Available online at www.sciencedirect.com
Cold Regions Science and Technology 53 (2008) 42 – 55
www.elsevier.com/locate/coldregions
Focused flow in the unsaturated zone
after surface ponding of snowmelt
Nils-Otto Kitterød ⁎
Norwegian Institute for Agricultural and Environmental Research, Norway
Received 4 December 2006; accepted 28 September 2007
Abstract
Surface ponding occurs if water flux from rain or snowmelt, increases the infiltration capacity of the soil. Such conditions are
frequently observed during spring time in Nordic countries and may represent hazards to water resources if the area is exposed to
pollution. During snowmelt water accumulates in local depressions due to frozen ground. At the end of the snowmelt period when
the frozen soil thaws, the flux of water may be extremely high in the unsaturated zone because of the accumulated volume of water.
In this study, flow velocities in the unsaturated zone were estimated by numerical flow simulations and cross validated by an
independent tracer test. The observed transport velocities of conservative tracers were about ten times higher than the applied
infiltration intensities and were explained by focusing of water flow in the vadose zone. The focusing effect was demonstrated by
transient numerical simulations. Numerical simulations were run for infiltration velocities ranging from very low (5 mm/day) to
extremely high (250 mm/day). Sensitivity analysis based on expected variation of the flow parameters illustrates the relative
importance of the grain size distribution index, intrinsic permeability, air entry pressure, soil porosity, residual water saturation, and
the ratio of horizontal to vertical permeability. The sensitivity analysis was performed for two different sedimentological
architectures, first for horizontal layers and then for a gently dipping low pervious layer above the groundwater table. Opposite to
what may be expected, the simulations indicate faster breakthrough in the presence of the low permeability layer because of the
focusing effect.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Unsaturated flow; Focused flow; Ponding; Grain size distribution; Tracer test; Unsaturated flow parameters; Sensitivity analysis
1. Introduction
The snowmelt period during spring is characterized by
repeated cycles of melting and freezing governed by solar
radiation and long wave energy out flux. In some years the
repetitive melting and freezing of snow gives rise to a solid
layer of ice below the snow cover, which reduces infiltration capacity. In the ground itself frost also reduces the
⁎ Fax: +47 63 00 94 10.
E-mail address: nils-otto.kitterod@bioforsk.no.
0165-232X/$ - see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.coldregions.2007.09.005
infiltration capacity (Stadler et al., 2000). The magnitude of
the reduction depends on the soil water content, which is
related to the spatial continuity of water in the vadose zone
prior to freezing. Stoeckeler and Weitzman (1960) distinguish between granular, porous, and solid ice in the soil,
and they found increasing resistance to the water flux with
increasing continuity of ice. Another physical reason for
reduced infiltration capacity is the suction gradient at the
freezing front. The pressure gradient is due to the phase
transition from liquid to solid water which transports water
to the frozen soil (Hansson et al., 2004). By theoretical
calculations the pressure at the solid water interface is
N.-O. Kitterød / Cold Regions Science and Technology 53 (2008) 42–55
estimated to about 160 MPa (Schenk, 1968). Hence, the
phase transition causes a significant suction gradient that
makes the soil below the freezing front extremely dry.
Because the unsaturated permeability of the soil is a function of the water content, the infiltration capacity in dry soil
is very low.
At the end of the snowmelt period when the frozen soil
thaws, infiltration intensities may be extremely high because of the accumulated volume of water, and the infiltration capacity increases as a consequence of increased water
saturation of the soil. French and Binley (2004) used time
lapse electrical resistivity to investigate infiltration during
snowmelt at the Gardermo aquifer. They concluded that the
small scale spatial variability in infiltration was to a large
extent related to micro topography. Infiltration starts in
micro depressions with an increasingly active area of infiltration during the snowmelt period. It was also observed
that infiltration started before the soil temperature was
above 0 °C, which means that fluid water bypasses zones of
frozen water. In another study related to infiltration after
ponding, Tuttle (2001) estimated infiltration intensities of
80 to 200 mm/day during the melting period. Tuttle's
(2001) calculations were based on volume calculations
combined with observations of time duration from maximum extension to total disappearance of the surface ponds.
At the same time the infiltration capacity in fine grained soil
may be increased due to fissures caused by desiccation of
fluid water at the freezing front. If the frost fissures have
good spatial connectivity, the effective permeability of the
soil increases significantly. Hence, frost fissures due to
desiccation are an important physical mechanism that explains the high infiltration capacity after ponding in fine
grained soil. Infiltration experiments on frozen soil in China
support our observations (Zheng et al., 2001a,b).
A large number of field tests have been reported on
different types of unfrozen soils (Flury and Flühler, 1995;
Hills et al., 1991; Kung, 1990a,b; 1993; Roth et al., 1991;
Schulin et al., 1987; Walter et al., 2000). All of the referred
studies documented focused flow in the unsaturated zone.
