The Relations between the Fractal Properties of the River Networks and the River Flow Time Series

All the geophysical phenomena including river networks and flow time series are fractal events inherently and fractal patterns can be investigated through their behaviors. A non-linear system like a river basin can well be analyzed by a non-linear measure such as the fractal analysis. A bilateral study is held on the fractal properties of the river network and the river flow time series. A moving window technique is utilized to scan the fractal properties of them. Results depict both events follow the same strategy regarding to the fractal properties. Both the river network and the time series fractal dimension tend to saturate in a distinct value.




References:
[1] A. Eke, P. Hermann, L. Kocsis and L.R. Kozak. Fractal characterization
of complexity in temporal physiological signals, Physiological
Measurement 23 (2002) 1-38.
[2] B. B. Mandelbrot. The Fractal Geometry of Nature, W H Freeman
publication, New York, 1982.
[3] P. Babinec, M. Kučera and M. Babincová.Global Characterization of
Time Series Using Fractal Dimension of Corresponding Recurrence
Plots: From Dynamical Systems to Heart Physiology; Harmonic and
Fractal Image Analysis (HarFA), 2005. - pp. 87 - 93.
[4] S. S. Manna, B. Subramanian. A quasi-random spanning tree model for
the early river network. Jan 29, 1996.
[5] Rodriguez-Iturbe, I. and A. Rinaldo. Fractal River Basins, Chance and
Self-Organization, Cambridge: Cambridge University Press, 1997.
[6] A. Rinaldo, R. Rigon and I. Rodriguez-Iturbe (1994): Geomorphological
width functions and random cascade. Geop. Res. Letters 21, 2123-2126.
[7] Troutman, B. and Karlinger, M. 1998. Spatial channel network models
in hydrology, In: Advanced Series in Statistical Sciences and Applied
Probability, Vol. 7: Statistical Methods in Hydrology: Rainfall,
Landforms and Floods, ed. O.
[8] J. T. Hack, U.S. Geological Survey, Professional Paper 294-B (1957).
[9] A. Rinaldo, I. Rodreguez-Iturbe, R. Rigon, R. Bras, E. Ijjasz-Vasquez,
A. Marani. Minimum energy and fractal structures of drainage
networks. Water Resources Research. 29 (10) (1993) Pp. 10.
[10] H. E.Hurst. Long-term storage: An experimental study. London:
Constable (1965).
[11] J. Bassingwaighte, L. Liebovitch and B. West. Fractal physiology.
Oxford University press. New York. 1994.
[12] M.H. Fattahi, N. Talebydokhti, G.R. Rakhshandehroo, A. Shamsai and
E. Nikooee. The robust fractal analysis of time series. Fractals Vol. 18,
(2010), 1-21.
[13] M.H. Fattahi, N. Talebydokhti, G.R. Rakhshandehroo, A. Shamsai and
E. Nikooee. Fractal assessment of wavelet based techniques for
improving the artificial neural network models. Journal of Food,
Agriculture and Environment. Vol. 10 (2010), 132-137.
[14] M.H. Fattahi, N. Talebydokhti, G.R. Rakhshandehroo, A. Shamsai and
E. Nikooee. Fractal assessment of wavelet based preprocessing of river
flow time series. Water Resources Engineering. Vol. 10, (2011), 1-10.