Alkalinity contributes at least a third of annual gross primary production in a deep stratified hardwater lake

In alkaline freshwater systems, the apparent absence of carbon limitation to gross primary production (GPP) at low CO2 concentrations suggests that bicarbonates can support GPP. However, the contribution of bicarbonates to GPP has never been quantified in lakes along the seasons. To detect the origin of the inorganic carbon maintaining GPP, we analyze the daily stoichiometric ratios of CO2–O2 and alkalinity–O2 in a deep hardwater lake. Results show that aquatic primary production withdraws bicarbonate from the alkalinity pool for two‐thirds of the year. Alkalinity rather than CO2 is the dominant inorganic carbon source for GPP throughout the stratified period in both the littoral and pelagic environments. This study sheds light on the neglected role of alkalinity in the freshwater carbon cycle throughout an annual cycle.

In aquatic ecosystems, gross primary production (GPP) converts dissolved inorganic carbon (DIC = CO 2 + HCO 3 À + CO 3 2À ) into organic matter. Nutrients (nitrogen and phosphorus) and light are the main limiting factors of GPP (Schindler et al. 1973;Dillon and Rigler 1974;Krause-Jensen and Sand-Jensen 1998;Karlsson et al. 2009). Because additions of DIC to lakes were not sufficient to increase GPP levels (Schindler 1971(Schindler , 1974, DIC limitation of GPP has been regarded as unlikely, especially since most inland waters are supersaturated with CO 2 (Cole et al. 1994). This statement has been questioned in cases of near-surface CO 2 undersaturation when GPP demand surpasses inward atmospheric CO 2 fluxes Finlay et al. 1999;Zhang et al. 2017;Zagarese et al. 2021). Under such conditions, the GPP in low-alkaline soft water lakes has been proven to be carbon-limited (Kragh and Sand-Jensen 2018).
In the same study, Kragh and Sand-Jensen (2018) did not detect any carbon limitation of GPP at such low near-surface CO 2 in high-alkaline hardwater lakes. The absence of carbon limitation was therein attributed to the high DIC stocks. However, at pH values typical for moderate hardwater lakes (7.8-9), the DIC pool is mainly composed of bicarbonates (HCO 3 À > 95%; Stumm and Morgan 1981) that cannot be readily fixed by most primary producers. At high HCO 3 À concentrations and high pH, atmospheric CO 2 invasion is greatly enhanced by chemical enhancement (Wanninkhof and Knox 1996). Yet, the carbonate buffering effect leads to fast hydration and deprotonation of incoming atmospheric CO 2 into HCO 3 À with limited effect on pH and dissolved CO 2 concentrations (Bade and Cole 2006). Thus, the chemical enhancement of atmospheric inward fluxes in alkaline lakes cannot directly supply CO 2 to primary producers. The apparent lack of carbon limitation of GPP in alkaline hardwater lakes despite low CO 2 concentrations suggests that alkalinity can deliver DIC to primary producers (Li et al. 2018). Primary producers, inhabiting environments with low CO 2 , high HCO 3 À , and high light levels (Maberly and Gontero 2017) have evolved complex strategies to use HCO 3 À for maintaining GPP (e.g., Steemann Nielsen 1946;Thomas and Tregunna 1968;Price et al. 2008;Maberly and Gontero 2017;Iversen et al. 2019). At low CO 2 concentrations, certain microalgae and cyanobacteria can mobilize active HCO 3 À uptake systems. Bicarbonate is transported to cell compartments where specific enzymes concentrate and convert HCO 3 À into CO 2 (CO 2 -concentrating mechanism [CCM]; e.g., carbon anhydrase; Colman et al. 2002;Li et al. 2018). For active HCO 3 À uptake, 1 mol of alkalinity is lost as 1 mol of inorganic carbon is fixed within photosynthesis. Another mechanism to ensure carbon supply to GPP involves the capture of the CO 2 released during calcite precipitation (CP: 2HCO 3 À + Ca 2+ ⇄ CaCO 3 + CO 2 + H 2 O) that can occur close to the membranes of many algae and macrophytes (Kelts and Hsü 1978;Larsson and Axelsson 1999;Pełechaty et al. 2013;Müller et al. 2016). For indirect HCO 3 À use through CP, 2 mol of alkalinity are lost for 1 mol of inorganic carbon fixed within photosynthesis, the remaining mole being precipitated as calcite. Alkalinity (Alk) was shown to be the main DIC source to macrophytes in a downstream reach of a river in the South of France (Maberly et al. 2015). A recent study of GPP in five US rivers (Aho et al. 2021) estimated that HCO 3 À could support up to 30% of the annual GPP in one large and sunny reach of the Connecticut River. The contribution of HCO 3 À in supporting GPP in lakes remains to be quantified, and its implications for the carbon cycle of hardwater lakes are to be understood. Lake Geneva is a moderately hardwater lake with surface CO 2 concentrations below saturation for the stratified period. Herein, we aim at detecting the origin of the dominant DIC supporting GPP in both the pelagic and littoral environments of Lake Geneva on a daily scale. By combining hourly CO 2 , O 2 , and alkalinity measurements over a complete annual cycle, we categorize the dominant daily source of DIC to GPP based on the stoichiometric changes of CO 2 -O 2 and Alk-O 2 . We relate the DIC source to the environmental conditions to estimate the importance of HCO 3 À use for the littoral and pelagic GPP at an annual scale.