For example Roth et al. (1991) reported that even though
the tracer was uniformly applied, the plume was separated
into several irregular flow channels with high flow velocities. Roth et al. (1991) argued that fast tracer pulses start if
infiltration intensities exceed a certain threshold. Based on
mass balance calculations, Roth et al. (1991) concluded that
probably more than 50% of total applied tracer was transported to deeper regions by preferential flow. These findings correspond to what Kung (1990a, 1993) reported
from field and laboratory tracer experiments. Kung's
(1990a, 1993) observations of preferential flow was called
“funneling” in order to distinguish it from other kinds of
preferential flow, such as short-circuiting in macro-pores
43
and fingering (Fetter, 1992, p196). Flury et al. (1994)
concluded from tracer tests in Switzerland that “preferential
flow is the rule rather than the exception” in the unsaturated
zone. At the Gardermo aquifer, several tracer tests indicate
similar rapid transport in the unsaturated zone (French et al.,
1995; Swensen, 1997). A well monitored tracer test at
Moreppen (Fig. 1), was undertaken by Søvik and Alfnes
et al. (2002), and the result from their tracer test was used
for cross validation of the numerical simulations presented
below.
A major issue for water quality in cold climates is the
application of deicing chemicals to roads and at airports. At
the Oslo Airport Gardermoen, for example, the consumption during winter 2005/2006 was 1750 ton of glycol and
350 ton of formiat (OSL, 2007). As much as possible of
these chemicals were recovered before they infiltrated into
the ground, but still the accumulated load may be significant. Formiat and glycol are easily degradable in natural
soil; French and Bakken et al. (2002) did experiments on
glycol and formiat in Gardermo soil and observed half-life
between 7 and 50 days. The variable degradation time
depended on: soil temperature, initial concentration of
contaminant, and previous contamination history. The previous contamination history was related to growth of the
microbiological population that was able to utilize the
contaminant as a nutrient. If conditions for degradation
were constant, then pristine soil had, in general, lower
remediation capacity than soil with previous experience of
degradation of that specific contaminant. However, even
though the natural degradation capacity is high, contaminants require a minimum of residence time in the unsaturated zone to be degraded by natural processes. Based on
the experiments carried out by French and Bakken et al.
(2002), more than 90% of the deicing chemicals were
degraded after 20 to 200 days.
The present study is based on observations from the
Gardermo delta, which is a marine ice contact delta in
Norway deposited during the last de-glaciation of the
Scandinavian crust approx. 10 000 years ago. Today the
delta structure is the largest precipitation fed aquifer of
mainland Norway (Tuttle and Aagaard, 1996). It is located
40 km north of Oslo (Fig. 1), and the groundwater quality
has been under pressure because of increasing urbanization
of the area. In 1998 the main airport of Oslo was located at
Gardermoen, which represents a new potential threat to the
groundwater resource. The groundwater quality is monitored continuously and great efforts are implemented to
protect the groundwater from contamination. A main concern for the aviation company has been surface ponding
close to the runways. These ponds contain deicing chemicals as glycol and formiat, and therefore pose a potential
threat to the groundwater quality.
The purpose of this study was to estimate residence
time of water in the unsaturated zone after ponding.
Residence time was estimated by numerical flow simulations based on available information of the geological structure and core samples taken prior to the
construction of the airport. 1875 soil samples were used
to estimate mean and variance of soil physical parameters used in the flow model. The results from a tracer test
undertaken at a location close to the airport (Søvik et al.,
2002), were was used to cross validate the simulated
flow velocities done in the present study. The sensitivity
analysis of the residence time of water in the unsaturated
zone shows the relative importance of: heterogeneity of
the individual soil units (expressed by the grain size
distribution index), intrinsic permeability, air entry pressure, soil porosity, residual water saturation, and ratio of
horizontal to vertical permeability.
2. Geology and soil structure
The Gardermo delta was deposited 9500 years ago and
covers today an area of about 80 km2 (Andersen, 2001). It
is classified as a Gilbert type delta, which consists of three
main sedimentary units: fluvial topset beds, near shore
N.-O. Kitterød / Cold Regions Science and Technology 53 (2008) 42–55
45
Fig. 2. Surface reflections from ground penetrating radar sampled at Moreppen (Fig. 1). The cross section indicate delta topset and delta foreset beds.
The reflection from the groundwater table is indicated by dotted line. The glacio-fluvial topset beds are heterogeneous, and the foreset beds consists of
fine homogeneous sand (green transparent reflectivity) with some silty laminas (red and blue). The profile direction is consistent to direction of delta
progradation (west–east). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
sensitive areas along the railway line and at the main airport
building (Fig. 1). Locally at Moreppen grain size
disribution was analyzed for 139 soil samples. In addition
28 soil samples were analyzed with respect to saturated
hydraulic conductivities, and 13 for water retention characteristics (Pedersen, 1994). The data set with grain size
distribution covers most of the area of interest, and is
therefore very suitable for estimation of soil physical parameters in the flow equation.
and g is the gravitational acceleration. In this study the
van Genuchten (1980) constitutive relation was used for
relative permeability (kr) and saturation (S):
o
pffiffiffiffiffin
1 m 2
kr ¼ Se 1 1 Sem
ð3aÞ
3. Method
where Se is called effective saturation, Se =(S −Sr)/ (1 −Sr).
From a mathematical point of view, the parameters Sr, 1/α,
m, and nvG, should be considered as fitting parameters. The
parameters however, can also be related to physical
quantities, namely to: the residual liquid saturation (Sr),
the air entry pressure (1/α), and, the pore size distribution
index also referred to as van Genuchten's n (nvG). Eqs. (3a)
and (3b) are coupled together by m = 1 − 1/nvG.
Summed up, the unknown parameters in this flow
problem are:
The numerical flow simulator TOUGH2 (Pruess, 1991)
was used for computation of unsaturated flow velocities.
