Unsaturated flow at Gardermoen
during periods of extreme
high infiltration
intensities.
Nils-Otto Kitterød
Department of Hydrology, University of Oslo
Estimation of residence time of
water from the surface to the groundwater table
Summary
The purpose of this study is to quantify the residence time of water in the unsaturated zone at
the Oslo Airport Gardermoen. Residence time is of interest because microorganisms require a
minimum of time to degrade contaminants. Two locations were considered as most
interesting, the northern part of the Eastern runway and the southern part of the Western
runway (NE and SW in fig. 1). At these two areas de-icing loads are usually highest because
the airplanes usually take off from one of these two locations. The NE and SW areas
represents at the same time extremes with respect to depth to the groundwater table within the
Airport area. At NE depth to groundwater is approx. 11 m and at SW approx. 4 m.
The question of residence time is
especially critical in springtime.
During an ordinary snow-melting
period a low pervious zone of
frozen soil and ice usually develop
below the snow layer. This is due to
melting and refreezing processes.
This happens especially in the early
period of spring when temperature
at daytime is above zero degrees
Celsius and drops below zero
during night. These natural
processes are enforced at the
Airport area mainly of two reasons:
Firstly the topsoil and the original
vegetation are removed, and
secondly; micro depressions at the
surface is constructed to avoid surface water at the runways. The
topsoil provides usually rapid infiltration because vegetation and
biological activities create preferential flow paths. This mechanism increases transport capacity
significantly. The second factor –
modification of micro topography,
is probably the most important. In
some areas depressions has been
constructed. During the snowmelting season, these depressions
develop into large surface ponds.
Maximum extension of these
surface ponds may be about 450 m
long with about 1.5 m maximum
depth (Tuttle, 2001). At late
springtime when a bypass is
created in the frozen zone, the
infiltration intensities below these
ponds may be very high.
utm-N
Oslo airport
Gardermoen
6678500
NE
6676500
6674500
SW
6672500
study area
railway
runways
614 000
616 000
618 000
utm-E
Figure 1.Location of study areas. At North East (NE)
depth to the groundwater table is about 11m, and at
the South-West position groundwater table is about 4
m below surface.
1
Extreme infiltration intensities are a groundwater hazard. Heterogeneities in the sediments
make the situation even more complicated. Preferential flow develops in the unsaturated zone
due to heterogeneities, which means that the water conductive cross-section of the sediment is
reduced. This reduction of conductive volume implies that the water saturation is very high in
limited zones or “channels”. The result of this concentration of water is high flow velocities.
From previous studies we know that the Gardermoen deposit is very heterogeneous. The data
presented in this report confirms this picture (fig. 2). The sedimentological origin of these
heterogeneities are well studied and understood (Tuttle, 1997). High sedimentation rates at
the period of deposition (approx 9000 BP) and rapidly changing river positions resulted in
highly heterogeneous sediments both in the delta topset and in the dipping foreset units. These
two units determine flow patterns in the unsaturated zone at the Gardermoen deposit. As
clearly indicated in the statistical analysis of flow parameters, the topset unit consists of two
groups. One group is interpreted to be coarse-grained channel deposits and the other group is
fine grained over bank sediments probably deposited during periods of flooding. The foreset
beds consist of two units as well. One unit is coarse sand, and the other is sandy silt. The
origin of the silty unit is probably due to changes in the position of the river mouth at the
interface between the delta plain and the water in the fjord. The foreset unit is highly anisotropic with a dip of approx. 15° in the direction of the delta progression.
scatter plot of Ks based on d10/d60
1.00E-01
1.00E-02
1.00E-03
1.00E-04
Empirical
Ks <m/s>
Figure 2. The scatterplot of
hydraulic conductivities
indicate three clusters, one
corresponding to the topset
beds, and two clusters in the
foreset beds.
1.00E-05
1.00E-06
1.00E-07
1.00E-08
1.00E-09
1.00E-10
1.00E-11
1.00E-12
150
160
170
180
190
200
210
220
m o.h.
The main focus in this report is the impact of uncertainties to recidence time. Three ‘levels’ of
uncertainty has been touched upon: uncertainty of infiltration intensity, uncertainty of
sedimentological architecture and uncertainty of flow parameters.
