عنوان مقاله [English]
A large number of geomorphological studies in drainage basins are referred to relations between basin components as a system, and therefore, drainage basins are known as geomorphic systems. The application of the system theory in geomorphology, leads geomorphologists to an analogy from biology in using the concept of allometry. The term allometry was first defined by Huxley and Teissier (1936) in biology. They also agreed on using terminology for discussing concepts and relations. Allometry is the study of the relationship of size to shape and states that relative change of part of a system is a constant fraction of changes of the entire system or another part of that system (Bull, 1975). This relation is expressed as a power function in the form of . Where y is some variable, x is a measure of size, and b is some scaling exponent. In this paper, in addressing this kind of scaling, Hackâs law was emphasized because it could show the basin shape changes under allometric relations. This relation is central to the study of scaling in river networks.
In current study, results of evaluations of 40 drainage basins morphology were presented to predict the changes of basin shape through evolution process. This evaluation was on the basis of location of these basins in four morphogenetic systems in Iran. Also the role of these systems (include humid, cold, warm and humid-warm systems) in creation of special relations (allometric relations) was studied. For this purpose, in each morphogenetic system, 10 basins were selected and to define the basin shape, compactness (gravelius) and circularity indices were calculated. Then, the relations between main stream length and basin area in each group of basins (in Hackâs law framework) were analyzed and the exponent of Hackâs equation was used as an index for the effect of morphogenetic systems on drainage basins shape. Hackâs exponent âhâ is empirically found to lie in the range from 0.5 to 0.7.
(l=main stream length, L= basin length, a=basin area).