Introduction

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., [1–5]).

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 [1,11–13]. 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 (S1–S3 Appendices), model sensitivity analyses (S4–S7 Appendices), detailed equations (S8 Appendix), and empirical relations (S9 Appendix).

Methods

Results

The values of pCO₂ in air measured with the CO₂-IRprobe on 23^rd June and 1^st 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).

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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.

https://doi.org/10.1371/journal.pone.0168393.g001

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 Z_mix (average Z_mix 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 7^th and 15^th of June and between the 16^th and 21^st of July. During these time periods Z_mix was smaller than 3.2 m (Fig Panel c in S1 appendix).

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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 C_O2 and C_CO2. 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 (F_O2,atm) and CO₂ (F_CO2,atm) to the atmosphere is depicted in panel (e). O₂-saturation and F_O2,atm (blue lines in (d) and (e)) are based on the C_O2 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).

https://doi.org/10.1371/journal.pone.0168393.g002

The temporal development of C_O2 and of C_CO2 was typically anti-correlated at time scales of several days but also at sub-daily time scales (Fig 2b and 2c). Both, C_O2 and C_CO2, showed daily concentration fluctuations consistent with metabolic transformations during different time periods of the day: C_O2 was elevated during daytime and reduced during night-time whereas C_CO2 showed the opposite pattern (Fig 2b and 2c). C_O2 measured at 1.2 m and at 3.2 m water depth agreed well when temperatures agreed well and Z_mix was larger than 3.2 m, but during time periods with Z_mix < 3.2 m C_O2 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 7^th and 10^th 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 Chl_a-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 Chl_a-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 mmol_eq L^-1 on June 23^rd and 2.93 mmol_eq L^-1 on June 30^th, suggesting that alkalinity did not change substantially over this one-week time period. In the following we use 2.95 mmol_eq L^-1 as value for Alk_Carb during the entire measuring period. The time series of pH calculated from Alk_Carb, 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. C_DIC 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. C_O2 increases while C_DIC decreases during daylight time and vice versa during night-time (Fig 3b). The amplitudes of the daily fluctuations in C_DIC are about the same as those in C_O2 at 1.2 m and 3.2 m water depth but are about 5 times larger than the amplitudes of the daily fluctuations in C_CO2. 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 C_DIC fluctuations is less than 1% of the daily mean C_DIC. Neglecting the daily fluctuations of pH in the calculation of C_DIC leads to ~20 times larger amplitudes of the daily fluctuations of C_DIC (Fig in S4 appendix) and thus would result in a severe overestimation of NEP_L__C.

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

(a) C_DIC and pH derived from C_CO2 and a constant alkalinity of 2.95 mmol_eq 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 C_DIC, C_CO2 and C_O2. 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).

https://doi.org/10.1371/journal.pone.0168393.g003

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).

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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 GPP_L and lake respiration rate R_L estimated with both techniques. (b) Comparison of the effect of different assumptions on vertical transport on GPP_L and R_L (approaches (i)-(iii) and Eqs 23i–23iii in the methods section) estimated with the diel CO₂-technique (GPP_{L_C} and R_{L_C}). (c) as in (b) but for GPP_L and R_L estimated with the diel O₂-technique (GPP_{L_O} and R_{L_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. GPP_{L_O,A} is often covered by GPP_{L_O} and GPP_{L_O,F.} Note that in all panels lake respiration rates are represented using a reverse axis, i.e. R_L is increasing in the downward direction. The grey bar indicates the time period shown in panels a-c.

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Lake gross primary production (GPP_L) 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 GPP_{L_O} and GPP_{L_C} are similar (Fig 4a). In the diel O₂- and diel CO₂-techniques lake respiration rates (R_L) are assumed to be constant during a day. The order of magnitude and the temporal changes in R_{L_O} and R_{L_C} are similar, but R_{L_O} shows larger fluctuations between days than R_{L_C} (Fig 4a and 4d), especially around the 10^th of June and the 20^th of July. The long-term average and the long-term trends of daily mean GPP_{L_O} and GPP_{L_C} agree well (Table 1, Fig 4d), but the daily mean GPP_{L_O} fluctuate more between days than the daily mean GPP_{L_C}. R_{L_O} and R_{L_C} show very similar long-term trends as daily mean GPP_{L_O} and GPP_{L_C}, respectively (Fig 4d). Hence, daily mean NEP_{L_O} and NEP_{L_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.

