Freshwater Biology (2000) 44, 493±507
Variability of photosynthesis±irradiance curves and
ecosystem respiration in a small river
È NIG AND PETER REICHERT
URS UEHLINGER*, CHRISTOF KO
Swiss Federal Institute for Environmental Science and Technology (EAWAG), CH-8600 DuÈbendorf, Switzerland
SUMMARY
1. We investigated photosynthesis±irradiance relationships (P±I curves; P = oxygen
production rate due to photosynthesis, I = light irradiance rate at the water surface) and
ecosystem respiration in a 9 km long reach of a river that is characterised by light
conditions favouring primary production, high ambient nutrient concentrations, a high reaeration rate, and frequent spates. We addressed the question of how disturbances (spates)
and season influence photosynthesis and ecosystem respiration.
2. We used an oxygen mass-balance model of the river to identify ecosystem respiration
rates and the two parameters of a hyperbolic P±I function (Pmax = maximum oxygen
production rate due to photosynthesis, a = the initial slope of the P±I function). The model
was fitted to dissolved oxygen concentrations quasi-continuously recorded at the end of
the reach. We estimated parameters for 137 three-day periods (during the years 1992±97)
and subsequently explored the potential influence of season and disturbances (spates) on
Pmax, a and ecosystem respiration using stepwise regression analysis.
3. Photosynthesis-irradiance relationships and ecosystem respiration were subject to
distinct seasonal variation. Only a minor portion of the variability of P±I curves could be
attributed to disturbance (spates), while ecosystem respiration did not correlate with
disturbance related parameters. Regular seasonal variation in photosynthesis and
ecosystem respiration apparently prevailed due to the absence of severe disturbances (a
lack of significant bedload transport during high flow).
Keywords: photosynthesis±irradiance, stream metabolism, disturbance, seasonal variation
Introduction
Nutrients, temperature, light and flow are major
factors controlling stream metabolism. Nutrient addition may enhance primary production and respiration
if ambient nutrient concentrations are low (Stockner &
Shortreed, 1978; Bowden et al., 1992; Guasch et al.,
1995). In streams and rivers draining urban and
agricultural areas, nutrient concentrations usually do
not limit primary production and algal growth.
Temperature is an important regulator of photosynthesis and respiration (DeNicola, 1996). In rivers with
moderate flow variability, linear temperature models
Correspondence: Urs Uehlinger, Swiss Federal Institute for
Environmental Science and Technology (EAWAG), CH-8600
DuÈbendorf, Switzerland. E-mail: [email protected]
ã 2000 Blackwell Science Ltd.
may account for 55±75% of the seasonal variation in
ecosystem respiration or gross primary production
(Servais et al., 1984; Uehlinger, 1993).
Light is the ultimate energy source for primary
production and algal growth. Variations in gross
primary production along the river continuum and
across geographical regions can be attributed to light
availability (e.g. Minshall, 1978; Vannote et al., 1980;
Naiman, 1983). Light varies strongly at different
temporal scales (from minutes to seasons). Photosynthesis-irradiance curves (P±I curves) describe the
short-term response of photosynthesis to changes in
light intensity. Parameters of P±I curves change with
light, temperature and the structure of the autotrophic
community (Kelly et al., 1983; Jasper & Bothwell, 1986;
Guasch & Sabater, 1995).
Disturbances, such as spates or extended periods of
high flow, may have a significant impact on stream
493
494
U. Uehlinger et al.
metabolism (Fisher et al., 1982; Young & Huryn, 1996;
Uehlinger & Naegeli, 1998). Such events shift ecosystem metabolism towards heterotrophy because primary producers are more susceptible to drag and
abrasion by moving bed-sediments or suspended
solids than the microbial community that is located
mainly in the hyporheic zone (Naegeli & Uehlinger,
1997; Uehlinger & Naegeli, 1998). Spate-induced
damage of algal mats and subsequent recovery may
result in significant variation in photosynthesis and
respiration rates (Uehlinger & Naegeli, 1998), and in
corresponding changes of P-I curves (Hill & Boston,
1991). In oceanic climates, the predictability of spates
is usually low. This is reflected by unpredictable
primary producer biomass, photosynthesis and
respiration rates (Uehlinger, 1991; Uehlinger et al.,
1996; Uehlinger & Naegeli, 1998).
Present knowledge of the relationship between light
and photosynthesis of benthic primary producers is
largely from chamber studies (e.g. McIntire & Phinney, 1965; Jasper & Bothwell, 1986; Boston & Hill,
1991; Guasch & Sabater, 1995) and few open system
investigations (Duffer & Dorris, 1966; Hornberger
et al., 1976; Uehlinger, 1993; Young & Huryn, 1996).
The chamber method enables replication of productivity measurements of particular benthic assemblages
but faces problems such as enclosure artefacts or
difficulties in scaling the results up to a stream reach
(e.g. Hornberger et al., 1976; Uehlinger & Brock, 1991;
Marzolf et al., 1994). The chamber method is also
relatively expensive (manpower for operation and
equipment), which limits the number of measurements in time. The open-system technique (Odum,
1956) makes continuous determination of photosynthesis and respiration rates possible over extended time
periods (weeks to months). The continuous measurement of light and oxygen concentrations required for
this technique can be gained with a relatively small
effort, but knowledge of the reaeration coefficient is
usually required to determine production and respiration rates. The open-system method integrates the
metabolism of local communities. Photosynthesisirradiance curves obtained with this method characterise the photosynthetic response of a stream reach
and yield key information for estimating or predicting
primary production at the ecosystem level.