Study sites
Lake Geneva is a large, deep, alkaline hardwater lake with surface alkalinity ranging from 1200 to 1700 μeq L À1 , a surface calcium concentration (Ca 2+ ) ranging from 38 to 46 mg L À1 , and a salinity of $0.2‰. The lake is stratified from April to September with a thermocline deepening from 3 to 30 m. Calcite precipitation occurs throughout during the stratification period (Müller et al. 2016;Escoffier et al. 2023). Two study sites (Fig. S1a-c), the LéXPLORE platform (110-m depth; Wüest et al. 2021) and the Buchillon mast (4-m depth), representative of the pelagic and littoral environments, were investigated over the years 2019 and 2020.

Field methods
Dissolved oxygen was measured by miniDOT sensors (PME). Dissolved pCO 2 was measured by miniCO 2 sensors (Pro-Oceanus System Inc.). Alkalinity is strongly correlated to the specific conductance over the whole year in Lake Geneva (R 2 = 0.95; Supporting Information Methods). The subdaily dynamics of alkalinity are thereby estimated using a conductivity logger (HOBO U24-001; Onset).
Local weather conditions were continuously recorded by a Campbell Scientific automatic weather station at each site. Water temperatures were measured from 0.7 to 30 m with 2.5 m of interval depth using Minilog II-T (VEMCO) in the pelagic area. These temperatures were used to compute the Schmidt stability (Idso 1973) and the mixed layer depth (Imberger 1985). Finally, all variables were gridded at an hourly time step ; more details about sensors and calibration in Supporting Information Methods).

Data analysis and modeling
The CO 2 and O 2 concentrations at the lake surface were expressed in terms of departure from atmospheric equilibrium in μmol L À1 as in Vachon et al. (2020). At the pH of Lake Geneva's surface waters (pH 7.8-9; see Fig. S2), HCO 3 À represents > 89% of the total alkalinity (Alk = HCO 3 À + 2CO 3 2À ; Perolo et al. Estimating alkalinity contribution to GPP Stumm and Morgan 1981). Besides, carbonate (CO 3 2À ) cannot be used by primary producers. We thereby assumed the Alk variations to be equal to the HCO 3 À variations (Groleau et al. 2000). The origin of the dominant DIC supporting GPP was detected from the analysis of paired CO 2 -O 2 and Alk-O 2 dynamics (Stets et al. 2017;Aho et al. 2021), following an approach inspired but expanded from Vachon et al. (2020) (Fig. S3).
Briefly, the slopes of the daily point clouds of CO 2 -O 2 (α) and Alk-O 2 (β; 95% confidence interval) were used to categorize the dominant source of DIC (i.e., >50% of CO 2 or HCO 3 À ) supporting GPP based on the following stoichiometric ratios. The photosynthesis from CO 2 uptake leads to daily molar ratios for CO 2 -O 2 between 1 : 1 and 1 :  S4). Daily rates of GPP (μmol O 2 L À1 d À1 ) were computed using a Bayesian Lake Metabolism model provided in the LakeMetabolizer R package (Winslow et al. 2016;Read et al. 2011;Supporting Information Method). We tested whether the dominant origins of DIC supporting GPP could be predicted from the four (littoral) and five (pelagic) daily averaged selected environmental variables (GPP rate, CO 2 departure, wind speed, solar radiation, and Schmidt stability) using classification trees (Supporting Information Method). The best models were used to reconstruct the dominant daily DIC sources of GPP for the not-classified days for which GPP could be computed.

