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

Publication ,  Journal Article
Thompson, SE; Katul, GG
Published in: Advances in Water Resources
March 1, 2012

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.

Duke Scholars

Published In

Advances in Water Resources

DOI

ISSN

0309-1708

Publication Date

March 1, 2012

Volume

37

Start / End Page

94 / 103

Related Subject Headings

  • Environmental Engineering
  • 4901 Applied mathematics
  • 4005 Civil engineering
  • 3707 Hydrology
  • 0907 Environmental Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics
 

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Thompson, S. E., & Katul, G. G. (2012). Multiple mechanisms generate Lorentzian and 1/f α power spectra in daily stream-flow time series. Advances in Water Resources, 37, 94–103. https://doi.org/10.1016/j.advwatres.2011.10.010
Thompson, S. E., and G. G. Katul. “Multiple mechanisms generate Lorentzian and 1/f α power spectra in daily stream-flow time series.” Advances in Water Resources 37 (March 1, 2012): 94–103. https://doi.org/10.1016/j.advwatres.2011.10.010.
Thompson SE, Katul GG. Multiple mechanisms generate Lorentzian and 1/f α power spectra in daily stream-flow time series. Advances in Water Resources. 2012 Mar 1;37:94–103.
Thompson, S. E., and G. G. Katul. “Multiple mechanisms generate Lorentzian and 1/f α power spectra in daily stream-flow time series.” Advances in Water Resources, vol. 37, Mar. 2012, pp. 94–103. Scopus, doi:10.1016/j.advwatres.2011.10.010.
Thompson SE, Katul GG. Multiple mechanisms generate Lorentzian and 1/f α power spectra in daily stream-flow time series. Advances in Water Resources. 2012 Mar 1;37:94–103.
Journal cover image

Published In

Advances in Water Resources

DOI

ISSN

0309-1708

Publication Date

March 1, 2012

Volume

37

Start / End Page

94 / 103

Related Subject Headings

  • Environmental Engineering
  • 4901 Applied mathematics
  • 4005 Civil engineering
  • 3707 Hydrology
  • 0907 Environmental Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics