Evaluation of the methane paradox in four adjacent pre-alpine lakes across a trophic gradient

Abstract

Contrasting the paradigm that methane is only produced in anoxic conditions, recent discoveries show that oxic methane production (OMP, aka the methane paradox) occurs in oxygenated surface waters worldwide. OMP drivers and their contribution to global methane emissions, however, are not well constrained. In four adjacent pre-alpine lakes, we determine the net methane production rates in oxic surface waters using two mass balance approaches, accounting for methane sources and sinks. We find that OMP occurs in three out of four studied lakes, often as the dominant source of diffusive methane emissions. Correlations of net methane production versus chlorophyll-a, Secchi and surface mixed layer depths suggest a link with photosynthesis and provides an empirical upscaling approach. As OMP is a methane source in direct contact with the atmosphere, a better understanding of its extent and drivers is necessary to constrain the atmospheric methane contribution by inland waters.

Introduction

The widely reported methane (CH₄) oversaturation in surface oxic waters in oceans¹ and lakes (also referred to as the methane paradox; Tang et al.²) contrasts with the current understanding that biogenic CH₄ formation occurs exclusively under anoxic conditions³. Methane production in oxic conditions (also called oxic methane production or OMP) has been reported for an increasing number of lakes^2,4,5,6,7,8. While recent studies have shown that OMP may have contributed up to 80% of lake-diffusive CH₄ emissions^7,8, other researchers suggest that CH₄ produced in anoxic littoral sediments is enough to resolve the CH₄ paradox^9,10,11,12. Thus, the drivers and OMP contribution to global lake CH₄ emissions remain unclear.

Atmospheric CH₄ concentrations have more than doubled since the onset of the industrial era¹³. Although CH₄ is less abundant in the atmosphere than carbon dioxide (CO₂), the global warming potential (GWP) of CH₄ is ~80 times higher than CO₂ over a 20-year period¹⁴. Its GWP combined with its ~12-year lifetime means that reducing CH₄ emissions is a priority for mitigating climate change¹⁵. Lakes represent ~25% of natural CH₄ atmospheric sources, but large uncertainties remain about the contribution of internal sources and sinks^16,17,18. Methane in lakes can be emitted to the atmosphere through bubbles (ebullition) and diffusive fluxes at the air-water interface (AWI)¹⁷. Ebullition is driven by high CH₄ production rates in anoxic sediments¹⁹ and the diffusive fluxes at the AWI are driven by CH₄ concentrations and turbulence in surface waters²⁰. As OMP occurs in surface waters, the CH₄ can be quickly emitted to the atmosphere².

Several mechanisms have been proposed for OMP^{1,2,4,5,21,22,23}, however, recent studies have shown correlations between CH₄, oxygen, and phytoplankton concentrations^4,6, suggesting a direct role of phytoplankton in OMP^6,12,24,25. Although the mechanisms remain unclear, OMP has been shown to follow light-dark cycles in different phytoplankton cultures^24,25. It is likely that multiple pathways produce CH₄ in oxic lake environments, and that these may vary from lake-to-lake and seasonally based on trophic properties and light conditions.

OMP rates have been reported using different methodologies, such as laboratory and in-situ water incubations^4,24,25, in-lake mesocosms^5,8, a physical lateral transport model²⁶, and lake mass balances^7,8. OMP has also been reported from different freshwater environments, including both temperate²⁷ and polar regions²⁸, high altitude lakes (above 2500 m.a.s.l)²⁹, tropical latitude lakes¹², and across a range of trophic states^27,30. While these studies show the occurrence of OMP in lakes across geographic and trophic gradients, OMP has not been investigated in pre-alpine lakes.

Pre-alpine lakes (from 1300 to 2000 m.a.s.l) are atmospheric CH₄ sources³¹ and, with air temperature increasing two times faster in the European Alps than the global mean³², these lakes are disproportionately experiencing climate change^33,34. Such an increase in air temperature can induce limnological change in pre-alpine lakes with implications for aquatic CH₄ emissions^33,34,35 such as: (1) a longer ice-free season that allows CH₄ to be emitted for a longer period³⁶; (2) an increase in surface water temperature that enhances littoral production rates of CH₄³⁷; and (3) a longer stratified season that allows for more CH₄ accumulation in the hypolimnion³⁸. These impacts will differ across lakes depending on the light regime and trophic state³⁹; therefore, the precise impact of climate change on the CH₄ budget in pre-alpine lakes needs further investigation.

This study focuses on four adjacent Swiss pre-alpine lakes under identical climate forcing but with different trophic states. The net CH₄ production rate (P_net, Fig. 1) is defined as the balance between OMP (adds CH₄) and CH₄ oxidation (MOx, removes CH₄) in the surface mixed layer (SML)⁴⁰. P_net in the SML was estimated using two independent mass balance approaches: a 0-D full-scale mass balance following Donis et al.⁷ and a 1-D lateral transport model adapted from Peeters et al.⁹. In the latter, we included two additional terms—diffusive CH₄ flux across the thermocline and CH₄ bubble dissolution (Fig. 1). In both models, we included all CH₄ sources in the SML and the loss to the atmosphere to determine P_net (Fig. 1). Note that MOx rates are not necessary to estimate P_net (Methods), but would be required to calculate OMP. Here, we determine P_net (P_net = OMP − MOx) as this is the component that contributes to the diffusive emissions.

Fig. 1: Conceptual schematic of the CH₄ budget components in the surface mixed layer (SML) and methodological approaches.

CH₄ mass balance components: diffusive CH₄ emissions to the atmosphere (F_a), vertical transport (F_z), bubble dissolution (R_dis), littoral sediment flux (F_s). The net CH₄ production rate (P_net) in the SML is estimated using a 1-D lateral transport model and a 0-D full-scale mass balance in a and b, respectively. P_net is the balance between oxic CH₄ production (OMP, adds CH₄) and CH₄ oxidation (MOx, removes CH₄). The full-scale mass balance assumes the SML as a well-mixed reactor where each component is based on measured values. The lateral transport model also used in situ measurements but estimates the diffusive flux to the atmosphere using the mass transfer coefficient (k_CH4) and P_net rates are obtained by finding the simulated transect CH₄ concentrations (C(r)) that best-fit the measured CH₄ concentrations.