This study focused on the question of how season
and disturbance influence primary production and
respiration at the ecosystem (reach) level. We inves-
tigated primary production and ecosystem respiration
in a river that is characterised by light conditions
favouring primary production, high ambient nutrient
concentrations, a high reaeration rate and relatively
frequent spates. We assumed that spates would have
a significant impact on stream metabolism, and
therefore expected to observe corresponding changes
in P±I parameters and ecosystem respiration. In the
absence of spates, P±I parameters and ecosystem
respiration should be related to regular seasonal
changes. To test these hypotheses we analysed diel
oxygen curves and identified parameters describing
P±I curves and ecosystem respiration using a river
oxygen-balance model.
Methods
Study site
The Glatt catchment (area = 416 km2) is in the northeastern part of the Swiss Plateau. The River Glatt,
outflow of the eutrophic lake Greifensee (river km
0.0), flows through a densely populated area to the
river Rhine (confluence at river km 35.5). The river
was channelised in the early 20th century. In the study
reach (river km 26.1±35.1) banks are protected with a
stone rip-rap. Channel cross-sections are trapezoidal.
Five artificial cascades and boulder ramps (length
about 8 m, height 0.9±1.76 m) and small drops (sills)
every 50 m along the river control channel slope,
prevent bed erosion during high flow, and cause high
Table 1 Morphological, hydrological and chemical characteristics of the River Glatt between river km 26.1 and 35.1
Average slope of reach (%)
Average slope between cascades (%)
Elevation (m a.s.l.)
Width at Q329 (m)
Depth at Q329 (m)
Mean annual discharge (m3 s±1)
Q329 (m3 s±1)*, y
Frequency of spates with Qmax > 30 m3 s±1 (n/y)y
NH4-N (mg L±1) concentrationy, z
NO2-N (mg L±1) concentrationy, z
NO3-N (mg L±1) concentrationy, z
Soluble Reactive Phosphorus (mg L-1)
concentrationy, z
0.67
0.56
335±396
16.2
0.43
8.56
3.98
5.5
0.45
0.11
5.5
0.41
*Discharge exceeded on 329d (90%) of a year.
y1992±96.
zAverage of 2-week cumulative samples.
ã 2000 Blackwell Science Ltd, Freshwater Biology, 44, 493±507
Variability of photosynthesis±irradiance curves
re-aeration rates. The surface layer is dominated by
relatively coarse gravel (mean diameter about
50 mm). The flow regime is characterised by relatively
frequent spates. Table 1 summarises information on
channel morphology, hydraulics and hydrology of the
River Glatt. Shading of the wetted channel is minimal
because the channel is wide (about 15 m) and there is
little riparian tree vegetation. The inflows to the river
of treated sewage from 7 treatment plants maintain
high concentrations of nitrate and soluble reactive
phosphorus (Table 1).
Data origin
The Swiss National Hydrological and Geological
Survey continuously measured discharge (Q), temperature (T) and dissolved oxygen (O2), as well as
nutrient concentrations of two-week cumulative samples at river km 35.1 (NADUF program, Jakob et al.,
1994). Global radiation was recorded at ZuÈrich
Airport (about 8 km south of the study reach) by the
Swiss Meteorological Institute (SMA). The Water
Protection Authority of the Canton ZuÈrich (AWEL)
provided data on channel morphology.
Model description
rate due to gas exchange between water and the
atmosphere. Respiration was parameterised as (Eqn 2)
r=−
∂C
∂C
+ν
= p + r + rex
∂t
∂x
(1)
where v is mean current velocity, p is the oxygen
production rate due to gross primary production, r is
the oxygen production rate due to respiration (`production' just indicates the sign; consumption due to
respiration is negative) and rex is the oxygen transfer
ã 2000 Blackwell Science Ltd, Freshwater Biology, 44, 493±507
ER
d
(2)
where ER is the ecosystem respiration rate per unit
surface area of the river bed (g O2 m±2d±1) and d is the
mean water depth. The ecosystem respiration rate
summarises the effect of all processes consuming oxygen,
including endogenous respiration of algae and bacteria,
degradation of organic matter by heterotrophic bacteria,
nitrification, oxygen consumption by consumers and
chemical processes. Eqn 3a describes p as a function of
incident light:
p=
Pmax I 1
K+I d
(3a)
Pmax is the parameter describing light saturated
photosynthesis (g O2 m±2d±1), I is the light intensity at
the water surface (W m±2), and K is the half-saturation
light intensity (W m±2). The slope of this curve at low
light intensities is given as a = Pmax/K. Eqn 3b is a
reparameterisation of Eqn 3a that is useful for parameter estimation (Ratkowski, 1986) and makes it
possible to switch from a model with light saturation
to a linear model of light intensity by setting P2 = 0:
p=
We used oxygen data and an oxygen mass-balance
model to calculate gross primary production and
ecosystem respiration. Model simulations, parameter
estimations and sensitivity analyses were performed
with the computer program AQUASIM (Version 2.0),
which is designed for the identification and simulation of aquatic systems (Reichert, 1994a,b, 1995;
http://www.aquasim.eawag.ch).
