SUPPLEMENTARY INFORMATION
Review of heterogeneity modelling approaches and additional tables/figures
There is a large body of research on estimating effective hydraulic parameters for
heterogeneous aquifer systems (e.g., Renard and de Marsily 1997; Sanchez-Vila et al. 2006).
These approaches range from averaging point data using an upscaling formula to interpreting
multiple drawdown curves from pumping tests through type curves (Neuman et al. 2007) or
inverse modeling to estimate effective parameters and to obtain uncertainty estimates. While
effective parameter estimates may be applicable for larger scale problems, or aquifer systems
with a relatively low variance, using effective parameters for highly heterogeneous systems to
predict drawdown responses or transport over short distances can pose a challenge. As such,
methods for mapping the heterogeneous distribution of hydraulic parameters are commonly
employed.
One of the most common approaches for interpolating small-scale data is to use
geostatistics (de Marsily et al. 2005). However, traditional geostatistics such as kriging tend to
provide a smooth image of the spatial heterogeneity and may not represent the subsurface
heterogeneity accurately. Although a variety of stochastic simulation techniques (e.g., Deutsch
and Journel 1998) exist that can overcome this issue of smoothing, many of them do not preserve
geological features such as its morphology and facies assemblages. This is due to the fact that
traditional geostatistical methods are based on variograms computed using two-point statistics.
To overcome this shortcoming, multiple point geostatistics (e.g., Guardiano and Srivastava
1993; Caers 2001; Strebelle 2002) has been developed through the use of more complex point
configurations, whose statistics are retrieved from training images that represent the geological
facies distributions obtained from outcrop mappings and/or geophysical imaging.
Alternative approaches to representing abrupt changes in parameters values from one layer
to the next or resolving facies is based on categorical interpolation methods such as indicator
kriging (e.g., Journel 1983; Journel and Isaaks 1984; Johnson and Driess 1989; Journel and
Alabert 1990; Journel and Gomez-Hernandez 1993) and Transition Probability/Markov Chain
geostatistical methods (Carle 1999; Carle and Fogg 1997; Weissmann et al. 1999). These
approaches interpolate categories, as opposed to discrete values, making it possible to reproduce
abrupt material changes and juxtapositional tendencies of different hydrofacies. For cases where
high resolution conditioning data are available, realistic hydrofacies models can be constructed.
Another approach is to construct geological models based on stratigraphic, or
hydrostratigraphic units (e.g., Martin and Frind 1998; Jones et al. 2008). These models are often
based on the interpretation of soil cores collected during the installation of wells. While soil
cores can provide information on material types along a given borehole, their collection and
analysis is expensive and, depending on the material, sample recovery can be poor. This can pose
a challenge for mapping the lateral extent of layers or their connectivity at a site. Due to the lack
of availability of lateral information, information on stratigraphy are often interpolated manually,
using interpolation algorithms or through genesis models that consider geological processes to
create sedimentary units (Koltermann and Gorelick, 1996; Teles et al. 2004; de Vries et al. 2009;
Ronayne et al. 2010). Once constructed, individual layers within these models can either be
assigned hydraulic parameters values deterministically or they can be estimated through
calibration of a groundwater model.
Over the last several decades, significant progress has also been made in the development
of geostatistical and stochastic inverse methods (e.g., Kitanidis and Vomvoris 1983; Hoeksema
and Kitanidis 1984, 1989; Rubin and Dagan 1987, 1992; Gutjahr and Wilson 1989; Harvey and
Gorelick 1995; Kitanidis 1995; LaVenue et al. 1995; RamaRao et al. 1995; Yeh et al. 1995,
1996; Gómez-Hernández et al. 1997; Vesselinov et al. 2001; Hernandez et al., 2003, 2006;
Alcolea et al., 2006, 2008; Riva et al. 2009) to obtain maps of K heterogeneity. Zimmerman et al.
(1998) compared seven geostatistically-based inverse approaches to estimate transmissivities for
modeling advective transport by groundwater flow using synthetic data. One important finding
from this study was that the proper selection of the variogram of the log10 transmissivity field
was found to have a significant impact on the accuracy and precision of the transport predictions.