In previous studies, the two models have shown contradictory results mainly due to the use of literature parameterizations to estimate surface diffusive emissions^7,8,9,41,42. Instead, we used direct flux measurements from floating chambers and found the two models agree well with each other (R² = 0.97). The results indicate that P_net contributes between 30 and 90% to diffusive emissions during the stratified period of pre-alpine lakes with different trophic states. Moreover, we performed a sensitivity analysis using five diffusive flux literature parameterizations and surface flux measurements to analyze the impact that modeled versus measured atmospheric diffusive fluxes have on P_net estimation. Finally, we present a P_net upscaling approach based on chlorophyll-a concentrations (Chla), light penetration, and SML depth. Ultimately, our findings highlight the need for P_net to be included in CH₄ lake budgets and for more research to understand OMP(P_net) drivers and its response to climate change.

Results

Study sites

The four pre-alpine lakes studied - Lac de Bretaye (BRE), Lac Noir (NOI), Lac des Chavonnes (CHA), and Lac Lioson (LIO)—are located between 1650 to 1850 m.a.s.l in the Swiss Alps and are eutrophic, meso/eutrophic, mesotrophic and oligotrophic, respectively (Supplementary Table 1 and 2). NOI and BRE are small lakes with a maximum depth of ~9 m, while CHA and LIO have a maximum depth of ~28 m (Supplementary Fig. 1 and Table 1). Throughout the three sampling campaigns (June 2018, September 2018, and July 2019), the surface waters of all four lakes were oxic and oversaturated in CH₄ (Table 1 and Supplementary Fig. 2). Temperature and CH₄ concentration profiles at the deepest point of the lakes showed that all the lakes were stratified (SML thickness 1–6 m, Table 1 and Supplementary Fig. 2). Secchi depths (Z_s), nutrients and Chla concentrations reflect the trophic gradient of the study lakes (Table 1).

Table 1 General characteristics of surface waters across the studied lakes

Surface methane concentration and isotopic signature

Surface CH₄ concentrations and their stable isotopic signatures (${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$) were measured at the deepest point of each lake (Supplementary Fig. 2) and along a transect from shore to shore to resolve their spatial variability in the SML (Fig. 2 and Supplementary Fig. 3). All four lakes were oversaturated with CH₄, with near the shore values 33 ± 32% higher than in the center (all results are reported in mean ± 1 standard deviation, SD, unless otherwise indicated), although only 40% of the time this difference was significant (Table 1). The eutrophic lakes BRE and NOI, on average, had one order of magnitude higher surface concentrations (3.13 ± 2.09 mmol m⁻³) than the oligo/mesotrophic lakes LIO and CHA (0.15 ± 0.13 mmol m⁻³) (Table 1). During two transects surveys in NOI (July-19 and Sep-18), one in BRE (Jun-18) and one in CHA (Jul-19) we observed one concentration data point close to the shore that was between 36 and 160% higher than the overall average transect concentration. In NOI and BRE, the presence of macrophytes could have decreased the horizontal dispersion, produce CH₄⁴³ and/or decreased surface CH₄ emissions, resulting in near-shore CH₄ accumulation not accounted for in the lateral transport model. Since we measured low CH₄ concentrations in CHA, any disturbance in the lake sediment could have caused an increase of CH₄ near the shore.

Fig. 2: Surface CH₄ concentrations along the transects sampled in each lake.

a Lac de Bretaye, b Lac Noir, c Lac des Chavonnes, and d Lac Lioson. Lines represent the CH₄ concentration simulated using the lateral transport model and dots are the measured values. Since the lateral transport model assumes that the CH₄ concentrations in the SML are radially symmetric, the concentrations are shown from shore to center. The bathymetry profile along the transects is shown in Supplementary Fig. 4.

The spatially averaged ${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ signature ranged between −62 ± −38‰ (Table 1). Isotopically enriched CH₄ (${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}} \sim$−40‰) was observed at the end of summer in the SML of the eutrophic lakes, while in the oligotrophic lakes ${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ was relatively consistent between sampling dates (Supplementary Table 3). Rather constant ${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ values were observed along the transect for most of the lakes, except for CHA in June 2018 when lighter ${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ was observed at the shore (~−65‰) than in the center of the lake (~−60‰) (Supplementary Fig. 3).

Diffusive CH₄ emissions to the atmosphere

Diffusive CH₄ emissions (F_a) at the air-water interface (AWI) were measured in each lake using a floating chamber⁴⁴ at the deepest point of the lake and along the transects. Average surface fluxes measured in the eutrophic lakes (NOI and BRE, 3.24 ± 0.88 mmol m⁻² d⁻¹) were an order of magnitude higher than in the oligotrophic lakes (LIO and CHA, 0.29 ± 0.43 mmol m⁻² d⁻¹). Surface diffusive fluxes of CH₄ remained relatively similar between sampling dates in each lake (Table 2).

Table 2 Inputs for the lateral transport model and full-scale mass balance in the surface mixed layer (SML) (mean ± SD)

Several parameterizations have been proposed for the mass transfer coefficient (k₆₀₀) used along with CH₄ concentrations to estimate atmospheric diffusive emissions (Klaus & Vachon⁴⁵ and references therein). We compared CH₄ mass transfer coefficients based on our chamber flux data (${k}_{600}^{{{{{{{{\rm{cb}}}}}}}}}$) to five k₆₀₀ parameterizations: CC98 based on Cole & Caraco⁴⁶; MA10-NP (negative buoyancy), MA10-MB (mixed buoyancy), and MA10-PB (positive buoyancy) based on MacIntyre et al.²⁰; and VP13 based on Vachon & Prairie⁴⁷ (Supplementary Fig. 5). These parameterizations weakly correlated with ${k}_{600}^{{{{{{{{\rm{cb}}}}}}}}}$ (R² = [0.01–0.037]; Supplementary Fig. 6) and underestimated ${k}_{600}^{{{{{{{{\rm{cb}}}}}}}}}$ (Mean Normalized Bias (MNB) = [16–81%]) (Supplementary Fig. 6). The best agreement was found with MA10-NB which is based on convective mixing (R² = [0.01–0.37], RMSE = [0.63–4.65 m d⁻¹], MNB = [16–57%]; Supplementary Fig. 6).