We had no time series available describing the real infiltration below a surface pond, thus a
extremely high infiltration rate was first analysed, 250 mm/day. With previous estimated flow
parameters 250 mm/d was close to what was numerically maximum to infiltrate. Thus 250
mm/day was chosen of numerically reasons. Two moderate infiltration rates were also
analysed 100 mm/day and 50 mm/day. Preliminary studies based on volume estimates of the
surface ponds indicate infiltration intensities in the range between 80 mm/day to about 200
mm/day, depending on conductive infiltration area below the ponds. In the flow computations
performed in this report all three infiltration rates were run in transient simulation for 16 days
after previous steady state infiltration velocity of 2.5 mm/day. Infiltration intensities of 250
mm/day are higher than minimum hydraulic conductivity of the silty unit. This condition
2
causes numerical problems in solving the flow equation. Of this reason minimum hydraulic
conductivity in the silty unit had to be increased a little bit.
Natural heterogeneity has to be simplified in numerical flow simulations. Because extreme
velocities are of interest, we consider the topset units to consist of coarse grain channel
deposits only. From previous studies we know that the silty unit appear irregularly in the
foresets. Two architectures are therefore modelled. The first architecture has a thin dipping
silty unit present in the foresets. This architecture is labelled with a ‘S’ (dipping silt). The
other architecture is without the silty unit, and has just two horizontal layers. This architecture
is labelled with ‘H’ (horizontal architecture).
Uncertainties in flow parameters is the ‘third level’ investigated. All together it is five flow
parameters, 1) saturated hydraulic conductivity (Ks, which is equivalent to absolute
permeability), 2) porosity, 3) residual liquid saturation, 4) a grain size distribution index
(which indicate the heterogeneity) and, 5) the air entry pressure. For each sedimentological
unit these parameters are unknown values. In this report we have estimated the most probable
value (or average value), a minimum value and a maximum value for each unit. Firstly, flow
is computed for the most probable parameters. Then max and min values are permuted for
each sedimentological unit, keeping the parameters for all other units fixed at the most
probable value. In addition there is an uncertainty in anisotropy, in principle all units are
anisotropic, but the most obvious anisotropy is present in the sandy foreset unit. This
anisotropy is also regarded as a flow variable with an associated uncertainty in this study
(labelled Kh_Kv in figures and tables).
To sum up, residence time is computed for three high infiltration intensities (labelled 42, 100
and 250). 42 mm/day is chosen in order to compare the simulation results with observations
from a tracer test where 42 mm/day was used as background infiltration (c.f. Appendix D). In
addition three moderate to low intensities are simulated (15, 10 and 5 mm/day). All
infiltration scenarios where run at two locations (NE and SW, labelled NO and SV in
Norwegian) with two different sedimentological achitectures, i.e. either with dipping silt in
the forests or without (S or H). This gives four architectures for six infiltration intensities
altogether twenty four cases. For each case the impact of uncertainty in the flow parameters is
evaluated. In this study five different parameters are considered, in addition to anisotropy in
the foreset unit. This sums up to 672 different flow fields each with a different residence time
in the unsaturated zone. Some cases gave extremely slow convergence and was therefore
discarded. Breakthrough curves for all successful flow cases are presented in the Appendix C.
Maximum and minimum residence time is summarized in tab. 4, and breakthrough curves are
plotted in Appendix C. The differences between max and minimum residences times are due
to changes in only one flow parameter for each curve, thus the results indicate the sensitivity
for each parameter. It should be emphasized that all the results in this report should be
interpreted as ‘average’ behaviour of water. This means that it is very likely that a large
portion of the water travels faster, and at the same time a large portion of the water travels
much more slowly. This spreading is due to heterogeneities in the sediment.
3
Method
In computation of residence times the numerical flow simulator TOUGH2 (Pruess, 1991) is
used to solve the flow equation. The unsaturated flow is 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 equation, (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:
d
M dV = F ⋅ n dΓ + q dV
(1)
dt V
Γ
V
∫
∫
∫
n
n
n
where t is the time, M is the mass per unit volume, n is the inward normal vector on surface
Γn, and q is a local sink/source term. In the present problem q is a source at the surface,
corresponding to infiltration rates of either 250, 100 or 50 mm/day.
The flux term F is given by Darcy’s law:
kρ
F = −k abs r (∇p − ρg )
(2)
µ
where kabs is the absolute permeability, ρ is the density of water, µ is the dynamic viscosity of
water and g is the gravitational acceleration. In this study the van Genuchten (1980)
constitutive relation was used for relative permeability and saturation (S):
1 m
 
 
m
k r = S e 1 − 1 − S e  
 
 
2
(3a)
and the Mualem (1976) constitutive relation for pressure and saturation:
1
n
1  − m1
p = − S e − 1
(3b)
α

Se is called effective saturation, Se=(S−Sr)/(1−Sr). From a mathematical point of view, the
parameters Sr; 1/α; and n, should be considered as fitting parameters. However, every
parameter is related to physical quantities, namely to the residual liquid saturation (Sr), the air
entry value (1/α), and to the pore size distribution index (n) which is referred to as “van
Genuchten’s n” in the following. Eq. 3a and 3b are coupled by m=1−1/n.
