A Multiscale Investigation of Ground Water
Flow at Clear Lake, Iowa
by William W. Simpkins
Abstract
Ground water flow was investigated at Clear Lake, a 1468-ha glacial lake in north-central Iowa, as part of
a comprehensive water quality study. A multiscale approach, consisting of seepage meters (and a potentiomanometer), Darcy’s law, and an analytic element (AE) model, was used to estimate ground water inflow to and outflow
from the lake. Estimates from the three methods disagreed. Seepage meters recorded a median-specific discharge
of 0.25 lm/s, which produced a lake inflow rate between 90,750 and 138,200 m3/d, but no detectable outflow. A
wave-induced Bernoulli effect probably compromised both inflow and outflow measurements. Darcy’s law was
applied to 11 zones around the lake, producing inflow and outflow values of 10,500 and 5000 m3/d, respectively.
The AE model, GFLOW, coupled with the parameter estimation model, UCODE, simulated ground water flow in
a 700-km2 region using 31 hydraulic head and base flow measurements as calibration targets. The model produced
ground water inflow and outflow rates of 14,300 and 9200 m3/d, respectively. Although not a substitute for field
data, the model’s ability to simulate ground water flow to the lake and the region, estimate uncertainty for model
parameters, and calculate a lake stage and associated lake water balance makes it a powerful tool for water quality
management and an attractive alternative to the traditional methods of ground water/lake investigation.
Introduction
Clear Lake, located in north-central Iowa, is the third
largest (1468 ha) of 34 glacial lakes in Iowa. Although it
is still a major regional destination for recreation, the
water quality and diversity of fish species have declined
markedly during the past 30 years. Concentrations of total
phosphorus in the lake have increased from ~60 lg/L
in the early 1970s to ~190 lg/L in 2000, due primarily to
increased inputs from agricultural and urban sources. As
a result of sedimentation, the lake has lost an estimated
38% of its volume since deglaciation—25% of that volume since 1935—and now has a maximum depth of 5.8
m and a mean depth of 2.9 m. Hence, what probably
began as an oligotrophic to mesotrophic lake is now
a eutrophic system (Downing and Kopaska 2001). A
series of events, beginning with the dumping of about one
Department of Geological and Atmospheric Sciences, 253
Science I, Iowa State University, Ames, IA 50011; (515) 294-7814;
fax (515) 294-6049; bsimp@iastate.edu
Received April 2003, accepted October 2004.
Copyright ª 2005 The Author(s)
Journal compilation ª 2006 National Ground Water Association
doi: 10.1111/j.1745-6584.2005.00084.x
million liters of raw sewage into the lake in June 1998,
initiated a comprehensive investigation of lake water
quality. In July 1998, a 9-year-old boy contracted a case
of E. coli Serotype 0157:H7 poisoning, which his parents
believe occurred after swimming in the lake (Mason City
Globe Gazette 1998a). Although it was unlikely that the
boy contracted the illness as a result of the sewage incident (Mason City Globe Gazette 1998b), subsequent
water testing in early August indicated fecal coliform and
E. coli counts as high as 8500 colony-forming units per
100 milliliters (Mason City Globe Gazette 1998c). This
precipitated closure of some or all of the three main beaches on the lake and caused an economic loss for the
region. Shortly thereafter, a study funded by the Iowa
Department of Natural Resources and based at the Iowa
State University Limnology Laboratory investigated
water quality–related problems in the lake and its watershed, their likely causes, and potential remedial measures.
A description of the principal findings of the lake analysis, its watershed, and the economic and sociological factors is given in Downing et al. (2001a). The study
described here provided the basis for estimates of nutrient
flux from ground water (Simpkins et al. 2001).
Vol. 44, No. 1—GROUND WATER—January–February 2006 (pages 35–46)
35
Purpose and Scope
The purpose of this paper is to compare and evaluate
a multiscale approach using seepage meters (and a potentiomanometer), Darcy’s law, and an analytic element
(AE) model to quantify ground water inflow to and outflow from Clear Lake. At the small scale, estimation of
ground water inflow and outflow (or specific discharge)
to lakes has traditionally been the domain of seepage meters and minipiezometers (Lee 1977; Lee and Cherry
1978; Shaw and Prepas 1990a, 1990b) and potentiomanometers (Winter et al. 1988). Data from individual seepage
meters (cross-sectional area ’ 0.25 m2) are extrapolated
to large lakes based on relationships between specific discharge and depth or distance from shore (Lee 1977). At
a larger scale, the application of Darcy’s law using
hydraulic gradient and hydraulic conductivity (K ) data
has provided reasonable estimates of inflow and outflow
(Pennequin and Anderson 1983; Shaw et al. 1990;
LaBaugh et al. 1997; Harvey et al. 2000; Hunt et al.
2003). Similar to seepage meter measurements, limited K
and hydraulic head data, coupled with inexact estimates
of the cross-sectional area of flow (Hunt et al. 2003), may
limit the application of Darcy’s law in large lakes. At the
largest scale, ground water modeling has aided our understanding of ground water–lake interaction (McBride and
Pfannkuch 1975; Winter 1976; Anderson and Munter
1981; Krabbenhoft et al. 1990; Hunt et al. 1998). Gridbased finite-difference models such as MODFLOW
(McDonald and Harbaugh 1988) have been the standard
approach for lake simulation (e.g., the LAK1 package
of Cheng and Anderson 1993; the ‘‘high-K lake’’ of
Anderson et al. 2002); however, models based on the AE
method (Strack 1989; Haitjema 1995a) have also been
used to simulate ground water–lake interaction (Hunt and
Krohelski 1996; Hunt et al. 2000, 2003). In addition to
providing a regional picture of ground water flow, some
AE models, such as GFLOW, solve equations for surface
water and ground water conjunctively, allowing for calculation of hydraulic head as well as stream base flow and
lake stage. The study of Clear Lake provided an opportunity to compare and evaluate the three methods in a
glacial, predominantly till landscape.
