United States
Environmental Protection
Agency
.Environmental Research
Laboratory
Duluth MN 55804
Research and Development
EPA-600/S3-81-008  July 1981
Project Summary
Water  Temperature
Dynamics  in  Experimental
Field  Channels:   Analysis and
Modeling

Heinz G. Stefan, John Gulliver, Alec Y. Fu, and Michael G. Hahn
  This report focuses on water tem-
perature dynamics in the shallow field
channels of the USEPA Monticello
Ecological Research Station (MERS).
The hydraulic and temperature envi-
ronment in the MERS channels was
measured and simulated to provide
some background for several biologi-
cal studies, including one on the
effects of artificially high water tem-
peratures on fish and invertebrate
populations. An analysis of the tem-
perature measurement problem, the
channel temperature regime, micro-
habitat conditions, and temporal* and
spatial water temperature dynamics
was essential. The results of this study
are also applicable to the study of
temperature dynamics in thermally
polluted shallow streams, to the design
of canals for cooling water disposal,
and to the study of natural water
temperature regimes of small streams.
  A dynamic stream temperature sim-
ulation model (MNSTREM) with a 3-
hour time resolution was developed
and verified to give predictions with a
standard error of only 0.2  to 0.3C
between measurements and predic-
tions.  A data  bank of 3-hour water
temperature data was developed and
analyzed statistically. A wind speed
function, Wftn = 0.0096 (A0V)V3 +
0.0083 W2. essential for the correct
prediction of water temperature, was
developed from on-site meteorologi-
cal and water temperature data. In this
formula, W2 is the windspeed at 2 m
and A9V represents a virtual temp-
erature difference. Longitudinal dis-
persion in the channels was measured.
Heat transfer into the bed material
below the pools of the experimental
channels was measured. A computer
simulation program (TSOIL) to predict
the unsteady water temperature dis-
tribution in the three-layered system
was also developed.
  This Project Summary was devel-
oped by EPA's Environmental Re-
search  Laboratory. Duluth. MN, to
announce key findings of the research
project which is fully documented in a
separate report of the same title (see
Project Report ordering information at
back).
Introduction
  The purposes of this study were to
validate water quality criteria data
produced in the laboratory under semi-
natural field (mesoscale) conditions and
to identify significant response by
aquatic organisms under field monitor-
ing conditions. The field channels in
which the experimental studies were
conducted were supplied with water

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heated artificially by waste heat from a
nuclear electric generating plant.
  The MERS is northwest of Minneapo-
lis, near Monticello, Minnesota, on 34
acres adjacent to a nuclear electric
generating plant owned and operated by
Northern States Power Company. The
MERS has eight soil bottom experimen-
tal open channels of approximately 520
m (1700 ft) length each. The Mississippi
River serves as the main source of water
for the  channels which operate in a
once-through mode with the discharge
returned to the river. Heat exchangers
using waste heat (i.e.  maximum At
19C in winter, 13C in summer) from
the power plant can be used to artificial-
ly heat the water in any of the channels.
Flow  rates in each of the channels  as
well as  water stages can be controlled.
  To provide assistance in the ecological
studies, it was necessary to document,
analyze, and predict water temperature
characteristics in the field channels and
to identify sources of variation and
error. Water temperatures in small open
channels are highly dynamic due to the
time-dependent character of the con-
trolling  processes: advective transport,
wind and flow induced mixing, and heat
exchange with the air and the channel
bed. In  the MERS field channels the
unsteady character of water temperature
is especially acute since both the mixing
characteristics and the effect of advec-
tive transport in the channels are of a
magnitude that must be considered. The
channels are exposed to a wide range of
air temperatures, humidity, wind veloc-
ities,  and solar radiation. The corre-
sponding heat transfer with the envi-
ronment is significant: a difference  in
temperature between the upper and
lower end as high as 15C has been
recorded and diurnal variations above
5C have been  observed at the down-
stream end. The experimental channels
provide an excellent medium for the
study of unsteady water temperatures
in open  channel flow and their relation-
ship to meteorological parameters.
  The work performed for the USEPA
Monticello Ecological Research Station
(MERS)  under this grant had two basi-
cally different purposes. One was to
provide  background material and gen-
eral information  in support of the biolog-
ical work conducted by the MERS field
station staff. The second purpose was to
investigate surface heat transfer, longi-
tudinal dispersion, and water tempera-
ture predictions in streams under field
conditions. This second purpose is basic
 and includes verification of the applica-
 bility of relationships developed for
 larger water bodies to smaller streams.


 Accomplishments
 Measurement of Hydraulic
 and Thermal Parameters
  The field channels of the MERS rep-
 resent a mesoscale ecosystem whose
 hydraulic characteristics have been
 measured and estimated.
  The investigators intermittently col-
 lected data on flow velocity profiles,
 surface water slope, flow cross sections,
 bed material  size,  bed porosity and
 permeability, and water temperature
 stratification below the channel bed.
 These data have  been used to derive a
 number of hydraulic parameters  as
 follows.
  The hydraulic characteristics of the
 experimental channels  under study in
 1975-1977 include:
  Manning's roughness: n = 0.06 in the
                      clearchannels
                      n= 0.3 with ex-
                      tensive weed
                      growth
  Mean flow velocities:  U  0.1 m/s in
                      riffles
                      U^ 0.02 m/s
                      in pools
 depending on flow rate and downstream
 channel control.  (U  is based on fixed
 conditions of flow and channel dimen-
 sion.) Velocity profiles are strongly
 affected by growth of filamentous algae
 in the rock sections and macrophytes in
 the pools.
  The soil profile below pool beds is
 composed of four layers: a highly organic
 surface layer, water saturated sandy
 loam, water saturated  bentonite clay
 layer, and a dry sandy loam, in downward
 order. The depth of the highly organic
 surface  layer is variable and increases
 with time.  The thermal diffusivity  of
 each layer was determined by fitting soil
 temperature prediction to temperature
 measurements.
  0 = 0.0017 cmVs in the organic
     surface layer
  D = 0.013 cmVs in the wet sandy loam
     below
  D = 0.0013 cmVs in the dry sandy loam
     below the bentonite seal
  The bed of the riffle is composed  of
coarse rock with mean size dso = 30 mm.
The rock porosity was estimated at c =
0.42 and its Darcy permeability coeffi-
cient at k = 0.18 m/s. The thermal
diffusivity of the riffle bed was estimated
to be D = 0.0031 cmVs in the rock/water|
system without natural convection.    
 Water Temperature
Instrumentation
  Development and operation of instru-
 mentation for continuous monitoring of
flow rates and water temperatures in
the channels from 1975 to 1977 was
done by the MERS staff. The investiga-
tors participated  in the selection of the
temperature sampling sites.
  Temperature sensors (thermocouples)
were installed at the upstream and
downstream ends and  in the center
pools and riffles  of each of the experi-
mental channels 1, 4, 5, and 8 analyzed
in 1975-1977. The sensors provided
continuous water temperature informa-
tion which was recorded on strip charts.
Three stations per channel were not
sufficient, however, for the analysis of
stratification, surface heat transfer, and
mixing. Channel  1 was selected for in-
depth study of temperature regimes,
and 21 continuous recording sensors
were installed in it. Ten of the sensors
measured water temperature 12.5 cm
(5 in.) to 25 cm (10 in.) below the water
surface. There were two vertical arrays
of four sensors each installed in Pools 6
and 12 which provided information on
water temperature stratification and
soil temperature. Three  sensors were
within 12.5 cm (5 in.) from the bottom of
pools 4, 10, and 18, and one sensor 2 to
5 cm (1 to 2 in.) in the rocks of riffle 17.
All temperature sensors were connected
to Leads-Northrup multi-channel color-
coded temperature chart recorders.
Temperatures were recorded from No-
vember 1975 through December 1977,
Water Temperature Data
Processing
  Water temperature data processing
had the following elements:
   Extraction of 3-hour data from strip
    charts
   Review and estimation of missing
    or faulty data
   Calibration
   Storage on magnetic tape
Water temperature data for Channel 1
(strongly heated). Channels 4 and E
(unheated), and Channel 8 (intermedi
ately heated) were processed for the
period  from December 1975 through
September 1977.

