Skip to main content
Browse Subject Areas

Click through the PLOS taxonomy to find articles in your field.

For more information about PLOS Subject Areas, click here.

  • Loading metrics

Lake Metabolism: Comparison of Lake Metabolic Rates Estimated from a Diel CO2- and the Common Diel O2-Technique

  • Frank Peeters ,

    Affiliation Department of Biology, Environmental Physics, University of Konstanz, Konstanz, Germany

  • Dariia Atamanchuk,

    Affiliations Department of Marine Sciences, University of Gothenburg, Gothenburg, Sweden, Department of Oceanography, Dalhousie University, Halifax, Canada

  • Anders Tengberg,

    Affiliations Department of Marine Sciences, University of Gothenburg, Gothenburg, Sweden, Aanderaa Data Instruments AS, Bergen, Norway

  • Jorge Encinas-Fernández,

    Affiliation Department of Biology, Environmental Physics, University of Konstanz, Konstanz, Germany

  • Hilmar Hofmann

    Affiliation Department of Biology, Environmental Physics, University of Konstanz, Konstanz, Germany


Lake metabolism is a key factor for the understanding of turnover of energy and of organic and inorganic matter in lake ecosystems. Long-term time series on metabolic rates are commonly estimated from diel changes in dissolved oxygen. Here we present long-term data on metabolic rates based on diel changes in total dissolved inorganic carbon (DIC) utilizing an open-water diel CO2-technique. Metabolic rates estimated with this technique and the traditional diel O2-technique agree well in alkaline Lake Illmensee (pH of ~8.5), although the diel changes in molar CO2 concentrations are much smaller than those of the molar O2 concentrations. The open-water diel CO2- and diel O2-techniques provide independent measures of lake metabolic rates that differ in their sensitivity to transport processes. Hence, the combination of both techniques can help to constrain uncertainties arising from assumptions on vertical fluxes due to gas exchange and turbulent diffusion. This is particularly important for estimates of lake respiration rates because these are much more sensitive to assumptions on gradients in vertical fluxes of O2 or DIC than estimates of lake gross primary production. Our data suggest that it can be advantageous to estimate respiration rates assuming negligible gradients in vertical fluxes rather than including gas exchange with the atmosphere but neglecting vertical mixing in the water column. During two months in summer the average lake net production was close to zero suggesting at most slightly autotrophic conditions. However, the lake emitted O2 and CO2 during the entire time period suggesting that O2 and CO2 emissions from lakes can be decoupled from the metabolism in the near surface layer.


The balance of the metabolic rates net production, NEP, gross primary production, GPP, and respiration rate, R, is given by: (1)

Thereby, R is defined to assume positive values characterizing respiration. Metabolic rates have not only been defined for individual organisms but also for entire ecosystems or parts of them (e.g., [15]).

Lake metabolism describes the turnover of biomass and energy in lake ecosystems. Primary production utilizing light energy to generate chemical energy and converting inorganic carbon into biomass is the basis for the energy flux in food webs and hence is crucial for the understanding of food web dynamics. Respiration, which is associated with oxygen consumption and release of inorganic carbon from the organic carbon pool, may lead to anoxic conditions in the deep-water of lakes and may cause oversaturation of CO2 (e.g., [6,7]). The sign of ecosystem net production indicates whether a Lake is a net sink or net source of atmospheric CO2. Hence estimates of ecosystem metabolism contribute to the understanding of habitat conditions and food-web dynamics within lake ecosystems as well as of the mass and energy balance of the entire ecosystem. The metabolism of lake ecosystems and of reservoirs is an important factor affecting the carbon flux from terrestrial systems to the ocean and CO2 emissions to the atmosphere [8,9]. Estimates of short- and long-term changes in metabolic rates may improve the understanding on how short-term disturbances and long-term environmental change, e.g., climate warming or changes in nutrient loads, may affect the energy and carbon budget of lakes, the fate of terrestrial carbon, and the CO2 emission from lakes.

Several techniques have been proposed to measure metabolic rates in aquatic systems (e.g., [10]) and we focus here on open-water techniques utilizing diel changes in dissolved oxygen or carbon [1,1113]. With the development of oxygen optodes providing reliable long-term data sets on dissolved oxygen at a high temporal resolution (e.g., [14]), the diel O2-technique [1] has become widely used to estimate ecosystem metabolism in numerous aquatic systems (e.g., [15] and references in [4,13,16]).

However, the diel O2-technique only provides an indirect measure of the metabolic transformations of carbon and the consumption or release of CO2. The recent development of CO2 optodes [17] opens up the opportunity to utilize long-term data on dissolved CO2 concentrations to estimate metabolic rates based on diel changes in dissolved inorganic carbon [18]. Estimates of metabolic rates in lakes utilizing the diel cycle of dissolved inorganic carbon are available for typically only a few days and have been based on diel changes in the concentration of total dissolved inorganic carbon (DIC) measured chemically from collected water samples (e.g., [11,12]) or on diel changes in CO2 concentrations neglecting the other components of the carbon balance [2]. The open-water diel CO2-technique discussed here enables the estimation of metabolic rates from the diel cycle of DIC concentrations over long time periods at comparatively little field effort. The technique utilizes the combination of a few alkalinity measurements with long-term CO2 data measured at sub-hourly resolution to estimate diel changes in DIC concentrations. Such an approach has recently been employed in mesocosm experiments [19] and is adopted here to provide continuous data on carbon based metabolic rates in the surface water of an alkaline lake over several weeks.

Diel CO2- and diel O2-technique provide independent estimates of lake metabolic rates. However, we hypothesize that the CO2-technique is less sensitive to effects by gas exchange than the diel O2-technique because the molar atmospheric equilibrium concentration of CO2 is much smaller than that of O2 and the carbonate balance channels parts of the changes in CO2 to carbonate and bi-carbonate.

In the following, we first present the main concepts behind the diel O2- and the diel CO2-technique and then provide details on the measuring site, instrumentation and deployment of the instruments. After an overview of field data and estimates of metabolic rates covering several weeks at sub-daily resolution, the results are discussed in detail focusing on the comparison of metabolic rates estimated with the diel O2- and the diel CO2-technique and on the influence of transport processes on these estimates. Supporting information used in this study includes additional data (S1S3 Appendices), model sensitivity analyses (S4S7 Appendices), detailed equations (S8 Appendix), and empirical relations (S9 Appendix).



The diel O2-technique.

The diel O2-technique determines net production from the change in the concentration of dissolved oxygen CO2 with time t. Assuming that transport and all sources and sinks of dissolved oxygen other than production and respiration can be neglected: (2)

The metabolic rates based on the diel O2-technique are denoted by subscript O. The effects of transport processes on CO2, e.g., the flux across the air–water interface and vertical mixing, will be discussed later (see Eq 13).

The standard procedure to calculate gross primary production GPPO from diel changes in dissolved oxygen assumes that the respiration rate RO is constant during a day [3,20,21] and that GPPO is zero at night. The night-time respiration rate RO,night is commonly estimated from the mean NEPO during night (e.g., [3]): (3)

Night-time (darkness) and daylight time periods are distinguished on the bases of the timing of dusk, tdusk, and the timing of dawn, tdawn. In the calculations of RO.night the night-time period is commonly defined as the time period between ts,night = tdusk + Δt and te,night = tdawn—Δt and Δt is here chosen to be one hour to ensure darkness. A day extends from dusk to dusk and the respiration rate RO,night determined for the night starting after the first dusk of this day applies to the entire day until the next dusk.

At night NEPO and RO,night must have opposite sign (Eq 2). Note that the sign convention in Staehr et al. [16, 13] seems to be inconsistent. Note further, that estimates of RO,night based on the mean NEPO at night utilize the difference between only two O2 concentrations in the dissolved oxygen balance, i.e. CO2(ts,night) and CO2(te,night): (4)

The estimate of RO,night based on the mean NEPO during night may therefore be sensitive to the choice of (ts,night) and (te,night) and the errors in the oxygen measurements at these specific times. As an alternative, the estimate of RO,night can be based on all dissolved O2 measurements during night by using the slope of a linear fit: (5)

If the original data are collected at a high temporal resolution the derivatives of CO2 are very sensitive to measurement errors and the metabolic rates obtained from such data are rather noisy. Therefore, we smooth the time series of metabolic rates using a simple box-car filter with an averaging period of 6 hours.

The diel CO2-technique.

Metabolic rates based on the diel CO2-technique are denoted by subscript C. The diel CO2-technique assumes that biomass production is reflected in a loss of carbon from the inorganic carbon pool whereas respiration is associated with an increase in inorganic carbon. Hence, carbon production, GPPC, can be determined from the rate of decrease in the concentration of total dissolved inorganic carbon, CDIC, and the carbon respiration rate RC. The latter can be estimated from the rate of increase in CDIC at night [11,12]. Making the same assumptions as in the diel O2-technique (GPPC,(tnight) = 0; RC = RC,night) the metabolic rates based on the balance of inorganic carbon can be determined from: (6)

As in the diel O2-technique night-time respiration rate RC,night can be determined from the mean NEPC at night or from linear regression: (7) (8)

These equations for the assessment of metabolic rates from diel changes in CDIC are essentially the same as for the diel O2-technique, but the net production is based on the rate of change of DIC rather than that of O2, and the relations between the rate of concentration change and the metabolic rates have opposite sign compared to the diel O2-technique.

The calculation of the metabolic rates with the diel CO2-technique requires data on CDIC at sub-daily resolution. Because CDIC can be estimated from concentrations of CO2 if pH is known (see further below), CO2 measurements with high temporal resolution available from CO2-optodes can be utilized to estimate metabolic rates. This is the basis of the diel CO2-technique.

Estimation of time series of CDIC from CCO2 data.

CO2-sensors typically provide the partial pressure of CO2, i.e. pCO2. The sum of the concentrations of dissolved CO2(aq) and un-dissociated hydrated CO2(H2CO3(aq)) in the sampled water, CCO2 in this study, can be determined from pCO2 using Henry’s Law. The Henry coefficient, H, depends on the water temperature T and salinity S and was calculated from the empirical relations of Weiss [22]. The calculation of CDIC from CCO2 is straight forward if the pH of the water is known [23]: (9) (10)

The coefficient α0 depends on pH, T, and S (see Table in S9 appendix). Values of pH typically show daily cycles in response to production and respiration. The values of pH also change if CO2 is introduced or removed by gas exchange, e.g., with the atmosphere. Hence, the calculation of CDIC from CCO2 and pH requires precise data on pH at sub-daily resolution over long time periods. Unfortunately, submersible in-situ pH-sensors that can be deployed for several weeks and have sufficient long-term stability, absolute accuracy and precision are currently difficult to encounter. Therefore, it is advantageous to base the calculation of CDIC from CCO2 data on measurements of alkalinity rather than on pH measurements (see also [24]). The pH values required for the calculation of CDIC can be estimated from carbonate alkalinity ALKCarb [mmoleq L-1] and CCO2 [mmol L-1]: (11) (12) whereby CHCO3- and CCO3— are the concentrations of HCO3- and CO3--, respectively, COH- and CH3O+ the concentrations of OH- and H3O+ ions. The coefficients α1and α2 depend on pH, T, and S. The empirical relations for α1, α2 and KW are listed in Table in S9 appendix. Eq (12) is an implicit equation for pH.

Alkalinity may change in case of calcite precipitation and dissolution of solid carbonates but also due to several other biogeochemical processes ([25]). However, changes in CCO2 due to gas exchange with the atmosphere or due to uptake or release by phytoplankton during production and respiration, respectively, do not alter alkalinity [25] because the dissociation of H2CO3(aq) to negatively charged carbonate ions is associated with the generation of an equivalent number of positively charged hydronium ions. Also nutrient uptake by phytoplankton has only minor effects on alkalinity [19]. Phosphate and nitrate assimilated during primary production or released during remineralization of organic material alter alkalinity [25] but the molar fraction of phosphate and nitrogen in phytoplankton is rather small (i.e. the typical ratios C:N:P = 106:16:1 [26]). Hence, if the only processes affecting inorganic carbon are production/respiration and gas exchange of CO2 with the atmosphere, the carbonate alkalinity ALKcarb can be treated as essentially conserved quantity. Then, pH and the daily cycle of pH can be calculated from a single measurement of ALKcarb and the time series of pCO2.

All coefficients in Eq (12) depend on T and S, and α0, α1, α2 additionally on pH. If T, S, CCO2 and ALKcarb are known, pH can be calculated from Eq (12) by solving this implicit equation numerically. We employ a least squares fitting procedure varying pH to minimize the root mean square difference between calculated and measured ALKcarb (fminsearch of MATLAB using the Nelder Mead simplex algorithm). With the pH determined from Eq (12), α0 can be calculated and CDIC be determined from Eq (10).

Considering vertical transport.

In lake ecosystems, temporal changes in the concentrations of dissolved O2 and DIC are caused not only by metabolic processes but also by transport processes. Assuming horizontally homogeneous conditions, the temporal change of the vertical distribution of CO2 considering metabolic processes and vertical fluxes due to transport processes is given by: (13) where CO2 is the concentration of dissolved oxygen as function of z, z is the vertical coordinate (positive in the upward direction), A is the cross-section at z, FO2 is the vertical flux of dissolved oxygen at z, FO2,sed is the flux of O2 from the sediments at z into the water, FO2,surf and FO2,bot are the fluxes of O2 in direction z at the surface and at the bottom boundary, respectively. At the bottom FO2,bot = FO2,sed. At the surface, FO2,surf is determined by the flux due to gas exchange with the atmosphere FO2,atm. CO2,equ is the equilibrium concentration of O2 at ambient surface water temperature and salinity and atmospheric pressure, vO2 is the gas exchange velocity of dissolved oxygen.

Within the sediments dissolved O2 is consumed by bacteria that mineralize organic material which typically results in anoxic conditions in deeper lake sediments. Hence, FO2,sed is typically negative and acts as a sink of dissolved O2 in the water column. In lake metabolism studies this sedimentary flux is often not explicitly considered (e.g., [3,5]) and thus implicitly included in the system respiration rate. The commonly used lake respiration rate RL_O therefore is: (14)

Additionally, the oxygen loss due to the flux at the lake bottom is also attributed to the system respiration rate and included in RL_O by assuming a zero-flux boundary condition at the lake bottom (FO2,bot = 0). The equation for NEPL_O becomes: (15) with FO2,surf = FO2,atm and FO2,bot = 0 as boundary conditions.

The budget of dissolved inorganic carbon can be described analogously: (16) where FDIC is the vertical flux of inorganic carbon, FDIC,sed is the flux of DIC from the sediments into the water column, FDIC,surf and FDIC,bot are the fluxes of DIC in direction z at the surface and the bottom boundary, respectively. The fluxes, concentrations and metabolic rates are functions of z.

At the bottom, FDIC,bot = FDIC,sed. At the surface, the flux of DIC is the flux of CO2 due to gas exchange with the atmosphere, FCO2. CCO2,equ is the equilibrium concentration of CO2 at ambient water temperature and salinity and atmospheric pressure, vCO2 is the gas exchange velocity of CO2.

Note that gross primary production is a source of dissolved oxygen whereas it is a sink of DIC, which is accounted for by the opposite signs in Eqs (13) and (16). Note further, that in case of DIC the surface flux is determined by CCO2 only and not by CDIC.

In analogy to the system metabolic rates based on dissolved oxygen one can define system metabolic rates based on carbon that include mineralization of organic material in the sediments and sediment fluxes into the system respiration rate: (17) (18) with FDIC,surf = FCO2,atm and FDIC,bot = 0 as boundary conditions. Note the opposite sign in Eq (18) compared to Eq (15).

