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Grid lysimeter study of steady state chloride transport in two Spodosol types using TDR and wick samplers

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Solute transport in soils is affected by soil layering and soil-specific morphological properties. We studied solute transport in two sandy Spodosols: a dry Spodosol developed under oxidizing conditions of relatively deep groundwater and a wet Spodosol under periodically reducing conditions above a shallow groundwater table. The wet Spodosol is characterized by a diffuse and heterogeneous humus-B-horizon (i.e., Spodic horizon), whereas the dry Spodosol has a sharp Spodic horizon. Drainage fluxes were moderately variable with a coefficient of variation (CV) of 25% in the wet Spodosol and 17% in the dry Spodosol. Solute transport in 1-m-long and 0.8-m-diameter soil columns was investigated using spatial averages of solute concentrations measured by a network of 36 Time Domain Reflectometry (TDR) probes. In the dry Spodosol, solute transport evolves from stochastic-convective to convective-dispersive at a depth of 0.25 m, coinciding with the depth of the Spodic horizon. Chloride breakthrough at the bottom of the soil columns was adequately well predicted by a convection-dispersion model. In the wet Spodosol, solute transport was heterogeneous over the entire depth of the column. Chloride breakthrough at 1 m depth was predicted best using a stochastic-convective transport model. The TDR sampling volume of 36 probes was too small to capture the heterogeneous flow and concomitant transport in the wet Spodosol.
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Ž.
Journal of Contaminant Hydrology 51 2001 13–39
www.elsevier.comrlocaterjconhyd
Grid lysimeter study of steady state chloride
transport in two Spodosol types using TDR and
wick samplers
P. Seuntjens a,), D. Mallants b,1, N. Toride c,2, C. Cornelis a,
P. Geuzens a
aVito, Flemish Institute for Technological Research, Boeretang 200, 2400 Mol, Belgium
bSCK-CEN, Belgian Nuclear Research Centre, Boeretang 200, 2400 Mol, Belgium
cDepartment of Agricultural Sciences, Saga UniÕersity, Saga 840-8502, Japan
Received 9 May 2000; received in revised form 12 January 2001; accepted 15 March 2001
Abstract
Solute transport in soils is affected by soil layering and soil-specific morphological properties.
We studied solute transport in two sandy Spodosols: a dry Spodosol developed under oxidizing
conditions of relatively deep groundwater and a wet Spodosol under periodically reducing
conditions above a shallow groundwater table. The wet Spodosol is characterized by a diffuse and
Ž.
heterogeneous humus-B-horizon i.e., Spodic horizon , whereas the dry Spodosol has a sharp
Ž.
Spodic horizon. Drainage fluxes were moderately variable with a coefficient of variation CV of
25% in the wet Spodosol and 17% in the dry Spodosol. Solute transport in 1-m-long and
0.8-m-diameter soil columns was investigated using spatial averages of solute concentrations
Ž.
measured by a network of 36 Time Domain Reflectometry TDR probes. In the dry Spodosol,
solute transport evolves from stochastic–convective to convective–dispersive at a depth of 0.25 m,
coinciding with the depth of the Spodic horizon. Chloride breakthrough at the bottom of the soil
columns was adequately well predicted by a convection–dispersion model. In the wet Spodosol,
solute transport was heterogeneous over the entire depth of the column. Chloride breakthrough at
1 m depth was predicted best using a stochastic–convective transport model. The TDR sampling
volume of 36 probes was too small to capture the heterogeneous flow and concomitant transport in
the wet Spodosol. q2001 Elsevier Science B.V. All rights reserved.
Keywords: Solute transport; Spodosols; TDR; Capillary wicks
)Corresponding author. Fax: q32-14-33-69-53.
Ž. Ž.
E-mail addresses: seuntjep@vito.be P. Seuntjens , dmallant@sckcen.be D. Mallants ,
Ž.
nobuo@cc.saga-u.ac.jp N. Toride .
1Fax: q32-14-32-35-53.
2Fax: q81-952-28-8709.
0169-7722r01r$ - see front matter q2001 Elsevier Science B.V. All rights reserved.
Ž.
PII: S0169-7722 01 00120-6
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3914
1. Introduction
Recent and historical soil contamination from point or non-point sources have
stressed the importance of understanding contaminant transport phenomena in soils. The
protection of water resources relies to a large extent on our ability to describe and
explain contaminant pathways through soil and groundwater. Transport of solutes in
Ž. Ž
soils is most commonly described as a convective–dispersive CD process Saffman,
.
1960 , which assumes that solute velocity variations are small as compared to the scale
over which transport is described. Theoretically, CD-transport is expected at some
distance from the inlet where solutes from different pore regions have had time to
exchange. Close to the inlet, i.e., the upper boundary of a soil profile, solute transport is
often conceptualized as a process where solutes are transported at different velocities in
Ž
isolated regions or stream-tubes without mass exchange between the regions Simmons,
.
1982; Jury and Scotter, 1994 . This process is called stochasticconvective SC ,
referring to the random distribution of solute particle travel times needed to reach a
certain depth. Several laboratory and field experiments have illustrated the transition of a
Ž
stochastic–convective to a convectivedispersive transport process Butters and Jury,
.
1989; Vanclooster et al., 1995 .
The theoretical formulation of the two limiting transport processes acting at the short
Ž. Ž .
SC and the long distance CD , respectively, is applicable to statistically homogeneous
soils. However, soils are known to be heterogeneous with depth owing to specific soil
forming processes. The morphological heterogeneity at greater depths invalidates the
aforementioned transition between the stochastic–convective and convective–dispersive
transport. Field evidence of heterogeneous flow and concomitant transport was provided
Ž
for macroporous soils Beven and Germann, 1982; Mallants et al., 1996; Vanderborght
.
et al., 1997 .
Furthermore, soil layering induces unstable flow at the transition of a less permeable
Ž.
to a more permeable layer Baker and Hillel, 1990 , which results in the transition of a
homogeneous to a more heterogeneous solute flow deeper in the soil profile, contrary to
the process described above. Funneling mechanisms were shown to have a profound
Ž.
impact on solute behavior in sandy soils Kung, 1993; Ju and Kung, 1997 . In seemingly
homogeneous soils, soil water repellency directs solutes to flow in isolated fingers
Ž.
Ritsema et al., 1993 . Preferential flow in homogeneous sandy soils was also observed
under continuous non-ponding infiltration due to wetting front instability similar to
Ž.
transport in layered soils Selker et al., 1992 . Field studies of solute transport in layered
Ž. Ž.
soils were made by Ellsworth et al. 1991 and Ward et al. 1995 .
Despite the considerable progress that has been made the past decade in describing
transport processes in heterogeneous soils, there is still a great need for quantitative data
relating observed transport processes to soil morphological properties. Such relationships
may be particularly useful to estimate transport behavior if only soil morphological
information is available.
Ž
This paper evaluates the two limiting transport concepts i.e., stochasticconvective
.
and convective–dispersive at the column-scale i.e., 1-m scale for two types of
multi-layered undisturbed sandy Spodosols. A grid-lysimeter equipped with Time Do-
Ž.
main Reflectometry TDR probes and capillary wicks is used to measure solute
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 15
breakthrough and to assess the influence of morphological features on the transport
properties of both soil types.
