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


Journal Article

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 α in the range -1 to -5. In the studied basins, α tended to increase with drainage area. The power-law generating mechanisms analyzed included linear and nonlinear 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 α 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. © 2011 Elsevier Ltd.

Full Text

Duke Authors

Cited Authors

  • Thompson, SE; Katul, GG

Published Date

  • March 1, 2012

Published In

Volume / Issue

  • 37 /

Start / End Page

  • 94 - 103

International Standard Serial Number (ISSN)

  • 0309-1708

Digital Object Identifier (DOI)

  • 10.1016/j.advwatres.2011.10.010

Citation Source

  • Scopus