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Multiscale running correlation analysis of water quality datasets of Noyyal River, India, using the Hilbert–Huang Transform

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Abstract

This study performs the multiscale decomposition of six water quality parameters from Elunuthimangalam station in Noyyal River, a water quality hotspot in Southern India, using the complete ensemble empirical mode decomposition with adaptive noise method. Then, the intrinsic mode functions (IMFs) obtained are subjected to normalized Hilbert transform-direct quadrature-coupled framework for their time–frequency characterization. The time–frequency–amplitude spectra revealed that the dominant frequency is dynamic in characteristics and the marginal spectra successfully captured the significant high anthropogenic interventions in the form of pollutant disposals in the study area. Then, an in-depth examination of the association of different water quality parameters such as pH, temperature, dissolved oxygen (DO), biochemical oxygen demand (BOD) and total hardness (TH) with electrical conductivity (EC) is done through a running correlation method, namely time-dependent intrinsic correlation (TDIC) in which the sliding window size is adaptively fixed based on instantaneous frequencies estimated by HT. The TDIC analysis revealed that with the exception of TH, the association of water quality parameters with EC in different time scales is not alike in both nature and strength. Also the well-debated DO–temperature and DO–BOD relationships displayed diverse correlation properties in different time scales and over the time domain.

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Abbreviations

\(\overline{\overline{{C_{1} (t)}}}\) :

First mode obtained by CEEMDAN

υo, υ1, υm :

Noise parameters for different steps

Ci(t), Cj(t):

ith and jth IMFs

Em(.):

Operator representing development of the mth mode by EMD

M :

Number of IMFs

n :

Index for the number of realizations

N :

Number of realizations

N t :

Length of the signal

rm(t):

mth residual series

wn(t):

nth realization of a white noise series

X(t):

Time series signal

Xn(t):

nth artificial signal obtained by addition of white noise

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Acknowledgements

The leading author expresses his gratitude to Dr. Francois G. Schmitt, Director, Laboratory of Oceanology and Geosciences (LOG), University of Lille, Wimereux, France, for the technical discussions on HHT and TDIC methods held at LOG in 2014. The authors thank Yongxiang Huang (https://zenodo.org/record/9748#.XBhUF2lS-Uk) and Patrick Flandrin (http://perso.ens-lyon.fr/patrick.flandrin/emd.html) for providing the basic source codes of TDIC and CEEMDAN methods with the intention of promoting non-commercial scientific research.

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  1. Department of Civil Engineering, TKM College of Engineering, Kollam, Kerala, India

    S. Adarsh & K. L. Priya

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  1. S. Adarsh
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Editorial responsibility: Ta Yeong Wu.

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Adarsh, S., Priya, K.L. Multiscale running correlation analysis of water quality datasets of Noyyal River, India, using the Hilbert–Huang Transform. Int. J. Environ. Sci. Technol. 17, 1251–1270 (2020). https://doi.org/10.1007/s13762-019-02396-2

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