2. Materials and methods
2.1. Soil used
Two distinctly different soil profiles, classified as sandy Spodosols, were used for the
migration experiments. They are located within a toposequence at the AKattenbosB
Ž.
experimental site Lommel, Belgium in the vicinity of a non-ferrous industry. The site
consists of an old land dune landscape covered with spots of heath, abundant Molinea
Ž.
caerulea and solitary pine trees Pinus silÕestris . The two profiles have been contami-
nated during nearly one century by atmospheric deposition of heavy metals, including
Ž
cadmium, zinc, lead and copper. One profile is described as a sandy typic Aquod Soil
Survey Staff, 1998 , which has developed under wet conditions average depth of
.
groundwater 1.5 m . The other Spodosol is a sandy typic Placohumod developed under
Ž.
dry conditions average depth of groundwater 3 m . The profiles are separated by a
distance of about 150 m. Both soil types are shown in Fig. 1. Characteristic for both
profiles is the presence of a Spodic horizon, represented by the humus Bh layers,
situated at a depth of 0.2–0.4 m. Reducing conditions in a wet Spodosol enhance the
mobility of the organic matter and have resulted in a diffuse and heterogeneous Spodic
horizon, while oxidizing conditions in the dry Spodosol limit the mobility of colloidal
Ž.
organic matter resulting in a sharp Spodic horizon De Coninck, 1980 . In case of the
dry Spodosol, a Placic horizon, i.e., a black to dark reddish mineral soil horizon of 125
mm thickness cemented with Fe, has developed due to high concentrations of Fe,
present in the original soil profile.
Before sampling, the soil columns at both ends of the toposequence, 0.12-m-diameter
and 1-m-long steel cores were driven mechanically into the surrounding soil. In each
plot, three undisturbed soil cores were obtained. From these cores, thickness and
composition of each pedological layer was obtained. Subsequently, samples were taken
in each layer from the soil core and transferred to the laboratory for analysis. Organic
Ž.
carbon oc % was determined using an infrared spectrometer after combustion in a
Ž. Ž .
furnace at 5008C total carbon and acidification total inorganic carbon .
Triplicate field measurements of field-saturated hydraulic conductivity Kwere
fs
Ž
made in each pedological horizon, using a pressure infiltrometer Elrick and Reynolds,
.
1992 . During the measurement, a constant head of water was maintained using a
mariotte system, connected to a tube. The tube was fitted to a ring, inserted at the upper
surface of a soil layer to a depth of approximately 0.04 m. General physical and
chemical properties of the two Spodosols are given in Table 1, together with the
estimated hydraulic properties.
2.2. Chloride displacement experimental setup
Two 1-m-long and 0.8-m-diameter intact soil columns were taken within the topose-
quence, one at the wet and one the dry end side. The vegetation cover and the litter layer
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3916
Ž. Ž . Ž . Ž .
Fig. 1. Photographs of the soils used in the experiments: left typic sandy Aquod wet Spodosol and right typic sandy Placohumod dry Spodosol . Arrows indicate
horizon boundaries.
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 17
Table 1
Ž.
Properties of the two Spodosols used in the migration experiment values are means of three replicates
Horizon Depth Organic
r
Kfs
y3y5y1
Ž. Ž. Ž . Ž .
zm carbon % kg m 10 m s
Aquod
A 0.07 5.83 1300 5.3
E 0.15 1.32 1540 4.0
Bh1 0.25 2.57 1440 0.61
Bh2 0.36 1.2 1570 4.2
Bh2 0.51 0.48 1660 7.5
Bh2 0.66 0.45 1620 4.7
Placohumod
A 0.07 3.65 1310 1.1
E 0.15 0.78 1590 3.6
Bh1 0.23 3.03 1300 0.45
Bh2 0.28 1.23 1380 10
BhrC1 0.38 0.55 1410 1
C1 0.49 0.3 1520 1
C2 0.77 0.13 1560 1
were removed before sampling. This resulted in a partly truncated A-horizon for the
Aquod profile, given the abundant Molinea cover. The sampling procedure was similar
Ž.
to the one described by Vanclooster et al. 1995 . The grid lysimeter is a slightly
Ž.
modified version of the one described by de Rooij 1996 .
In the laboratory, a stainless steel grid was attached to the bottom of each column.
The 0.15-m high grid consists of 10 cells protruding 0.05 m into the soil. The surface
area of the individual grid cells is 0.0367 m2for the curved surfaces and 0.0529 m2for
Ž.
the inner grid cells see Fig. 2 . The remaining 0.1-m-thick bottom part of the grid was
homogeneously packed with soil from the bottom of the profile. Subsequently, a
0.01-m-thick rubber sheet was attached to the bottom of the grid. The rubber sheet is
divided into 10 surfaces having the same size and shape as the grid cell areas. Untwisted
Ž.
rope ends of one wick AM 3r8 HI, Amatex, Norristown, PA covered each surface of
the rubber sheet. The wick protruded through a hole in the center of each surface on the
rubber sheet. The length of the capillary wicks depends on the imposed flow rate, the
hydraulic properties of the soil, the characteristics of the wick used and the surface to be
Ž.
drained. We used the procedure of Knutson and Selker 1994 to calculate the optimal
Ž.
wick length. The method was further improved by Rimmer et al. 1995 to account for
effects of the wick on the distribution of soil hydraulic conductivity and pressure head
above the wick. For wick type AM 3r8 HI with constant as4.7 my1, saturated
hydraulic conductivity Ks65.5 m dayy1, for a sandy soil with exponential constant
s
as36 my1and Ks1200 cm dayy1, and for flow rates ranging between 0 and 0.02 m
s
dayy1, the optimal wick length was 0.24 m.
Flexible sealing strips on the boundaries of the rubber surfaces ensured a perfect
match between rubber sheet and grid. A 0.012-m-thick stainless steel plate, perforated at
10 locations corresponding to the holes in the rubber sheet, was attached to the drainage
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3918
Ž.
Fig. 2. Schematic presentation of the soil column setup. a Front view showing position of the TDR-probes
Ž.
relative to soil layering. b Top view showing the position of the TDR-probes relative to the wicks.
grid. The plate was embedded in a short cylinder having the same diameter as the soil
column. This cylinder was tightly screwed onto the soil column. The columns were
Ž.
placed on a pedestal allowing to collect drainage water in 2-l poly-ethylene PE vessels.
Ž.
The vessels were screwed onto small poly-vinylchloride PVC tubes surrounding the
hanging capillary wicks.
The exact delineation of the horizons in the soil columns was determined by coring
through holes made in the soil column PVC-wall, along six transects spaced 608apart.
Small horizontal 0.05-m-long and 0.005-m-wide core samples were taken every 0.05 m
to identify the horizons. At the expected horizon boundaries, the sampling density was
increased to 0.01 m. Afterwards, the bore-holes were refilled with a paste of the original
soil. The soil surface was covered with a 0.02-m-thick gravel layer.
Along four transects, spaced alternating 608and 1208apart, a total of 36 triple-wire
Ž. Ž
Time Domain Reflectometry TDR probes wire spacing 0.02 m, wire length 0.35 m,
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 19
.
wire diameter 0.003 m were inserted at nine depths into each soil column. A schematic
representation of the soil columns with the indication of horizon boundaries and probe
locations is given in Fig. 2. The probes were inserted into each horizon and at those
horizon boundaries where a significant increase in hydraulic conductivity is observed,
Ž.
notably at the transition of the upper humus-B-horizon Bh1 to the lower humus-B-
Ž.
horizon Bh2 in the Aquod, and at the transition of the Bh-horizon to the C-horizon in
the Placohumod. The large contrast between the hydraulic conductivity of the Spodic
horizon and the deeper layers is illustrated in Table 1.
The TDR probes were multiplexed manually to a 1502B Tektronix cable tester for the
measurement of volumetric soil water content and solute concentration. Temperature
probes were installed at three depths and were used to correct the TDR-impedance
measurements for temperature changes in the laboratory. The TDR probes were con-
structed in the laboratory. The unbalanced connection between the probe wires and the
Ž.
coaxial cable was embedded in an epoxy resin probe head Ledieu et al., 1986 . The
travel time of the electromagnetic wave in the probe head was determined by holding
Ž.Ž.
the probe in air relative dielectric permittivity
´
s1 and in water
´
s80 following
Ž.
the procedure of Heimovaara et al. 1995 . Calibration of TDR probes for the determina-
tion of volumetric water content was achieved following the procedure described by
Ž. Ž
Young et al. 1997 . Rectangular PVC-boxes lengths0.4 m; heights0.1 m; widths
.
