The dynamical foundation of fractal stream chemistry: The origin of extremely long retention times

By Harvey Scher, G. Margolin, Ralf Metzler, Joseph Klafter, Brian Berkowitz. 2001

153 citations recorded by the source corpus.

We present a physical model to explain the behavior of long‐term, time series measurements of chloride, a natural passive tracer, in rainfall and runoff in catchments [Kirchner et al., Nature, 403(524), 2000]. A spectral analysis of the data shows the chloride concentrations in rainfall to have a white noise spectrum, while in streamflow, the spectrum exhibits a fractal 1/f scaling. The empirically derived distribution of tracer travel times h(t) follows a power‐law, indicating low‐level contaminant delivery to streams for a very long time. Our transport model is based on a continuous time random walk (CTRW) with an event time distribution governed by ψ(t) ∼ Aβt−1−β. The CTRW using this power‐law ψ(t) (with 0 < β < 1) is interchangeable with the time‐fractional advection‐dispersion equation (FADE) and has accounted for the universal phenomenon of anomalous transport in a broad range of disordered and complex systems. In the current application, the events can be realized as transit times on portions of the catchment network. The travel time distribution is the first passage time distribution F(t;l) at a distance l from a pulse input (at t = 0) at the origin. We show that the empirical h(t) is the catchment areal composite of F(t;l) and that the fractal 1/f spectral response found in many catchments is an example of the larger class of transport phenomena cited above. The physical basis of ψ(t), which determines F(t;l), is the origin of the extremely long chemical retention times in catchments.

Subfields: Condensed Matter Physics, Environmental Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/6254c37e41c4fdb01fb7c82d5edf5aae63ab612d

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Citations in the corpus

The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics (2004, methodology): “The MFPT diverges both in the absence of a bias and under a constant drift, pertaining to both finite as well as semi-infinite domains (Metzler and Klafter 2000e, Rangarajan and Ding 2000a, 2000b, 2003, Scher et al 2002a, Barkai 2001)22.”
Modeling non‐Fickian transport in geological formations as a continuous time random walk (2006, methodology): “We account for this behavior with the CTRW framework [Scher et al., 2002b] because the transport is dominated by subsurface flow of the catchment basin, which can be modeled as a heterogeneous porous medium and/or a random fracture network.”
Time behavior of solute transport in heterogeneous media: transition from anomalous to normal transport (2003, methodology): “The parameter values in the following discussion are equal to the values given in [ 29 ].”