Hydrogeological Setting
Clear Lake is set within the Algona-Altamont
Moraine Complex on the eastern edge of the Des Moines
Lobe (Figure 1), which advanced into Iowa during the
late Wisconsinan ~14 ka and was at this location ~12.5 ka
(Prior 1991). Clear Lake may be a classic ‘‘kettle lake’’ or
the remnants of a subglacial tunnel channel (e.g., Cutler
et al. 2002) that drained to the east. The watershed contains drainage tiles and is typified by hummocky topography formed in the Morgan Member till of the Dows
Formation (Prior 1991), although outwash of the Noah
Creek Formation and lake sediment deposits occur on
the margin of the lake. Well logs indicate ~30 m of
Wisconsinan Morgan and Alden Member till, loess, and
probably Pre-Illinoian till below the lake and on top of
the Devonian Lime Creek Formation (Simpkins et al.
2001). An outwash deposit begins at Clear Creek, the
36
W.W. Simpkins GROUND WATER 44, no. 1: 35–46
Figure 1. Base map of the domain for the AE model. Dashed
lines are far-field elements, and continuous lines are nearfield elements. Inhomogeneities used in the model include
Kow (outwash, open circle pattern), Kse (southeast mound,
vertical hatchore pattern), and Kcl (City of Clear Lake, diagnoal hatchore pattern). Triangles indicate piezometer nests;
squares are measurement points for stream discharge. Clear
Creek is the surface water outlet for the lake. The topographic profile in Figure 2 is oriented along line A-A9.
natural surface outlet for the lake (Figure 1), and continues eastward onto an older and incised till plain (Hershey et al. 1970). A concrete spillway keeps the lake level
at 373.94 m above mean sea level, and Clear Creek flows
only when water splashes over the spillway on windy
days or during periods of higher-than-normal precipitation. Hence, it is mostly a losing or disconnected
stream (Winter et al. 2002). The elevation decrease from
the moraine toward the east suggests that Clear Lake is
a flow-through lake system, with ground water entering
on the western edge of the lake and exiting the moraine in
the outwash deposits on the east side (Figure 2).
Methods
Seepage Meters
Standard seepage meters, consisting of about the top
one-fourth of a 55-gallon (204 L) metal barrel, were emplaced at 21 sites around the lake (Figure 3). Measurements (N = 341) of seepage (synonymous with discharge)
were made in July to August and November 1999 and
again in May to June 2000. Ventura Marsh (Figure 3) was
excluded from seepage measurements because of the
extremely mucky bottom. Most measurements were made
within 3 to 4 m of shore, although some were made at
100 m offshore (site 21). Inflow was collected in a 4-L
polyethylene bag ~1 h after emplacement, and volume
was measured in a graduated cylinder. Although allowing
a lag time for equilibration (e.g., Rosenberry and Morin
2004) may have produced better measurements, this procedure could not be done at Clear Lake because of potential vandalism and boat and beach traffic. Instead, meters
water flow at the lake bottom by measuring the difference
(with a manometer) between hydraulic head at depth and
at the lake sediment surface. If the distance between the
piezometer tip and the lake sediment surface is known,
a hydraulic gradient may be calculated. When paired with
a nearby seepage meter, this device may also provide an
estimate of K for the lake bottom sediments by dividing
specific discharge (q) from the seepage meter by the
hydraulic gradient (i) from the potentiomanometer (Lee
and Cherry 1978).
Figure 2. Southwest to northeast topographic profile of
the Clear Lake region showing the decrease in elevation
from the Algona-Altamont moraine into the valley of the
Winnebago River. Till of the Dows Formation comprises
most of the section in this diagram, although outwash deposits of the Noah Creek Formation predominate east of the
City of Clear Lake.
were emplaced just prior to use, removed, and then
moved to another measurement site. All bags were filled
with an initial 200 mL of lake water to preclude problems
with bag infilling or induced flow (Shaw and Prepas
1989). Seepage was measured at sites 1 to 4, 6 to 9, and
12 to 21 in 1999, with sites 7, 9, 12, and 13 visited twice
(N = 171). Seepage was measured at sites 3 to 5, 7 to 10,
14, 15, and 22 in 2000, with sites 3 to 5, 7, and 8 visited
twice (N = 170). Sequential measurements were made at
sites 8, 9, 10, and 13 in 2000 to estimate the intrasite variability. Sites 3, 4, 7, 8, 9, 14, and 15 were visited both in
1999 and 2000 to estimate interannual variation. Seepage
estimates were computed in mL/min and converted to
a specific discharge (in lm/s).
Potentiomanometer Measurements
Hydraulic gradient measurements were also made in
lake bottom sediments in the same areas as the seepage
meters (Figure 3) using a potentiomanometer (Winter
et al. 1988). The device consists of a hand-driven, stainless steel piezometer that shows the direction of ground
Figure 3. Map showing location of seepage meters and associated potentiomanometer measurements.
