Abstract
The present study analyzes fractal dimensions for the daily discharge data series of 12 karstic springs registered over two decades in Northeast Hungary. Fluctuation in the observed data is frequent and irregular, producing rough time series. The level of roughness is measured by the fractal dimension defined in different ways and corresponds to the intensity of fluctuation. That, in turn, results from the structure of the karstic aquifer, its conduits’ geometry, and the water migration in them. In the given case of springs, p-variogram based fractal dimensions reflect the karstification level primarily. On the other hand, box-count and information dimensions are associated with mixing karstic and hydrothermal components when the latter is present. Therefore, the analysis of fractal dimensions of spring discharges may provide a way to obtain information on the complexity of the hidden subsurface conduits and the water flows in them in an exploratory and comprehensive way.
Highlights
Karstic catchments are characterized by spatial and physical heterogeneity, very complex fractured and porous structures, and water migration in these media appears to be highly non-linear
The present study considers the fractal character of the observed daily discharge time series of 12 karstic springs located in Northeast Hungary
In order to analyze the relationship between the multifractal dimensions and the fractal dimensions previously mentioned, the concept of phase space embedding will require some elaboration (for more details, see, e.g., Theiler (1990), Addison (1997), Kantz and Schreiber (2004), and references therein.) Instead of studying the temporal course of spring discharge through the hydrograph, it is possible to regard the phenomenon as the output of a dynamical system driven by a random noise generator and consider its time evolution in some phase space
Summary
Karstic catchments are characterized by spatial and physical heterogeneity, very complex fractured and porous structures, and water migration in these media appears to be highly non-linear. Linear models are unable to reconstruct the temporal variability of karstic spring discharge with sufficient accuracy. For a deeper understanding of the processes, other methods must be used.
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