Notes
1787
Limnol. Oceanogr., 37(8), 1992, 1787-1795
0 1992, by the American Society of Limnology and Oceanography, Inc.
Seepage meter errors
Abstract-Although the seepagemeter has been
widely used in limnology, measurement errors
are commonly ignored. These errors result in the
need for meter correction factors due to flow field
deflection and frictional resistance and head losses
within the meter and prefilled bags to avoid shortterm influx of water caused by the pulling action
of deformed bags. Tank-test data indicate a ratio
of measured to actual inseepage of 0.77 (at inseepagerates < 20 mm h- I), with a ratio of meter
to interstitial seepageflux of 0.50. Provided these
precautions are observed and the adjustment factor is applied, field test “point estimates” of seepage inflow with replicate seepagemeters generally
have relative root-mean-square error(s) ~20%.
Data from measurements at single locations in
tank tests indicate a constant bias and show that,
once installed, the actual instrument error is even
less (w 5%). These errors are small compared to
spatial and temporal components of sampling error typically encountered in the field.
Groundwater seepage estimation has relied primarily
on indirect
techniques.
Groundwater flow near bodies of water can
be complicated, and serious misinterpretation of the interaction of water bodies and
groundwater can occur due to errors in estimating geological boundaries, hydraulic
conductivities,
and hydraulic
gradients
(Winter 1976, 1978, 198 1, 1983). The seepage meter (Lee 1977) allows direct measurement of seepage flux. Our objective here
is to clarify device and spatial sampling errors associated with use of seepage meters.
Any hydrologic budget includes instrumental (device) errors and both spatial and
temporal components of sampling error. The
former result from measurement with imperfect instruments while the latter result
from estimating fluxes in a time-space continuum from site-specific point data (Winter 198 1). Meter (device) errors can only be
quantified through tank testing under known
conditions. Early tank tests were conducted
by both Lee (1977) and Erickson (198 1) under various hydraulic gradients (- 0.07 l0.120) and flow rates (-3.6-7.2
mm h-l).
For the range of rates tested, close linear
relationships were found between the quan-
tity of upward seepage (r > 0.96) and downward seepage (r > 0.98) measured by the
meter and the magnitude of the hydraulic
gradient through the tank. However, the
slopes for the regression lines varied with
tank location, probably due to heterogeneity
in the test tank (Lee 1977).
Erickson (198 1) stated that seepage meters disturb the flow field in which they are
installed, resulting in consistent but lower
measured seepage. This disturbance is apparently related to frictional resistance along
the internal boundaries of the meter and
plastic reservoir bags and head loss induced
at the tubing orifice. An investigation of bag
type indicated it was not a significant factor,
but prewetting the bags with - 1 liter of water consistently resulted in more accurate
results. Inflow may be induced in the plastic
bags in response to deformation and subsequent “relaxation”
when submerged (Erickson 198 1). Shaw and Prepas (1991) also
reported an anomalous, short-term influx
of water to plastic bags attached to seepage
meters; the effect was eliminated when bags
were prefilled with 1,000 ml of water.
Our tests provide more rigorous and
comprehensive data on the accuracy and
precision of the meters under various hydraulic gradients and flow rates commonly
encountered in Florida water bodies. Seepage was generated inside a cylindrical fiberglass tank (Fig. 1). A 19-liter bucket served
as a constant-head reservoir; flow into the
bucket was stabilized by the pump and kept
large enough so that there was always overflow through the outlet near the top of the
bucket. A 2.5-cm-diameter
PVC pipe provided connection from the outlet at the bottom of the bucket to the tank inlet at the
center of the tank bottom. An open space
of - 3 cm was left between the tank bottom
and the first layer of fill to create a uniform
head across the bottom of the tank. A grate
(a plywood sheet perforated with 1.3-cmdiam holes spaced - 10 cm apart) was placed
4 cm above the bottom of the tank. The
grate was supported by 4-cm-wide boards
Notes
1788
1g-liter
U-Tube
Manometer
Test tank L
I
-
t
I
183cm
i
Ah
20 cm water
T
122cm
I
fi. .-.&I-...
b
c
Concrete Pad
L Grate
2.5-cm-diam
PVC Pipe
/
L 3.2-cm-diam
Flexible Pipe
Electric Water
Pump
F‘rom Well
Fig. 1. Tank test setup.
laid out in radial pattern to allow flow to
move outward from the center. On top of
the grate, a 15-cm layer of coarse, drainfield gravel was distributed, followed by another 1%cm layer of finer gravel. Finally, a
60-cm layer of sand (Table 1) was placed
on top of the gravel.