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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.

https://doi.org/10.1371/journal.pone.0168393.t001

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 R_{L_O},_A than R_{L_O} in case of the diel O₂-technique (Fig 4c and 4e; Table 1), but to higher estimates of the lake respiration R_{L_C},_A than R_{L_C} in case of the diel CO₂-technique (Fig 4b, Table 1). The difference between R_{L_C,A} and R_{L_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 R_{L_C,A} and R_{L_C} is also much smaller than that between R_{L_O} and R_{L_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 R_{L_O,D} that are slightly larger than R_{L_O,A} but still substantially smaller than R_{L_O} (Table 1). Respiration rates R_{L_O,F} estimated by considering atmospheric fluxes, fluxes due to turbulent diffusion and mixed layer deepening have values intermediate between R_{L_O,A} and R_{L_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 GPP_L were similar for diel O₂- and diel CO₂-technique and the different assumption on vertical transport, but R_L strongly depended on the assumptions on transport (Table 1). Hence, the estimates of NEP_L also strongly depended on the estimates of concentration changes due to transport processes (Table 1).

Discussion

The CO₂-optode provides reliable long-term data on C_CO2 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 (GPP_{L_O} and GPP_{L_C}). Because CO₂-optodes have a low power consumption they are ideally suited for long-term measurements of C_CO2. 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 GPP_{L_C} and GPP_{L_O} agree well, suggesting that the production quotient PQ = GPP_{L_O} / GPP_{L_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 C_DIC compared to that of molar C_CO2. In Lake Illmensee where pH ~ 8.5 the amplitude of the diel cycle of molar C_DIC is about five times larger than that of the diel cycle of molar C_CO2 (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 C_DIC.

Similar to the system production quotient, the respiratory quotient RQ = R_{L_O} / R_{L_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 GPP_{L_O} and R_{L_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 GPP_{L_C} and GPP_{L_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 GPP_{L_C} and GPP_{L_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 GPP_{L_C} / R_{L_C} and GPP_{L_O} / R_{L_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 GPP_{L_C}, GPP_{L_O}, R_{L_C}, and R_{L_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 GPP_L is estimated from the difference between daylight NEP_L and average night-time NEP_L, the estimates of GPP_L 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 GPP_L, 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 R_{L_O} and R_{L_O,A} was much larger than that between R_{L_C} and R_{L_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 C_CO2 may be much smaller than C_O2 (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) C_CO2,equ = 0.014 mmol L^-1 and C_O2,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 (|C_CO2-C_CO2,equ| < |C_O2-C_O2,equ|). In alkaline Lake Illmensee much of the carbon taken up or released during metabolic processes is channeled to HCO₃^- and CO₃^2- and only about 20% of consumed or respired CO₂ is visible in changes in C_CO2 (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 C_CO2 [2] and thus may lead to larger effects of gas exchange on the estimated respiration rate than in alkaline Lake Illmensee. However, estimates of R_{L_C} and R_{L_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 R_{L_O,F} compared to the estimate R_{L_O,A} which considers only the gas exchange with the atmosphere (Table 1). Below the mixed surface layer C_O2 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 K_z 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 C_DIC calculated from the profiles of C_CO2 and T measured on the 1^st of July and the profile of alkalinity measured on the 30^th 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 (R_{L_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. R_{L_C} ≈R_{L_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 C_O2 and most likely also C_DIC increase below Z_mix 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 R_{L_O,A} whereas in the diel CO₂-technique a positive upward flux of DIC implies lake respiration rates lower than R_{L_C,A}. Thus, in Lake Illmensee, the respiration rates R_{L_O,A} and R_{L_C,A} can be considered as the lower and upper bounds of the true lake respiration rates.