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Water Temperature Data
Analysis and Results
  The water temperature data analysis
included:
   Development of statistical analysis
    computer programs WTEMP1  and
    WTEMP2
   Computation of a number of statis-
    tical parameters from 3-hour data
   Determination of the seasonal
    water temperature cycle
   Determination of the diurnal water
    temperature cycle
   Analysis of longitudinal water
    temperature gradients
   Analysis of water temperature
    stratification in the pools


Development of Computer
Programs
  The computer program WTEMP1  is
designed to extract from the 3-hour
water temperature data statistical infor-
mation including:
   Water temperatures at three prob-
    abilities of occurrence specified by
    the user
   Maximum  and minimum water
    temperature in the period analyzed
   Mean, standard deviation,  and
    dimensionless skewness coeffi-
    cient of the water temperature
WTEMP1 can handle a series containing
up to 19,200 individual water tempera-
tures, equivalent to 400 days of  data
from six stations in a single channel.
WTEMP1 can also handle sliding statis-
tic calculations for sample periods of up
to seven days. The output is in tabular
form.
  A second interactive program WTEMP2
for computing statistics on specified
date-time intervals, composite station
location, etc., from daily statistics was
also  developed.
  Computations were carried out for
individual stations and channel com-
posites using weekly sliding samples.
The  complete output comprised 151
pages for Channel 1 and  126 pages
each for Channels 4, 5, and 8.
Seasonal Water Temperature
Cycles
  The amplitude of the seasonal water
temperature was of the order of 15C.
The annual mean differed by channel
and station depending on artificial
heating. Channel 1  was artificially
heated, and Channel 5 was not.
  Water temperature fluctuations su-
perimposed on the seasonal cycle were
either due to irregularities in the artifi-
cial heating of the inflowing water or to
weather.
Diurnal Water  Temperature
Cycles
  Inflowing water was taken from the
Mississippi River. Because the field
channels are shallower than the river,
diurnal water temperature amplitudes
at the downstream end of the channels
were larger than upstream. Amplitudes
of diurnal water temperature cycles
Table 1.    Monthly Mean and Standard Deviation fa) of Daily Minimum and Daily
           Maximum Longitudinal (Spatial) Temperature Difference, and of Diurnal
           (Temporal) Temperature Difference at the Outflow from Heated
           Channel 1. December 1975 - November 1976
                        Minimum        Maximum          Diurnal
        Month         Longitudinal AT"   Longitudinal AT"    AT" at Outflow


December (1975)
January (1976)
February
March
April
May
June
July
August
September
October
November (1976)
Mean
PC)
5.2
6.0
4.6
3.2
1.9
1.8
2.7
1.7
0.9
1.7
0.9
1.0
a
PC)
2.0
1.5
1.3
2.7
1.8
1.3
1.5
0.9
1.1
0.7
1.0
1.0
Mean
PC)
8.0
9.5
7.7
6.9
5.6
5.7
4.8
4.0
4.5
3.5
3.4
5.7
a
fC)
2.5
1.8
1.7
3.1
1.6
1.4
1.6
0.9
2.0
0.9
2.6
3.9
Mean
PC)
1.9
2.3
2.5
3.4
5.3
4.4
4.0
3.5
3.7
2.9
2.9
2.5
a
PC)
0.9
1.0
1.3
1.6
1.9
2.2
0.0
0.8
1.5
1.2
1.2
2.4
varied strongly with the season. Winter
values were of the order of 1 C upstream
and 2 to 3C downstream. In the sum-
mer, a 2C amplitude upstream and a
5C amplitude downstream were not
uncommon.
Longitudinal Water
Temperature Gradients
  Water temperature differentials be-
tween the upstream and the downstream
ends of the channel were of interest for
fish studies in the field channels. Such
longitudinal water temperature gradi-
ents were dependent on several other
hydrothermal parameters. The longitu-
dinal At can be expected to rise with the
addition of artificial heat. A greater flow
rate will decrease the longitudinal AT
Since the geometry of the MERS chan-
nels is fixed in terms of length and
width,  the two most important control-
lable parameters  were flow rate and
heat input. Actual values of longitudinal
AT's depended on the amount of heat
released to the atmosphere, which is a
weather-dependent process.
  The  daily  minimum and  maximum
temperature difference  between the
inflow  and outflow of the  artificially
heated Channel  1 was recorded  over a
one-year period  from  December 1975
through November 1976.  Table 1 sum-
marizes the monthly mean and standard
deviation of the longitudinal temperature
differences of Channel 1. Flow rates
ranged from 0.015 to 0.039 mVs.
  Daily diurnal water temperature vari-
ations at the outflow of Channel 1 were
recorded over a one-year period and are
also reported in Table  1. These charac-
teristics are for a heated  channel with
inflow  temperatures  increased up  to
15C above the temperature of the
Mississippi River water.  Longitudinal
temperature gradients and diurnal
variations are not as large in a channel
with ambient unheated inflow.
                                                                             Temperature Stratification
                                                                             in Pools
                                                                               Vertical stratification of the pool
                                                                             sections was studied in the artificially
                                                                             heated Channel 1 and was found to
                                                                             occur  most frequently in August The
                                                                             temperature gradient was found to
                                                                             occur primarily in the lowermost 20cm
                                                                             of the pool below a 60 cm isothermal
                                                                             layer; the temperature difference was
                                                                             up to  5C strong. Analyses  of some

