A consistent framework for Horton regression statistics that leads to a modified Hack's law

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A statistical framework is introduced that resolves important problems with the interpretation and use of traditional Horton regression statistics. The framework is based on a univariate regression model that leads to an alternative expression for Horton ratio, connects Horton regression statistics to distributional simple scaling, and improves the accuracy in estimating Horton plot parameters. The model is used to examine data for drainage area A and mainstream length L from two groups of basins located in different physiographic settings. Results show that confidence intervals for the Horton plot regression statistics are quite wide. Nonetheless, an analysis of covariance shows that regression intercepts, but not regression slopes, can be used to distinguish between basin groups. The univariate model is generalized to include n > 1 dependent variables. For the case where the dependent variables represent ln A and ln L, the generalized model performs somewhat better at distinguishing between basin groups than two separate univariate models. The generalized model leads to a modification of Hack's law where L depends on both A and Strahler order ??. Data show that ?? plays a statistically significant role in the modified Hack's law expression. ?? 2008 Elsevier B.V.
Publication type Article
Publication Subtype Journal Article
Title A consistent framework for Horton regression statistics that leads to a modified Hack's law
Series title Geomorphology
DOI 10.1016/j.geomorph.2008.06.002
Volume 102
Issue 3-4
Year Published 2008
Language English
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Geomorphology
First page 603
Last page 614
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