Spatiotemporal variability
The annual CO 2 -O 2 dynamics of the littoral and pelagic environments are illustrated at an hourly resolution in Fig. 1 (time series in Fig. S6). Two distinct periods are observed in the littoral and pelagic environments (Fig. 1a,b): a cold period (September-March) corresponding to the first windy event in fall until the end of the winter mixing and a warm period (April-August) corresponding to the highest levels of solar radiation and stratification strength.
During the cold period, the conditions are mainly undersaturated in O 2 and oversaturated in CO 2 . The slope of the CO 2 -O 2 dynamics remains close to À1, reflecting the classical stoichiometry of photosynthesis (i.e., use of CO 2 ). The range of CO 2 departures is similar for the littoral and pelagic sites, while the O 2 departures are, on average, $30 μmol L À1 lower in the littoral as compared to the pelagic site.
These conditions shift to an O 2 oversaturation and a CO 2 undersaturation during the stratified period. Over these months, the slope of the CO 2 -O 2 dynamic strongly deviates from À1 and becomes much steeper. This high production of O 2 and low consumption of CO 2 sheds light on the potential CO 2 limitation in this system.
The data distribution within the CO 2 -O 2 diagram is more scattered for the shoulder seasons (March-April and September-October; Fig. S7), especially for the littoral site. For those shoulder months, the CO 2 -O 2 variability within a single day can be almost as wide as the monthly and annual CO 2 -O 2 variability (Fig. S8). Figure 1c,d shows the results of the two processes including CO 2 uptake or HCO 3 À use for GPP. More examples are provided in Fig. S9. The distribution of DIC sources is broadly partitioned depending on O 2 -CO 2 departures, with most days of CO 2 uptake at CO 2 supersaturated and O 2 undersaturated daily conditions and HCO 3 À use at CO 2 undersaturated and O 2 oversaturated conditions. However, GPP could rely on HCO 3 À use even on days with supersaturated daily averaged CO 2 values, especially in the pelagic site. Figure 2 presents the relationships between the CO 2 uptake and HCO 3 À use of GPP and the daily chemical and physical conditions. Figure 2a shows a clear partition of DIC source according to GPP and average daily CO 2 departures in the littoral site with HCO 3 À use for CO 2 departures < À4.4 μmol L À1 and GPP > 16 μmol O 2 L À1 d À1 (classification tree for the littoral in Table S1). The physical conditions, such as wind speed, have a limited impact on DIC use (Fig. S10). In the pelagic site, the water column stability is the main driver of DIC use, followed by the GPP level, with HCO 3 À use for a Schmidt stability >116 J m À2 and a GPP >5 μmol O 2 L À1 d À1 (Fig. 2b and classification tree for the pelagic in Table S2). Moreover, for the highest GPP level > 50 μmol O 2 L À1 d À1 , the slopes of the CO 2 -O 2 ratio tend to infinity, while the slopes of Alk-O 2 ratio align to the 1 : -1 involving an assimilation >95% of HCO 3 À to maintain these GPP levels (Fig. S9).