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1975/76 data in pools 6 and 12 showed
that a temperature differential of more
than 1C developed during 33 percent
of all hours in August and less frequently
during other months. The more down-
stream pool showed a stronger tendency
to stratify, presumably because the
cumulative effect of atmospheric heat-
ing of the water in it is stronger.
Dynamic Soil Temperature
Prediction Model, TSOIL
  A dynamic soil temperature computer
model TSOIL for the pool sections was
developed, primarily to assist in inverte-
brate studies. The  model solves the
unsteady heat conduction equation and
predicts the soil temperature profile for
a specified time variation of the water
temperature at the soil/water interface.
It was verified that strongly transient
soil temperatures may be accurately
predicted with this model, as shown in
Fig. 1.
Longitudinal Dispersion Study
  The flow field in the MERS channels
is very non-uniform and mean flow
velocities are small. Water moves through
the MERS channels in a way far different
from the movement of a piston in a
cylinder (plug flow). Transverse and/or
vertical mixing takes place between the
faster and the slower water masses.
Vegetation is present in pools and riffles
in the summer. There is a weak jet effect
at the transition from the riffles to the
pools. In the pools, water masses may
be entrapped near the banks. As a result
of all these interacting processes, heat
or material contained in the water willJ
spread out longitudinally  along the*
channel. The effect of longitudinal
spreading had to be incorporated in the
channel water temperature model.
  Since detailed study of the very com-
plex low velocity channel hydrodynamics
was not part of the research objective,
the water temperature simulation was
based on a uniform channel flow model
with a longitudinal dispersion term.
"Longitudinal dispersion coefficient" is
used herei n to describe a bu Ik coefficient
which lumps the effects  of all the
processes  mentioned above. To use
separate coefficients for riffles and
pools was considered, but the frequent
transition and short lengths of these
elements made  it advisable not to.
  The use  of a diffusion equation to
describe longitudinal mass transport in
a channel  is only justified after the
     20
     15
                          Measured Soil Temperature:

                                  O 6 cm depth


                                  Q 16 cm depth


                                  A 28 cm depth


                                   41 cm depth
 I
 I
 s
     10
                                                   0    0
"  " 
19 | 20 21
22 23 | 24 | 25
December
| 26 | 27 | 28 | 29 \ 30 \ 31 \
1977
7 | 2 | 3
January 1978
 Figure 1.    Comparison of measured and predicted (solid lines) soil temperatures in Pool 12 during heat wave test.
             Notation for depth of predicted soil temperatures: (1) soil surface, (2) 2.5 cm, (3) 6 cm, (4) 16 cm. (5) 28 cm,
             (6) 41 cm, 17) 60 cm, 18) 1 m.

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 nitial corrective period. The MERS
channels begin with a pool into which
water is discharged from a weir produc-
ing a very well mixed upstream condi-
tion. The mean residence time of the
water in a pool was anywhere from 10
to 30 minutes depending  on flow rate.
The convective length of the first pool
was estimated to be approximately 5 m,
far less than its total length of 30 m. It
was therefore considered that the con-
vective length did not reach beyond the
length of the first pool.
  Longitudinal dispersion  in the MERS
field channels was studied using tem-
perature fronts. The longitudinal disper-
sion coefficient  was found to be best
approximated by:

