Fractal Dimension of Structurally Controlled River Networks of Pinar del Río, Cuba

Authors

  • Robert Ramírez-Hernández UPR
  • Alina Rodríguez-Infante Departamento de Geología, Instituto Superior Minero Metalúrgico
  • Alexis Ordaz-Hernández Universidad Autónoma del Estado de México

Keywords:

fractal dimension, tectonics, drainage networks, morphometric parameters, hydrographic basins, Pinar del Río province.

Abstract

River networks were studied applying the fractal systems approach and based on morphometric parameters. Procedures are applied to Cangre, Los Pozos, Paso Viejo, San Diego, Los Palacios, Santa Cruz and San Cristóbal river basins (Pinar del Río, Cuba). Drainage areas were extracted taking into account isolevel lines configurations and river lengths. For every stream the Euclidian length was also estimated, to calculate the river network fractal dimension. It seems that Takayasu approach is the most appropriate to describe basins with the geological characteristics like those included in this study. The shift of order 2 streams with respect to order 1 streams is explained by the presence of drainage zones where streams have short lengths, typically in tectonically active areas. The lithologic factor seems to have influenced the drainage characteristics of Cangre basin, although, in general, the numerous faults and fractures exert a major control on every basin, which is supported by the high fractal values of Cangre, San Diego and Los Palacios basins. The Hurst coefficients of these basins are close to one, revealing a self-similar behavior of the river network. For the remaining basins it is no possible to assume a typical behavior because of the Hurst values are greater than one.

Downloads

Download data is not yet available.

References

CLARK, M. K.; SCHOENBOHM, L. M.; ROYDEN, L. H.; WHIPPLE, K. X.; BURCHFIEL, B. C.; ZHANG, X.; TANG, W.; WANG, E. & CHEN, L. 2004: Surface uplift, tectonics and erosion of eastern Tibet from large-scale drainage patterns. Tectonics 23(1): 1-21.

COBIELLA-REGUERA, J. L. 2008: Reconstrucción palinspástica del paleomargen mesozoico de América del Norte en Cuba occidental y el sudeste del Golfo de México. Implicaciones para la evolución del SE del Golfo de México. Revista Mexicana de Ciencias Geológicas 25(3): 382-401.

COFIÑO, C. E. & CÁCERES, D. 2003: Efectividad de la utilización de métodos microtectónicos en el desciframiento de la evolución de estructuras tectónicas (Falla Pinar). Minería y Geología 19(3-4): 29-34.

HACK, J. T. 1957: Studies of longitudinal stream profiles in Virginia and Maryland. U.S. Geological Survey, Professional Paper 294: 45-97.

HORTON, R. E. 1932: Drainage basin characteristics. Transactions American Geophysical Union 13(1): 350-361.

HORTON, R. E. 1945: Erosional development of streams and their drainage basins: hydrophysical approach to quantitative morphology. Geological Society America Bulletin 56(3): 275-370.

HUGGETT, R. J. 2007: Fundamentals of Geomorphology. Second edition. Routledge, London, 458 p.

JAIN, V. E. 1973: Geotectónica General. Parte I. Mir, Moscú, 357 p.

LA BARBERA, P. & ROSSO, R. 1990: Reply. Water Resources Research 26(9): 2245–2248.

LIU, T. 1992: Fractal structure and properties of stream networks. Water Resources Research 28(11): 2981-2988.

MANDELBROT, B. B. 1977: Fractals, form, chance and dimension. W. W. Freeman and Company, San Francisco.

MANDELBROT, B. B. 1983: The fractal geometry of nature. W. H. Freeman and Company, New York.

NIKORA, V. I. & SAPOZHNIKOV, V. B. 1993: River network fractal geometry and its computer simulation. Water Resources Research 29(10): 3569-3575.

NIKORA, V.; IBBITT, R. & SHANKAR, U. 1996: On channel network fractal properties: A case of study of the Hutt River basin, New Zealand. Water Resources Research 32(11): 3375-3384.

ORDAZ, A. 2013: Evaluación de las condiciones ingeniero-geológicas para el pronóstico de la respuesta dinámica de los suelos. Caso de estudio: Ciudad de San Cristóbal, Cuba occidental. Tesis de doctorado. Universidad de Pinar del Río.

PIOTROWSKA, K. 1978: Nappe structure of Sierra de los Órganos, western Cuba. Acta Geologica Polonica 28(1): 97-170.

ROBERT, A. & ROY, A. G. 1990: On the fractal interpretation of the mainstream length-drainage area relationship. Water Resources Research 26(5): 839-842.

ROSSO, R.; BACCHI, B. & LA BARBERA, P. 1991: Fractal relation of mainstream length to catchment area in river networks. Water Resources Research 27(3): 381-387.

STRAHLER, A. N. 1946: Elongate intrenched meanders of Conodoguinet Creek. American Journal of Science 244(1): 31-40.

STRAHLER, A. N. 1952: Dynamic basis of geomorphology. Geological Society of America Bulletin 63(9): 923–938.

TAKAYASU, H. 1990: Fractals in the physical sciences. Manchester University Press, Manchester.

TARBOTON, D. G.; BRAS, R. L. & RODRÍGUEZ‐ITURBE, I. 1990: Comment on “On the fractal dimension of stream networks” by Paolo La Barbera and Renzo Rosso. Water Resources Research 26(9): 2243-2244.

TARBOTON, D. G. 1996: Fractal river networks, Horton's laws and Tokunaga cyclicity. Journal of Hydrology 187(1-2): 105-117.

VELTRI, M.; VELTRI, P. & MAIOLO, M. 1996: On the fractal description of natural channel networks. Journal of Hydrology 187(1-2): 137-144.

Published

2017-04-11

How to Cite

Ramírez-Hernández, R., Rodríguez-Infante, A., & Ordaz-Hernández, A. (2017). Fractal Dimension of Structurally Controlled River Networks of Pinar del Río, Cuba. Minería & Geología, 33(2), 163–176. Retrieved from https://revista.ismm.edu.cu/index.php/revistamg/article/view/art3_No2_2017

Issue

Section

Geología

Most read articles by the same author(s)

1 2 3 4 > >>