Darcy’s Law
An alternative for estimating ground water inflow
and outflow involves Darcy’s law, where Q is discharge,
K is hydraulic conductivity, i is hydraulic gradient, and A
is the cross-sectional area through which flow occurs (Q =
2KiA). Nests of three piezometers each were installed at
11 sites on the perimeter of the lake in June 2000, primarily to intercept ground water flow paths just prior to
entering the lake (Figure 4). Of the 33 piezometers
installed in the project, 13 were in till, 18 in sand, one in
loess, and one in fill. Till was the predominant material
adjacent to the lake on the north and west sides of the
lake, while sand was more common on the south and east
sides (Simpkins et al. 2001). Piezometers consisting of
3.2-cm I.D., polyvinyl chloride standpipes with 20-slot,
factory-slotted screens 0.61 to 0.91 m in length were
installed at depths between ~0.9 and 9.5 m using hollow
stem augers. In sands, a filter pack of silica sand was tremied from the bottom of the borehole to ~0.3 m above the
screen, and chip bentonite was used to seal the measurement interval to the ground surface. Piezometers in till
and loess were installed using a modified, overcored
Shelby tube method (Simpkins and Johnson 1996) to
reduce the chance of formation damage. All piezometers
were protected by a steel casing cemented into the top of
the borehole. Absolute elevation of the standpipes and
USGS stage gage were surveyed to less than ±1 cm (NAD
83 datum) by a professional surveyor using Global Positioning System (GPS) and total station equipment. Cores
Figure 4. Map showing location of points used for hydraulic
head measurements and calibration targets. Sites A through
K are piezometer nests. Sites L, O, and Q are temporary
piezometers. Sites M and P are ponds and site Q is a wetland; all are in contact with the water table. Site N is the
USGS stage gage on the lake.
W.W. Simpkins GROUND WATER 44, no. 1: 35–46
37
were taken from the boreholes and described using standard methods. Falling- and rising-head slug tests were
performed in the piezometers in January 2001, July 2001,
and August to September 2002. Values of K were estimated using the Hvorslev (1951) method.
Hydraulic head in the piezometers was measured
monthly between July 1, 2000, and July 1, 2001. The horizontal hydraulic gradient at the water table was calculated by taking the difference between the lake stage and
the water table elevation on that day and dividing by the
horizontal distance between the piezometer and the lake.
Vertical hydraulic gradients were calculated for ground
water between each piezometer in the nest (sites A to K
in Figure 4) using the mean hydraulic heads in the study
period divided by the difference in elevation of the screen
midpoints. To determine the ground water inflow and outflow, 11 zones, each represented by a Kh and a horizontal
hydraulic gradient value from the nearest piezometer nest,
were delineated along the shoreline of the lake. The saturated thickness of units in contact with the lake was calculated as follows: (1) the mean water table depth was
used to calculate the depth of the top of the zone and (2)
the thickness of the more permeable units (weathered,
fractured till, and/or sand) was used to calculate the bottom of the zone. Values of inflow or outflow were determined for the 11 sites during the entire measurement
period and summed to provide a total value in units of
m3/d.
AE Model
A Windows-based AE model, GFLOW2000 version
1.3.2 (hereafter termed GFLOW), was used to simulate
the ground water flow system in the vicinity of Clear
Lake. GFLOW is a two-dimensional, steady-state AE
model that assumes that ground water flow is horizontal.
When compared to the USGS finite-difference model,
MODFLOW (McDonald and Harbaugh 1988), AE models are less well known and have only recently been
applied to ground water/lake interaction (e.g., Hunt et al.
2003; Dunning et al. 2002). The AE method is based on
superposition of analytic functions, each representing
a feature of the aquifer (Strack 1989; Haitjema 1995a).
Wells, linesinks (streams), and inhomogeneities (areas
with differing K, porosity, or recharge values) are addressed in the model. The method assumes that the aquifer is infinite in extent and boundaries consist of rivers,
creeks, and lakes. Stream channel elevations determined
at multiple points from those maps were used to specify
hydraulic head along stream linesinks in the model. Values for stream resistance, c, are given by
c=
d
Kv
ð1Þ
where d = thickness of the resistance layer beneath
the stream and Kv is the vertical K value of that layer
(Haitjema 1995a, p. 234–239).
This version of GFLOW includes a new AE Lake
Package, which lets the model calculate lake stage rather
than specifying stage a priori and accounts for surface
water inflow and outflow. The applicability of the package in similar lake systems has been demonstrated by
38
W.W. Simpkins GROUND WATER 44, no. 1: 35–46
Dunning et al. (2002). It includes a resistance and a width
parameter (area of leakage near the perimeter of the lake;
width = 3.3 m in the model) to calculate the ground water
inflow and outflow in response to hydraulic heads and
lake stage (Hunt et al. 2003). The lake can stand alone or
be part of a stream network, including surface water
inflow from a stream upgradient and outflow through an
outlet stream. The outflow discharge depends on the lake
stage, and it is calculated using a linear interpolation
between a lake stage table and stream outflow rate at that
stage (Hunt et al. 2003). The model calculates lake stage
iteratively based on ground and surface water inflow and
outflow, precipitation, and evaporation using the secant
method (Hunt et al. 2003). In this method, the user specifies an upper- and lower-stage estimate for the lake, u1
and u2, based on prior data. A conjunctive ground water–
surface water solution is generated for each lake stage,
which produces values of Q1 and Q2, known as the
water balance ‘‘deficiency’’ and given by
X
X
X
X
Q =
ri 1 l i 1
Qi0 1
Qin 2
Qout 1 AðuÞE
ð2Þ
where ri is the sink density of the ith linesink, li is the
length of the ith linesink, Qi0 is the overland flow into the
ith linesink, and Qin and Qout are the contributions
from inlet streams to the lake and discharge from the lake
into outlet streams, respectively. The last term A(u)E is
the product of the lake area (which is dependent on stage)
and the net precipitation rate (precipitation rate minus
evapotranspiration rate). The model calculates a new lake
stage, u, using the equation
u = u1 2
ðu2 2u1 ÞQ1
Q2 2Q1
ð3Þ
and the process is repeated and values reentered into the
equation until a lake stage solution is attained. The number of iterations is controlled by the user, and the water
balance can be checked manually. Comparisons of this
approach to those calculated by LAK packages in MODFLOW showed good agreement (Hunt et al. 2003).
The GFLOW model domain comprises a regional,
‘‘far-field’’ area of ~400 km2 and ‘‘near-field’’ zone of
~300 km2 (Figure 1). Ventura Marsh (adjoining the western end of the lake) was included within the lake area.