We used the following equation (Eqn 1), which
neglects longitudinal dispersion, to describe O2
dynamics in the investigated study reach (dispersion
was irrelevant for the daily variations observed for
oxygen; the same methodology could easily be
applied with consideration of dispersion):
495
I
1
P1 + P2 I d
(3b)
with the inverse of the slope a, P1 = K/Pmax = 1/a, and
the inverse maximum photosynthesis rate, P2 = 1/Pmax.
The gas exchange rates along river sections and
across river cascades was determined with the aid of
SF6 tracer experiments (Cirpka et al., 1993 and additional measurements performed for this study). The
gas exchange rate rex (g O2 m±3d±1) along river
sections between cascades or ramps was calculated as:
(
)
rex = Ks , 0 (Csat − C ) exp β(T − T0 )
(4)
where Ks,0 is the reaeration coefficient at T0 (d±1), b
describes temperature dependence (°C±1), T0 is the
reference temperature (20 °C), and Csat is the saturation
concentration of oxygen. The results of the tracer
experiments showed no significant discharge-dependence of Ks. In our model we set b to the literature
value of 0.0238 °C±1 (Elmore & West, 1961) because our
reaeration measurements did not cover a temperature
interval large enough to provide an estimate with
reasonable accuracy. A value of Ks,0 = 43 d±1 led to
best agreement with all available SF6 tracer experiments
496
U. Uehlinger et al.
the results of which had been converted to the gas
transfer of oxygen. Across cascades or ramps turbulence
and air bubbles enhance reaeration. The reaeration
efficiency E of a ramp describes the extent to which
super- or subsaturation will be reduced across the ramp
(Gameson, 1957; Cirpka et al., 1993):
E=
Cup − Cdown
(5a)
Cup − Csat
where Cup is the oxygen concentration upstream of the
ramp and Cdown is the oxygen concentration downstream
of the ramp. To account for discharge and temperature
dependence we used the following equation (Gulliver
et al., 1990; Cirpka, 1992):
E(T , Q) = 1 − (1 − E0 )(Q / Q0 )

(
o −1
0.214  1.0 + 0.02103 C (T −T0 )

)
(5b)
where E0 is the reaeration efficiency at the reference
temperature, T0 = 20 °C, for the reference discharge,
Q0 = 1 m3s±1. Values for E0 of 0.64, 0.67, 0.66, 0.62 and
0.57 for the five cascades within the modelled river
section led to best agreement with all available measurements.
Because we lacked oxygen data for the upstream
station, we arbitrarily set upstream oxygen concentrations equal to the saturation concentration. A sensitivity analysis demonstrated that the upstream
concentration did not influence oxygen concentrations
at the downstream station (Fig. 1), and thus did not
influence estimates of primary production and
respiration. We estimated parameters for 3-day
periods with no flow peaks and Q < 15 m3 s±1.
Determination of Ks and E
Estimates of Ks and E were based on measurements
for gas exchange of sulphur hexa-fluoride (SF6). A
gas mixture of SF6 and N2 (1% v/v SF6) was
injected at a constant flow rate of 0.4 L min±1
through 4 fritted glass diffusers. The diffusers
were mounted on the stream bed at river km 29.1.
We added uranine (fluorescent dye) at river km
29.08 about 30 min after the beginning of the SF6
injection. We monitored the uranine cloud with an
in situ fluorometer at 5 ramps. We collected water
samples immediately upstream and downstream of
each ramp at the peak of the uranine cloud using
50-mL glass syringes equipped with three-way
valves, leaving no head space. The filled syringes
were transferred to the laboratory and SF6 was
determined on a gas chromatograph. A more
detailed description of the sampling procedure and
the subsequent analysis is given by Cirpka et al.
(1993). SF6 was also added by `slug' injection. About
10 L SF6-saturated water were added to the river a
few minutes after the uranine solution had been
added. Samples were taken at 4 stations (station 2
and 3 were upstream and downstream of a ramp as
described above). For the calculation of Ks and E,
we also used data of Cirpka (1992), who measured
SF6 exchange in the same reach of the River Glatt.
All measured SF6 rates were converted to oxygen
exchange rates by multiplication with the square
root of the ratio of the diffusion coefficients of these
substances in water.
Determination of production and respiration rate parameters
Fig. 1 Simulated oxygen concentration along the study reach
(noon of 19 July 1992). Calculations were performed with 3
different input concentrations at river km 26: 15 mg O2 L±1
(short dashes), saturation concentration (solid line), and 0 mg O2
L±1 (long dashes). The dotted line is the saturation concentration.
Discontinuities of the oxygen curves correspond to the ramps.
After the 3rd ramp (river km 31.71) oxygen concentrations
become independent of upstream concentrations at river km 26.
