[1] Non-Fickian (or anomalous) transport of contaminants has been observed at field and laboratory scales in a wide variety of porous and fractured geological formations. Over many years a basic challenge to the hydrology community has been to develop a theoretical framework that quantitatively accounts for this widespread phenomenon. Recently, continuous time random walk (CTRW) formulations have been demonstrated to provide general and effective means to quantify non-Fickian transport. We introduce and develop the CTRW framework from its conceptual picture of transport through its mathematical development to applications relevant to laboratoryand field-scale systems. The CTRW approach contrasts with ones used extensively on the basis of the advectiondispersion equation and use of upscaling, volume averaging, and homogenization. We examine the underlying assumptions, scope, and differences of these approaches, as well as stochastic formulations, relative to CTRW. We argue why these methods have not been successful in fitting actual measurements. The CTRW has now been developed within the framework of partial differential equations and has been generalized to apply to nonstationary domains and interactions with immobile states (matrix effects). We survey models based on multirate mass transfer (mobile-immobile) and fractional derivatives and show their connection as subsets within the CTRW framework.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2005RG000178

Modeling non‐Fickian transport in geological formations as a continuous time random walk

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 episodes. 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.

Fractal stream chemistry and its implications for contaminant transport in catchments

https://pubag.nal.usda.gov/download/7446/PDF

A review and evaluation of catchment transit time modeling

DETERMINING THE TURNOVER TIME OF GROUNDWATER SYSTEMS WITH THE AID OF ENVIRONMENTAL TRACERS 1. Models and Their Applicability

624 km 2 ) that represent diverse geologic and geomorphic conditions in the western Cascade Mountains of Oregon Our primary objective was to determine the dominant physical controls on catchment-scale water residence time and specifically test the hypothesis that residence time is related to the size of the basin Residence times were estimated by simple convolution models that described the transfer of precipitation isotopic composition to the stream network We found that base flow mean residence times for exponential distributions ranged from 08 to 33 years Mean residence time showed no correlation to basin area (r 2 < 001) but instead was correlated (r 2 = 091) to catchment terrain indices representing the flow path distance and flow path gradient to the stream network These results illustrate that landscape organization (ie, topography) rather than basin area controls catchment-scale transport Results from this study may provide a framework for describing scale-invariant transport across climatic and geologic conditions, whereby the internal form and structure of the basin defines the first-order control on base flow residence time

/pdf/the-role-of-topography-on-catchment-scale-water-residence-2m0hfx1v8a.pdf

A. Kreft

Papers

On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions