Lakes are important actors in biogeochemical cycles and a powerful natural
source of CO

Lakes are very important actors in the local and global carbon cycles

In freshwater ecology, productivity studies have usually relied on the light
and dark bottle method

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 O

To study the in-water photosynthesis and respiration,

In

Here we tested the method of

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.

The study site is the boreal lake Kuivajärvi, in southern Finland
(61

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 CO^{®} GMP343,
Vaisala Oyj, Vantaa, Finland) for the CO

The net ecosystem productivity (NEP,

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

A sample period of stable stratification in July 2010,
representative of the studied periods (DOY is day of the year). In panel

Resuming our calculation of the NEP in aquatic ecosystems through Eq. (3), to
increase the precision of the concentration data, half-hourly averages of

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

In humic lakes, photosynthesis is strongly driven by PAR, and the
relationship can be described for instance by the Michaelis–Menten equation

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

Each year was handled separately, since the conditions (PAR and water

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 CO

Figure 1 shows the CO

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

Fit statistics, parameters of the NEP vs. PAR and water

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

Data and fitted NEP versus PAR and water

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

The maximum photosynthetic rate

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

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

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,

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

The lateral transport of CO

Regarding oligotrophic lakes, it has been suggested that diurnal patterns in
the epilimnion stratification and water convective motions (causing nighttime
upwelling of CO

Fit statistics (

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

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 CO

The high-frequency direct CO

Overall, we believe that the method proposed in

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 CO

The data sets and the codes used in this paper can be obtained from the authors upon request.

The supplement related to this article is available online at:

The authors declare that they have no conflict of interest.

We thank Jacob Zwart and another anonymous reviewer for their constructive comments and suggestions, which helped improve the manuscript. This study was funded by the University of Helsinki and the Finnish Cultural Foundation – Häme fund (Hämeen rahasto – Suomen Kulttuurirahasto). Support also came from the Academy of Finland, through the Academy Professor projects (1284701 and 1282842), the CarLAC project (281196), ICOS-Finland (1281255), the Finnish Centre of Excellence in Atmospheric Science and from the EU project GHG-LAKE (612642). Edited by: David Gillikin Reviewed by: Jacob Zwart and one anonymous referee