Estimates of the parameters P1, P2 and ER are based
on the minimisation of the squared deviations
between measurements and model results (Eqn 6):
RSS =
∑ (C(ti ) − Cmeas ,i )
n
2
(6)
i −1
Where n is the number of observations, Cmeas,i is the
oxygen concentration measured at time ti at the end of
the study reach, and C(ti) is the oxygen concentration at
ã 2000 Blackwell Science Ltd, Freshwater Biology, 44, 493±507
Variability of photosynthesis±irradiance curves
497
Table 2 Influence factors used for the multiple regression analysis
Factor
Symbol
Variable characterics:
Time (d)
Days since the last spate with Qmax > 25 m3 s ± 1
Days since the last spate with Qmax > 30 m3 s ± 1
Discharge (m3 s±1)*
Global radiation (W m±2)*
Temperature (°C)*
Smoothed 1st derivative of temperaturey
t
DS25
DS30
Q
I
T
dT/dt
Long-term trend
Disturbance influence of spates
Disturbance influence of spates
Current environmental conditions
Seasonal change, current environmental conditions
Seasonal change, current environmental conditions
Seasonal change with a phase shift to temperature or light
*Average of 3-day interval.
yThe 1st derivative used for calculations was the analytical derivative of a second order polynomial. This polynomial was fitted to
the temperature data that were weighted with a normal distribution centered at ti (d) and with a standard deviation of 30 d.
the time ti calculated with the model as the numerical
solution of the partial differential Eqn 1 with rate terms
given by Eqns (2), (3b) and (4), and boundary conditions
at the cascades and ramps that consider the gas exchange
efficiency given by Eqn 5a,b.
Statistical analysis
We used stepwise regression analysis to explore the
potential influence of season, disturbance and current
environmental conditions on ER, P1 and P2. The
influence factors considered in this study are
described in Table 2. The small correlation between
the influence factors shown in Table 3 indicates that
the stepwise regression analysis may be able to
discriminate among the different factors. Preliminary
analyses led to the conclusion that nonlinear effects in
some of the influence factors were relevant for some
of the modeled variables (especially for the dependence of P1 on I). For this reason, the regression model
included the influence factors listed in Table 2 as well
as the squares of the factors that refer to current
environmental conditions. Note that the correlation
coefficients between T and T2, Q and Q2, and I and I2
Table 3 Correlation matrix of the influence factors listed in
Table 2
t
t
DS25
DS30
T
dT/dt
Q
I
±
±
±
±
±
±
1
0.13
0.45
0.03
022
0.12
0.08
DS25
DS30
1
0.46
± 0.01
0.24
± 0.29
0.04
1
± 0.05
0.32
± 0.24
0.07
T
1
± 0.03
± 0.14
0.74
dT/dt
1
0.23
0.52
Q
I
1
0.05
1
ã 2000 Blackwell Science Ltd, Freshwater Biology, 44, 493±507
(0.98, 0.97, and 0.97), respectively, were much larger
than those between the influence factors themselves
(Table 3). These high correlation coefficients are
caused by the limited range of values (which leads
only to a moderate curvature) and by the absence of
statistical fluctuations in the functional relationships.
Because negative values for ER, P1 and P2 are
unreasonable, the regression model was forced to
return a non-negative output. This makes the model
nonlinear in the parameters. The full model is given as
X = max
 a + bt + cDS25 + dDS30 + eT + fT 2 +


 g dT + hQ + iQ 2 + jI + kI 2 ,0



 dt

(7)
where X is either ER, P1 or P2 and a, b, c, d, e, f, g, h, i, j and
and k are model parameters quantifying the influence
of the factors with which they are multiplied (see
Table 2). The full model given by Eqn 7 can be
simplified to a series of submodels that omit the
influence of certain factors by setting the corresponding
parameters to zero.
To assess the importance of the factors on the
modeled variables ER, P1 and P2, a backward
elimination analysis was performed starting with the
full model (7) and iteratively eliminating the least
important factor at each step (for each modelled
variable we tested 2p9±1 models, p9 = number of
parameters of the full model, light was not considered
a factor influencing ER). This resulted in the ranking
of factors for each of the modeled variables ER, P1 and
P2 according to the significance of their influence. The
results of this analysis were compared with those of a
complete stepwise analysis of all submodels.
To support the decision about which factors should
be considered to be significant, two information
498
U. Uehlinger et al.
criteria, the Akaike Information Criterion, AIC
(Akaike, 1969; Rawlings et al., 1998) and the Schwarz
Bayesian Criterion, SBC (Schwarz, 1978; Rawlings
et al., 1998), were calculated for the submodels
selected in the backward analysis:
AIC = n ln(RSS) + 2 p − n ln(n)
(8)
SBC = n ln(RSS) + p ln(n) − n ln(n)
(9)
where RSS is the residual sum of squares of the
submodel, n is the number of data points and p is the
number of parameters of the submodel. These criteria try
to formalize the trade-off between quality of fit and
model complexity. An increase in the complexity of a
model leads to a decrease of the first term due to a
decrease in RSS but at the same time to an increase of the
second term due to an increase in the number of
parameters, p (the third term remains constant for all
investigated alternatives). This means that a more
complex model is only accepted (significantly smaller
value of the information criterion), if the decrease in RSS
leads to a significantly larger decrease of the first term in
comparison to the increase of the second term. The
model is selected at which the AIC- or SBC-curve as a
function of the number of parameters of the submodel
selected in the backward analysis becomes flat or starts to
increase (in most cases, this is not the model with a
minimum value of the criterion). According to the
differences in the second term, the AIC-criterion tends
to select more complicated models than the SBC-criterion
if n is larger than 7. Scientific judgment of the results is
used to select the criterion to be applied for the selection.
We performed the final regression analysis with data
from 123 of the evaluated 137 3-day periods. We
excluded periods with suspicious O2 measurements (in
most cases supersaturation during night; eight periods)
and periods that were identified as outliers (six periods)
in the regression analysis.
