Introduction
Lakes are very important actors in the local and global carbon cycles
. They both fix carbon, through photosynthesis of the
in-lake primary producers, and release it, through respiration of all the
aquatic organisms (primary producers, consumers and microbes), through
photochemical reactions and by transmitting the received carbon from the
catchment (lateral transport) back to the atmosphere in gaseous form
(primarily as CO2). Many lakes – especially the oligotrophic ones typical
of high latitudes – are net heterotrophic systems where the rate of
community respiration exceeds that of primary production ;
this contributes to make lakes one of the most important natural sources of
greenhouse gases . However, they are not yet fully integrated into
the local and global carbon budgets, and the lacustrine carbon cycle is still
poorly known .
In freshwater ecology, productivity studies have usually relied on the light
and dark bottle method and the 14C labelling technique
. The first provides estimates both of the gross
and the net primary productivity, whereas the latter gives an estimate that
is between the gross and the net productivity, depending on the incubation
time. These traditional methods require time- and effort-demanding
measurements and have a poor temporal resolution. Periods of high
productivity are easily missed and, because of the low temporal
resolution, the non-linear relationship between photosynthetically active
solar radiation (PAR) and photosynthesis cannot be properly investigated. As
a consequence, carbon balances may be imprecise and for instance the net
ecosystem productivity (NEP) cannot be parameterised robustly as a function
of ambient variables. Moreover, communities enclosed in bottles experience
light and nutrient conditions far from the natural ones, since the movement
of water or of the organisms themselves is limited , and the
results can be unrealistic. Thus, advances in the methodology are necessary
to better estimate freshwater ecosystem productivity and to expand our
understanding of the carbon cycle in the water column.
In the last 15 years, free-water methods, not requiring sampling and
incubation, have become more common. These methods, however, are usually
based on the measurement of the O2 concentration in the water, which is
then used as a proxy for CO2 ; this introduces uncertainties
. The respiratory quotient that has to be applied when
transforming rates from O2 to CO2 has, in fact, large variations
.
To study the in-water photosynthesis and respiration, proposed a
free-water method based on the direct measurement of the CO2 concentration
in the water with non-dispersive infra-red (NDIR) CO2 probes, associated
with a concomitant assessment of the CO2 flux between the lake and the
atmosphere. The probes are designed to measure the CO2 concentration in
the air, but by building a gas collection system the concentration in the
water is obtained. Similar probes have also been used in ,
albeit not for productivity studies. The temporal resolution is 5 seconds,
more than a hundredfold improvement over the traditional approaches.
A requirement of the method is the concomitant assessment of the CO2 flux
from the lake to the atmosphere. Information on the in-lake vertical CO2
flux is also needed (and, ideally, on the lateral transport as well). If such
data are missing the method can be applied under specific conditions (e.g.
stable stratification); it still allows for the parameterisation of the NEP from
PAR and water temperature, from which the NEP can then be calculated under
different conditions.
In , the method was tested on a small boreal lake in Finland over
3 days only, during the autumn turnover. A cross comparison was carried
out between different measurement methods, but the NEP was not mathematically
parameterised and the method was not quantitatively verified. Despite the
very short data set and the specific conditions, the results were promising:
the relationship between PAR and NEP was clearly visible, the measured
respiration rate was 16 times higher than with the bottle method and the
measured productivity was 5 times higher than with the 14C technique.
The numbers are in line with previous studies: reported similar
discrepancies between an oxygen-based free-water approach and the bottle
method in small lakes in Michigan, and a tendency of the 14C method to
underestimate the productivity is well known . However, the method
has been overlooked and has not been used for productivity calculations since
2008, possibly because of the limited testing.
Here we tested the method of on a different boreal lake, under
different conditions and on a much longer data set, quantitatively verifying
it. We continuously collected data for four summers, and then we focused on
the periods when the lake was stably stratified, i.e. summer conditions
typical of boreal dark-water lakes, in order to rule out the lateral CO2
flux and the CO2 flux from the deeper layers of the lake. Overall, we
analysed 40 days of data. We calculated the NEP using the equations that are
typically used in forest ecology, where high-frequency measurements are more
common, in an effort of harmonising the procedures between different fields.
Once we had the NEP with a high temporal resolution, we verified the
relationship between the NEP and irradiance, using a saturating
Michaelis–Menten model. We found an excellent agreement between the data and
the model. From that, we could also estimate the parameters of the
productivity–irradiance (PI) curves, specific to the in-lake communities.
These parameters are very important because they allow for the calculation of the
NEP from PAR and water temperature.
