Articles | Volume 12, issue 6
Nonlin. Processes Geophys., 12, 767–774, 2005
https://doi.org/10.5194/npg-12-767-2005
Nonlin. Processes Geophys., 12, 767–774, 2005
https://doi.org/10.5194/npg-12-767-2005

  03 Aug 2005

03 Aug 2005

Scaling collapse and structure functions: identifying self-affinity in finite length time series

S. C. Chapman1, B. Hnat1, G. Rowlands1, and N. W. Watkins2 S. C. Chapman et al.
  • 1Space and Astrophysics, University of Warwick, UK
  • 2British Antarctic Survey (NERC), Cambridge, UK

Abstract. Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the special case of self affine time series in the context of a stochastic process. We highlight two complementary approaches to the differenced variable of the data: i) attempting a scaling collapse of the Probability Density Functions which should then be well described by the solution of the corresponding Fokker-Planck equation and ii) using structure functions to determine the scaling properties of the higher order moments. We consider a method of conditioning that recovers the underlying self affine scaling in a finite length time series, and illustrate it using a Lévy flight.