Environmental Engineering Reference
In-Depth Information
heads and temperatures are set equal to meas-
ured values and are allowed to vary over time,
usually over periods of about 15 min for match-
ing diurnal patterns and days or weeks for
matching annual patterns. The bottom bound-
ary can be represented by a specified pressure
head (corresponding to a measured water level)
or a free-drainage condition and a specified or
variable temperature. Simulated temperatures
are compared with measured temperatures
at various depths. Because simulation results
are more sensitive to hydraulic properties of
sediments than to thermal properties, thermal
properties are held constant. Model calibration
consists mainly of varying hydraulic proper-
ties, either manually or automatically, to obtain
agreement between simulated and measured
subsurface temperatures. Fluxes to or from the
stream are calculated by the calibrated model.
Analytical solutions to the heat-flow equa-
tion also can be used to estimate the rate of
exchange of ground and surface waters through
a streambed (Silliman
et al
.,
1995
; Keery
et al
.,
2007
; Schmidt
et al
.,
2007
). These methods
require temperature histories in the streambed
and at least one depth beneath the stream.
Hatch
et al
. (
2006
) developed an approach that
does not require streambed temperatures. The
method requires temperature histories at two
depths and analyzes the attenuation of the
phase and amplitude of the diurnal tempera-
ture pattern between the two depths. Assuming
a sinusoidal upper temperature boundary, the
Stallman (
1963
) solution to the heat-flow equa-
tion is applied; the solution is optimized to
find the drainage rate that best reproduces the
attenuation of the temperatures between the
two measurement depths.
Distributed temperature sensors described in
Section 8.2.1
have been employed in a few hydro-
logic studies. Lowry
et al
. (
2007
) used a DTS sys-
tem to obtain temperature measurements along
a 650 m reach of Allequash Creek in northern
Wisconsin. Quantitative estimates of exchange
between surface and groundwater could not be
made, but on the basis of the daily range in meas-
ured temperatures, zones of groundwater dis-
charge to the stream could be identified. Westhoff
et al
. (
2007
) used a DTS system to measure stream
temperatures along a 580 m reach of stream in
central Luxemburg. These data were used to cali-
brate a stream energy-budget model that gener-
ated estimates of groundwater discharge rates
along the reach. Model results were similar to
those determined with a stream water-budget
method, but processes that are not included in
the model, such as shading of the stream and
sudden changes in weather conditions, can affect
measured stream temperatures.
Example: Rillito Creek, Tucson, Arizona
Rillito Creek in southeastern Arizona displays
a flow pattern that is typical for many streams
in the arid and semiarid southwestern United
States. For most days of the year there is no
flow in the stream. Following periods of pro-
longed rainfall or snowmelt, water flows in the
stream for periods of several hours to several
days. Ephemeral streams such as Rillito Creek
are often an important source of recharge for
underlying groundwater systems. An extended
effort to quantify drainage rates from the creek
was undertaken by Hoffmann
et al
. (
2003
,
2007
)
and Blasch
et al
. (
2006
). Several different meth-
ods were used to estimate the rate of movement
of water from the stream to the underlying
aquifer, including a heat-transport method,
a stream water budget, chemical and isotopic
tracers, and a temporal gravity method.
A two-dimensional array of temperature and
water-content sensors was installed on a tran-
sect beneath and perpendicular to the stream
channel (Hoffmann
et al
.,
2007
). Sensors were
installed at seven depths (ranging from 0.5 to
2.5 m) at four points on the transect, separated
by a distance of 3 m. Data indicated that hori-
zontal water movement was insignificant, so
a one-dimensional water- and heat-transport
simulation using the VS2DH model (Healy and
Ronan,
1996
) was constructed for each of the
four locations for each period of streamflow.
Simulated temperatures were in good agree-
ment with temperatures measured in April 2001
(
Figure 8.6
); the model-calculated infiltration
rates were similar for the four locations, aver-
aging 0.32 m/day for this period. The authors
calculated an average volumetric flow rate per
unit length of stream channel by multiplying
