Evaluation of Vertical Temperature Profiles
in a Streambed
April 25, 2012
Geology 492
Joshua E. Smith
1831 Muscovy Way,
Seneca, SC 29678
jes@clemson.edu
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Abstract
The objective of this project is to characterize the distribution of temperature
in streambeds and evaluate the feasibility of using this characterization to estimate
groundwater discharge. The affect of groundwater discharge on the streambed
temperature was evaluated, so measuring the temperature profile may allow the
discharge to be estimated.
Project methods include constructing a probe to measure the temperature at
different depths in a streambed and then deploying the probe in the field. The
thermistors were proven to be accurate within ±0.2°C. The equilibration time of the
probe was calculated to be less than 200s. A location in Pickens, SC was chosen for
testing.
The results show that the temperature of a sandy streambed is variable in
the upper 0.45 meters and decreased linearly after this depth. The surface
temperature was determined to change hourly and diurnally. COMSOL Multiphysics
was used to model the subsurface temperature pulse created by the surface water in
the streambed.
Pan and bag seepage meters were used to determine groundwater discharge.
The maximum groundwater flux discharging into the river was 1.14E-5 m/s. This
value will serve to validate ongoing estimates of groundwater flux based on
temperature profiles.
Key Words: thermistor, water temperature, baseflow, seepage, groundwater, Darcy
velocity
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Introduction
Groundwater temperatures maintain a relatively constant temperature
throughout the year, while surface water temperatures fluctuate throughout the
year (Kalbus et al. 2011). In the winter, the groundwater will be warmer than
surface water and visa-versa in the summer (Carey and Bilhimer 2005). This
difference in water temperature, and the thermal properties of the subsurface,
create unique vertical temperature profiles. The streambed temperature will
change at various rates depending on the rate of interaction between groundwater
and surface water. If there is no interaction between groundwater and surface
water, the streambed temperature changes linearly as a function of depth. The
higher the rate of groundwater discharge, the greater the curvature of the vertical
temperature profile. This is shown in Figure 1. If this were a losing stream, the
graphs would have negative curvatures.
Figure 1: Theoretical model of vertical temperature profiles in a streambed
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Oberg et al. (2011) and Caray and Bilhimer (2005) used thermistors to
measure how a canal’s temperature may be affected by the reversal of water flowing
through the canal. Craig (2005) used thermistors ands thermocouples to measure
the groundwater discharge rates of streams. In these previous studies, piezometers
were installed and left in the streambed. This could prove time-consuming. For this
research, a handheld probe was constructed to protect a series of thermistors. A
multimeter was then used to measure the resistivity of the individual thermistors.
The probe was designed to allow for quick results during field-testing.
The probe was created using a series of soldering and metal working
techniques. A handle was added to the probe to allow for easy insertion into a
streambed. The thermistors were then calibrated using a water bath and ambient
air temperatures. The accuracy of the device was determined before field tests were
conducted.
A location along Twelve Mile River, Pickens, SC was chosen for field-testing.
The river at this location had a shallow streambed of unconsolidated sand. The field
site was roughly 100m downstream of Lay Bridge.
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Figure 2: Location of field site along Twelve Mile River
Field tests were conducted to test the feasibility of using the probe to
characterize the groundwater discharge rates of a stream. A vertical profile of the
temperature of the streambed was created to show the spatial change in a
streambed. The effect of the changing surface water temperature on the streambed
profiles needed to be checked. The temporal variation of temperature was
measured by creating vertical temperature profiles at one location during 3
different times of the day. In order to understand how the surface water
temperature changes over a longer period of time, the surface water temperature
was recorded for 1½ months.
The effect of the changing surface water temperature on the streambed was
determined using COMSOL Multiphysics. The properties of the water and the
subsurface material were input to show the propagation of the surface water
temperature through the subsurface. At times the surface water stayed relatively
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constant, allowing for the groundwater discharge rate to be calculated. The rates
recorded using the probe were compared to rates measured using a seepage meter
from previous testing
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Materials and Methodology
Micro-BetaCHIP Thermistors were chosen for this research. This brand was
chosen as the instruments provide a fast response time at an effective temperature
range of -40°C to 125°C (Measurement Specialties 2008). The expected
temperatures of the environment are included within this range of temperatures.
The thermistors were soldered to CAT 5e 24 AWG braided cable. These
seven feet unshielded cables had banana plugs secured to the opposite end of the
wires. Heat shrink tubing was then applied over the individual solder joints. The
pair of joints had an adhesive lined heat shrink tube applied to provide further
insulation.
