Investigation into Temperature Multifractrality According to Zugspitze Weather Station Data

Abstract

The main multifractal properties of time series of mean, maximum, and minimum daily temperatures are analyzed using multifractal fluctuation analysis. 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.