Whilst our efforts were mainly focused on method testing and development, we
also checked whether the parameters of the PI curves we estimated changed
significantly between the years. Our goal was to gather information on how
sensitive the parameters are to variations in the communities living in the
lake or in the environmental conditions. We investigated whether their
behaviour could be related to their main drivers, water temperature and
irradiance.
Materials and procedures
Study site
The study site is the boreal lake Kuivajärvi, in southern Finland
(61∘50.743′ N, 24∘17.134′ E). Lake Kuivajärvi is a
typical dark-water boreal lake. It is small and oblong and it is surrounded
by managed coniferous forests. Its surface area is 0.62 km2 and its
length is 2.6 km; its mean depth and maximum depth are 6.3 and 13.2 m,
respectively. The lake is humic (surface median dissolved organic carbon
concentration = 11.8 mg L-1 in 2011) and mesotrophic (surface
median annual total nitrogen concentration = 370 µg L-1
and annual total phosphorus concentration = 14 µg L-1 in
2011), with a chlorophyll a (Chl a) concentration in the surface layer usually
between 3 and 5 µg L-1 (median 4.8 µg L-1 in
2011), with summer values that can reach 30 µg L-1
. The lake is dark coloured: the Secchi depth ranges from 1.2 to
1.5 m . The lake is dimictic and it is frozen for 5 months
every year on average; the spring turnover occurs immediately after the ice-out
in late April or early May, and after the turnover a thermocline starts
developing. The thermocline deepens until the autumn turnover, and finally
the lake freezes over in late November or early December .
Most of the inflow is through a permanent stream at the northern end, while
the role of groundwater is small during summer. Temporary inflows appear at
snowmelt, through several small ephemeral streams. The outflow is located at
the southern end. The residence time was 522 days in 2011 and 655 days in
2013. A map with the location and bathymetry of the lake is available in the
Supplement (Figs. S1 and S2).
Measurements
All the instruments were mounted on a raft, which was moored in the middle of
the lake (see Fig. S2, for the exact position of the raft on the lake).
To measure the CO2 concentration in the water, a closed system
consisting of a NDIR probe (CARBOCAP® GMP343,
Vaisala Oyj, Vantaa, Finland) for the CO2 concentration in the air, gas-impermeable
tubes (stainless steel and Teflon) and a submerged gas-permeable
tube (silicone rubber, Rotilabo 9572.1, Carl Roth GmbH and Co. KG, Karlsruhe,
Germany) was built; the air was circulated continuously in the system by a
diaphragm pump (KNF Neuberger Micro gas pump, KNF Neuberger AB, Stockholm,
Sweden). Analog voltage outputs were used, logged with a Nokeval RMD680
serial transmitter to a ASCII file on a Windows-based computer. Since
silicone rubber has an excellent permeability to CO2 ,
the concentration of CO2 in the air circulating in the system
equilibrated with that in the water around the submerged tube. Hence, the
CO2 concentration in the water could be obtained from that in the air
using the dependence of CO2 solubility on temperature and pressure. The
CO2 concentration in the water CCO2 (dissolved CO2),
in µmol m-3, was calculated as
CCO2=χCO2PKH,
where χCO2 is the CO2 gas phase mole fraction in the
tube measured by the probe (in µmol mol-1), P is the total
air pressure inside the system and KH is Henry's law constant
(temperature dependent). For more details on the set-up see ,
and the Supplement (Fig. S3). The CO2 concentration in the
water was measured at a depth of 0.2 m (determined by the depth of the
submerged silicone tube). The system was operating continuously from May to
September 2010–2014, but the data from year 2012 are not used here due to
technical problems. The silicone tube was cleaned once a week to avoid
biofouling and changed once a month. The CO2 sensors were calibrated using
span and zero gases. A thermistor chain of 16 Pt100 resistance thermometers
(depths: 0.2, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 6.0, 7.0,
8.0, 10.0 and 12.0 m) was deployed and a PAR sensor (LI-192, LI-COR Inc.,
Nebraska, USA) for photosynthetic photon flux density (PPFD) was submerged in
the water at the same depth as the CO2 measurement (0.2 m). An eddy
covariance (EC) system (with ultrasonic anemometer USA-1, Metek GmbH,
Germany and closed-path infra-red gas analyzer LI-7000, LI-COR Inc.,
Nebraska, USA; replaced in 2011 by enclosed-path infra-red gas analyzer
LI-7200, LI-COR Inc., Nebraska, USA) was used to detect the CO2 flux
between the lake and the atmosphere. The fluxes were calculated and quality
screened according to the standard procedures, see ,
and the Supplement (Sect. S2). All the
instruments were powered by mains electricity.
