Abstract
The Multifractal Detrended Fluctuation Analysis (MF-DFA) is used to examine the scaling behavior and the multifractal characteristics of the mean daily temperature time series of the ERA-Interim reanalysis data for a domain centered over Greece. The results showed that the time series from all grid points exhibit the same behavior: they have a positive long-term correlation and their multifractal structure is insensitive to local fluctuations with a large magnitude. Special emphasis was given to the spatial distribution of the main characteristics of the multifractal spectrum: the value of the Hölder exponent, the spectral width, the asymmetry, and the truncation type of the spectra. The most interesting finding is that the spatial distribution of almost all spectral parameters is decisively determined by the land–sea distribution. The results could be useful in climate research for examining the reproducibility of the nonlinear dynamics of reanalysis datasets and model outputs.
Highlights
Many processes in nature are governed by nonlinear laws and they can be considered to be nonlinear systems that are described by nonlinear differential equations
Following the findings of Kalamaras et al [49], which are based on observational temperature records over Greece, the scope of this study is to examine the behavior and the spatial distribution of multifractal spectrum characteristics using temperature time series from a reanalysis dataset
The Multifractal Detrended Fluctuation Analysis (MF-Detrended Fluctuation Analysis (DFA)) analysis of the ERA-Interim reanalysis temperature data revealed that the time series are long-range positively correlated
Summary
Many processes in nature are governed by nonlinear laws and they can be considered to be nonlinear systems that are described by nonlinear differential equations. A nonlinear system can be described effectively by the time series of a characteristic set of the system’s parameters. A noticeable characteristic of many time series that result from nonlinear systems is the self-similarity, where, when part of the time series is enlarged, it is exactly the same as, or approximately similar to, the whole time series. There are many time series with a fractal structure and, ever since the primary studies of Benoite B. Mandelbrot [1,2], a great number of studies and books about fractals have been published [3,4,5]
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