 3.5. Hence, the negative trend of 310 meters per decade was found to be significant at a level of 86 %. This level could be raised if the time series were longer.

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References

  1. J. Bartels, Physik.-Math. Klasse B4 30, 504 (1935)

    Google Scholar 

  2. J. Taubenheim, Statistische Auswertung geophysikalischer und meteorologischer Daten (Geest and Portig, 1969), p. 386

  3. R. Stratonovich, Topics in the Theory of Random Noise (Gordan and Breach, New York & London, 1963)

  4. H.v. Storch, F.W. Zwiers, Statistical Analysis in Climate Research (Cambridge University Press, 1999), p. 484

  5. L. Schimansky-Geier, Ch. Zülicke, Z. Physik B 79, 451 (1990)

    Article  ADS  Google Scholar 

  6. J. Bremer, D.H.W. Peters, J. Atmos. Sol.-Terr. Phys. 70, 1473 (2008)

    Article  Google Scholar 

  7. J. Taubenheim, Gerlands Beiträge zur Geophysik (Leipzig) 83, 121 (1974)

    Google Scholar 

  8. J. Taubenheim, G. Entzian, K. Berendorf, Adv. Space Res. 20, 2059 (1997)

    Article  ADS  Google Scholar 

  9. G. Beig, P. Keckhut, R.P. Lowe, R.G. Roble, M.G. Mlynczak, J. Scheer, V.I. Fomichev, D. Offermann, W.J.R. French, M.G. Shepherd, A.I. Semenov, E.E. Remsberg, C.Y. She, F.-J. Lübken, J. Bremer, B.R. Clemesha, J. Stegman, F. Sigernes, S. Fadnavis, Rev. Geophys. 41, 4 (2003)

    Article  Google Scholar 

  10. I.N. Bronstein, K.A. Semendjajew, Taschenbuch der Mathematik (Verlag Nauka, Moskau and BSB B.G.Teubner Verlagsgesellschaft, Leipzig, 1983), p. 840

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  1. Leibniz Institute of Atmospheric Physics at the University of Rostock, Kühlungsborn, Mecklenburg, Germany

    Ch. Zülicke & D.H.W. Peters

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  1. Ch. Zülicke
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  2. D.H.W. Peters
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Zülicke, C., Peters, D. On the estimation of persistence in geophysical time series. Eur. Phys. J. Spec. Top. 187, 101–108 (2010). https://doi.org/10.1140/epjst/e2010-01275-2

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  • DOI: https://doi.org/10.1140/epjst/e2010-01275-2

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