More recently, Hendricks Franssen et al. (2009) compared more modern methods for
geostatistical inverse modeling, but again, the study was based on synthetic data and only one
groundwater flow and transport scenario was considered.
Additional references not provided in the main text
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Table S1: Geometric mean, variance, and correlation lengths of ln K for each approach.
Ln K (m/s)
Approach
Kx, Ky, Kz
(m/s)
1. Kriging
2. Effective parameter model
Case 1 (PW1-3)
Case 2 (PW3-3)
Case 3 (PW4-3)
Case 4 (PW5-3)
1.4 × 10-5
7.3 × 10-5
2.0 × 10-7
4.0 × 10-6
4.8 × 10-6
3.0 × 10-8
2.9 × 10-5
3.0 × 10-5
1.0 × 10-6
4.2 × 10-6
9.6 × 10-6
2.0 × 10-7
KG

2
ln K
Sill
x
y
z
Model
4.0 × 10-8
5.5
4.3 (8z)
19.4
19.4
7.2
Exponential
(Gaussianz)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3. Transition Probability/Markov
Chain model
Case 1 (PW1-3)
1.3 × 10-6
6.5
6.5
1.4
0.9
0.5
Case 2 (PW3-3)
5.6 × 10-8
25
25
2.3
1.85
0.5
Case 3 (PW4-3)
6.5 × 10-7
15.2
15.3
1.4
1.4
0.5
Case 4 (PW5-3)
3.5 × 10-7
13.8
13.6
1.4
1.4
0.5
4. Geological model
Case 1 (PW1-3)
1.6 × 10-7
3.7
3.8
11.7
11.7
2.3
Case 2 (PW3-3)
9.0 × 10-8
0.2
0.2
8.1
7.2
1.4
Case 3 (PW4-3)
2.3 × 10-7
5.5
5.2
13.5
12.2
3.2
Case 4 (PW5-3)
1.6 × 10-7
4.1
4.0
21.1
18.5
4.1
5. Stochastic inverse model with
conditioning
Case 1 (PW1-3)
1.1 × 10-6
3.7
3.5
15.3
14.0
4.1
Case 2 (PW3-3)
9.2 × 10-7
3.3
3.5
14.9
14.9
4.1
Case 3 (PW4-3)
1.4 × 10-6
4.1
4.0
13.5
11.7
4.1
Case 4 (PW5-3)
9.8 × 10-7
4.0
4.0
8.6
8.6
3.2
6. Transient hydraulic
7.0 × 10-6
4.3
4.7
5.4
5.4
1.8
tomography (unconditioned;
(PW1-3, PW3-3, PW4-3, PW5-3)
7. Transient hydraulic
1.3 × 10-6
4.8
5.3
9.5
9.5
2.3
tomography (conditioned; PW13, PW3-3, PW4-3, PW5-3)
* = Calculated from raw data; KG for the EPM-calibrated case is the geometric mean of the K in the principal
directions; - = data not available, z = vertical orientation
Exponential
Exponential
Exponential
Exponential
Exponential
Exponential
Exponential
Exponential
Exponential
Exponential
Exponential
Exponential
Exponential
Exponential
Table S2: Geometric mean, variance, and correlation lengths of ln Ss for each approach.