Diffusive CH₄ fluxes from littoral sediments

Diffusive CH₄ fluxes at the sediment-water interface (SWI) in the littoral zone (F_s) were estimated using benthic chambers and porewater measurements of dissolved CH₄ (Supplementary Fig. 7 and Supplementary Table 4). The highest average littoral sediment flux was found in eutrophic BRE (8.3 ± 6.7 mmol m⁻² d⁻¹), followed by NOI (eutrophic), CHA (mesotrophic) and LIO (oligotrophic) with the lowest value (0.3 ± 0.1 mmol m⁻² d⁻¹) (Table 2). ${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ in the upper part of the sediments ranged between −66 and −48‰ (Supplementary Table 3). Littoral sediment was ~20% isotopically less enriched than the surface waters of NOI and BRE but similar for CHA (−60‰, Supplementary Table 3 and Fig. 7). No porewater measurements were performed in LIO due to the rocky nature of the littoral sediments (Methods).

CH₄ ebullition rates and bubble dissolution

CH₄ ebullition rates at the SWI were estimated using the gas composition of bubbles collected during each sampling campaign, the CH₄ fluxes measured at the SWI (Supplementary Table 4), and modeling the dissolved porewater gas concentration in the sediments following Langenegger et al.¹⁹. Bubble dissolution rates in the SML (R_dis) were obtained using a discrete bubble model⁴⁸ (Methods). The spatially averaged ebullitive fluxes (F_eb) for BRE and NOI (1.14 and 0.43 mmol m⁻² d⁻¹, respectively), resulted in bubble dissolution rates between 17 and 51 μmol m⁻³ d⁻¹ (Table 2). Ebullition was not detected in CHA and LIO.

Vertical diffusive fluxes from/to the epilimnion

The vertical transport from/to the epiliminion (F_z) is determined with Fick’s 1st Law using the turbulent vertical diffusivity (K_z) and concentration gradients at the base of the epilimnion. K_z values at the top of the thermocline ranged between 0.03 and 14.4 × 10⁻⁶ m² s⁻¹ (Table 2). In all lakes, F_z was typically low (−0.1–0.5 mmol m⁻² d⁻¹), except in BRE and NOI at the end of the summer when fluxes were 13.3 and 3.1 mmol m⁻² d⁻¹, respectively.

Horizontal dispersion

In the lateral transport model, we estimated the horizontal dispersion coefficient (K_H) for each lake using Peeters & Hofmann⁴⁹ parametrization (Methods). Water level fluctuations were minimal in BRE, NOI, and LOI (± 1 m). In CHA, the highest water level was observed at the beginning of summer after ice-off and slowly decreased during the summer by about 4 m (Supplementary Fig. 8), which changed the length scale (L) and thus K_H (Eq. (4)). The calculated K_H values were 2034, 903, and 2564 m² d⁻¹ for BRE, NOI, and LIO, respectively, and ranged between 2004–2366 m² d⁻¹ for CHA (Table 2).

Surface mass balances

The full-scale mass balance (0-D) proposed by Donis et al.⁷ (Eq. (1)) and a modified version of the lateral transport model (1-D) proposed by Peeters et al.⁹ (Eq. (2)) were used to determine P_net in the SML of each lake and campaign based on the input values listed in Table 2. P_net is the net result of OMP and MOx (i.e., P_net = OMP − MOx), which adds and removes CH₄ to the SML, respectively. Thus, when P_net is positive the true OMP rate is actually higher than P_net.

Despite the different modeling approaches and underlying assumptions, the P_net rates calculated with both models under steady-state conditions correlated well with each other (Supplementary Fig. 9, R² = 0.97). Monte Carlo simulations were applied to assess uncertainties using all sources and sinks in both models during the stratified period (Methods). The average P_net rates for the three sampling dates were 305, 1504, 22, and 246 μmol m⁻³ d⁻¹ for BRE, NOI, CHA, and LIO, respectively (Fig. 3). On average, P_net rates in eutrophic lakes (BRE and NOI) were about seven times higher than in the oligotrophic lakes (CHA and LIO). A decrease of P_net rates from the beginning to the end of the summer was observed in NOI and BRE, whereas in CHA and LIO P_net remained relatively consistent across campaigns.

Fig. 3: P_net rates estimations in the surface mixed layer of each lake using two approaches.

The full-scale mass balance (P_net,fs; filled boxes) and lateral transport model (P_net,lt; open boxes). The lakes were divided as a eutrophic and b oligotrophic lakes. Boxes show the first and third quartiles with the median (line), whiskers extend to most extreme data point within 1.5 times the interquartile range from the box. The white dot represents the average of the P_net distribution. Note different scales on y-axes of the two panels.

Sensitivity analysis of surface diffusive emission to the atmosphere

Several studies have used k₆₀₀ literature parameterizations to estimate F_a (Tan et al.⁵⁰ and references therein), although other studies have shown that these estimates often do not correspond with field measurements (Klaus & Vachon⁴⁵ and Supplementary Fig. 5). Therefore, we analyzed the impact of k₆₀₀ parameterizations on P_net as it is one of the main parameters affecting the mass balance in the epilimnion.

Since the P_net results from both models were similar, we used P_net from the full-scale mass balance in the following sensitivity analysis. In the lateral transport model (Eq. (2)), we simulated surface CH₄ concentrations either with the addition of P_net as obtained from the full-scale mass balance approach (P_net = P_net,fs), or without any addition from P_net (i.e., P_net = 0). We also used five different mass transfer coefficient parameterizations (k₆₀₀) to model diffusive CH₄ emissions to the atmosphere in the lateral transport model (Table 3). Thus, the resulting surface CH₄ concentrations were obtained from the combinations of P_net and k₆₀₀, as they determined different boundary conditions of the mass balance in the SML. The analysis is focused on the best and worst fits of the mass transfer coefficient parameterizations (MA10-NB and CC98, respectively) when compared with chamber-based estimations for CH₄ (${k}^{{{\rm{cb}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$) (Supplementary Figs. 5 and 6). The results of the three remaining parameterization comparisons are available in Table 3 and Supplementary Fig. 10.

