Generality of fractal 1/f scaling in catchment tracer time series, and its implications for catchment travel time distributions

Sarah E. Godsey, Wenche Aas, Thomas A. Clair, Heleen A. de Wit, Ivan J. Fernandez, J. Steve Kahl, Iain A. Malcolm, Colin Neal, Margaret Neal, Sarah J. Nelson, Stephen A. Norton, Marisa C. Palucis, Brit Lisa Skjelkvåle, Chris Soulsby, Doerthe Tetzlaff, James W. Kirchner

Research output: Contribution to journalArticle

86 Citations (Scopus)

Abstract

Catchment travel time distributions reflect how precipitation from different storms is stored and mixed as it is transported to the stream. Catchment travel time distributions can be described by the mean travel time and the shape of the distribution around the mean. Whereas mean travel times have been quantified in a range of catchment studies, only rarely has the shape of the distribution been estimated. The shape of the distribution affects both the short-term and long-term catchment response to a pulse input of a soluble contaminant. Travel time distributions are usually estimated from conservative tracer concentrations in precipitation and streamflow, which are analyzed using time-domain convolution or spectral methods. Of these two approaches, spectral methods are better suited to determining the shape of the distribution. Previous spectral analyses of both rainfall and streamflow tracer time series from several catchments in Wales showed that rainfall chemistry spectra resemble white noise, whereas the stream tracer spectra in these same catchments exhibit fractal 1/f scaling over three orders of magnitude. Here we test the generality of the observed fractal scaling of streamflow chemistry, using spectral analysis of long-term tracer time series from 22 catchments in North America and Europe. We demonstrate that 1/f fractal scaling of stream chemistry is a common feature of these catchments. These observations imply that catchments typically exhibit an approximate power-law distribution of travel times, and thus retain a long memory of past inputs. The observed fractal scaling places strong constraints on possible models of catchment behavior, because it is inconsistent with the exponential travel time distributions that are predicted by simple mixing models.

Original languageEnglish
Pages (from-to)1660-1671
Number of pages12
JournalHydrological Processes
Volume24
Issue number12
Early online date26 Apr 2010
DOIs
Publication statusPublished - 15 Jun 2010

Keywords

  • travel-time distribution
  • tracer
  • mixing
  • lakes
  • transit time
  • acadia national-park
  • stream chemistry
  • transit times
  • plynlimon catchments
  • residence times
  • New-York
  • water
  • hydrology
  • nitrogen
  • USA

Cite this

Godsey, S. E., Aas, W., Clair, T. A., de Wit, H. A., Fernandez, I. J., Kahl, J. S., ... Kirchner, J. W. (2010). Generality of fractal 1/f scaling in catchment tracer time series, and its implications for catchment travel time distributions. Hydrological Processes, 24(12), 1660-1671. https://doi.org/10.1002/hyp.7677

Generality of fractal 1/f scaling in catchment tracer time series, and its implications for catchment travel time distributions. / Godsey, Sarah E.; Aas, Wenche; Clair, Thomas A.; de Wit, Heleen A.; Fernandez, Ivan J.; Kahl, J. Steve; Malcolm, Iain A.; Neal, Colin; Neal, Margaret; Nelson, Sarah J.; Norton, Stephen A.; Palucis, Marisa C.; Skjelkvåle, Brit Lisa; Soulsby, Chris; Tetzlaff, Doerthe; Kirchner, James W.

In: Hydrological Processes, Vol. 24, No. 12, 15.06.2010, p. 1660-1671.

Research output: Contribution to journalArticle

Godsey, SE, Aas, W, Clair, TA, de Wit, HA, Fernandez, IJ, Kahl, JS, Malcolm, IA, Neal, C, Neal, M, Nelson, SJ, Norton, SA, Palucis, MC, Skjelkvåle, BL, Soulsby, C, Tetzlaff, D & Kirchner, JW 2010, 'Generality of fractal 1/f scaling in catchment tracer time series, and its implications for catchment travel time distributions', Hydrological Processes, vol. 24, no. 12, pp. 1660-1671. https://doi.org/10.1002/hyp.7677
Godsey, Sarah E. ; Aas, Wenche ; Clair, Thomas A. ; de Wit, Heleen A. ; Fernandez, Ivan J. ; Kahl, J. Steve ; Malcolm, Iain A. ; Neal, Colin ; Neal, Margaret ; Nelson, Sarah J. ; Norton, Stephen A. ; Palucis, Marisa C. ; Skjelkvåle, Brit Lisa ; Soulsby, Chris ; Tetzlaff, Doerthe ; Kirchner, James W. / Generality of fractal 1/f scaling in catchment tracer time series, and its implications for catchment travel time distributions. In: Hydrological Processes. 2010 ; Vol. 24, No. 12. pp. 1660-1671.
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abstract = "Catchment travel time distributions reflect how precipitation from different storms is stored and mixed as it is transported to the stream. Catchment travel time distributions can be described by the mean travel time and the shape of the distribution around the mean. Whereas mean travel times have been quantified in a range of catchment studies, only rarely has the shape of the distribution been estimated. The shape of the distribution affects both the short-term and long-term catchment response to a pulse input of a soluble contaminant. Travel time distributions are usually estimated from conservative tracer concentrations in precipitation and streamflow, which are analyzed using time-domain convolution or spectral methods. Of these two approaches, spectral methods are better suited to determining the shape of the distribution. Previous spectral analyses of both rainfall and streamflow tracer time series from several catchments in Wales showed that rainfall chemistry spectra resemble white noise, whereas the stream tracer spectra in these same catchments exhibit fractal 1/f scaling over three orders of magnitude. Here we test the generality of the observed fractal scaling of streamflow chemistry, using spectral analysis of long-term tracer time series from 22 catchments in North America and Europe. We demonstrate that 1/f fractal scaling of stream chemistry is a common feature of these catchments. These observations imply that catchments typically exhibit an approximate power-law distribution of travel times, and thus retain a long memory of past inputs. The observed fractal scaling places strong constraints on possible models of catchment behavior, because it is inconsistent with the exponential travel time distributions that are predicted by simple mixing models.",
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T1 - Generality of fractal 1/f scaling in catchment tracer time series, and its implications for catchment travel time distributions