The unknown parameters in this flow problem is thus:
(1) absolute permeability kabs 1 or hydraulic conductivity (Ks),
(2) porosity (φ),
(3) liquid saturation (Sr),
(4) the air entry value (1/α), and
(5) the pore size distribution index parameter, the van Genuchten’s n (vG_n).
All these five flow parameters are unknown in each sedimentological unit, thus for the flow
cases with three units (topset, foreset sand and foreset silt) 15 parameters has to be estimated.
For flow cases with only two units, 10 parameters has to be entered.
1
The relation between saturated hydraulic conductivity Ks [L/T] and absolute permeability kabs [L2] is Ks=ρ g
kabs/µ, which inserted for the constants µ,ρ,g is Ks [m/s] ≈ 10−7⋅kabs [m2] at 20° C, and Ks [m/s] ≈ 0.55⋅ 10−7⋅kabs
[m2] at 0° C. Hydraulic conductivity as a function of temperature is ignored in this report.
4
Basically it is two different ways to estimate unknown flow parameters, either by inverse
modelling or by deriving parameters (directly or indirectly) from measurements. Inverse
modelling has been done in another study. Kitterød and Finsterle (2001) estimated flow
parameters based on liquid saturation measurements from the research area Moreppen. The
estimated flow parameters reproduced essentially an independent tracer test performed by
Søvik and Alfnes et al. (2001).
In the present report flow parameters are derived from grainsize distribution curves, which
requires semi analytical and/or semi empirical relations between grain size distribution curves
and the requested flow parameters. Here the Gustavson (1983) relation is used to estimate
effective porosities (φe) and hydraulic conditivities (Ks). Gustavson use the ratio u=d60/d10
where d10 and d60 are 0.1 and 0.6 quantiles of the cumulative grain size distribution curve:
θ1
φe
−
θ1
u −1
θ 
 θ1

− 2 1  + 1
 2 ln(u ) u − 1 
2 ln(u )
=
2
θ1
(4)
θ1
. Note that the relation between absolute porosity φ ,
u −1
and effective porosity φe, is φ =φe + φ Sr. The ‘absolute’ porosity is measured in laboratory by
heating the sample.
The void ration is e =
2 ln(u )
−
2
Saturated hydraulic conductivity is expressed by:
φ e3  log u 
Ks = θ2


(1 − φ e )2  1.3 
2
2
 u 1.8  2
 d 10
 2
 u −1
(5)
The parameters θ1, and θ2 were estimated to 0.8 and 10.2 by Gustavson (1983) and can be
considered as ‘global’ estimates of a stochastic variable Θ=(θ1,θ2). However, in all stochastic
variables there are uncertainties. To indicate the effect of uncertainties in Θ, ±0.2Θ
Θ is
introduced in (4) and (5). The effect is illustrated in fig. 3. In the following parameter
estimation Gustavson’s global constants is used.
Histogram of Ks
900
N
800
700
NGI
theta(emp)
600
500
400
300
200
100
0
1.00E-10
+0.2*theta
-0.2*theta
1.00E-08
1.00E-06
1.00E-04
1.00E-02
Figure 3. Histogram of
scatterplott in fig. 2.
Note the impact
of the estimates by
employing Θ ± 0.2Θ
Θ.
1.00E+00
Ks
5
We have employed Jonasson’s (1991) empirical method for estimating flow parameters in the
the van Genuchten (1980) and Mualems (1976) constitutive relations. Jonason uses the the
ratio v=d75/d25 , i.e. the 0.25 and 0.75 quantiles of the cumulative grain size distribution curve.
The grain size distribution index n (labelled vG_n in the following) is adapted:
(
n = λ1 + λ2 L + λ3 L2 + λ4 L2
)
−1
(6)
where λ1,λ2,λ3,λ4 is weights estimated to (-0.0983,1.0566,-0.5487,0.1008) by Jonasson
(1991). L=logw, where w is a pressure relation given by w= h75/h25 =vγ where γ is related to
the empirical parameter αAP = exp(0.312logv) given by Arya and Paris (1982), γ=(3αAP −1)/2.