Unsaturated flow was modeled according to Richards'
assumption (1931) where the gas-phase has infinite mobility, thus only the liquid phase is considered. Richards'
equation consists of (1) a mass balance Eq. (2) a flux
equation and (3) constitutive relations between permeability, pressure, and saturation. Written in terms of the integral
finite difference, which is the numerical scheme used in
TOUGH2, the mass balance equation for a volume Vn
bounded by the surface Γn is:
Z
Z
Z
d
Y
MdV ¼
F ndC þ
qdV
ð1Þ
dt Vn
Cn
Vn
where t is the time, M is the mass per unit volume, Y
n is the
inward normal vector on surface Γn, and q is a local sink/
source term. Here, q is a source at the surface,
corresponding to estimated infiltration rates below the
surface ponds.
The flux term F is given by Darcy's law:
kr q
ð jp qgÞ
ð2Þ
F ¼ kabs
l
where kabs is the absolute (or intrinsic) permeability, ρ is
the density of water, μ is the dynamic viscosity of water
and the Mualem (1976) constitutive relation for pressure
and saturation:
on 1
1 n 1
vG
p ¼ Se m 1
ð3bÞ
a
(1) absolute permeability kabs (or hydraulic conductivity, Ks)1,
(2) porosity, ϕ,
(3) liquid saturation, Sr,
(4) air entry pressure, 1/α, and,
(5) pore size distribution index, nvG.
These five flow parameters are unknown in each
sedimentological unit, which implies that all together 15
parameters have to be estimated for the three unit cases
1
The relation between saturated hydraulic conductivity Ks [L/T]
and absolute permeability kabs [L2] is Ks = ρgkabs/m, which inserted
for the constants m, ρ, g is Ks [m/s] ≈ 0.55 × 10−7 × kabs [m2] for
water temperature close to 0°C.
46
N.-O. Kitterød / Cold Regions Science and Technology 53 (2008) 42–55
(topset, foreset sand and foreset silt) and 10 parameters
for the two unit cases (topset and forest sand).
There are two ways to estimate unknown flow parameters, either by inverse modeling or by estimating parameters from measurements. Inverse modeling has been
used in a previous study where the estimated flow parameters were conditioned on liquid saturation measurements
from the Moreppen research area (Kitterød and Finsterle,
2004). In the present study, flow parameters are estimated
directly from grain size distribution curves. This approach
requires analytical and/or empirical relations between grain
size distribution curves and the requested flow parameters.
For this purpose the Gustafson's (1983, 1986) equations are
used to estimate porosities (ϕ) and saturated hydraulic
conductivities (Ks). Gustafson's (1983, 1986) equations are
more general than other empirically derived equations and
are better adapted to glacio-fluvial deposits. For example
are Hazen's and Kozeny–Carmen's equations (Smith and
Wheatcraft, 1992) special cases of Gustafson's equations
(Gustafson, 1983). Independent laboratory measurements
of saturated hydraulic conductivities from soil samples
taken at Gardermoen confirm the validity of Gustafson's
equation for the Gardermo aquifer (Pedersen, 1994).
Gustafson derived an analytical equation between the
ratio u = d60/d10 and the porosity ϕ, where d10 and d60
are 0.1 and 0.6 quantiles of the cumulative grain size
distribution curve:
1
u2h1
h1
h1
2lnðuÞ u2 1 þ 1
/¼
h1
2lnðuÞ
ð4Þ
and the saturated hydraulic conductivity is expressed by:
2
/3
logu 2 u1:8
2
d10
ð5Þ
Ks ¼ h2
u2 1
ð1 /Þ2 1:3
Gustafson (1983) estimated the two stochastic parameters θ1 and θ2 by well pumping analysis in locations
where grain size distribution curves were available. In
this way he related (4) and (5) to measurements of Ks
and ϕ. Gustafson's yield: θ1 = 0.8 and θ2 = 10.2, which
can be considered as an optimal or global average of the
stochastic variable Θ = (θ1,θ2). Goshu and Omre (2003)
used a Bayesian framework to improve estimation of Θ
by conditioning on local pumping tests done at the
Gardermo aquifer, but the deviation from Gustafson's
global estimates were not very significant, thus in the
present study Gustafson's original estimates were
applied.
For estimation of parameters in the van Genuchten's
(1980) and Mualem's (1976) constitutive Eqs. (3a) and
(3b), results from Jonasson's (1991) study were employed.
Jonasson (1991) used a database of 156 different Swedish
soils to derive water retention characteristics and grain size
distribution curves. Jonasson (1991) modified the Arya and
Paris (1981) equation and used non-linear regression analysis to estimate parameters in the van Genuchten's equation. The method was validated on 18 different soil types
not used in the calibration procedure. Jonasson (1991) used
two parameters in the grain size distribution curve, namely
d25 and d75 corresponding to the 0.25 and 0.75 quantiles of
the cumulative grain size distribution curve. In this way
Jonasson's method is easy to employ. The grain size
distribution index was estimated by:
1
nvG ¼ k1 þ k2 L þ k3 L2 þ k4 L3
ð6Þ
where L is a pressure relation given by L =log(w), where
w =h25/h75 = (d75/d25)γ, h25 and h75 are pressures corresponding to 25% and 75% saturation, and the empirical
parameter γ = (3αAP − 1)/2, where αAP =exp[0.312log(d75/
d25)] is given by Arya and Paris (1981). Jonasson (1991)
estimated the parameters in Eq. (6) (λ1, λ2, λ3, λ4) to
(−0.0983, 1.0566, −0.5487, 0.1008).