Calculation of the net ecosystem productivity
The net ecosystem productivity (NEP,
µmol(CO2) m-2 s-1), also called net ecosystem uptake,
can be defined as
NEP=GPP-Rh,
where GPP (gross primary productivity) is the amount of carbon fixed by the
primary producers through photosynthesis and Rh (ecosystem
respiration) is the amount of carbon lost through respiration, both
autotrophic and heterotrophic. Provided that there are no inorganic sinks or
sources of CO2, the NEP is the opposite of the net ecosystem exchange
(NEE), whose expression can be derived from the conservation of mass. Hence,
considering the mass balance of CO2 in the mixed layer of the lake,
where most of the photosynthesis takes place, and assuming that lateral
transport of CO2 is of no importance, the NEP can also be expressed as
NEP=-NEE=-∫-hmix0∂CCO2z,t∂tdz-Fa+Fu.
In Eq. (3), CCO2 is the CO2 concentration in the water
calculated from Eq. (1), Fa is the CO2 flux between the
lake and the atmosphere (positive if from the lake to the atmosphere),
Fu is the CO2 flux between the deeper and the mixed layer
of the lake (positive if upwards), t is time and z is depth. The
integration is computed between the mixing depth hmix and the
surface. The mixing depth is defined as the depth at which the water
temperature starts decreasing faster than one degree per metre ;
in our case the average value for the entire study period was
hmix=1.5 m. Given the dark water colour and the resulting
low light conditions in the lake, there was no benthic primary production in
the profundal zone. For years 2010 and 2011, another CO2 probe was located
at a depth of 0.5 m, and its readings were consistent with those from the
probe at 0.2 m, hence showing homogeneous CO2 concentrations in the mixed
layer. While CCO2 was measured by the probe and
Fa by the EC system, we had no precise way of measuring
Fu. This is the main reason behind our choice to limit the
analysis to the summer days when the lake was stably stratified and it was
safe to assume no gas was exchanged through the thermocline: Fu=0. The periods of stable stratifications were chosen on the basis of
temperature plots and of the Schmidt stability of the lake, calculated with
the LakeAnalyzer program, according to . For all the chosen days,
the stability (Sc) is > 100 J m-2. However, not all days
with Sc>100 J m-2 were used: days with strong winds or
stable atmospheric stratification were discarded because of their impact on
fluxes (for more detailed information, see the end of this section). For the
time series of isotherms for the whole summers (from 1 June to 31 August),
and the time series of isotherms, Schmidt stability, CO2 concentration and
PAR at 0.2 m and air temperature for the periods of stable stratification
chosen for analysis each year see the Supplement (Figs. S4–S14). Overall, we
analysed 40 days in 10 periods occurring between mid-June and the end of July
of each year.
It is worth pointing out that Eq. (3) resembles the equation used in
terrestrial ecology to estimate the NEP. In fact, considering for example
forest EC calculations , neglecting lateral transport, the NEP is
NEP=-NEE=-∫0hmρd∂χCO2z,t∂tdz-ρdw′χCO2′‾.
In Eq. (4), ρdχCO2
(ρd = dry air density,
χCO2 = CO2 mixing ratio) replaces
CCO2 as the CO2 concentration in the air instead of in
the water, and z is the height (with hm = measuring
height); ρdw′χCO2′‾ is
Fa, the CO2 flux from the forest to the atmosphere,
calculated as the covariance between the fluctuations of the vertical wind
velocity and the gas mixing ratio. High-frequency measurements for
productivity are common in forest ecology. They are, however, less common in
aquatic ecology, where traditional approaches are still widespread despite
their limitations (low temporal resolution, unnatural conditions). Having
different methodologies and different time resolutions creates a gap between
the two fields, and makes comparing the estimates more difficult. Given that
the terrestrial and aquatic ecosystems are a continuum through which carbon
is cycled, using shared procedures is a step in the direction of connecting
and integrating these ecosystems, in order to have more precise carbon
budgets and a deeper knowledge of the carbon cycle.
A sample period of stable stratification in July 2010,
representative of the studied periods (DOY is day of the year). In panel (a), the solid line
(sto) is the first term of Eq. (3), the CO2 concentration change in time
over the mixed layer, which is usually referred to as storage flux in forest
ecology calculations; the dashed horizontal lines are the daytime and
nighttime average CO2 fluxes from the lake to the atmosphere
(Fa). In panel (b), the solid line is the NEP and the
dotted line is the zero rate. In panel (c), the solid line is the
PAR (photon flux density measured in the PAR wavelength range) average value
in the mixed layer. The resolution is 30 min, except for the
Fa average values.