Finally the air entry value (1/α) at a pressure corresponding to 0.75 effective saturation is
given by:
1

2 
−
1
 n
 1 − φe

1
−γ
  0.75
= λ5 
− 1 (d 75 )
(7)
α

 φe  


where the weight λ5 is estimated to 0.0614 by Jonasson (1991). All Jonassons estimated
weights are adapted in the parameter estimation in this project.

1 

−
 1 − n −1 


Data
Precipitation and temperature
A statistical summary of monthly precipitation values from 1957 to 2001 is given in fig.4. and
tab. 1. Note that during a period of 44 years the two years 1999 and 2000 has three (almost
four) monthly records of max precipitation. Only one month has monthly precipitation more
than 250 mm, namely the wettest month in this period November 2000 with close to 300 mm.
The second highest precipitation was recorded in October 1967 with 216.4 mm. October 2001
had 209.5 mm, which is second highest ever recorded in October at Gardermoen. Figures
showing snow and rain statistics from 1963 to 2000 is presented in Appendix A. In the period
1963-2000 average yearly snow volume is 240 mm.
300.0
1957-2001
200.0
M ID-std
M ID+std
150.0
M ID
M IN
M AKS
100.0
1999
2000
50.0
ov
ct
ec
D
N
O
Se
p
Ju
l
Au
g
0.0
Ja
n
Fe
b
M
ar
Ap
r
M
ay
Ju
n
Figure 4.Max. min, and mean
precipitation volumes for the
period 1957-2001 is plotted
together with observations
from 1999 and 2000.
Compared to rest of the
observation period these two
years were quite wet.
mm/month
250.0
Daily max, minimum and average temperature for two typical snowmelt months is shown in
the Appendix A. Note that even though daily average temperature is above zero degree
Celsius, it may be many hours with freezing temperature during one day, which indicate
refreezing and reduction of infiltration capacities in the soil.
6
Tabel 1) Monthly precipitation from 1957 to 2001 at the Oslo Airport Gardermoen
Jan Feb Mar Apr May
Jun
Jul
Aug Sep
Oct Nov
Dec
MID
59.7 46.3 50.5 50.2 59.2 75.7 81.7 89.5 89.8 99.8 94.0
69.0
MIN
4.1 1.2 2.2
0.0
0.9
9.9
7.4
5.0 23.1 13.2 15.2
2.9
MAKS 156.7 127.4 133.9 126.2 135.4 176.3 209.0 197.9 210.7 216.4 294.5 197.7
Groundwater level and soil moisture
Figures illustrating observation of soil moisture and groundwater levels are included in the
Appendix A. The rapid increase in groundwater level after period with precipitation is not a
surprise. However, it does not imply that travel time of water from the surface is that fast. If
the unsaturated zone is wetted close to field capacity, relatively small amounts of
precipitation will mobilize equal amount of water close to the water table. The release is due
to a reduction of suction in the soil profile. Transport of pressure is several times faster than
transport of water even in a medium that is only partially saturated. During the observed
springtime the most significant increase of groundwater levels correspond to increase of
temperature, which of course is a beautiful illustration of the importance of snow melting at
the Gardermoen aquifer.
Notice also the difference in groundwater response at the western and eastern part of the
runway. On the western part there is a drop in groundwater level from middle of May, while
at the eastern part there is no indication of a recession. This difference in response has not
been investigated in this study, but the most likely explanation is different distance to the
boundaries, i.e. the ravine creeks Songa and Vikka in the southwest, and the kettle lake
Transjøen in northeast.
Data from soil moisture measurements are not analysed in detail in this report. The figures are
included in the Appendix A in order to illustrate the complexity in the soil moisture response.
Notice that only a few measurements show a increase in soil moisture even though water
obviously is transported to the groundwater. Most of the sensors are more or less
“untouched”. This may indicate a concentration of water transport to a confined volume of the
soil profile. Notice also the short delay time between the increase of soil moisture at 3.8 m
and the increase of the ground water table. Delay time is less than four days. To understand
the responses in the sensors of the soil watch stations it is necessary to have access to exact
position of sensors and knowledge of sedimentological architecture at each soil watch station.
Grain size distribution curves
The main data source in this study was d10 and d60 values from grain size distribution curves.
All together 1875 single grain size distribution curves were available. Gustavson’s (1983)
equations (eq. 4 and 5) were employed for estimation of effective porosity (φe) and hydraulic
conductivities (Ks).
A scatter plot of hydraulic conductivities (Ks) indicates a total variability of 10 orders of
magnitude (fig. 2). The scatter plot indicates furthermore, a quite clear clustering of values.