0.1 m having the same wall thickness as the soil columns were packed with homoge-
nized soil originating from each horizon separately. The boxes were saturated from the
bottom by placing them into a water reservoir. The water level in the reservoir was
raised gradually until the soil was completely saturated. TDR probes were inserted into
the bottom of the boxes. The boxes containing the TDR probes were placed into an oven
Ž.
at 508C and were allowed to evaporate from the top. At regular times twice a day the
apparent dielectric permittivity of the soil was determined by connecting the probes to
the cable tester. At the same time soil water content was determined by weighing the
boxes. Horizon-specific calibration curves were obtained by fitting a third-order poly-
nome relating apparent dielectric permittivity to soil water content.
Solute resident concentrations were determined from TDR impedance measurements.
The calibration constant relating impedance to concentration was obtained by numerical
convolution of the solute pulse response. This method assumes homogeneous flow
within the TDR-detection volume and complete mass recovery. The method is discussed
Ž. Ž.
at length by Ward et al. 1994 and Mallants et al. 1996 . The method is preferred over
two other calibration methods, i.e., the direct method relating soil bulk electrical
conductivity to soil water conductivity and soil water content, and the continuous pulse
method. The continuous pulse method requires prohibitive large application times for
undisturbed soils exhibiting non-equilibrium transport. The direct method suffers from
effects of soil repacking and destruction of soil structure that alters the transmission
coefficient Tused in the calibration.
Mass recovery calculated from chloride concentrations at the bottom of the soil
Ž.
columns i.e., the capillary wicks ranges from 63% to 105% in the Aquod soil and from
90% to 112% in the Placohumod soil. Measurement times within the TDR measurement
window are long enough to assume nearly complete mass recovery in the TDR sampling
volume.
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3920
The columns were allowed to evaporate during 6 weeks before the migration
experiment started. Then, a daily dose of 0.01 m of 0.005 M CaCl was applied
2
homogeneously at the top of each column using a hand spray gun. After obtaining
stationary water flow, i.e., after 14 days, an instantaneous pulse of 0.05 M CaCl was
2
given at the top boundary and leached subsequently with 0.005 M CaCl . Daily
2
measurements of volumetric soil water content and resident solute concentration were
Ž.
made along four transects and nine observation depths see Fig. 2 using TDR. For each
Ž.
column, pH, drainage fluxes and solute chloride concentrations were determined on a
daily basis for each of the 10 wicks.
2.3. Determination of transport concept
Two limiting concepts of solute transport in soil were evaluated for average concen-
trations in the entire cross-sectional area of the soil columns, i.e., a convective–disper-
Ž.
sive and a stochastic–convective process Jury and Roth, 1990; Jury and Scotter, 1994 .
A stochastic–convective transport process refers to solute transport in regions with
Ž.
different velocities without solute exchange between those regions Simmons, 1982 . It
is assumed to be an early-time or early-depth process since it is believed that shortly
after solute addition or close to the soil surface, transport is dominated by convection in
isolated stream tubes. A stochastic–convective transport process was modeled using a
Ž.
transfer function model Jury, 1982 . In this type of models, a given solute pulse input is
convoluted over time using an impulse–response function to obtain a solute output at a
certain depth. Therefore, the boundary conditions at the inlet of the flow domain are
specified as a function of time. When the inlet condition is an instantaneous application
Ž.
Dirac pulse , the response function equals the flux concentration breakthrough curve
Ž.
BTC . For a non-reactive solute, this BTC equals the travel-time probability density
Ž. Ž .
function pdf . In case of a convective-lognormal transfer function CLT , the pdf is
lognormal and is given by:
2
tl
ln y
m
ž/
ž/
1z
f
ct;zsexp y1
Ž. Ž.
2
'2
s
s
t2
p
where cfis a time-integral-normalized flux concentration, and
m
and
s
2are the travel
time mean and variance. Time series of chloride flux concentrations obtained at the
Ž.
bottom of the soil column using the wicks were optimized to Eq. 2 to determine
m
and
s
. Similarly, a resident concentration depth profile can be predicted by convoluting an
initial resident concentration depth profile over depth using a resident concentration
impulse–response function. In this case, the initial resident concentration depth profile
Ž.
has to be known. Jury and Scotter 1994 have shown that the resident concentration
impulse response function and the flux concentration impulse response function are
related to each other. It can also be shown that time-integral-normalized resident
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 21
r() Ž
concentrations c t;z of a conservative solute can be expressed using Vanderborght et
.
al., 1996 :
2
tl 2
ln y
m
y
s
ž/
ž/
1z
r
ct;zsexp y2
Ž. Ž.
2
'2
s
s
t2
p
where
m
and
s
2are mean and variance of the resident concentration BTC at depth z,
2Ž.
and lis the reference depth. Both
m
and
s
are estimated by optimizing Eq. 2 to time
series of TDR-measured impedances using a non-linear least-squares optimization
Ž.
procedure programmed in MATHCAD Mathsoft Inc., 1995 .
The second limiting model concept, the convective–dispersive model, assumes
complete mixing of solutes between regions of different velocity. The model concept is
likely to be valid at greater depths where solutes from different pore regions are mixed.
The mathematical formulation describing the convective–dispersive transport process is
Ž.
the convection–dispersion equation CDE . Assuming steady water flow conditions and
one-dimensional solute transport of a conservative chemical, the CDE is given by:
EcE2cEc
sDyÕ3
Ž.
2
EtEz
Ez
Žy3. Ž.
where cssolute concentration M L , tstime T , zsspatial coordinate L ,
Ž2y1
y1.
Dsdispersion coefficient L T and Õspore water velocity L T . For each of
Ž.
the 36 observation depths, the solution of Eq. 3 subject to a third-type upper boundary
Ž.
condition BC and a zero-gradient BC at infinite depth is fitted to time series of resident
Ž.
solute concentrations measured by TDR. Alternatively, the analytical solution of Eq. 3
subject to a first-type upper BC is used to determine transport parameters from chloride
Ž.
flux concentrations determined at the bottom of the soil column wicks . Parameters D
and Õwere optimized using the non-linear least-squares analysis provided in CXTFIT
Ž.
Toride et al., 1995 . Local dispersivities were calculated from
l
sDrÕ.
The validity of CLT- and CDE-model concepts can only be tested using data from
Ž.
more than one observation depth Jury and Roth, 1990 . Since the flow velocity Õis
dependent on the water content
u
of the profile, i.e., ÕsJ
u
y1,Õis expected to be
w
larger in the drier layers and smaller in the wet layers. Using the CDE or the CLT in
terms of real-depth coordinates does not allow to distinguish between effects from
varying soil water content with depth and effects of soil heterogeneity. To eliminate the
effects of varying soil water content in a layered soil profile, a coordinate transformation
Ž.
proposed by Ellsworth and Jury 1991 is used:
z
XX
)
zs
u
zdz.4
Ž. Ž.
H
0
The transformed depth z)is physically defined as the amount of water stored in the
soil profile between soil surface and depth z. A reduced pore water velocity Õowing to
)Ž)
a higher soil water content is compensated by an increase of transformed depth zz
.
is proportional to soil water content at which Õis estimated. Similarly, a higher Õ
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3922
owing to a lower soil water content is compensated by a decrease of transformed depth
z)at which Õis estimated from the CDE. Introducing z)into the convection–disper-
sion equation, results in a fluid coordinate Õ
)and D). Fluid coordinate pore water
velocity Õ
)sJ
uu
y1, where
u
is the soil water content and
u
is the effective transport
we e
Ž.
)
volume at depth zEllsworth and Jury, 1991 . This implies that Õis larger than or
equal to Jdepending on the water volume contributing to transport. If
u
-
u
, then
w e
J-Õ
)and not all soil water is transporting solutes, implying that preferential transport
w)ŽŽ.
takes place. Fluid coordinate dispersion Ds
uu
DrJfrom Eq. 8 in Ellsworth and
ew
.))
