ARTICLE IN PRESS
COLTEC-01270; No of Pages 14
ARTICLE IN PRESS
Available online at www.sciencedirect.com
Cold Regions Science and Technology xx (2007) xxx
– xxx 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
Please cite this article as: Kitterød, N.-O., Focused flow in the unsaturated zone after surface ponding of snowmelt, Cold Regions Science and
Technology (2007), doi: 10.1016/j.coldregions.2007.09.005
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– xxx
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.
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,
estimated infiltration intensities of
80 to 200 mm/day during the melting period.
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
reported that even though the tracer was uniformly applied, the plume was separated into several irregular flow channels with high flow velocities.
argued that fast tracer pulses start if infiltration intensities exceed a certain threshold. Based on mass balance calculations,
concluded that probably more than 50% of total applied tracer was transported to deeper regions by preferential flow. These findings correspond to what
reported from field and laboratory tracer experiments.
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 and fingering (
, p196).
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 (
), 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
, 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 (
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.
). It is located
), 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
Please cite this article as: Kitterød, N.-O., Focused flow in the unsaturated zone after surface ponding of snowmelt, Cold Regions Science and
Technology (2007), doi: 10.1016/j.coldregions.2007.09.005
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N.-O. Kitterød / Cold Regions Science and Technology xx (2007) xxx
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Fig. 1. Location of the Gardermo delta, the airport area, and the Moreppen research station. The glacier-paleo-portals (triangles) and paleo-river channels indicate the spatial development of the delta structure. The location of soil samples represents bore holes where several samples were taken
in vertical direction ( Fig. 3
).
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 (
), 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 km
2
is classified as a Gilbert type delta, which consists of three main sedimentary units: fluvial topset beds, near shore foreset beds, and brackish-marine bottomset beds. The thickness of the units varies as a function of distance to the
main glacier paleo-portals ( Fig. 1
). The topset is heterogeneous and consists mainly of coarse material (gravel and sand), but also of some finer material (channel backfill or overbank deposits). The foreset unit is more homogeneous than the topset and consists mainly of laminas of fine sand that are dipping with an angle of 15
–
30° to the horizontal plane. The post glacial rebound of the Scandinavian crust caused a regional marine regression and the land was lifted about 200 m, which is the altitude of the Gardermo area
today ( Tuttle et al., 1996; Tuttle, 1997; Tuttle and Aagaard,
1996 ). At Moreppen, the location where the tracer tests was
performed, the topset is approx. 2 m thick and consists of mainly gravel and sand with some finer material. The foreset consists of about 95% fine sand with some lenses of sandy silt.
A surface ground penetrating radar survey at Moreppen revealed areas in the delta foreset with distinct dipping reflectors while other areas had more transparent reflections
( Fig. 2 ). The strong reflections are low permeability layers
that cause funneling of water in the foreset. A large number of soil samples were taken as part of a geotechnical survey prior to the airport construction, and grain size distribution was analyzed for 1875 soil samples. The soil samples were concentrated laterally and vertically around the most
Please cite this article as: Kitterød, N.-O., Focused flow in the unsaturated zone after surface ponding of snowmelt, Cold Regions Science and
Technology (2007), doi: 10.1016/j.coldregions.2007.09.005
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– xxx
Fig. 2. Surface reflections from ground penetrating radar sampled at Moreppen (
). 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 cha-
). 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.
3. Method
The numerical flow simulator TOUGH2 ( Pruess, 1991 )
was used for computation of unsaturated flow velocities.
Unsaturated flow was modeled according to
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 V n bounded by the surface
Γ n d dt
Z
V n
MdV
¼
Z
C n
F
Y
C is:
þ
Z
V n qdV
ð
1
Þ where t is the time, M is the mass per unit volume, inward normal vector on surface
Γ
Y is the n
, 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:
F
¼ k abs k r l q
ð j p q g
Þ ð
2
Þ where k abs is the absolute (or intrinsic) permeability,
ρ is the density of water,
μ is the dynamic viscosity of water and g is the gravitational acceleration. In this study the
constitutive relation was used for relative permeability ( k r
) and saturation ( S ): k r
¼ p ffiffiffiffiffi
S e n
1 1 S
1 m e m o
2
ð
3a
Þ and the
constitutive relation for pressure and saturation: p
¼
1 a n
S e
1 m 1 o
1 nvG ð
3b
Þ where S e is called effective saturation, S e
= ( S
−
S r
) / (1
−
S
From a mathematical point of view, the parameters S r r
).
