United States
Environmental Protection
Agency
Environmental Research
Laboratory
Duluth MN 55804
'W*
Research and Development
EPA-600/S3-82-052 Dec. 1982
Project Summary
Numerical and Graphical
Procedures for Estimation of
Community Photosynthesis and
Respiration in Experimental
Streams
John S. Gulliver, Tedd W. Mattke, and Heinz G. Stefan
A numerical dissolved oxygen (D.O.)
routing model DORM is developed to
determine total stream community
photosynthesis (P) and community
respiration rates (R) through successive
routing of two-station die! D.O.
measurements in a stream. The model
differs from existing procedures for
die! curve productivity analysis in that
it uses the complete D.O. transport
equation, including D.O. surface ex-
change, longitudinal dispersion, de-
pendence of respiratory rates on water
temperature and D.O. The model is
applied to the experimental field
channels at the USEPA Monticello
Ecological Research Station to com-
pute P and R values at different seasons
and under different water temperature,
solar radiation, and pH conditions. A
sensitivity analysis shows that com-
puted P and R values are most
sensitive to residence times and
surface oxygen exchange, (reaeration)
coefficients. New equations for surface
exchange, including the effect of
wind, have been developed and sum-
marized.
A graphical, simplified routing
procedure produced P and R values
which were 82 and 89 percent,
respectively, of those obtained by
complete routing, with a standard
deviation of less than 5 percent.
Nighttime longitudinal D.O. gradients
were used to derive respiration rates,
R.
Maximum values of P and R in the
MERS channels were 14.8gm~2day~1
and 10.7 g irT2 day~1, respectively.
P/R ratios ranged from 0.3 to 2.1. A
seasonal dependence of P and R
values was found, as expected.
Hysteresis i n plots of hourly P versus
photosynthetically active radiation
(PAR) intensity was observed fre-
quently. It was of such magnitude that
it could not be caused by errors in sur-
face exchange estimates or other
physical processes.
This Project Summary was devel-
oped by EPA's Environmental Re-
search Laboratory, Duluth, MN, to
announce key findings of the research
project that is fully documented in a
separate report of the same title (see
Project Report ordering information at
back).
Introduction
Dissolved oxygen, an important
stream water quality indicator, is used
for respiration by organisms. Plant
organisms produce oxygen by photo-
synthesis and account for most of the
oxygen production and respiration in
many aquatic systems.
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For streams which do not have a large
chemical waste load, the oxygen sources
and sinks may be represented as
Sources-Sinks = total community
photosynthetic rate
- total community
respiratory rate
+ surface exchange
(reaeration)
Photosynthesis occurs only during day-
light hours, and surface exchange
varies with stream hydraulic features,
water temperature, and D.O. concentra-
tion. Total community respiratory rate is
usually assumed to remain fairly
constant. For this reason, the diel (daily)
D.O. cycle in a water body shows D.O.
concentration as decreasing through-
out the night and increasing during
daylight hours (see Fig. 1). Since D.O.
concentration is usually high during the
day and low at night, surface oxygen
exchange is typically a D.O. sink during
daylight hours and a source during night
hours.
A graphical analysis of the diel D.O.
curve is often used (Odum's and other
methods) to quantify stream community
productivity or to measure the functional
response of the autotrophic and hetero-
trophic community to pollutant stresses
such as heat loading or toxic substances.
If D.O. surface exchange is known, night
D.O. measurements may be used to
determine total community respiratory
rate. Then total community photosyn-
thetic rates may be determined from
D.O. measurements taken during day-
light hours.
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Respiration is expressed as a function of
temperature and limited by low D.O.
C+CKM
(2)
where T = water temperature (°C), 6 =
temperature coefficient, and C =
Michaelis-Menton coefficient for
respiratory inhibition at low D.O.
concentrations.
By the routing procedure (DORM) one
finds R20 and P(t). R(t) values are
subsequently computed from Eq. (2).