Jury, 1991 . Both Õand Dhave the same dimensions as the real-depth Õand D.
Consequently, fluid coordinate dispersivity
l
), calculated from D)rÕ
), has dimension
)Ž.
length. Introducing zinto the stochasticconvective model CLT only affects the
parameter
m
and not
s
2. Mean travel time fluid-depth
m
)has the same dimensions as
the real-depth
m
. To optimize
m
), real-depth coordinate zis replaced by fluid
)Ž. )PP )
coordinate zin Eq. 3 , while zand lare replaced by zand l, respectively, in
Ž. Ž. )
Eqs. 1 and 2 . The reference depth lis arbitrary set to 10 cm.
The validity of the respective transport concepts may be tested by comparing travel
)Ž
time standard deviations
s
obtained at different observation depths zJury and Roth,
.
1990 . In case
s
remains constant with depth, the stochastic–convective transport
concept can be accepted. When
s
decreases with depth, a convective–dispersive
transport process is more appropriate. Similarly, a linear increase of dispersivity with
depth indicates a transport according to the stochastic–convective model, while a
constant dispersivity is attributed to convective–dispersive transport. The validity of the
two transport concepts is, thus, evaluated using model parameters from both the CDE,
i.e., dispersivity
l
), and the CLT-model, i.e., travel time standard deviation
s
.
Column-scale transport is represented here by spatial averages of solute concentra-
tions measured by TDR probes on one hand and the wicks on the other. Spatially
Ž
averaged resident concentrations obtained with TDR are calculated from Toride et al.,
.
1995 :
n
1
r)) )
²:
cz,tscz ,tscz 5
Ž.
Ž.
Ž. Ž.
ˆÝi
n
i
s1
with nbeing the number of TDR probes at the average fluid coordinate observation
))
depth z. Individual transformed depths zcan be different for the same observation
i
depth zdue to a varying layer thickness and, consequently, a different water content at
i
the same depth in the soil profile. Therefore, we averaged similar transformed depths z)
i
))
to obtain a mean transformed depth z. For each average observation depth z,
Ž Ž . Ž .. Ž Ž ..
solutions of the CLT Eqs. 1 and 2 and the CDE Eq. 3 are fitted to time series of
²rr
rr:
the average resident concentrations to obtain pedon-scale
m
,
s
and Õ,D,
²r
rr:
respectively. Pedon-scale dispersivity is calculated from
l
sDrÕ.
Ž.
Column-scale flux concentrations are defined as Toride et al., 1995 the ratio of the
mean solute and water fluxes determined by the wicks:
)
²:
ÕcL,t
Ž.
f
f)
cL,ts.6
Ž.
Ž.
ˆ²:
Õ
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 23
²:
The ensemble average Õfor the entire drainage surface of the soil column is
²: Ž 2.2
calculated from Õsexp
m
q0.5
s
,
m
and
s
being the mean and the variance
ln ln ln ln
of the ln-transformed variable. Similar to resident concentrations, solutions of the CLT
Ž Ž .. Ž Ž ..
Eq. 2 and the CDE Eq. 3 are fitted to time series of the average flux concentra-
fŽ)
ff
ff:
tions cL,tto obtain pedon-scale
m
,
s
and Õ,D, respectively.
3. Results and discussion
3.1. Water flow
Drainage fluxes Jwere measured at the bottom of the soil columns for each of the
w
10 wicks. Water flow in the Aquod and the Placohumod is moderately variable,
expressed by the low CV of 25% and 17%, respectively. Fig. 3 illustrates the spatial
variability of the cumulative drainage fluxes within the soil columns. The range in
Fig. 3. Spatial variability of cumulative drainage for the Aquod and the Placohumod soil. Numbers in columns
Ž.
refer to wick numbers see Fig. 2 .
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3924
cumulative drainage fluxes for individual wick samplers in the Aquod extends from 0.32
to 0.69 m for a period of 47 days. Close inspection of Fig. 3 further indicates a region
with consistently larger drainage fluxes in the Aquod profile. Grid cells 6, 7 and 10
account for 27% of the total cross-sectional area and drain 40% of the total volume of
water passing the lower boundary. Cumulative drainage fluxes for individual samplers in
the Placohumod profile range from 0.36 to 0.68 m for a period of 46 days, without
showing a clear spatial pattern.
Soil water content within each of the TDR sampling volumes remained quasi constant
during the migration experiment. Vertical distributions of mean soil water content
measured at four transects in the Aquod and the Placohumod are shown in Fig. 4.
Because of the variability in layer thickness in both profiles, water content differs at a
certain observation depth from one measurement transect to another. Of note here is the
thick eluvial E horizon in transect 1 of the Aquod causing the low soil water content at
depth zs0.3 m. The eluvial E-horizon displays a dip in soil water content
u
followed
by a considerable increase of
u
in the Spodic Bh horizon and a gradual decrease
towards the deeper layers. Soil water content finally increases again as a result of water
built-up above the wicks at the bottom boundary. Note that in the Spodic horizon of the
Placohumod, one of the observation depths shows a significant higher value of soil
water content. This high water content value is attributed to the presence of the low
permeable Placic horizon.
On the basis of a comparison between CVs for soil water content
u
, the variability
Ž
within horizons is slightly higher in the Aquod compared to the Placohumod results not
.
shown . The E and Bh2 horizons of the Aquod show the largest variation in soil water
content
u
, i.e., from 0.12 to 0.21 m3my3and from 0.18 to 0.25 m3my3, respectively.
Variability in soil water content between horizons is comparable for the two soils
Ž.
CVs20% .
3.2. Local-scale solute transport
Solute transport across different layers in both soils is not homogeneous, as shown by
Ž.
the variety of shapes of the breakthrough curves BTC recorded by the TDR probes in
the individual soil layers or at the interface between two layers. Fig. 5 illustrates the
variation of the local BTC-shapes with depth for two vertical series of TDR probes, one
in the Aquod and one in the Placohumod. Three different types of local solute
Ž.
breakthrough curves BTC were observed, each representing a different transport
process. Type-I BTCs have a symmetrical bell shape, possibly reflecting transport which
Ž. Ž
can be described best by the convective–dispersive CD model e.g., the BTCs in the
.
Placohumod, Fig. 5 . Type-II BTCs are asymmetrical, showing fast breakthrough and
Ž).
considerable tailing e.g., BTCs at zs0.042 and 0.055 m in the Aquod, Fig. 5 . Such
Ž
shapes are typical for soils where transport is limited to a mobile region e.g.,
.
unsaturated soils, macropores, root channels and where solute moves into and out of
Ž.
stagnant water phases the immobile region through diffusion. This solute transport
Ž. Ž
process is often represented by a mobileimmobile MI model van Genuchten and
.
Wierenga, 1976 . Type-III BTCs exhibit multiple peaks, indicating solute is transported
Ž
through multiple regions with limited interactions between the flow regions e.g., BTCs
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 25
Fig. 4. Soil water content profiles measured by the four TDR-transects. Dashed lines indicate the average
boundary between pedological horizons.
).
at zs0.16 m in the Aquod, Fig. 5 . Each region individually is characterized by a
CD- or MI-like transport process. Different transport processes exist in different layers,
indicating that local-scale transport can be homogeneous at one observation depth, but
heterogeneous deeper in the soil. Type-I BTCs are recorded in 56% and 61% of all
Ž.
observation depths i.e., 36 in total in the Aquod and the Placohumod, respectively.
Type-III transport behavior is observed in 31% and 36% of all observation points in the
Aquod and the Placohumod, respectively.
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3926
Ž. Ž.
Fig. 5. Local resident concentration BTC at one vertical series of TDR-probes in a the Aquod and b the
Placohumod.
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 27
Ž.
Fig. 5 continued .
