A continuous time random walk approach to the stream transport of solutes

Abstract

[1] The transport of solutes in rivers is influenced by the exchange of water between the river and the underlying hyporheic zone. The residence times of solutes in the hyporheic zone are typically much longer than traveltimes in the stream, resulting in a significant delay in the downstream propagation of solutes. A new model for this process is proposed here on the basis of the continuous time random walk (CTRW) approach. The CTRW is a generalization of the classic random walk that can include arbitrary distributions of waiting times, and it is particularly suited to deal with the long residence times arising from hyporheic exchange. Inclusion of suitable hyporheic residence time distributions in the CTRW leads to a generalized advection-dispersion equation for instream concentration breakthrough curves that includes the effects of specific hyporheic exchange processes. Here examples are presented for advective hyporheic exchange resulting from regular and irregular series of bedforms. A second major advantage of the CTRW approach is that the combined effects of different processes affecting overall downstream transport can be incorporated in the model by convolving separate waiting time distributions for each relevant process. The utility of this approach is illustrated by analyzing the effects of local-scale sediment heterogeneity on bedform-induced hyporheic exchange. The ability to handle arbitrarily wide residence time distributions and the ability to assess the combined effects of multiple transport processes makes the CTRW model framework very useful for the study of solute transport problems in rivers. The model presented here can be easily extended to represent different types of surfacesubsurface exchange processes and the transport of both conservative and nonconservative substances in rivers.

Quantifying the impact of groundwater discharge on the surface–subsurface exchange

“…A certain separation traditionally exists between the studies of surface and subsurface flows, mainly because of the marked physical differences between the two environments. However, it is well known that rivers and aquifers are strongly connected (Bencala and Walters, 1983;Worman et al, 2002;Boano et al, 2007a), and that the frequent surface-subsurface exchange of water and solutes exerts a significant influence on the water quality (Brunke and Gonser, 1997;Bencala, 2000;Hayashi and Rosenberry, 2002). An example of this connection is given by the exchange between the river and the hyporheic zone, that is often defined as the part of the aquifer where surface water and groundwater mix (Triska et al, 1989;Boulton and Hancock, 2006).…”

Quantification of advective solute travel times and mass transport through hydrological catchments

“…Different factors and mechanisms may control the dynamics and timescales of hydrological mass transport through drainage basins [14][15][16][17]. The travel time variability that exists at all scales in all catchments may to smaller or greater degree mask some important effects of these factors and mechanisms and lead to disparities between different solute transport models and results for different measurement and model scales [4,[18][19][20].…”

A general real-time formulation for multi-rate mass transfer problems

“…Non-equilibrium also has been observed in solute transport through rivers that are influenced by the exchange of water between the river and the underlying hyporheic zone (Fernald et al, 2001;Boano et al, 2007;Marion et al, 2008) or by aggregated dead-zones (Beer and Young, 1983;Lees et al, 1998Lees et al, , 2000Davis et al, 2000). Dead zones can be associated to a number of effects, such as reverse flows induced by bends and pools, side pockets, zones between dikes, turbulent eddies, and wakes behind bed irregularities and roughness elements (Deng et al, 2004).…”