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

Abstract

The falling limb of the hydrograph - the streamflow recession - is frequently well approximated by power law functions, in the form dq/dt = -aqb, 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.