In the following we determine NEPL_O and NEPL_C from Eqs (15) and (18), respectively, and test the consequences of several assumptions regarding the vertical fluxes of dissolved oxygen and of DIC:

  1. As the simplest approach we assume that the gradients of the vertical fluxes are zero, i.e. that the vertical fluxes due to transport processes in the water column are independent of depth and agree with the flux at the lake surface. (19)
  2. The second approach includes gas exchange with the atmosphere at the lake surface but neglects all other transport. This approach was used by, e.g., Cole et al. [20] and was recommended by Staehr et al. [16] for experiments in which measurements are available only from one water depth. The change in concentration due to the gas exchange at the lake surface can be estimated assuming a mixed surface layer with depth Zmix [16,20,21]. Zmix is estimated from temperature profiles as outlined in S1 appendix. The volume of the mixed surface layer is Vmix and the surface area Ao. (20)
  3. The third approach considers the full mass balance of O2 in the surface mixed layer by including not only the fluxes of O2 at the lake surface due to gas exchange with the atmosphere but also the fluxes at the bottom boundary of the mixed surface layer, i.e. at Zmix, (FO2,Zmix) due to mixing processes. The flux FO2,Zmix is assumed to comprise of fluxes due to turbulent diffusion, FO2,turb, and fluxes associated with mixed layer deepening, FO2,deepen: (21) (22)

Turbulent diffusion coefficients Kz were calculated as in Staehr et al. [3] from the empirical relation of Hondzo and Stefan [27] using data from a thermistor chain (see S1 and S2 Appendices). Vertical gradients of CO2 at Zmix were determined by linear interpolation of the gradients of CO2 obtained from O2-measurements at 1.2 m, 3.2 m and 5.2 m depth. AZmix, is the area of the cross section at Zmix. The oxygen profile at time 1, CO2, was integrated from Zmix at time 1, Zmix (1), to the surface and from Zmix after the time interval Δt, i.e. from Zmix (2) at time 2, to the surface. The time interval Δt was chosen to be one hour which allows resolving day-night changes in Zmix while avoiding influences from measurement noise and high-frequency oscillations.

The lake net production rates for the different approaches are: (23i) (23ii) (23iii) (23iv)

The metabolic rates determined with the approaches (ii) and (iii) are indicated by subscript labels A and F, respectively. Metabolic rates estimated from approach (iv) that adopts approach (iii) but neglects fluxes due to mixed layer deepening are labeled with subscript D. Eq (23)) requires estimates of CO2,equ, CCO2,equ, vO2, and vCO2. The equilibrium concentrations were determined from [28] in case of O2 and from [22] in case of CO2. Gas exchange velocities were calculated by combining the empirical relation of Cole and Caraco [29] for the gas-exchange velocity of CO2 in freshwater at 20°C (i.e. at Schmidt number SC = 600) with the Schmidt number dependence of the gas-exchange velocity suggested by Liss and Merlivat [30]. The Schmidt number dependence is required to include the effect of temperature on the gas-exchange velocity and also allows using the same parametrization of the gas-exchange velocity for CO2 and O2.

From the NEPL_O and NEPL_C the other metabolic rates (RL_O, GPPL_O, RL_C, GPPL_C) were calculated assuming that during each day the lake respiration rate remains constant and that lake gross primary production is zero at night. Hence, the lake respiration rate is equal to the negative of the lake net production during the night of the respective day (RL_C = -NEPL_C,night and RL_O = -NEPL_O,night). The respiration rates can be obtained by averaging: (24) or by the application of linear regression to flux modified concentrations CO2,mod and CDIC,mod: (25)

Daily mean metabolic rates were calculated for days at which at least 23 hours of data were available (55 days for the diel O2- and 50 days for the diel CO2- technique). Long-term averages of metabolic rates were calculated from daily mean metabolic rates considering only 49 days for which data were available from the diel O2- and the diel CO2-technique.

Field experiments

In 2014 field experiments were conducted in Lake Illmensee, a small (surface area: 64 ha, maximum water depth: 16.5 m) alkaline (pH of ~8.5) lake located in southern Germany (47° 51’ 19” N, 9° 22’ 49”E) at 670 m above sea level. The field studies did not involve endangered or protected species and were permitted by the Landratsamt Sigmaringen. From May 26th to July 28th moorings were installed at the deepest station of the lake. The moorings were equipped with thermistors (RBRsolo T, RBR) measuring temperature every 10 s and eight O2-optodes (MiniDOT, PME, accuracy ~-10 μmol L-1) measuring every 60 s dissolved oxygen concentrations (CO2). The O2 data were calibrated by scaling O2 measurements in air to provide 100% saturation. One of the temperature loggers additionally had a pressure sensor (TDR, RBR) that was used to measure the height of the water column above the sensor and air pressure during lifts of the mooring. The vertical spacing of the O2-optodes was 2 m and of the thermistors 1 m. The uppermost O2-optode and thermistor were mounted at ~1.2 m water depth. At ~1.7 m water depth a CO2-optode (Aanderaa Data Instruments, Norway; Atamanchuk et al. [17]) measured pCO2 and temperature every 30 s during the entire time period. The data from the CO2-optode was stored in a data logger built by the electronic workshop at the University of Konstanz. Another CO2-sensor based on IR absorption spectroscopy (HydrocC CO2, Contros; in the following: CO2-IRprobe) was mounted at 2 m water depth and measured pCO2 every 5 s. The CO2-IRprobe had comparatively large power consumption and was therefore deployed for continuous measurements only from June 23rd 4 pm to June 28th 12 am requiring one battery change during this 4.8 day time period. The CO2-optode required only one battery change during the 63 days of deployment. Breaks in the time series of pCO2 data from the CO2-optode resulted from lifting the mooring for maintenance of the other instruments. The pCO2 data from the pre-calibrated CO2-optode were corrected for the conditioning effect by introducing a single constant scaling factor [17]. The calibration of this scaling factor was based on the data from the CO2-IRprobe. The conditioning effect results from chemical reactions between the foil of the CO2-optode and the ambient water when the foil is deployed for the first time [17].

On June 23rd and June 30th a vertical profile of water samples was collected at the deepest station. Total alkalinity was measured by titration. ALKcarb was assumed to correspond to the total alkalinity. On 23rd June and July 1st vertical profiles of pCO2 including atmospheric partial pressures of CO2 were measured with the CO2-IRprobe. At each depth the CO2-IRprobe was deployed for 20 minutes allowing adjustment of the probe to the high concentrations at larger water depths. Wind speed was measured every 15 minutes 1.5 m above the lake water level on a buoy installed close to the deepest station of the lake (ISF Langenargen). Wind speed at 10 m above lake level WS10 was calculated from these wind speed data assuming a log-boundary layer, wind speed dependent drag coefficients C10 according to Wu [31] and assuming C10 ≥ 10−3 (S1 appendix). Further, profiles were taken with a multi-parameter CTD (RBR) equipped with an oxygen optode (fast optode model 4330F, Aanderaa Data Instruments, Norway), Chl.-a sensor (Seapoint), two PAR sensors (Licor) and a turbidity sensor (Seapoint), and with a multi-spectral fluorescence probe (Moldaenke FluoroProbe).


The values of pCO2 in air measured with the CO2-IRprobe on 23rd June and 1st July were 364 and 352 μatm, respectively. These values correspond to 394 and 382 ppm at local air pressure of 0.924 and 0.922 atm, respectively, and thus agree well with the current atmospheric concentration of ~400 ppm CO2 [32]. The long-term changes and the amplitude of the daily fluctuations of pCO2 measured with the CO2-optode agree well with those measured with the CO2-IRprobe (Fig 1). The good agreement of the amplitude and the timing of the daily fluctuations in pCO2 measured with the CO2-optode and the CO2-IRprobe support that the CO2-optode provides reliable data on pCO2 over an extended period of time. Four days after the calibration period the CO2-optode still agreed well with an independent measurement of the CO2-IRprobe (Fig 1, red circle).

Fig 1. Comparison of time series on pCO2 measured with the CO2-optode (blue line) at 1.7 m water depth and the CO2-IRprobe (red line) at 2.0 m water depth.

The red symbols represent additional individual measurements with the CO2-IRprobe.

Water temperatures increased at the beginning of the measuring period and were around 22°C thereafter (Fig 2a). The water temperatures at the water depths of the uppermost O2-optode (1.2 m) and of the CO2-optode (1.7 m) were essentially the same (blue and red lines in Fig 2a) indicating that the top 1.7 m of the water column was rather homogeneously mixed. This conclusion is consistent with the typical values for the mixed layer depth Zmix (average Zmix is 2.9 m, Fig Panel c in S1 appendix). The water temperatures measured with the O2-optode located at 3.2 m water depth (Fig 2a, black line) were similar to the temperatures at 1.2 and 1.7 m depth but were substantially lower between the 7th and 15th of June and between the 16th and 21st of July. During these time periods Zmix was smaller than 3.2 m (Fig Panel c in S1 appendix).

Fig 2. Surface water temperature and concentrations, saturation, and surface fluxes of O2 and CO2.