Published (Hershey et al. 1970) and unpublished glacial
geologic maps from the Iowa Geological Survey (Quade
2001) were used to map the extent of the outwash inhomogeneity (Figure 1). Stream width (a GFLOW parameter) was measured in 29 creeks in June and July 2001, and
discharge was estimated there using the six-tenths depth
method (Rantz et al. 1982). Because of the heavy precipitation that immediately preceded that stream gauging,
measurements were repeated during a time of stable
stream stage in November 2001. Based on a comparison
with continuous stream discharge records from the nearest USGS gauging station (Winnebago River near Mason
City, Iowa, ~17 km east of the lake), the discharges measured in the Clear Lake region appear to represent base
flow conditions at that time. Hydraulic heads from
the water table piezometers were used as targets for
model calibration. An additional six hydraulic head measurements were obtained from three temporary piezometers and three surface water bodies in November 2001
(Figure 4).
Estimates of lake stage, precipitation, and overland
flow to and evaporation from the lake were also needed
for the lake element. Data from the USGS gage on the
lake show that the mean lake stage during the July 2000
to July 2001 period was 373.82 m (Miller 2002). Because
the spillway elevation at the Clear Creek outlet is 373.88 m
(NAD 83), fixing the lake stage at this elevation precludes discharge to the creek. However, this is a typical
situation for the lake (the 1998 to 2002 average was
373.86 m), and water actually flows over the spillway on
windy days and after heavy precipitation. Precipitation
for this period (Mason City NWS station, 10 km to the
northeast) was 82.22 cm (http://www.ncdc.gov/oa/pdfs/
cd.html), which is only 0.94 cm less than the mean annual
precipitation of 83.16 cm. Because the station does not
record pan evaporation data, a value of 121.78 cm was
interpolated from Ames 8 WSW station in Iowa and the
Waseca Experiment Station near Waseca, Minnesota
(http://www.ncdc.gov/oa/pdfs/cd.html). Both stations are
~136 km due south and due north, respectively, from
Clear Lake. A pan coefficient of 0.73 converted this value
to an annual value of 88.90 cm, which is similar to the
values for lake evaporation in the region given in Kohler
et al. (1959).
The AE model was calibrated using parameter estimation techniques. Application of parameter estimation
to calibration is relatively new (Poeter and Hill 1997; Hill
1998). The benefit of parameter estimation over a ‘‘trial
and error’’ calibration is the ability to estimate parameter
values (such as K or recharge) automatically that are a best
fit between simulated model output and observed data.
Other benefits include quantification of the quality of the
calibration and a statistical measure of uncertainty (or confidence interval) of the hypothesized simulations in the optimized model (Hunt et al. 2000; Kelson et al. 2002). Finally,
parameter correlation and sensitivity may be assessed. For
this study, GFLOW was coupled with the parameter estimation code, UCODE, version 3.02 (Poeter and Hill 1998).
Results and Discussion
Seepage Meters
Seepage meter data were characterized by high coefficients of variation, indicating variability (Table 1).
Although parametric statistics were calculated, the data
did not adhere to a normal distribution; hence, nonparametric statistics (Conover 1980) are emphasized here
for description and comparison. Significant differences
(Mann-Whitney test; a = 0.05) occur between medianspecific discharge measured in 1999 (0.51 lm/s; N = 170)
and 2000 (0.17 lm/s; N = 171). Four out of seven sites
visited in both 1999 and 2000 showed significant differences in their median-specific discharge values (a = 0.05).
The main cause for this difference was precipitation (at
Mason City), which was 112.2 cm in 1999 and 77.7 cm in
2000. A 31-cm rainfall also occurred during many of the
seepage meter measurements in 1999, resulting in a rapid
increase in discharge to the meters, an effect that has been
recognized elsewhere (Downing and Peterka 1978; Boyle
1994; Sebestyen and Schneider 2001; Rosenberry and
Morin 2004). To allow for the use of the entire 1999 to
2000 data, the 1999 specific discharge data were reduced
by the difference in precipitation between 1999 and
2000—approximately 31% (Simpkins et al. 2001).
The adjusted median-specific discharge during the 2year period was 0.25 lm/s (Table 1), a value similar to
that observed by Lee (1977), Krabbenhoft and Anderson
(1986), and Shaw et al. (1990) for lakes in Minnesota,
Wisconsin, and Alberta, respectively. Significant trends in
the magnitude of specific discharge around the lake were
absent, so no effort was made to assign specific discharge
values to areas of the lake. Seepage meters overwhelmingly showed inflow to the lake. Sites 5, 6, and 17
(Figure 4) showed the highest values, despite the fact that
sites 5 and 6 occur in an area shown by the other two
methods in this study as exit points for ground water.
Four sites showed near-zero net specific discharge and
only four showed negative values at any time during the
measurement period (Table 1). Repeat measurements
made at sites 8, 9, and 10 in 2000 in consecutive 1-h readings indicate no significant difference (a = 0.05) in
median-specific discharge rates. At site 13 (City Beach),
however, median-specific discharge rates increased from
0.13 to 0.60 to 0.88 lm/s in consecutive 1-h measurements. This is not surprising, as the beach was very busy
and recent research has shown that seepage meters are
very sensitive to disturbances of this type (Rosenberry
and Morin 2004).
Extrapolation of individual ground water inflow
measurements to the entire lake was difficult because the
middle of the lake was not sampled. In addition, plots of
specific discharge with water depth or distance from
shore were inconclusive. Studies have suggested that
ground water discharge (log Q) decreases with distance
Table 1
Statistical Summary of Specific Discharge Data Using Adjusted 1999 Specific Discharge Measurements
All (adjusted)
1999 (adjusted)
2000
N
Median
Mean
Standard Deviation
Standard Error
CV (%)
Maximum
Minimum
341
171
170
0.25
0.35
0.17
0.34
0.41
0.28
0.31
0.31
0.30
0.02
0.02
0.02
92
76
109
1.72
1.41
1.72
20.02
20.01
20.02
Note: Values in lm/s. Negative values (N = 4) indicate outflow from the lake.