The outlet from the tank was located on
its side, near the top, allowing -20 cm of
water to stand above the top of the sand
layer when the tank was full. The overflow
from the tank was allowed to free fall into
a catchment where it entered the drainage
system. The overflow could also be collected in a volumetric container to calculate the
flow rate leaving the tank. Average rate of
seepage through the test tank was calculated
by measuring flow rate through the tank
Table 1. Particle-size distribution
ment.
of tank sedi-
Mean grain diam
(mm)
Fraction
Classification
0.03 l-0.062
0.062-o. 125
0.125AI.250
0.250-0.500
0.500-l .ooo
0.01
0.11
0.70
0.14
0.03
Coarse silt
Very fine sand
Fine sand
Medium sand
Coarse sand
outlet and dividing by the cross-sectional
area of the tank (2.63 m2).
The flow rate through the tank could be
controlled by adjusting the head difference
between the inlet reservoir and the free surface in the tank (Ah in Fig. 1). The head in
the surface water was essentially constant
because the position of the tank outlet was
fixed, but the head at the bottom of the tank
could be adjusted by increasing or lowering
the elevation of the inlet reservoir (Fig. 1).
After experiment 1 (see below), the tank was
covered to shield it from the wind because
wind stress caused errors in the measure of
outflow (actual seepage). The tank was allowed to run undisturbed for at least 3 h
before outflow measurements were taken.
The outflow from the tank was measured
repeatedly to ensure that a constant flow
rate had been reached.
Seepage meters used in our tests were constructed according to Lee (1977) with slight
modifications.
The body of a meter was
made by cutting off the end of a 2.1 -m3 steel
drum (0.257 m2). A hole, drilled into the
top of the meter, accommodated a cored
rubber stopper fitted with a hard polyethylene tube (5.6-mm i.d., 8.3-mm o.d.)
through its center. This tube served as the
Notes
connection point for the collection bag,
which acted as a seepage reservoir. The open
end of a 4-liter plastic bag was connected
to a piece of hard polyethylene tubing by a
rubber band. The tube from the collection
bag was connected to the meter outlet tube
with a piece of flexible Tygon tubing (6.7mm i-d., 10.2-mm o-d.). When the meter
was ready (>3 h), 1,000 ml of water was
funneled into an empty reservoir bag. The
timing for the test began when the bag tube
was connected to the meter outlet tube. After a suitable period, the bag was removed
from the meter and the water in the bag was
measured in a graduated cylinder. The seepage inflow or outflow is expressed in liters
m-2 h-l (eq uivalently mm h-l).
Three separate sets of tests (experiments)
were performed with the test tank. Experiment 1 was designed to assess the uniformity of flow in the tank and to pinpoint any
problems with the seepage meters. In this
experiment the same meter was used to
measure seepage at 13 different locations
covering most of the tank (Fig. 2a). As a
measure of pure device error, two measurements were taken at each location, the second immediately
after completion of the
first.
In experiment 2, three different meters
were installed at the locations corresponding to 3a, center, and 7a in Fig. 2a, and left
there for the entire series of tests. To further
test the precision of the measurement procedure after installation,
we measured the
seepage rate through each meter separately
at different times and then simultaneously
at all three locations. Each measurement was
made twice, as in the first experiment. The
tests were performed twice with average
seepage rates (calculated from the tank total)
of 9.5 and 18.5 mm h-l, respectively.
Flow variation in the test tank was assessed further in experiment 3. Seven meters (Fig. 3) permitted seepage across the
area of the tank to be measured completely
in one simultaneous measurement test. Four
different tank-mean flow rates were tested,
ranging from 4.6 to 28.8 mm h-l. Two measurements were taken from each meter for
each flow rate. One measurement was taken
from each meter individually
while the other meters were left undisturbed, followed by
1789
another measurement taken from all seven
meters simultaneously.