Temperature (a) and concentrations of dissolved O2 and dissolved CO2 (b and c) were measured with the O2-optodes at 1.2 m (blue) and 3.2 m (black) water depth and the CO2-optode at 1.7 m water depth (red). (c) depicts an enlargement of (b) to illustrate details of the daily changes in CO2 and CCO2. Both, O2 and CO2 concentrations are oversaturated compared to atmospheric equilibrium at in-situ temperature during most of the time (d). The flux of O2 (FO2,atm) and CO2 (FCO2,atm) to the atmosphere is depicted in panel (e). O2-saturation and FO2,atm (blue lines in (d) and (e)) are based on the CO2 data measured at 1.2 m water depth. The large short-term fluctuations in the fluxes to the atmosphere result from the variation in wind speed (see Fig Panel a in S1 appendix).

The temporal development of CO2 and of CCO2 was typically anti-correlated at time scales of several days but also at sub-daily time scales (Fig 2b and 2c). Both, CO2 and CCO2, showed daily concentration fluctuations consistent with metabolic transformations during different time periods of the day: CO2 was elevated during daytime and reduced during night-time whereas CCO2 showed the opposite pattern (Fig 2b and 2c). CO2 measured at 1.2 m and at 3.2 m water depth agreed well when temperatures agreed well and Zmix was larger than 3.2 m, but during time periods with Zmix < 3.2 m CO2 at 3.2 m depth was larger than at 1.2 m depth (Fig 2a and 2b, blue and black lines and Fig Panel c in S1 appendix). Below 3.2 m water depth O2 concentrations increased substantially with depth during most of the time period reaching maximum values at ~7 m depth (Fig Panels b and c in S2 appendix and Fig Panel f in S3 appendix). Below the peak concentration O2 decreased rapidly to anoxic conditions in the deep water. The vertical O2-gradients were small initially but they increased substantially between the 7th and 10th of June, when very high O2 concentrations developed at intermediate depths (Fig Panel b in S2 appendix).

During the measuring period CO2 and O2 near the lake surface were typically oversaturated (Fig 2d). Hence, the lake emitted carbon and oxygen to the atmosphere. During most of the measuring period, the daily fluctuations in the oversaturation of CO2 and O2 were small compared to the total oversaturation suggesting that the emissions were not controlled by the daily metabolic cycle during the time period of measurements (Fig 2d). Note that the molar fluxes of O2 to the atmosphere were substantially larger than those of CO2 (Fig 2e), although the oversaturation of CO2 was much larger than that of O2 (Fig 2d). On average the emissions of O2 and CO2 were 64 mmol m-2 d-1 and 7 mmol m-2 d-1, respectively. During the measuring period no extreme wind events occurred and wind speeds were typically below 10 m s-1 (Fig Panel a in S1 appendix). The O2 oversaturation in the surface water increased substantially at the beginning of June. The timing of this change in oversaturation corresponds closely with the onset of the development of the dissolved oxygen peak at ~7 to 8 m water depth (Fig 2d and Fig Panel b in S2 appendix and Fig Panel f in S3 appendix). Note that the O2-optodes were located at 7.2 and 9.2 m water depth and that the maximum O2 concentration measured with the O2 sensor of the CTD-probe was at ~8 m depth.

Profiles of Chla-equivalent concentration measured with the multi-spectral fluorescence probe showed a pronounced maximum at ~8 m depth (Fig Panel g in S3 appendix). Analysis of water samples and the spectral information from the fluorescent probe suggest that this peak in the Chla-equivalent concentration was generated by a dense layer of Plankthotrix rubescens (see [33] for measuring P. rubescens with the Moldaenke FluoroProbe).

At 2 m water depth alkalinity was 2.98 mmoleq L-1 on June 23rd and 2.93 mmoleq L-1 on June 30th, suggesting that alkalinity did not change substantially over this one-week time period. In the following we use 2.95 mmoleq L-1 as value for AlkCarb during the entire measuring period. The time series of pH calculated from AlkCarb, pCO2 and T shows periodic fluctuations. Within a day the values of pH varied by ~0.1 (Fig 3a). For the time period shown in Fig 3a the average pH was ~8.45. CDIC determined from the estimated time series of pH and the measured time series of pCO2 and T typically decreases during the day and increases at night (Fig 3a). The daily changes in DIC and O2 concentrations are anti-correlated, i.e. CO2 increases while CDIC decreases during daylight time and vice versa during night-time (Fig 3b). The amplitudes of the daily fluctuations in CDIC are about the same as those in CO2 at 1.2 m and 3.2 m water depth but are about 5 times larger than the amplitudes of the daily fluctuations in CCO2. This indicates that a substantial fraction of the dissolved inorganic carbon taken up and released during production and respiration alters HCO3- and CO3-- concentrations much more than CO2 concentrations. However, the amplitude of the CDIC fluctuations is less than 1% of the daily mean CDIC. Neglecting the daily fluctuations of pH in the calculation of CDIC leads to ~20 times larger amplitudes of the daily fluctuations of CDIC (Fig in S4 appendix) and thus would result in a severe overestimation of NEPL_C.

Fig 3. Comparison of the temporal development of DIC, pH, CO2 and O2 concentrations.

(a) CDIC and pH derived from CCO2 and a constant alkalinity of 2.95 mmoleq L-1. (b) Deviation of DIC, O2 and CO2 concentrations from the respective mean concentration within the time interval shown (ΔDIC, ΔO2 and ΔCO2, respectively). Note that the scaling of the axis for the molar deviations ΔDIC and ΔO2 is five times larger than the scaling of the axis for ΔCO2. (c) Long-term changes of CDIC, CCO2 and CO2. In (c) y-axes have shifted origin but the same scaling. The grey bar in (c) indicates the time period depicted in (a) and (b).

Lake metabolic rates determined from O2 and CO2 measurements are shown in Fig 4. Lake respiration rates were determined from linear regression of lake net production as function of time during night-time (Eq (25)). These respiration rates agree well with respiration rates estimated by averaging lake net production during night-time as in Eq (24) (Fig Panel a in S5 appendix).

Fig 4. Comparison of lake metabolic rates estimated with the diel CO2- and the diel O2-technique.

(a) Comparison of box-car filtered lake gross primary production GPPL and lake respiration rate RL estimated with both techniques. (b) Comparison of the effect of different assumptions on vertical transport on GPPL and RL (approaches (i)-(iii) and Eqs 23i23iii in the methods section) estimated with the diel CO2-technique (GPPL_C and RL_C). (c) as in (b) but for GPPL and RL estimated with the diel O2-technique (GPPL_O and RL_O). (d) Long-term changes in daily mean lake metabolic rates estimated with both techniques assuming that the net fluxes are zero (approach (i)). (e) Implications of different assumptions on the vertical fluxes for the daily mean metabolic rates estimated with the diel O2-technique. GPPL_O,A is often covered by GPPL_O and GPPL_O,F. Note that in all panels lake respiration rates are represented using a reverse axis, i.e. RL is increasing in the downward direction. The grey bar indicates the time period shown in panels a-c.

Lake gross primary production (GPPL) shows a pronounced daily cycle with minimum values occurring around midnight and maximum values around noon (Fig 4a). The phase and amplitude of the daily cycles of GPPL_O and GPPL_C are similar (Fig 4a). In the diel O2- and diel CO2-techniques lake respiration rates (RL) are assumed to be constant during a day. The order of magnitude and the temporal changes in RL_O and RL_C are similar, but RL_O shows larger fluctuations between days than RL_C (Fig 4a and 4d), especially around the 10th of June and the 20th of July. The long-term average and the long-term trends of daily mean GPPL_O and GPPL_C agree well (Table 1, Fig 4d), but the daily mean GPPL_O fluctuate more between days than the daily mean GPPL_C. RL_O and RL_C show very similar long-term trends as daily mean GPPL_O and GPPL_C, respectively (Fig 4d). Hence, daily mean NEPL_O and NEPL_C are substantially smaller than the other metabolic rates (Table 1), suggesting that lake gross primary production during daylight is sufficient to compensate lake respiration during day and night.

Table 1. Comparison of long-term mean lake metabolic rates estimated with the diel O2- and the diel CO2-technique and the influence of assumptions on vertical fluxes.