Resuming our calculation of the NEP in aquatic ecosystems through Eq. (3), to
increase the precision of the concentration data, half-hourly averages of
CCO2 from the raw 5-second data were used. A 30 min resolution is
enough to capture the variations caused by the biological activity and at the
same time filter out the ones caused by the physical mixing of the water
. However, the EC data set, which also has a resolution of
30 min, had many gaps, due to inherent problems of the EC technique (wind
not blowing along the lake, stability or not fully developed turbulence
resulting in quality criteria not met) and technical problems (instrument
failures). Approximately 70 % of the data points for the summers were
rejected or missing, with occurrences of consecutive days having no
acceptable data points at all. Hence, for our data set, a point by point
calculation of Fa in Eq. (3) was not possible. Even though in general it would not be needed,
we had to use a daytime and a nighttime average value for Fa;
we maintained the half-hourly calculation of the NEP to preserve the temporal
resolution. The daytime and nighttime average Fa values were
calculated separately for each year, combining all the studied periods of
water stable stratification of the same summer. Before doing so, we checked
that the environmental conditions (temperature and relative humidity cycles,
incoming radiation, wind speed and direction, atmospheric stability) were
similar for all the analysed days in the summer. In particular, since wind
and atmospheric stability have the greatest influence on the fluxes (given
that the lake water is thermally stratified), as verified in ,
we discarded any day with winds > 5 m s-1 or with stable
atmospheric stratification. For the remaining days, the wind was always weak,
with averages < 2.5 m s-1; at such low speeds, the influence of the
wind on the flux is negligible . Under these circumstances (i.e.
warm and sunny summer days without strong wind events), the CO2 flux is
expected to have similar daily cycles across the studied days, as is shown by
the available EC data and by the EC data from years with more complete data
sets. Day and night were defined on the basis of PAR. When using PAR, we are
referring to the average PAR value in the mixed layer, obtained from the
0.2 m value through the lake light extinction coefficient (1.5). The
threshold between day and night was set to
20 µmol(ph) m-2 s-1 and it was chosen by calculating
the average value of PAR at which the CO2 concentration in the water
started decreasing in the morning after accumulating during the night, or
increasing again in the evening. Using this procedure, “day” represents the
fraction of the time series when photosynthesis dominates over respiration,
and not the times when photosynthesis takes place in absolute terms. We also
estimated the uncertainties in the daytime and nighttime average values of
Fa. We decided not to use the standard deviation, since
individual 30 min EC data are characterised by significant scatter. Instead,
we recalculated the daytime and nighttime averages randomly choosing only
half of the data in the sample, and repeated the process 100 times. Then we
checked how far apart the minimum and maximum average values we obtained
were, and used that as uncertainty.
At this point, we were able to calculate the half-hourly values of NEP for
each period.
The NEP versus PAR plots for each year; each dot represents a
30 min interval. The fitted curve shown is calculated using the average
water T of the studied periods of the year.
Relationship between NEP and PAR
In humic lakes, photosynthesis is strongly driven by PAR, and the
relationship can be described for instance by the Michaelis–Menten equation
. Assuming that the daytime respiration rate equals the
nighttime respiration rate and that they depend exponentially on temperature
, the NEP can be expressed as
NEP=GPP-Rh=pmaxPARPAR+b-r0Q10T/10.
In Eq. (5), T is the water temperature (in ∘C) and Q10 is a
non-dimensional temperature coefficient whose generally accepted value for
freshwater communities (and the value we used) is 2; in the literature,
values between 1.88 and 2.19 are reported: ,
and . The
parameters pmax, b and r0 represent the maximum
potential photosynthetic rate, the half-saturation constant (i.e. the value
of PAR at which the photosynthetic rate is half of the maximum rate) and the
basal respiration rate, respectively. These parameters are important, since
they allow the calculation of NEP from water temperature and PAR; their
values can be obtained by fitting the model to the data.
After calculating the NEP, we plotted the NEP versus irradiance curves. We
then fitted the model (Eq. 5) to the NEP data with the least-squares fitting
method, in order to check the agreement between the data and the model and in
order to estimate pmax, b and r0.
Each year was handled separately, since the conditions (PAR and water T)
varied. We then verified whether the changes in the parameter values between
the years were statistically significant. To do so, we calculated the
parameters difference and its confidence interval (calculated as the
uncertainty in the difference, from the confidence intervals of the
parameters themselves), and checked whether it overlapped 0. If it did not,
then the values were statistically significantly different.