The air entry pressure (1/α) [m] was estimated for
effective saturation Se = 0.75 (Jonasson, 1991):
0 1nvG
1
nvG
1
1 / 2 @ 1nvG
¼ k5
Se
1A ðd75 Þg
ð7Þ
a
/
where φ is the porosity and nvG is the grain size
distribution index (6), and the empirical parameter γ is
explained above. The parameter λ5 is estimated to
0.0614 (Jonasson, 1991).
4. Analysis of grain size distribution curves
The main data source in this study was grain size distribution curves from 1875 soil samples. Gustafson's
(1983) equations (eqs. 4 and 5) were employed for estimation of porosity (ϕ) and saturated hydraulic conductivities
(Ks). For the following analysis Gustafson's global average
of Θ = (0.8, 10.2) was employed. The scatter plots in Fig. 3
indicate the variability of estimated saturated hydraulic
conductivities (1× 10− 11 b Ks b 3.5 ×10− 2 m/s) and porosity (0.06 b ϕ b 0.28). The pattern of estimated Ks values
shows three distinctive clusters corresponding to the sedimentological architecture of the delta. There is one cluster
centered around 200 m a.m.s.l., which has hydraulic conductivities ranging from about 1× 10− 7 m/s to about
1× 10− 3 m/s. The isostatic rebound at the Gardermoen area
is about 200 m, hence this altitude is consistent with a
fluvial environment corresponding to the delta topset beds.
N.-O. Kitterød / Cold Regions Science and Technology 53 (2008) 42–55
47
Fig. 3. a) Estimated hydraulic conductivity (Ks) and b) porosity plotted against the altitude of soil samples. Ks and porosity was derived from grain
size distribution by Eqs. (4) and (5). Ks was grouped into three clusters: 1) heterogeneous topset with 1 × 10− 7 b Ks b 1 × 10− 3 m/s at ∼ 200 m a.m.s.l.,
2) sandy foreset from with Ks ≈ 1 × 10− 4 m/s from ∼ 170 to ∼ 200 m a.m.s.l., 3) silty layer with Ks ≈ 5 × 10− 7 m/s from ∼170 to ∼ 200 m a.m.s.l.
Because of significant discharge due to rapid melting of the
glacier, the distribution channels eroded into sediments
below sea level in proximal part of the delta (Tuttle, 1997).
A minor part of the soil samples below the marine limit may
therefore belong to the delta topset. Glacio-fluvial depositional environments comprise dynamic changes of water
fluxes in time and space. Hence, topset beds in the Gardermo delta span everything from highly permeable, well
sorted gravel from channel beds to slowly permeable, fine
grained overbank deposits. Furthermore, the topset cluster
has a clear bimodal probability density distribution, which
supports the interpretation of channel deposits and
Table 1
Summary of empirical parameter estimation
Flow
parameter a
Geological
unit
Mean
Std
Quantiles
0.025
0.159
0.841
0.975
Ks (m/s)
Topset
Foreset sand
Foreset silt
Topset
Foreset sand
Foreset silt
Topset
Foreset sand
Topset
Foreset sand
5.5 × 10− 4
2.8 × 10− 4
2.4 × 10− 8
0.22
0.23
0.14
1.98
4.28
–
10.00
3.2 × 10− 4
3.5 × 10− 4
2.0 × 10− 8
0.02
0.02
0.03
0.63
0.56
–
–
1.6 × 10−4
2.7 × 10− 5
4.5 × 10− 9
0.19
0.19
0.08
0.73 b
3.17
–
5.00
2.8 × 10−4
6.7 × 10− 5
8.9 × 10− 9
0.20
0.21
0.11
1.35
3.73
–
–
8.2 × 10−4
4.7 × 10− 4
3.8 × 10− 8
0.23
0.24
0.17
2.60
4.84
–
–
1.4 × 10−3
1.2 × 10− 3
7.6 × 10− 8
0.25
0.26
0.20
3.23
5.40
–
15.00
ϕ (−)
nvG
α− 1 (cm)
Saturated hydraulic conductivity Ks, was estimated by Eq. (5), porosity ϕ, by Eq. (4), grain size distribution index nvG, by Eq. (6), and air entry
pressure α− 1, by Eq. (7). For nvG and α− 1 no samples were avaiable in the silty layer. For α− 1 it was not possible to estimate values in topset, or
standard deviation and the quantiles 0.159 and 0.841 in the forset sand based on the available data.
b
Nonphysical value.
a
48
N.-O. Kitterød / Cold Regions Science and Technology 53 (2008) 42–55
overbank deposits. Because channels in a glacio-fluvial
environment are continuously migrating over the delta
plain, the channel deposits are connected to each other both
laterally and vertically. The most conductive part of the
topset is of major interest for estimation of residence time
after ponding, hence for this study only the coarse part of
the topset is included in the numerical computations.
The foreset is more homogeneous than the topset. Two
separate clusters were identified in the foreset. Both clusters
are located at altitudes between 170 and 200 m a.m.s.l.,
which is consistent with the foreset altitude. The main
foreset unit, which consists of fine sand, corresponds to the
cluster which is centered on a hydraulic conductivity of
1× 10− 4 m/s. The second cluster has hydraulic conductivities between 1× 10− 7 m/s and 1 ×10− 9 m/s corresponding
to sandy silt. Some of the samples in the second foreset
cluster may belong to the delta bottom set, but it is more
likely that the majority of these samples belong to the
foreset. Layers of silt were observed in the foreset during
excavation of a lysimeter trench, which supports the
interpretation of two distinct clusters in the foreset.