Ln Ss (m-1)
Approach
-1
Ss (m )
SsG
 ln2 S
Sill
x
y
z
Model
-
-
-
-
-
0.3
0.3
0.1
0.1
1.8
1.4
1.4
1.4
1.4
1.4
1.4
1.4
0.9
0.5
0.5
0.5
Exponential
Exponential
Exponential
Exponential
1.0
0.2
4.5
0.6
6.3
5.9
13.1
2.3
6.3
5.9
12.2
1.8
0.9
1.8
5.0
0.5
Exponential
Exponential
Exponential
Exponential
0.7
0.5
0.7
0.9
0.7
10.4
11.7
10.8
9.5
9.9
10.4
11.7
10.8
8.1
9.9
5.0
4.1
8.1
3.2
5.9
Exponential
Exponential
Exponential
Exponential
Gaussian
1.3
8.6
8.6
3.6
Exponential
s
2. Effective parameter model
Case 1 (PW1-3)
1.0 × 10-7
Case 2 (PW 3-3)
6.8 × 10-4
Case 3 (PW4-3)
1.9 × 10-6
Case 4 (PW5-3)
1.4 × 10-7
3. Transition Probability/Markov
Chain model
Case 1 (PW1-3)
1.3 × 10-7
0.2
Case 2 (PW 3-3)
6.5 × 10-8
0.3
Case 3 (PW4-3)
1.3 × 10-6
0.1
Case 4 (PW5-3)
1.3 × 10-6
0.1
4. Geological model
Case 1 (PW1-3)
1.4 × 10-4
1.0
Case 2 (PW 3-3)
7.8 × 10-5
0.2
Case 3 (PW4-3)
4.3 × 10-5
4.6
Case 4 (PW5-3)
1.5 × 10-4
0.7
5. Stochastic inverse model with
conditioning
Case 1 (PW1-3)
8.3 × 10-5
0.5
Case 2 (PW3-3)
7.2 × 10-5
0.4
Case 3 (PW4-3)
1.1 × 10-4
0.6
Case 4 (PW5-3)
8.7 × 10-5
0.6
6. Transient hydraulic
8.9 × 10-5
0.7
tomography (unconditioned;
(1.3z)
PW1-3, PW3-3, PW4-3, PW5-3)
7. Transient hydraulic
1.1 × 10-4
1.1
tomography (conditioned; PW13, PW3-3, PW4-3, PW5-3)
* = Calculated from raw data; - = data not available, z = vertical orientation,
Table S3: Statistics of the linear model fit and coefficient of determination (R2) from scatterplots
of simulated versus observed drawdowns during model calibration.
Approach
2. Effective parameter model
3. Transition
Probability/Markov Chain
model
4. Geological model
5. Stochastic inverse model
with conditioning
6. Transient hydraulic
tomography (unconditioned)
7. Transient hydraulic
tomography (conditioned)
Slope
Intercept
R2
Slope
Intercept
R2
Slope
Intercept
R2
Slope
Intercept
R2
Slope
Intercept
R2
Slope
Intercept
R2
PW1-3
0.64
0.08
0.62
0.15
0.19
0.16
0.43
0.03
0.38
0.18
0.02
0.39
0.96
-0.01
0.89
0.29
-0.01
0.57
PW3-3
0.06
0.06
0.05
0.23
0.05
0.26
0.04
0.00
0.36
0.58
0.02
0.66
0.87
0.01
0.86
0.82
0.01
0.94
PW4-3
0.60
0.06
0.57
0.74
0.50
0.14
1.54
0.00
0.34
0.71
0.03
0.79
0.83
0.04
0.95
0.76
0.02
0.85
PW5-3
0.41
0.06
0.39
0.08
0.04
0.25
0.19
0.00
0.31
0.58
0.01
0.90
0.58
0.01
0.93
0.56
0.00
0.88
Average
0.43
0.07
0.41
0.30
0.20
0.20
0.55
0.01
0.35
0.51
0.02
0.69
0.81
0.01
0.91
0.61
0.01
0.81
Table S4: Statistics of the linear model fit and coefficient of determination (R2) from scatterplots
of simulated versus observed drawdowns during model validation.