Assessment
General results
The NEP had the same trend as the incoming radiation, as expected; it had
bigger negative values during the night, when only respiration took place,
and smaller negative values during the day, when photosynthesis contributed
with an uptake of CO2. However, the net productivity values are almost
always negative, meaning that the ecosystem, overall, is heterotrophic and a
source of CO2. In fact, the daytime and nighttime average values of the
CO2 flux were also always positive, albeit having lower values during the
day than during the night. This is not surprising: many lakes, especially at
high latitudes, are supersaturated with respect to CO2 ;
as a result, the CO2 flux is from the lake to the atmosphere also during
the day, when the aquatic primary producers are photosynthesising and
absorbing CO2.
Figure 1 shows the CO2 concentration change in time over the mixed layer
(the first term in Eq. 3), which is usually referred to as storage flux in
forest ecology calculations, the NEP, the average daytime and nighttime
values of the CO2 flux (Faday and
Fanight) and PAR for a sample period of stable
stratification in July 2010, representative of the analysed periods. The
9-day period in Fig. 1 is the longest of the entire data set. Generally,
stable stratification lasted from 2 to 5 days; its short duration is due
to the oblong shape of the lake, that makes it sensitive to wind action: as
soon as the wind increases the mixing is enhanced (although complete mixing
takes place only in spring and autumn).
The NEP versus PAR plots for each year. Each dot represents a
30 min interval, colour-classified according to water temperature classes,
and the curves are calculated for the different temperatures. Note that the
curves are not individual fits, but are the result of the year's 3-D fit,
evaluated for the different temperatures. Water T is in ∘C.
Fit statistics, parameters of the NEP vs. PAR and water T model
with 95 % confidence intervals (from Eq. 5), and average, minimum and
maximum values of water T and PAR in the mixed layer for the studied
periods of each year. RMSE, pmax and r0 in
µmol(CO2) m-2 s-1, b and PAR in
µmol(ph) m-2 s-1 and T in ∘C.
Year
R2
RMSE
pmax
b
r0
Tave
Tmin
Tmax
PARave
PARmax
2010
0.73
0.23
1.05±0.05
22±5
0.228±0.008
22.9
19.9
26.2
195
634
2011
0.84
0.25
1.47±0.06
29±6
0.399±0.009
22.7
20.7
25.3
197
708
2013
0.71
0.14
0.63±0.04
33±10
0.290±0.007
21.5
20.0
23.5
162
699
2014
0.74
0.33
1.55±0.10
31±11
0.482±0.013
25.6
23.2
28.3
227
741
For the NEP versus PAR curves (Figs. 2–3), as mentioned above, we decided to
draw a different plot for each year, instead of combining all the data points
from all the years, since the conditions varied from year to year. Figure 2
displays the model curve calculated using the average water T of the
studied periods of each year. From the plots, we can see that for low values
of PAR, the NEP was strongly negative; then, as PAR increased, the NEP quickly
increased as well; however, as already noted, the NEP always remained
negative, indicating net heterotrophy. None of the years exhibited signs of
photoinhibition: the NEP did not seem to decrease even at high (>500 µmol(ph) m-2 s-1) values of PAR. Differences can
be seen between the years, with 2014 showcasing the smallest values of NEP.
Year 2014 was particularly hot, so the strongly negative NEP can be due to
increased respiration rates, given the strong dependency of Rh
on temperature; year 2010 though displays the highest values of NEP despite
having an intermediate average water temperature. Figure 3 concentrates on
the dependence of the NEP on T. The model is calculated for different
values of water T, ranging from the minimum to the maximum water
temperatures recorded during the studied periods of each year. The NEP
decreases with increasing temperature, due to higher respiration rates. Note
that in both Figs. 3 and 4 and especially for years 2010 and 2014 there is a
large separation between NEP across the chosen PAR threshold between night
and day. This is caused by having to resort to daytime and nighttime average
values for Fa. Finally, Fig. 4 features 3-D plots of the data
and the curves, to visualise simultaneously the dependence of the NEP on PAR
and water T. The curves have the expected trends, and this suggests that
the measurement method and the equation used are proper tools for estimating
the NEP at a high temporal resolution. The results of the fittings of the NEP
versus PAR and T are reported in Table 1. Considering the assumptions
we had to adopt, there is a very good agreement between the model and the
data: the R2 values range from 0.71 to 0.84. This clearly indicates that
the method used here allows the NEP to be parameterised as a function of
irradiance and water temperature.
Data and fitted NEP versus PAR and water T 3-D curves for each
year; each dot represents a 30 min interval.
