Multifractal analysis of meteorological time series to assess climate impacts

Abstract

Agro-meteorological quantities are often in the form of time series, and knowledge about their temporal scaling properties is fundamental for transferring locally measured fluctuations to larger scales and vice versa. However, the scaling analysis of these quantities is complicated due to the presence of localized trends and nonstationarities. The objective of this study was to characterise scaling properties (i.e. statistical self-similarity) of the chosen agro-meteorological quantities through multifractal detrended fluctuation analysis (MFDFA). For this purpose, MFDFA was performed with 11 322 measured time series (31 yr) of daily air temperature, wind velocity, relative air humidity, global radiation and precipitation from stations located in Finland, Germany, Poland and Spain. The empirical singularity spectra indicated their multifractal structure. The richness of the studied multifractals was evaluated by the width of their spectrum, indicating considerable differences in dynamics and development. In log-log plots of the cumulative distributions of all meteorological parameters the linear functions prevailed for high values of the response, indicating that these distributions were consistent with power-law asymptotic behaviour. Additionally, we investigated the type of multifractality that underlies the q-dependence of the generalized Hurst exponent by analysing the corresponding shuffled and surrogate time series. For most of the studied meteorological parameters, the multifractality is due to different long-range correlations for small and large fluctuations. Only for precipitation does the multifractality result mainly from broad probability function. This feature may be especially valuable for assessing the effect of change in climate dynamics.

Statistical modelling of agrometeorological time series by exponential smoothing

“…The presented results suggest that structures of the time series of particular quantities obtained in various climatic zones differ substantially. This is in agreement with results obtained by Baranowski et al (2015), who analyzed multifractal properties of meteorological time series coming from different climatic zones and noticed large differences in the multifractal spectra and sources of multifractality for series in different climatic zones. Earlier studies (Bartos and Jánosi, 2006;Lin and Fu, 2008;Trnka et al, 2014) also indicated that the analysis of temporal scaling properties is fundamental for transferring locally measured fluctuations to larger scales and vice-versa.…”

Multifractal Detrended Fluctuation Analysis of Temperature Reanalysis Data over Greece

“…A thorough presentation of multifractal statistics and an application of nonlinear dynamics to weather and climate is presented by Lovejoy and Schertzer [35]. In general, meteorological time series have a multifractal structure and the MF-DFA has been used for the analysis of temperature time series [36], precipitation amount data [37][38][39], wind speed records [40][41][42], climate studies [43,44], agrometeorological data [45,46], particulate matter data [47], and paleoclimatic records [48], among others.…”

Fractal Analysis of Deep Ocean Current Speed Time Series

“…In particular, climatological and hydrological series exhibit persistence over a wide range of time scales (e.g., Pelletier and Turcottte 1997;Baranowski et al 2015). However, a broad bibliographic review on the topic shows that oceanographic processes have received scant attention in comparison with other branches of Earth sciences, such as hydrology, seismology, and meteorology.…”

“…Additionally, time series with persistent behavior exhibit positive and negative deviations from the average value for long periods. Hence, long-term persistence represents a natural mechanism that leads to the clustering of extreme events; therefore, it has important implications for climate change and natural hazards forecasting (Eichner et al 2011;Sharma et al 2012;Baranowski et al 2015).…”