There is a cluster centred around 200 m a.s.l., which has hydraulic conductivities ranging
from about 10-8 m/s to about 10-3 m/s. This cluster corresponds to delta topsets. According to
Tuttle (1997) delta topsets goes below 200 m a.s.l. at proximal part of the delta ( i.e. close to
7
the glacier front). There is another cluster that is centred on hydraulic conductivity of approx.
10-4 m/s, and yet another cluster with hydraulic conductivities between 10-7 m/s to 10-9 m/s.
These two clusters correspond to delta foresets. Mean sea level at the time of deposition was
approx. 200 m a.s.l.. These two clusters are therefore confined to 200 m a.s.l.. Histograms of
Ks and porosity indicate also a clear bimodal structure of the data. Note also the impact of
uncertainty in the stochastic parameter Θ in the Gustavson’s equations. ±0.2Θ
Θ is probably
conservative, yet the most likely value of Ks is reduced by one order of magnitude. In the
following analysis Gustavsons (1983) ‘global’ estimates of Θ is employed Θ= (0.8,10.2).
For each of the three clusters statistical moments were derived. Firstly we analysed the spatial
structure. The hypothesis was that distance to the glacier front would determine flow
parameters. Close to the front we expected coarser sediments, and at distant parts finer
sediments. As the scatter plots in the Appendix B indicate no such structure were found in the
present data. More surprisingly was that there were no apparent dependencies on depth below
surface either. The sedimentological structure that we know exist was determined by the
locations of the fluvial channels at the time of deposition. The channel geometry on the delta
plain was probably changing frequently, which resulted in the complex sediment pattern we
observe today. This complex pattern is not possible to observe with the spatial resolution of
the data set available for this report. The conclusion so far is that the probability to have high
hydraulic conductivities are independent on where you are located within the Airport area.
Based on this conclusion, the statistical analysis is straightforward. Statistical moments were
derived for each cluster as documented in the Appendix B. A summary of the moments is
given in tab. 2 below. Note that in the topset cluster there is a bimodal probability density
function. In sedimentological terms this bimodality is interpreted to reflect channel and
overbank deposits. We expect channel deposits to be connected both laterally and vertically
and thus represent the conductive part of the topset beds, we concentrate therefore only on the
coarse channel deposits in the computations.
Unfortunately d25 and d75 was not available at the same locations (a fact I regret very much).
The pore size distribution index n (vG_n) and the air entry pressure (1/α) was therefore not
possible to derive at the same locations as the effective porosity (φe) and hydraulic
conductivity (Ks). However, to have some indications of air entry pressure and the pore size
distribution index n we took published grain size distribution curves from the Moreppen
reseach site close to the Airport (Pedersen, 1994). We employed Jonason’s (1991) empirical
method (eq. 6 and 7). The results are given in the attached Appendix B as scatterplots and
histograms. The pore size distribution index n (vG_n) had a bimodal structure at Moreppen as
well, which was interpreted to represent topset and foreset sediments. Air entry pressure had
most probable value about 10 cm, but it was not possible to find any difference between
topset and foresets.
Simulation set-up
Infiltration
Prior to this report we had no access to empirical results indicating infiltration velocities
below the surface ponds. Based partly on numerical limitations and simple analysis of
average volumes of monthly precipitation, three different infiltration intensities were chosen;
250 mm/d, 100 mm/d and 50 mm/d. Compared to recorded precipitation values max
infiltration rate employed in the computations means that max monthly precipitation is
8
infiltrated each day in 16 days. Or put into other words the accumulated volume of water in
the surface ponds must be about 25 times max monthly precipitation, which is extremely high
values. Infiltration rate of 100 mm/day means that max monthly snow volume is melted and
infiltrated during one day. Intuitively speaking 50 mm/day is more realistic as max infiltration
volumes, but 50 mm/day is still high infiltration rates compared to recorded values of
precipitation. At this point however, real infiltration rates below these surface ponds are
unknown. Preliminary analysis based on volume calculations of water in the surface ponds
and ‘disappearance’ during snow melt, infiltration rates is estimated to be between 80
mm/day and 200 mm/day (for more details cf. Tuttle 2001).
The flow computations started form initial steady state condition with infiltration
corresponding to 2.5 mm/d, and then a time series of 16 days with either 250, 100 or 50 mm/d
was infiltrated through the model. Simple steady state simulations were employed for the low
intensity cases (15, 10 and 5 mm/d). Residence time form surface to groundwater was
computed by pure advection for all cases.
