An entropy‐based morphological analysis of river basin networks

Under the assumption that the only information available on a drainage basin is its mean elevation, the connection between entropy and potential energy is explored to analyze drainage basins morphological characteristics. The mean basin elevation is found to be linearly related to the entropy of the drainage basin. This relation leads to a linear relation between the mean elevation of a subnetwork and the logarithm of its topological diameter. Furthermore, the relation between the fall in elevation from the source to the outlet of the main channel and the entropy of its drainage basin is found to be linear and so is also the case between the elevation of a node and the logarithm of its distance from the source. When a drainage basin is ordered according to the Horton-Strahler ordering scheme, a linear relation is found between the drainage basin entropy and the basin order. This relation can be characterized as a measure of the basin network complexity. The basin entropy is found to be linearly related to the logarithm of the magnitude of the basin network. This relation leads to a nonlinear relation between the network diameter and magnitude, where the exponent is found to be related to the fractal dimension of the drainage network. Also, the exponent of the power law relating the channel slope to the network magnitude is found to be related to the fractal dimension of the network. These relationships are verified on three drainage basins in southern Italy, and the results are found to be promising.

[1]  D. Gray,et al.  Interrelationships of watershed characteristics , 1961 .

[2]  V. Gupta,et al.  Statistical self-similarity in river networks parameterized by elevation , 1989 .

[3]  J. Lienhard.  A statistical mechanical prediction of the dimensionless unit hydrograph , 1964 .

[4]  Michael R. Karlinger,et al.  On the expected width function for topologically random channel networks , 1984 .

[5]  Chih Ted Yang,et al.  Potential Energy and Stream Morphology , 1971 .

[6]  Edward C. Waymire,et al.  A Large Deviation Rate and Central Limit Theorem for Horton Ratios , 1991, SIAM J. Discret. Math..

[7]  I. Rodríguez‐Iturbe,et al.  The geomorphologic structure of hydrologic response , 1979 .

[8]  R. Rosso,et al.  On the fractal dimension of stream networks , 1989 .

[9]  J. Flint.  Stream gradient as a function of order, magnitude, and discharge , 1974 .

[10]  Luna Bergere Leopold,et al.  The concept of entropy in landscape evolution , 1962 .

[11]  Alessandro Marani,et al.  Energy dissipation, runoff production, and the three-dimensional structure of river basins , 1992 .

[12]  Renzo Rosso,et al.  Fractal relation of mainstream length to catchment area in river networks , 1991 .

[13]  Alessandro Marani,et al.  A Note on Fractal Channel Networks , 1991 .

[14]  J. O. Sonuga.  Principle of maximum entropy in hydrologic frequency analysis , 1972 .

[15]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[16]  V. Singh.  Hydrologic modelling using entropy , 1989 .

[17]  Ignacio Rodriguez-Iturbe,et al.  A physical explanation of an observed link area‐slope relationship , 1991 .

[18]  M. Fiorentino,et al.  A HISTORICAL PERSPECTIVE OF ENTROPY APPLICATIONS IN WATER RESOURCES , 1992 .

[19]  A. Scheidegger.  SOME IMPLICATIONS OF STATISTICAL MECHANICS IN GEOMORPHOLOGY , 1964 .

[20]  A. G. Wilson,et al.  The Use of the Concept of Entropy in System Modelling , 1970 .

[21]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[22]  Spatial uniformity of power and the altitudinal geometry of river networks , 1990 .

[23]  D. J. White,et al.  The Use of the Concept of Entropy in System Modelling , 1970 .

[24]  David G. Tarboton,et al.  Comment on "On the fractal dimension of stream networks" , 1990 .

[25]  C. T. Wang,et al.  A representation of an instantaneous unit hydrograph from geomorphology , 1980 .

[26]  Jerry E. Mueller.  Re-evaluation of the Relationship of Master Streams and Drainage Basins , 1972 .

[27]  I. Rodríguez‐Iturbe,et al.  The fractal nature of river networks , 1988 .