Table 3 Results of the sensitivity analysis of the use of five literature mass transfer coefficients (${k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$), with and without net CH₄ production (P_net), to simulate the CH₄ concentrations using the lateral transport model

The best agreement between measured and simulated CH₄ concentrations was found using P_net from the full-scale mass balance (P_net,fs) and ${\overline{k}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ (P_net-${\overline{k}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$, Table 3, Supplementary Fig. 11b). When using ${\overline{k}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ with P_net set to zero (P_net0-${\overline{k}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$), average CH₄ concentrations along the transect were underestimated relative to the measured values (MNB = −1.83, Table 3, Supplementary Fig. 11a). Using P_net,fs with the MA10-NB or CC98 parameterizations (P_net-MA10-NB and P_net-CC98) resulted in an overestimation of CH₄ concentrations (Table 3, Supplementary Figs. 11d, f), whereas when P_net was set to zero (P_net0-MA10-NB and P_net0-CC98) with those k₆₀₀ parameterizations, the average CH₄ concentrations along the transect were underestimated (Table 3, Supplementary Figs. 11c, e).

Contribution of methane sources to atmospheric diffusive emissions

The sediment flux (F_s) and P_net were the two major sources of CH₄ in the SML. Using the results obtained from the full-scale mass balance we found that P_net contributed ~30% of the CH₄ emissions in BRE and CHA, while it reached up to 60% and 90% for NOI and LIO, respectively (Fig. 4). P_net was a dominant source in all lakes in June and July except for CHA in July. Negligible P_net contributions (<8%) were found in all lakes in September 2019, except for LIO (91%). On average, F_s contributed about 10, 30, 50, and 65% to the CH₄ emissions in LIO, NOI, BRE, and CHA, respectively. For CHA and NOI, the F_s contribution increased at the end of the summer and reached up to 90% for CHA in September. For BRE and LIO, the F_s contribution remains relatively constant during the different months. On average, F_s contributed about the same in the oligotrophic and eutrophic lakes. The vertical turbulent flux (F_z) contributed about 50% of the atmospheric CH₄ emission from BRE and NOI in September and about 30% from CHA in July, but was negligible (<9%) for the other campaigns. The contribution from bubble dissolution (R_dis) was negligible (<4%) in BRE and NOI and absent in CHA and LIO.

Fig. 4: Contribution to diffusive atmospheric CH₄ emissions from each component of the CH₄ budget.

The sediment flux (F_s), diffusive flux from hypolimnion (F_z), bubble dissolution (R_dis), and net production rates (P_net) in the SML of Lac de Bretaye (BRE), Lac Noir (NOI), Lac des Chavonnes (CHA) and Lac Lioson (LIO). The lakes were divided as a eutrophic and b oligotrophic lakes. The results from the full-scale mass balance were used as representative P_net rates of the studied lakes.

Discussion

In most of our study lakes, the P_net values were positive, indicating that OMP was greater than MOx, and that P_net thus acted as a CH₄ source during daytime conditions over the stratified season (Fig. 3). P_net was near zero in CHA, which is the meso-oligotrophic lake with the largest water level changes throughout the summer, in contrast to the other pre-alpine lakes in our study that maintained relatively consistent water levels. The observed average P_net rates were within the range of values previously reported⁴², except for NOI with the highest P_net rate reported to date (2308 ± 2024 μmol m⁻³ d⁻¹).

P_net rates were temporally variable in each lake and varied between study sites. While P_net and ${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ were relatively constant during the stratified season in the oligotrophic lakes, highly positive P_net rates at the beginning of the summer indicated that OMP was an active source of CH₄ to the atmosphere in the eutrophic lakes. By the end of the stratified season, P_net became negative indicating that MOx was dominating, which was corroborated by isotopically enriched CH₄ (Table 1). This seasonal trend in P_net was also observed by Günthel et al.⁸ and may be related to the CH₄ production rates of different algal species²⁵ and their concentration during the stratified season. In addition, the eutrophic lakes BRE and NOI had P_net rates one order magnitude higher than the more oligotrophic lakes (CHA, LIO), suggesting that P_net may also be related to trophic state. From this perspective, productive lakes in general may experience higher P_net rates than less productive ones.

The dominant sources of CH₄ to the surface waters of our lakes were P_net and F_s, although individual rates of these sources varied across campaigns. Despite eutrophic lakes have generally higher P_net rates compared to more oligotrophic ones, the P_net contribution fraction to surface diffusive CH₄ emissions were independent of the trophic status of the lake. For example, the fraction of P_net contribution to emissions was similar and even higher in oligotrophic LIO than that in eutrophic NOI. This was mainly due to the substantial contribution of CH₄ from the littoral sediments to the SML in the eutrophic lakes. Therefore, our results suggest that there is no relationship between the contribution of the two dominant CH₄ sources (P_net and F_s) and trophic state, even though each of these sources are higher in more productive systems.

The methodologies for determining P_net are limited by the accuracy of the boundary conditions of the mass balance (i.e., diffusive CH₄ emissions at the AWI, CH₄ flux from littoral sediment, ebullition, etc.). These boundary conditions are often based on a few measurement locations and are naturally variable. The variability and uncertainty of such estimations led to the observed range of P_net in mass balance approaches obtained with the Monte Carlo simulations (Fig. 3). Therefore, to assess the robustness and the validity of the models used, we compared the boundary condition components (F_a, F_s, and R_dis) with literature values and examined how their variability may alter the outcome of the two mass balance models.

Diffusive CH₄ emissions to the atmosphere are temporally and spatially variable. We accounted for the spatial variability by using the average of ten surface flux measurements along a lake-wide transect for each P_net calculation. In addition, the average diffusive CH₄ emissions estimated for NOI, CHA, and BRE are well within the range reported for the stratified season of these lakes in previous studies (0.06–4.38 mmol m⁻² d⁻¹; Rinta et al.³¹). There are no previous data for LIO.

A large uncertainty in the estimation of surface diffusive CH₄ emissions is due to the parameterization of mass transfer coefficient (k₆₀₀). Therefore, we applied five alternative k₆₀₀ parameterizations to estimate CH₄ diffusion at the AWI in the four pre-alpine lakes and compared these fluxes with direct measurements using floating chambers. The comparison of the chamber-based mass transfer coefficient (${k}_{600}^{{{{{{{{\rm{cb}}}}}}}}}$) with all the tested parameterizations resulted in a low correlation (R² < 0.38) and clear underestimation of the measured k₆₀₀ values (Supplementary Fig. 5), reflecting the limitations of the k₆₀₀ models across different lakes⁴⁵. The underestimation by k₆₀₀ parameterizations has also been reported in previous studies (Tan et al.⁵⁰ and references therein). We hypothesize that the presence of oxygen microbubbles produced by photosynthesis in the water column⁵¹ might enhance the mass transfer coefficient⁴⁴. This phenomenon would be more relevant in high altitudes lakes, such as our study lakes, due to the lower air pressure and oxygen saturation concentration.