Fig. 5 shows local heterogeneous transport, represented by the multiple peak BTCs in
the Aquod soil. Multiple-peak breakthrough generally originates within or below the
Spodic Bh horizon. These multiple-peak-BTCs likely reflect the local heterogeneity of
the Spodosols due to morphological features, i.e., the irregular accumulation of soil
organic matter in the deeper layers. The irregular distribution of organic matter may be
Ž.
the result of originally instability-driven preferential flow paths Ritsema et al., 1998 .
Heterogeneous flow and transport could possibly be further enhanced by the presence of
living or decayed plant roots, preferentially accumulating in the wet and nutrient-rich
regions below the humus-Bh-horizon.
On the other hand, an illustration of homogeneous transport across layers is given in
Fig. 5 for a single vertical transect of TDR probes in the Placohumod. No double-peak
breakthrough is observed in the deeper layers below the Spodic horizon, indicating that
the probes are sampling in a homogeneous section of the profile.
3.3. Column-scale solute transport
Ž.
Local resident concentrations were averaged according to Eq. 5 to obtain spatially
averaged BTCs. Spatial averaging of BTCs observed at the local-scale results in
so-called pedon-scale BTCs, representing transport behavior at the scale of an entire soil
profile, i.e., the pedon. Fig. 6 shows breakthrough of the spatially averaged concentra-
r)
²:
tion cat the average transformed depth zin both soils. The E and Bh1 horizons
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3928
exhibit transport, characterized by spatially uniform tracer velocity. Multi-region trans-
)
Ž.
port originates in the Bh2-horizon at zs0.139 m of the Aquod and in the transitional
)
Ž.
BhrC-horizon at zs0.108 m of the Placohumod. The spatially heterogeneous
transport, observed in the deeper layers below the Spodic horizon, likely reflects the
local morphological heterogeneity due to the irregular presence of soil organic matter in
these layers.
Tables 2 and 3 give the optimized CDE- and CLT-model parameters in fluid- and
real-depth coordinates based on time series of spatially averaged resident concentrations.
Based on the coefficient of determination, the model performance to predict break-
through at the observation depths is essentially the same for both models. Since fluid
coordinate travel time variance and real depth coordinate travel time variance are the
²r
r:
same, only one
s
is given in Table 3. The average pore water velocities Õin the
Aquod are significantly lower than the average water flux, i.e., Js0.99 cm dayy1.
w
Ž. Ž.
Fig. 6. Spatially averaged resident concentrations versus time in a the Aquod and b the Placohumod.
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 29
Ž.
Fig. 6 continued .
This indicates that the TDR probes are sampling in a low-flux region of the Aquod soil.
²r:
Conversely, average Õin the Placohumod are somewhat larger than J, indicating
w
Ž
slightly preferential flow in the total TDR-sampling volume represented by four probes
.
per observation depth .
Also given is the coefficient of variation CV of the average model parameters derived
²r:
from all observation depths. The CV of Õis comparable to field-scale CVs reported
Ž.
by Jury 1985 for several soil types and to a CV for a Plaggen soil presented by
Ž. ²
r:
Vanderborght et al. 1997 , while for the latter soil the CV of Dwere smaller.
²r:
Average real-depth-dispersivities
l
are similar for the wet and the dry Spodosol, i.e.,
²r
r:
l
s2.5–2.7 cm. Values for
l
based on fluid coordinates range from 0.56 to 0.66
²r
r
r:
cm. CVs of
m
are similar to CVs of Õ, whereas CVs of
s
are generally
²r:
smaller than CVs of D.
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3930
Table 2
Ž.
Transport parameters for the convection–dispersion model CDE optimized to time series of area-averaged
resident concentrations
2
Horizon Fluid depth Real depth R
)rrr rrr
²: ² : ²: ²: ² : ²:
zÕD
l
zÕD
l
y12y1y12y1
Ž.Ž .Ž. Ž.Ž .Ž.
cm cm day cm day cm cm cm day cm day cm
Aquod
E 1.5 0.68 0.11 0.16 8 3.42 2.68 0.78 0.99
E 2.5 0.68 0.22 0.32 14 3.63 6.37 1.75 0.99
ErBh1 3.9 0.79 0.34 0.43 20 4.00 8.58 2.15 0.99
Bh1 5.5 0.84 0.38 0.45 27 4.04 8.76 2.17 0.99
Bh1 7.5 0.74 0.55 0.74 35 3.47 12.1 3.50 0.96
Bh2 13.9 0.72 0.54 0.75 62 3.17 10.6 3.34 0.91
Bh2 15.9 0.79 0.78 0.99 70 3.49 15.1 4.34 0.91
Bh2 17.9 0.81 0.45 0.56 78 3.50 8.35 2.39 0.95
Bh2 20.4 0.84 0.38 0.45 88 3.60 6.97 1.94 0.94
CV 61 72 70 61 68 69
Placohumod
A 1.5 0.80 0.16 0.20 6 3.11 2.44 0.78 0.98
E 4.6 1.16 0.80 0.69 18 4.59 12.5 2.72 0.96
Bh1 7.8 0.90 0.37 0.41 30 3.43 5.32 1.55 0.99
BhrC 10.8 1.01 0.78 0.77 42 3.92 11.86 3.03 0.88
BhrC 12.7 1.08 0.86 0.80 51 4.34 13.94 3.21 0.90
C 15.0 1.13 0.67 0.59 63 4.7 11.68 2.49 0.92
C 16.7 1.07 0.84 0.79 72 4.64 15.74 3.39 0.94
C 18.5 1.02 0.85 0.83 82 4.53 16.68 3.68 0.89
CV 61 73 68 61 75 70
The data reveal no meaningful difference in variability, i.e., CV, between parameters
expressed in fluid coordinates and real-depth parameters. The coordinate transformation
does not reduce the variability of the transport parameters. Consequently, vertical
variations in soil water content caused by the layering cannot explain the variability of
the transport parameters.
3.4. Identification of solute transport concept
Since no inference about the appropriate transport model can be made from model
²r
r:
performance at individual depths, the depth-behavior of
l
and
s
is used to
determine the transport concept in the region sampled by the TDR probes. In order to be
consistent with the assumption of a random velocity field for testing both model
²r:
concepts, fluid coordinate parameters were used. For both soils, dispersivity
l
s
²rr
r:
DrÕand travel time standard deviation
s
are plotted versus mean trans-
)
formed depth zin a double log-plot in Fig. 7. The dotted vertical line in Fig. 7
²r:
indicates the top of the Spodic horizon. It is evident that
l
increases from the upper
)Ž.
boundary of the flow domain up to a depth zof 0.046 m real depth zs0.15–0.2 m
)Ž.
in the Placohumod and up to zs0.075 m real depth zs0.30–0.40 m in the Aquod,
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 31
Table 3
Ž.
Transport parameters for the stochastic–convective model CLT optimized to time series of area-averaged
resident concentrations
Horizon Fluid depth Real depth
)rr r2
Ž. ²: ²: Ž. ²:
zcm
ms
zcm
m
R
Aquod
E 1.5 2.51 0.46 8 0.90 0.98
E 2.5 2.34 0.52 14 0.78 0.99
ErBh1 3.9 2.34 0.48 20 0.73 0.99
Bh1 5.5 2.33 0.42 27 0.77 0.98
Bh1 7.5 2.43 0.46 35 0.88 0.96
Bh2 13.9 2.53 0.33 62 0.99 0.92
Bh2 15.9 2.43 0.35 70 0.94 0.92
Bh2 17.9 2.46 0.27 78 0.99 0.96
Bh2 20.4 2.44 0.22 88 0.98 0.94
CV 61 63 61
Placohumod
A 1.5 2.29 0.52 6 0.94 0.97
E 4.6 1.90 0.53 18 0.52 0.96
Bh1 7.8 2.31 0.32 30 0.97 0.99
Bh1rC 10.8 2.16 0.38 42 0.81 0.89
Bh1rC 12.7 2.11 0.35 51 0.72 0.91
C 15.0 2.11 0.29 63 0.68 0.92
C 16.7 2.14 0.32 72 0.68 0.94
C 18.5 2.20 0.31 82 0.71 0.90
CV 61 62 62
respectively. Deeper in the soil profile dispersivity no longer increases systematically,
²r:
but fluctuates within a fairly narrow range. Conversely,
s
remains constant in the
Ž.
upper layer of the Placohumod i.e., before it reaches the Spodic horizon , but decreases
²r:
in the deeper layers. The behavior of
s
in the Aquod is rather constant in the
E-horizon, whereas it shows a clear decreasing trend in the deeper layers.
