Fracture Control of Ground Water Flow and
Water Chemistry in a Rock Aquitard
by Timothy T. Eaton 1 , Mary P. Anderson 2 , and Kenneth R. Bradbury 3
There are few studies on the hydrogeology of sedimentary rock aquitards although they are important controls
in regional ground water flow systems. We formulate and test a three-dimensional (3D) conceptual model of
ground water flow and hydrochemistry in a fractured sedimentary rock aquitard to show that flow dynamics
within the aquitard are more complex than previously believed. Similar conceptual models, based on regional observations
and recently emerging principles of mechanical stratigraphy in heterogeneous sedimentary rocks, have
previously been applied only to aquifers, but we show that they are potentially applicable to aquitards. The major
elements of this conceptual model, which is based on detailed information from two sites in the Maquoketa Formation
in southeastern Wisconsin, include orders of magnitude contrast between hydraulic diffusivity (K/Ss) of
fractured zones and relatively intact aquitard rock matrix, laterally extensive bedding-plane fracture zones extending
over distances of over 10 km, very low vertical hydraulic conductivity of thick shale-rich intervals of the aquitard,
and a vertical hydraulic head profile controlled by a lateral boundary at the aquitard subcrop, where
numerous surface water bodies dominate the shallow aquifer system. Results from a 3D numerical flow model
based on this conceptual model are consistent with field observations, which did not fit the typical conceptual
model of strictly vertical flow through an aquitard. The 3D flow through an aquitard has implications for predicting
ground water flow and for planning and protecting water supplies.
Aquitards are lithologically diverse, and their hydrogeology
is poorly understood because characterization
methods are more challenging than for aquifers (van der
Kamp 2001; Cherry et al. 2006). The relative lack of
studies on aquitards, particularly indurated sedimentary
aquitards, accounts for a common misconception that
aquitards are hydrogeologically homogeneous and flow is
predominantly vertical. Classic aquifer system testing
1 C orresp onding author: Q ueens C ol l eg e— The C ity U niv ersity
of N ew Y ork , S c hool of Earth and Env ironmental S c ienc es, 6 5 - 30
Kissena Boul ev ard, F l ushing , N Y 1136 7 ; ( 7 18 ) 9 9 7 - 3327 ; f ax ( 7 18 )
9 9 7 - 329 9 ; timothy.eaton@ q c .c uny.edu
2 U niv ersity of W isc onsin— Madison, D ep artment of G eol og y
and G eop hysic s, 1215 W . D ayton S t., Madison, W I 5 37 0 6 .
3 W isc onsin G eol og ic al and N atural H istory S urv ey, 38 17
Mineral Point Road, Madison, W I 5 37 0 5 .
Rec eiv ed J ul y 20 0 6 , ac c ep ted Marc h 20 0 7 .
C op yrig ht ª 20 0 7 The Author( s)
J ournal c omp il ation ª 20 0 7 N ational G round W ater Assoc iation.
doi: 10 .1111/ j .17 4 5 - 6 5 8 4 .20 0 7 .0 0 335 .x
methods rely on the vertical propagation of drawdown
through overlying aquitards for estimating aquitard properties
(Neuman and Witherspoon 1972). However, there is
increasing evidence that flow through many aquitards is
much more complex (Remenda 2001; Cherry et al. 2006)
than can be accounted for by simple one-dimensional
(1D) vertical flow models. Indurated rock aquitards, in
particular, appear to be very different from the more commonly
studied shallow glaciolacustrine aquitards because
of the multiple sedimentary layers of differing properties
found in stratified rock sequences.
Detailed studies of rock aquitards are rare. In contrast,
unlithified surficial aquitards, which are generally
more homogeneous than interbedded indurated aquitards,
have been studied more extensively (Cherry et al. 2006).
Surficial weathering in unlithified aquitards causes the
formation of vertical fractures that can become important
preferential flowpaths for contaminant transport and
result in increased bulk hydraulic conductivity (Bradbury
et al. 1985; Keller et al. 1989; Jorgensen and Fredericia
1992; Simpkins and Bradbury 1992; McKay et al. 1993a,
Vol. 45, No. 5—GROUND WATER—September–October 2007 (pages 601–615) 601
1993b; McKay and Fredericia 1995; Jorgensen et al.
2004 ). However, this study and previous work (Cherry
et al. 2006) indicate that such a conceptual model does
not always apply to rock aquitards.
Recent work (described subsequently) has emphasized
that ground water flow through sedimentary rock is
controlled by fractures that are themselves constrained by
mechanical stratigraphic properties of sedimentary layers.
O bservational evidence for preferential flow along subhorizontal
bedding-plane fractures has been used to construct
conceptual and numerical models for wellhead
protection (Muldoon et al. 2001; Rayne et al. 2001), as
well as understanding contaminant transport and ground
water flow (P effer 1991; Michalski and Britton 1997;
Maguire 1998) and the origin of springflow (Swanson
et al. 2006). E xtensive study of the P aleozoic sedimentary
sequence in Minnesota has caused a complete revision
of the regional hydrostratigraphy (Runkel et al. 2003;
Tipping et al. 2006), resulting in delineation of new hydrostratigraphic
units based on fracturing. These studies
show that in relatively undeformed sedimentary rock,
fracturing associated with bedding planes or changes in
lithology can be correlated laterally over scales of kilometers
to tens of kilometers.
Furthermore, the following studies explain why, in
contrast to the conceptual model of vertical fractures in
unlithified materials, the lithologic heterogeneity in rock
aquifers and aquitards favors the formation of beddingplane
fractures. Fracture propagation is inhibited across
the interfaces created by sedimentary layers with contrasting
lithologies and mechanical stiffness (Helgeson
and Aydin 1991; Rijken and Cooke 2001; U nderwood
et al. 2003; Cooke et al. 2006; G raham Wall 2006). V ertical
fractures in indurated sedimentary rock tend to be
isolated within individual layers and their frequency
dependent on layer thicknesses (P ollard and Aydin 1988;
Narr and Suppe 1991; G ross et al. 1995; Renshaw 1997).
Therefore, in thick rock aquitards that contain numerous
shale and siltstone beds, few if any vertical fractures will
propagate across all the layer interfaces. In the absence
of continuous vertical flowpaths, these aquitards can be
very effective confining units (E aton and Bradbury
In addition to our study of the Maquoketa aquitard in
Wisconsin (E aton 2002), we are aware of only one other
major rock aquitard in the U nited States, the P ierre Shale,
that has been characterized extensively (Neuzil 1980, 1986,
1993; Bredehoeft et al. 1983), although hydrogeologic
properties of low-conductivity fractured chalk have been
characterized for geotechnical purposes (Dutton et al.
