Two approaches were used in the Ardabil Plain to determine the relationship between hydrological time-series (rainfall and runoff) and the groundwater level (GWL). The wavelet-entropy measure (WEM) and the wavelet transform coherence (WTC) were used as two approaches of the wavelet transform (WT). The WEM was considered as a criterion for the degree of fluctuation of the time-series and the WTC represents a common time–frequency space. In the calculation of the WEM, the monthly rainfall, runoff, and the GWL time-series were divided into three different time periods and decomposed into several frequent time-series. Wavelet energies were then calculated for each sub-series. The WEM results show a decrease in rainfall, runoff, and the GWL. The reduction in the WEM represents the reduction in the natural variation of the time-series. The reduction of entropy for runoff, rainfall, and the GWL time-series was about 1.58, 1.36, and 29%, respectively. It can be concluded that the reduction in the fluctuation of the hydrological time-series has relatively little effect on the oscillation patterns of the GWL signal. In this regard, it could be concluded that human activities such as pumping water from wells play a main role in reducing the GWL in the Ardabil Plain. The WTC results show that runoff has the highest coherence (0.9–1) among hydrological variables with the GWL time-series in the frequency bands of 4–8 and 8–16 months.

  • Using the wavelet-entropy measure (WEM) and wavelet transform coherence (WTC) as two approaches of the wavelet transform (WT) in the relation between hydrological parameters and groundwater level

Graphical Abstract

Graphical Abstract
Graphical Abstract
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