The depth where stochastic–convective transport changes to convectivedispersive,
coincides with the presence of the Spodic horizon. Solutes from different stream tubes
are mixed laterally and redistributed in the Bh1-horizon before they enter the deeper
²r:
layers. As shown in Table 2, fairly small values of
l
are found in the Bh1-horizon of
)
Ž.
the Placohumod i.e., at a depth zs0.078 m indicating a compression of the solute
plume.
Ž.
In case of the Placohumod, no statistically significant p-0.01 relation was found
r)
²: Ž .
between
l
and zps0.017 , indicating transport according to the convection–dis-
r)
²:
persion model. This is further confirmed by the significant relation between
s
and z
Ž. ²
r:
ps0.0001 . For the Aquod, a statistically significant relation exists between
l
and
)r)
Ž. ²:Ž .
zps0.002 , but also between
s
and zps0.0003 . From the former relation,
stochastic–convective transport seems appropriate, while from the latter convective–dis-
rr )
²: ² :
persive transport is concluded. Based on the
l
and
s
versus zrelation obtained
for the Aquod, we cannot discriminate between the two model concepts. Therefore,
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3932
rr)
²: ² :
Fig. 7. Double log-plot of average dispersivity
l
and mean travel time standard deviation
s
versus average transformed depth z.
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 33
chloride flux concentrations measured over the entire cross-sectional area of the soil
columns by the wicks will be used to decide which of the two concepts is valid for an
entire soil profile.
3.5. Identification of the solute transport concept at the scale of an entire soil profile
²pp
p
p:
Depth-average CDE-parameters Õ,D, and CLT-parameters
m
and
s
²r:
based on average resident concentrations care shown in Table 4. Also shown are the
CDE- and CLT-parameters optimized to average flux concentrations cf. Note that in the
ˆ
²p
p:y1
Aquod, Õobtained from resident concentrations, i.e., Õs0.77 cm day , equals
²X:
the average drainage flux Jmeasured in wicks 1, 2, 4 and 5. These wicks were
w
located under the region sampled by the TDR probes and are therefore considered
representative of the integral effect of soil layering on solute fluxes. The resemblance
²p
X:
between Õand Jindicates that on average no preferential transport was observed
w²p
X:
in the region of the Aquod sampled by the TDR probes. Conversely, Õexceeds Jw
in the Placohumod indicating slightly preferential flow in the region sampled by TDR.
Table 4 also indicates that the average water flux across the entire drainage area of the
²: ²
X:
Aquod soil Jis larger than J. As shown in Fig. 2, higher soil water fluxes in the
ww
Aquod are measured by the wicks outside the region where the TDR probes sample, i.e.,
²p:
by wicks 6, 7, 10. This observation is further confirmed by the higher Õbased on
²p:²:
flux-concentrations. Since Õ)J, preferential flow and transport occurs at the
w²p:
pedon-scale in the Aquod. In the Placohumod, the pedon-scale Õbased on both
²:
resident and flux concentrations only slightly exceeds the average drainage flux J.
w
This means that, at the scale of the entire soil column, transport is rather homogeneous
and that the TDR-sampling volume is large enough to capture the heterogeneity of the
pedon. fŽŽ..
Column-scale breakthrough of flux-averaged concentrations cEq. 6 is shown in
ˆ
Fig. 8. Transport in the Aquod is characterized by early breakthrough, multiple peaks
and considerable AtailingB. The shape of the BTC reflects transport through multiple
flow regions. The chloride BTC in the Placohumod is symmetrical and bell-shaped,
indicating transport through a homogeneous flow region. The parameters of Table 4
Table 4
²r:
Pedon-scale CDE- and CLT-parameters obtained from average resident concentrations cand average flux
concentrations cf
ˆ
²: ²:
Aquod, Js0.99 cm Placohumod, Js1.00 cm
ww
y1y1
Ž. Ž.
day all wicks , day all wicks ,
XX
y1y1
²: ²:
Js0.77 cm day Js0.90 cm day
ww
Ž. Ž.
wicks 1, 2, 4, 5 wicks 1, 2, 4, 5
rf rf
²: ²:
cc cc
ˆˆ
py1
²:Ž .
Õcm day 0.77 1.26 1.02 1.05
p2y1
²:Ž .
Dcm day 0.43 3.59 0.71 1.09
p
²:
m
2.44 2.28 2.15 2.21
p
²:
s
0.39 0.53 0.38 0.30
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3934
Fig. 8. Observed and predicted pedon-scale flux concentrations with the CDE and CLT model.
based on resident concentrations are used to predict column-scale breakthrough in the
two soils. The results of the calculations are given in Fig. 8. The convective–dispersive
Ž.
model CDE predicts the column-scale breakthrough adequately well in the Placohu-
mod. Observed breakthrough is faster than predicted, whereas the calculations underesti-
mated the tail of the BTC. This presumably owes to preferential transport at the
Ž.
column-scale in the Placohumod. The stochasticconvective model CLT better pre-
dicts the tail of the BTC and predicts faster breakthrough, but clearly underestimates the
solute peak.
In case of the Aquod, the CLT-model performs better compared to the CDE-model.
The CDE-model fails to predict the observed fast breakthrough and the maximal flux
concentration. The CLT-model better describes the overall behavior of the observed
breakthrough. Since model parameters are derived from average resident concentrations,
they are representative for the regions sampled by the 36 TDR probes. Predictions of
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 35
chloride breakthrough from the Aquod using model parameters from resident concentra-
tion data compare favorably well with observed breakthrough from the low-flux-region.
The rapid breakthrough from the fast-flux-region is not predicted. This again shows that
TDR is not covering the complete heterogeneity of the soil column.
To better predict breakthrough from all flux regions in the Aquod, the following
approach was used. Column-scale transport was calculated by considering variations of
pore water velocity over the entire soil column rather than over the TDR sampling
volume. In modeling field-scale solute transport, one often observes that the field-scale
dispersion is composed of local dispersion effects and dispersion due to fluctuations of
Ž.
the local pore water velocity around its mean value e.g., Schulin et al., 1987 . The
²fp
fp:2
column-scale mean travel time
m
and travel time variance
s
are calculated for
the entire set of stream tubes or pore water velocities from:
²fp
rp:2
m
s
m
y0.5
s
ln Õ
²fp:2²rp:22
s
s
s
q
s
7
Ž.
ln Õ
2²rp:
where
s
is the heterogeneity of Õbetween sets of stream tubes, and
m
and
ln Õ
²rp:2
s
are CLT-parameters obtained from spatially averaged resident concentrations
Ž
representing heterogeneity within a sampled set of stream tubes Vanderborght et al.,
.2
1997 . The variance of local pore water velocities
s
is calculated from individual Õ
ln Õ
optimized to time series of flux concentrations obtained from 10 individual wicks. The
variance
s
2s0.17, which is of the same order of magnitude as the local-scale travel
ln Õ
²rp:2
time variance
s
. This indicates that the heterogeneity between sets of stream tubes
significantly affects the column-scale travel time variance and that stream tube flow and
transport is valid at the scale of the soil column. By comparison, velocity variations
Ž2.
between stream tubes is small in the Placohumod i.e.,
s
s0.01 , illustrating that
ln Õ
solute travel time variance is affected by lateral mixing rather than by velocity
differences between isolated stream tubes.