Sedimentological architecture
Based on prior knowledge of the delta structure at Gardermoen, we employed an idealized
architecture of the sediments. Two architectures were considered one with a fine grained silty
unit present in the foreset, and another with horizontal layers only. The first is labelled ‘S’
and the second ‘H’ (fig. 5). Two locations was modelled, North-East and South-West of the
Airport area, labelled NE and SW in the flow cases (fig. 1). At NE depth to groundwater was
about 11 m and at SW about 4 m. Rectangular grid were used with 0.5 × 0.5 m in horizontal
plane and 0.05 m resolution vertically.
S
-0.7
-0.7
-1.7
-1.7
-2.7
-2.7
-3.7
-3.7
0
2
4
6
8
10
12
West-East <m>
depth below surface <m>
Figure 5. Sketch
of sedimentological architecture at the
southwestern
location (cf. fig.1).
Identical
resolution and
geometry is used
at the northeastern
location, but the
scale is expanded
to 11 m vertically
and about 40 m
horizontally.
depth below surface <m>
Flow parameters
A critical point in flow computations is the question of how to represent parameter
uncertainty in the flow model. A difficult point is the question of cross-correlation between
the flow parameters. Extreme combinations of flow parameters may be highly unlikely and
may even be unphysical. The effect of combining extreme parameters may be serious
overestimation of the variability of the response variable.
H
-0.7
-0.7
-1.7
-1.7
-2.7
-2.7
-3.7
-3.7
0
2
4
6
8
10
12
West-East <m>
9
Tabel 2) Summary of empirical flow parameter data
Ks <m/s>
topset_channel
foreset_sand
foreset_silt
porosity (effective)
topset_channel
foreset_sand
foreset_silt
van Genuchten's n
topset_channel
foreset_sand
1/a [cm]
topset_channel
foreset_sand
mY
stdY
2.50 % 15.87 % 84.13 % 97.50 %
5.49E-04 3.21E-04 1.64E-04 2.76E-04 8.15E-04 1.37E-03
2.83E-04 3.52E-04 2.66E-05 6.73E-05 4.66E-04 1.18E-03
2.38E-08 1.97E-08 4.46E-09 8.91E-09 3.78E-08 7.55E-08
mY
0.22
0.23
0.14
stdY
0.02
0.02
0.03
2.50 %
0.19
0.19
0.08
15.87 %
0.20
0.21
0.11
84.13 %
0.23
0.24
0.17
97.50 %
0.25
0.26
0.20
mY
stdY
1.98
0.63
4.28
0.56
* nonphysical value
2.50 %
0.73*
3.17
15.87 %
1.35
3.73
84.13 %
2.60
4.84
97.50 %
3.23
5.40
2.50 %
15.87 %
84.13 %
97.50 %
mY
10.00
stdY
5.00
15.00
For the simulations done in this project, we firstly evaluated the effect of anisotropy in the
sandy foreset unit (dip1), which is regarded as the unit with most significant anisotropy. We
evaluated three ratios between horizontal and vertical conductivity (labelled Kh_Kv): 1:1,
10:1 and 100:1. We have no direct indications of this anisotropy, but a ratio of 10:1 between
horizontal and vertical hydraulic conductivity was regarded as the most probable. Thus the
flow cases labelled Kh_Kv =10_1 indicates the flow case with all parameters set equal to the
most probable values. To avoid the problem of overestimation the uncertainty in residence
time, we let all parameters be equal to the most probable value except for one parameter that
we first entered at minimum value and afterwards maximum value. This was repeated for all
flow parameters and for all sedimentological units.
Based on the data analysis presented above the values in tab 3 was entered in the simulation
code TOUGH2. Values for air entry value pressure (1/α) and the pore size distribution index n
(vG_n) were taken from Handbook of Hydrology (tab 5.3.2, page 5.14). Values of porosity
(φ) are based on laboratory measurements from samples taken at Moreppen. Accepting the
estimates of effective porosity (φe) based on the Gustavson’s (1983) method, residual liquid
saturation (Sr) was derived from the relation: φ =φe + φ Sr. The variance of the values of
residual liquid saturation is very high, but this is the price we have to pay if we want to
honour all the other empirically derived flow parameters.
10
Tabel 3) ’Rock’ parameters entered in TOUGH2 for unsaturated flow computations
por.