Perolo et al.
Estimating alkalinity contribution to GPP DIC pool contribution to GPP along the year The predictions accuracies for the classification trees are > 80% and reveal the strong predictive power of some specific drivers (i.e., CO 2 departure and GPP for the littoral environment, stability, and GPP for the pelagic environment; Tables S1, S2). Trained classification models are thereafter used to reconstruct the dominant DIC use for days that could not be categorized from their stoichiometric relationships (approximately two-thirds of the datasets). The distributions of GPP within DIC use categories are very similar between the training dataset and the predictions (see violin plots BeforejAfter in Fig. 3).
In the littoral site, GPP is exclusively supported by CO 2 uptake in winter and late fall, while HCO 3 À use is the dominant source for GPP in summer (June-August), when the highest GPP rates are recorded. From March to May, GPP is alternatively supported by HCO 3 À and CO 2 because of strong daily fluctuations in CO 2 (Fig. 3a). Overall, we estimate that 75% of the total annual littoral GPP (sum of GPP with a dominant HCO 3 À source divided by sum of total GPP; from data in Fig. 1. Panels (a, b) show the annual dynamic of CO 2 departure vs. O 2 departure (μmol L À1 ) in littoral and pelagic environments colored according to the months of the year. The two annual cycles present more than 65% of the days of the year distributed over all months (see also Fig. S4). Panels (c, d) highlight the two categorisations of CO 2 uptake (α slopes from À1 to À1.4: red points) and HCO 3 À use (α slope < À1.4 and β slopes from À0.5 to À1.4: green points) as well as the not attributed days (gray points). The dashed line represents the À1 slope.

Fig. 3) occurs under dominant HCO 3
À fixation. In summer, when GPP rates are the greatest, the littoral GPP is exclusively under dominant HCO 3 À fixation.
DIC use is more seasonally partitioned for the pelagic site (Fig. 3b)

