Horton's Laws of Stream Lengths and Drainage Areas

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Abstract
Most customary explanations for Horton's metric laws of stream lengths and drainage areas are based on the idea that in river nets one can speak of cycles or generations of rivers. However, this customary explanation presupposes certain topological features in river basins that do not seem to occur in nature. Hence, the theory in which river nets are assumed to be simply random connections of channels is further applied. Upon this basis, a rational explanation of the two metric laws is obtained which is free from any specific structural assumption regarding a river net.