For each of the three clusters a statistical analysis was
carried out. Firstly, the spatial structure was analyzed. The
hypothesis was that distance to the glacier front would
reveal a trend in the flow parameters. Close to the front we
expected coarser sediments, and at distant parts finer sediments. However, it was not possible to identify any trend
with the spatial resolution of the available soil samples. The
channel geometry on the delta plain was probably changing
frequently, which resulted in the complex sediment pattern
we observe today. We consider therefore the probability of
observing a specific hydraulic conductivity (high or low) as
independent of the location within the airport area for this
study. Based on this argument, the statistical analysis is
straightforward, and statistical moments were derived for
Fig. 4. Two alternative sedimentological geometry with delta topset
and foreset layers. The interpretation was based on the ground
penetrating radar image in Fig. 2. ‘S’ indicate dipping silty layer in
homogeneous foreset sand, and ‘H’ indicates horizontal structure.
each sedimentological unit: (i) the coarse part of the topset,
(ii) foreset sand, and (iii) foreset silt (Table 1).
Since the grain size parameters d25 and d75 were not
available for the total data set, the pore size distribution
index (nvG) and the air entry pressure (1/α) were not calculated at the same locations as porosity (ϕ) and saturated
hydraulic conductivity (Ks). However, 247 grain size distributions curves were published by Pedersen (1994), but this
data set was not significant enough to distinguish between
two clusters in the foreset. Based on Pedersen's (1994)
grain size distribution curves we employed Jonasson's
(1991) empirical Eqs. (6) and (7). The pore size distribution
index nvG revealed a bimodal structure, which again was
interpreted to represent topset and foreset sediments. The
air entry pressure had a most probable value about 10 cm,
but it was not possible to find any difference between topset
and foreset.
Table 2
Flow parameters used for unsaturated flow computations in TOUGH2 based on empirical data analysis (Table 1) and Rawls et al. (1993)
Kx
Ky
2
(m )
Most likely
0.025 quantile
0.975 quantile
Topset sand
Foreset sand
Foreset silt
Topset sand
Foreset sand
Foreset silt
Topset sand
Foreset sand
Foreset silt
Kz
2
2
(m )
− 10
9.26 × 10
4.77 × 10− 10
4.02 × 10− 15
2.57 × 10− 10
2.25 × 10− 10
7.52 × 10− 16
2.13 × 10− 9
2.00 × 10− 9
1.27 × 10− 14
(m )
− 10
9.26 × 10
4.77 × 10− 10
4.02 × 10− 15
2.75 × 10− 10
2.25 × 10− 10
7.52 × 10− 16
2.13 × 10− 9
2.00 × 10− 9
1.27 × 10− 14
− 11
9.26 × 10
4.77 × 10− 11
1.08 × 10− 15
2.75 × 10− 11
2.25 × 10− 11
2.06 × 10− 16
2.13 × 10− 10
2.00 × 10− 10
3.37 × 10− 13
ϕ
Sr
nvG
α− 1
(−)
(−)
(−)
(Pa)
0.28
0.28
0.20
0.20
0.20
0.10
0.40
0.40
0.40
0.23
0.20
0.33
0.08
0.04
0.25
0.39
0.36
0.35
2.00
3.10
2.10
1.1
1.5
1.5
2.5
4.6
3.6
300
1000
2000
100
500
1000
500
2500
3000
Kx, Ky and Kz is saturated hydraulic conductivities in x, y, and z-direction, ϕ is porosity, Sr is residual water saturation, nvG is grain size distribution
index and α− 1 is air entry pressure. All units are given in brackets.
N.-O. Kitterød / Cold Regions Science and Technology 53 (2008) 42–55
5. Numerical simulations
Most of the input parameters for flow simulations
were taken directly from the empirical data analysis of
grain size distribution curves from the Gardermo soil
(Table 1). As explained above, local estimates of Sr, nvG,
49
and 1/α were not possible to deduce for all geological
units due to lack of data. In these cases flow parameters
were taken from Rawls et al. (1993). Input flow
parameters are given in Table 2.
Residence time of water in the vadose zone depends
on boundary conditions and flow parameters. Boundary
Fig. 5. Simulated breakthrough curves with groundwater table at 4 m below the surface for the geological geometries (S and H) given in Fig. 4.
Infiltration velocities were 15 mm/day (upper), and 42 mm/day (lower). Only curves indicating min. and max. breakthrough time were included in
this plot to indicate the sensitivities of the flow parameters in Table 2. Kh/Kv indicate horizontal to vertical anisotropy of hydraulic conductivity, α− 1 is
air entry value, Ks is saturated hydraulic conductivity, ϕ is porosity, nvG is grain size distribution index, and Sr is residual water saturation.
50
N.-O. Kitterød / Cold Regions Science and Technology 53 (2008) 42–55
conditions are infiltration velocities and depth to the
groundwater table. Depth to groundwater table and
structure of flow parameters are given by the geometry
of the flow domain. No quantitative observations of
infiltration velocities I, were available, but qualitative
observations indicate a maximum infiltration velocity of
around 250 mm/day. I = 250 mm/day was therefore
employed as an upper limit for infiltration velocity.