1994 ; Wang and Myer 1994 ). In Switzerland, the O palinus
Clay, a fractured, diffusion-dominated shale, is being
studied for possible nuclear waste disposal sites (Mazurek
et al. 1998; G autschi 2001; Croise et al. 2004 ; Wersin et al.
2004 ). P ore water chemistry and transport processes also
have been studied in the Tournemire tunnel argillites in
France (Boisson et al. 2001; P atriarche et al. 2004 ).
New conceptual models are needed to explain complex
flow in stratified rock aquitards, particularly in
regionally important aquitards such as the Maquoketa
Formation. In this paper, we use detailed data collected
at two field sites 10 km apart (Figure 1) to describe a
conceptual model for the O rdovician-age Maquoketa
shale aquitard in southeastern Wisconsin, emphasizing
the importance of bedding-plane fractures in lithologically
complex rock aquitards. The work presented here extends
and amplifies the findings of E aton and Bradbury (2003),
who showed that the vertical distribution of hydraulic
head in the Maquoketa aquitard is currently not at equilibrium
in response to drawdown in the underlying aquifer
system. An early, widely cited study of the Maquoketa
aquitard (Walton 1960) used a steady-state analysis of
flow between the overlying and underlying aquifer systems
to estimate rates of leakage through the aquitard.
Similarly, the selection of parameters assigned to the
Maquoketa aquitard for recent regional simulation studies
relies on an equilibrium assumption (Y oung 1976, 1992;
Feinstein et al. 2004 ). Although Hart et al. (2006)
recently used one of these regional models to investigate
cross-connecting well and fracture hypotheses about
Figure 1. Generalized bedrock geology near field sites (inset) at DOT and Minooka Park, showing proximity to western
Maquoketa subcrop (shown in black shading). The Paleozoic bedrock sequence dips gently eastward into the Michigan
Basin. Diamond shape around DOT site is the boundary of the flow model in Figure 8.
602 T.T. Eaton et al. GROUND WATER 45, n o. 5: 601–615
egional properties of the Maquoketa aquitard, our work
suggests that significant deviations from steady-state conditions
occur within the aquitard at the tens of kilometers
scale of our study.
In order to understand hydraulic properties and flow
through regional aquitards, data are needed at multiple
scales. L arge-scale simulations can be used to estimate
regional hydraulic properties (Bredehoeft et al. 1983;
Hart et al. 2006) but may not have the resolution to incorporate
features that control flow. Data from field studies
can also provide insight into hydrologic conditions such
as whether hydraulic heads have equilibrated to pumping
stresses (Husain et al. 1998; E aton and Bradbury 2003). If
these hydrologic conditions are different from previous
assumptions, alternative conceptual models are needed
and can lead to new interpretations of aquitard properties.
The more local scale of field observations avoids the
uncertainty that anthropogenic factors such as multiaquifer
wells can introduce in parameterization of large
We evaluate a three-dimensional (3D) conceptual
model (Figure 2) developed for flow through the Maquoketa
aquitard to show how detailed hydrogeologic and hydrogeochemical
data point to a complex internal flow
system at the site scale. While simple 1D vertical flow
models do not explain these data, the conceptual model
we propose provides a basis for numerical modeling and
understanding of vertical hydraulic head distribution
within the aquitard. As more field data are collected on
other sedimentary rock aquitards, this model can be further
tested and refined in other similar settings.
H ydrog eolog ic S etting
The Cambrian-O rdovician Aquifer underlying the
Maquoketa Formation is heavily pumped for municipal
supply in the rapidly growing inland suburban area near
Milwaukee, Wisconsin (Figure 1). As a result, hydraulic
head in the aquifer system has been drawn down considerably
below land surface since the early 1900s (Fetter
1981), forming a regional cone of depression extending
south into Illinois (Feinstein et al. 2004 ). O ver the past
50 years, the rate of regional head decline averages more
Figure 2. C onceptual geological model of conditions within
10 km of the subcrop of a rock aquitard based on the
Maquoketa Formation. I n this hydrostratigraphic setting,
subcrops of different units at the bedrock surface are ov erlain
by a shallow unlithified aquifer. The aquitard is shaded,
with laterally extensiv e bedding- plane fracture zones shown
by lines. V ertical scale is greatly exaggerated.
than 2 m/year, and total head loss exceeded 130 m over
the last century. The Maquoketa Formation constituting
the aquitard is 50 to 60 m thick and dips gently eastward
into the Michigan Basin. It overlies the 600-m-thick sandstone
and dolomite aquifer system and isolates it from
a shallower Silurian dolostone aquifer and unlithified
P leistocene sediments near the land surface. The Maquoketa
Formation in southeastern Wisconsin, described
from rock core (E aton 2002), consists of numerous lithofacies
ranging from a fissile greenish-gray dolomitic
shale at the base to multiple interbeds of mudstone and
more resistant crystalline dolomitic packstone and grainstone
in the upper part of the formation (Figure 3). As
with all the bedrock formations, it is traversed by
a regional fault zone, the Waukesha Fault (Figure 1),
whose hydraulic properties are unknown.
S tudy Ap p roach and M ethods
The conceptual model proposed in this paper is
based on a large and detailed data set from two field sites
10 km apart (Figure 1) within the regional cone of
depression produced from municipal pumping in the
underlying aquifer. It consists of, to our knowledge, the
first hydraulic head profiles with depth within the aquitard,
data from single- and multiple-well hydraulic testing
and laboratory core tests, as well as hydrogeochemical
data from water samples. More details of the two field
sites and the methods of downhole geophysical logging
and single-well hydraulic testing of multiple boreholes
are given by E aton (2002) and E aton and Bradbury
From the analysis of these data, we develop the
hypothesis of a 3D conceptual model for the hydrogeology
of rock aquitards and describe the construction of
a site-scale numerical flow model to test this hypothesis.
Finally, we compare simulated hydraulic heads to measured
hydraulic heads with depth in and below the
Maquoketa aquitard and conclude with some implications
for regional hydrogeology.