W.W. Simpkins GROUND WATER 44, no. 1: 35–46
39
from the shoreline (McBride and Pfannkuch 1975; Lee
1977; Brock et al. 1982; Cherkauer and Zager 1989;
Boyle 1994). Other studies have shown the opposite or no
trend (Woessner and Sullivan 1984; Belanger and Mikutel
1985; Krabbenhoft and Anderson 1986). Numerical analyses have also shown that discharge is concentrated near
the shoreline (McBride and Pfannkuch 1975; Fukuo and
Kaihotsu 1988). As an alternative to the method of
Belanger and Kirkner (1994), ground water inflow was estimated using the adjusted median-specific discharge value
and applying it to a percentage of the lake area near the
shoreline. Based on the bathymetry of the lake (Downing
et al. 2001b), the majority of discharge probably occurs
from shore out to a depth of 2.4 m (28.6% of the lake
area; 90,750 m3/d) or perhaps even to 3.1 m (44% of the
lake area; 138,200 m3/d).
The lack of measured outflow in the eastern part of
the lake was a serious drawback to the application of seepage meters in Clear Lake. Lee (1977) believed that meters
would have their greatest use in ‘‘. high to moderately
permeable material’’ presumably where ground water discharge would be uniformly distributed; hence, precise
measurements in fine-grained, low-permeability sediments
could be compromised by lower discharge values and preferential flow out of or into the lake bottom (Lee 1977;
Pennequin and Anderson 1983). It is also possible that
the areas of outflow from the lake are so limited in lateral
extent that they were not identified or not measured.
The most likely explanation, however, is that the
seepage meters were at fault. Clear Lake is a windy, recreational lake. Downing et al. (2001c), citing data from
Bachmann et al. (1994), showed that fishing, swimming,
and pleasure boating activities alone provided 281,000
visitors to the lake during 1991 to 1992. In addition, the
shallowness of the lake (mean = 2.9 m) and wind speeds
up to 27.8 m/s during 2000 can produce waves that resuspend bottom sediment on a regular basis (Anthony
et al. 2001). The net result of wave action on the seepage
meters is production of an airfoil (Bernoulli) effect, which
creates a negative pressure around the seepage bags, allowing the bag to expand and effectively increasing
ground water discharge to the meter (Shinn et al. 2002;
Murdoch and Kelly 2003; Rosenberry and Morin 2004).
Conversely, the process precludes the loss of water from
the bag in areas of outflow, perhaps explaining why no
outflow was measured in seepage meters on the eastern
(outflow) side of the lake. Shinn et al. (2002) suggest that
seepage meters are most reliable in ‘‘. wave-free lakes
and marshes’’ and that data from meters that experience
current or wave action should be ‘‘. viewed with caution.’’ More recent studies have suggested that the bags be
shielded within a chamber to minimize the Bernoulli
effect (Shinn et al. 2002). In short, application of the traditional seepage meters of Lee (1977) was not optimal in
Clear Lake, due most likely to the effect of wave action
generated by wind and boating activities, and the data
should be viewed with caution.
Darcy’s Law
Vertical and horizontal hydraulic gradients at piezometer nests provided strong evidence for the areas of
40
W.W. Simpkins GROUND WATER 44, no. 1: 35–46
ground water flow in and out of Clear Lake. Ground
water inflow dominated at sites A, B, C, H, I, J, and K,
while outflow dominated at sites E, F, and G (Figure 4).
Site D showed ground water inflow and outflow about
evenly during the monitoring period, a phenomena that
reflects movement of the hinge line (separating inflow
and outflow) due to reversals in hydraulic gradient over
time. Water table gradients ranged from 0.005 (site H) to
0.028 (site F) during the study period. Downward hydraulic gradients ranged from 0.001 (site H) to 0.135 (site F),
and upward hydraulic gradients ranged from 0.003 (site
C) to 0.094 (site D). The range of gradients recorded in
135 potentiomanometer measurements in the lake bottom
showed similar, if not slightly greater, values. Upward
hydraulic gradients ranged from 0.0002 (near site H) to
~1 (near site B), and downward hydraulic gradients
ranged from 0.03 (on the sand spit at McIntosh Woods
State Park, west of site B) to 0.74 (near site A). In general, the direction of the hydraulic gradient shown in the
lake sediment was the same as that shown in the piezometer nests. However, there is not a good correlation
between the magnitude of the hydraulic gradients recorded on shore and in adjacent offshore lake sediment.
The difference may reflect the influence of as much as
2 m of sediment deposited in the lake since 1935 on the
till substrate (Downing et al. 2001b).
The geometric mean of horizontal hydraulic conductivity (Kh) from slug tests for all units (N = 33) is
0.26 m/d (Table 2). This value represents Kh in four different lithologies: till of the Morgan and Alden Members,
sand (outwash) of the Noah Creek Formation, loess of the
Peoria Formation, and sandy fill. Geometric mean values of
Kh varied from 0.01 m/d in loess and 0.03 m/d in till to 1.3
m/d in sand and 7.5 m/d in sandy fill. Values of Kh in sand
are most similar to the geometric mean of vertical hydraulic conductivity (Kv) values in lake bottom sediments
(Table 2), although the latter must be viewed with caution
due to the problems noted with the seepage meters (see
previous section). In general, Kh values in shallow, weathered till (<3 m) are 1 order of magnitude higher (0.39 m/d)
than those in deeper (>3 m), unweathered till (0.01 m/d). In
addition to being weathered and containing fractures,
most of the shallow till probably belongs to the sandier
and less compact Morgan Member of the Dows Formation. It is this part of the till that probably has the best
hydraulic connection with the lake. Well-sorted ‘‘clean’’
sand present at sites E, F, and G shows Kh values (18 m/d)
higher than those of silty sand (0.78 m/d). The geometric
mean Kh of materials most likely to be in contact with the
lake at the water table, including both till and sand, was
1.4 m/d—a value similar to the overall Kh of the sand
units and the Kv of lake bottom sediments (Table 2).
