In this study, Multifractal Detrended Fluctuation Analysis (MF-DFA) is applied to daily temperature time series (mean, maximum and minimum values) from 22 Greek meteorological stations with the purpose of examining firstly their scaling behavior and then checking if there are any differences in their multifractal characteristics. The results showed that the behavior is the same at almost all stations, i.e., time series are positive long-term correlated and their multifractal structure is insensitive to local fluctuations with large magnitude. Moreover, this study deals with the spatial distribution of the main characteristics of multifractal (singularity) spectrum: the dominant Hurst exponent, the width of the spectrum, the asymmetry and the truncation type of the spectrum. The spatial distributions are discussed in terms of possible effects from various climatic features. In general, local atmospheric circulation and weather conditions are found to affect the shape of the spectrum and the corresponding spatial distributions. Furthermore, the intercorrelation of the main multifractal spectrum parameters resulted in a well-defined group of stations sharing similar multifractal characteristics. The results indicate the usefulness of the non-linear analysis in climate research due to the complex interactions among the natural processes.

The Multifractal Detrended Fluctuation Analysis (MF-DFA) is used to examine the scaling behavior and the multifractal characteristics of the mean daily temperature time series of the ERA-Interim reanalysis data for a domain centered over Greece. The results showed that the time series from all grid points exhibit the same behavior: they have a positive long-term correlation and their multifractal structure is insensitive to local fluctuations with a large magnitude. Special emphasis was given to the spatial distribution of the main characteristics of the multifractal spectrum: the value of the Hölder exponent, the spectral width, the asymmetry, and the truncation type of the spectra. The most interesting finding is that the spatial distribution of almost all spectral parameters is decisively determined by the land–sea distribution. The results could be useful in climate research for examining the reproducibility of the nonlinear dynamics of reanalysis datasets and model outputs.

Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) was applied to time series of global methane concentrations and remotely-sensed temperature anomalies of the global lower and mid-troposphere, with the purpose of investigating the multifractal characteristics of their cross-correlated time series and examining their interaction in terms of nonlinear analysis. The findings revealed the multifractal nature of the cross-correlated time series and the existence of positive persistence. It was also found that the cross-correlation in the lower troposphere displayed more abundant multifractal characteristics when compared to the mid-troposphere. The source of multifractality in both cases was found to be mainly the dependence of long-range correlations on different fluctuation magnitudes. Multifractal Detrended Fluctuation Analysis (MF-DFA) was also applied to the time series of global methane and global lower and mid-tropospheric temperature anomalies to separately study their multifractal properties. From the results, it was found that the cross-correlated time series exhibit similar multifractal characteristics to the component time series. This could be another sign of the dynamic interaction between the two climate variables.

An important aspect in environmental sciences is the study of air quality, using statistical methods (environmental statistics) which utilize large datasets of climatic parameters. The air-quality-monitoring networks that operate in urban areas provide data on the most important pollutants, which, via environmental statistics, can be used for the development of continuous surfaces of pollutants’ concentrations. Generating ambient air-quality maps can help guide policy makers and researchers to formulate measures to minimize the adverse effects. The information needed for a mapping application can be obtained by employing spatial interpolation methods to the available data, for generating estimations of air-quality distributions. This study used point-monitoring data from the network of stations that operates in Athens, Greece. A machine-learning scheme was applied as a method to spatially estimate pollutants’ concentrations, and the results can be effectively used to implement missing values and provide representative data for statistical analyses purposes.

Precipitation is widely considered an important parameter and a key indicator of the evolving climate change. The intensity as well as the frequency of precipitation can be largely affected by disturbances of the hydrological cycle as a result of the increasing temperature of the atmosphere and the oceans. Through a variety of statistical methods, it is possible to assess changes in precipitation over the recent years, both regionally and globally. In this work, precipitation data from seven WMO stations in the Greek region were studied over the period of 1990−2020. By analyzing a set of extreme precipitation indices and applying the Sen and Mann-Kendall statistical methods, the trends and statistical significance of precipitation in the area of study were investigated. The results reveal an increase in the yearly number of days with extreme precipitation events as well as in the total amount of precipitation.

An important aspect in environmental sciences is the study of air quality, using statistical methods (environmental statistics) which utilize large datasets of climatic parameters. The air quality monitoring networks that operate in urban areas provide data on the most important pollutants, which via environmental statistics can be used for the development of continuous surfaces of pollutants’ concentrations. Generating ambient air quality maps can help guide policy makers and researchers to formulate measures to minimize the adverse effects. The information needed for a mapping application can be obtained by employing spatial interpolation methods to the available data, for generating estimations of air quality distributions. This study used point monitoring data from the network of stations that operates in Athens. A machine learning scheme was applied as a method to spatially estimate pollutants’ concentrations and the results could be effectively used to implement missing values and provide representative data for statistical analyses purposes.