Inter-annual variability
We then focused on the inter-annual variability in the values of the model
parameters (reported in Table 1). The differences in the parameter values
between the years are mainly statistically significant. Only the value of b
does not change significantly between any of the years: this means that the
algal communities adapted to the light conditions in a similar way every
year. The values of the other parameters change: pmax is
comparable only between 2011 and 2014, and r0 is never comparable. The
difference in pmax and r0 can be due to different total
algal biomass in the lake. In general, we can say that variations in the
environmental conditions might have led to changes in the communities living
in the lake, or the communities might have responded differently to the
environmental conditions; pmax and r0 seem to be more
sensitive to variations than b.
The maximum photosynthetic rate pmax ranged between 1.55 (2014)
and 0.63 (2013) µmol(CO2) m-2 s-1, and it was higher
in 2011 and 2014 than in 2010 and 2013. The half-saturation constant b
ranged between 22 (2010) and 33 (2013) µmol(ph) m-2 s-1,
being higher in 2011, 2013 and 2014 than in 2010. The values of b are
relatively small. It indicates that the phytoplankton communities were well
adapted to the low light conditions (boreal area and dark-water lake) and
were able to start photosynthesising even when the incoming radiation was
low. The basal respiration r0 ranged between 0.228 (2010) and 0.482
(2014) µmol(CO2) m-2 s-1, being higher in 2011 and
2014 than in 2010 and 2013, as was the case with pmax. The
parameters, however, do not appear to be strictly correlated to each other, and
a clear and uniform pattern in their behaviour cannot be identified.
Finally, we investigated whether the changes in the model parameters can be
explained in terms of changes, during the analysed periods, of the ambient
variables that act as NEP drivers: water temperature and irradiance. The
model parameters and the average, minimum and maximum values of water T and
PAR for each year are reported in Table 1 (only the 40 analysed days are
considered in these statistics). In 2010 and 2011 the surface water
temperatures had similar average values of 22.9 and 22.7 ∘C,
respectively.
Year 2013 was slightly colder, with an average value of
21.5 ∘C, while year 2014 was warmer, with an average value of
25.6 ∘C. The minimum temperatures of the study periods were similar
for 2010 and 2013 (≈20 ∘C), slightly higher for 2011
(20.7 ∘C) and notably higher for 2014 (23.2 ∘C). The
maximum temperatures ranged between 23.5 (2013) and 28.3 (2014) ∘C.
Overall, 2013 can be considered as a cold year, 2014 as a hot year, and 2010 and
2011 as intermediate years. The temperature variation pattern between the
years cannot be easily linked to the variations in b. Concerning
pmax, even though the largest value of pmax is
associated with the warmest year (2014), and the smallest value of
pmax with the coldest year (2013), years 2010 and 2011 had
different values of pmax despite having similar temperatures.
Besides, pmax and b are expected to depend more strongly on
PAR than on T. Conversely, r0 can be expected to be larger when
temperatures are higher. This happened in 2011 and 2014, but not in 2010,
which still had relatively high temperatures. Possible explanations are
changes in the Q10 value or the influence of other environmental
variables. We did not investigate further possible changes in the Q10
value, because we did not have an independent way to estimate it and
because its range is narrow according to the literature . Concerning PAR, in the analysed periods the average values in the mixed
layer ranged from 162 (2013) to 227
(2014) µmol(ph) m-2 s-1, being higher in 2010 and 2011
than in 2013, and notably higher in 2014 than in all the other years.
Remarkably also in 2014, despite the high values of PAR, the communities did
not show signs of photoinhibition (a PARmax value of 741 for
the mixed layer corresponds to a surface value of ≈1900 µmol(ph) m-2 s-1, given the light extinction
coefficient of the lake of 1.5). Higher average PAR values could be
responsible for larger pmax values, as observed in 2011 and
2014, and partially in 2010. However, the average PAR values are very similar
in 2010 and 2011, while pmax values are not. Still, the very
low value of pmax in 2013 could be explained by the low
PARave value. The variations in b between the years, though,
cannot be linked to the changes in PAR: 2013 and 2014, despite having very
different PAR values, had similar b values. The trend in r0 also cannot
be associated with the trend in PAR between the years. From what is said so
far, the changes in PAR and water temperature alone cannot fully account for
the changes in the model parameters. The long-term variations in the
parameters probably have other drivers too, such as the composition of the
algal communities; as already stated, a more extensive analysis would require
such information and is beyond the scope of this paper.
Model choice
In aquatic sciences, other models for describing the dependence of
photosynthesis on irradiance are more commonly used than the Michaelis–Menten
equation. The Michaelis–Menten equation was chosen in an effort of
harmonising productivity studies between aquatic and forest sciences, in
order to study the carbon cycle consistently in the forest–lake continuum.
