NHC Røros, 2002
THINKING SCALE
IN UNSATURATED FLOW
PARAMETER ESTIMATION
Thorgeir Holm,
Nils-Otto Kitterød and
Lars Gottschalk
Dept. of Geophysics,
University of Oslo,
P.O.Box 1022 Blindern,
N-0315 Oslo, Norway
thorgeih@geofysikk.uio.no,
nilsotto@geofysikk.uio.no
Lars.Gottschalk@geofysikk.uio.no
Background
The Oslo Airport Gardermoen
Pollution hazard
Different scales
NHC Røros, 2002
Problem
Forecasts based on unsaturated flow models
indicate safe conditions for the groundwater
In real life pollution breakthrough
to the groundwater do occur
Why?
flow model
discrete
volume averages
finite resolution
real sediment/soil
heterogeneous at
all scales
NHC Røros, 2002
Purpose
Use inverse modelling to estimate
(homogenized) flow parameter
conditioned on different data sets, and
compare calculated breakthrough curve to
”observed” breakthrough curve.
Different data sets?
What is best,
lot of observations with low sensitivity, or
few observations with high sensitivity?
NHC Røros, 2002
Method
Generate realizations (a,b,c)
with high spatial resolution
(0.2 m x 0.05 m)
Based on observed
sedimentological
architecture
p47
Delta topset
Delta foreset
scatter plot of Ks based on d10/d60
1.00E-01
1.00E-02
1.00E-03
1.00E-04
Empirical
Ks <m/s>
And simulation of
ks, 1/α and nvg based on
”hard” physical observations
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
m o.h.
200
210
220
Method
Simulate ”real” (Søvik and Alfnes et al.) tracer experiment
Infiltration time series:
2.5 mm/day from -∞ to day 0
42 mm/day from day 0 to day 16 day (≈ ∞)
NHC Røros, 2002
Flowpattern in synthetic realizations
a
b
NHC Røros, 2002
Flowpattern in synthetic realizations
a
c
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Breakthrough curves
Observed breakthrough curves
based on syntetic data
(Søvik and Alfnes et al, 2001)
from all over the Gardermoen area
a
c
0.80
F(x) for [Br] and [HTO]
b
1.00
-2.95 m (Br)
-3.09 m (Br)
-3.30 m (Br)
0.60
0.40
-2.95 m (HTO)
-3.09 m (HTO)
-3.30 m (HTO)
0.20
0.00
0.00
5.00
10.00 15.00 20.00 25.00 30.00
time <days>
NHC Røros, 2002
Recall database
scatter plot of Ks
6682000
Oslo Airport Gardermoen
foreset sand
1.00E-01
1.00E-02
6680000
1.00E-03
1.00E-04
Empirical
Ks <m/s>
UTM-N
6678000
Glacier
fronts:
6676000
topset
1.00E-05
1.00E-06
1.00E-07
1.00E-08
1.00E-09
6674000
1.00E-10
foreset silt
1.00E-11
6672000
1.00E-12
150
borehole
locations
6670000
612000
614000
160
170
180
190
200
210
220
m o.h.
616000
618000
620000
622000
UTM-E
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Purpose with conditional homogenization
heterogeneous
isotropic
0
-1
How to get
same response
(breakthrough)?
homogeneous
anisotropic
-2
-3
2
4
6
8
10
12
NHC Røros, 2002
The answer is Inverse modelling
find model parameters
that
minimize | cal. – obs. |
homogeneous flow parameters
to estimate:
kp,kt, 1/α, nvg
NHC Røros, 2002
Conditional data sets (synthetic) ”observations”:
1) soil moisture (or saturation)
| θcalc – θobs |
2) pressure
| pcalc – pobs |
3) pressure and soil moisture
| pcalc – pobs | and | θcalc – θobs |
4) the breakthrough curve
(for the future)
| c(t)calc – c(t)obs |
NHC Røros, 2002
number of particles
Results
breakthrough curves (42 mm/d infiltration)
15
10
5
7
8
10
9
time (days)
11
12
heterogeneous isotropic (case a)
homogeneous anisotropic saturation (all)
pressure (all)
pressure and saturation
saturation (no dip2)
pressure (no dip2)
NHC Røros, 2002
Conclusion
structure is crucial
internal arrangment of heterogeneity is important
(cf. flowpaths in realization a,b and c)
difficult to compare breakthrough curves from
a,b,c with homogenous model
Future work:
evaluate importance of boundary conditions
are effective parameters possible to derive or
is equvalent parameters the only realistic result?
is reliable forecasts (of NOE) possible without
conditioning on observations (of noe)?
NHC Røros, 2002