AU - Godsey, Sarah E.

AU - Aas, Wenche

AU - Clair, Thomas A.

AU - de Wit, Heleen A.

AU - Fernandez, Ivan J.

AU - Kahl, J. Steve

AU - Malcolm, Iain A.

AU - Neal, Colin

AU - Neal, Margaret

AU - Nelson, Sarah J.

AU - Norton, Stephen A.

AU - Palucis, Marisa C.

AU - Skjelkvåle, Brit Lisa

AU - Soulsby, Chris

AU - Tetzlaff, Doerthe

AU - Kirchner, James W.

PY - 2010/6/15

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N2 - Catchment travel time distributions reflect how precipitation from different storms is stored and mixed as it is transported to the stream. Catchment travel time distributions can be described by the mean travel time and the shape of the distribution around the mean. Whereas mean travel times have been quantified in a range of catchment studies, only rarely has the shape of the distribution been estimated. The shape of the distribution affects both the short-term and long-term catchment response to a pulse input of a soluble contaminant. Travel time distributions are usually estimated from conservative tracer concentrations in precipitation and streamflow, which are analyzed using time-domain convolution or spectral methods. Of these two approaches, spectral methods are better suited to determining the shape of the distribution. Previous spectral analyses of both rainfall and streamflow tracer time series from several catchments in Wales showed that rainfall chemistry spectra resemble white noise, whereas the stream tracer spectra in these same catchments exhibit fractal 1/f scaling over three orders of magnitude. Here we test the generality of the observed fractal scaling of streamflow chemistry, using spectral analysis of long-term tracer time series from 22 catchments in North America and Europe. We demonstrate that 1/f fractal scaling of stream chemistry is a common feature of these catchments. These observations imply that catchments typically exhibit an approximate power-law distribution of travel times, and thus retain a long memory of past inputs. The observed fractal scaling places strong constraints on possible models of catchment behavior, because it is inconsistent with the exponential travel time distributions that are predicted by simple mixing models.

AB - Catchment travel time distributions reflect how precipitation from different storms is stored and mixed as it is transported to the stream. Catchment travel time distributions can be described by the mean travel time and the shape of the distribution around the mean. Whereas mean travel times have been quantified in a range of catchment studies, only rarely has the shape of the distribution been estimated. The shape of the distribution affects both the short-term and long-term catchment response to a pulse input of a soluble contaminant. Travel time distributions are usually estimated from conservative tracer concentrations in precipitation and streamflow, which are analyzed using time-domain convolution or spectral methods. Of these two approaches, spectral methods are better suited to determining the shape of the distribution. Previous spectral analyses of both rainfall and streamflow tracer time series from several catchments in Wales showed that rainfall chemistry spectra resemble white noise, whereas the stream tracer spectra in these same catchments exhibit fractal 1/f scaling over three orders of magnitude. Here we test the generality of the observed fractal scaling of streamflow chemistry, using spectral analysis of long-term tracer time series from 22 catchments in North America and Europe. We demonstrate that 1/f fractal scaling of stream chemistry is a common feature of these catchments. These observations imply that catchments typically exhibit an approximate power-law distribution of travel times, and thus retain a long memory of past inputs. The observed fractal scaling places strong constraints on possible models of catchment behavior, because it is inconsistent with the exponential travel time distributions that are predicted by simple mixing models.

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KW - tracer

KW - mixing

KW - lakes

KW - transit time

KW - acadia national-park

KW - stream chemistry

KW - transit times

KW - plynlimon catchments

KW - residence times

KW - New-York

KW - water

KW - hydrology

KW - nitrogen

KW - USA

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DO - 10.1002/hyp.7677

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VL - 24

SP - 1660

EP - 1671

JO - Hydrological Processes

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SN - 0885-6087

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ER -