H ydrog eolog ic D ata Collection
In this study, due to the depth (60 m) of the Maquoketa
aquitard below land surface, hydrogeologic characterization
was limited to borehole studies. At both study
sites (Figure 1), rock-core (Figure 3) and downhole geophysical
logs (Figure 4 ) were collected from boreholes
through the aquitard. L aboratory hydraulic testing of
Maquoketa rock core (E aton et al. 2000) is described
in detail by Hart et al. (2006). P neumatic packers and
multilevel monitoring systems to measure hydraulic head
with depth were then installed in two boreholes, one at
each site, which were also used for ground water sampling.
Horizontal hydraulic conductivity (Figure 4 ) was
estimated from single-well hydraulic testing at both locations.
The multilevel monitoring systems were constructed,
to the extent possible, to isolate fracture zones in
different vertical intervals. After initial stabilization over
several months, hydraulic head measurements in these
and another type of multilevel monitoring system (E aton
T.T. Eaton et al. GROUND WATER 45, n o. 5: 601–615 603
Figure 3 . C orrelation of six lithofacies recognized in the Maquoketa Formation based on rock- core analysis from (A )
Minooka Park and (B) DOT field sites. The S innipee Group dolostone ov erlies the most productiv e sandstone formations in the
C ambrian- Ordov ician A quifer system.
Figure 4 . S ingle- well hydrogeological data at (A ) Minooka Park and (B) DOT field sites (note the formation elev ation differences):
(at left) representativ e downhole geophysical logs from selected wells with dashed lines showing maj or bedding- plane
fracture zones and triangles indicating no measured flow; (at right) results from slug testing and straddle- packer testing in the
same wells. Bar thickness indicates interv al length tested, gray bars indicate the use of a submersible pump, and triangles indicate
v alues below testing limit (E aton and Bradbury 20 0 3 ).
604 T.T. Eaton et al. GROUND WATER 45, n o. 5: 601–615
2002; E aton and Bradbury 2003) responded to various
pumping tests, then equilibrated to similar long-term values
within the aquitard (Figure 5). Head values in the bottommost
monitoring intervals below the Maquoketa Formation
continued to exhibit a slow decline over time, and the
unusual vertical profile has remained essentially the same
up to the present (K.R. Bradbury, personal communication).
At the Department of Transportation (DO T) field site
(Figure 1), two additional wells of differing construction
(bentonite sealed with transducers embedded in sandpacks—
see E aton and Bradbury [ 2003] for details) were installed
to verify the observed hydraulic head profile with depth,
and a third deep well open to the Maquoketa Formation
was then constructed for hydrogeologic testing. The addition
of this well did not change the stable hydraulic head
distribution with depth, attributed to the small crosssectional
well area (0.018 m 2 ) and the anastomosing
nature of fracture pathways (Tsang and Neretnieks 1998).
A downhole video log indicated that either single large
fractures up to 0.001-m aperture or clusters of hairline
fractures correspond to each of the three zones identified
at the two sites (E aton 2002). Subsequent digital borehole
imaging also showed multiple bedding-parallel fractures.
Bedding fracture zone transmissivity and storage coefficient
were estimated from two pumping tests in this well
that caused rapid head changes in fractured intervals of
multilevel observation wells at distances of 15 to 25 m,
indicating interconnected transmissive flowpaths. Head
drawdown and recovery were analyzed using standard
time– drawdown methods (Cooper and Jacob 194 6; Jacob
1963), as described in E aton (2002). A constant aperture
value, b, of 0.001 m was used to obtain estimates of interwell
fracture hydraulic conductivity from the pumping
test results (Figure 6). More sophisticated methods of analyzing
effective fracture apertures (Halihan et al. 1999)
indicate that the selected value is a conservative estimate
of fracture aperture based on the range of assumed hydraulic
V alues from field and laboratory hydrogeologic testing
(Figure 6) were used to assign parameters for the
numerical model. With the enormous contrast in hydraulic
properties between fractures and rock matrix in the
shale, it is assumed that field transmissivity and storage
coefficient values estimated from interwell testing are
primarily representative of the fracture network rather
than the rock matrix. Complex flowpaths (Tsang and
Neretnieks 1998) are likely through such fracture systems,
similar to those that have been studied in detail in
carbonate outcrop settings elsewhere (Muldoon et al.
2001; Cooke et al. 2006; G raham Wall 2006; Tipping
et al. 2006).
H ydrog eochemical D ata Collection
Anticipating primarily slow vertical fluxes and very
low hydraulic conductivity within the Maquoketa aquitard,
we designed monitoring wells and sampling for
analysis of vertical hydrogeochemical trends. However,
the significant heterogeneity observed during field hydrogeologic
testing complicates interpretation of hydrogeochemical
Figure 5. H ydraulic head in multilev el wells at (A ) Minooka Park site and (B) DOT site. Outermost plots in both (A ) and (B)
prov ide detail of the same data at an expanded horizontal scale. Open circles represent data from longer open interv als in
W aterloo TM systems, while solid circles represent data from embedded pressure transducers in different sealed wells. S mall
arrows at the locations of packers (gray) or bentonite seals (black) show flow directions interpreted from head measurements.
T.T. Eaton et al. GROUND WATER 45, n o. 5: 601–615 605
Figure 6 . R ange in hydraulic conductiv ity (K) estimated
from rock- core testing, slug and straddle- packer testing, and
interwell pumping. A fracture aperture b ¼ 0 .0 0 1 m was
used to calculate K from transmissiv ity for interwell pumping.
N ote that many single- well field results were less than
10 25 m/ d, below the assumed equipment testing limit.
Samples were collected from each of the intervals in
the multilevel packer systems within the Maquoketa aquitard
at the two field sites (Figure 7). Due to low sampling
flow rates and depths of the sampled intervals, only limited
purging was possible. Measurements of electrical
conductivity, pH, dissolved oxygen, redox potential (E h),
and temperature were taken in the field prior to filtering
through 0.4 5-lm membrane filters. Samples were acidified
in the field and collected in polyethylene containers
and preserved on ice for delivery to the laboratory (Wisconsin
State L aboratory of Hygiene and a commercial
lab), where they were analyzed for major ions using
inductively coupled plasma mass spectroscopy and other
standard methods. Saturation indexes of mineral phases
and pCO 2 for major ion analyses were calculated using
the geochemical speciation program P HRE E Q C (P arkhurst
1995) using the thermodynamic data provided. Charge
balance errors in all samples were less than 10% .
N umerical M odeling
A 3D, transient numerical ground water flow model
was constructed to test the new conceptual model (Figure 2)
and specifically to evaluate the hydrogeologic role of
laterally extensive bedding-plane fracture zones in the
aquitard. The MO DFL O W96 (McDonald and Harbaugh
1996) code was used to represent the flow system. E quivalent
porous medium models have been used successfully
in sedimentary fractured rock settings (Y ager 1997;
Rovey 1998; Rayne et al. 2001; Swanson and Bahr 2004 ;
Swanson et al. 2006) and even in crystalline fractured
rock settings (Shapiro and Hsieh 1998; Tiedeman and
Hsieh 2001) by previous researchers. As in other modeling
applications, important differences exist between
606 T.T. Eaton et al. GROUND WATER 45, n o. 5: 601–615
centimeter- or meter-scale model fracture zone layers and
the sets of discrete submillimeter-scale features they represent.
Therefore, parameter values often need to be
adjusted from field values during the calibration process.
The model was designed to represent a vertical parallelepiped
through the aquitard centered on the DO T field
site (Figure 8) within the regional cone of depression in
the deep aquifer system. The principal output of interest
is the vertical distribution of head within and below
the Maquoketa aquitard. Therefore, 30 layers were used
allowing delineation of head at a high vertical resolution
(Figure 8). Mapped regional hydrostratigraphic data
(E aton et al. 1999) were interpolated to layer elevations
across the model domain. Specific layers of uniform
thickness (0.33 m) at certain depths were used to represent
major fractured zones in the Silurian Aquifer and
Maquoketa aquitard (Figure 4 ), but other layer thicknesses
varied across the model domain. At the subcrop at
the western corner of the model, all layer thicknesses
within the Silurian Aquifer and upper Maquoketa aquitard
were reduced to 0.33 m where the bedrock is erosionally
truncated. A variable column and row spacing was
used, from 900 m at the periphery to 1 m at the central
area of interest. The major elements of surface hydrography
(Figure 8) are represented by constant-head and
head-dependent nodes in MO DFL O W’ s River P ackage.
Recharge is estimated to range between 0 and 100 mm/
year over the model domain based on precipitation-runoff
modeling of stream low-flow discharge data in southeastern
Wisconsin (Cherkauer 2004 ). A uniform recharge rate
of 8 3 10 25 m/d (29 mm/year) best reproduced observed
head and flux values in the shallow aquifer system.
L ateral boundary conditions were selected to represent
the hydrogeologic conditions at the western Maquoketa
subcrop and correspond to the regional drawdown
on the other sides. L ateral boundary conditions in layers
2 to 8 were set at constant heads of generally higher
values than those of layer 1, consistent with the local
recharge-discharge conditions in the water table aquifer
in the unlithified sediments. At the western corner of the
model domain, where the Maquoketa subcrop is in contact
with the shallow aquifer system (Figures 2 and 8),
constant-head boundaries were specified for layers 9 to
24 , at 260 m above mean sea level (msl), the elevation
of P ewaukee L ake (Figure 8). Head-dependent (G eneral
Head Boundary [ G HB] ) boundaries were used for all
other edges and the bottom of the model, to simulate transient
decreasing hydraulic heads caused by regional drawdown
in the Cambrian-O rdovician Aquifer system.
Hydraulic conductivities were based on field and laboratory
data for the Maquoketa aquitard (Figure 6) and
unpublished and published data for the other formations
(E aton 2002). Hydraulic conductivity zones were delineated
in layer 1 representing the lateral and vertical variation
in unlithified P leistocene materials (Clayton 2001),
but hydraulic conductivity for layers 2 to 30 was specified
as constant and isotropic across the model domain. Two
classes of hydraulic conductivity and storage values
(Table 1), reflecting the vastly different properties of
fractured zones and relatively unfractured rock matrix
(Figures 4 and 6), were specified for both the Silurian
Figure 7 . Field parameters and maj or ion concentrations at different lev els through the Maquoketa Formation at
(A ) the Minooka Park site and (B) the DOT site. C ircle data symbols correspond to lower axis, while triangle symbols correspond
to upper axis. S haded area represents thickness of the Maquoketa Formation. The central column is a schematic
diagram of packers (black) and sampled open interv als (white). The approximate elev ation of bedding- plane fractures is
shown with asterisks.
Aquifer and the Maquoketa aquitard. During initial model
runs, hydraulic conductivity for fracture zone layers was
reduced from 100 to 1 m/d to avoid rapid lateral drainage
and dry cells. Hydraulic conductivity of relatively unfractured
Maquoketa model layers was reduced from 1 3
10 28 to 1 3 10 29 m/d, and hydraulic conductivity for the
Sinnipee G roup model layers was increased to 1.5 3
10 27 m/d in order to simulate the observed head profile.
V alues of specific storage, Ss, calculated from laboratory
rock-core testing (E aton et al. 2000; Hart et al. 2006)
ranged between 1 3 10 28 and 7 3 10 26 /m, so the initial
value of storage coefficient, S, used for unfractured model
layers of thickness 4 to 5 m was 1 3 10 26 , later adjusted
during calibration to 1 3 10 25 . In contrast to dual
overlapping continuum or double-porosity fracture models,
the thin fracture layers here do not represent entire
fractured rock systems in which storage is relatively low
because it depends on the extremely small ratio of fissure
volume to bulk rock volume (Moench 1984 ). In this
study, model layers representing fractured rock zones
were assigned a storage coefficient of 1 3 10 23 , consistent
with field hydraulic testing values as reported later,
and higher than values in layers representing relatively
unfractured rock (Table 1).
The model was used to simulate steady-state predevelopment
conditions (circa 1900) when hydraulic head
was considerably higher (Weidman and Schultz 1915) in
the underlying Cambrian-O rdovician Aquifer system,
T.T. Eaton et al. GROUND WATER 45, n o. 5: 601–615 607
Figure 8. The 3 D flow model showing (A ) a plan v iew of layer 1 with local hydrographic features forming boundary conditions
around DOT field site. C ontours represent mapped water table elev ations (S E W R PC / W GN H S 20 0 2), and arrows indicate
locations of cross sections; (B) cross sections showing relativ e elev ations and thicknesses of layers representing different
formations. The bottom and lateral boundary conditions in lower layers are head dependent except for the western corner of
the model where there are constant heads in the upper 24 layers as described in the text. Fracture zone layers are not apparent
at this scale.
inducing an assumed upward gradient across the Maquoketa
Formation. For all steady-state and subsequent transient
simulations, the P reconditioned Conjugate G radient
(P CG 2) solver (Hill 1990) was used. For model calibration,
we used eight head targets in the water table aquifer
in the Silurian and glacial aquifers and three flux targets
from observed streamflow, in addition to head measured
in and below the Maquoketa aquitard. These were used to
identify standard deviation and 90% confidence intervals
following Hill (1998).