Implicit, hybrid differences are used in
the routing program. The routing
involves iterative prediction of down-
stream D.O. versus time values with
increasingly accurate estimates of P(for
daytime) and R (for nighttime), until a
match of desired accuracy between
predicted and measured values is
achieved. The parameters U, DL, h, Ks, 6
and CKM in Eq. (1) must be known for
each channel segment. The input data
to DORM are:
a. initial longitudinal D.O. profile
b. stream segment lengths
c. cross-sectional areas of stream
segments
d. surface widths of stream segments
e. stream segment orientation (direc-
tion)
f. water surface slope
g. channel flow rate
h. day of year
i. longitude and latitude of study site
j. measured D.O. concentrations and
corresponding measurement times
at the upstream and the down-
stream locations
k. measured water temperature ver-
sus time at the upstream and the
downstream locations
I. measured wind velocity, wind
direction and air pressure (mb) at
the stream site as a function of
time
2. A theory for the prediction of the air-
water oxygen exchange coefficient Ks
in Eq. (1) was also developed. It
considers the effects of shear stresses
on a stream bed due to gravity, wind
shear on the water surface, wind
generated waves, and in a qualitative
way, secondary currents. The rela-
tionships proposed for the prediction
of Ks values are of the form:
a. For streams without wind effects
Ks = Ai u*b L0.804 (A5 Pe)"1'3 +
0.468 (As Pe)"1/2° ] (3)
where Pe = u*b n = a shear Peclet
Dm number
u*b = VT»/P = shear velocity
(m/s)
Tt> = gravity flow induced bed
shear (N/m2)
p = water density (g/m3)
Dm = molecular diffusivity of
D.O. in water (mVs)
Ai = coefficient related to bed
shear induced turbulence
A5 = Ai (1 + a5)
as = coefficient related to se-
condary currents in a stream
reach
The coefficient Ai = 5.44*10"* was
determined from literature data, while
a$ is stream specific and must be
evaluated in the field.
b. For streams with wind effects
Ws=2.64*10
Ks = 4(u*c + as u*b)
/ X+.1'
Fsa-X/lnl -
where X =
Ds=
(4)
Aih(u*c+a5u*b)
U*c = [(7-s
TS = wind induced surface shear
(N/m2)
Fsa = coefficient for increase in
water surface area without
waves (-)
v - kinematic viscosity of water
(mVs)
Ws = wave parameter (-)
The parameters Fsa and Ws are both
related to wind waves. For moderate
wind velocities (u*a/g < 0.02 m) the
following relationships have been
proposed:
r /—\21
1+(91)
L w/ J
1/2
(5)
= 0.112;r
77-C
F8-F
where g = acceleration pf gravity =
9.81 m/s2
a = wave amplitude (m)
c = wave speed (m/s)
Fa = wind fetch at downstream
end of stream reach (m)
Fi = wind fetch at upstream end
of stream reach (m)
u% = air shear velocity = x/rs/pa
(m/s)
Pa = air density (kg/m3)
p = density of water (kg/m3)
a - surface tension (N/m)
Ka = u*a3/(gv)= Keulegan param-
eter
Similar relationships were developed
for strong winds (u*a/g > 0.02 m). The
theory implies the following:
a. The circulation of the water under
wind waves makes an important
contribution to surface oxygen
exchange. Therefore, wind speed
and fetch are important factors.
b. Secondary currents in the water
provide an important contribution
to surface oxygen exchange. Since
these currents cannot be predicted,
a parameter related to secondary
currents must be estimated or
measured in each stream reach.
3. Night D.O. measurements in the field
channels of the USEPA Monticello
Ecological Research Station were
used to determine surface exchange
coefficients. Parameters related to
secondary currents and wind in the
equations for surface exchange
coefficients were back-calculated
from the surface exchange coeffi-
cients. These parameters are specific
to the MERS channels. Predictions
made with these parameters for the
MERS channels were superior to
predictions made with equations from
the literature. Values of surface
exchange coefficients in the MERS
channels predicted by literature
equations spanned three orders of
magnitude. The large scatter in
surface exchange coefficients from
literature equations is very likely due
to omission of secondary currents and
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wind effects. Each equation for a
surface exchange coefficient is appli-
cable only to the stream reach from
which data were taken.
4.Thirty-two diel D.O. surveys in four
stream reaches were made in the
MERS experimental streams in late
summer and fall of 1978 and spring
and summer of 1979. Diel curve
productivity was estimated with
DORM, using data from each survey.
A temperature coefficient for total
community respiratory rate, 6 =
1.045, was determined from a se-
quence of predawn longitudinal D.O.
surveys in September 1978 with a
temperature range from 15 to 24°C. A
half-saturation coefficient for respira-
tory inhibition at low D.O. concentra-
tion, CKM = 2.3 g/m3, was determined,
from diel D.O. data obtained in a
channel reach during three consecu-
tive nights. Computed R values
ranged from 2.6 g m"2 day"1 D.O. in
October 1978 to 10.7 g m~2 day"1 in
August 1979, and P values ranged
from 1.50g m"2day"1 in October 1978
to 14.8 g m"2 day"1 in June 1979. P/R
ratios varied between 0.3 in Septem-
ber 1978 and 2.1 in May 1979. In the
MERS channels, the P/R ratio is a
good indicator of community photo-
synthetic efficiency.
