Quantification and mapping of
solute travel times in catchments:
Spatial, statistical and source/flowspecific distributions
Gia Destouni
Stockholm University
State of the art of catchment-scale residence
time: conceptualization, modeling and analysis
• Own pathway into this problem field:
>25 year history of theoretical developments on the
solute travel/arrival time - mass flux connection and
conceptualization for
unsaturated zone, groundwater, stream networks,
coupled systems and whole catchments
• Examples of ongoing work on reactive solute (nutrient,
pollutant) transport-biogeochemistry on catchment scale
Stochastic solute advection in 1D porous media: Simmons
(1982)
Basin-scale solute transport: Rinaldo and Marani (1987)
Reactive solute transport in heterogeneous aquifers:
Cvetkovic and Shapiro (1990)
Reactive solute transport through unsaturated zone to
groundwater: Destouni and Cvetkovic (1991)
Generalized solute travel time - mass flux framework for
heterogeneous aquifers: Dagan et al. (1992)
Generalized framework for solute travel time - mass flux
uncertainty in heterogeneous aquifers: Cvetkovic et al.
(1992)
Reactive solute travel time - mass flux uncertainty in
unsaturated zone: Destouni (1992)
Generalized 3D conceptualization of reactive solute travel
time - mass flux in heterogeneous aquifers: Cvetkovic
and Dagan (1994)
Reactive solute travel time - mass flux in coupled soil non-uniform groundwater system: Destouni and Graham
(1995)
Non-linear reaction extension for solute travel time - mass
flux concept in heterogeneous aquifers: Simmons et al.
(1995)
Immiscible flow - reaction system extension for solute
travel time - mass flux concept in heterogeneous aquifers:
Dagan and Cvetkovic (1996)
Cachment-scale 18O transport interpretation with
stochastic travel time - mass flux concept: Simic and
Destouni (1999)
Extensions to multi-component reactive solute
transport
Metal transport-precipitation-dissolution: Eriksson and
Destouni (1997)
General multi-component transport-reaction model:
Yabusaki et al. (1998)
Hydrocarbon transport-biodegradation: Kaluarachi et al.
(2000)
Radionuclide transport-reaction system: Tompson et al.
(2002)
Coupling with general geochemical PHREEQC model:
Malmström et al. (2004)
Extensions to transport-mass transfer-reactions on
catchment scales … What we hear more about in this
workshop
The Abiskojokken catchment,
566 km2 - travel time
quantification for permafrost
change - C and weathering
product cycling investigations see poster by Lyon et al.
The Forsmark catchment area,
30 km2- fine-resolution travel
time quantification for generic
solute transport investigations
The Norrström drainage basin,
22!103 km2 - travel time
quantification for nutrient
transport and generic largebasin solute transport
investigations
Hannerz & Destouni, 2006
Nutrient mass flows in the Norrström drainage basin
22!103 km2
Studied extensively with different modelling approaches: Baresel and Destouni, 2005, 2006;
Darracq et al., 2005, 2008; Darracq and Destouni, 2005,2007; Destouni and Darracq, 2006;
Destouni, 2007; Lindgren et al., 2007; Darracq et al., 2008
7
Total mass load from all
sources to the recipient
Quaternary
deposits
i
i
! gw"s
# gw"s
Fractured
rock
(1! "
i
gw!s
)#
i
gw
Mass inputs from
different sources
General advective solute travel time definition along any
source-to-recipient pathway:
Moving coordinate system
along transport pathway
xCP
p
direction
!p =
"
dx
a
v(x p )
Xp=XCP
Xp
V(Xp)
Control
plane
Example linkages between physical travel time and
biogeochemical attenuation rate that yield delivered mass
fraction to Control Plane/Recipient from any source i:
Through soil-gw to stream or directly to other recipient (lake, coast)
1
i
!gw
(xCP ) = i
Agw
&
% % exp[" #
$ (agw ,xCP )]ggw($ gw;agw ,xCP )d$ gwdagw
gw gw
i
0 Agw
From direct input or from soil-gw system to stream to recipient (lake, coast)
1
!si = i
As
&
% % exp[" #$ (a ,x
s s
s
out
)] fs($ s;as ,xout )d$ sdas
0 Asi
Extended from Lindgren and Destouni (2004)
Without slow/deep (?) gw
transport
! (years)
0
0.1
0.2
0.5
1
2
3
4
5
10
0
20 km
±
With slow/deep gw (?)
transport
20
200
1000
Travel time CDF in water subsystem j
and in combined Norrström
Cumulative distribution
1
0.8
0.6
in surface water, to outlet
in surface runoff, to outlet
0.4
in groundwater, to nearest
downstream surface water
0.2
in combined Norrström, to outlet
0
0.01
0.1
1
10
100
Travel time (year)
1000
Total mass delivery fraction
!=9.10-6/year
1
0
!=9.10-6 /year
±
0
50 km
!=9.10-5 /year
!=9.10-5 /year
!=9.10-4 /year
!=9.10-4/year
Studied extensively in connection with nuclear waste repository studies: numerous technical
SKB reports and, e.g., Jarsjö et al. (JHydrol, 2008), Destouni et al. (GRL, 2008), Destouni et al. (in
review 2009)
Physical (advective) solute travel times to the coast (yr)
Transport through groundwater
Transport through groundwater
and stream network
Hypothetical source location-extent examples
Delivered mass fraction to the coast
Transport through groundwater
Transport through groundwater
and stream network
Workshop definition:
Residence time - the transit time from the soil surface to the
stream channel
Needs for catchment-scale nutrient-pollutant transport
applications:
• More general travel time definition, with dependencies on
various source-to-recipient pathways
• Source-specific travel time distributions
• Spatio-(temporal) and randomness dependencies of travel
times and travel time distributions for different flow-transport
conditions
• Travel time role in general, spatially distributed,
mechanistic conceptualization of multi-source transportbiogeochemistry over whole catchment scales