A stainless steel wire was formed into a loop, allowing the thermistor
terminal to be secured inside the loop with thermally conductive epoxy. The ends of
the wire were connected to the stainless steel rod using strong glue. The stainless
steel was then bent to maintain a constant connection with the inner diameter of the
probe. This was done for a total of six thermistors. Starting at one end of shaft, the
thermistors were set in intervals of 0.0 ft, 0.5 ft, 1 ft, 2 ft, 3 ft, and 3.5 ft. An
aluminum cap was placed on the end of the rod to be inserted into the sediment.
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Figure 3: Inner construction of thermistor probe
Once the probe was constructed, the thermistors were calibrated by a series
of water baths and tests at ambient air temperatures. A total of 11 tests were
conducted for each thermistor. The accuracy of the thermistors was determined by
the summation of the maximum error of the thermistors, the multimeter, and the
calibration of the probe.
In order to determine the equilibration time necessary for the thermistors,
the resistance of the thermistors was initially recorded at air temperature. The
probe was then inserted into the streambed and the resistance of the thermistors
was recorded as a function of time. This testing was done roughly 100m south of
Lay Bridge.
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Figure 4: Model of a seepage meter
A seepage meter was used to determine the discharge rates at the field
location. The seepage meter consists of a collection pan protected by a carapace and
a collection bag attached to the pan. The pan is pushed into the streambed, which
along with the carapace, blocks the streamflow. Any water that enters the pan flows
into a collection bag. Using the geometry of the pan and the time the seepage meter
is allowed to collect water, the groundwater flux was calculated. The equation is
shown in Figure 5, where: q is the groundwater discharge, ΔV is the volume of water
collected over time t, and A is the area of the collection pan.
Figure 5: Groundwater discharge from a seepage meter
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A profile perpendicular to the flow of Twelve Mile River was created to test
how the groundwater discharge rate changes spatially. Vertical temperature
profiles were collected in 1ft increments from the river-right to the river-left banks.
In order to test temporal variations in the streambed temperature, a site was
marked in the river and the streambed temperature was measured at 3 different
times of the day. Measurements were taken at in the morning (9:45 am), midday
(1:30 pm), and dusk (7:15 pm). This tested the hourly temperature change.
A HOBO temperature logger was placed into the river to measure the
temperature change of the surface water over 1½ months. The logger was placed in
a shaded location of steady streamflow. This data was then input into COMSOL
Multiphysics to determine what effect the changing surface water temperature may
have on the vertical profiles. The change in subsurface temperature was modeled
using the thermal conductive properties of a poorly sorted, medium-grain sand
matrix. This theoretical model was then compared to field results.
Vertical profiles were taken during times of relatively constant surface water
temperatures. These could be used to estimate groundwater discharge. The data
points collected in the field were inserted into Microsoft Excel. Using Solver, curves
were fitted to the data. Using the dimensionless equation shown in Figure 6, Solver
output a solution of groundwater discharge. The groundwater discharge is q, and DT
is the thermal diffusivity. The average temperature at the streambed is Ťo and the
assumed temperature at z = L is a constant TL. The effective porosity is ne.
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Figure 6: Governing equation of streambed temperature profiles
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Results
Once the probe was completed, all the thermistors were calibrated with an R2
greater than 0.993. The accuracy of the thermistors was determined to be ±0.2°C.
The time needed for the thermistors to equilibrate to an expected streambed
temperature is 200s, though the thermistors are within the error range by 60s. The
result of the spatial variation of streambed temperature is shown in Figure 7. The
temporal variation of one specific location along the stream is shown in Figure 8.
Figure 9 is a graph of the surface water temperature over a period of 1½ months.
Figure 10 models the effect of changing surface water temperature in the
streambed. The discharge rate from the thermistor probe was measured to be
1.18E-7 m/s. An earlier study using a seepage meter determined the max discharge
rate to be 1.14E-5 m/s.
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Figure 7: Spatial variation across a streambed
Figure 8: Temporal variation in streambed
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Figure 9: Variation in surface water temperature
Model of Streambed Temperature Pulse
Depth (m)
Figure 10: COMSOL model of temperature pulses across time
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Discussion
The probe was determined to be accurate within ±0.2°C. This is an
acceptable error range, as the subsurface temperature change recorded during field
tests was on the order of 2-6°C. The equilibration time allows for the probe to
deliver fast results from the field. When the probe was taken to the test site, it was
determined to deliver results of the streambed temperature to depths just over 1m.