All but one of the simulated water table head values
and all the flux values fell within the target confidence
intervals for both transient and steady-state runs and were
used in combination with the measured vertical head
distribution in the field to assess model calibration.
Monitoring well open intervals correspond to multiple
model layers, so transmissivity-weighted arithmetic mean
head calculations (Sokol 1963; Bennett et al. 1982) were
needed for calibration purposes. These mean simulated
hydraulic head values were compared to composite field
hydraulic head values measured in open intervals
608 T.T. Eaton et al. GROUND WATER 45, n o. 5: 601–615
spanning more than one model layer thickness. The root
mean square (RMS) error criterion was used for both flux
and head calibration. Head RMS error (5.791 m) was less
than 10% of the simulated total head gradient and flux
RMS error (176.1 m 3 /d) was less than 5% of the maximum
simulated flux. Model results are presented here as
head profiles at the location of the DO T field site, for
comparison to measured hydraulic head data (Figure 5).
More detailed model analyses, including comparison to
models without fracture zone layers and two-dimensional
models with no-flow lateral boundaries, showed that the
fully 3D model presented here best matched the field data
(E aton 2002).
Results and D iscussion
Field D ata
Transmissivity values of fractures within the Maquoketa
aquitard calculated from five analyses of drawdown
or recovery in observation wells during the two interwell
Parameter A ssignments for N umerical Model S howing S ignificant C ontrast in Transmissiv ity (Bold)
between Fractures and Matrix
L ayer Type Thickness b (m) S torage 1 Kx ¼ Ky (m/ d) Kz (m/ d) T ¼ Kxb (m 2 / d)
U nlithified V arious 0.3 0.2– 30 2E -6– 0.03 V arious
Silurian matrix 9– 13 1 E -5 1E -3 1E -3 2 1E - 2
Silurian fracture 0.33 1E -3 1 1 0 .3 3
Transition 3 0.33 1E -3 0.1333 0.1333 0.0399
Maquoketa matrix 4 – 5 1E -5 1E -9 1E -9 2 4 E - 9
Maquoketa fracture 0.33 1E -3 1 1 0 .3 3
Sinnipee V arious 1E -5 1.5E -7 1.5E -7 V arious
St. P eter V arious 1E -6 1 1 V arious
1 Specific yield in the unconfined, unlithified layer 1, storage coefficient in all other layers.
2 E xcept where these formations are represented by thin layers at the subcrop, and vertical hydraulic conductivity is 1 m/d.
3 A transition layer with intermediate values of hydraulic conductivity was required for numerical convergence.
pumping tests were within a range of 0.7 to 5 m 2 /d, with
storage coefficient values between 1 3 10 25 and 6 3
10 23 (E aton 2002). The overall range of estimated
hydraulic conductivity exceeds 11 orders of magnitude,
from less than 1 3 10 28 m/d to greater than 1 3 10 13 m/d,
assuming a fracture aperture of 0.001 m (Figure 6).
Hydraulic conductivity of rock core is generally limited
to between 1 3 10 29 and 1 3 10 27 m/d. Horizontal
hydraulic conductivity of the Maquoketa aquitard from
single-well hydrogeologic testing ranged over 5 orders of
magnitude, from 3 3 10 25 to 3 m/d (Figure 6). Many
hydraulic conductivity testing results were below the limit
of the field equipment (estimated at 2 3 10 25 m/d) and
are not included on Figure 6.
Based on detailed lithology and downhole geophysical
logging data (E aton 2002; E aton and Bradbury 2003),
three major bedding-plane fracture zones were correlated
in the heterogeneous upper part of the Maquoketa aquitard
(Figure 4 ). They account for the range of hydraulic
conductivity (Figure 6) above that of the unfractured and
lithologically homogeneous basal shale (less than 1 3
10 28 m/d). The hundred or more meters of drawdown in
the underlying aquifer system have affected head only in
the bottommost monitoring intervals in the Sinnipee
G roup dolostone, where heads are 60 to 80 m lower than
in the Maquoketa aquitard (Figure 5).
G round water in the Maquoketa aquitard is primarily
a calcium-magnesium– bicarbonate type, with abundant
sodium and sulfate. Saturation indexes, log(IAP /Ksp),
indicated that ground water is oversaturated with CO 2(g),
and generally in equilibrium with calcite and dolomite,
but undersaturated with respect to gypsum (E aton 2002).
V ariation in field-measured parameters and concentrations
of major ions with depth is shown (Figure 7) in comparison
to data from the overlying Silurian Aquifer (interval
7) and the underlying Sinnipee G roup dolomite (interval
1). The variation in values with depth at both sites is particularly
notable because samples presumably represent
mixing over long open intervals between packers. The
trend in hydrochemical parameters with depth provides
clues to the principal directions (horizontal or vertical) of
high-conductivity flowpaths within the Maquoketa Formation.
Relative variations in ground water chemistry are
especially pronounced between intervals containing
major horizontal fracture zones and adjacent unfractured
intervals. While the vertical boreholes of necessity sample
primarily horizontal fractures, variations in hydrochemical
parameters at different levels in the aquitard
strongly suggest that there is little mixing of water from
top to bottom. Hydrogeochemical parameter values vary
between the sites, which is not unexpected for ground
water in complex fractured systems. However, relative
variations in hydrochemistry at different levels, observed
at both sites, are difficult to explain by simple 1D vertical
flow, and suggest that hydrochemical differences
result from sampling water from different sources.
Water chemistry distribution in the Maquoketa Formation
is inferred to represent complex local mixing of
sodium bicarbonate (Na-HCO 3)– rich water from the
unfractured rock matrix and calcium-magnesium bicarbonate
(Ca-Mg-HCO 3)– rich water from major beddingplane
fracture zones (E aton 2002). The high-sodium,
low-chloride concentrations in the Maquoketa water
probably originate from cation exchange processes in the
clay-rich shale (Na/Cl molar ratios 3 to 19). High-sulfate
water are consistent with possible localized occurrences
of gypsum in the shale (Weaver and Bahr 1991; E aton
2002). The calcium-magnesium bicarbonate (Ca-Mg-
HCO 3) water, thought to be representative of fracture
zones, is similar to water from shallow aquifer systems in
the region (Saad and Thorstenson 1998).