Although care was taken in designing and
building the test tank, sediment heterogeneity or inflow short-circuiting
caused considerable variation in the flow rates measured at different locations in the tank (Fig.
2b). Flow variations due to the test setup
thus had to be separated from measurement
variations due to the meter itself. This separation was achieved by comparing variation in seepage rates measured among locations and comparing
the average of
seepage measurements across the tank to
the measured seepage.
In experiment 1, the measured seepage
rates ranged from 2.1 to 15.7 mm h-l, with
a mean value of 6.0. The variation in replicate measurements taken at the same location, however, was consistently small (Fig.
2b), indicating the variation was due to conditions in the tank and not the measurement
device. For the 13 pairs of duplicate measurements (Exp. l), the relative difference
between pairs of measurements averaged
6.2%. Seepage values measured in experiments 2 and 3 for the same location and
driving head also exhibited small variation
(Fig. 4) with average relative differences of
1.5 and 4.1% between pairs of measurements, respectively. The seepage rates measured at each meter location were regressed
against the total head difference used in each
test (Figs. 5, 6). Although the rates of seepage varied from one location to the next, as
evidenced by the differing slopes of the regression lines, the correlation between head
difference and seepage for each location was
very high (r > 0.99). This finding verifies
the previous conclusion that the distribution of seepage flow in the tank was not
uniform.
Accuracy of the meters was estimated in
tank experiment 3 by comparing the average seepage rate measured by the meters to
the actual average seepage rate determined
by measuring the outflow from the tank (Fig.
6). At the highest flow rate, the flow rate
measured through the tank appears to have
deviated from its linear relationship with
head difference. However, when only the
first three data points are considered, the
regression analysis indicates an almost per-
1790
Notes
(a)
8a *.
jb
*.*.
.*
‘.‘. ::.
5a .. ... . . .
Outlet [ ..... ... . la ... . jb..($&..5b r..5b . .... 5a
(W
16 ,
I
. 30
8
6
la
2a
3a
4a
5a
6a
7a
8a
lb
3b
5b
7b
c
Meter Location
Fig. 2. Seepage meter test locations used in experiment 1 (a) and comparison of duplicate seepage rates at
each location at a head difference of 3.94 (b).
feet linear relationship (r = 1.00; n = 56)
between head difference and flow rate, with
a slope of 3.08 mm h-l cm-l and an intercept of 0.26 mm h-r. When the last point
is included in the linear regression, the slope
increases to 3.67 mm h-l cm-l, the intercept is lowered significantly to - 1.46 mm
h-l, and the correlation coefficient is low-
ered slightly (Y = 0.99). The offset of the last
point could be due to measurement error or
to nonlinear effects in the tank such as channelization of flow.
The relationship between the average meter seepage rates and head difference was
linear, as regression analysis of these data
yielded a correlation coefficient of r = 0.998
Notes
Fig. 3. Meter measurement locations used during
tank experiment 3 (seven meters cover 68% of the tank
area).
(n = 56) and a slope of 2.3 1 mm h-l cm-l.
The average seepage rates in the tank in this
experiment were 4.6, 12.7, 18.3, and 28.8
mm h- l, for which the average seepage meter values were 77, 76, 78, and 64% of the
respective average rates in the tank. The
decreased ratio at the highest flow rate may
1791
be due to increased deflection of the flow
field around the seven meters because of
increased resistance to flow by the tubing
and meter.
Further analysis was completed to determine if the ratios of measured to actual
seepage in experiment 3 were biased due to
the large fraction (68%) of tank area covered
by the seven meters. In experiment 1, at a
head difference of 3.94 cm and a seepage
rate of 12.0 mm h- l, the mean seepage rate
determined from one meter positioned at
13 different locations was 57% of the calculated interstitial seepage rate (seepage rate
of the uncovered sediment). This ratio is
less affected by site-specific location effects
in the tank than is the meter:tank ratio. In
experiment 3, with seven seepage meters in
place, the measured mean seepage rate at
head potentials of 1.40, 4.06, and 5.84 cm
represented 5 1, 50, and 47% of the calculated interstitial
seepage (seepage rate between meters). These percentages were calculated from experimental data where actual
seepage rates varied from 4.6 to 18.3 mm
h- l. At a higher head potential (7.87 cm)
and seepage rate (28.8 mm h-l), however,
40
I
0
Individual, tank seepage = 9.5 mm h-’
m
Simultaneous, tank seepage = 9.5 mm h-’
I
Individual, tank seepage = 18.5 mm h-’
3a
Center
Meter Location
7a
Fig. 4. Comparison of seepagerates measured in experiment 2 at sites 3a, center, and 7a. Results are presented
for measurements made sequentially (one meter at a time) and simultaneously at actual tank seepage rates of
9.5 and 18.5 mm h-l.