However, we checked whether other models provided a better fit to the data.
We used the equations by and by . Even though they
agreed well with the data, they did not perform significantly better than the
Michaelis–Menten equation: the R2 and RMSE values of the fits were very
similar. Hence, we decided to proceed with our first choice. The
and model equations and fit statistics are reported in the
Supplement (Sect. S3 and Table S1).
Out-of-sample validation
The analysis we performed was based on an in-sample comparison, since our
goal was to check whether our method to calculate the NEP was in agreement
with the PI models typically used (Michaelis–Menten, and
equations). However, for the Michaelis–Menten model, we also
ran an out-of-sample validation for each year, in order to further verify the
correspondence between the calculated NEP and the model. For each year, we
randomly selected half of the data points and used them for the fit to
calculate the model parameters. Then, for the other half of the sample, we
estimated the NEP using the equation and the parameters we had obtained, and
compared it to the originally calculated NEP. We both evaluated the
correlation coefficient r between the two NEPs (the one calculated from the
data and the one calculated from the model trained on half of the data
points, then discarded), and the RMSE of the validations. The results are
reported in Table 2, and show that the two NEP values compared well. The
correlation coefficient r varies between 0.84 and 0.92 and the RMSE varies
between 0.15 and 0.31 µmol(CO2) m-2 s-1.
Discussion
Assumptions and uncertainties
Firstly, it is important to notice that we are working under the assumption
that the NEE, which is what can be measured, is equal in magnitude to the
NEP. This concept is widely accepted in the scientific community ,
for forests as well as for other environments such as lakes. The assumption
is indeed strictly valid only when there are no sources and sinks of CO2
that do not involve conversion to or from organic C . Such sources
and sinks, however, are usually negligible, except for oceans.
The lateral transport of CO2 had to be ruled out for the sake of the
calculations. A similar challenge is encountered in forest ecology studies as
well, where the lateral transport in the air (advection) is also usually
neglected. We are of course fully aware of the lake being a 3-D dynamic
system. Besides, since this study focuses on the summer periods when the lake
was stably stratified and there were no high winds or rains, the lateral
transport is not expected to play a significant role here. This assumption is
supported by , who showed that for lake Kuivajärvi most of the
CO2 discharge happens at snowmelt or during heavy rains in the autumn. It
is also supported by the mixed layer CO2 concentration time series, which
show no sign of a long-term trend on top of the diurnal cycles (see
Figs. S5–S14 in the Supplement).
Regarding oligotrophic lakes, it has been suggested that diurnal patterns in
the epilimnion stratification and water convective motions (causing nighttime
upwelling of CO2) are important drivers of the diurnal variation in the
surface water CO2 concentration . Lake Kuivajärvi though is
mesotrophic (Chl a concentration is 5–30 µg L-1 during summer) and the
primary production can be assumed to be the main driver of the CO2
concentration, as observed also in some other lakes with high Chl a
. Also, we implemented strict selection criteria for the
analysed periods to minimise the effect of upwelling CO2: the thermistor
data indicate that the winds, despite being weak, were strong enough to keep
the top 1.5 m of the water column well mixed both day and night, without
disrupting the thermocline. Thus, no sign of hypolimnetic upwelling
was detected. Under these conditions, diurnal stratification patterns and
convective motions had a minor impact on the mixed layer of our lake. It is
also important to note that the photochemical production of CO2 is
generally negligible in humic lakes ; its maximum contribution to
the flux for a lake with similar characteristics as the one in our study lake
was < 4 % over the whole growing season, and was detectable only in
the top 10 cm of the water column .
Fit statistics (R2 and RMSE) calculated for half of the sample,
correlation coefficient r and validation RMSE using the other half of the
sample. RMSE in µmol(CO2) m-2 s-1.
Year
R2
RMSE
r
validation RMSE
2010
0.72
0.23
0.85
0.23
2011
0.84
0.25
0.92
0.25
2013
0.71
0.15
0.84
0.14
2014
0.77
0.31
0.88
0.31
Our analysis was hindered by issues in the EC data set: due to inherent EC
limitations and technical problems, the data set had many gaps and average
daytime and nighttime Fa values had to be used. The relative
uncertainty in them was, on average, 50 %. This uncertainty propagates to
NEP through Eq. (3), and therefore to the parameter values as well. However,
it does not undermine the good agreement between the model and the data,
given that the average Fa values were calculated putting
together all the periods of the same year. Therefore, each NEP data point has
the same uncertainty and the same weight in the fit. The calculations could
be improved with a better EC data set. Different methods could also be
adopted to estimate the flux between the lake and the atmosphere. Chamber
measurements could be used, but the time resolution could be an issue. They
would need to be performed regularly. They could, however, be used to
integrate the EC data set for example. Surface renewal models could also be
used . For further information on the comparison between
different flux measurement methods, see .