Fig. 6. Simulated breakthrough curves with groundwater table at 4 m below the surface for the geological geometries (S and H) given in Fig. 4.
Infiltration velocities were 100 mm/day (upper), and 250 mm/day (lower). Only curves indicating min. and max. breakthrough time were included in
this plot to indicate the sensitivities of the flow parameters in Table 2. Kh/Kv indicate horizontal to vertical anisotropy of hydraulic conductivity, α− 1 is
air entry value, Ks is saturated hydraulic conductivity, ϕ is porosity, nvG is grain size distribution index, and Sr is residual water saturation.
N.-O. Kitterød / Cold Regions Science and Technology 53 (2008) 42–55
Three high infiltration rates and three moderate to low
infiltration rates were used as input for transient
simulations: I = [5, 10, 15, 42, 100, 250] mm/day. The
infiltration rate of 42 mm/day was chosen to compare the
simulated breakthrough curves with results from the
field tracer test conducted by Søvik and Alfnes et al.
(2002).
The geometry of the flow domain is related to sedimentological structures and depth to the groundwater table.
The real sedimentological structures, however, have to be
simplified to make numerical computation feasible. The
flow domain was therefore derived from the ground penetrating radar profile in Fig. 2 and simplified according to the
image shown in Fig. 4. As argued above, the probability
density function including the most permeable part of the
topset layer was used to deduce flow parameters for numerical simulations. The bimodal probability density function
of topset flow parameters was consequently simplified to
an ordinary single modal probability density function.
Given the context of the present study, this was a valid
assumption for two reasons. Firstly, there is high lateral and
vertical connectivity in fluvial deposits, and secondly, the
high flow velocities are of the main interest in this study.
The ground penetrating radar reveals areas with strong
reflectors and other areas with transparent reflectors
(Fig. 2). Two alternative foreset structures were therefore
applied: The first alternative had a thin dipping silty unit
present in the foreset, (labelled ‘S’ for silt, Fig. 4a). The
second alternative was without the silty unit, and had
therefore only one foreset layer (labelled ‘H’, Fig. 4b). The
lower boundary of the flow domain is the groundwater
table. Breakthrough curves for two different groundwater
tables were calculated (4 and 11 m), but in this paper only
simulation results with groundwater table at 4 m were
included.
Residence time of water in the unsaturated time were
computed for six infiltration velocities (I= [5, 10, 15, 42,
100, 250] mm/day). For each infiltration velocity the following flow parameters were substituted successively: saturated hydraulic conductivity, Ks, porosity, ϕ, residual
liquid saturation, Sr, grain size distribution index, nvG, and
air entry pressure, 1/α. In addition the anisotropy Kh/Kv,
was taken into account for the topset unit and the sandy
forset unit: Kh/Kv = [1:1, 10:1, 100:1]. First, residence time
was computed for the most likely flow parameters for each
sedimentological unit. Then parameter values corresponding to 0.025 and 0.975 quantiles were stepwise permuted
for each sedimentological unit for the six infiltration velocities. This procedure was repeated for different geological
geometry and different depths to the groundwater table.
This permutation can be considered as a simple sensitivity
analysis of flow parameters for residence time.
51
All flow computations were initiated using a steady state
infiltration velocity of 2.5 mm/day. After the steady state
condition was achieved, transient simulations were run for
the given range of infiltration intensities I= [5, 10, 15, 42,
100, 250] mm/day. Each transient simulation was run for
16 days, which corresponds to the expected duration of the
surface ponds. After 16 days close to steady state flow was
achieved and residence time was calculated by particle
tracking from the surface to the groundwater table. Some
cases gave extremely slow numerical convergence and
were therefore discarded. Computed breakthrough curves
for the four highest infiltration velocities are shown in
Figs. 5 and 6 for groundwater table at 4 m below the ground
surface. In Table 3, maximum and minimum median residence time for different infiltration intensities and different
flow parameters were compared for the flow domain with
Table 3
Maximum and minimum median residence time in number of days for
water traveling from the surface to the groundwater table 4 m depth
below surface
Ks
Kh/Kv
ϕ
Sr
nvG
α− 1
max
min
max
min
max
min
max
min
max
min
max
min
88.4
59.3
47.5
31.5
33.2
21.9
12.5
9.2
6.0
4.5
2.3
2.0
67.8
64.5
36.9
36.1
107.4
24.9
158.1
10.2
126.4
4.7
95.5
2.1
81.6
54.4
44.7
30.5
30.9
21.0
13.2
9.3
6.8
4.7
2.6
1.8
106.5
51.8
101.9
29.7
82.2
20.7
71.7
9.4
45.9
4.9
27.2
1.9
117.9
61.0
99.0
35.7
96.8
23.2
108.0
10.1
87.4
5.2
36.7
2.0
110.0
61.7
96.3
33.2
84.4
22.9
86.6
9.2
82.7
4.3
2.1
1.9
max
min
max
min
max
min
max
min
max
min
max
min
74.0
65.2
39.3
34.2
27.6
23.5
11.5
9.2
5.3
4.2
2.4
1.8
73.8
63.9
39.0
33.4
27.5
22.9
11.4
8.9
5.2
4.0
2.4
1.8
83.6
56.6
44.1
29.8
30.4
20.5
12.2
8.1
5.5
3.7
2.5
1.7
81.7
53.7
42.4
28.8
29.0
20.1
11.2
8.2
5.0
3.9
2.2
1.8
120.4
62.9
61.9
33.0
41.9
22.7
15.7
9.0
6.9
4.1
2.9
1.8
75.3
65.3
39.3
34.5
26.9
23.9
10.5
9.5
4.7
4.4
2.1
2.0
mm/day
S
5
10
15
42
100
250
H
5
10
15
42
100
250
Residence time is computed for different: (i) geometries (S and H,
Fig. 4), (ii) infiltration intensities (5, 10, 15, 42, 100, 250) mm/day,
and, (iii) flow parameters (Ks, Kh/Kv, ϕ, Sr, nvG, α− 1)⁎. Boldfaced
numbers shows absolute max. and min. median residence time for all
parameter combinations.
