Articles | Volume 20, issue 1
Nonlin. Processes Geophys., 20, 97–106, 2013
https://doi.org/10.5194/npg-20-97-2013

Special issue: Multifractional Brownian motions in geosciences

Nonlin. Processes Geophys., 20, 97–106, 2013
https://doi.org/10.5194/npg-20-97-2013

Research article 06 Feb 2013

Research article | 06 Feb 2013

Characterization of turbulence stability through the identification of multifractional Brownian motions

K. C. Lee K. C. Lee
  • Department of Industrial Engineering, Hanyang University, Seoul, Korea

Abstract. Multifractional Brownian motions have become popular as flexible models in describing real-life signals of high-frequency features in geoscience, microeconomics, and turbulence, to name a few. The time-changing Hurst exponent, which describes regularity levels depending on time measurements, and variance, which relates to an energy level, are two parameters that characterize multifractional Brownian motions. This research suggests a combined method of estimating the time-changing Hurst exponent and variance using the local variation of sampled paths of signals. The method consists of two phases: initially estimating global variance and then accurately estimating the time-changing Hurst exponent. A simulation study shows its performance in estimation of the parameters. The proposed method is applied to characterization of atmospheric stability in which descriptive statistics from the estimated time-changing Hurst exponent and variance classify stable atmosphere flows from unstable ones.