Multiple mechanisms generate Lorentzian and 1/f(alpha) power spectra in daily stream-flow time series

Sally E. Thompson, Gabriel G. Katul

Research output: Contribution to journalArticlepeer-review

19 Citations (Web of Science)


Power-law scaling is an ubiquitous feature of the power spectrum of streamflow on the daily to monthly timescales where the spectrum is most strongly affected by hydrologic catchment-scale processes. Numerous mechanistic explanations for the emergence of this power-law scaling have been proposed. This study employs empirical spectra obtained for eight river basins in the South Eastern US and synthetic spectra generated from a range of proposed mechanisms to explore these explanations. The empirical analysis suggested that streamflow spectra were characterized by multiple power-law scaling regimes with high-frequency exponents alpha in the range -1 to -5. In the studied basins, alpha tended to increase with drainage area. The power-law generating mechanisms analyzed included linear and non-linear catchment water balance arguments, power-law recession behavior, autonomous and non-autonomous responses of channel hydraulics and the n-fold convolution of linear reservoirs underpinning Dooge or Nash hydrographs. Of these mechanisms, only n-fold convolutions with n = 2 or 3 generated power spectra with features that were consistent with the empirical cases. If the effects of daily streamflow sampling on truncating power spectra were considered, then the trends in alpha with drainage area were also consistent with this mechanism. Generalizing the linear convolution approach to a network of reservoirs with randomly distributed parameters preserved the features of the power spectrum and maintained consistency with empirical spectra. (C) 2011 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)94-103
Number of pages10
JournalAdvances in Water Resources
Publication statusPublished - Mar 2012
Externally publishedYes


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