Environmental Engineering Reference
In-Depth Information
to that of the surface-flow terms and often
insignificant relative to measurement errors
of surface flow. Rantz (
1982
) provides a simple
formula for estimating Δ
S
sw
for the case where
stream stage changes over the course of a dis-
charge measurement. Hence, application of the
surface-water budget methods usually is based
on a simplified form of Equation (
4.2
):
is accurate, then
Q
seep
in Equation (
4.3
) must be
substantially larger in magnitude than 2.2% of
the sum of the magnitudes of all other terms
in the equation in order to provide some con-
fidence in its value. As such, application of the
method is limited to relatively small streams.
For large streams, errors in discharge meas-
urements may mask any gains or losses. For
example, consider a 1-km reach of stream that
loses 0.2 m
3
/s (
Q
seep
= -0.2 m
3
/s) and has no tribu-
taries. If measured
Q
sw
in
= 1 m
3
/s and
Q
sw
out
= 0.8
m
3
/s, then the estimated value of
Q
seep
would be
0.2 ± (1.8 × 0.022 = 0.04) m
3
/s or 0.2 ± 0.04 m
3
/s. If,
on the other hand,
Q
sw
in
= 100 m
3
/s and
Q
sw
out
=
99.8 m
3
is the estimated value of
Q
seep
is still 0.2,
but the error bounds are ± 199.8 × 0.022 = ± 4.4
m
3
/s. Obviously, little reliability can be placed on
the estimate in the latter case. Turco
et al
. (
2007
)
deemed seepage rates to be acceptable only if
they exceeded 10% of the sum of upstream
and downstream measured discharges on the
Brazos River and tributaries in Texas.
The stream water-budget method is usu-
ally applied to estimate focused recharge from
losing streams. However, if a stream reach is
found to be gaining, the gain in base flow can
be attributed to diffuse recharge occurring in
the areas of the aquifer that contribute to base
flow. Accurate delineation of these contributing
areas is not always a straightforward endeavor,
but it can be accomplished in some situations,
the simplest case being that of the upper end of
a watershed to which there is no surface inflow
and all measured flow at a gauging site can be
attributed to diffuse recharge over the surface
area draining to that site.
Ideally, flows in Equation (
4.3
) are measured
simultaneously; however, this is often difficult
to accomplish in practice. A long lapse between
measurement times can result in additional
uncertainty in seepage estimates. Among other
limitations of the stream water-budget method,
identifying and accessing locations suitable
for discharge measurements can be difficult.
Substantial resources can be required, espe-
cially if manual discharge measurements with
conventional velocity meters are required; these
measurements are labor intensive. The seepage
estimates determined apply only to the period
Q Q
=
sw
− −
QQ
sw
in
(4.3)
seep
out
trib
The procedure is to make simultaneous dis-
charge measurements at the upstream and
downstream ends of a stream reach and on
any tributaries that empty into that reach. This
approach is sometimes referred to as a seep-
age run and is often used in hydrologic studies
(e.g. Donato,
1998
; Dumouchelle,
2001
; Simonds
et al
.,
2004
; Turco
et al
.,
2007
). Discharge meas-
urement can be made directly with a current or
velocity meter or by installing a flume or weir
and monitoring stream stage (
Section 2.3.4
).
Oftentimes measurements are made at multiple
points on a stream to identify losing and gain-
ing subreaches within the reach of interest.
For a losing stream, the stream water-
budget method provides a direct measurement
of focused recharge that is integrated over the
length of the reach; within that reach there can
be gaining and losing subreaches. Data obtained
from seepage runs can be useful for calibration
of groundwater flow and watershed models
(
Chapter 3
). Because uncertainties in discharge
measurements are fairly well understood, error
bounds in recharge estimates can be calcu-
lated. Rantz
et al
. (1982), following the analyses
of Carter and Anderson (
1963
) and Carter
et al
.
(
1963
), determined that the standard error
for an average discharge measurement with
a conventional current meter was 2.2%. Rantz
et al
. (1982) also implied that discharge deter-
mined from a stage-discharge rating curve is,
at best, within 5% of measured discharge. The
US Geological Survey rates a streamflow gaug-
ing station's record as excellent if 95% of aver-
age daily flows are considered to be within 5%
of true values. Oberg
et al
. (
2005
) suggested that
acoustic velocity current profilers be calibrated
to within 5% of known discharge at a test loca-
tion annually. If the smaller error term (2.2%)