, 1/
α
, m , and n vG
, should be considered as fitting parameters. The parameters however, can also be related to physical quantities, namely to: the residual liquid saturation ( S r
), the air entry pressure (1/
α
), and, the pore size distribution index also referred to as van Genuchten's n ( n vG
). Eqs. (3a) and (3b) are coupled together by m = 1 − 1/ n vG
.
Summed up, the unknown parameters in this flow problem are:
(1) absolute permeability k abs tivity, K s
)
1
,
(2) porosity, ϕ
,
(or hydraulic conduc-
(3) liquid saturation, S r
,
(4) air entry pressure, 1/
α
, and,
(5) pore size distribution index, n vG
.
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 K s and absolute permeability k abs for the constants m ,
ρ
, g is K s
[ L
2
] is K s
=
ρ gk abs
[ L / T ]
/ m , which inserted
[m/s]
≈
0.55 × 10
−
7
× k abs
[m
2
] for water temperature close to 0°C.
Please cite this article as: Kitterød, N.-O., Focused flow in the unsaturated zone after surface ponding of snowmelt, Cold Regions Science and
Technology (2007), doi: 10.1016/j.coldregions.2007.09.005
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N.-O. Kitterød / Cold Regions Science and Technology xx (2007) xxx
– xxx
(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,
). 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
equations are used to estimate porosities ( ϕ
) and saturated hydraulic conductivities ( K s
).
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
) 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 (
Gustafson derived an analytical equation between the ratio u = d
60
/ d
10 and the porosity ϕ
, where d
10 and d
60 are 0.1 and 0.6 quantiles of the cumulative grain size distribution curve:
/ ¼ h
2ln
1
ð Þ h
2ln
1
ð Þ u 2 h
1
1 h
1 u 2 1
þ
1
ð
4
Þ and the saturated hydraulic conductivity is expressed by:
K s
¼ h
2
/ 3
ð 1 / Þ 2 log u
1
:
3
2 u 2 u
1 : 8
1
2 d
2
10
ð
5
Þ
estimated the two stochastic parameters
θ
2 by well pumping analysis in locations where grain size distribution curves were available. In this way he related (4) and (5) to measurements of K s and ϕ
. Gustafson's yield:
θ
1
= 0.8 and
θ
2
= 10.2, which can be considered as an optimal or global average of the stochastic variable
Θ
= (
θ
1
,
θ
2
).
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
1 and and
θ
(3b), results from
constitutive Eqs. (3a) and
study were employed.
used a database of 156 different Swedish soils to derive water retention characteristics and grain size distribution curves.
modified the
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.
used two parameters in the grain size distribution curve, namely d
25 and d
75 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: n vG
¼ k where
1
φ
þ k
2
L
þ k
3
L
2
).
þ k
4
L
3 is the porosity and n
1 vG
ð
6
Þ where L is a pressure relation given by L = log( w ), where w = h
25
/ h
75
= ( d
75
/ d
25
)
γ
, h
25 and h
75 are pressures corresponding to 25% and 75% saturation, and the empirical parameter
γ
= (3
α
AP
−
1)/2, where
α
AP
= exp[0.312log( d
75
/ d
25
)] is given by
.
estimated the parameters in Eq. (6) (
λ
1
,
λ
2
,
λ
3
,
λ
4
) to
(
−
0.0983, 1.0566,
−
0.5487, 0.1008).
The air entry pressure (1/
α
) [m] was estimated for
1 a effective saturation S e
):
¼ k
5
1
/
/
1
2
0
@
S e nvG
1 nvG
1
1 n vG
A
75 g ð
7
Þ is the grain size distribution index (6), and the empirical parameter
γ is explained above. The parameter
λ
5 is estimated to
4. Analysis of grain size distribution curves
The main data source in this study was grain size distribution curves from 1875 soil samples.
equations (eqs. 4 and 5) were employed for estimation of porosity ( ϕ
) and saturated hydraulic conductivities
( K s
). For the following analysis Gustafson's global average of
Θ
= (0.8, 10.2) was employed. The scatter plots in
indicate the variability of estimated saturated hydraulic conductivities (1 × 10
− 11 b
K s b
3.5 × 10
− 2 m/s) and porosity (0.06
b ϕ b
0.28). The pattern of estimated K s 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.
Please cite this article as: Kitterød, N.-O., Focused flow in the unsaturated zone after surface ponding of snowmelt, Cold Regions Science and
Technology (2007), doi: 10.1016/j.coldregions.2007.09.005
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Fig. 3. a) Estimated hydraulic conductivity ( K s
) and b) porosity plotted against the altitude of soil samples.