²fp:
Fig. 8 shows the predictions of column-scale breakthrough in the Aquod using
m
²fp:2Ž. Ž.
and
s
from Eq. 7 . The CLT-model with parameters from Eq. 7 predicts the
early breakthrough and the tail of the BTC significantly better.
4. Conclusions
Solute transport was studied in morphologically different Spodosols at the scale of a
soil profile limited to the size of a 1-m-long and 0.8-m-diameter soil column. Based on
outflow measurements using a grid collector system and capillary wick samplers, water
flow in the Spodosols was found to be moderately variable. Water flow was more
Ž. Ž
heterogeneous in the Aquod soil wet Spodosol compared to the Placohumod dry
.
Spodosol .
Local solute transport processes change from one soil layer to another, as shown by
the variety of breakthrough curves recorded by individual TDR probes in different layers
of both soils. Average flux concentrations in the column effluent from the dry Spodosol
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–3936
could be adequately well predicted using a convectiondispersion model. Measurements
of solute concentrations inside the 1-m-long soil column using a network of 36 Time
Ž
Domain Reflectometry probes revealed that the distinct Spodic horizon i.e., at a depth
.
of 0.25 m behaves like a transitional layer between stream-tube transport in the topsoil
horizons and homogeneous transport in the subsoil. Solutes from different isolated flow
regions in the topsoil, e.g., presumably due to wetting front instability or the presence of
root channels, are mixed in the Spodic horizon before they enter the subsoil. A similar
analysis for the wet Spodosol showed that transport is heterogeneous over the entire soil
profile and that a stochastic–convective model predicted solute breakthrough best.
The observation that soil morphology directs solute transport either into a
stochastic–convective or a convective–dispersive process is of particular importance
when large areas have to be characterized in terms of transport behavior. In such case,
easy-to-obtain soil morphological information may be a good basis to select appropriate
transport models and associated parameters.
List of symbols and abbreÕiations
)
zaverage transformed depth
²f:
m
average mean travel time based on flux concentration
²p:
m
pedon-scale mean travel time
²r:
m
average mean travel time based on resident concentration
²fp:
m
pedon-scale mean travel time based on flux concentration
²r:
cŽy1.
spatially averaged time-normalized resident concentration T
²f:
DŽ2y1.
average dispersion coefficient based on flux concentration L T
²p:
DŽ2y1.
pedon-scale dispersion coefficient L T
²r:
DŽ2y1.
average dispersion coefficient based on resident concentration L T
²f:
ÕŽy1.
average pore water velocity based on flux concentration L T
²p:
ÕŽy1.
pedon-scale pore water velocity L T
²r:
ÕŽy1.
average pore water velocity based on resident concentration L T
²f:
l
Ž.
average dispersivity based on flux concentration L
²p:
l
Ž.
pedon-scale dispersivity L
²r:
l
Ž.
average dispersivity based on resident concentration L
²f:
s
average travel time standard deviation based on flux concentration
²p:
s
pedon-scale travel time standard deviation
²r:
s
average travel time standard deviation based on resident concentration
²fp:2
s
pedon-scale travel time variance based on flux concentration
m
mean solute travel time
m
)transformed mean solute travel time
cŽy3.
resident concentration M L
cfŽy1.
time-normalized flux concentration T
crŽy1.
time-normalized resident concentration T
DŽ2y1.
dispersion coefficient L T
D)Ž2y1.
transformed dispersion coefficient L T
hŽ.
soil water pressure head L
JwŽy1.
water flux density L T
Kfs Žy1.
field-saturated hydraulic conductivity L T
()
P. Seuntjens et al.rJournal of Contaminant Hydrology 51 2001 13–39 37
l
)Ž.
transformed dispersivity L
n,m shape parameters water retention curve: ms1y1rn
oc Ž.
organic carbon content %
tŽ.
time T
ÕŽy1.
pore water velocity L T
Õ
)Žy1.
transformed pore water velocity L T
zŽ.
depth from surface L
z)Ž.
transformed depth L
zXŽ.
dummy integration depth L
l
Ž.
dispersivity L
u
Ž3y3.
soil water content L L
u
rŽ3y3.
residual soil water content L L
u
sŽ3y3.
saturated soil water content L L
a
Žy1.
shape parameter water retention curve L
u
eŽ3y3.
effective transport volume L L
s
2solute travel time variance
BTC breakthrough curve
CDE convective–dispersive equation
CD convective–dispersive
CLT convectivelognormal transfer function
CV coefficient of variation
pdf probability density function
PE poly-ethylene
PVC poly-vinylchloride
SC stochastic–convective
TDR time domain reflectometry
Acknowledgements
The authors wish to thank Diederik Jacques, Anthony Timmerman and Jan Vander-
borght of the Institute of Land and Water Management for their useful comments and
help during the sampling and setup of the soil columns. The author is very grateful to
the team of the Vito laboratory of Inorganic Analyses for carrying out the analysis.
References
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... For distinctly-layered podzolic soils, possible water accumulation over a less permeable spodic layer is mentioned by Kutílek and Nielsen (1994). This lower permeability arises from an accumulation of fine particles and various substances in the spodic layer, and from a corresponding increase in the tortuosity and decrease in the size of the effective pores (Rezaei et al., 2016;Seuntjens et al., 2001;Wang and McKeague, 1982). However, for mountain podzols, insufficient number of studies (about water flow and accumulation, and changes in the crucial SHP among soil layers) has been reported in the literature. ...
... Rezaei et al. (2016) pointed out that lower K s of the illuvial (spodic) layer located at a depth of 47-52 cm could be also partially caused by compaction by heavy machinery. Seuntjens et al. (2001) measured K s using a pressure infiltrometer in horizons of two different lowland podzols, i.e., a drier podzol, characterized by a lower situated groundwater level and a sharply-defined spodic horizon; and a wetter podzol with a diffuse spodic horizon located in an old land dune landscape covered with spots of vegetation of various types. For the spodic illuvial horizons of the two podzols, considerably lower mean K s values were also noted than for the surrounding horizons. ...
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... It is very important to monitor the water content in time because it can show the variability of unsaturated hydraulic conductivity and related permeability [32]. However, this kind of data can usually be used only when the pedological pits are excavated and different instruments are installed [52][53][54]. Additionally, water content can also be defined when sampling is carried out [33], but, in that case, unsaturated hydraulic conductivity can be only estimated during the sampling time. ...
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... Dispersivity is a transport parameter that is often obtained experimentally by fitting measured breakthrough curves with analytical solutions of the advection-dispersion equation (Seuntjens et al. 2001). ...
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... Dispersivity is a transport parameter that is often obtained experimentally by fitting measured breakthrough curves with analytical solutions of the advection-dispersion equation (Mallants, 2014;Seuntjens et al., 2001). In this study a dispersivity = 0.1 m was taken, or one tenth of the total travel distance (i.e. 1 m) from top to bottom of the soil profile. ...
Technical Report
In this report, the fate of hydraulic fracturing chemicals and naturally occurring organic chemicals in soil as a result of unintentional release from storage ponds containing produced water has been evaluated. Exposure pathways and relevant hydrobiogeochemical processes along such pathways have been reviewed. A collation of physico‐chemical properties of organic contaminants served as input to a set of generic simulations of transport and attenuation in variably saturated soil profiles. Attenuation was simulated by means of a coupled equilibrium partitioning ‐ first‐order biodegradation model. The coupled processes of unsaturated flow, transport and attenuation in soil of selected contaminants that are associated with hydraulic fracturing fluids or that occur naturally in coal seams have then been modelled. Results showed that for all chemicals considered in the assessment, the combined effect of strong sorption and fast biodegradation resulted in complete degradation of all chemicals, including their transformation products, in the top 5 to 10 cm of the soil profile. These results are true for a broad range of sorption and degradation parameter values. This indicates that the risk of bioaccumulation in soil and leaching to groundwater is very small for the scenarios considered in this study.