Results
Figure 2 shows the flow regime of the River Glatt
between 1992 and 1997. During this period, the
average frequency of spates with a maximum discharge exceeding 30 m3 s±1 was 5.5 per year. Initiation
of sediment transport is considered to be a useful
disturbance threshold for benthic primary producers.
Estimates of the dimensionless critical shear stress
(based on channel geometry and grain size distribution, Gessler, 1965) suggest that bed sediments in
River Glatt should start to move if discharge exceeds
about 30 m3 s±1. However, sediment transport during
high flow is small in River Glatt. Upper reaches and
tributaries only supply small amounts of sediments,
and cascades, boulder ramps and numerous sills keep
bed erosion at a low level. The persistence of
macrophytes (mainly Ranunculus fluitans) indicates
high bed stability in the face of spates. Shear stress
and suspended solids may damage benthic primary
producers before bed sediments start to move. This
makes it difficult to define a disturbance threshold
(considering the particular geomorphic and hydraulic
settings the threshold of 30 m3 s±1 may be arbitrary to
some extent), and as consequence to describe the
disturbance regime of the River Glatt.
Calculated O2 concentrations based on parameter
estimates performed with AQUASIM tracked the
measured O2 data reasonably well. Figure 3 shows
four selected oxygen time series that demonstrate
typical observations. The top left plot (May, 1992)
shows an excellent simulation for three days with
similar radiation. Such a situation could be modelled
with a nearly linear P(I) curve. The top right plot
(October 1997) shows similar oxygen curves on
October 19 and 20 despite differences in radiation.
Fig. 2 Discharge of River Glatt at river km 35.1 (1992±97). The dashed line indicates the spate threshold of 30 m3 s±1.
ã 2000 Blackwell Science Ltd, Freshwater Biology, 44, 493±507
Variability of photosynthesis±irradiance curves
499
Fig. 3 Global radiation (small upper panels) and measured and simulated concentrations of dissolved oxygen (large lower panels) on 4
selected 3-day periods. Large lower panels: circles = measured oxygen concentrations, bold line = simulated oxygen concentrations,
fine line = oxygen saturation concentrations
Only the significantly larger decrease in radiation on
October 21 led to a decrease in oxygen concentration
during the day. Such a behaviour can only be
achieved in the model with a significant saturation
effect in primary production at high light intensities.
The two bottom plots show typical deviations of the
calculations from the measurements. In the situation
shown in the bottom left plot (February 1992) the
actual respiration rate seemed to be higher in the
nights from January 31 to February 1 and from
February 3 to February 4 than in the two nights
between. This cannot be reproduced with a model
using a constant respiration rate. The deviations in the
bottom right plot (February 1996) are much more
erratic. In addition to the differences in respiration
visible during the night, there were also deviations
during the day. Note, however, that the amplitude of
ã 2000 Blackwell Science Ltd, Freshwater Biology, 44, 493±507
oxygen concentrations in this situation was about 1
gO2 m±3, whereas it is 4 gO2 m±3 in the situation
shown in the top left plot.
Figure 4 reveals distinct seasonal patterns of the
three investigated metabolic variables. Because P1 is
the inverse slope of the linear part of the P±I curve its
small values during the winter reflect a large slope of
the P±I curve at reduced light intensities. This
indicates a population that is adapted to reduced
light conditions during the winter. The low P2 values
observed during summer reflect a lack of light
saturation (linear P±I curve). Light saturation of
photosynthesis, characterised by low values of P1
and high values of P2, was mainly restricted to the
winter season. Differences between the summer and
winter values of P1 and P2 were highly significant
(Table 4). Ecosystem respiration was significantly
500
U. Uehlinger et al.
Fig. 4 Seasonal variation in photosynthetic parameters and respiration: (A) P1 (B) P2 and (C) ER. Data of 123 three-day periods were
pooled in each graph.
greater in summer than in winter; however, the
variance was also much larger in summer (Table 4).
The results of the backward elimination analysis of
influence factors starting with the full model (Eqn 7)
(for ER with omission of the factors I and I2) are
shown in Table 5 for all three modelled variables. As
shown in Table 6, a full analysis of all possible
submodels of the model given by Eqn 7 only led to
improvements in the three and four parameter
submodels for P1 and in the two and three parameter
submodels for P2 (for ER the full analysis led to
exactly the same results as the backward analysis).
Because these deviations are small and affect only
submodels that are simpler than the selected model
(see below), our discussion is limited to the consistent
results of the backward analysis.