Slope
Max
7.58
Approach
Min
Mean
1. Kriging
0.08
3.15
2. Effective parameter model
Case 1 (PW1-3)
0.20
1.19
0.55
Case 2 (PW3-3)
-0.05
0.32
0.10
Case 3 (PW4-3)
0.09
0.55
0.25
Case 4 (PW5-3)
0.36
2.12
0.88
3. Transition Probability/Markov Chain model
Case 1 (PW1-3)
0.07
0.38
0.22
Case 2 (PW3-3)
0.02
1.29
0.38
Case 3 (PW4-3)
0.03
2.77
0.37
Case 4 (PW5-3)
0.03
0.47
0.18
4. Geological model
Case 1 (PW1-3)
0.27
1.06
0.57
Case 2 (PW3-3)
0.36
4.02
1.30
Case 3 (PW4-3)
0.27
2.90
1.11
Case 4 (PW5-3)
0.04
31.69
10.69
5. Stochastic inverse model with conditioning
Case 1 (PW1-3)
0.11
1.28
0.46
Case 2 (PW3-3)
Case 3 (PW4-3)
Case 4 (PW5-3)
6. Transient
hydraulic
tomography
(unconditioned)
7. Transient
hydraulic
tomography
(conditioned)
Min
0.03
R2
Max
0.25
Mean
0.14
0.04
0.28
0.02
0.07
0.09
0.00
0.19
0.14
0.57
0.04
0.63
0.67
0.29
0.02
0.39
0.35
0.40
0.55
12.13
0.09
0.11
0.18
1.38
0.04
0.05
0.01
0.01
0.00
0.24
0.29
0.18
0.48
0.17
0.14
0.09
0.26
-0.01
0.09
0.02
-2.64
0.09
1.00
0.14
0.35
0.03
0.32
0.08
-0.29
0.04
0.02
0.08
0.00
0.70
0.13
0.37
0.73
0.43
0.08
0.23
0.35
Min
0.02
Intercept
Max
0.61
Mean
0.13
0.01
0.04
0.01
0.01
0.08
0.98
0.05
0.13
0.02
0.01
0.11
0.00
0.17
0.10
0.11
1.74
1.08
1.87
0.65
0.34
0.61
0.02
0.03
0.01
0.02
0.28
0.42
0.09
0.27
0.02
0.12
0.04
0.09
0.09
0.03
0.09
0.02
0.30
0.40
0.48
0.75
0.15
0.14
0.20
0.21
0.05
0.93
0.46
0.00
0.12
0.03
0.00
0.82
0.50
0.16
0.87
0.44
0.01
0.14
0.05
0.01
0.83
0.36
Figure S1: Location of core samples used for permeameter analysis to create the kriged K field
in Alexander et al. (2011) and this study. These data are also utilized to condition some of the
models in this study.
Figure S2: Transition probability matrix for the horizontal direction. The dots are the measured
transition probabilities and the solid line is the data fit by the Markov chain.
Figure S3: Transition probability matrix in the vertical direction. The dots are the measured
transition probabilities and the solid line is the data fit by the Markov chain.
Figure S4: Observed vs. simulated drawdown for each of the 10 TPROGs realizations. The solid
line is a 1:1 line indicating a perfect match. The dashed line is a best fit line, and the parameters
describing this line are on each plot.
Figure S5: K and Ss fields from the stochastic inversion of a pumping test performed at PW3-3
conditioned to permeameter K data (Approach 5, Case 2): a) K-field; b) variance associated with
the estimated K field; Ss field; and d) variance associated with the estimated Ss field. Note that
the square formed by the slices in the main figure corresponds to the outer edges of the field plot.
The inset image for each figure is a cross-section through the middle of the central square. This
corresponds to cross-sections through CMT2 to CMT1 (section oriented N to S), and CMT4 to
CMT3 (section oriented E to W). Black open circle indicates the pumped location.
Figure S6: K and Ss fields from the stochastic inversion of a pumping test performed at PW4-3
conditioned to permeameter K data (Approach 5, Case 3): a) K-field; b) variance associated with
the estimated K field; Ss field; and d) variance associated with the estimated Ss field. Note that
the square formed by the slices in the main figure corresponds to the outer edges of the field plot.
The inset image for each figure is a cross-section through the middle of the central square. This
corresponds to cross-sections through CMT2 to CMT1 (section oriented N to S), and CMT4 to
CMT3 (section oriented E to W). Black open circle indicates the pumped location.
Figure S7: K and Ss fields from the stochastic inversion of a pumping test performed at PW5-3
conditioned to permeameter K data (Approach 5, Case 4): a) K-field; b) variance associated with
the estimated K field; Ss field; and d) variance associated with the estimated Ss field. Note that
the square formed by the slices in the main figure corresponds to the outer edges of the field plot.
The inset image for each figure is a cross-section through the middle of the central square. This
corresponds to cross-sections through CMT2 to CMT1 (section oriented N to S), and CMT4 to
CMT3 (section oriented E to W). Black open circle indicates the pumped location.