Figure 7 shows some significant differences when compared to the
theoretical model (Figure 1). The temperature changes exponentially in the shallow
subsurface. Once the depth reaches about ½m, the temperature change occurs as a
linear function. The magnitude of the exponential temperature change varies across
the profile. This is a result of different groundwater discharge rates across the
stream profile. Reasons for this variation in discharge are shown in Figure 11. The
reason for the difference in field results compared to the theoretical model was
caused by the fluctuation of surface water temperature.
Figure 11: Causes of variation in groundwater discharge
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The streambed temperature at one location of the stream was tested to
determine the effect of the changing surface water temperature on the streambed
profile. As shown in Figure 8, the stream starts at a cooler temperature in the
morning, and then warms up during midday. Once the sun begins to set again in the
afternoon, the river begins to cool off. A cold front that moved through the area on
the day of testing accelerated the afternoon cooling effect. In order to understand
the magnitude of surface water temperature change, a temperature logger recorded
the temperature over the course of 1½ months. The results show that there is a
relatively constant oscillation of 4°C. Depending on the variation in atmospheric
temperature, the water temperature may drop by as much as 15°C over about 3
days.
The surface water temperature flux was input into COMSOL Multiphysics to
represent the temperature pulse created in the subsurface. As shown in Figure 10,
the field results can be recreated in the model. Therefore, the variable surface water
temperature causes a significant pulse in the data.
The vertical temperature profiles were similar to the theoretical model at
times. When this occurred, the groundwater discharge rate could be determined.
The groundwater discharge rate was determined to be 1.18E-7 m/s. The
groundwater flux was measured to be 1.14E-5 m/s from an earlier study with a
seepage meter. This variation was determined to be the result of a very high
discharge rate on the day of the seepage meter test. The testing occurred after a
recent storm, so the seepage meter was measuring the expected groundwater flux,
and the bank storage being released back into the river.
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Conclusion
For this project, soldering and metal working techniques were combined to
create a probe that measures streambed temperature to a depth of 3.5ft. This probe
measures the streambed temperature within 0.2°C, which is much less than the
temperature variations that occur in the subsurface. The changing surface water
temperatures were shown to create temperature pulses that move down through
the streambed. These pulses cause an exponential effect to a depth of roughly 1.5ft.
Then the temperature profile becomes a linear function.
This research proves that it is feasible to use vertical temperature profiles to
measure the localized groundwater discharge rate into a river. At times of near
constant surface water temperature, a direct correlation can be made. The effect of
the changing surface water on the streambed temperature was modeled in COMSOL
Multiphysics. Therefore, it is feasible for this analysis software program to be used
derive the groundwater discharge rate. This requires a measurement of both the
streambed temperature and surface water temperature over time.
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Acknowledgments
The author of this report would like to thank the following people for their
contribution to this study:

Clemson University Environmental Engineering and Earth Sciences staff:
o Lawrence Murdoch, for project direction and overview
o John Wagner and John Coates for editorial and publication assistance

Jonathan Baldwin, Brian Bastian, William Chamlee, Benjamin Douglas, Daniel
Good, Andrew Simmons, and Tyler Waterhouse for assistance collecting field
data
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References
Carey, Barbara, and Dustin Bilhimer. Surface Water/ Groundwater Exchange Along the
East Fork Lewis RIver (Clark County), 2005. Publication no. 09-03-037.
Olympia, WA: Washington State Department of Ecology, 2009. Web. 9 Sept.
2011.
Craig, Allison L. Evaluation of Spatial and Temporal Variation of Groundwater
Discharge to Streams. Thesis. Clemson University, 2005. Print.
Kalbus, E., F. Reinstof, and M. Schirmer. "Measuring Methods for Groundwater- Surface
Water Interactions: A Review." Hydrology and Earth System Sciences 10 (2006):
873-87. Authors. Web. 9 Sept. 2011. <http://www.hydrol-earth-systsci.net/10/873/2006/hess-10-873-2006.pdf>.
Measurement Specialties, Inc. Measurement Specialties. Micro-BetaCHIP Thermistor
Probe (MCD). Measurements Specialties, 18 July 2008. Web. 4 Nov. 2011.
<http://www.meas-spec.com/downloads/MCD_10K3MCD1.pdf>.
Oberg, Kevin A., Jonathan A. Czuba, and Kevin K. Johnson. "Measuring Gravity
Currents in the CHicago River, Chicago, Illinois." United States Geological
Survey. Web. 15 Aug. 2011.
<http://hydroacoustics.usgs.gov/publications/MeasuringGravityCurrents.pdf>.
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Appendix
Sample calibration curve of a thermistor:
Equilibration of the thermistor probe:
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Temperature profile used to determine groundwater discharge:
Values obtained from seepage meter tests: