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

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Abstract

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.

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Acknowledgements

Authors express their sincere thanks to Dr. Marcin Wa̧torek, Department of Theory of Complex Systems (NZ44), Institute of Nuclear Physics, Kraków, Poland for the valuable guidance and constructive suggestions for implementing the codes of MFCCA as part of this research work. Authors thank the service of India Meteorological Department for supplying necessary data for performing this research work.

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Authors and Affiliations

  1. TKM College of Engineering Kollam, Kollam, Kerala, 691005, India

    S. Adarsh, L. J. Nityanjaly, R. Sarang & P. Nandhineekrishna

  2. Institute of Applied Technology, Thu Dau Mot University, Binh Duong Province, Vietnam

    Quoc Bao Pham

  3. Deakin-SWU Joint Research Centre on Big Data, School of Information Technology, Deakin University, Deakin, VIC, 3125, Australia

    Mumtaz Ali

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Adarsh, S., Nityanjaly, L.J., Pham, Q.B. et al. Multifractal characterization and cross correlations of reference evapotranspiration time series of India. Eur. Phys. J. Spec. Top. 230, 3845–3859 (2021). https://doi.org/10.1140/epjs/s11734-021-00325-4

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