2. Effective Parameter Model
3. Transition Probability/Markov Chain model
4. Geological model
5. Stochastic inverse model with conditioning
6. Transient hydraulic tomography
(unconditioned; PW1-3, PW3-3, PW4-3, PW5-3)
7. Transient hydraulic tomography (conditioned;
PW1-3, PW3-3, PW4-3, PW5-3)
Max
60th Percentile
Min
PW1-3
0.04
0.10
0.09
0.12
PW3-3
0.01
0.01
0.01
0.003
PW4-3
0.02
0.37
0.25
0.012
PW5-3
0.06
0.06
0.06
0.01
Average
0.034
0.135
0.102
0.039
Rank
2
6
5
4
0.01
0.001
0.003
0.01
0.008
1
0.11
0.001
0.009
0.02
0.034
3
0.37
0.04
0.001
Figure S8: L2 norms of observed versus simulated drawdowns from the four pumping tests used
for model calibration at the NCRS. The minimum L2 norm is assigned a color of dark green, the
maximum value a color of dark red, and the 60 percentile value a color of yellow.
2. Effective Parameter Model
3. Transition Probability/Markov Chain model
4. Geological model
5. Stochastic inverse model with conditioning
6. Transient hydraulic tomography
(unconditioned; PW1-3, PW3-3, PW4-3, PW5-3)
7. Transient hydraulic tomography (conditioned;
PW1-3, PW3-3, PW4-3, PW5-3)
Max
60th Percentile
Min
PW1-3
0.79
0.40
0.62
0.62
PW3-3
0.23
0.51
0.60
0.81
PW4-3
0.75
0.38
0.58
0.89
PW5-3
0.44
0.50
0.56
0.95
Average
0.55
0.45
0.59
0.82
Rank
5
6
4
3
0.95
0.93
0.98
0.97
0.95
1
0.76
0.97
0.92
0.94
0.90
2
0.98
0.81
0.23
Figure S9: Correlation (R) of observed versus simulated drawdowns from the four pumping tests
used for model calibration at the NCRS. The minimum R is assigned a color of dark red, the
maximum value a color of dark green, and the 60 percentile value a color of yellow.
Figure S10: Scatterplots of observed vs. simulated drawdown for a) PW1-3, b) PW3-3, c) PW43, and d) PW5-3 at observation ports for various times. Simulated drawdown values are
computed with the estimated Keff and Sseff values obtained using the calibrated effective
parameter modeling method (Approach 2). The solid line is the 45 degree line, while the dashed
line is the linear model fit to the data.
Figure S11: Scatterplots of observed vs. simulated drawdown for a) PW1-3, b) PW3-3, c) PW43, and d) PW5-3 at observation ports for various times. Simulated drawdown values are
computed with the heterogeneous K and Ss distributions obtained using the calibrated Transition
Probability/Markov Chain modeling method (Approach 3). The solid line is the 45 degree line,
while the dashed line is the linear model fit to the data.
Figure S12: Scatterplots of observed vs. simulated drawdown for a) PW1-3, b) PW3-3, c) PW43, and d) PW5-3 at observation ports for various times. Simulated drawdown values are
computed with the heterogeneous K and Ss distributions obtained using the calibrated geological
modeling method (Approach 4). The solid line is the 45 degree line, while the dashed line is the
linear model fit to the data.
Figure S13: Scatterplots of observed vs. simulated drawdown for a) PW1-3, b) PW3-3, c) PW43, and d) PW5-3 at observation ports for various times. Simulated drawdown values are
computed with the heterogeneous K and Ss distributions obtained using the stochastic inverse
modeling method (Approach 5) conditioned to permeameter K data. The solid line is the 45
degree line, while the dashed line is the linear model fit to the data.
Figure S14: Scatterplots of observed vs. simulated drawdown for a) PW1-3, b) PW3-3, c) PW43, and d) PW5-3 at observation ports for various times. Simulated drawdown values are
computed with the heterogeneous K and Ss tomograms obtained using the transient hydraulic
tomography method (Approach 6) unconditioned to permeability K data. The solid line is the 45
degree line, while the dashed line is the linear model fit to the data.
Figure S15: Scatterplots of observed vs. simulated drawdown for a) PW1-3, b) PW3-3, c) PW43, and d) PW5-3 at observation ports for various times. Simulated drawdown values are
computed with the heterogeneous K and Ss tomograms obtained using the transient hydraulic
tomography method (Approach 7) conditioned to permeameter K data. The solid line is the 45
degree line, while the dashed line is the linear model fit to the data.