As O2 and CO2 are both oversaturated during most of the time (Fig 2d) the lake is emitting both gases, and the gas fluxes of both gases are therefore positive (Fig 2e). Consistently, including gas exchange with the atmosphere in the calculation of metabolic rates leads to lower estimates of the lake respiration RL_O,A than RL_O in case of the diel O2-technique (Fig 4c and 4e; Table 1), but to higher estimates of the lake respiration RL_C,A than RL_C in case of the diel CO2-technique (Fig 4b, Table 1). The difference between RL_C,A and RL_C in Fig 4b is particularly small because during the time period shown the oversaturation of CO2 is small (Fig 2d). However, the long-term average of the difference between RL_C,A and RL_C is also much smaller than that between RL_O and RL_O,A (Table 1), although the oversaturation of CO2 is on average 2.5 times larger than the oversaturation of O2 (average saturation of CO2 and O2 is 162% and 129%, respectively). Considering the fluxes due to turbulent mixing at the bottom of the mixed layer in addition to the surface flux results in respiration rates RL_O,D that are slightly larger than RL_O,A but still substantially smaller than RL_O (Table 1). Respiration rates RL_O,F estimated by considering atmospheric fluxes, fluxes due to turbulent diffusion and mixed layer deepening have values intermediate between RL_O,A and RL_O (Fig 4c and 4e, Table 1).

Estimates of lake gross primary production were comparatively insensitive to the assumptions on the transport processes, independent of whether the diel CO2- or the diel O2-technique was used (Fig 4b and 4c, respectively; Table 1). For all approaches considering different transport processes long-term averages of the lake gross primary production estimated from the diel CO2-technique had essentially the same values as those determined from the diel O2-technique (Fig 4d and 4e, Table 1).

The values of GPPL were similar for diel O2- and diel CO2-technique and the different assumption on vertical transport, but RL strongly depended on the assumptions on transport (Table 1). Hence, the estimates of NEPL also strongly depended on the estimates of concentration changes due to transport processes (Table 1).


The CO2-optode provides reliable long-term data on CCO2 over several weeks at sub-hourly resolution, as is indicated by the good agreement between CO2 concentrations measured with the CO2-optode and the CO2-IRprobe, and by the long-term consistency of lake gross primary production estimated from the diel O2- and the diel CO2-technique (GPPL_O and GPPL_C). Because CO2-optodes have a low power consumption they are ideally suited for long-term measurements of CCO2. Such data can be utilized to estimate metabolic rates using the diel CO2-technique and to determine CO2 fluxes from lakes based on direct measurements rather than indirect estimates of CO2.

Metabolic rates determined from the diel CO2-technique directly provide uptake and release of dissolved inorganic carbon due to production and respiration, whereas the diel O2-technique requires assumptions on the production and respiratory quotients if the contribution of metabolic transformations to the carbon balance is assessed. In alkaline Lake Illmensee (pH of ~8.5) the long-term averages of GPPL_C and GPPL_O agree well, suggesting that the production quotient PQ = GPPL_O / GPPL_C is close to one and thus within the range suggested by Oviatt et al. [34] and at the lower end for a typical algal cell [35]. However, according to measurements by Hanson et al. [2] in lakes with pH > 8 metabolic rates estimated with the diel O2-technique are substantially larger than estimates based on the diel change in CO2. This discrepancy can be explained by the dissociation of CO2 to bicarbonate and carbonate which substantially increases the temporal change in molar CDIC compared to that of molar CCO2. In Lake Illmensee where pH ~ 8.5 the amplitude of the diel cycle of molar CDIC is about five times larger than that of the diel cycle of molar CCO2 (Fig 3b and 3c). In contrast to the analysis of Hanson et al. [2], the diel CO2-technique employed in our study accounts for the dissociation of CO2 into different carbon species and estimates metabolic rates from the diel change in CDIC.

Similar to the system production quotient, the respiratory quotient RQ = RL_O / RL_C is close to one and thus within the range and close to the average value observed in estuarine mesocosm experiments [33]. However, the variability between days especially of GPPL_O and RL_O suggests considerable uncertainties in the estimates of the metabolic rates. Note that the production and respiratory quotients depend on the community of organisms responsible for the metabolic transformations and that the lake metabolic rates additionally depend on the exchange rates between the water column and the sediment (Eqs (14) and (17)).

The absolute values of GPPL_C and GPPL_O agree well with data on gross production measured with the diel O2-technique in other lakes (e.g., Lake Hampen, [3]; Lakes Peter and Paul, [21]). The pronounced daily cycle of GPPL_C and GPPL_O (Fig 4a) is consistent with the daily light cycle and light dependent production by phytoplankton. The ratios between lake gross production and lake respiration rate GPPL_C / RL_C and GPPL_O / RL_O, respectively, are close to one, which is consistent with the observations on metabolic ratios from several lakes [4,21]. Note that although the estimates of GPPL_C, GPPL_O, RL_C, and RL_O do not include corrections for transport, they provide metabolic rates, metabolic ratios, and metabolic quotients PQ and RQ that are consistent with observations in other studies.

The estimates of lake gross primary production were not very sensitive to vertical fluxes due to transport processes (gas exchange, vertical mixing), which was in contrast to the estimates of lake respiration rates (Table 1). Because GPPL is estimated from the difference between daylight NEPL and average night-time NEPL, the estimates of GPPL are only affected by the difference between the gradients of vertical fluxes during daytime and the average gradient of the vertical fluxes during night-time (for details see S6 appendix). Thus, if the gradients of the fluxes of O2, or of carbon respectively, do not change substantially between day and night, their effects on the estimates of lake gross primary production is small. In contrast to GPPL, estimates of lake respiration rates are affected directly by the average gradient of the vertical fluxes during night-time (Eqs (23) and (24); S6 appendix). Hence, if the gradients of the vertical fluxes have the same sign during day and night, as it was the case in our study, lake respiration rates are much more sensitive to the assumptions on the fluxes considered in the diel O2- and the diel CO2-techniques than lake gross primary production (Table 1).

Estimates of respiration rates based on the diel CO2-technique were much less sensitive to fluxes due to atmospheric gas exchange than estimates based on the diel O2-technique. As CO2 and O2 were nearly always oversaturated during day and night-time (Fig 2d) the fluxes due to gas exchange with the atmosphere are positive (Fig 2e). Hence, correcting estimates of metabolic rates for fluxes due to atmospheric gas exchange leads to increased respiration rates in the case of the diel CO2-technique and decreased respiration rates in case of the diel O2-technique (Table 1). However, the absolute change between RL_O and RL_O,A was much larger than that between RL_C and RL_C,A (Table 1), because the molar fluxes at the lake surface of CO2 were much smaller than those of O2 (Fig 2e). Even if the oversaturation of CO2 is larger than that of O2, the molar concentration CCO2 may be much smaller than CO2 (Fig 2b and 2c), since the molar atmospheric equilibrium concentration of CO2 is much smaller than that of O2 (e.g., at 20°C and local pressure (93600 Pa) CCO2,equ = 0.014 mmol L-1 and CO2,equ = 0.261 mmol L-1).

In general, the daily absolute change in the molar concentration difference between in-situ and atmospheric equilibrium concentration can be expected to be smaller for CO2 than for O2 (|CCO2-CCO2,equ| < |CO2-CO2,equ|). In alkaline Lake Illmensee much of the carbon taken up or released during metabolic processes is channeled to HCO3- and CO32- and only about 20% of consumed or respired CO2 is visible in changes in CCO2 (Fig 3b and 3c). Thus only a fraction of the change in carbon associated with metabolic processes contributes to the gas exchange of CO2 with the atmosphere. In acidic lakes, the same production and respiration rates as in alkaline Lake Illmensee lead to substantially larger daily fluctuation in CCO2 [2] and thus may lead to larger effects of gas exchange on the estimated respiration rate than in alkaline Lake Illmensee. However, estimates of RL_C and RL_O can be expected to differ in their sensitivity to atmospheric gas exchange in many lakes because the atmospheric concentration of O2 is substantially larger than that of CO2 (20% O2 versus 0.04% CO2). Therefore, physical processes such as, e.g., introduction of gas-bubbles at the lake surface by breaking surface waves or changes in surface water temperature affecting solubility and thus atmospheric equilibrium concentrations alter molar under- or oversaturation of O2 much more than that of CO2.

Considering vertical transport due to turbulent diffusion and mixed layer deepening in the calculation of metabolic rates increases the estimated respiration rate RL_O,F compared to the estimate RL_O,A which considers only the gas exchange with the atmosphere (Table 1). Below the mixed surface layer CO2 typically increased with increasing water depth (Fig 2b, Fig Panels b and c in S2 appendix and Fig in S3 appendix). Turbulent diffusion and mixed layer deepening therefore cause a positive upwards flux of O2. Neglecting this flux leads to an underestimation to the lake respiration rate. The quantification of the effects of vertical mixing on the O2 budget is however rather crude. For example, the fluxes due to turbulent diffusion require values for turbulent diffusivities. These were determined from the empirical relations of [27] that however provide rather crude estimates of the turbulent diffusivities and are not validated for Lake Illmensee by independent means. Further, the 2 m spacing of the optodes does not provide a good vertical resolution of the O2 distribution.

