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Analysis of length distribution of drainage basin perimeter
Author(s) -
Werner Christian
Publication year - 1982
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr018i004p00997
Subject(s) - perimeter , structural basin , constraint (computer aided design) , randomness , mathematics , geometry , ridge , topology (electrical circuits) , geology , statistics , combinatorics , geomorphology , paleontology
To establish a theoretical base for the study of the length distribution of basin perimeters, the paper introduces a descriptive model of the topology of interlocking channel and ridge networks. Assuming topological randomness within and between both, the expected number of links of basin perimeters is derived; for large basin magnitudes n , it approximates a square root function in n . Observed link numbers of perimeters deviate significantly, showing a 0.69 regression exponent for their growth rate relative to the basin magnitude rather than the expected value of 0.5. The spatial constraint of possible perimeter/(area;) ½ proportions as defined by the circle is translated into a corresponding topological constraint but fails to provide a sufficient explanation. The paper then explores the possibility that the relatively large length of the perimeter reflects the basin elongation which, following Hack, might be linked to the length of the mainstream. Although basin perimeter, elongation, and mainstream length are highly correlated and the elongation axis is oriented to the outlet in two‐thirds of the sample basins, the data indicate that the mainstream link number does not account for the basin elongation, nor does it account for the number of links of the basin perimeter.