1792
Notes
Table 2. Comparison of experiment 1 and experiment 3 mean seepage rates (mm h-l) at similar tank
locations and the same head difference (3.94 cm). Tank
locations in parentheses (cf. Figs. 2a, 3).
c.v.96
Exp. 1
15.8 (3a)
8.3 (7a)
8.2 (2a, 8a)
5.3 (4a, 6a)
2.9 (c)
0
0
1
2
3
4
5
6
7
6
Exp. 3
21.1 (2)
7.4 (5)
ll.O(l + 6)
5.3 (3 + 4)
4.6 (c)
Head Difference (cm)
C.V.% (among locations)
59.9
68.3
(between
experiments)
20.3
8.1
20.6
0.0
32.0
R = 16.3
R = 64.1
40
'i
r
E
L
30
iti
f
KJ
20
10
0
0
1
2
3
4
5
6
7
6
7
8
Head Difference (cm)
0
1
2
3
4
5
a
Head Difference (cm)
Fig. 5. Measured seepage vs. tank-head difference
in experiment 3.
the ratio of measured to interstitial seepage
dropped significantly (to 36%). These data
indicate that, except at the higher seepage
rate (28.8 mm h-l), the measured seepage
was a similar percentage of the interstitial
or unmeasured seepage in both experiment
1 and 3 (47-57%). This variation was even
less (0.50-0.57%) at similar head potentials
(3.94 cm, 4.06 cm).
The relatively stable measured : interstitial ratio indicates that coverage effects from
the seven meters in experiment 3 did not
significantly bias the results at normal seepage rates. At the highest seepage rate, effects
discussed above increased greatly, increasing the seepage between meters and changing the correction factor. Although further
testing should be done to determine the
source of this decrease in accuracy, it appears that the meter: tank and meter: interstitial seepage rate ratios of 0.77 and 0.55,
respectively, are accurate for normal seepage rates encountered in the field (O-20 mm
h-l). The 0.77 meter : tank flux ratio is similar to the average ratio (0.76) found in tank
tests by Erickson (198 1) at various flow rates
(6.3-61.9 mm h-l) with the same seepage
meter design used in our study. The importance of prefilled bags was discussed earlier.
In all experiments, the meters and sediment were allowed to equilibrate and settle
for several days prior to measurement to
minimize
insertion effects. Seepage data
from experiment 1, where only one meter
was used at a time, and experiment 3, where
seven meters were used simultaneously, were
compared under similar head values (Table
2) to determine if the true variance at a point
arose primarily
from changes in the hydraulic conductivity of the substrate accompanying meter insertion (installation error).
Meter sites 2, 5, 1 and 6, 3 and 4, and center
in experiment 3 (Fig. 3) correspond closely
to locations 3a, 7a, 2a and 8a, 4a and 6a,
and center, respectively in experiment 1 (Fig.
2a). Experiment 1 measurements were run
at a slightly lower head potential (3.94 cm)
Notes
0
Average Tank Seepage Rate
0
Average of Seven Meter Seepage Rates
1793
Possible Outlier
Head Difference (cm)
Fig. 6. Average meter seepage and average tank seepage vs. tank-head difference in experiment 3. Dotted
line represents correlation of average tank seepage and head difference when all data points are included; one
solid line (0) represents the correlation of average tank seepage and head difference when the possible outlier
is omitted; the other solid line (0) represents correlation of meter seepage and head difference.
than experiment 3 (4.06 cm). After adjusting for this 3% head difference, data from
the two experiments were compared. The
cross-experiment
coefficients of variation
(C-V.) at these five locations ranged from 0
to 32%. The average C.V. (between experiments) was 16%. Slight differences in meter
locations in the two experiments may have
contributed to this variation. The cross-site
C.V.s from the same two experiments were
60 and 68% (Table 2), illustrating that even
within the small tank, location effects are
much more important than meter insertion
effects.