Our calculations are based on the mass balance of O2 in the entire mixed surface layer and not in a shallower top layer of fixed vertical extension within the mixed surface layer as in Staehr et al. [3] and Obrador et al. [5]. The latter approach has the disadvantage that within the mixed surface layer vertical gradients of dissolved oxygen are very small and therefore cannot reliably be determined with O2-optodes. Furthermore, the empirical relations for Kz by Hondzo and Stefan [27], which were developed for stratified hypolimnia and not for mixed surface layers, provide unrealistically low diffusivities within the surface mixed layer.

The consequences of considering the turbulent flux of DIC and mixed layer deepening in the diel CO2-technique could not be assessed because of the lack of long-term data from which DIC could be determined at a second depth in addition to the time series at 1.7 m. However, the vertical profile of CDIC calculated from the profiles of CCO2 and T measured on the 1st of July and the profile of alkalinity measured on the 30th of June, suggests that DIC increases with water depth (Fig in S3 appendix). In this case turbulent diffusion and mixed layer deepening leads to upward transport of carbon. A positive upwards flux of carbon implies that the lake respiration rates estimated with the diel CO2-technique considering only gas exchange with the atmosphere (RL_C,A) overestimate the true lake respiration rate.

The assumption that the gradient in the vertical fluxes of CO2 and of O2, respectively, is negligible leads to rather similar estimates of lake respiration rates with the diel CO2- and diel O2-techniques, i.e. RL_CRL_O (Table 1). Consistently, considering only gas exchange with the atmosphere and neglecting turbulent transport from deeper layers leads to an increase in the discrepancies between the respiration rates, because the flux to the atmosphere is positive for both, CO2 and O2. Because CO2 and most likely also CDIC increase below Zmix with increasing water depth, also the vertical flux due to mixing is positive for O2 and DIC. In the diel O2-technique a positive upward flux of O2 into the observation layer implies lake respiration rates higher than RL_O,A whereas in the diel CO2-technique a positive upward flux of DIC implies lake respiration rates lower than RL_C,A. Thus, in Lake Illmensee, the respiration rates RL_O,A and RL_C,A can be considered as the lower and upper bounds of the true lake respiration rates.

Lake respiration rates RL_O estimated from CO2 measured at 3.2 m depth, RL_O (3.2 m), and lake respiration rates estimated from CO2 measured at 1.2 m depth, RL_O (1.2 m), show similar long-term development (Fig Panel b in S5 appendix) and differ on average by less than 15% (S5 appendix). The similarity in metabolic rates at the two depths is not surprising, because during most of the time, measurements from both depths were within the mixed surface layer. However, also during time periods when Zmix < 3 m, e.g., between 7th and 15th of June, the estimates of RL_O (3.2 m) and RL_O (1.2 m) agreed rather well, except on the 10th of June, when RL_O (1.2 m) showed particularly strong deviations from the mean (Fig Panel b in S5 appendix). Considering the time period from the 7th to the 15th of June but excluding the 10th of June, the average of RL_O (3.2 m) (0.025 mmol L-1 d-1) agrees very well with the average of RL_O (1.2 m) (0.023 mmol L-1 d-1), but the average of RL_O,A (1.2 m) is negative (-0.005 mmol L-1). Note that the estimates of RL_O neglect effects due to gradients in the vertical fluxes of oxygen whereas RL_O,A considers gas exchange with the atmosphere but no other vertical fluxes. During the time period considered gas exchange with the atmosphere may influence the oxygen concentrations at 1.2 m but not at 3.2 m water depth because Zmix < 3 m. The values of RL_O,A (1.2 m) and RL_O (3.2 m) agree well with each other but not with RL_O,A (1.2 m) which assumes negative values that are conceptually impossible. These results suggest that considering gas exchange without including vertical transport into the mixed layer from below may result in a substantial underestimation of lake respiration rates and support the assumption that the net effect of all vertical fluxes is small.

Lake respiration rates not only include respiration in the open water but also oxygen consumption and carbon production at and within the sediments (Eqs (14) and (17)). Therefore, lake respiration rates not only depend on metabolic transformations but also on the exchange velocities between the sediment and the water column. The latter are controlled by the intensity of turbulence near the sediments and thus are affected by hydrodynamic processes that therefore indirectly influence the overall lake respiration rate.

In the surface mixed layer the aspect ratio between sediment area and water volume is small suggesting that the influence of fluxes into and from the sediments have only a small influence on the overall budget of O2 and CO2. However, the contribution of respiration within the sediments to overall oxygen consumption increases with water depth [36], because of the increase in the aspect ratio of sediment area to water volume. In the aphotic deep water zone of lakes oxygen depletion due to oxygen uptake by the sediments can be as large as or even larger than oxygen depletion in the open water column (e.g. [37]). Because in the deep water of lakes primary production may become very small due to light limitation NEP can be expected to become increasingly negative with increasing water depth leading to anoxic deep water bodies characterized by high concentrations of DIC (Fig Panels b, e, and f in S3 appendix). The deep water can thus act as a source of DIC for the surface layer, because the vertical gradient in CDIC together with turbulent mixing leads to a positive vertical flux of DIC. If the conditions in the surface layer are at steady state this flux of DIC from below together with the effects of NEP on CDIC are compensated by a CO2 flux to the atmosphere requiring oversaturation of CO2 in the surface mixed layer. Hence, the vertical flux of DIC from the anoxic deep water may explain the large oversaturation of CO2 at the beginning of the measuring time in early June (Fig 2d).

After the 7th of June, primary production at intermediate water depth altered the vertical gradients of DIC and O2, as is indicated by the development of the oxygen maximum at ~7–8 m depth (Fig Panel b in S2 appendix and Fig Panel f in S3 appendix) and a local minimum in the vertical profile of CDIC at this depth (Fig Panel e in S3 appendix). The decrease in CO2-oversaturation in the surface mixed layer during June and in July may thus be explained by reduced vertical fluxes of DIC. Analogously, the increase in the O2-oversaturation in the surface mixed layer after the 7th of June was most likely caused by an increase in the vertical flux of O2 that was produced at intermediate depths.

The conditions under which it is advantageous to apply the diel CO2-technique and the limitations of this technique have been explored in a sensitivity study (S7 appendix). The main conclusions of this analysis can be summarized as follows. In lakes with pH < 8 the daily change in CO2, ΔCCO2, is an excellent estimator of the daily change in DIC, ΔCDIC, with ΔCCO2 typically being only ~10% smaller than ΔCDIC. However, in lakes with pH ≥ 8 the difference between ΔCCO2 and ΔCDIC can be substantial and increases strongly with increasing pH, e.g., ΔCCO2 underestimates a ΔCDIC of 0.02 mmol L-1 by more than 20% at pH = 8 and by a factor of ~5 at pH = 8.5 (Table A in S7 appendix). Hence, in alkaline lakes the assessment of daily changes in CDIC from daily changes in CCO2 requires consideration of the carbonate balance.

If ΔCCO2 and pH and the balance of dissolved carbonates is used to estimate ΔCDIC, very small uncertainties in pH can introduce large errors in the estimate of ΔCDIC especially if the water has pH ≥ 8, e.g., an uncertainty of 0.005 in pH may result in an overestimation of ΔCDIC by a factor of two or more (Table B in S7 appendix), depending on the true ΔCDIC. Note that a systematic overestimation of pH has essentially no effect on the estimate of ΔCDIC.

The diel CO2-technique estimates pH from CCO2 and carbonate alkalinity and assumes that carbonate alkalinity is constant. In case alkalinity changes with time also carbonate alkalinity changes. The diel CO2-technique underestimates metabolic rates if ΔCDIC due to metabolic processes and the change in carbonate alkalinity ΔALKCarb have the same sign and overestimates metabolic rates if ΔCDIC due to metabolic processes and ΔALKCarb have opposite sign (Table C in S7 appendix). Changes in alkalinity caused by calcite precipitation or dissolution of solid carbonate have a smaller effect on the estimates of ΔCDIC than the same alkalinity change caused by other ions (Table D in S7 appendix). However, because in many lakes alkalinity is dominated by bicarbonate and carbonate ions, calcite precipitation may be the primary cause of substantial changes in alkalinity. Note that a systematic underestimation or overestimation, respectively, of carbonate alkalinity has essentially no effect on the predicted ΔCDIC. Hence, slow changes in carbonate alkalinity over several days have only small effects on predicted daily changes in CDIC and thus on the estimated metabolic rates. Further, using total alkalinity as measure of carbonate alkalinity has essentially no consequences for the estimated ΔCDIC.