Limitations and further development
In this study, we could not clearly link the environmental variables to the
changes in the Michaelis–Menten model parameters, and more information on the
algal communities living in the lake would have been required in order to
expand the analysis. However, it is important to stress that the simplicity
of this method lies in the fact that to estimate the parameters, which can
then be used to calculate the productivity, information on the algal
communities is not needed. It is needed only when widening the scope of the
productivity studies: when, for example, the parameters themselves and their
relationship with the environmental conditions or the specific phytoplankton
communities are investigated. Knowledge on the algal communities would also
help when extending the productivity calculation to the whole year. In our
case, for example, the NEP rates and hence the parameters are representative
of the late summer. In lake Kuivajärvi, where diatoms are abundant, it can
be expected for the productivity to have a peak in the spring and another
smaller peak in the autumn, at the turnover. More measurements at those times
would be needed in order to understand whether the parameterisation is still
valid under those conditions.
At the current stage, the method we present here is still very system
specific, and assumptions about lateral and vertical CO2 exchange and
photo-oxidation had to be made (negligible lateral exchange and
photo-oxidation, no in-lake vertical exchange). However, the method can in
principle be applied to any lake and under any condition, with an expansion
of the instrumental set-up. Measurements or estimates of Fu,
the CO2 flux from the deeper layer to the surface layer of the lake, would
be needed in order to not limit the analysis to isothermal (as in
) or stable stratification (as here) conditions. This could be
achieved for example by adding water column turbulence measurements to the
CO2 concentration and temperature measurements. Chemical measurements
would be needed to apply the method in clear-water lakes, where
photo-oxidation could play an important role. Finally, information about
CO2 discharge would be needed for lakes where or periods when lateral transport
is not negligible.
Conclusions
The high-frequency direct CO2 concentration measurement method suggested
in and tested only on 3 days of data under autumn turnover
conditions was tested more extensively and under different conditions here,
on a data set of 40 days of stable stratification typical of summer for
dark-water lakes. The method proved to be suitable for lake productivity
studies under isothermal or stable stratification conditions:
its high temporal resolution allowed us to calculate the net ecosystem
productivity (NEP) at a temporal scale of minutes. A quantitative comparison
between the NEP calculated with this method and the modelled NEP was also
carried out for the first time, and it showed a very good agreement between
the two, further validating the method. From that, we were able to accurately
parameterise the net productivity as a function of the ambient variables,
estimating the productivity parameters typical of the communities in the
lake.
Overall, we believe that the method proposed in and further
tested and developed here represents an improvement over the traditional
approaches (bottle method and 14C technique), given its time resolution
and the fact that it is a free-water approach. We also think that it is promising
compared to the other more common free-water approach, the O2 method,
since it is direct and the respiratory quotient is not needed. However, at
the present stage it can be applied under a limited set of conditions
(isothermal or stable stratification). Still, our study is an important step
towards testing and developing the approach so that it becomes more general,
also given the scarcity or even lack of high-frequency direct CO2
measurements for productivity studies (we are aware of only one other study
where free-water CO2 measurements were used for metabolism
studies; see ). We are looking for further contributions by the research
community and we think the method should be widely adopted, first in order to
gather more information about its usability under different conditions and
then also to have a broader network of productivity studies on lakes. This is
all the more true given that the CO2 probes are also easy to set up and
relatively inexpensive. The method requires at least a concomitant estimation
of the CO2 flux from the lake to the atmosphere. In our case the EC
technique was used, which is expensive and can be laborious in the data
processing phase. However, chamber measurements or surface renewal models
could be equally good options.
Additionally, the method also relies on equations that are typically adopted
in terrestrial ecology studies for the calculation of the NEP, where
high-frequency measurements are more commonplace than in aquatic research.
Extensively applying the method would reduce the gap in the CO2 exchange
measurements between aquatic and terrestrial ecology, which is beneficial in
the framework of integrating research in different ecosystems, for which
purpose a common language between different disciplines is needed. It would
also help us achieve a better understanding of the biological processes
behind the CO2 exchange. This, in turn, would expand our knowledge on the
carbon cycle in the water, which is still limited, and would lead to a better
integration of aquatic ecosystems in the local and global carbon budgets.