Lake respiration rates R_{L_O} estimated from C_O2 measured at 3.2 m depth, R_{L_O} (3.2 m), and lake respiration rates estimated from C_O2 measured at 1.2 m depth, R_{L_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 Z_mix < 3 m, e.g., between 7^th and 15^th of June, the estimates of R_{L_O} (3.2 m) and R_{L_O} (1.2 m) agreed rather well, except on the 10^th of June, when R_{L_O} (1.2 m) showed particularly strong deviations from the mean (Fig Panel b in S5 appendix). Considering the time period from the 7^th to the 15^th of June but excluding the 10^th of June, the average of R_{L_O} (3.2 m) (0.025 mmol L^-1 d^-1) agrees very well with the average of R_{L_O} (1.2 m) (0.023 mmol L^-1 d^-1), but the average of R_{L_O,A} (1.2 m) is negative (-0.005 mmol L^-1). Note that the estimates of R_{L_O} neglect effects due to gradients in the vertical fluxes of oxygen whereas R_{L_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 Z_mix < 3 m. The values of R_{L_O,A} (1.2 m) and R_{L_O} (3.2 m) agree well with each other but not with R_{L_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 C_DIC 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 C_DIC 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 7^th 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 C_DIC 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 7^th 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, ΔC_CO2, is an excellent estimator of the daily change in DIC, ΔC_DIC, with ΔC_CO2 typically being only ~10% smaller than ΔC_DIC. However, in lakes with pH ≥ 8 the difference between ΔC_CO2 and ΔC_DIC can be substantial and increases strongly with increasing pH, e.g., ΔC_CO2 underestimates a ΔC_DIC 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 C_DIC from daily changes in C_CO2 requires consideration of the carbonate balance.

If ΔC_CO2 and pH and the balance of dissolved carbonates is used to estimate ΔC_DIC, very small uncertainties in pH can introduce large errors in the estimate of ΔC_DIC especially if the water has pH ≥ 8, e.g., an uncertainty of 0.005 in pH may result in an overestimation of ΔC_DIC by a factor of two or more (Table B in S7 appendix), depending on the true ΔC_DIC. Note that a systematic overestimation of pH has essentially no effect on the estimate of ΔC_DIC.

The diel CO₂-technique estimates pH from C_CO2 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 ΔC_DIC due to metabolic processes and the change in carbonate alkalinity ΔALK_Carb have the same sign and overestimates metabolic rates if ΔC_DIC due to metabolic processes and ΔALK_Carb 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 ΔC_DIC 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 ΔC_DIC. Hence, slow changes in carbonate alkalinity over several days have only small effects on predicted daily changes in C_DIC and thus on the estimated metabolic rates. Further, using total alkalinity as measure of carbonate alkalinity has essentially no consequences for the estimated ΔC_DIC.

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 ΔC_DIC. However, calcite precipitation and dissolution of solid carbonates not only affect alkalinity but also change C_DIC. The diel CO₂-technique treats all changes in C_DIC 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, GPP_L estimated with the diel CO₂-technique is much less sensitive to these processes than R_L. This conclusion follows from the same argument that explained why GPP_L is less sensitive than R_L 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 R_{L_C} but possibly do not substantially affect the reliability of estimates of GPP_{L_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 C_CO2 and alkalinity rather than on C_CO2 and pH or C_CO2 alone.

Conclusions

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 C_DIC. In alkaline Lake Illmensee C_DIC estimated from C_CO2 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 C_DIC from C_CO2. 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 C_CO2 may provide reliable estimates of C_DIC.

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 C_CO2 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 R_L directly depends on the night-time net source of DIC or O₂, respectively, whereas the estimate of GPP_L 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, R_L 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, R_{L_O,A} and R_{L_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 NEP_{L_O} and NEP_{L_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 NEP_{L_C} estimated from the C_DIC 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

Acknowledgments

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.