PW1-3
0.13
PW1-4
0.03
PW1-5
0.63
PW3-3
0.10
PW3-4
0.08
PW4-3
18.89
PW5-3
0.56
PW5-4
0.39
PW5-5
1.01
Average
2.42
Rank
6
0.04
0.04
0.10
0.05
0.02
0.02
0.03
0.03
0.007
0.01
0.002
0.017
0.01
0.01
0.02
0.01
0.0007
0.00
0.0005
0.0011
0.21
0.21
0.04
0.51
0.05
0.05
0.07
0.04
0.02
0.02
0.01
0.03
0.02
0.02
0.02
0.03
0.04
0.04
0.03
0.08
0.05
3
3. Transition Probability/Markov Chain model
Case 1 (PW1-3)
Case 2 (PW3-3)
Case 3 (PW4-3)
Case 4 (PW5-3)
0.08
0.11
0.11
0.11
0.03
0.07
0.03
0.02
0.01
0.02
0.002
0.001
0.02
0.01
0.02
0.02
0.0004
0.0014
0.001
0.0006
0.30
0.65
0.06
0.06
0.06
0.05
0.08
0.07
0.01
0.05
0.01
0.01
0.01
0.02
0.02
0.02
0.06
0.11
0.04
0.03
0.06
4
4. Geological model
Case 1 (PW1-3)
Case 2 (PW3-3)
Case 3 (PW4-3)
Case 4 (PW5-3)
0.16
0.08
0.16
0.16
0.11
0.45
0.11
0.11
0.30
3.52
0.31
0.31
0.01
0.54
0.01
0.01
0.0159
0.32
0.0165
0.0165
6.89
189.87
0.07
0.07
0.06
3.85
0.07
0.07
0.08
1.01
0.08
0.08
0.52
4.42
0.44
0.44
0.91
22.67
0.14
0.14
5.96
7
5. Stochastic inverse model with conditioning
Case 1 (PW1-3)
Case 2 (PW3-3)
Case 3 (PW4-3)
Case 4 (PW5-3)
0.08
0.10
0.11
0.08
0.03
0.04
0.03
0.05
0.02
0.04
0.006
0.03
0.01
0.01
0.02
0.01
0.0006
0.0026
0.0004
0.001
0.37
0.95
0.03
0.35
0.06
0.06
0.06
0.02
0.01
0.03
0.01
0.04
0.02
0.03
0.01
0.02
0.07
0.14
0.03
0.07
0.08
5
0.02
0.02
0.001
0.004
0.0004
0.03
0.03
0.04
0.01
0.017
1
0.06
0.04
0.002
0.003
0.0004
0.03
0.02
0.04
0.01
0.025
2
1. Kriging
2. Effective parameter model
Case 1 (PW1-3)
Case 2 (PW3-3)
Case 3 (PW4-3)
Case 4 (PW5-3)
6. Transient hydraulic tomography
(unconditioned; PW1-3, PW 3-3, PW4-3, PW5-3)
7. Transient hydraulic tomography (conditioned;
PW1-3, PW 3-3, PW4-3, PW5-3)
Max
60th Percentile
Min
1.00
0.05
0.0003
Figure S16: L2 norms of observed versus simulated drawdowns from the nine pumping tests
used for model validation at the NCRS. The minimum L2 norm is assigned a color of dark green,
the maximum value a color of dark red, and the 60 percentile value a color of yellow.