In general, data from tank tests indicate
relative root-mean-square
(rms) errors for
measurements are <5% at a particular location once a meter is installed. The meter
insertion error is larger but still < 20%. These
device errors are small compared to spatial
and temporal components of sampling error
typically encountered in the field. Data from
120 measurements at duplicate meters located at five locations along a 3-km transect
in the Indian River lagoon also indicate ex-
cellent field precision, particularly considering that field problems such as clogging of
tubing, incomplete sealing in the sediment,
etc. may have caused wide variations in
some duplicate meter data. At these sites,
the rms relative difference between adjacent
meters (12%) was small compared to mean
square variability over time (108%).
Although the variable nature of the seepage rates in the tank tests were not expected,
the highly nonuniform moisture and solute
transport in sandy soils has long been noted.
Research by Glass et al. (1989a,b) shows
how wetting front instability occurs when
water infiltrates into an unsaturated porous
medium. When a wetting front becomes unform and move down
stable, “fingers”
through the vadose zone bypassing much of
the unsaturated medium. Heterogeneities
cause the merger of fingers and the formation of faster, wider fingers, a process not
accounted for directly in the linear theory
(Glass et al. 1989a,b). Although Glass et al.
discuss how a wetting front moves through
unsaturated soil, it is known that these pre-
18 19 20 21 22 2324a24b25
26 2728a28b2930
31
Distance (m)
Fig. 7. Location, depth, and mean seepage rate for each meter in a transect across Indian River lagoon near
Jensen Beach, Florida.
ferred paths of flow persist after the medium
is fully saturated and this phenomenon may
have contributed to the tank test variability.
Although the tank test variability
discussed above cannot be easily generalized
to actual field situations, it illustrates the
location-specific
variability problem in using seepage meters. Localized variations in
seepage rates over short distances have been
documented in field studies (e.g. Belanger
and Walker 1990; Brock et al. 1982; Isiorho
and Matisoff 1990; Shaw et al. 1990).
For example, data from 33 seepage meters positioned along a 3-km transect across
the Indian River lagoon showed site seepage
rates varying from -0.0 13 to 5 5.2 liters mm2
h-l (Fig. 7) (Belanger and Walker 1990). In
Mountain Lake, Florida, a 43-ha lake in
which 47 seepage meters were placed, maximum site-to-site variation of - 5.1 to + 1.2
liters m-2 h- l was measured (Belanger unpubl.). The large variations in seepage in the
two bodies of water were not expected based
on adjacent well and hydrogeologic data,
but they are reasonable considering the variety of factors influencing groundwater flow
near water bodies and the well-known occurrence of natural springs. In particular,
the distribution
of groundwater
seepage
across the sediment surface is greatly influenced by “leakance” (hydraulic conductivity/thickness) of the benthic sediments and
water-table
configuration
(Winter 1976,
1983; Winter et al. 1988; McBride and
Pfannkuch 1975).
Although tank test results discussed here
have established seepage meters as precise
measurement devices with relatively constant bias, there is considerable uncertainty
and misunderstanding
about the design of
seepage meter studies and the interpretation
of data to obtain useful water budget information. Generally, temporal variability
is
much less than site-to-site variability (Brock
et al. 1982; Belanger and Walker 1990), and
this should be reflected in the sampling design. Due to the complexity of groundwater-surface water interactions
and variations in the direction and magnitude of
seepage rates recorded in a single water body,
special concern must be placed on extrapolation of seepage data for entire systems
based on a limited number of seepage meters. It is imperative that whole-lake seepage
estimates be made from a large data set obtained from sites throughout the water body.
Notes
T. V. Belanger
M. T. Montgomery
Department of Oceanography, Ocean
Engineering and Environmental
Science
Florida Institute of Technology
Melbourne 32901-6988
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Submitted: 12 December 1990
Accepted: 29 January 1992
Revised: 16 July 1992