Assessment of Multifractal Fingerprints of Reference Evapotranspiration Based on Multivariate Empirical Mode Decomposition

Abstract

This study analyzed the multifractal characteristics of daily reference evapotranspiration (ETo) time series of the Tabriz and Urmia stations of northwestern Iran and its cross-correlation with five other meteorological variables. The results of multifractal detrended fluctuation analysis (MFDFA) of ETo, temperature, pressure, relative humidity solar radiation, and wind velocity showed that all the time series of both stations exhibited multifractality and long memory persistence with higher persistence and complexity in the datasets of Urmia station. Then, a multivariate empirical mode decomposition (MEMD)-(MFDFA) coupled framework was proposed to identify the dominant modes suitable for the forecasting of the different variables. The examination of reconstructed time series consistently displayed an increase in persistence and multifractality. The cross-correlation between different candidate variables and ETo was examined using a recently proposed multifractal cross-correlation analysis (MFCCA) method. The results showed that in each pair-wise cross-correlation analysis, the joint persistence is approximately half of the persistence of an individual time series, reinforcing the universality in the fractal cross-correlation analysis. The cross-correlation properties displayed diverse patterns in different pair-wise combinations of cross-correlation analysis despite the similarity of patterns among the data of the two stations.