The effects of changes in alkalinity on the estimates of metabolic rates could be avoided if high-precision pH measurements were available for the calculation of ΔCDIC. However, calcite precipitation and dissolution of solid carbonates not only affect alkalinity but also change CDIC. The diel CO2-technique treats all changes in CDIC as consequence of metabolic transformations and transport processes and therefore cannot provide reliable results during time periods during which calcite precipitation and dissolution of solid carbonate result in large sinks or sources of DIC, respectively. However, if calcite precipitation or the dissolution of solid carbonates, respectively, occurs continuously during day and night, GPPL estimated with the diel CO2-technique is much less sensitive to these processes than RL. This conclusion follows from the same argument that explained why GPPL is less sensitive than RL to transport processes if the gradient of the vertical flux has the same sign during day and night. In our study the time series of CO2 does not indicate sudden changes in CO2 which would accompany short-term events of calcite precipitation. The agreement between estimates of metabolic rates based on diel O2- and diel CO2-technique suggests that calcite precipitation was not a major factor in the balance of DIC but the same metabolic processes were responsible for the changes in DIC and O2.

The sensitivity study above suggests that it depends on the system whether metabolic rates can be reliably estimated with the diel CO2-technique or not. In shallow lakes and in littoral zones the dissolution of solid carbonates associated with the sediments may result in unreliable estimates of RL_C but possibly do not substantially affect the reliability of estimates of GPPL_C. In the open water of deep lakes, the diel CO2-technique should provide reliable metabolic rates except during time periods of calcite precipitation. In small lakes with short residence times external loading of dissolved carbonates may affect reliability of the estimates of metabolic rates. Finally, in lakes with high alkalinity it is advantageous to base the diel CO2-technique on CCO2 and alkalinity rather than on CCO2 and pH or CCO2 alone.


The diel CO2- and the diel O2-technique are complementary open-water methods for the estimation of metabolic rates in lakes. The diel CO2-technique has the advantage that it provides metabolic rates in terms of carbon produced or consumed and that it is less sensitive to gas exchange with the atmosphere. The assessment of metabolic rates with the diel CO2-technique is in principle not restricted to oxygenated regions of aquatic systems but can also be applied in anoxic waters, if instruments are available that can tolerate anoxic conditions. The diel CO2-technique could therefore be applied to investigate e.g. anaerobic methane oxidation which cannot be assessed with the diel O2-technique.

However, in contrast to the diel O2-technique, the diel CO2-technique requires additional measurements for the estimation of metabolic rates especially in alkaline lakes. In such lakes data on alkalinity or long-term pH measurements with sub-daily resolution must be available to determine the daily cycle of CDIC. In alkaline Lake Illmensee CDIC estimated from CCO2 is very sensitive to pH (Fig in S4 appendix). Because sufficiently precise pH data with sub-daily temporal resolution over several weeks were not available, we utilized alkalinity to determine CDIC from CCO2. In less alkaline lakes, e.g., in lakes with pH < 8 and an alkalinity that does not substantially exceed conditions at atmospheric equilibrium, time series of CCO2 may provide reliable estimates of CDIC.

The CO2-technique presented here treats alkalinity as an essentially conservative property because alkalinity is not affected by CO2 exchange with the atmosphere and changes due to production or respiration can be neglected. However, alkalinity may change due to several geochemical processes ([25]), e.g., calcite precipitation, nitrification and de-nitrification, inflow of water that has different alkalinity than the lake water, or vertical mixing, if alkalinity varies with water depth as in Lake Illmensee (Fig Panel c in S3 appendix). All these processes may increase the uncertainty of the metabolic rates estimated from the diel CO2-technique based on the combination of highly resolved time series of CCO2 with only a few alkalinity data.

Lake respiration rates are typically more difficult to estimate with the CO2- and O2-open-water techniques than gross primary production, because RL directly depends on the night-time net source of DIC or O2, respectively, whereas the estimate of GPPL depends on the difference between day-time and average night-time net source of DIC or O2, respectively. If the gradient in the vertical fluxes has the same sign during day and night, RL is more sensitive to transport processes than gross primary production. Especially the assessment of fluxes due to mixing near the lake surface is demanding.

Comparison of metabolic rates estimated from diel CO2- and diel O2-technique can help to improve the reliability of conclusions on metabolic processes and the associated consumption or release of dissolved oxygen and carbon. For example, during periods of intense gas exchange with the atmosphere, RL_O,A and RL_C,A may provide the lower and upper bounds for the true respiration rate if O2 and CO2 are oversaturated. Time periods of calcite precipitation may be visible in systematic long-term shifts between lake respiration rates estimated with the diel CO2- and the diel O2-technique.

In this study the comparison of lake metabolic rates indicates that the production of dissolved oxygen and the uptake of dissolved inorganic carbon associated with gross primary production agree well in alkaline Lake Illmensee at a pH of ~8.5. Further, dissolved oxygen in the surface water is not only strongly affected by gas exchange with the atmosphere and metabolic processes within the surface layer but also by the transport of dissolved oxygen from deeper waters that originates from production in deep water. This suggest that lake respiration rates estimated from the oxygen balance within the surface layer considering gas-exchange with the atmosphere but neglecting turbulent transport within the water column may include parts of the net production from deeper layers that may have occurred at earlier times. In this case lake respiration rates are underestimated whereas primary gross production may not be affected if the oxygen flux from deeper layers does not vary within a day.

The long-term average of NEPL_O and NEPL_C were both close to zero. Nevertheless, CO2 and O2 were oversaturated with respect to atmospheric equilibrium and the system was emitting both gases at the same time. Apparently, O2 emissions were not dominated by the current metabolism in the surface mixed layer but mainly linked to vertical transport of oxygen from an oxygen maximum at ~7–8 m water depth that must have been the result of net oxygen production at this depth most likely during the build-up of a phytoplankton layer in the deep water. Similarly, the CO2 emissions were not linked directly to the NEPL_C estimated from the CDIC in the surface water but resulted from vertical transport of DIC that had been released in deeper waters and in the anoxic sediments. The comparison of lake metabolic rates estimated from the diel CO2- and the O2-technique demonstrates that estimates of NEP based on measurement in the surface water do not reliably indicate system heterotrophy or autotrophy even if the data cover time periods of two months indicating the need for seasonal vertically-resolved carbon and oxygen-based estimates of metabolic rates.

Supporting Information

S1 Appendix. Background data on wind speed, water column characteristics and transport.


S2 Appendix. Long-term development of temperature stratification and the vertical distribution of dissolved oxygen.


S3 Appendix. Vertical distribution of pCO2, temperature, alkalinity, pH, CDIC, CO2 and Chla.


S4 Appendix. Sensitivity of the concentration of DIC to daily changes in pH.


S5 Appendix. Comparison of metabolic rates obtained using two different approaches to estimate night-time respiration and of metabolic rates determined from CO2 measured at 1.2 m and 3.2 m water depth.


S6 Appendix. Estimates of lake gross primary production GPPL are less sensitive to vertical transport than estimates of lake respiration rates RL obtained from the diel CO2-technique: Mathematical illustration.


S7 Appendix. Metabolic rates estimated with CO2-technique: Sensitivity to pH and alkalinity.


S8 Appendix. Compilation the main equations of the CO2- and the O2-technique.


S9 Appendix. Compilation of the empirical relations used in this study.



We thank J. Halder and B. Rosenberg for their support in the field, Pia Mahler for identification of P. rubescens in water samples, Georg Heine and his colleagues from the electronic and mechanical workshop at the University of Konstanz for the development of the logging unit for the CO2-optode, and T. Wolf from the Institut für Seenforschung der LUBW for the data on wind speed. JEF received funding from the Ministry of Science, Research and the Arts of the federal state Baden-Württemberg, Germany (grant: Water Research Network project: Challenges of Reservoir Management—Meeting Environmental and Social Requirements). University of Konstanz (grant: AFF 38/03) and the German Research Foundation (grant: YSF-DFG 419–14) financially supported the field work and construction of field instruments. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Author Contributions

  1. Conceptualization: FP HH.
  2. Data curation: FP.
  3. Formal analysis: FP JEF.
  4. Funding acquisition: FP HH.
  5. Investigation: FP JEF HH.
  6. Methodology: FP DA AT.
  7. Project administration: FP HH.
  8. Resources: FP DA AT.
  9. Software: FP JEF.
  10. Supervision: FP.
  11. Validation: FP DA.
  12. Visualization: FP.
  13. Writing – original draft: FP.
  14. Writing – review & editing: FP DA AT JEF HH.