⁎ Ks is saturated hydraulic conductivity, Kh/Kv is anisotropy
(horizontal to vertical saturated hydraulic conductivity), ϕ is porosity,
Sr is residual water saturation, nvG is grain size distribution index, and,
α− 1 is air entry pressure.
52
N.-O. Kitterød / Cold Regions Science and Technology 53 (2008) 42–55
Fig. 7. Breakthrough curves of bromide (Br−) and tritiated water (HTO)
plotted together with simulations. Br− and HTO are plotted as relative
accumulated concentrations for each sampling point. The simulations
indicate breakthrough curves for two different geological geometries (S
and H) and with two different sets of flow parameters (max and min). S
is geometry with dipping silt layer in foreset, and H is geometry with
two horizontal layers. Max and min indicate parameters sets giving max
and min travel time. Longitudinal hydrodynamic dispersion (αL) is
included for H min and H max corresponding to αL = 0.2 and αL = 0.5 m
respectively. The tracer experiment was conducted by Søvik and Alfnes
et al. (2002).
and without a dipping low permeability layer (labeled S and
H in Table 3). The median breakthrough is the time duration
from start of the tracer application at the surface until 50%
of the applied tracer had reached the groundwater table.
5.1. Cross validation by independent tracer test
Søvik and Alfnes et al. (2002) used tritiated water
(HTO) and Bromide (Br−) as conservative tracers in a
carefully monitored tracer experiment at Moreppen
(Fig. 1). They extracted tracer from a 3.5 m deep trench
with 25 suction cups installed horizontally into the
ground. Horizontal suction cups were used to avoid
vertical flow along the sampling tubes. The tracer test
started with a background wetting of the field by constant irrigation of 30 mm/day in 7 days, which gave local
saturation similar to infiltration after surface ponding or
an extreme snowmelt. Then 1000 mg/liter of Br− was
added in pulses of 25 l of water and repeated for every
second hour for 3 days. The tracer was applied in a 3 m
long drip-tube. At the time of tracer application, the
background infiltration was increased to 48 mm/day.
Estimated evaporation during the experiment was 5 to
6 mm/day, thus effective infiltration velocities was set to
42 mm/day. At the 3rd day of the experiment, a pulse of
18.5 MBq/ml in 25 l of water with HTO was applied. In
Fig. 7 the breakthrough curves for Br− and HTO are
plotted as a function of time together with simulated
breakthrough curves. The accumulated amounts of
tracers were plotted relative to the total amount of
extracted tracer at each sampling position to make the
comparison with simulated breakthrough curves easier.
Two important results can be deduced from Fig. 7: First,
the applied infiltration velocities (42 mm/day) gave pore
flow velocities of tracers from 2–300 mm/day. This result
indicates focusing of water flow due to soil structures.
Secondly, the simulated breakthrough curves which include
a dipping low permeability layer in the foreset (S min and S
max), envelop HTO and to some extent Br−. The same is
true if the low permeability layer in the foreset is omitted
(H min and H max), but then dispersion has to be included
in the simulations. This result demonstrates that the main
features in the observed breakthrough curves were reproduced by the simulations.
6. Discussion and conclusions
Residence time of water in the unsaturated zone controls the residual contaminant risk of deicing chemicals in
unconfined aquifers. It is therefore important to understand infiltration and percolation processes of water in the
unsaturated zone. In a polar or sub-polar climate where
precipitation accumulates in the snow package during
winter, the most important recharge period of groundwater takes place during snowmelt. Focusing effects as surface ponding and soil structures may increase infiltration
velocities significantly and cause locally rapid water flow
in the unsaturated zone. In such situations unconfined
aquifers are vulnerable if the area is exposed to pollution.
Søvik and Alfnes et al. (2002) performed a tracer test
close to the airport area (Fig. 1) that to a large extent
mimicked infiltration after ponding. They used two
conservative tracers, bromide and tritiated water, which
were compared to simulated flow velocities in this
study. The observed breakthrough curves were not used
for calibration of the numerical simulations. Our simulation result can therefore be considered as a crossvalidation of the flow parameters given the geological
geometry of the tracer site. Such cross validation increases the reliability of breakthrough curves for higher
and lower infiltration velocities, given the same kind of
geological geometry.
Differences between maximum and minimum median
residence times (Table 3) indicate the sensitivity to infiltration velocities, geometry of the flow domain, and flow
parameters. It should be emphasized that only one flow
parameter was changed for each simulation while all other
parameters were kept equal to the most likely value. All
simulations should therefore be interpreted as an average
N.-O. Kitterød / Cold Regions Science and Technology 53 (2008) 42–55
behavior of water. Simulations with mean parameters
imply that one fraction of the water travels faster and
another fraction of the water travels more slowly than the
simulations indicate. The sensitivity analysis reveals the
overruling importance of infiltration velocities (Table 3).