0.28
0.28
0.20
Kx
m2
9.26E-10
4.77E-10
4.02E-15
Ky
m2
9.26E-10
4.77E-10
4.02E-15
Kz
m2
9.26E-11
4.77E-11
1.08E-15
Slr
vG_n 1/a
[Pa]
0.23 2.00
300
0.20 3.10 1000
0.33 2.10 2000
por.
0.20
0.20
0.10
Kx
m2
2.57E-10
2.25E-10
7.52E-16
Ky
m2
2.75E-10
2.25E-10
7.52E-16
Kz
m2
2.75E-11
2.25E-11
2.06E-16
Slr
vG_n 1/a
[Pa]
0.08
1.1
100
0.04
1.5
500
0.25
1.5 1000
Max (.975 quantile) por.
topset sand (top2)
0.40
foreset sand (dip1)
0.40
foreset silt (dip2)
0.40
Kx
m2
2.13E-09
2.00E-09
1.27E-14
Ky
m2
2.13E-09
2.00E-09
1.27E-14
Kz
m2
2.13E-10
2.00E-10
3.37E-13
Slr
vG_n 1/a
[Pa]
0.39
2.5
500
0.36
4.6 2500
0.35
3.6 3000
Most likely' (E{X})
topset sand (top2)
foreset sand (dip1)
foreset silt (dip2)
Min (.025 quantile)
topset sand (top2)
foreset sand (dip1)
foreset silt (dip2)
Results
Residence times of water from the surface to the groundwater illustrated as breakthrough
curves are presented in Appendix C for all flow cases. The labels 1/a, Kh_Kv, Ks, por, Slr,
vGn_n indicate that the actual flow parameter, i.e. the air entry value (1/α); anisotropy in the
foreset sand unit; saturated hydraulic conductivity (Ks); porosity (φ); liquid saturation (Sr); or
the pore size distribution index parameter, the van Genuchten’s n (vG_n). All these are
permuted in each unit by min and max values. Hence for the architecture with one topset unit
(t2), and two foreset units (d1 and d2) six breakthrough curves are computed for each flow
parameter, and similarly for the architecture with two units, four curves are computed (max
and min for t2 and d1). Some of the flow parameters were beyond physical limits, which
resulted in numerical problems and thus discarded. For the most cases this is happening with
the extreme values for residual liquid saturation. For each flow case a simple analytical
expression for dispersion is included, which employ average (advective) velocities for each
case and add a constant dispersion factor of 10cm. Note that for most cases this simple model
map the variability between max and mean values. In most cases residual liquid saturation is
the most sensitive parameter for minimum residence time while the air entry value is the most
sensitive parameter for maximum residence time.
The most likely flow parameters are entered in the Kh_Kv cases. However, also the most
likely flow parameters must be regarded as uncertain. Of that reason also maximum and
minimum estimated residence time for each flow case is included in tab. 4.
11
Tabel 4. Maximum and minimum estimated recidence time of 50% of the applied tracer
for 5, 10, 15, 42, 100 and 250 mm/day of infiltration. Each infiltration intensity is broken
down to five flow variables each with two different sedimentological architecures and two
different depths to the groundwater table.
mm/day
5
10
15
SW/H
42
100
250
max
min
max
min
max
min
max
min
max
min
max
min
1/α
75.3
65.3
39.3
34.5
26.9
23.9
10.5
9.5
4.7
4.4
2.1
2.0
Kh_Kv
73.8
63.9
39.0
33.4
27.5
22.9
11.4
8.9
5.2
4.0
2.4
1.8
Ks
74.0
65.2
39.3
34.2
27.6
23.5
11.5
9.2
5.3
4.2
2.4
1.8
por
83.6
56.6
44.1
29.8
30.4
20.5
12.2
8.1
5.5
3.7
2.5
1.7
Slr
81.7
53.7
42.4
28.8
29.0
20.1
11.2
8.2
5.0
3.9
2.2
1.8
vG_n
120.4
62.9
61.9
33.0
41.9
22.7
15.7
9.0
6.9
4.1
2.9
1.8
max
min
max
min
max
min
max
min
max
min
max
min
1/α
110.0
61.7
96.3
33.2
84.4
22.9
86.6
9.2
82.7
4.3
2.1
1.9
Kh_Kv
67.8
64.5
36.9
36.1
107.4
24.9
158.1
10.2
126.4
4.7
95.5
2.1
Ks
88.4
59.3
47.5
31.5
33.2
21.9
12.5
9.2
6.0
4.5
2.3
2.0
por
81.6
54.4
44.7
30.5
30.9
21.0
13.2
9.3
6.8
4.7
2.6
1.8
Slr
106.5
51.8
101.9
29.7
82.2
20.7
71.7
9.4
45.9
4.9
27.2
1.9
vG_n
117.9
61.0
99.0
35.7
96.8
23.2
108.0
10.1
87.4
5.2
36.7
2.0
max
min
max
min
max
min
max
min
max
min
max
min
1/α
202.1
192.2
106.5
101.8
73.4
70.4
28.9
28.0
13.3
13.0
6.0
5.8
Kh_Kv