In our analysis of the k₆₀₀ parameterizations for the lateral transport model, we observed that when using the literature parameterizations for surface CH₄ fluxes, the simulated surface CH₄ concentrations were underestimated when P_net was not included in the simulations (i.e., P_net = 0). This is explained by the fact that these parameterizations underestimate ${k}_{600}^{{{{{{{{\rm{cb}}}}}}}}}$ for all lakes and they do not correlate well with ${k}_{600}^{{{{{{{{\rm{cb}}}}}}}}}$ (Supplementary Fig. 6). In our case, lake-specific (i.e., chamber-based) k₆₀₀ values provided the best results. To further corroborate this finding, we calculated the P_net error due to an over- or underestimation of k_CH4 caused by using k₆₀₀ parameterizations instead of ${k}_{600}^{{{{{{{{\rm{cb}}}}}}}}}$. Our analysis showed a linear relationship between the P_net error and the ${k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ error, where the slope is defined by the ratio between the F_a and the P_net rates estimated using the measured values (Methods, Supplementary Fig. 12). Excluding the cases when P_net was negligible (BRE: Jul-19, CHA: Sept-18 and Jul-19 and NOI: Sept-18), the slope varied between 0.5 to 2.9 with an average value of 1.3, meaning that the P_net error is on average 30% higher than the ${k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ error. This result highlights the need to use lake-specific in-situ measured fluxes to compute k₆₀₀ in a mass balance as suggested by various researchers (e.g., Klaus & Vachon⁴⁵ and Cole et al.⁵²).

The littoral diffusive sediment fluxes were within the range of values reported in the literature (0.001–8.8 mmol m⁻² d^{−1 9,37,53}). In the full-scale mass balance, we assumed that the initial lateral flux towards the center of the lakes was equal to the diffusive CH₄ flux coming from the littoral sediment (i.e., SML exposed). As the CH₄ production rates in sediments increase with increasing temperature³⁷, it has been hypothesized that sediment CH₄ diffusion will also follow this relationship⁹. As most of our sediment flux measurements in the littoral zone were performed in July when the temperatures were highest in all lakes (Supplementary Table 4), we assume that those observed sediment fluxes were on the higher end of possible values. Therefore, using a presumably high sediment flux from July for the mass balance of other months would result in a conservative P_net estimate.

Assuming that OMP does not occur (i.e., P_net = 0) in the full-scale mass balance, the littoral sediment fluxes would have to be two to three times higher than our measured fluxes to compensate for the diffusive CH₄ emissions measured at the AWI (Supplementary Fig. 13). In oligotrophic LIO, a littoral sediment flux of about 2.23 ± 1.12 mmol m⁻² d⁻¹ is needed, which is unlikely given that that flux is an order of magnitude higher than what we measured (0.3 ± 0.1 mmol m⁻² d⁻¹). In fact, in BRE we measured one of the highest littoral sediment fluxes yet reported (8.3 ± 6.7 mmol m⁻² d⁻¹)^9,37,53,54, and we still required one of the highest P_net rates ever reported in the literature (June 2018: 2314 ± 2046 μmol m⁻³ d⁻¹) to close the CH₄ budget. Therefore, littoral sediment CH₄ flux alone cannot account for diffusive CH₄ emissions in our lakes and OMP needs to be included to close their CH₄ budget.

We also conducted a sensitivity analysis on the ebullitive CH₄ fluxes (F_eb, Methods). Assuming that OMP does not occur in the SML, the measured ebullitive fluxes would have to be 42 and 770 times higher for BRE and NOI in June 2018, respectively, to close the mass balance (Supplementary Table 5). These high estimates are due to the low contribution of bubble dissolution given the short contact time between the bubble and the water in the SML, especially within a very shallow SML depth at the beginning of the summer. Hence, even considering F_eb two or three times higher than what we estimated, positive P_net rates are required to close the SML CH₄ mass balance. Moreover, our ebullitive rates are in the same order of magnitude of what has been reported for similar lakes^31,55. Ultimately, the sensitivity analyses conducted on ebullitive, littoral sediment, and AWI diffusive fluxes suggest that our P_net rates are robust, and that OMP is likely a dominant source of atmospheric CH₄ from these lakes.

We conducted a first analysis of potential mechanisms behind OMP based on data we collected. Some studies have suggested that Methylphosphonate (MPn) biodegradation could lead to CH₄ production in oxic waters of the ocean¹ and lakes²², specifically in phosphorus-limited environments. In our pre-alpine lakes, however, we did not observe any correlation between P_net and phosphorus in the SML (Supplementary Fig. 14a). Another study suggested OMP mechanism is the production of CH₄ in nitrogen-limited environments via the transformation of CO₂, nitrogen gas, and hydrogen by the nitrogenase enzyme²³ that is commonly present in cyanobacteria. We observed a weak negative correlation between P_net and dissolved inorganic nitrogen (DIN) (R² = 0.37, Supplementary Fig. 14b), which could indicate the use of nitrogen for OMP. However, to our knowledge CH₄ production due to nitrogenase activity in cyanobacteria has not yet been observed. Our data do, however, suggest links between OMP and trophic parameters, similar to relationships found in Bogard et al.⁵ and Günthel et al.²⁵.

Considering the importance of the P_net contribution to atmospheric CH₄ emissions, it is necessary to derive approaches to estimate and upscale P_net. Günthel et al.⁸ proposed that the OMP contribution to diffusive CH₄ emissions from lakes can be estimated as a function of littoral sediment area and SML volume. In our study, the P_net contribution to diffusive CH₄ flux to the atmosphere was highly variable and disagreed with this simple upscaling approach (Supplementary Fig. 15). While it is plausible that the OMP proportion to diffusive emissions may partially depend on lake bathymetry (i.e., the fraction between the sediment area and the SML volume), our results indicate that OMP is a complex phenomenon that is also related to lake trophic properties (e.g., productivity).

