Abstract
The aim of this short note is to test whether the morphological skeletal network (MSN) of water bodies that resembles a river network follows Horton's laws. A fractal relationship of MSN of a water body is also shown. This investigation shows that the MSN of the Nizamsagar reservoir follows Horton's laws. Furthermore, this reservoir has a fractal dimension (D m) of 1.92 which was computed by using two morphometric quantities and the fractal dimension of the main skeletal length (d). This value tallies exactly with the fractal dimension (D f) of the whole MSN computed through box-counting method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Beer, T., and Borgas, M., 1993, Horton's laws and the fractal nature of streams: Water Resources Res., v. 29, no. 5, p. 1457–1487.
Feder, J., 1988, Fractals: Plenum, New York, 283 p.
Horton, R. E., 1945, Erosional development of stream and their drainage basin: Hydrological approach to quantitative morphology: Bull. Geophys. Soc. Am., v. 56, p. 275–370.
Lantuejoul, C., 1980, Skeletonization in quantitative metallography, in Haralick, R. M., and Simon, J. C., eds., Digital image processing: Sijthoff and Neordhoff, Groningen, The Netherlands.
Mandelbrot, B. B., 1982, Fractal geometry of nature: Freeman, San Francisco, 468 p.
Maragos, P. A., and Schafer, R. W., 1986, Morphological skeleton representation and coding of binary images: IEEE Trans. Acoustics Speech and Signal Processing, ASSP-34, no. 5, p. 1228–1244.
Sagar, B. S. D., 1996, Fractal relation of a morphological skeleton: Chaos, Solitons, Fractals, v. 7, no. 11, p. 1871–1879.
Schumm, S. A., 1956, Evolution of drainage systems and slopes in badlands at Perth Amboy: NJ Bull. Geol. Soc. America, v. 67, p. 597–646.
Serra, J., 1982, Image analysis and mathematical morphology: Academic Press, New York, 610 p.
Shreve, R. L., 1967, Infinite topologically random channel networks: Jour. Geology, v. 77, p. 397–414.
Strahler, A. N., 1957, Quantitative analysis of watershed geomorphology: Eos Trans. AGU 38, p. 913–920.
Smart, J. S., 1972, Channel networks: Adv. Hydrosciences, v. 8, p. 305–346.
Strahler, A. N., 1964, Quantitative geomorphology of drainage basins and channel networks, in Chow, V. T., ed. Handbook of applied hydrology: McGraw-Hill, New York, pp. 4-39–4-76.
Tarbotan, D. G., Bras, R. L., and Rodriguez-Iturbe, I., 1990, On the fractal dimension of stream networks by Paolo La Barbera and Rosso Renzo: Water Resources Res. v. 26(9), p. 2243–2244.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sagar, B.S.D., Venu, M. & Murthy, K.S.R. Do Skeletal Networks Derived from Water Bodies Follow Horton's Laws?. Mathematical Geology 31, 143–154 (1999). https://doi.org/10.1023/A:1007505717002
Issue Date:
DOI: https://doi.org/10.1023/A:1007505717002