The differences in hydrochemistry at different levels
within the Maquoketa aquitard (Figure 7), as well as the
head differences (Figure 5), suggest few to no vertical interconnections
between bedding-plane fractures or flow
due to vertical fractures but are consistent with lateral
advective transport along bedding-plane fractures (E aton
and Bradbury 2003). This analysis is also in agreement
with ground water tritium and oxygen isotope data (E aton
2002) that indicate water in the Maquoketa aquitard is
probably of P leistocene age compared to recent water in
the overlying Silurian dolomite aquifer.
T.T. Eaton et al. GROUND WATER 45, n o. 5: 601–615 609
Concep tual M odels for Aquitards
Neither hydrogeochemical (Figure 7) nor hydraulic
head data (Figure 5) in the Maquoketa aquitard are
consistent with the conventional conceptual model that
flow is predominantly downward in aquitards overlying
heavily pumped aquifers (Remenda et al. 1996; E aton and
Bradbury 2003). In the traditional conceptual model, vertical
flow under steady-state conditions is associated with
a linear head decrease with depth, and under transient
conditions, a monotonic head decrease with depth, both
characteristic of uniformly downward gradients. Instead,
we find that flow between monitoring intervals is bidirectional,
and there is an abrupt decline in head across the
base of the formation at both field sites (Figure 5), indicating
nonequilibrium and a very low effective vertical
hydraulic conductivity (E aton and Bradbury 2003).
High-transmissivity channels (Tsang and Neretnieks
1998) within fracture planes greatly increase the effective
hydraulic conductivity in a porous medium depending on
fracture orientation, extent, and especially connectivity
(Robinson 1984 ; L ong and Witherspoon 1985). In the
P ierre Shale, through-going vertical fractures spaced at
kilometer intervals may explain the discrepancy between
effective vertical hydraulic conductivity values estimated
from small-scale measurements on rock core and relatively
higher values based on results of regional flow
modeling (Bredehoeft et al. 1983; Neuzil 1986, 1994 ). A
similar discrepancy in estimates from field data (this
paper) and regional model values (Hart et al. 2006) exists
for the Maquoketa aquitard. However, in contrast to the
P ierre Shale, the Maquoketa aquitard in southeastern
Wisconsin is penetrated by numerous, old multiaquifer
wells (SE WRP C/WG NHS 2002; Hart et al. 2006). The
Maquoketa Formation is usually cased off in these wells,
but many wells are uncased above and below the shale,
allowing flow through the borehole from the surficial
aquifer to the deeper aquifer. In regional flow modeling
under transient pumping conditions, borehole flux
through such wells can be accommodated using an apparent
higher vertical hydraulic conductivity of the aquitard.
A major structural discontinuity whose hydraulic
properties are poorly known (the Waukesha Fault) occurs
directly between the field sites (Figure 1). Y et, a conceptual
model of through-going vertical fractures is inconsistent
with available field evidence at the tens of kilometers
scale encompassed by our two sites. Flowpaths through
such vertical fractures, if they existed, would intersect
the numerous bedding-plane fractures that have been
observed in the Maquoketa aquitard (E aton 2002; E aton
and Bradbury 2003) and are known from similar hydrogeologic
settings. In such a hypothetical high-diffusivity
interconnected fracture network, hydraulic head must
respond rapidly to more than 100 m of drawdown caused
by pumping in the underlying Cambrian-O rdovician Aquifer
system. The hydraulic response time to equilibrium
(Alley et al. 2002; E aton and Bradbury 2003) in such
a fracture network would be on the order of days. Furthermore,
flow within a through-going fracture network would
cause vertical head profile equilibration to a monotonic
pattern and homogeneous hydrogeochemistry with depth
in the formation, contrary to observations (Figure 7).
610 T.T. Eaton et al. GROUND WATER 45, n o. 5: 601–615
Measurements over a period of 3 to 4 years indicated
that there is no drawdown trend in head change or systematic
head fluctuation within the Maquoketa Formation
at our sites (Figure 5). Several large municipal supply
wells within a few miles of the field sites were concurrently
being pumped on various schedules, and the underlying
aquifer system has been pumped for over a century.
Together, the hydraulic head data (Figure 5), the stratified
hydrogeochemistry (Figure 7), and limitations on vertical
fracture propagation due to heterogeneous mechanical
stratigraphy provide important evidence against continuous
large vertical fractures in the Maquoketa aquitard, at
least at the scale of our two field sites.
A new geological conceptual model for the aquitard
(Figure 2) accounts for all the available hydrogeological
observations in the Maquoketa aquitard at our study sites
and is consistent with recent understanding of the mechanisms
and patterns of fracture formation and porosity
development in similar, relatively undeformed, heterogeneous
sedimentary rocks. The major elements of the new
conceptual model are as follows:
1. O rders of magnitude contrast between hydraulic diffusivity
(K/S s) of horizontal bedding-plane fractured zones and
relatively intact aquitard rock matrix. In the case of the
Maquoketa aquitard, this accounts for the rapid responses
in observation wells to the interwell pumping tests and
horizontal fracture flow, resulting in the vertically stratified
ground water chemistry (Figure 7).
2. L aterally extensive bedding-plane fracture zones extending
over distances of at least 10 km and probably more. Development
of bedding-plane fracture porosity in carbonate
rocks is similar to evolution of preferential flowpaths in
karst through progressive dissolution (Kaufmann and Braun
1999; G abrovsek and Dreybrodt 2001; Bloomfield et al.
2005). These studies have shown that fracture porosity is
highly dependent on boundary conditions. For example,
given a carbonate rock subcrop in an aquifer system,
increased fracture porosity and transmissivity develop progressively
over time with distance away from the subcrop. If
numerous interbeds of different lithology impose a mechanical
stratigraphic control on vertical fractures but allow the
development of bedding-plane fractures, the result would be
laterally extensive bedding-plane fracture zones extending
over distances of up to tens of kilometers in carbonate rocks.
3. V ery low vertical hydraulic conductivity in thick unfractured
shale intervals. In this case, effective hydraulic
conductivity of the apparently unfractured shale near the
base of the Maquoketa aquitard appears to be similar
to values from laboratory rock-core testing (E aton and
Bradbury 2003), a type of scale independence suggested
for some aquitards by Neuzil (1994 ).
4 . Hydraulic influence of the aquitard subcrop, where
hydraulic head in the shallow aquifer system is controlled
by numerous surface water bodies. This last element of
the conceptual model does not excessively limit its general
applicability because unrecognized edges and proximity
to areas where the aquitard has been eroded through
to the aquifer are common uncertainties about aquitards
(Cherry et al. 2006).
N umerical M odeling Results and S ensitiv ity
Simulation results are shown using vertical profiles
of head (Figure 9A) for comparison to hydraulic head
data collected at the field sites (Figure 5). V ertical head
distribution for the Maquoketa aquitard and below is
illustrated from predevelopment steady-state conditions
(1900) to present-day transient conditions (2000), with
head profiles at two intermediate time periods: 1960
and 1980. Simulated head values in different layers
(curves) are most different from measured head values
(points) at the base of the formation, where head
changes rapidly over a short vertical distance. The discrepancy
is likely due to inadequate vertical resolution
of the model grid.
The simulated 2000 head profile with depth generally
matches the observed abrupt loss in head across the
bottom contact of the Maquoketa Formation. The match
between simulated transient heads at present (year 2000)
and the observed head distribution with depth (Figure 5)
suggests that the flow field in the Maquoketa aquitard is
not at steady state with respect to pumping in the underlying
aquifer system, as previously inferred (E aton and
Bradbury 2003). Since long-term changes in head values
were not observed within but only below the Maquoketa
Formation, model parameters represent an upper bound
on aquitard vertical diffusivity, and hence indicate a long
time constant to equilibrium.
The model was also used to investigate the transient
nature of the ground water flow system. The evolution of
head is dependent on inherently unpredictable patterns of
pumping for municipal supply. However, if the current
head in the deep aquifer system is assumed to remain at
the present value of 14 0 m above msl, the evolution of
head in the Maquoketa aquitard can be projected. Results
of predictive simulations (shown in Figure 9B for years
2200 and 2500, and steady state), using initial heads from
the present-day (year 2000) simulation, show that the current
hydraulic head profile is far from steady state. The
steady-state head profile shows a distinct change in vertical
gradient below the upper fractured portion of the
Maquoketa aquitard, where the hydraulic head gradient
with depth becomes constant and linear. In all simulations,
head in the transmissive bedding-plane fracture
layers tends to maintain the vertical head distribution
close to the head values at the lateral model boundary
(260 m above msl). The difference between present-day
(year 2000) and future profiles suggests that a steady-state
flow system within the Maquoketa aquitard might not
occur for many hundreds of years.
In order to test the effect of both the constant-head
boundary condition at the aquifer subcrop (represented
by P ewaukee L ake) and the bedding-plane fracture zones
on the head profile in the aquitard, we arbitrarily reduced
the value of the western constant-head boundary condition
by 80 m and reran the steady-state and transient
simulations. Bedding-plane fracture zones that are laterally
extensive over scales of kilometers can provide highdiffusivity
flowpaths, causing distant lateral boundary
conditions to become more important than much closer
lower boundary conditions for rock aquitards. The resulting
effect on the head profile (Figure 9C) indicates that
hydraulic head at the lateral boundary can play a more
important role in controlling the Maquoketa vertical head
distribution than the lower boundary condition in the
immediate underlying heavily pumped aquifer. Although
it is well known that boundary conditions affect steadystate
hydraulic heads, the dominant influence of lateral
boundary conditions here, under transient conditions, is
Figure 9 . Field- measured v ertical head distribution (points) within the Maquoketa Formation (shaded) and modeling results
(curv es) at the DOT field site (A ) after different stress periods (dates) to present; (B) from present (20 0 0 ) to years 220 0 and
250 0 and steady- state future head distribution; (C ) with constant- head boundary condition v alues reduced by 80 m to demonstrate
role of head at western subcrop. Dashed lines indicate approximate elev ation of layers representing bedding- plane fracture
zones. Open and solid circles as in Figure 5. The simulated decrease in head across the bottom of the Maquoketa
Formation is discretized by the number of layers used— it would be more abrupt with ev en thinner layers.
T.T. Eaton et al. GROUND WATER 45, n o. 5: 601–615 611
a significant contrast to the dominance of the top or bottom
boundaries inherent to the traditional vertical flow
A sensitivity analysis was conducted using the
inverse code U CO DE (P oeter and Hill 1998). Composite
scaled parameter sensitivities, which are an aggregate of
all the dimensionless scaled sensitivities, were calculated
for each rock parameter value in Table 1. Results indicated
that sensitivity to all horizontal hydraulic conductivity
parameters was negligible. The highest sensitivities
were to the vertical hydraulic conductivity of the Sinnipee
G roup dolostone, followed by the storage coefficient of
model layers representing unfractured Maquoketa rock.
Next most sensitive was the vertical hydraulic conductivity
of layers representing unfractured Maquoketa rock,
followed by recharge. Sensitivity to the storage coefficient
of layers representing bedding-plane fracture zones
was very low, indicating that results would not change
with lower storage values than used in the calibrated
model. High sensitivity to storage coefficient of layers
representing Sinnipee G roup and unfractured Maquoketa
rock is consistent with the simulated reduction in hydraulic
head caused by pumping over the 20th century
(Figure 9) and with the interpretation that the flow field
in the Maquoketa Formation has not yet equilibrated to
the aquifer drawdown.
Results from this study indicate the vertical hydraulic
conductivity of the Maquoketa aquitard is on the order of
1 3 10 29 m/d based on field data and numerical modeling
at the tens of kilometers scale of our field sites. This
very low conductivity is due largely to the bottom shale
layer in the formation, which the hydraulic head profile
suggests is unfractured at this scale. A complex flow system
(Figure 10B) surrounding the bedding-plane fracture
zones is inferred to exist within the aquitard. A remnant
higher head zone may be present within the very low conductivity
base of the aquitard, accounting for the observed
head distribution measured within the multilevel monitoring
systems. Slow drainage from the low-conductivity
rock matrix into high-diffusivity bedding fractures causes
the variation in water chemistry signatures and the
converging vertical flow directions observed between
fractured and unfractured intervals. Additional field
observations are needed to determine the farthest lateral
extent of the fractured zones away from the aquitard subcrop.
There are significant differences in the inferred flow
field in the aquitard under predevelopment steady-state
(Figure 10A) and present transient conditions (Figure 10B)
caused by municipal pumping.