The 11 zones delineated around the lake ranged from
280 to 7400 m in length. Sediment thicknesses in those
zones ranged from 2.2 to 9.7 m, with a mean thickness of
6.4 m. These values were used along with horizontal
hydraulic gradient and Kh data to estimate a ground water
inflow of 10,500 m3/d and an outflow of 5000 m3/d. Values of ground water inflow to the lake from this method
are ~1 order of magnitude lower than estimates from the
seepage meters.
Table 2
Hydraulic Conductivity (K) Values for Clear Lake Sediments Estimated from Slug Tests and
Seepage Meter/Potentiomanometer Measurements
Material
All materials
Till
(<3 m)
(>3 m)
All sands
Clean sand
Silty sand
Loess
Sandy fill
Water table piezometers
Lake bottom sediments
(seepage meter and potentiomanometer)
Number of Values
Geometric Mean K (m/d)
Log Standard Deviation
33
13
3
10
18
3
15
1
1
11
26
0.26
0.03
0.39
0.01
1.3
18
0.78
0.01
7.5
1.4
1.4
1.58
0.93
0.39
0.80
1.04
0.15
0.87
N/A
N/A
0.53
1.11
Note: Data from slug tests represent Kh. Data from lake bottom sediments represent Kv. N/A, not applicable.
AE Model
Application of the AE model required additional parameters, including the base elevation and thickness of
the aquifer system, elevations, resistances, and widths of
stream segments, a global ground water recharge rate
(~10% of precipitation during the study period), Kh values, and estimated lake precipitation and evaporation
rates (Table 3). In addition, stage-discharge and stagearea (lake) tables were necessary for the lake package in
the model. A stage-discharge table was created using
stage data from the USGS stage recorder on the lake and
infrequently measured discharge data from Clear Creek
(Kopaska 2002). A stage-area table was created for lake
stages between 373.68 and 373.99 m using bathymetric
maps (Downing et al. 2001b).
Hydraulic conductivity for the entire model was initially set at 4.6 m/d, which is >1 order of magnitude higher
than Kh estimated by slug tests for the till at the lake
but similar to Kh and Kv values in sands and sediments in
and abutting the lake (Table 2). Drainage tiles, which
were not explicitly modeled here because their distribution is not well known in the region, may have the effect
of increasing K at this scale (Haitjema 1995b). The Kh of
the outwash inhomogeneity (Kow) east of the lake was set
initially to 152.4 m/d based on representative values of Kh
in outwash sand elsewhere in Iowa. Two other inhomogeneities were needed in order to accurately reflect the
hydraulic head relationships seen in the field. The K in
sediments beneath the City of Clear Lake (shown as Kcl
on Figure 1) was lowered to 0.15 m/d in order to create
a water table mound beneath the town (Figure 1). Presence of the mound that induces ground water flow from
downtown toward the lake is supported by hydraulic head
data (point O in Figure 4) and data from underground
storage tank sites on file at the Iowa Department of Natural Resources. Another zone of K = 0.46 m/d (Kse on
Figure 1) was placed southeast of the lake where field
hydraulic head data (point Q on Figure 4) suggested
a ground water high in the moraine. Linesink resistances
(Haitjema 1995a) were initially used in all streams but in
the end were applied only to streams in outwash (i.e.,
Willow and Clear creeks). This is probably due to the fact
that stream sediments form the bulk of the stream resistance in high-K sediments such as outwash, while the
‘‘aquifer’’ provides most of the resistance in lower-K sediments such as till.
The initial model solution showed ground water
flowing in on the west, east, and south sides and flowing
out along parts of the eastern edge of the lake, corroborating the overall regional ground water flow directions
depicted in Hershey et al. (1970) and the direction of gradients measured in the field at the piezometer nests.
Using 18 observations of hydraulic head as calibration
points, lake stage was simulated, and the model showed
an average difference of 20.5 m (observed hydraulic
heads slightly lower than those simulated by the model),
mean absolute difference (MAD) of 0.6 m, and mean
squared error (MSE) of 0.9 m. In general, simulated base
flow discharge was close to field-measured discharges
with an MAD of 0.014 m3/s.
The parameter estimation code, UCODE (Poeter and
Hill 1998), was then coupled with GFLOW and used to
determine the optimal set of parameters for the model.
Calibration targets for the parameter estimation consisted
of hydraulic head observations and base flow discharges.
Thirteen near-field streams (Figure 1), including an
unnamed creek entering the southwestern end of Ventura
Marsh, Clear Creek (the lake outlet), Willow Creek (north
and east of the lake), Beaver Dam creek (south of the
lake), and ditches 13 and 18 (west of the lake), were used
as calibration targets in addition to hydraulic head data.
Weights were assigned to each calibration target based on
the uncertainty associated with their field measurements,
similar to the method described in Hunt et al. (2000).