          DL = 7.47  * Q.
                      D
where Q is flow rate and B is mean
surface  width.
  In the range of very low mean flow
velocities investigated (0.04 mVs dis-
charge and U =* 0.02 m/s in pool to 0.1
m/s in  riffle), the typical wind and
vegetation effects could not be distin-
guished separately. A typical value of DL
was 0.1  mVs.
Air- Water Interaction
  Evaporative and convective surface
heat exchange were found to be depen-
dent on wind speeds and natural con-
vection potential. A wind speed function:
 Wftn = 0.0096 (A,)1'3 + 0.0083 W2
was found to fit the experimental field
data well.  A0U represents  a virtual
temperature differential and \Nz  is the
wind speed at 2 meters above the
ground in m/s. The windspeed function
is used to calculate evaporative surface
heat transfer and convective surface
heat transfer.
Finite Difference, Implicit
Computer Model (MNSTREM)
  A finite difference,  implicit computer
model (MNSTREM) for the simulation of
the very dynamic channel  water tem-
perature regime was  developed. It was
shown capable of simulating 1 hr, 3 hr,
or 6 hr water temperatures over periods
up to one month with standard errors of
0.2 to 0.3C between measurements
and predictions. Weather data, specifi-
cally solar radiation, air temperature,
dewpoint, and wind velocity, are required
as input at least every six hours. Three-
hour input data are  standard for the
model. If intervals of  more than six
hours are used, the accuracy of the
prediction suffers. MNSTREM has un-
usually high time resolution (3  hrs
normal At,  1 hr possible At), meaning
that it can predict rapid water tempera-
ture changes in very shallow water (Fig.
2).
            42
            40
            38
            36
       
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Conclusions

  In  addition to  providing information
on some physical characteristics of the
MERS experimental channels,  this
research produced material applicable
to the study of temperature dynamics in
thermally polluted streams in general,
to the design of canals for cooling water
disposal, and to the understanding and
analysis of natural water temperature
regimes of small streams. Some of the
information  may also be of use  in
studies  of mass  transport and ecosys-
tem dynamics in shallow channels.
  Continuously recording flow metering
and channel stage metering devices at
each end of a channel should be installed
in the MERS channels since flow rates
were only recorded manually once a day
and stages only intermittently.
Recommendations

  Water temperature variations in time
and  space are  a  characteristic of any
aquatic environment and especially the
MERS field channels. Standard methods
for the characterization of water tem-
perature dynamics and incorporation of
these into water temperature criteria for
pollution control are needed. The MERS
field channels  are ideal for dynamics
studies. They should be used for contin-
ued studies of fate and effect of various
pollutants in an ecosystem at the meso-
scale.
  The focus of this study was on water
temperature as a water quality param-
eter. For the  model  formulation, a
dispersion parameter and a  surface
exchange relationship appropriate for
water temperature modeling were de-
rived. Studies of pollutant (mass) trans-
port  in the MERS channels require more
refined and detailed information on the
flow and dispersion in a bed of macro-
phytes since uptake and precipitation
are  added factors not present in the
temperature model.
   If  further ecosystem studies in the
MERS channels are conducted, detailed
investigations of the hydrodynamic and
transport  dynamics of a pool and of a
riffle, including the effects of vegetation,
must be conducted. For example, the
effect of  vegetation on longitudinal
dispersion needs investigation. Flow
effects must be sorted out from the field
observations to derive the true biological
and  chemical kinetics of the system.
   The 3-hour water temperature data
base derived from continuous recordings
should be analyzed further  by time
series (spectral, correlation) analysis. In
addition,  weather data and flow data
should be digitized.
  Heinz G. Stefan.  John Gulliver, and Alec Y. Fu are with the University of
    Minnesota. St. Anthony Falls Hydraulic Laboratory, Minneapolis. MN55414,
    and Michael G. Hahn is with Mead & Hunt, Madison, Wl 537O5.
  Kenneth E. F. Hokanson is the EPA Project Officer (see below).
  The complete report, entitled "Water Temperature Dynamics in Experimental
    Field  Channels: Analysis  and Modeling," (Order  No.  PB  81-218  349;
    Cost: $15.50, subject to change) will be available from:*
          National Technical Information Service
          5285 Port Ftoyal Road
          Springfield, VA 22161
          Telephone: 703-487-4650
  The EPA Project Officer can be contacted at:
          Monticello Ecological Research Station
          U. S.  Environmental Protection Agency
          Box 500
          Monticello, MN 55362
'The final report and six additional memoranda (Project Report 193, Cost. $12 00, subject to change) is
 also available from
      St Anthony Falls Hydraulic Laboratory
      University of Minnesota
      Mississippi River at 3rd A venue, S 
      Minneapolis, MN 55414
                                                                                        U.S. OOVCTNMENT PRINTING OFFICE 101 -757-012/723

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