Mass balance calculations were made to estimate
leakage fluxes for the calibrated flow model in the area
encompassed by the field sites, assuming constant aquifer
drawdown. They show that transient leakage fluxes from
the aquitard to the underlying aquifer system peak at
about 0.017 m 3 /d/km 2 , declining to about 0.006 m 3 /d/km 2
at steady state. Intrinsic hydraulic conductivity and leakage
fluxes presented here for the Maquoketa aquitard are
almost 3 orders of magnitude lower than values previously
reported by others, who based estimates on steadystate
flow assumptions (Walton 1960; Y oung 1992).
Results presented here suggest that recent higher estimates
based on regional numerical modeling reported by Hart
et al. (2006) are attributable to numerous cross-connecting
multiaquifer wells rather than through-going vertical
Conclusions and Imp lications
We developed a 3D conceptual model for flow in
a rock aquitard that emphasizes the importance of laterally
extensive, transmissive fracture zones along bedding
planes. The conceptual model allows explanation of the
unusual but observed vertical profiles of head and hydrochemical
data at two sites 10 km apart in the Maquoketa
aquitard, southeastern Wisconsin. Results from a numerical
model show that lateral head boundaries at the rock
Figure 10 . S chematic diagram showing complex flow system within the Maquoketa aquitard (shaded) within 10 km of subcrop.
(A ) C orresponds to steady- state predev elopment conditions and (B) corresponds to transient present- day conditions.
H eav y lines represent transmissiv e bedding- plane fracture zones extending east from the subcrop and dashed contours represent
hydraulic head. N ote that field sites are within the area of fracture zones (Figure 2), but the extent of these away from the
subcrop is uncertain. I n (A ), hydraulic head is highest in the underlying aquifer system. I n (B), closed contour in lower
unfractured Maquoketa Formation represents highest head. Deep well at right represents municipal pumping that has drawn
down head in underlying aquifer system.
612 T.T. Eaton et al. GROUND WATER 45, n o. 5: 601–615
aquitard subcrop can be a dominant control on the vertical
distribution of hydraulic head and hydrochemistry in
the aquitard because of the presence of transmissive
Major conclusions from this study are as follows:
1. The traditional conceptual model of 1D vertical flow
through an aquitard was inadequate to explain the field
data in an indurated rock aquitard while a 3D conceptual
model of flow and hydrochemical mixing satisfactorily
explained the pattern of both the heads and water chemistry
observed in the field. The Maquoketa aquitard, while
restricting downward ground water flow, has a complex
internal flow system (Figure 10) due to near-horizontal
bedding-plane fractures. Accordingly, conceptual models
of similar aquitards should not necessarily assume strictly
vertical flow of water and/or solutes/contaminants.
2. Transmissive bedding-plane fractures play an important
role in the hydrogeology and hydrogeochemistry of rock
aquitards such as the Maquoketa Formation. These fractures
promote a range of water chemistry with depth as
pore water from the rock matrix mixes with very different
ground water from the more fractured horizons.
3. Simulation results show that the effects of lateral boundary
conditions are propagated over multikilometer-scale
distances through transmissive, high-diffusivity, beddingplane
fractures controlling the vertical distribution of
head and delaying equilibration to pumping from underlying
aquifers. In the Maquoketa aquitard, the flow field
has not equilibrated to the effects of pumping in the
underlying aquifer system (E aton and Bradbury 2003),
partly owing to the presence of the highly transmissive
fractures in the upper part of the aquitard and partly
owing to the extremely low hydraulic conductivity (10 29
m/d) of the apparently unfractured base of the aquitard.
4 . Numerical models that incorporate the most important
elements of the conceptual model presented in this study,
in combination with stresses (for example, pumping in an
underlying aquifer) that allow the development of a significant
vertical hydraulic gradient, are likely to be useful in
interpreting hydrogeologic data in other rock aquitards.
O ur conceptual model for control of hydraulic head
and hydrogeochemistry in rock aquitards potentially is
applicable to a broad area within at least 10 km of the
subcrop of the Maquoketa Formation, which extends over
parts of the states of Iowa, Illinois, Wisconsin, Indiana,
O hio, and Michigan in the northern Midwest U nited
States. It also provides a framework for evaluating hydrogeologic
and hydrogeochemical data from similar settings
in other rock aquitards, where multilevel hydraulic head
data are available from within and below the aquitard.
The results of this study have implications for assessment
of effective properties of rock aquitards on regional
scales. E stimates of intrinsic vertical hydraulic conductivity
of the Maquoketa aquitard reported here are up to 3
orders of magnitude lower than previously reported for
regional studies of this aquitard, as are estimates of flux
to the underlying Cambrian-O rdovician Aquifer system.
Since the results of this study are based on site-specific
field data from within the aquitard, the estimates of fluxes
to the underlying aquifer system do not include the effects
of the numerous deep wells that are cased through
the Maquoketa aquitard but open to the aquifers above
and below (SE WRP C/WG NHS 2002; Hart et al. 2006).
Flow through these multiaquifer wells could explain the
discrepancy between our estimates of aquitard properties
and the larger values reported in regional studies.
O n a regional scale, the proliferation of multiaquifer
wells over the 20th century in southeastern Wisconsin
(SE WRP C/WG NHS 2002) has increased the effective
vertical hydraulic conductivity of the aquitard. Therefore,
a higher vertical hydraulic conductivity for the aquitard
than used in this study is appropriate for assessments of
regional leakage to the underlying aquifer system. Such
assessments are needed for projections of regional municipal
water supply, and the change in effective properties
presents challenges for regional numerical modeling studies.
Regional models often do not explicitly represent
multiaquifer wells or have the resolution to account for
hydrogeologic field data needed to evaluate intrinsic
properties of aquitards. However, the results presented
here provide a baseline for evaluation of predevelopment
conditions or intrinsic properties of the Maquoketa aquitard
and therefore may be useful for isolating the effects
of the multiaquifer wells.
Funding for this work was provided by the Wisconsin
Department of Natural Resources and the U niversity of
Wisconsin Water Resources Institute. The authors gratefully
acknowledge the comments and thorough reviews
provided by Chris Neuzil, who acted as editor-in-chief for
this paper, two anonymous reviewers, and Tamie Weaver.
Their input has greatly improved the paper.
E ditor’ s N ote: The use of brand names in peer-reviewed
papers is for identification purposes only and does not
constitute endorsement by the authors, their employers, or
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