Figure 5 shows the values of the information
criteria AIC and SBC (according to the Eqns 8 and 9)
for all models resulting from the backward analysis
and for all modelled variables. The criterion of
Table 4 Result of a t-test for comparison of summer (May, June, July) and winter (November, December, January) values of P1, P2 and
ER (n = 27)
Mean
Variance
t-statistic
p (2-tail)
P1 summer
P1 winter
P2 summer
P2 winter
ER summer
ER winter
11.83
28.50
5.60
5.59
0.0062
9.8 10±5
0.0414
4.4 10±4
17.65
73.96
7.79
5.23
5.54
< 0.00001
7.87
< 0.00001
5.76
< 0.00001
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Variability of photosynthesis±irradiance curves
501
Table 5 Evaluation of the best submodels for a given number of influence factors using the backward elimination procedure. p =
number of parameters (including the constant) (+) indicates, which parameters were considered in each submodel. Finally selected
models and factors contained in these models are marked in bold
Dependent
variable
p
Influence factor and model parameter
t
DS25
DS30
T
T2
dT/dt
b
c
d
e
f
g
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
P1
11
10
9
8
7
6
5
4
3
2
1
a
+
+
+
+
+
+
+
+
+
+
+
P2
11
10
9
8
7
6
5
4
3
2
1
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
ER
9
8
7
6
5
4
3
2
1
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
selecting the model, where the values of AIC and SBC
(as a function of the number of submodel parameters)
becomes flat or start to increase, led to the clearer
results for SBC-criterion than for AIC. Depending on
the interpretation of 9significant changes', the AICcriterion led to the selection of a submodel in the
range between that selected by the SBC-criterion to a
significantly more complicated submodel. According
to our judgement, it is not meaningful selecting more
complex models than those selected by the SBCcriterion, which therefore was applied. This agrees
with other studies demonstrating that the AICcriterion tends to select too complicated models
(Judge et al., 1980) and supports the selection of the
ã 2000 Blackwell Science Ltd, Freshwater Biology, 44, 493±507
2
2
Q
h
+
+
+
+
+
Q
i
+
+
I
j
+
I
k
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
RSS
r2
Added
factor
367.9
367.9
370.4
379.9
393.3
413.1
459.7
555.2
713.4
791.3
2200
0.833
0.833
0.832
0.827
0.821
0.812
0.791
0.748
0.676
0.640
0.000
I
Q2
t
DS25
Q
DS30
T2
T
dT/dt
I2
0.01027
0.01027
0.01027
0.01033
0.01038
0.01084
0.01121
0.01189
0.02000
0.02896
0.04387
0.766
0.766
0.766
0.765
0.763
0.753
0.745
0.729
0.544
0.340
0.000
I
Q
t
DS25
T2
I2
DS30
Q2
dT/dt
T
3284
3294
3320
3386
3461
3842
4175
4991
6427
0.489
0.487
0.483
0.473
0.461
0.402
0.350
0.223
0.000
Q
DS25
T2
DS30
Q2
dT/dt
t
T
submodel with 6 parameters for P1, the submodel
with four parameters for P2, and the submodel with
five parameters for ER. Table 7 shows the estimated
parameter values and standard errors for the selected
models for all three modelled variables.
The results of the stepwise regression procedure
indicate a dominant influence of season or current
environmental conditions (dT/dt, T, I) on P1 and P2.
The six-parameter submodel, which was finally
evaluated for prediction of P1, considered I2, dT/dt,
T, T2 and DS30 (in the order of importance) as
important factors. Additional parameters led only to
minor decreases of RSS (Fig. 5A). The four parameter
model with the factors T, dT/dt and Q2 explained 75%
502
U. Uehlinger et al.
Table 6 Parameter combinations of the full regression analysis of all submodels that yielded lower RSS than the best model of the
backward procedure. p = number of parameters (including the constant) (+) indicates parameters that were considered in the
submodel
Dependent
p
Influence factor and model parameter
variable
P1
P2
4
3
3
a
+
+
+
3
3
3
3
3
3
3
2
2
+
+
+
+
+
+
+
+
+
t
b
DS25
c
DS30
d
+
+
T
e
T2
f
dT/dt
g
Q
h
Q2
i
I
j
+
+
+
+
+
+
+
+
+
+
+
+
+
+
I2
k
+
+
+
+
+
+
+
+
RSS
r2
527.4
632.9
657.3
0.760
0.712
0.701
0.01474
0.01520
0.01559
0.01682
0.1789
0.1910
0.01915
0.02233
0.02391
0.664
0.654
0.645
0.617
0.592
0.565
0.564
0.491
0.45
of the variation in P2. The exclusion of Q2 decreased
the r2 by 25%, but the effect of excluding DS30 was
rather small (r2 decreased by only 2%).
About 20% of the variation in ER could be
attributed to T. The second most important factor for
ER was time, t, which reflected a decrease in ER from
1992 and 1997 superimposed on the seasonal variation. The last selected 5-parameter model considered
T, t, dT/dt and Q2 as important factors, but did not
include the disturbance related parameters DS25 and
DS30. This model explained only 46% of the variation
of ER, distinctly lower than the corresponding models
for P1 and P2.
Discussion
The results of our investigation of the river Glatt
showed that parameters of P±I curves and ecosystem
respiration (ER) were subject to distinct seasonal
variation. Only a minor extent of the variability of
P±I curves could be attributed to spates, and no
significant correlation was found between ER and
spates. The magnitude of spates was apparently too
small to severely affect the biologically mediated
energy flow in this river.
Fig. 5 Results of stepwise multiple regression analysis.
Evaluation of best models for (A) P1 (B) P2 and (C) ER. The
residual sum of squares (RSS = open circles), and the
information criteria AIC (open squares) and SBC (filled squares)
as function of the number of submodel parameters.
The influence of flow on P±I curves and ER
The results of the stepwise regression analysis
indicated a modest influence of spates with Qmax
ã 2000 Blackwell Science Ltd, Freshwater Biology, 44, 493±507
Variability of photosynthesis±irradiance curves
503
Table 7 Parameter values of selected models
Factor Parameter
P1
Value
t
DS25
DS30
T
T2
dT/dt
Q
Q2
I
I2
a
b
c
d
e
f
g
h
i
j
k
10.71
0
0
± 0.0806
± 1.10
0.0303
± 19.7
0
0
0
0.000193
P2
s.e.
