Multifractal characterization and comparison of meteorological time series from two climatic zones

Jaromir Krzyszczak,Krzysztof Siwek,Monika Zubik,Jerzy Kozyra,Veska Georgieva,Anna Nieróbca,Cezary Sławiński,Piotr Baranowski,Valentin Kazandjiev

doi:10.1007/s00704-018-2705-0

Abstract

The results of the multifractal analysis performed for meteorological time series coming from four stations in Poland and Bulgaria located in varying climatic zones are presented. To assess climatic shift response (in 2001/2002), the analysis was conducted separately for two subsets. To analyze long-distance power-law correlations within the studied time series and evaluate the differences in dynamics of the climate between the analyzed sites and periods of time, the multifractal detrended fluctuation analysis methodology (MF-DFA) was proposed. It was revealed that the multifractal properties of precipitation differ considerably from other analyzed quantities. The singularity spectra were susceptible to climatic shift, what was indicated by the changes of spectra parameters. It was especially apparent for asymmetry, which changed from being right- to left-skewed, implying the occurrence of more extreme events. Similarities in the dynamics of meteorological processes for each of the climatic zones were proven by the close relation of respective multifractal spectra parameters coming from closely spatially related localizations.

Highlights

One of the major scientific challenges in climatology is to understand the basics of mechanisms leading to climate changes
The multifractal analysis was performed using the time series of basic weather elements from the meteorological stations located in two European countries: Poland and Bulgaria, which vary with climatic conditions
It can be stated that climatic conditions and climatic shifts have some impact on fluctuations present in the time series, as the slopes of fluctuation functions Fq(s) of time series of meteorological elements are influenced by them

Summary

Introduction

One of the major scientific challenges in climatology is to understand the basics of mechanisms leading to climate changes. Oscillations of the relevant meteorological quantities (Balling et al 1998), more exquisite methods including fractal analysis and chaos theory are being established and successfully used to grasp the dynamics of processes occurring in the individual layers of the atmosphere (Higuchi 1988; Kalauzi et al 2005) These novel approaches permit to derive trend and seasonality within the analyzed time series, and to assess other features, such as the long-distance power-law correlations, what means that decay of those correlations takes place in accordance with the power law, instead as the more intuitive exponential decay. Two specific features can be linked with a time series when its dimension is non-integer—inhomogeneity, which means the occurrence of extreme fluctuations at irregular intervals, and scaling symmetries, which define relationships between fluctuations over different separation distances (Scarlat et al 2007)

Methods

Results

Conclusion