K size distribution by Eqs. (4) and (5).
K
2) sandy foreset from with K s
≈
1 × 10 s
−
4 was grouped into three clusters: 1) heterogeneous topset with 1 × 10
−
7 m/s from
∼
170 to
∼
200 m a.m.s.l., 3) silty layer with K s
≈
5 × 10
−
7 s b and porosity was derived from grain
K s b
1 × 10
−
3 m/s at
∼
200 m a.m.s.l., 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 (
).
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
K ϕ n
α s
( vG
−
1
(m/s)
−
)
(cm)
Topset
Foreset sand
Foreset silt
Topset
Foreset sand
Foreset silt
Topset
Foreset sand
Topset
Foreset sand
5.5 × 10
2.8 × 10
2.4 × 10
0.22
0.23
0.14
1.98
4.28
–
10.00
−
4
−
4
−
8
0.03
0.63
0.56
–
–
3.2 × 10
−
4
3.5 × 10
−
4
2.0 × 10
−
8
0.02
0.02
1.6 × 10
−
4
2.7 × 10
−
4.5 × 10
−
9
0.19
0.19
0.08
0.73
b
3.17
–
5.00
5
2.8 × 10
−
4
6.7 × 10
−
0.20
0.21
0.11
1.35
3.73
–
–
5
8.9 × 10
−
9
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
−
7.6 × 10
−
8
0.25
0.26
0.20
3.23
5.40
–
15.00
3 a
Saturated hydraulic conductivity K s
, was estimated by Eq. (5), porosity ϕ
, by Eq. (4), grain size distribution index n vG
, by Eq. (6), and air entry pressure
α −
1
, by Eq. (7). For n vG 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.
Please cite this article as: Kitterød, N.-O., Focused flow in the unsaturated zone after surface ponding of snowmelt, Cold Regions Science and
Technology (2007), doi: 10.1016/j.coldregions.2007.09.005
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– xxx 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
‘
S
’ indicate dipping silty layer in homogeneous foreset sand, and
‘
H
’ indicates horizontal structure.
7 each sedimentological unit: (i) the coarse part of the topset,
(ii) foreset sand, and (iii) foreset silt ( Table 1 ).
Since the grain size parameters d
25 and d
75 were not available for the total data set, the pore size distribution index ( n vG
) and the air entry pressure (1/
α
) were not calculated at the same locations as porosity ( ϕ
) and saturated hydraulic conductivity ( K s
). However, 247 grain size distributions curves were published by
, but this data set was not significant enough to distinguish between two clusters in the foreset. Based on
grain size distribution curves we employed
empirical Eqs. (6) and (7). The pore size distribution index n vG 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 (
) and
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
K x
(m
2
)
9.26 × 10
−
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
K y
(m
2
)
9.26 × 10
4.77 × 10
4.02 × 10
2.75 × 10
2.25 × 10
7.52 × 10
2.13 × 10
2.00 × 10
1.27 × 10
−
10
−
10
−
15
−
10
−
10
−
16
−
9
−
9
−
14
K z
(m
2
)
9.26 × 10
−
11
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
(
−
)
0.28
0.28
0.20
0.20
0.20
0.10
0.40
0.40
0.40
S
( r
−
)
0.23
0.20
0.33
0.08
0.04
0.25
0.39
0.36
0.35
n
( vG
−
)
2.00
3.10
2.10
1.1
1.5
1.5
2.5
4.6
3.6
α −
1
(Pa)
300
1000
2000
100
500
1000
500
2500
3000
K x
, K y and index and
K
α z
−
1 is saturated hydraulic conductivities in x , y , and z -direction, ϕ is porosity, S r is air entry pressure. All units are given in brackets.
is residual water saturation, n vG is grain size distribution
Please cite this article as: Kitterød, N.-O., Focused flow in the unsaturated zone after surface ponding of snowmelt, Cold Regions Science and
Technology (2007), doi: 10.1016/j.coldregions.2007.09.005
8
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N.-O. Kitterød / Cold Regions Science and Technology xx (2007) xxx
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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
(
). As explained above, local estimates of S r
, n vG
, 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
. Input flow parameters are given in
.
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
.
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
.
K h
/K air entry value, K s is saturated hydraulic conductivity, ϕ is porosity, n vG v indicate horizontal to vertical anisotropy of hydraulic conductivity,
α is grain size distribution index, and S r is residual water saturation.
−
1 is
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– xxx 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.
