Multifractal characterization and cross correlations of reference evapotranspiration time series of India

This study performs the multifractal characterization of reference evapotranspiration (ET0) and its controlling factors of five locations in India with climatic diversity. First, the ET0 and the predictor variables like minimum air temperature (T-min), maximum air temperature (T-max) and average wind speed (AW) of five stations are analysed using multifractal detrended fluctuation analysis (MFDFA). The investigation could detect long-term persistence and multifractality of different series, irrespective of the climatic condition and geographical location. Higher persistence (>0.8) is noted in the ET0 and T-min series indicating higher predictability in all the stations and highest multifractality was noted for the highly complex wind speed time series. Further, the ET0 estimates by Hargreaves Samani (HS) and Droogers and Allen (DA) methods differs in their persistence and multifractal properties, controlled by the geographic location of the station. Subsequently, multifractal cross correlation analysis (MFCCA) is used to investigate the correlations between ET0 and other variables. MFCCA analysis showed that, for all the time series considered, the joint scaling exponent is roughly the average of individual scaling exponents, and base width of the joint spectra is lower than that of individual series, validating two universal properties of multifractal cross correlation studies for agro-meteorological datasets.

Automated summary

This study performs multifractal characterization of reference evapotranspiration (ET0) and its controlling factors in five locations in India. The investigation reveals long-term persistence and multifractality of different series under diverse climatic conditions and geographical locations. Higher persistence is observed in ET0 and T-min series, while wind speed series shows the highest multifractality. Differences in persistence and multifractal properties of ET0 estimates by different methods are influenced by geographic locations.