Chloride migration in heterogeneous soil: 2. Stochastic modeling

Abstract

In the paper "Chloride migration in heterogeneous soil, 2, Stochastic modeling" by G. Destouni et al. (Water Resources Research, 30(3), 747-758, 1994), equation (7) should read as follows: •0 t s(t, z)/p,4 = exp [-kitiSm(t; z) + 3'(t, T)Sm(T; Z) d, (7a) y(t, r) = kik2r exp I-kit-k2t + k2r] ß ]•[k•k2,(t-,)]H(t-,) (7b) in which •-= ,(z) is the arrival time to z of an indivisible solute particle that is advected along an individual streamline within a soil monolith. The function Sm(t; Z) (equation (8) or (9)) quantifies the relative frequency of arrival times •-= t in the considered monolith with mean arrival time T = ZOm/qs. Note also that in (3b) and (7b) •[k•k2r(t-r)] is a Bessel function with argument k•k•,(t-,) and not a multiplication of two functions.

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

“…With regard to more significant effects of diffusive mass transfer between mobile and immobile water zones, it is one of the main advantages of Lagrangian travel time-based approaches that their first-step quantification of advective solute travel time distributions can readily be coupled with relevant process models of diffusive mass transfer [5,33,34,36,37,46,49], as well as with biogeochemical reaction process models of various degrees of complexity [34,[38][39][40][41][42][43]45,47,50,55]. The resulting coupled advection-sorption and/or advection-reaction models account then both for the physical solute spreading effect of advection variability and the diffusive mass transfer and/or biogeochemical reaction process effects on large-scale pollutant transport.…”

“…Some of these approaches have particularly developed the use of advective solute travel times and their distributions as a main basis for Lagrangian conceptualizations and derivations of field-scale solute transport and spreading in different subsurface water systems (unsaturated soil and groundwater, e.g. [2,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]). Parallel studies also extended the theoretical basis of the Lagrangian travel time-based approaches to link the solute transport through the different water subsystems (unsaturated soil, groundwater, streams and stream networks) that are hydraulically connected at the larger scales of hydrological catchments [4,5,44,[48][49][50].…”

Scale and model resolution effects on the distributions of advective solute travel times in catchments

“…For example, Jarsjö et al (2007) specifically investigated the effect of local random variability around the advective travel times for the Forsmark catchment area, confirming that in this specific catchment case also, the effect of such local variability within mobile water is small on the expected largescale solute transport (Jarsjö et al, 2007). Numerous coupled advection-sorption and/or advection-reaction modelling studies based on advective travel time quantification approaches have also shown that and how a first-step quantification of advective solute travel time distributions can readily be coupled with relevant process models of diffusive mass transfer (Cvetkovic and Shapiro, 1990;Destouni and Cvetkovic, 1991;Cvetkovic and Dagan, 1994;Destouni et al, 1994;Destouni and Graham, 1995;Cvetkovic and Haggerty, 2002;, as well as with biogeochemical reaction process models of various degrees of complexity (Destouni and Cvetkovic, 1991;Ginn et al, 1995;Simmons et al, 1995;Berglund and Cvetkovic, 1996;Cvetkovic and Dagan, 1996;Eriksson and Destouni, 1997;Yabusaki et al, 1998;Tompson et al, 2002;Malmström et al, 2004Malmström et al, , 2008Botter et al, 2005). Furthermore, the present neglect of the travel time contributions of the transport through the unsaturated zone, from the soil surface to the groundwater zone, can readily be relaxed by the subsystem convolution methodology proposed and used by Destouni and Graham (1995) and Foussereau et al (2001).…”

“…Numerous studies (Maloszewsi and Zuber, 1982;Simmons, 1982;Rinaldo and Marani, 1987;Cvetkovic and Shapiro, 1990;Destouni and Cvetkovic, 1991;Destouni, 1993;Dagan, 1994, 1996;Destouni et al, 1994;Destouni and Graham, 1995;Ginn et al, 1995;Simmons et al, 1995;Berglund and Cvetkovic 1996;Eriksson and Destouni, 1997;Shapiro and Cvetkovic, 1998;Yabusaki et al, 1998;Foussereau et al, 2001;Cvetkovic and Haggerty, 2002;Tompson et al, 2002;Malmström et al, 2004;Botter et al, 2005) have by now used and developed the conceptualization and quantification of the large-scale, physical spreading of solute transport in heterogeneous geological formations in terms of prevailing advection variability. Commonly, the advective travel times and travel time distributions that have been quantified and used to link the solute transport through different water subsystems (unsaturated soil, groundwater, streams and stream networks) have been approximated by assuming some common type of probability density function (e.g.…”

“…Furthermore, with regard to solute that, in addition to advection, is also subject to (bio)geochemical reaction processes and/or diffusive mass transfer between mobile and immobile water zones, the present first-step quantification of advective solute travel times and their distributions can readily be coupled with relevant process models of such reactive processes (Destouni and Cvetkovic, 1991;Ginn et al, 1995;Simmons et al, 1995;Berglund and Cvetkovic, 1996;Cvetkovic and Dagan, 1996;Eriksson and Destouni, 1997;Yabusaki et al, 1998;Tompson et al, 2002;Malmström et al, 2004Malmström et al, , 2008Botter et al, 2005) or diffusive mass transfer processes (Cvetkovic and Shapiro, 1990;Destouni and Cvetkovic, 1991;Cvetkovic and Dagan, 1994;Destouni et al, 1994;Destouni and Graham, 1995;Cvetkovic and Haggerty, 2002;. The resulting coupled advection-reaction and/or advection-mass transfer models account then both for the physical solute spreading effect of advection variability and the diffusive mass transfer and/or (bio)geochemical reaction process effects on the largescale solute transport.…”