For most of the parameter combinations median residence
time of water was increasing exponentially as infiltration
velocities decreased. For 5 mm/day the calculated residence
time of water from the surface to the groundwater table at
4 m depth was between 50 and 120 days independent of
geological geometry. For infiltration intensities equal to
250 mm/day, minimum mean residence time varies around
2 days for horizontal geometry and 6 days if a dipping silty
layer is included.
The numerical simulations demonstrated funneling of
water flow in the unsaturated zone. In this case funneling
was caused by a low permeability dipping layer (Fig. 4a).
Compared to the horizontal layered flow geometry
(Fig. 4b) the low permeability dipping layer gave a relative
increase of water saturation above the layer and a relative
decrease of water saturation underneath it (Fig. 8). Focusing and defocusing of water have significant impact on
the flow velocities because unsaturated hydraulic conductivity varies non-linearly as a function of water saturation (Eq. (3a)). Hence, the variance of residence time
increases with the presence of a low permeability dipping
layer. The increased variance of residence time can be seen
by comparing the simulated breakthrough curves (Figs. 5
and 6) for the two alternative flow geometries (Fig. 4) with
each other. The effect of funneling increases if infiltration
velocities approaches saturated hydraulic conductivity in
the low permeability layer.
As a consequence of the focusing effect, a shadow (or
sheltered) zone with low water saturation, can be seen
underneath the low permeability layer (Fig. 8). The
shadow zone appears because water is funneled on top
of the low permeability layer and only minor amount of
Fig. 8. Simulated velocity field in unsaturated zone through delta
topset and foreset with a dipping silty layer. Blue color indicates water
saturation, green color is flow vectors, and the red lines is flow lines.
The low permeable silty layer cause funnel flow in the high permeable
foreset above, and a dry (shadow) zone below. (For interpretation of
the references to colour in this figure legend, the reader is referred to
the web version of this article.)
53
water infiltrates into the shadow zone. Low water saturation implies low effective hydraulic conductivity
which means that some portion of the water will travel
more slowly to the groundwater compared to a situation
without any low permeability layer. This explains why
most of the breakthrough curves for the dipping geometry case sum up to less than 1 (Figs. 5 and 6). The
impact of the low permeability layer on median residence time is related to infiltration intensities (Table 3).
For high infiltration intensities (250 and 100 mm/day)
mean residence time is generally higher if there is a
dipping low permeability layer in the flow domain
compared to a flow domain without the low permeability layer. The opposite was true for low infiltration
intensities. This comparison is valid if median residence
time is of main importance. On the other hand, if
breakthrough time (first arrivals), is of primary interest,
the pattern is different: For the same parameter combinations the first arrival of tracers is always faster if
there is a dipping low permeability layer in the flow
domain (Figs. 5 and 6).
Given the empirical variance of flow parameters in this
study, it can be seen from the simulated breakthrough
curves (Figs. 5 and 6) that the most sensitive parameter
was the grain size distribution index (nvG). Because nvG
captures the heterogeneity within each sedimentological
unit, this makes good sense when we take into account the
variability that was documented in the coarse part of the
topset beds (Fig. 3). The impact of porosity (ϕ) and
residual liquid saturation (Sr) was correlated. This is to be
expected because they are both related to the effective
porosity ϕe, which describes the pore volume available
for advective flow: ϕe = ϕ(1 − Sr). Saturated hydraulic
conductivity (Ks) and the air entry pressure (1/α) tended to
have a similar impact on the residence time. High Ks
implies higher effective hydraulic conductivities, which
results in fast unsaturated flow. 1/α has a similar effect.
For example, a high 1/α in the foreset sand entails high
water content in the sandy layer above the low permeability silt. Again, the result yields high effective hydraulic conductivity in the foreset sand.
The most critical variable for the calculation of residence time in unsaturated zone is infiltration velocity.
Unfortunately, infiltration velocity is difficult to estimate
because the most important processes governing infiltration (viz precipitation, evaporation, transpiration, snowmelt, freezing ground) vary in time and space. Local
infiltration velocities related to surface ponding require
volume measurements of accumulated water and time
duration of maximum extension to disappearance of the
pond and should therefore, in principle, be easier to estimate. However, the physical conditions for ponding are
54
N.-O. Kitterød / Cold Regions Science and Technology 53 (2008) 42–55
quite complex: Some year ponding is frequent, while
other years with apparently similar weather conditions,
ponds are absent. Based on our experiences, ponding
seems to be related to: soil moisture content before freezing, depth of frozen ground, snow cover, and number of
temperature fluctuations above and below the freezing
point during the snowmelt period. Due to principal
uncertainties affecting infiltration velocities, a broad spectrum of velocities spanning from 5 to 250 mm/day, was
used to simulate residence time of water in the unsaturated
zone in this study. If more precise infiltration velocities
were possible to quantify, the corresponding uncertainties
in residence time of water in the unsaturated zone will also
be reduced.
Acknowledgements
Thanks to the staff at Oslo Airport Gardermoen for
providing data, and the colleagues at Lawrence
Berkeley National Laboratory for help in TOUGH2
simulations. I am grateful to Anne Kristine Søvik and
Eli Alfnes for explaining the tracer experiment in detail
and also for giving me access to all their observations. I
acknowledge the financial support from the Norwegian
Institute for Agricultural and Environmental Research
and the University of Oslo.
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