Multifractal analysis of temperature in Europe: Climate change effect

Abstract

We investigated multifractality of temporal series of daily mean air temperature anomalies over the entire European continent by applying the method Multifractal detrended fluctuation analysis (MFDFA) on high resolution E-OBSv26.0e dataset. The spatial resolution is 0.1⁰ which corresponds to 120,866 grid cells, and the time span of daily temperature series is from 1961 to 2020, which permits to compare two climate periods (1961–1990 and 1991–2020) and evaluate the impact of climate change. For each grid cell and each of the two periods we calculated the multifractal spectrum $f\left(\alpha \right)$ which contains the information about specific properties of temperature series: persistence (described by the position of the maximum of the spectrum ${\alpha }_0$), strength of multifractality (described by the spectrum width $W$) and the contribution of large/small fluctuations (described by the spectrum skew parameter $r).$We found that in both periods temperature series exhibit properties of a multifractal process, with persistent long-term correlations (${\alpha }_0>0.5)$and the dominance of scaling of small fluctuations ($r>0$). The spatial distribution of multifractal parameters exhibits a distinct gradient during the first period. The parameter ${\alpha }_0$ (persistence) increases from west to east and from south to north. In contrast, $W$ (strength of multifractality) decreases from south to north in regions outside Eastern Europe, whereas it increases from south to north within Eastern Europe. In the second period, the area with stronger multifractality (higher $W$ values) of temperature anomalies expanded significantly in Eastern Europe. The spatially averaged value and the range of the width W of the multifractal spectrum increased in the second period following the increase of the mean daily temperature. These results reveal the impact of climate change on multifractal properties of air temperature.