Multifractal analysis of meteorological time series to assess climate impacts

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.