Hydraulic head observations in piezometers, which were
monitored only once per month, were given weights as
standard deviations equal to 0.3 m—a reflection of their
steady-state values over the long term. The more uncertain hydraulic heads (measured only once) in temporary
piezometers and surface water bodies were accorded
W.W. Simpkins GROUND WATER 44, no. 1: 35–46
41
Table 3
Parameters Used in the AE Model
Parameter
Value
Aquifer base
343 m
(above mean sea level)
Up to 91.4 m
Aquifer thickness
(varies depending on
water table elevation)
Global recharge
Initial model
Calibrated model
Global horizontal K
Initial model
Calibrated model
Outwash inhomogeneity (Kow)
Initial model
Calibrated model
8.23 cm/year
9.17 cm/year
(95% CI: 8.23 to
10.22 cm/year)
4.6 m/d
6.6 m/d
(95% CI: 5.5 to
7.9 m/d)
152.4 m/d
136.6 m/d
(95% CI: 116.1 to
160.6 m/d)
City of Clear Lake inhomogeneity (Kcl)
Initial model
0.15 m/d
Calibrated model
0.15 m/d
Southeast inhomogeneity (Kse)
Initial model
0.46 m/d
Calibrated model
0.46 m/d
Streams in near field
Number of gauging sites
29
Near field used for calibration 13
Widths
3 to 10.5 m
Bed resistances, depths
Creeks in till
0 d, 0 m
Clear and Willow creeks
0.3 d, 0.3 m
(in outwash)
Clear Lake
Lake area
1468 ha
Target lake stage
373.82 m
(above sea level;
NAD 83)
Precipitation
74.0 cm/year
Evaporation
88.9 cm/year
correlation between the global recharge, global K, and
Kow, whose final values were 9.17 cm/year, 6.6 m/d, and
136.6 m/d, respectively (Table 3). The new parameter
values were placed into GFLOW, and a final solution was
obtained for the water table map (Figure 5). Simulation of
base flow discharge improved using the new values, and
MAD was reduced to 0.005 m3/s. The unweighted statistics for hydraulic heads (comparing observed hydraulic
heads to those simulated by the model) improved the
average difference to 20.24 m, the MAD to 0.46 m, and
the MSE to 0.82 m.
The final model results also reinforced the general
areas of ground water inflow and outflow shown by the
hydraulic gradients at the piezometer nests. Ground water
enters the lake from the south, west, and north sides
(Figure 5). Piezometer nest D (Figure 4) is near the hinge
line between inflow and outflow regions of the lake;
hence, the direction of flow at this site may reverse seasonally in response to recharge. The model also identified
the major ground water divides in the region, such that
a ground watershed for the lake may be delineated. The
outlet of the lake, Clear Creek, remains dry during the
simulations, which corroborates the field evidence that
it is a disconnected stream under these conditions
(Figure 5). The ground water high that is produced by the
Kse inhomogeneity does force some ground water discharge northwestward toward the lake in a very small
zone; however, particle tracking suggests that flow is diverted along the lakeshore where it joins ground water
that flows away from the lake.
In addition to calculating lake stage, an attractive
aspect of this version of GFLOW is the direct calculation
of a lake water balance. Previous versions of the model
represented lakes as inhomogeneities of high K, which
often work well except in a thin lake in a thick aquifer
(it overstates the transmissivity under the lake) and in
lakes with surface water inflow and outflow (Hunt et al.
2003). Ground water discharge out of high-K lakes was
Note: CI, confidence interval.
a standard deviation of 1.52 m. Streams in the near field
of the model were weighted according to a coefficient of
variation (CV) of 0.2 due to the even larger uncertainty
associated with the single discharge measurement at each
location.
Five parameters (one global recharge and four K values) and 31 calibration targets were entered in the calibration procedure. Calculation of the composite-scaled
sensitivities (Hill 1998) indicated that the model calibration was most sensitive to global K (119.0), global R
(13.5), and Kow (48.7) but relatively insensitive to Kcl
(0.106) and Kse (0.413); therefore, the latter two parameters were omitted during future UCODE runs. The final
optimized solution from UCODE showed no significant
42
W.W. Simpkins GROUND WATER 44, no. 1: 35–46
Figure 5. Contours (m) of the water table in the vicinity of
Clear Lake simulated by the AE model. Main contour interval is 5 m (solid lines) with intermediate contours at 2.5 m
(dashed lines). Lack of contour deflection along Clear Creek
(CC) suggests that it is a disconnected stream (Winter et al.
2002), which is consistent with field evidence.
Table 4
GFLOW Water Balance for the Calculated
Lake Stage of 373.82 m
(above mean sea level; NAD 83)
Category
Inflow (m3/d)
Outflow (m3/d)
Ground water
Precipitation
Evapotranspiration
Channeled streamflow
Total
14,300 (32%)
29,700 (66%)
N/A
900 (2%)
44,900
9200 (21%)
N/A
35,700 (79%)
0
44,900
also calculated as a residual in the water balance equation
(Hunt et al. 2000). The lake water balance from the final
GFLOW solution with the lake element package
(Table 4) indicates that the lake receives slightly more
ground water inflow (14,300 m3/d) than outflow (9200
m3/d). Thirty-two percent of the water arriving at Clear
Lake is from ground water and 66% from precipitation, as
opposed to only ~2% from surface water. Evapotranspiration provides the largest outflow mechanism from the
lake (35,700 m3/d or 79%); ground water outflow is only
9200 m3/d (21%). Under the simulated lake stage, there is
no surface water outflow from the lake. Clearly, this is
a ground water–dominated, flow-through lake under these
conditions, which is consistent with anecdotal evidence
from lakeshore residents, but different from previous
assessments (e.g., Downing et al. 2001a). The latter
included surface water inputs from storm sewers and
drainage tiles that were not simulated in the model
(Kopaska and Knoll 2001). During cooler periods, ground
water that discharges upgradient and collects in wetlands
may also be routed to the lake in channels, a process suggested by Winter (1999).
Summary and Conclusions
The ground water flow at Clear Lake was investigated by three methods reflecting three different scales—
seepage meters (and a potentiomanometer), Darcy’s law,
and an AE model (GFLOW). Estimates of ground water
inflow and outflow from the three methods disagreed, but
were the differences due solely to measurement scale?