Unit
Value
0.96
±
±
0.0022
0.17
0.0068
3.4
±
±
±
0.000014
g±1 Wd
0.0407
g±1 W
0
g±1 W
0
g±1 W
0
g±1 Wd K±1
± 0.00329
g±1 Wd K±2
0
g±1 Wd2 K±1
± 0.200
g±1 m±3 Ws d
0
g±1 m±6 Ws2 d
3.03 10±4
g±1 m2 d
0
g±1 m4 W±1 d
0
> 30 m3 s±1 (DS30) on P±I curves. Time since the last
spate of this magnitude was the parameter with the
least significance in the selected model for P1 = 1/a.
For P2, DS30 was not considered a significant factor in
the selected model. The sign of the parameter d (see
Table 7) indicates an increase of a with increasing
DS30. This response may reflect post-spate recovery of
primary producers. Hill & Boston (1991), who
examined P±I curves of periphyton in developmental
sequences, found that in shaded and partly shaded
sites Pmax and a significantly increased 3±13 fold
within 2 months, and Dodds et al. (1999) reported
positive correlations between algal biomass and Pmax
and a. We lack information on primary producer
biomass but we assume that the relatively high
stability of bed sediments (cascades, boulder ramps
and sills stabilise the riverbed) and the lack of
substantial sediment supply from tributaries kept
bedload transport low and reduced damage to the
autotrophic community. Besides moving bed sediments high shear stress during spates may also have
resulted in partial elimination of benthic algae and
macrophytes, but these losses were presumably too
small to result in distinct changes to P±I curves during
subsequent recovery periods. The studies of Hill &
Boston (1991) and Dodds et al. (1999) suggests that
spates, which severely damage the autotrophic community, may have a stronger impact on P±I curves
than that observed in the River Glatt. Biggs et al.
(1999) examined 12 New Zealand headwater streams
subject to spates of different intensities and frequencies and found only a moderate effect of disturbance
on Pmax. However, the influence of spates on the
shape of P±I curves was not evaluated because the
ã 2000 Blackwell Science Ltd, Freshwater Biology, 44, 493±507
ER
s.e.
Unit
0.0029
±
±
±
0.00030
±
0.019
±
0.31 10±4
±
±
g±1
g±1
g±1
g±1
g±1
g±1
g±1
g±1
g±1
g±1
g±1
m2 d
m2
m2
m2
m2 d K±1
m2d K±2
m2d2 K±1
m±1 s d
m±4 s2 d
W±1 d
m2 W±2 d
Value
s.e.
132
27
± 0.00356 0.00076
0
±
0
±
0.567
0.087
0
25.1
6.3
0
±
± 0.050
0.014
0
±
0
±
Unit
gm±2 d±1
gm±2 d±2
gm±2 d±2
gm±2 d±2
gm±2 d±1 K±1
gm±2 d±1 K±2
gm±2 K±1
gm±5 s d±1
gm±8 s2 d±1
g W±1 d±1
gm2 W±2 d±1
assessment of a was not possible with their experimental setup.
Spates with Qmax > 30 m3 s±1 had no significant
effect on ER in the river Glatt. The apparent lack of
significant bedload transport during spates prevented
severe damage to the heterotrophic community and
primary producers (autotrophic respiration). Moreover, the hyporheic zone, which is a major site of
metabolic activity in streams with alluvial channels,
may only be severely disturbed if high flow disrupts
the surface layer of the riverbed (Grimm & Fisher,
1984; Pusch & Schwoerbel, 1994; Naegeli & Uehlinger,
1997; Uehlinger & Naegeli, 1998).
Seasonal variation of P±I curves and ER
Our study demonstrated a distinct seasonal variation
in P±I curves of the River Glatt. Light and temperature
(or derivatives of the seasonal variation of these two
factors) were major predictors of P1 and P2 or Pmax and
a respectively. Temperature and light vary in a regular
manner during the annual cycle. Changes in water
depth and turbidity affect light availability near the
river bottom. In River Glatt significant increases in
water depth are unpredictable and limited in time and
periods of high turbidity are presumably restricted to
spates. Regular seasonal variations in P±I curves
apparently prevail in the absence of severe disturbance. Kelly et al. (1983) investigated primary productivity in a macrophyte-rich stream with constant flow
using the open system method. Based on daily
integrals of photosynthesis and incident light, they
identified parameters of hyperbolic P±I functions for
periods of 2 ±3 months. These parameters were subject
504
U. Uehlinger et al.
to seasonal changes like those in the River Glatt.
Similar temporal trends of Pmax and a also have been
reported for periphyton growing on macrophytes and
artificial substrata under stable flow conditions (Jones
& Adams, 1982; Jasper & Bothwell, 1986).
Light and temperature were apparently the most
important factors governing the shape of P±I curves.
However, apart from light and temperature, grazing
and changes in the structure of the autotrophic
community can also affect P±I curves (e.g. Hill et al.,
1992; Guasch & Sabater, 1995). The influence of these
factors is difficult to separate in field studies; for
example, changes in species composition or biomass
usually coincide with changes in temperature and
light during the annual cycle, and light and temperature both vary with solar radiation. We lack information in our study on invertebrates and the structure of
the autotrophic community. The lack of such information may increase the proportion of the variance that
cannot be explained by the regression models.
