a, b careful: The challenge of scale invariance for comparative analyses in power law models of the streamflow recession

David Dralle, Nathaniel Karst, Sally E. Thompson

Research output: Contribution to journalArticle

26 Citations (Scopus)


The falling limb of the hydrograph-the streamflow recession-is frequently well approximated by power law functions, in the form dq/dt = -aq(b), so that recessions are often characterized in terms of their power law parameters (a, b). The empirical determination and interpretation of the parameter a is typically biased by the presence of a ubiquitous mathematical artifact resulting from the scale-free properties of the power law function. This reduces the information available from recession parameter analysis and creates several heretofore unaddressed methodological "pitfalls." This letter outlines the artifact, demonstrates its genesis, and presents an empirical rescaling method to remove artifact effects from fitted recession parameters. The rescaling process reveals underlying climatic patterns obscured in the original data and, we suggest, could maximize the information content of fitted power laws.

Original languageEnglish
Pages (from-to)9285-9293
Number of pages9
JournalGeophysical Research Letters
Issue number21
Publication statusPublished - 16 Nov 2015
Externally publishedYes

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