We observed that for an individual lake P_net can be explained mostly by changes in light climate (LC) (Fig. 5a). LC defines the average light intensity that phytoplankton can be exposed to in the SML during the day⁵⁶. A lower LC means that surface waters are turbid or the lake experiences a deep SML decreasing the average light intensity. In contrast, higher LC implies clearer waters or smaller SML depth, increasing the average light intensities in the SML. We noticed that increases in LC strongly increase P_net rates in eutrophic lakes whereas in oligotrophic lakes P_net is nearly independent of LC (Fig. 5a). Recent evidence indicates that OMP could be a photosynthesis-derived process^6,24,25. Therefore, we hypothesize that the P_net-LC relationship could also indicate the inhibition of MOx at high-light intensities^12,40 and/or enhanced CH₄ production due to production of reactive oxygen species by photoautotrophs at high-light intensities⁵⁷.

Fig. 5: Linking net CH₄ production (P_net) in the surface mixed layer (SML) with trophic variables.

a Relationship between P_net and light climate (LC, m m⁻¹) and trophic state. Per lake, the minimum P_net rate (${P}_{{{{{{{{\rm{net}}}}}}}},\min }$) and the minimum LC (LC_min) were subtracted to be able to compare the slope of each curve. P_net becomes more independent of LC in more oligotrophic lakes. b Interaction between P_net (mmol m⁻³ d⁻¹) and the average surface concentration of chlorophyll-a (Chla, mg m⁻³), LC (m m⁻¹) and Secchi depth (Z_s, m) suggest a direct role of photosynthesis on OMP. Specific production/oxidation rate calculated as P_net normalized by the average surface concentration of CH₄ (${C}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ mmol m⁻³) versus Chla × light climate ($LC=2.5\frac{{Z}_{{{{{{{{\rm{s}}}}}}}}}}{{H}_{{{{{{{{\rm{SML}}}}}}}}}}$) × Z_s; where H_SML is the surface mixed layer depth. Chla was obtained from fluoroprobe profiles measured at the center of the lake. All the parameters were calculated at each sampling campaign. The results from the full-scale mass balance were used as representative P_net rates of the studied lakes.

The P_net versus LC relationship strongly depends on the trophic state of each lake and thus cannot alone be used to upscale P_net in different lake ecosystems. We suggest an empirical approach using additional trophic state parameters (Fig. 5b). CH₄ concentrations (and often CH₄ emissions) are dependent on trophic state, as indicated by higher CH₄ concentrations typically observed in eutrophic lakes relative to oligotrophic lakes²⁷. Therefore CH₄ concentration in the SML can be used as a proxy to reflect the trophic state of each lake and to normalize P_net rates found in the eutrophic and oligotrophic lakes (Fig. 3). This interaction between P_net normalized by the SML CH₄ concentration versus Chla × LC × Secchi depth indicates the direct role of phytoplankton and light availability in OMP^6,24,25. Including the data from Donis et al.⁷, Günthel et al.⁸, and Thottathil et al.⁵⁸, this parameterization explains around 80% of the dataset (R² = 0.79, Fig. 5b). While more data are needed, this provides an important step towards estimating P_net in the SML that helps to define OMP dynamics across systems, identify lakes with potentially high OMP rates, and work towards a global upscaling of OMP (or P_net).

In this study, we quantified the P_net rates of CH₄ (i.e., net balance between OMP and MOx) in the oxic SML of four pre-alpine lakes using two models that have previously produced contradictory results when resolving OMP in lowland lakes^7,8,9,41,42. The good agreement between the adaptation of these approaches used in our study shows that there are no methodological issues with the models themselves when the appropriate boundary conditions are used to estimate OMP (or P_net, in our case). We also conducted a thorough sensitivity analysis on the three main parameters that lead to the highest uncertainties. This analysis shows that measured surface fluxes must be used instead of literature k₆₀₀ parameterizations to estimate the diffusive CH₄ flux to the atmosphere. Our results indicate that in three out of four lakes a positive P_net (i.e., a net input of CH₄ from OMP) needs to be included in the SML CH₄ budget. In fact, up to 85% of atmospheric CH₄ emissions that occurred at the beginning of summer resulted from P_net, and even in systems with some of the highest recorded littoral sediment fluxes, we still obtained some of the highest reported P_net (or OMP) rates.

Finally, while the mechanisms behind OMP need further investigation, this study (in agreement with previous ones^6,12,24,25) show that light and photoautotrophs may play a significant role in OMP. Consequently, future changes in light availability and temperature may induce positive feedbacks by promoting algal species capable of producing CH₄. Although the contribution of OMP to total diffusive emissions from inland waters is still not well constrained, we have shown that it can be a dominant source from lakes in the pre-alpine region where climatic changes occur at higher rates than the global average^33,34. It is thus crucial to continue quantifying the contribution of P_net from various aquatic systems and identifying the main drivers of OMP that will help to better understand the impact of OMP on the global CH₄ cycle and how to predict or possibly mitigate its impact in a changing climate.

Methods

Study sites

Lac de Bretaye (BRE), Lac Noir (NOI), Lac des Chavonnes (CHA), and Lac Lioson (LIO) are pre-alpine lakes (above 1600 m.a.s.l) located in Canton Vaud, Switzerland (Supplementary Table 1). All lakes are of glacial origin and have a wide-range of trophic states (oligotrophic-eutrophic). BRE, NOI, and CHA are ~500 m away from each other, while LIO is located ~7 km away from the others. BRE and NOI are small and shallow lakes without inflow or outflow streams located in alpine meadows used for animal grazing. CHA has a small inflow stream while LIO has a small creek outflow that is the origin of the Hongrin River.

Limnological measurements

During each campaign, water column profiles were measured at the deepest point of each lake (M1, Supplementary Fig. 1) with a CTD profiler (Conductivity-Temperature-Depth, Seabird SBE19plus) equipped with temperature, conductivity, oxygen, PAR, turbidity, Chla, and pH sensors, and a spectrofluorometer (bbe Moldaenke GmbH, Schwentinental, Germany) to measure total Chla concentrations.