Although 80 and 75% of the variation in P1 and P2
were attributed to the selected independent variables
(Eqn 7 and Table 6), the influence of primary producer life cycles may be higher than 25% if they parallel
changes in light and temperature. On the other hand,
Dodds et al. (1999) found that photosynthetic parameters did not vary with taxonomic composition of
algal communities.
Distinct seasonal variation of ER, as observed in our
study reach, is common in many rivers (e.g. Flemer,
1970; Duffer & Dorris, 1966; Cushing & Wolf, 1984;
Servais et al., 1984; Uehlinger, 1993). Temperature is
considered to be a major factor regulating respiration
although the effect of temperature on benthic respiration has not been measured directly (Webster et al.,
1995). The apparent control by temperature of respiration rates in the River Glatt was relatively modest; only
22% of the variation in ER could be explained by
temperature. Similar poor correlations between temperature or season and ER have been reported from
systems receiving large amounts of dissolved organic
substances during the winter (Edwards & Meyer, 1987;
Meyer & Edwards, 1990). Due to our analysis
technique, oxygen consumption by nitrification cannot
be separated from oxygen consumption by respiration
processes and is included in our estimates of ER. For
the River Glatt, the contribution of nitrification to total
oxygen consumption is usually small (P. Reichert
unpublished data) but exceptions may occur in winter,
when respiration rates are small and ammonia concentrations are significantly higher than in the summer. The significant decrease of ER between 1992 and
1997 may be attributed to improved performance of
several sewage treatment plants.
The shape of P±I curves
In the River Glatt, P±I curves were linear or almost
linear functions of incident light (mainly during
summer) or exhibited a moderate light saturation
(during winter). This corroborates results of a metabolism study performed between river km 0.05 and
2.45 (Uehlinger, 1993). Linear P±I curves or P±I curves
lacking substantial light saturation are usually
obtained with the open system technique (Duffer &
Dorris, 1966; Kelly et al., 1974; Hornberger et al., 1976).
Young & Huryn (1996) reported complete light
saturation of photosynthesis in a New Zealand stream
during a period of dry weather, and attributed this to
the limitation of photosynthetic rates by nutrients,
temperature and autotrophic biomass.
Most studies focusing on photosynthesis±irradiance
relationships have been based on chamber experiments performed under controlled light conditions,
and with periphyton grown on natural or artificial
substrata (e.g. McIntire & Phinney, 1965; Jones &
Adams, 1982; Jasper & Bothwell, 1986; Boston & Hill,
1991; Hill & Boston, 1991; Guasch & Sabater, 1995).
This approach yields community-specific information
on photosynthesis at a spatial scale of usually less
than 0.05 m2. Saturation or even inhibition of photosynthesis at high light intensities is a phenomenon
almost exclusively reported from chamber studies
(e.g. McIntire & Phinney, 1965; Hill & Boston, 1991;
Hill et al., 1992, 1995). Dodds et al. (1999) suggested
that photoinhibition in periphyton communities
might be a rare phenomenon, and Hornberger et al.
(1976) argued that light saturation or inhibition might
result from nutrient depletion during incubation,
because communities contained in chambers lack the
continuous supply available in freely flowing water.
The open system technique measures photosynthesis at the ecosystem level. The corresponding P±I
curves integrate the response of local communities to
local light conditions over a reach length of less than
3v/Ks (v is mean current velocity and Ks the
reaeration coefficient). Light conditions in stream
ecosystems are subject to high spatial variability that
ã 2000 Blackwell Science Ltd, Freshwater Biology, 44, 493±507
Variability of photosynthesis±irradiance curves
ranges from centimetres (single rocks, Hill, 1996) to
kilometres (e.g. changes in canopy cover along the
river continuum). The complex spatial structure of
the river bottom and presence of macrophyte stands
creates habitats that are highly diverse with respect
to light. We assume that in such environments a
substantial fraction of photosynthesis by epilithic and
epiphytic algae and macrophytes are light limited,
which finally results in ecosystem P±I curves lacking
substantial light saturation.
Changes in photosynthesis±irradiance curves and
ecosystem respiration of the river Glatt were dominated by a regular seasonal trend despite frequent
spates. The observed variation in P±I curves may be
explained by the adaptation of primary producers to
the seasonally changing light and temperature conditions, by primary producer life cycles, and by changes
in the composition of the primary producer population. This study and others (Kelly et al., 1983) suggest
that modelling of primary production in streams
lacking significant bed load transport during high
flow, may only require one class of primary producers
that is characterised by few model parameters. Light
and temperature are the major input variables of such
a model. However, further investigations are needed
to evaluate the temporal dynamics of P±I curves in
streams where severe disturbances such as bed
moving spates are common features.
Acknowledgments
The Swiss National Hydrological and Geological
Survey kindly provided data on discharge, dissolved
oxygen, water temperature and nutrient concentrations, the Swiss Meteorological Institute (SMA) data
on light intensity and air pressure and the Water
Protection Authority of the Canton ZuÈrich (AWEL)
data on river geometry and morphology. Comments
by Chris Robinson and two anonymous reviewers
improved the manuscript.
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