... Dispersivity is a transport parameter that is often obtained experimentally by fitting measured breakthrough curves with analytical solutions of the advection-dispersion equation (Seuntjens et al. 2001). ...
Technical Report
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... As shown in Table 1, bulk density increased with depth. The very high bulk density at deeper depth (P60 cm) is primarily due to the very high sand content, whereas the high bulk density at 47-52 cm depth is due to soil compaction from the use of heavy machinery and cementation due to higher organic carbon content (OC) ( Table 1), humus and iron accumulations (typical for Podzol) compared to the upper layers (Seuntjens et al., 2001). Note that the higher value of OC at topsoil of profile B (upland) is due to compost application at that location. ...
... As shown in Table 1, bulk density increased with depth. The very high bulk density at deeper depth (≥60 cm) is primarily due to the very high sand content, whereas the high bulk density at 47-52 cm depth is due to soil compaction from the use of heavy machinery and cementation due to higher organic carbon content (OC) ( Table 1), humus and iron accumulations (typical for Podzol) compared to the upper layers (Seuntjens et al. (2001). ...
... Another modelling approach is the use of independent stream tubes, which each have a different velocity and dispersion coefficient (Vanderborght et al., 2006;Russo and Fiori, 2009). Solute transport can evolve from a stochastic-convective (independent stream tubes) to a convective-dispersive regime with increasing depth (Seuntjens et al., 2001). ...
... Another modelling approach is the use of independent stream tubes, which each have a different velocity and dispersion coefficient (Vanderborght et al., 2006;Russo and Fiori, 2009). Solute transport can evolve from a stochastic-convective (independent stream tubes) to a convective-dispersive regime with increasing depth (Seuntjens et al., 2001). ...
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... They can be applied to solve realistic field and laboratory situation problems as opposed to analytical models (Šimůnek and van Genuchten, 2008). The Hydrus-1D model (Šimůnek et al., 2008a) that is used in this study has been used in a wide range of applications in research and irrigation management (e.g., Hanson et al., 2008;Forkutsa et al., 2009;Roberts et al., 2008Roberts et al., , 2009, water harvesting (Verbist et al., 2009), and also to simulate the fate of nutrients by evaluating and comparing fertilization strategies for different crops and contaminants in soils (e.g., Seuntjens et al., 2001Seuntjens et al., , 2002aCote et al., 2003;Gärdenäs et al., 2005;Ajdary et al., 2007;Crevoisier et al., 2008). ...
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The initial results obtained in the first yearshowed that a new data set would be necessary to validate the results of this part. 5 In the third year, quasi 3D-modelling of water flow at the field scale will be conducted. In this modeling set -up, the field will be modeled as a collection of 1D-columns representing the different field conditions (combination of soil properties, groundwater depth, root zone depth). The measured soil properties are extrapolated over the entire field by linking them to the available spatially distributed data (such as the EMI-images). The data set of predicted Ks and other soil properties for the whole field constructed in the previous steps will be used for parameterising the model. Sensitivity analysis ‘SA’ is essential to the model optimization or parametrization process. To avoid overparameterization, the use of global sensitivity analysis (SA) will be investigated. In order to include multiple objectives (irrigation management parameters, costs, …) in the parameter optimization strategy, multi-objective techniques such as AMALGAM have been introduced. We will investigate multi-objective strategies in the irrigation optimization. Keywords: soil, Hydrus, modeling, water flow and solute transport, tensiometers, water content profile probes, sensitivity analysis, Ks, PTFs, ECa, model calibration, validation and optimization
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We propose an upward infiltration method to calibrate a time domain reflectometry (TDR) system. The method is rapid, allows the soil to remain unchanged during the experiment, and provides hundreds of data points. Three experiments were conducted using 18.7-cm-long probes in soils of three textures (nine experiments total). Calibrations also were performed by packing soil cores with soil at progressively higher water contents. The data from the two methods were fitted using regression techniques to two published models of the dielectric constant-water content relationship. The results show that the calibration curves of all three soils, fitted simultaneously to replicate experiments, were similar in shape and statistically the same. A single calibration curve, fitted simultaneously to the replicate experiments of the three soils, was compared with Topps equation and was statistically the same. The results support the conclusion that the upward infiltration method provides a fast and repeatable calibration method, consistent with conventional calibration.
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The solute concentrations measured in the field experiment of G. L. Butters et al. (this issue) are used to compare two models of vadose zone solute transport: the deterministic one-dimensional convection-dispersion model, which represents solute transport far from the source of solute entry, and the stochastic-convective lognormal transfer function model, which represents solute transport near the source. The stochastic-convective model provided an excellent representation of the spreading of the solute pulse to a depth of 3 m after calibration at 0.3 m. Conversely, the deterministic model dramatically underpredicted solute spreading beyond 0.3 m after calibration. An analysis of the area-averaged solute concentration revealed a nearly linear scale effect in the dispersivity to a depth of at least 14.8 m. A change in the growth pattern of dispersion observed in the breakthrough curve at 4.5 m was attributed to a soil texture change near 3 m, which caused the apparent dispersivity of the pulse to decrease between 3.0 and 4.5 m, after which it increased significantly between 4.5 m and the final profile sampling between 0 and 25 m.
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A stochastic-convective transport formulation based upon solute travel time probability is presented and is shown to include Fickian transport as a special subcase. It is further demonstrated that a travel time probability associated with a lognormal distribution of hydraulic conductivity will yield concentration breakthrough curves nearly equivalent to those of Fickian transport when the coefficient of variation in travel time is sufficiently small, i.e., less than unity. When applied to column tracer experiments, the results suggest that typical laboratory-measured hydrodynamic dispersion may be ascribed to local variations in hydraulic conductivity. Moreover, stochastic-convective transport is shown to conserve solute mass under a flux boundary condition but to fail to do so under a held concentration condition. This result indicates the importance of boundary conditions for properly formulated stochastic transport. The travel time formulation is shown to provide a direct link between measured dispersivity and the autocovariance of local flow velocity variations that are a consequence of media inhomogeneity and the system boundary conditions. Dispersivity is shown to manifest a scale effect by increasing in proportion to the length of a system when the velocity correlation range is greater than that length. An expression for the effective dispersivity is derived for the case of long-range velocity correlations and is shown to represent non-Fickian behavior.
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This study develops the complete theory for a vertically homogeneous soil by creating a stochastic-convective medium made up of stream tubes that do not exchange solute during transport. By creating a field-scale medium made up of an ensemble of such tubes, both solute travel time and travel distance probability density functions (pdfs) were described for the stochastic-convective problem. It is shown that there are two possible formulations of the pdfs, depending on the way in which mass is introduced to the solute transport volume during the time of calibration. After development of the theory, three examples are used to illustrate the application of the principles of stochastic-convective modeling to practical problems of interest in solute transport research. -from Authors
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Unsaturated hydraulic conductivities, K(h), were measured in wicks. Moisture contents, θ(h) were measured in wicks. Hysteresis was observed, and the draining curves were used to predict K(h) using the van Genuchten equation coupled with the Mualem conductivity model. A solution for unsaturated flow was used to calculate h in wicks given the flux, q, and length. Calculated values of h were within 25% of the measured values for high fluxes and within 5% of the measured values for low fluxes. A least-squares procedure for matching the h vs. q curve of a wick to a soil was used to design passive capillary samplers for application in two soils. -from Authors
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Experiments demonstrate that wetting front instability occurs in two- and three-dimensional homogeneous columns of sandy soils under continuous nonponding infiltration, simulating rain-fed conditions. Instabilities were visualized in two-dimensional experiments by observing the light transmitted through partially saturated silica sand, and by dye staining in a three-dimensional experiment. The dimensions of the instabilities observed corresponded well to the previous results found in studies of layered soils, indicating that the theories developed previously apply to rain-fed infiltration without layering. The study extends the range of situations where fingered flow is predicted to occur. -from Authors