PW1-3
0.30
PW1-4
0.17
PW1-5
0.49
PW3-3
0.39
PW3-4
0.39
PW4-3
0.50
PW5-3
0.29
PW5-4
0.31
PW5-5
0.40
Average
0.36
Rank
7
0.79
-0.06
0.76
0.72
0.51
0.08
0.53
0.56
0.62
-0.09
0.62
0.57
0.77
0.15
0.80
0.82
0.40
0.16
0.41
0.37
0.68
0.11
0.72
0.70
0.61
0.17
0.64
0.62
0.33
0.20
0.39
0.41
0.44
0.15
0.45
0.38
0.57
0.10
0.59
0.57
0.46
3
3. Transition Probability/Markov Chain model
Case 1 (PW1-3)
Case 2 (PW3-3)
Case 3 (PW4-3)
Case 4 (PW5-3)
0.46
0.52
0.59
0.53
0.26
0.08
0.63
0.62
0.32
0.43
0.58
0.69
0.41
0.42
0.39
0.49
0.28
0.18
0.30
0.33
0.23
0.54
0.44
0.47
0.36
0.46
0.46
0.52
0.40
0.13
0.44
0.59
0.32
0.17
0.05
0.06
0.34
0.32
0.43
0.48
0.39
5
4. Geological model
Case 1 (PW1-3)
Case 2 (PW3-3)
Case 3 (PW4-3)
Case 4 (PW5-3)
0.54
0.50
0.73
0.53
0.25
0.16
0.42
0.25
0.58
0.21
0.39
0.59
0.55
0.29
0.56
0.52
0.60
0.34
0.48
0.60
0.63
0.30
0.49
0.60
0.48
0.24
0.54
0.46
0.30
0.19
0.48
0.28
0.35
0.18
0.14
0.35
0.47
0.27
0.47
0.46
0.42
4
5. Stochastic inverse model with conditioning
Case 1 (PW1-3)
Case 2 (PW3-3)
Case 3 (PW4-3)
Case 4 (PW5-3)
0.55
0.41
0.38
0.59
0.30
0.23
0.30
0.19
0.46
0.45
0.58
0.50
0.44
0.63
0.49
0.32
0.30
0.18
0.33
0.37
0.40
0.41
0.70
0.51
0.40
0.32
0.42
0.87
0.31
0.31
0.30
0.12
0.30
0.28
0.33
0.19
0.38
0.36
0.42
0.41
0.39
5
0.90
0.56
0.740
0.88
0.44
0.80
0.84
0.02
0.73
0.66
1
0.68
0.20
0.65
0.91
0.31
0.79
0.83
0.08
0.26
0.52
2
1. Kriging
2. Effective parameter model
Case 1 (PW1-3)
Case 2 (PW3-3)
Case 3 (PW4-3)
Case 4 (PW5-3)
6. Transient hydraulic tomography
(unconditioned; PW1-3, PW 3-3, PW4-3, PW5-3)
7. Transient hydraulic tomography (conditioned;
PW1-3, PW 3-3, PW4-3, PW5-3)
Max
60th Percentile
Min
0.91
0.48
-0.09
Figure S17: Correlation (R) of observed versus simulated drawdowns from the nine pumping
tests used for model validation at the NCRS. The minimum R is assigned a color of dark red, the
maximum value a color of dark green, and the 60 percentile value a color of yellow.
Figure S18: Scatterplots of simulated versus observed drawdowns for all 9 pumping tests using
the kriged K field and a homogeneous Ss value (Approach 1). The solid line is a 1:1 line
indicating a perfect match. The dashed line is a best fit line, and the parameters describing this
line are on each plot.
Figure S19: Scatterplots of simulated versus observed drawdowns for all 9 pumping tests using
the effective K and Ss values from the calibration of an effective parameter groundwater model to
the pumping test at PW1-3 (Approach 2, Case 1). The solid line is a 1:1 line indicating a perfect
match. The dashed line is a best fit line, and the parameters describing this line are on each plot.
Figure S20: Scatterplots of simulated versus observed drawdowns for all 9 pumping tests using
the effective K and Ss values from the calibration of an effective parameter groundwater model to
the pumping test at PW3-3 (Approach 2, Case 2). The solid line is a 1:1 line indicating a perfect
match. The dashed line is a best fit line, and the parameters describing this line are on each plot.
Figure S21: Scatterplots of simulated versus observed drawdowns for all 9 pumping tests using
the effective K and Ss values from the calibration of an effective parameter groundwater model to
the pumping test at PW4-3 (Approach 2, Case 3). The solid line is a 1:1 line indicating a perfect
match. The dashed line is a best fit line, and the parameters describing this line are on each plot.