The potential effect of scale was evaluated by quantifying
the initial measurement area and the final area after
extrapolation. For seepage meters, 341 measurements of
specific discharge were made initially at the cross-
sectional area of a seepage meter (0.25 m2) and extrapolated to a final area of the lake of 4 3 106 m2 (2.1-m
depth) to 6 3 106 m2 (3-m depth) (Table 5). For the
Darcy’s law method, the initial measurement area was
represented by the length used for the hydraulic gradient
calculation (dl) times the unit width (1 m) perpendicular
to flow at each piezometer where Kh was estimated. Thus,
the initial area for the ‘‘average’’ site was 13.8 m2, which
was extrapolated to a final area around the lake of 2 3
105 m2 (Table 5). For the AE model, measurements and
calibration occur at the scale of the model domain, which
is 7 3 1010 m2 (Table 5), although most of the calibration
targets are at the near-field scale (3 3 1010 m2).
Because the methods differ significantly in their initial measurement and final measurement scales (Table 5),
differences in the values of inflow and outflow to the lake
might be expected due to the propagation of small errors
up to the larger lake area. Errors in seepage meter data,
which have the smallest measurement scale, might be expected to be the greatest when extrapolated to the scale of
the lake. As previously mentioned, the inability of the
seepage meters to identify outflow, and their somewhat
higher value of inflow, suggest that the specific discharge
measurements were inaccurate. In fact, this study suggests that the use of traditional seepage meters is probably not justified in lakes of this type, unless devices are
designed specifically to avoid generating a Bernoulli
effect (e.g., Rosenberry and Morin 2004). The Darcy’s
law method showed reasonable values, particularly given
the uncertain location of zones of ground water inflow
to and outflow from the lake. The goals of this study
could have been achieved using only the Darcy’s law
estimates—an approach that has been used with success
at other lakes (e.g., LaBaugh et al. 1997). If Darcy’s law
is the method of choice, then the inflow and outflow,
hydraulic heads, and K values could be compared to those
from a ground water model.
The AE model is based on a much larger scale and is
relatively free from the extrapolations and uncertainty
inherent in the other two methods. It not only provided
a reasonable estimate of ground water inflow and outflow
at the lake, but it produced a reasonable representation of
ground water flow in the region. The larger-scale view
provided by the AE model also allowed an assessment of
whether the smaller, point-scale measurements might be
consistent within the larger-scale hydrologic system. For
example, the larger ground water discharge predicted by
seepage meter measurements in this study would likely
require greater precipitation and higher hydraulic heads
Table 5
Scales of Measurement and Summary of Inflow and Outflow Data for Clear Lake Using the
Three Methods Discussed in the Text
Method
Seepage meters
Darcy’s law
AE Model
Initial Area (m2)
Final Area (m2)
Inflow (m3/d)
Outflow (m3/d)
0.25
13.8
7 3 1010
4 3 106 to 6 3 106
2 3 105
7 3 1010
90,750 to 138,200
10,500
14,300
None measured
5000
9200
W.W. Simpkins GROUND WATER 44, no. 1: 35–46
43
in the watershed surrounding the lake. These could, in
turn, increase stream discharge to values not supported
by the field evidence. In short, the AE model approach
produces a more holistic view of the regional hydrology.
AE models are a good alternative to the USGS
model, MODFLOW (McDonald and Harbaugh 1988).
Side-by-side comparisons of GFLOW and MODFLOW
results indicate very good agreement between the two approaches (Hunt and Krohelski 1996; Hunt et al. 2003).
AE models have been shown to be useful screening models for MODFLOW (Hunt et al. 1998; Feinstein et al.
2003). The method of simulating lakes in GFLOW,
although not as detailed as the LAK3 package in MODFLOW 2000 (Harbaugh et al. 2000; Merritt and Konikow
2000), appears to provide reasonable results comparable
to those from the previous LAK package (Anderson et al.
2002; Hunt et al. 2003). Data input requirements, setup,
and run time are also modest in comparison to a gridbased, finite-difference model such as MODFLOW. Digital base maps (binary base maps or *.bbm files) can be
downloaded from the U.S. EPA Web site (http://www.
epa.gov/ceampubl/gwater/whaem/us.htm) for most areas
of the United States. Using those and topographic maps
(or digital elevation models), the elevation of stream segments can be entered into GFLOW in a day’s time and the
model can be working in a few days to a week.
The degree of uncertainty in AE model parameters—
a concept somewhat more difficult to apply in the seepage meter and Darcy’s law estimates—was accomplished
by coupling GFLOW with UCODE, a parameter estimation code. Field data were necessary to calibrate the
model and provide that level of certainty; thus, the model
itself should not be viewed as a substitute for field data.
In addition to calculating a lake stage and associated
water balance, the ability of the AE model to identify
ground water boundaries and larger-scale patterns of
ground water flow around the lake make it a more powerful tool than the other methods in this study for future
water quality studies in lakes and streams in glacial terrain. Future work will apply the model to identification
of watershed source areas for nutrients, siting of potential
dredge spoil piles for the remediation phase of the project, and examining the effect of climate change on Clear
Lake.
Acknowledgments
The author acknowledges the dedicated work of graduate assistants Keri Drenner, Tim Wineland, Martin
Helmke, and Carrie Thimmesch and undergraduates David
Hopper, Tamara Ewoldt, and Sarah Fortin on this project.
The assistance of David Knoll of the CLEAR project,
Clear Lake Mayor Kirk Kraft, Jim Wahl of the Iowa
Department of Natural Resources, and Brian Diehl of
WHKS Surveyors is gratefully acknowledged. John Downing provided the necessary funding, seepage meters, and
analytic support via the original Diagnostic and Feasibility
Study of Clear Lake. Jeff Kopaska provided important
stream discharge data. Deb Quade of the Iowa Geological
Survey provided glacial geology maps. Henk Haitjema
44
W.W. Simpkins GROUND WATER 44, no. 1: 35–46
and Randy Hunt provided timely advice on GFLOW and
UCODE, respectively. The modeling portion of this paper
was funded by a grant from USGS through the Iowa State
Water Resources Research Institute. Donald Rosenberry,
Matthew Becker, Charles Dunning, and Randy Hunt
provided helpful critical review of the manuscript.
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