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Analyzing the Hydrologic Variability of Kallada River, India Using Continuous Wavelet Transform and Fractal Theory

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Abstract

The presence of storage and water conservation structures significantly influences the characteristics of hydrologic time series. This paper first analyzes the daily streamflow and total suspended sediment (TSS) concentration of the Kallada River in southern Kerala, India using continuous wavelet transform (CWT). The wavelet power spectra of streamflow displayed a complete removal of annual periodicity since ~ 2002–2003 period, and the wavelet coherence analysis confirmed the effect of human interventions on hydrological variability of the Kallada River. The study further confirmed the direct influence of reduction in precipitation on the variability of streamflow and the impact of hydrologic regulations and human interventions on the variability of TSS concentration of the Kallada River. Further, both of the hydrologic series were analyzed using multifractal detrended fluctuation analysis (MFDFA) for its fractal characterizations, after splitting the series to pre and post 2002–2003 period. MFDFA analysis showed that both streamflow and TSS data possess long-term persistence with Hurst exponent varying between 0.74–0.99 for different series. It is further noticed that multifractal degree of the TSS concentration series is greater than that for streamflow in all cases. The MFDFA analysis displayed a reduction in the intercept of the fitted fluctuation function plots of streamflow and TSS concentration series of the Kallada River. The degree of multifractality of both streamflow and TSS concentration series of post 2002–2003 period is reduced by 26% and 82% respectively over the corresponding series of pre 2002–2003 period. The study implied the effect of hydrologic regulations by the water conservation reservoirs of the Kallada basin on the hydrologic variability of the river.

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Abbreviations

∣W(τ, s)∣:

Amplitude of wavelet fucntion

ω o :

Dimensionless angular frequency

∣W XY∣:

Cross-wavelet power

f(α):

Singularity spectrum

F q(s):

q order fluctuation function

H :

Hurst exponent

h(q):

Generalized Hurst exponent

k :

Fourier frequency index

\( \overline{x} \) :

Mean of the time series

ψ o(η):

Morlet wavelet function with dimensionless parameter η

ψ(t) :

Mother wavelet

N :

Length of the time series

ψ τ, s(t):

Normalized scaled and translated wavelet function, and τ is the translation factor

N s :

Number of non-overlapping segements

P k X and P k Y :

Background power spectra of series X and Y

q :

Moment order

s :

Scale or segment sample size in MFDFA analysis

s o :

Smallest scale in Morlet wavelet

u(t):

Progressive series

u’(t):

Retrograde series

W n XY :

Cross-wavelet transform between time series series X and Y

X(t):

Time series

Y i(t):

Profile of the time series

y υ(i):

Fitting polynominal in segment υ

α :

Sigularity expoenent

δ j :

Scale step size in wavelet

σ X 2, σ Y 2 :

Variance of the series X and Y

τ(q):

q-order mass exponent

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Authors and Affiliations

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

    S. Adarsh, S. Drisya Dharan & P. K. Anuja

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  1. S. Adarsh
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  2. S. Drisya Dharan
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  3. P. K. Anuja
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Correspondence to S. Adarsh.

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Adarsh, S., Dharan, S.D. & Anuja, P.K. Analyzing the Hydrologic Variability of Kallada River, India Using Continuous Wavelet Transform and Fractal Theory. Water Conserv Sci Eng 3, 305–319 (2018). https://doi.org/10.1007/s41101-018-0060-8

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