Irregularity and Multifractal Structure of Precipitation Patterns in Europe, the Mediterranean, the Middle East, and North Africa

Abstract

Abstract This study proposes a new perspective on analysing precipitation patterns in a large geographic region covering Europe, the Mediterranean, the Middle East, and North Africa. The primary objective is to investigate the multifractal singular spectrum structure of precipitation patterns, which is an important contribution to understanding the complex spatiotemporal variability of precipitation in this region. By using advanced statistical techniques such as multifractal detrended fluctuation analysis (MF-DFA), cross-correlation analysis (MF-DCCA), and empirical orthogonal functions (EOF) on precipitation data from the Climate Prediction Centre’s Combined Precipitation Analysis (CMAP), this study aims to enhance our understanding of precipitation patterns in the region and provide valuable insights into their multifractal singular spectrum structure. The DCCA technique was used to analyse the EOF functions of precipitation time series in the 12-month, 60-month (5-year), and 120-month (10-year) moving-window periods. In addition to the EOF patterns of the conventional (Pearson) correlation matrix, 864 precipitation time series from latitudes 20° to 75° N and longitudes 23°W to 61° E were used. The broad research area was chosen to encompass the Mediterranean basin, which is in a transition zone between the semi-arid North African belt and the moist western and central European regions. The present research employed the MF-DFA technique to compute the Hurst exponents and multiple fractal spectra of the top five significant empirical orthogonal functions (EOFs) across the studied region. Overall, this study offers a novel approach to analysing precipitation patterns in this region and can significantly contribute to our knowledge of their multifractal singular spectrum structure. The findings show that minor-scale fluctuations have a greater impact on the fixed larger-scale components, as evidenced by the q-dependent multifractal singular spectrum of the Hurst exponents. This could account for the non-uniform fractal shape and positively skewed inclination of the probability density functions of the precipitation data. The study reveals that the multifractal q-dependent structure of the EOFs remains persistent up to the 12th month or sub-year, after which it disappears. This observation is consistent with the finding that the EOF patterns, which provide insights into the geographical distribution of precipitation, are generally preserved over intervals of 12 months or more. Thus, the analysis of precipitation records across a large region highlights a prevalent climatological pattern that varies and evolves at sub-year intervals but is more stable and essentially consistent over longer timescales.