Diel curve analysis was performed
in three channel reaches with a
respective pH of 8.0, 6.3, and 5.4. The
channel reaches with low pH reached
maximum total community photosyn-
thetic and respiratory rates earlier in
the growing season than the one with
highest pH. Although this could be
due to the lower pH, it is more likely
attributable to a difference in vegeta-
tion history and shading by emergent
vegetation in the low pH channel
reaches.
Total community photosynthetic
rates (P) over the day were plotted
against photosynthetically active
radiation (PAR) for each diel D.O.
survey. The relationship between P
and PAR was usually nonlinear, and
hysteresis in the P versus PAR curves
was frequent. Counterclockwise
hysteresis was observed for three
channel reaches on a cloudy day in
late July 1979 and a clear day in mid-
September 1979. Other surveys in
May, June, and August generally
gave clockwise hysteresis. Sensitivity
analysis with the D.O. routing model
indicates that in the MERS channels,
physical parameters cannot be held
responsible for the hysteresis; rather,
4
it is believed to be caused by biological
processes. Several hypotheses have
been proposed to explain the cause of
hysteresis, but further studies are
needed to determine it.
5.The potential errors in P and R values
for the MERS channels resulting from
several simplifications of the D.O.
transport equation and from inaccu-
rate data input were investigated.
a. Neglecting D.O. surface exchange
(K2 = 0) gave substantially reduced
values of P and R (typically 8% and
16%, respectively).
b. Longitudinal dispersion can be
neglected for the MERS channels.
Only small «2%)changes in P and
R are produced when DL ^ 0 is
included in Eq. (1).
c. Using a linear interpolation be-
tween upstream D.O. input data
collected at two-hour intervals is
acceptable. More complete curve
fitting to input D.O. data resulted in
only minor (0.4%)changes in P and
R.
d. Correct residence times are re-
quired. Using incorrect residence
times (± 20%) changed P and R
values significantly (± 18%).
e. Temperature dependence of respir-
atory rates is of importance in the
MERS channels. A diel variation of
5°C would result in a 7 percent
error in respiratory rates.
6. A graphical method by which the up-
stream measured D.O. curve, correc-
ted for residence time of flow of the
water mass to the downstream
station, is subtracted from the down-
stream measured D.O. curve was also
applied to the MERS data. The method
solves the simplified equation graphi-
at
(8)
cally. Of all the processes included in
the complete Eq. (1), Eq. (S)considers
only advection, community photosyn-
thesis and community respiration and
ignores surface oxygen exchange and
longitudinal dispersion. The graphical
method gave P and R values which
were on the average 89 and 82
percent, respectively, of the values
obtained by the complete DORM. The
standard deviation was ± 5 percent.
The P/R ratio given by the graphical
method was on the average 1.07
times that obtained by the complete
DORM with a standard deviation of
0.04.
7. Separate studies were conducted in
the MERS channels to answer several
additional questions related to the
diel curve analysis.
a. It was examined to determine
whether the water pumped into
the channels from the Mississippi
River had enough nutrients from
the observed plant growth in the
channel. Nutrient limitation is not
believed to be a limiting factor.
b. Biochemical oxygen demand
(B.O.D.) in the channels is included
in the reported R values. It was
established that the water supply
contained less than 12 g/m3
BODs, which made no significant
contribution to R because of the
short residence times of 2 to 5
hours in the channels and the
effect of the first pool as a settling
basin.
c. The sedimentary oxygen demand
in the bed of a stream pool was
estimated using dark cylinders and
was found to be on the order of
from 0.01 to 0.04 g m"2 hr"1. With
water residence times from 2 to 5
hours this uptake was considered
negligible in the D.O. routing
process.
d. Diel D.O. measurements and con-
trol volume techniques in several
riffles and pools helped to sub-
divide the total community P and R
values into contributions by macro-
phytes, epiphyton, and phytoplank-
ton. During August 1978, the
macrophytic and epiphytic sub-
communities in pools 14 contri-
buted on the average of 5.3 g O2
m"2 day"1 to photosynthesis and
10.5 g O2 m"2 day"1 to respiration,
while the planktonic contributions
were only 0.4 g 02 m"2 day"1 and
0.6 g Oz m"2 day"1, respectively. In
riffle 13 the dominance of the
subcommunity over the planktonic
community was equally pro-
nounced. However, the photosyn-
thetic rate of the benthic sub-
community in the more shallow
riffle was higher (9.9 g Oz m"2
day"1) than in the pool, while its
respiration rate was about equal
(9.8 g 02 m"2 day"1) to that in the
pool.
S.The limitation of macrophyte respira-
tion rates by less than 3.5 g/m3 D.O.
in the water was observed using
incubation experiments. This provided
verification of the CKM value deter-
mined through D.O. routing with
DORM.