Total (TP) and dissolved phosphorus (DP), dissolved inorganic nitrogen as nitrate plus nitrite (DIN), dissolved silica (DSIL), and total carbon concentration (TC) were measured at each campaign in the upper mixed layer (from the surface to the bottom of the thermocline) and in the hypolimnion (Supplementary Table 6). Water samples were collected with a Niskin sampler and equal amounts of water from several depths were transferred into two 1 L glass bottle (Duran, GmbH, Mainz, Germany). 50 mL of water was filtered through 0.45 μm (PES) syringe filters to measure dissolved nutrient fractions. An AQ2 Discrete Analyzer (SEAL Analytical) based on spectophotometric methods was used to measure TP and DP by Acidic molybdate/antimony with ascorbic acid reduction⁵⁹, Nitrate-N plus Nitrite-N by Cadmium coil reduction followed by sulfanilamide reaction in the presence of N-(1-naphthylethylenediamine)⁵⁹ and DSIL by Acidic molybdate with ANSA reduction⁶⁰. A Shimadzu carbon analyzer (TOC-L_CPH/CPN) measured TC.

Mass balance

P_net in the SML was estimated using two independent mass balance approaches: a 0-D full-scale mass balance following Donis et al.⁷ and a 1-D lateral transport model adapted from Peeters et al.⁹.

Full-scale mass balance

The full-scale mass balance approach assumes that at each sampling date the surface layer can be modeled as a well-mixed reactor and P_net,fs can be estimated as follows:

$$\frac{\partial C}{\partial t}{\forall }_{{{{{{{{\rm{SML}}}}}}}}}={A}_{{{{{{{{\rm{s}}}}}}}}}{F}_{{{{{{{{\rm{s}}}}}}}}}-{A}_{{{{{{{{\rm{a}}}}}}}}}{F}_{{{{{{{{\rm{a}}}}}}}}}+{A}_{{{{{{{{\rm{z}}}}}}}}}{F}_{{{{{{{{\rm{z}}}}}}}}}+{R}_{{{{{{{{\rm{dis}}}}}}}}}{\forall }_{{{{{{{{\rm{SML}}}}}}}}}+{P}_{{{{{{{{\rm{net}}}}}}}},{{{{{{{\rm{fs}}}}}}}}}{\forall }_{{{{{{{{\rm{SML}}}}}}}}};\quad [{{{{{{{\rm{mol}}}}}}}}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]$$

(1)

where C is surface CH₄ concentration, ∀_SML is SML volume, and A_s, A_a, and A_z are sediment area, lake surface area, and planar area at the bottom of the SML (Supplementary Table 7), respectively. The spatial average values for the surface fluxes (F_a), bubble dissolution rates (R_dis) in the SML, and hypolimnetic fluxes (F_z) were used as boundaries conditions (Table 2). A sonar survey was performed to obtain the bathymetry of each lake (Supplementary Fig. 1) and A_a, A_s, and A_z were determined using the software Surfer® (Golden Software, LCC) (Supplementary Table 7). The bottom of the SML (H_SML) was defined when ∂T/∂z becomes smaller than −1 °C m^−1 61 (Table 1). The net CH₄ production (P_net) in the SML was estimated using Eq. (1) assuming steady-state conditions $\left(\frac{\partial C}{\partial t}{\forall }_{{{{{{{{\rm{SML}}}}}}}}}=0\right)$ and that the lateral contribution to the mass balance is equal to the littoral sediment flux times the area of the sediment.

Lateral transport model

Using a modified version of the lateral transport model presented by Peeters et al.⁹, P_net,lt rates for each lake were obtained by finding the simulated transect CH₄ concentrations that best-fit to the measured CH₄ concentrations. In this study, the lateral transport model includes vertical diffusive CH₄ flux through the bottom of the SML and bubble dissolution:

$$\frac{\partial C(r)}{\partial t}={K}_{{{{{{{{\rm{H}}}}}}}}}\frac{1}{H(r)r}\frac{\partial }{\partial r}\left(H(r)r\frac{\partial C(r)}{\partial r}\right)+\frac{1}{H(r)}{K}_{{{{{{{{\rm{z}}}}}}}}}\frac{{C}_{{{{{{{{\rm{hyp}}}}}}}}}-C(r)}{\Delta z}-\frac{{\overline{k}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}}{H(r)}\\ \left(C(r)-{H}_{{{{{{{{\rm{cp}}}}}}}}}p{{{\mbox{CH}}}}_{4,{{{{{{{\rm{atm}}}}}}}}}\right)+\frac{{F}_{{{{{{{{\rm{s}}}}}}}}}(r)}{H(r)}+{R}_{{{{{{{{\rm{dis}}}}}}}}}(r)+{P}_{{{{{{{{\rm{net}}}}}}}},{{{{{{{\rm{lt}}}}}}}}};\quad [{{{{{{{\rm{mol}}}}}}}}\,{{{{{{{{\rm{m}}}}}}}}}^{-3}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]$$

(2)

where H(r) is the spatially varying thickness of the SML. The mass transfer coefficient for CH₄ was calculated based on the average gas transfer coefficient obtained from the flux chambers (${\overline{k}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$), C_hyp is the CH₄ concentration 1 m below the bottom of the SML, Δz = 1 m, pCH_4,atm is the partial pressure of atmospheric CH₄ and H_cp is the Henry constant of CH₄ dissolution at in-situ temperature. This model considers that the surface layer is fully mixed in the vertical and, therefore, the vertical CH₄ concentrations are homogeneous within the SML.

In the simulations of each lake, we assumed that the SML, sources, and sinks are radially symmetric in the horizontal plane. Therefore, the development of CH₄ concentration can be described based on the radial distance r from the shore to the center of the lake (${r}_{\max }=\scriptstyle\sqrt{{A}_{a}/\pi }$).