215.6
183.4
115.8
96.1
80.8
66.0
35.0
25.7
15.5
11.7
7.1
5.2
Ks
216.4
186.8
116.3
98.1
81.2
67.6
35.6
26.4
15.6
12.1
7.2
5.4
por
240.4
163.7
127.1
86.6
87.9
59.8
35.3
23.7
16.1
11.0
7.2
7.0
Slr
238.1
150.6
124.2
81.4
85.1
57.0
32.9
23.4
14.9
11.2
5.3
5.2
vG_n
344.2
181.6
177.4
95.8
120.5
66.1
45.3
26.1
20.0
12.1
8.4
5.5
max
min
max
min
max
min
max
min
max
min
max
min
1/α
192.2
190.3
102.1
101.1
70.7
69.9
28.0
27.9
13.0
12.9
-
Kh_Kv
205.5
192.1
110.6
101.9
77.2
70.4
31.4
27.9
14.7
14.7
-
Ks
203.7
182.2
108.4
96.4
75.2
66.4
30.1
26.1
13.2
12.0
-
por
237.6
161.5
125.8
85.9
86.9
59.4
34.5
23.5
-
Slr
232.2
192.1
121.3
101.9
83.8
70.4
32.4
23.9
-
vG_n
340.0
184.9
175.1
98.2
118.9
67.8
35.1
26.8
16.2
12.4
-
mm/day
5
10
15
SW/S
42
100
250
mm/day
5
10
15
NE/H
42
100
250
mm/day
5
10
15
NE/S
42
100
250
12
Discussion
The computations presented in this report are average numbers. It is important to have in
mind that average numbers are crude simplifications of nature. Average residence times are
derived because each unit is represented as a homogeneous body. Nature is heterogeneous. At
the Gardermoen aquifer this heterogeneity imply that some of the water is transported faster
from the surface to the groundwater than indicated in the presented computations, while
another fraction is transported much more slowly. We don’t know how significant these ‘fast’
and ‘slow’ deviations are from average transport velocities.
The problem of heterogeneity leads to the question of preferential flow in the unsaturated
zone. Some observations indicate that preferential flow is an important flow mechanism in the
topset units at Gardermoen. We have a hypothesis that the silty layer in the foreset unit plays
a role for fast transport of water, but we have no clear direct observations that quantify this
effect. If the silty layer acts as a barrier for water, the flow velocities in the foresets will be
determined by saturated hydraulic conductivity in the sand above the silt. As seen from the
grain size distribution data, these conductivities may be higher than 10-4 m/s, or about 10
m/day. With a gradient in the potential field of 5% and an effective porosity of 25%, this
gives a transport velocity about 2 m/d. Depending on the tortuosity, a velocity in the order of
2 m/d leads to residence times consistent to what is given in tab 4.
Søvik and Alfnes et al. (2001) have performed a carefully monitored tracer test at the
Moreppen research site close to the Airport area. They used two conservative tracers,
broimide and tritiated water which behave very similar to pure water in the sediment.
Background infiltration rates were 42 mm/day during the experiment. A simulation based on
inverse modelled parameters is shown in Appendix D. A simple analytical advection
dispersions model was adapted to the breakthrough curve monitored at 3.3 m (fig. 6). A
dispersivity of 3.6 cm map the observed data was very good. These results cannot be
considered as validation of the computations in this report, but it is interesting to note that
independently observations are consistent to the average estimated resdence times in tab. 4.
Accepting this modelling approach, efforts should be made to understand transport processes
during snow melt. This knowledge can in a second step be combined into spatial risk maps by
recently developed fuzzy-logic methodology (Wong et al., 2001).
1
Moreppen tracer test,
Søvik & Alfnes et al. (2001)
0.75
F(x)
Figure 6.
Measured
relative
consentrati
on of
bromide
compared
to anlytical
advectiondispersion
modell.
Data in
courtesy to
Søvik and
Alfnes.
0.5
0.25
dispersion 3.6 cm
obs. depth 3.30m
0
5.00
10.00
15.00
20.00
25.00
30.00
35.00
time <days>
13
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14