9.The following reports and papers
contain details of the studies con-
ducted:
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a. Numerical and Graphical Proce-
dures for Estimation of Community
Photosynthesis and Respiration in
Experimental Streams, by John S.
Gulliver, Tedd W. Mattke, and
Heinz G. Stefan, St. Anthony Falls
Hydraulic Laboratory, University of
Minnesota, Project Report No.
198, 123pp.
b. Photosynthesis and Respiration
Rates in the Monticello Experi-
mental Streams: 1978-79 Diel
Field Data and Computed Results,
by John S. Gulliver and Heinz G.
Stefan, St. Anthony Falls Hydraulic
Laboratory, University of Minne-
sota, External Memorandum No.
172, February, 1981, 57pp.
c. Graphical Method to Estimate
Stream Community Respiration
and Primary Productivity from
Dissolved Oxygen Measurements,
by Tedd W. Mattke and Heinz G.
Stefan, St. Anthony Falls Hydraulic
Laboratory, University of Minne-
sota, External Memorandum No.
169, December, 1980, 53 pp.
d. Air-Water Oxygen Exchange:
Theory and Application to Experi-
mental Streams, by John S. Gulli-
ver and Heinz G. Stefan, St.
Anthony Falls Hydraulic Labora-
tory, University of Minnesota,
External Memorandum No. 173,
May, 1981, 108pp.
e. Community Photosynthesis and
Respiration in Experimental Chan-
nels, by M.K. Taylor and S.P.
Sheldon, Dept. of Ecological &
Behavioral Biology, University of
Minnesota, Minneapolis, Minne-
sota, Nov., 1979 (accepted by
Hydrobiologia, 1981).
Recommendations
Diel D.O. measurements should be
analyzed with a complete routing model
such as DORM in order to minimize
error in estimates of photosynthetic
production and respiration rates. Surface
exchange coefficients of oxygen (reaera-
tion coefficients) are stream specific
and wind dependent. Values of surface
exchange coefficients predicted with
literature equations for the MERS
experimental streams spanned three
orders of magnitude. Empirical surface
exchange equations are dependent on
secondary water movementand surface
waves and are therefore not readily
transferable from one stream to another.
Regarding general die! curve analysis
the following recommendations are
made:
1. Field measurements of D.O. should
be made in cross sections which
are well-mixed. D.O. analysis by
the Winkler method is much more
reliable than D.O. measurements
by sensors and continuous record-
ing. Channel geometry, channel
orientation, and flow rates need to
be documented with precision.
2. Extreme care should be taken to
accurately determine stream reach
residence time. This requires
precise documentation of channel
geometry and flow rates. Effects of
diurnal thermal stratification 'on
residence time measurements
need investigation in the MERS
channels.
3. Surface excha nge of oxygen (reaera-
tion) should be measured in the
stream reach of interest. Surface
oxygen exchange is often depen-
dent upon wind. Therefore, wind
velocity and wind direction need to
be measured.
4. Longitudinal dispersion need not
be included in the diel curve
productivity analysis in the MERS
channels but should be included in
a highly dispersive system.
5. The temperature dependence of
respiratory rates should be included
in diel curve analysis when the diel
variation in water temperature is
2°C or greater.
6. Respiratory inhibition at low D.O.
concentrations should be included
in diel curve analysis when D.O.
concentrations below 4 g/m3 are
encountered.
7. A linear interpolation between
upstream D.O. measurements is
acceptable when the data are
collected in two-hour intervals.
Greater time intervals may require
a higher order interpolation.
8. Further investigations should tbe
conducted to investigate the causes
of hysteresis in plots of photosyn-
thetic production versus light
intensity.
9. Additional research should also be
conducted on the D.O. limitation
and the effect of temperature on
respiration rates (parameters CKM,
R2o, and 6). Values of B may vary
seasonally. Only late summer data
were used to derive a 8 value
herein.
John S. Gulliver and Heinz G. Stefan are with the University of Minnesota, St.
Anthony Falls Hydraulic Laboratory, Minneapolis, MN55414; TeddW. Mattke
is with the CityofRobinsdale. Robinsdale, MN 56578.
Kenneth E. F. Hokanson is the EPA Project Officer (see below).
The complete report, entitled "Numerical and Graphical Procedures for Estima-
tion of Community Photosynthesis and Respiration in Experimental Streams,"
(Order No. PB 82-220 765; Cost: $13.50, subject to change) will be available
only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Monticello Ecological Research Station
Environmental Research Laboratory—Duluth
U.S. Environmental Protection Agency
Box 500
Monticello, MN 55362
•&U. S. GOVERNMENT PRINTING OFFICE: 1983/659-095/0565
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