Self-similarity analysis of chosen agro-meteorological time series

Piotr Baranowski, Jaromir Radosław Krzyszczak, Cezary Feliks Sławiński


The most usual records of observable agro-meteorological quantities are in the form of time series and the knowledge about their scaling properties is fundamental for  transferring locally measured fluctuations to larger scales and vice-versa. However, the scaling analysis of these quantities is complicated because of  the presence of localized trends and nonstationarities. The objective of this study was to characterize scaling properties (i.e. statistical self-similarity) of the  chosen agro-meteorological quantities through multifractal detrended fluctuation analysis (MFDFA). The MDFA analysis was performed  for time series of the air temperature, wind velocity and relative air humidity (at the height of 2 m above the  active surface) as well as the soil temperature (at 10 cm depth in the soil). The studied data were hourly interval, 12 years’ time series from the agro-meteorological station in Felin, near Lublin, Poland. The empirical singularity spectra  indicated their multifractal structure. The richness of the studied multifractals was evaluated by the width of their spectrum, indicating their considerable differences in dynamics and development. The log-log plots of the cumulative distributions of all the studied absolute and normalized meteorological parameters tended to linear functions for high values of the response  indicating that these distributions were consistent with the power law asymptotic behaviour. Additionally, we investigated the type of multifractality, that underlies the q-dependence of the generalized Hurst exponent, by analyzing the corresponding shuffled and surrogate time series. For majority of studied quantities, the multifractality was due to different long-range correlation for small and large fluctuations.

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