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Fractal stream chemistry and its implications for contaminant transport in catchments

Author

Listed:
  • James W. Kirchner

    (Department of Geology and Geophysics University of California)

  • Xiahong Feng

    (Dartmouth College)

  • Colin Neal

    (Institute of Hydrology, McLean Building)

Abstract

The time it takes for rainfall to travel through a catchment and reach the stream is a fundamental hydraulic parameter that controls the retention of soluble contaminants and thus the downstream consequences of pollution episodes1,2. Catchments with short flushing times will deliver brief, intense contaminant pulses to downstream waters, whereas catchments with longer flushing times will deliver less intense but more sustained contaminant fluxes. Here we analyse detailed time series of chloride, a natural tracer, in both rainfall and runoff from headwater catchments at Plynlimon, Wales. We show that, although the chloride concentrations in rainfall have a white noise spectrum, the chloride concentrations in streamflow exhibit fractal 1/f scaling over three orders of magnitude. The fractal fluctuations in tracer concentrations indicate that these catchments do not have characteristic flushing times. Instead, their travel times follow an approximate power-law distribution implying that they will retain a long chemical memory of past inputs. Contaminants will initially be flushed rapidly, but then low-level contamination will be delivered to streams for a surprisingly long time.

Suggested Citation

  • James W. Kirchner & Xiahong Feng & Colin Neal, 2000. "Fractal stream chemistry and its implications for contaminant transport in catchments," Nature, Nature, vol. 403(6769), pages 524-527, February.
    • Handle: RePEc:nat:nature:v:403:y:2000:i:6769:d:10.1038_35000537
    DOI: 10.1038/35000537
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    Cited by:

    1. Treena Basu, 2015. "A Fast O ( N log N ) Finite Difference Method for the One-Dimensional Space-Fractional Diffusion Equation," Mathematics, MDPI, vol. 3(4), pages 1-13, October.
    2. Stephen, Damian G. & Dixon, James A., 2011. "Strong anticipation: Multifractal cascade dynamics modulate scaling in synchronization behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 160-168.
    3. Xie, Yingying & Yin, Daopeng & Mei, Liquan, 2022. "Finite difference scheme on graded meshes to the time-fractional neutron diffusion equation with non-smooth solutions," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    4. Asma Alharbi & Rafik Guefaifia & Salah Boulaaras, 2020. "A New Proof of the Existence of Nonzero Weak Solutions of Impulsive Fractional Boundary Value Problems," Mathematics, MDPI, vol. 8(5), pages 1-16, May.
    5. Taohua Liu & Xiucao Yin & Yinghao Chen & Muzhou Hou, 2023. "A Second-Order Accurate Numerical Approximation for a Two-Sided Space-Fractional Diffusion Equation," Mathematics, MDPI, vol. 11(8), pages 1-15, April.
    6. Lv, Yujuan & Gao, Lei & Geris, Josie & Verrot, Lucile & Peng, Xinhua, 2018. "Assessment of water sources and their contributions to streamflow by end-member mixing analysis in a subtropical mixed agricultural catchment," Agricultural Water Management, Elsevier, vol. 203(C), pages 411-422.
    7. Reaney, Sim M. & Lane, Stuart N. & Heathwaite, A. Louise & Dugdale, Lucy J., 2011. "Risk-based modelling of diffuse land use impacts from rural landscapes upon salmonid fry abundance," Ecological Modelling, Elsevier, vol. 222(4), pages 1016-1029.
    8. Samer S. Ezz-Eldien & Ramy M. Hafez & Ali H. Bhrawy & Dumitru Baleanu & Ahmed A. El-Kalaawy, 2017. "New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 295-320, July.
    9. Wang, Wansheng & Huang, Yi, 2023. "Analytical and numerical dissipativity for the space-fractional Allen–Cahn equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 80-96.
    10. Zhang, Jingyuan, 2018. "A stable explicitly solvable numerical method for the Riesz fractional advection–dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 209-227.
    11. Hart, Rob, 2003. "Dynamic pollution control--time lags and optimal restoration of marine ecosystems," Ecological Economics, Elsevier, vol. 47(1), pages 79-93, November.
    12. Qu Simin & Wang Tao & Bao Weimin & Shi Peng & Jiang Peng & Zhou Minmin & Yu Zhongbo, 2013. "Evaluating Infiltration Mechanisms Using Breakthrough Curve and Mean Residence Time," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(13), pages 4579-4590, October.
    13. Abdelkawy, M.A. & Alyami, S.A., 2021. "Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    14. Du, Qiang & Toniazzi, Lorenzo & Zhou, Zhi, 2020. "Stochastic representation of solution to nonlocal-in-time diffusion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2058-2085.

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