Figure S22: Scatterplots of simulated versus observed drawdowns for all 9 pumping tests using
the effective K and Ss values from the calibration of an effective parameter groundwater model to
the pumping test at PW5-3 (Approach 2, Case 4). The solid line is a 1:1 line indicating a perfect
match. The dashed line is a best fit line, and the parameters describing this line are on each plot.
Figure S23: Scatterplots of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the calibration of a realization generated using the Transition
Probability Markov Chain method to the pumping test at PW1-3 (Approach 3, Case 1). The solid
line is a 1:1 line indicating a perfect match. The dashed line is a best fit line, and the parameters
describing this line are on each plot.
Figure S24: Scatterplots of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the calibration of a realization generated using the Transition
Probability Markov Chain method to the pumping test at PW3-3 (Approach 3, Case 2). The solid
line is a 1:1 line indicating a perfect match. The dashed line is a best fit line, and the parameters
describing this line are on each plot.
Figure S25: Scatterplots of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the calibration of a realization generated using the Transition
Probability Markov Chain method to the pumping test at PW4-3 (Approach 3, Case 3). The solid
line is a 1:1 line indicating a perfect match. The dashed line is a best fit line, and the parameters
describing this line are on each plot.
Figure S26: Scatterplots of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the calibration of a realization generated using the Transition
Probability Markov Chain method to the pumping test at PW5-3 (Approach 3, Case 4). The solid
line is a 1:1 line indicating a perfect match. The dashed line is a best fit line, and the parameters
describing this line are on each plot.
Figure S27: Scatterplot of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the calibration of a geological model to the pumping test at PW13 (Approach 4, Case 1). The solid line is a 1:1 line indicating a perfect match. The dashed line is
a best fit line, and the parameters describing this line are on each plot.
Figure S28: Scatterplot of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the calibration of a geological model to the pumping test at PW33 (Approach 4, Case 2). The solid line is a 1:1 line indicating a perfect match. The dashed line is
a best fit line, and the parameters describing this line are on each plot.
Figure S29: Scatterplot of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the calibration of a geological model to the pumping test at PW43 (Approach 4, Case 3). The solid line is a 1:1 line indicating a perfect match. The dashed line is
a best fit line, and the parameters describing this line are on each plot.
Figure S30: Scatterplot of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the calibration of a geological model to the pumping test at PW53 (Approach 4, Case 4). The solid line is a 1:1 line indicating a perfect match. The dashed line is
a best fit line, and the parameters describing this line are on each plot.
Figure S31: Scatterplot of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the stochastic inverse modeling of a pumping test at PW1-3
(Approach 5, Case 1) conditioned to permeameter K data. The solid line is a 1:1 line indicating a
perfect match. The dashed line is a best fit line, and the parameters describing this line are on
each plot.
Figure S32: Scatterplot of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the stochastic inverse modeling of a pumping test at PW3-3
(Approach 5, Case 2) conditioned to permeameter K data. The solid line is a 1:1 line indicating a
perfect match. The dashed line is a best fit line, and the parameters describing this line are on
each plot.
Figure S33: Scatterplot of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the stochastic inverse modeling of a pumping test at PW4-3
(Approach 5, Case 3) conditioned to permeameter K data. The solid line is a 1:1 line indicating a
perfect match. The dashed line is a best fit line, and the parameters describing this line are on
each plot.
Figure S34: Scatterplot of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss distributions from the stochastic inverse modeling of a pumping test at PW5-3
(Approach 5, Case 4) conditioned to permeameter K data. The solid line is a 1:1 line indicating a
perfect match. The dashed line is a best fit line, and the parameters describing this line are on
each plot.
Figure S35: Scatterplot of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss tomograms obtained through the transient hydraulic tomography analysis of 4
pumping tests (Approach 6). The solid line is a 1:1 line indicating a perfect match. The dashed
line is a best fit line, and the parameters describing this line are on each plot.
Figure S36: Scatterplot of simulated versus observed drawdowns for all 9 pumping tests using
the K and Ss tomograms obtained through the transient hydraulic tomography analysis of 4
pumping tests (Approach 7) conditioned to permeameter K data. The solid line is a 1:1 line
indicating a perfect match. The dashed line is a best fit line, and the parameters describing this
line are on each plot.