Discussion
The high-frequency data coupling of CO 2 , O 2 , and alkalinity provides meaningful ecosystem function information (e.g., Stets et al. 2017;Vachon et al. 2020). The analyses of stoichiometric slopes allow to detect the origin of the dominant DIC supporting GPP and, complemented by the classification tree, offer an interesting and easily reproducible approach for estimating alkalinity contribution for GPP over a full year. Because the relationship between CO 2 and O 2 departures (α slope) in alkaline and hardwater lakes such Lake Geneva is nonlinear (Fig. S5c), the daily Alk-O 2 analyze (β slope) is essential to assess the dominant DIC source for daily GPP. Our method, based on stoichiometric slopes, yet provides semi-quantitative estimates. First, the GPP's substrate can shift from CO 2 to HCO 3 À within the same day (Fig. S7,   S9), which limits the accuracy of our estimates. Second, the two mechanisms by which GPP can fix alkalinity differ in their stoichiometric ratios (1 : 2 for CP and 1 : 1 for CCM), affecting the expected values for the β slope. Future studied should focus on the intraday dynamics to improve the analysis of precise CO 2 -HCO 3 À cofixation. Besides, microbiology and C isotopic analysis could also help disentangle CCM from CP. Beyond their stochiometric differences, CCM, which is an active mechanism, and the supposed passive CP should differ in the induced energetic costs for primary producers (e.g., Maberly and Gontero 2017;Li et al. 2018). Whether alkalinity fixation occurred from CP or CCM might therefore have implications for GPP itself.
This study provides a semi-quantification of DIC pool contribution to GPP along an annual cycle in both the littoral and pelagic environments of a moderate alkaline and hardwater lake. The results show that GPP is not limited by carbon availability throughout the year, even during CO 2 depletion, as demonstrated in other freshwater systems (Maberly et al. 2015;Kragh and Sand-Jensen 2018;Li et al. 2018;Aho et al. 2021). To support the high rate of O 2 production, GPP relies on HCO 3 À withdrawal from the water to subsidize the missing CO 2 (Fig. S9), resulting in a depleted alkalinity pool (Fig. S6). Both lake environments are auspicious for CCM with specific conditions such as CO 2 depletion, high HCO 3 À availability and high levels of solar radiation (Maberly and Gontero 2017). Most of phytoplankton species are known to use CCM (e.g., Maberly and Gontero 2017;Mishra et al. 2018), among which picocyanobacterial that have been documented in relatively high abundances in Lake Geneva from spring to fall, when they can contribute up to 76% of the pelagic biomass of primary producers (Parvathi et al. 2014). In addition, authigenic CP, produced inorganically in the water column (Schrag et al. 2013) has previously been reported in the pelagic area Escoffier et al. 2023;Fig. S1g). CP is also directly observed on the leaves of macrophytes from the littoral site (Characea and Potamogeton perfoliatus; Fig. S1d-f).
Exploring the temporal and spatial variabilities also offers interesting insights into macro-and micropatterns at different resolutions. At the seasonal scale, an evident temporal Fig. 3. Panels (a, b) show the temporal evolution of estimated GPP levels (μmol O 2 L À1 d À1 ) along the year (left side) colored according to categorisations of the dominant daily DIC source: CO 2 uptake (red) and HCO 3 À use (green) and observed days (triangle) and reconstructed days (point). Circles show uncertain reconstructed days due to high wind speed > 5 m s À1 producing weak biological patterns. Panel (a) adds the temporal evolution of the CO 2 departure (μmol L À1 ) as the best predictor of the littoral environment as well as the atmospheric equilibrium (black line). Panel (b) adds the temporal evolution of the Schmidt stability (J m À2 ) as the best predictor of the pelagic environment. The distributions and the boxplots (violin plots) of GPP levels are shown on the right side of panels (a, b) for both DIC categories and the whole GPP levels before and after the reconstruction by the classification tree.
variability is observed between the cold (CO 2 uptake) and warm periods (HCO 3 À use), with heterogeneity in DIC sources during the shoulder periods (Figs. 1-3). At the annual scale, the proportion of total GPP produced under dominant HCO 3 À fixation is relatively similar in the two environments (i.e., 75% for the littoral environment and 82% for the pelagic environment). These results amount to a minimum conservative estimate of HCO 3 À used for GPP over the year of 37% and 41% close to the results given by Aho et al. (2021) in the Connecticut River ($ 30%). However, this dominant consumption of HCO 3 À in the littoral environment only occurred for 3-4 months (middle June to middle September) while in the pelagic environment it was spread over 8 months (March-October). This annual similarity comes from the fact that summer littoral GPP rates are almost twice as high as in the pelagic environment. The faster CO 2 depletion in the pelagic domain can be explained by the thermal stratification isolating the epilimnion from CO 2 fluxes coming from the hypolimnion and bottom sediments. In contrast, the shallower depth in the littoral area allows for greater proximity with sediment-derived CO 2 fluxes all year round and explains that CO 2 depletion appears later when GPP levels become higher. The daily observations support such dynamics in the littoral domain with changes in slopes between morning (lower) and afternoon (steeper), illustrating the cycling of different DIC sources. In contrast, the pelagic slopes stay linear and steeper all day (Figs. S7, S9). These daily patterns also highlight a greater dynamic from the littoral environment during the shoulder period with a constant return to early morning conditions (Fig. S7). In contrast, the pelagic environment has greater inertia, as observed in March, where the daily cycle of the littoral is the same as the monthly cycle in the pelagic (Fig. S8), linked to an increase in the Schmidt stability (Fig. 3).
To conclude, this study, as several recent studies (Maberly et al. 2015;Stets et al. 2017;Kragh and Sand-Jensen 2018;Khan et al. 2020;Aho et al. 2021), sheds light on the overlooked role of alkalinity in the freshwater carbon cycle and how it contributes to GPP. Half of the world's lakes are considered alkaline (> 1 meq L À1 ; Marcé et al. 2015), so we can expect alkalinity consumption by primary producers to be a widespread phenomenon. Moreover, alkalinity consumption by GPP might get more frequent with climate warming. Longer and stronger stratification and shallower mixing depths (Schwefel et al. 2016;Gaudard et al. 2017) would both fasten surface CO 2 depletion during stratification and limit winter replenishment of surface CO 2 . Therefore, less CO 2 at the surface could lead to a potential increase in HCO 3 À use and a shift in species communities capable of such an assimilation.