  1. 1. Odum HT. Primary Production in Flowing Waters. Limnol Oceanogr Methods. 1956;1(1):102–17.
  2. 2. Hanson PC, Bade DL, Carpenter SR, Kratz TK. Lake metabolism: Relationships with dissolved organic carbon and phosphorus. Limnol Oceanogr. 2003;48(3):1112–9.
  3. 3. Staehr PA, Christensen JPA, Batt R, Read J. Ecosystem metabolism in a stratified lake. Limnol Oceanogr. 2012; 57(5):1317–30.
  4. 4. Hoellein TJ, Bruesewitz DA, Richardson DC. Revisiting Odum (1956): A synthesis of aquatic ecosystem metabolism. Limnol Oceanogr. 2013;58(6):2089–100.
  5. 5. Obrador B, Staehr PA, Christensen JPC. Vertical patterns of metabolism in three contrasting stratified lakes. Limnol Oceanogr. 2014;59(4):1228–40.
  6. 6. Ducharme-Riel V, Vachon D, Del Giorgio PA, Prairie YT. The relative contribution of winter under-ice and summer hypolimnetic CO2 accumulation to the annual CO2 emissions from northern lakes. Ecosystems. 2015;2:547–59.
  7. 7. López Bellido J, Tulonen T, Kankaala P, Ojala A. Concentrations of CO2 and CH4 in water columns of two stratified boreal lakes during a year of atypical summer precipitation. Biogeochemistry. 2013;113(1–3):613–27.
  8. 8. Cole JJ, Prairie YT, Caraco NF, McDowell WH, Tranvik LJ, Striegl RG, et al. Plumbing the global carbon cycle: Integrating inland waters into the terrestrial carbon budget. Ecosystems. 2007;10(1):172–85.
  9. 9. Tranvik LJ, Downing JA, Cotner JB, Loiselle SA, Striegl RG, Ballatore TJ, et al. Lakes and reservoirs as regulators of carbon cycling and climate. Limnol Oceanogr. 2009;54(1):2298–314.
  10. 10. Robinson C, le B Williams PJ. Respiration and its measurement in surface marine waters. In: del Giorgio PA, Williams PJ le B, editors. Respiartion in aquatic ecosystems. Oxford University Press; 2005. p. 147–80.
  11. 11. Odum HT. Trophic structure and productivity of Silver Springs, Florida. Ecol Monogr. 1957;27(1):55–112.
  12. 12. Schindler DW, Fee E. Diurnal variation of dissolved inorganic carbon and its use in estimating primary producion and CO2 invasion in lake 227. J Fish Res Board Canada. 1973;30:1501–10.
  13. 13. Staehr PA, Testa JM, Kemp WM, Cole JJ, Sand-Jensen K, Smith S V. The metabolism of aquatic ecosystems: history, applications, and future challenges. Aquat Sci. 2012;74(1):15–29.
  14. 14. Tengberg A, Hovdenes J, Andersson JH, Brocandel O, Diaz R, Hebert D, et al. Evaluation of a life time based optode to measure oxygen in aquatic systems. Limnol Oceanogr Methods. 2006;4:7–17.
  15. 15. Reichert P, Uehlinger U, Acuña V. Estimating stream metabolism from oxygen concentrations: Effect of spatial heterogeneity. J Geophys Res. 2009;114(G3):G03016.
  16. 16. Staehr PA, Bade D, Koch GR, Williamson C, Hanson P, Cole JJ, et al. Lake metabolism and the diel oxygen technique : State of the science. Limnol Oceanogr Methods. 2010;628–44.
  17. 17. Atamanchuk D, Tengberg A, Thomas PJ, Hovdenes J, Apostolidis A, Huber C, et al. Performance of a lifetime-based optode for measuring partial pressure of carbon dioxide in natural waters. Limnol Oceanogr Methods. 2014;12(2):63–73.
  18. 18. Atamanchuk D., Kononets M, Thomas PJ, Hovdenes J, Tengberg A, Hall POJ. Continuous long-term observations of the carbonate system dynamics in the water column of a temperate fjord. J Mar Syst. 2015;148:272–84.
  19. 19. Verspagen JMH, Van de Waal DB, Finke JF, Visser PM, Van Donk E, Huisman J. Rising CO2 levels will intensify phytoplankton blooms in eutrophic and hypertrophic lakes. PLoS One. 2014;9(8):e104325. pmid:25119996
  20. 20. Cole JJ, Pace ML, Carpenter SR, Kitchell JF. Persistence of net heterotrophy in lakes during nutrient addition and food web manipulations. Limnol Oceanogr. 2000;45(8):1718–30.
  21. 21. Coloso JJ, Cole JJ, Pace ML. Difficulty in discerning drivers of lake ecosystem metabolism with high-frequency data. Ecosystems. 2011;14(6):935–48.
  22. 22. Weiss RF. Carbon dioxide in water and seawater: the solubility of a non-ideal gas. Mar Chem. 1974;2:203–15.
  23. 23. Stumm W, Morgan JJ. Aquatic chemistry, chemical equilibria and rates in natural waters. 3rd. ed. John Wiley & Sons, Inc., New York; 1996. 1022p p.
  24. 24. Millero FJ. Thermodynamics of the carbon dioxide system in the oceans. Geochim Cosmochim Acta. 1995;59(4):661–77.
  25. 25. Wolf-Gladrow DA, Zeebe RE, Klaas C, Körtzinger A, Dickson AG. Total alkalinity: The explicit conservative expression and its application to biogeochemical processes. Mar Chem. 2007;106(1–2):287–300.
  26. 26. Redfield AC, Ketchum BH, Richards FA. The influence of organisms on the composition of sea water. In: Hill MN, editor. The Sea: Vol 2. John Wiley and Sons, New York; 1963. p. 26–77.
  27. 27. Hondzo M, Stefan HG. Lake water temperature simulation model. J Hydraul Eng. 1993;119:1251–73.
  28. 28. Weiss RF. The solubility of nitrogen, oxygen and argon in water and seawater. Deep-Sea Res. 1970;17:721–35.
  29. 29. Cole JJ, Caraco NF. Atmospheric exchange of carbon dioxide in a low-wind oligotrophic lake measured by the addition of SF6. Limnol Oceanogr. 1998;43(4):647–56.
  30. 30. Liss PS, Merlivat L. Air−sea gas exchange rates: Introduction and synthesis. In: Reidel D, editor. The role of air−sea exchange in geochemical cycling. Publishing Company, Dordrecht, The Netherlands; 1986. p. 113–27.
  31. 31. Wu J. Wind-stress coefficients over sea surface near neutral conditions—A revisit. J Phys Oceanogr. 1980;10(5):727–40.
  32. 32. Balzer F, Bünger B, Dauert U, Drosihn D, Eckermann F et al. Data on the environment 2015. Eds: Federal Environment Agency Section I 1.5 “National and international Environmental Reporting”, Germany. 2015, 143pp.
  33. 33. Hofmann H, Peeters F. In-situ optical and acoustical measurements of the buoyant cyanobacterium P. rubescens: Spatial and temporal distribution patterns. PLoS One. 2013;8(11):e80913. pmid:24303028
  34. 34. Oviatt CA, Rudnick DT, Keller AA, Sampou PA, Almquist T. Measurements of metabolism in estuarine mesocosms. Mar Ecol Prog Ser. 1986;28:57–67.
  35. 35. Williams PJL, Robertson JE. Overall planktonic oxygen and carbon dioxide metabolisms: the problem of reconciling observations and calculations of photosynthetic quotients. J Plankton Res. 1991;13:153–69.
  36. 36. Livingstone DM, Imboden DM. The prediction of hypolimnetic oxygen profiles: a plea for a deductive approach. Can J Fish Aquat Sci. 1996;53:924–32.
  37. 37. North RP. The influence of climate change on the occurrence of hypoxia in Swiss lakes. ETH Zürich; 2012.