Investigation of Temperature Multifractrality According to Zugspitze Weather Station Data

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Abstract

The main multifractal properties of time series of mean, maximum and minimum daily temperatures are analyzed using the method of multifractal fluctuation analysis. As initial data, we used the results of instrumental temperature observations made at the Zugspitze meteorological station in the period from August 1, 1900 to January 31, 2023. In general, variations in the mean, maximum and minimum daily temperatures demonstrate multifractal behavior, especially for small time scales, up to about 90 days An analysis of the generalized Hurst exponent found that the considered time series have a long-term positive correlation and that the multifractality is weaker with large fluctuations. The singularity spectrum for all time series is truncated to the left, which means that the time series have a multifractal structure that is insensitive to local fluctuations of large values.

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S. A. Riabova Riabova

Sadovsky Institute of Geosphere Dynamics of Russian Academy of Sciences

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Email: riabovasa@mail.ru
Russian Federation, Leninsky prosp., 38, build. 1, Moscow, 119334

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2. Fig. 1. Dependence of the fluctuation function Fq(s) for moments q = -6, -3, 0, 3, 6 from s on a logarithmic scale for time series of minimum (a), maximum (b) and average temperature (c).

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3. Fig. 2. Dependence of generalized Hurst indices h(q) on the moment q for time series of minimum (a), maximum (b) and average temperature (c).

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4. Fig. 3. The singularity spectrum for the time series of minimum (a), maximum (b) and average temperature (c).

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