9
Fig. 6. Simulated breakthrough curves with groundwater table at 4 m below the surface for the geological geometries (S and H) given in
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
.
K h air entry value, K s
/K v is saturated hydraulic conductivity, ϕ is porosity, n vG indicate horizontal to vertical anisotropy of hydraulic conductivity, is grain size distribution index, and S r is residual water saturation.
α −
1 is
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– xxx
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
.
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
and simplified according to the image shown in
. 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,
a). The second alternative was without the silty unit, and had therefore only one foreset layer (labelled
‘
H
’
,
b). 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, K s
, porosity, ϕ
, residual liquid saturation, S r
, grain size distribution index, n vG air entry pressure, 1/
α
. In addition the anisotropy K
, and h
/K v
, was taken into account for the topset unit and the sandy forset unit: K h
/K v
= [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.
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 surface. In
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
for groundwater table at 4 m below the ground
Table 3 , maximum and minimum median resi-
dence 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 mm/day K s
K h
/ K v ϕ
S r n vG
α −
1
S 5 max 88.4
min 59.3
10 max 47.5
min 31.5
67.8
81.6
106.5
117.9
110.0
64.5
54.4
51.8
61.0
61.7
36.9
44.7
101.9
36.1
30.5
29.7
99.0
35.7
96.3
33.2
15 max 33.2
107.4
30.9
min 21.9
24.9
21.0
42 max 12.5
158.1
13.2
min 9.2
10.2
9.3
82.2
20.7
96.8
23.2
71.7
108.0
9.4
10.1
84.4
22.9
86.6
9.2
100 max min
250 max min
6.0
126.4
4.5
4.7
2.3
2.0
95.5
2.1
6.8
4.7
2.6
1.8
45.9
4.9
27.2
1.9
87.4
5.2
36.7
2.0
82.7
4.3
2.1
1.9
H 5
10
15
42
100
250 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
83.6
63.9
56.6
39.0
44.1
33.4
29.8
27.5
30.4
22.9
20.5
11.4
12.2
8.9
8.1
5.2
4.0
2.4
1.8
5.5
3.7
2.5
1.7
81.7
120.4
53.7
62.9
42.4
28.8
29.0
20.1
11.2
8.2
5.0
61.9
33.0
41.9
22.7
15.7
9.0
6.9
3.9
2.2
1.8
4.1
2.9
1.8
Residence time is computed for different: (i) geometries (S and H,
), (ii) infiltration intensities (5, 10, 15, 42, 100, 250) mm/day, and, (iii) flow parameters ( K s
, K h
/K v
, ϕ
, S r
, n vG
,
α −
1
)
⁎
. Boldfaced numbers shows absolute max. and min. median residence time for all parameter combinations.
⁎
K s is saturated hydraulic conductivity, K h
/K v is anisotropy
(horizontal to vertical saturated hydraulic conductivity), ϕ is porosity,
S
α r is residual water saturation,
−
1 is air entry pressure.
n vG is grain size distribution index, and,
75.3
65.3
39.3
34.5
26.9
23.9
10.5
9.5
4.7
4.4
2.1
2.0
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– xxx 11 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
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.
Fig. 7. Breakthrough curves of bromide (Br
− plotted together with simulations. Br
−
) and tritiated water (HTO) 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 (
α
L
) is included for H min and H max corresponding to
α
L
= 0.2 and
α
L
= 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
the breakthrough curves for Br
− and HTO are
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)
close to the airport area ( 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.
performed a tracer test
) that to a large extent
Differences between maximum and minimum median
residence times ( Table 3 ) indicate the sensitivity to infil-
tration 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
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– xxx 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. 4 a).
Compared to the horizontal layered flow geometry
b) 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 ). Fo-
cusing 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 (
) for the two alternative flow geometries (
the low permeability layer.
underneath the low permeability layer (
) with each other. The effect of funneling increases if infiltration velocities approaches saturated hydraulic conductivity in
As a consequence of the focusing effect, a shadow (or sheltered) zone with low water saturation, can be seen
). 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.) 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 (
). The impact of the low permeability layer on median resi-
dence 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
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 ( n vG
). Because n vG 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 (
). The impact of porosity ( ϕ
) and residual liquid saturation ( S r
) was correlated. This is to be expected because they are both related to the effective porosity ϕ e
, which describes the pore volume available for advective flow: ϕ conductivity ( K s e
= ϕ
(1
−
S r
). Saturated hydraulic
) and the air entry pressure (1/
α
) tended to have a similar impact on the residence time. High K s 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
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– xxx 13 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 T
OUGH
2 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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