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- Title
Power law or power flaw?
- Authors
Pattyn, Frank; van Huele, Wim
- Abstract
Since its introduction by Svensson in 1959, the power law curve y = axb (where x and y are horizontal and vertical direction, respectively) has been widely used in morphological analysis of glacial trough cross-profiles. The numerical constants a and b are obtained by a linear regression analysis of the logarithmic form of the power law curve (ln y = ln a + b ln x). The value b then gives a measure for the form of the cross-section. However, over the years this form of the power law has endured a lot of criticism. This criticism is well founded, since this particular form of the power law is not suitable for curve fitting in morphological analyses. In this paper a general power law is proposed, of the form y - y0 = a|x - x0|b (where x0, y0 are the coordinates ofthe origin of the cross-profile). A unique and unbiased solution forthis equation is obtained with a general least-squares method, thereby minimizing the error between the cross-profile data and the curve,and not between the logarithmic transform of the data and its regression line. This provides a robust way to characterize trough cross-section forms.
- Subjects
GEOMORPHOLOGY; MORPHOLOGY; COMPUTER software; GLACIOLOGY; MATHEMATICAL analysis
- Publication
Earth Surface Processes & Landforms, 1998, Vol 23, Issue 8, p761
- ISSN
0197-9337
- Publication type
Article
- DOI
10.1002/(SICI)1096-9837(199808)23:8<761::AID-ESP892>3.0.CO;2-K