Two regions were defined in the model, the littoral zone ($r\le {r}_{{{{{{{{\rm{s}}}}}}}}}=\scriptstyle\sqrt{\left({A}_{{{{{{{{\rm{a}}}}}}}}}-{A}_{{{{{{{{\rm{s}}}}}}}}}\right)/\pi }$) and the pelagic waters (r > r_s). The SML thickness (H(r)) is equal to the mixed layer depth in the pelagic region and, within the littoral zone, H(r) decreases linearly with r from the mixed layer depth to zero at the shore. The littoral sediment flux is zero in the pelagic zone (r < r_s) and equal to the measured average littoral sediment flux ($\overline{{F}_{{{{{{{{\rm{s}}}}}}}}}}$) in the shallow region (r≥r_s) as:

$${F}_{s}(r)=\left\{\begin{array}{ll}\overline{{F}_{{{{{{{{\rm{s}}}}}}}}}}\quad &\,{{\mbox{for}}}\,\,r\ge {r}_{{{{{{{{\rm{s}}}}}}}}}\\ 0\quad &\,{{\mbox{for}}}\,\,r \, < \, {r}_{{{{{{{{\rm{s}}}}}}}}}\end{array}\right.\quad [{{{{{{{\rm{mmol}}}}}}}}\,{{{{{{{{\rm{m}}}}}}}}}^{-2}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]$$

(3)

Average bubble dissolution rates (R_dis(h(r))) as a function of lake depth (h) were included in the SML. At the boundaries, horizontal fluxes were assumed as zero. To estimate the horizontal dispersion coefficient (K_H) we used Peeters & Hofmann⁴⁹ parameterization:

$${K}_{{{{{{{{\rm{H}}}}}}}}}=1.4\times 1{0}^{-4}{L}^{1.07}\quad [{{{{{{{{\rm{m}}}}}}}}}^{2}{{{{{{{{\rm{s}}}}}}}}}^{-1}]$$

(4)

where the length scale L [m] was calculated as L = r_s (Supplementary Table 7). Eq. (4) is the average of the results 1, 3, and 4 found in Table 2 of Peeters & Hofmann⁴⁹.

P_net rates were obtained using least square method optimization solver implemented with the curve fit function from Scipy⁶² in Python.

Monte Carlo simulation

To assess uncertainties, Monte Carlo simulations were performed (10,000 iterations) when solving the full-scale mass balance and the lateral transport models. P_net, R_dis, and F_z were selected within a normal distribution resulting from the mean (μ) and their standard deviation (SD) retrieved from the field measurements. Given the small contribution of R_dis to the CH₄ in the SML, its variability was not included in the Monte Carlo simulations of the lateral transport model. To prevent negative values, F_a and F_s were chosen from a gamma distribution defined by shape (κ = μ²/SD²) and the scale (θ² = SD²/μ). Here the gamma distribution has the density $f(x)=({x}^{\kappa -1}\frac{{e}^{-x/\theta }}{{\theta }^{\kappa }\Gamma })$ where Γ is the gamma function. Random.normal and random.gamma functions from the Numpy package⁶³ in Python were used for each normal and gamma distributions, respectively.

Water column CH₄ and ${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ signature

At each sampling campaign CH₄ and ${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ concentration profiles were taken at the deepest location of each lake (M1, Supplementary Fig. 1) and along a transect composed of 10–11 stations across the lake (shore to shore, T1–T11, Supplementary Fig. 1).

Dissolved CH₄ concentration profiles were performed at a maximum depth resolution of 0.5 m where the metalimnetic CH₄ gradient was expected. For the profile, the water samples were obtained with a 5-L Niskin bottle and then gently transferred into a 1-L glass bottle (Duran GmbH, Mainz, Germany) while for the transect the samples were obtained directly with a 1-L glass bottle (Duran GmbH, Mainz, Germany). For both methodologies, the water was overflowing to replace the volume three times. CH₄ concentrations and ${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ were measured using the headspace method⁷. The samples were measured on a Cavity Ring-Down Spectrometer analyzer (Picarro G2201-i, Santa Clara, CA, USA) for CH₄ concentrations in the gas phase (ppm) and stable isotope ratio (${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ in ‰). Water CH₄ concentrations were back-calculated according to Wiesenburg & Guinasso⁶⁴ accounting for water temperature, air concentration, and the headspace/water ratio (500 mL air/500 mL water) in the bottle.

CH₄ diffusive fluxes to the atmosphere

Diffusive CH₄ emissions to the atmosphere (F_a) were measured using a floating chamber attached to a portable GHG analyzer (UGGA; Los Gatos Research, Inc.). Instrument-specific precision at ambient concentrations (1 − σ of 100 s average) for [¹²CH₄] is 0.25 ppb. The floating chamber consists of an inverted plastic container with foam elements for floatation (as in McGinnis et al.⁴⁴). To minimize artificial turbulence effects, the buoyancy element was adjusted that only ~2 cm of the chamber penetrated below the water level. The chamber was painted white to minimize heating. Two gas ports (inflow and outflow) were installed at the top of the chamber via two 5 m gas-impermeable tubes (Tygon 2375) and connected to the GHG analyzer measuring the gaseous CH₄ concentrations in the chamber every 1 s. Transects were performed with the chamber deployed from a boat. The chamber was allowed to freely drift to minimize artificial disturbance. Fluxes were obtained by the slopes of the resolved CH₄ curves over the first ~5 min when the slopes were approximately linear (R² > 0.97).

To simulate the fluxes to the atmosphere in the lateral transport model, chamber-based mass transfer coefficient (${k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}^{{{{{{{{\rm{cb}}}}}}}}}$) was estimated using the chamber-based surface fluxes and Fick’s 1st Law⁴⁴ as:

$${F}_{a}={k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}\left({C}_{{{{{{{{\rm{w}}}}}}}}}-{H}_{{{{{{{{\rm{cp}}}}}}}}}p{{{\mbox{CH}}}}_{4,{{{{{{{\rm{atm}}}}}}}}}\right);\quad [{{{{{{{\rm{mmol}}}}}}}}\,{{{{{{{{\rm{m}}}}}}}}}^{-2}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]\\ {k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}={k}_{600}{(600/{{\mbox{Sc}}})}^{n};\quad [{{{{{{{\rm{m}}}}}}}}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]$$

(5)

where C_w is the CH₄ concentration in the surface water, Sc is the Schmidt number for CH₄ and the exponent is taken as n = 2/3 for wind speed < 3.7 m s⁻¹ and n = 1/2 for wind speed > 3.7 m s^−1 44.

Sensitivity analysis of ${k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ on P _net estimation

We calculated the error on ${P}_{{{{{{{{\rm{net}}}}}}}}}^{{{{{{{{\rm{err}}}}}}}}}$ caused by an inaccuracy on the estimation of ${k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ due to the use of k₆₀₀ literature parameterization as:

$${P}_{{{{{{{{\rm{net}}}}}}}}}^{{{{{{{{\rm{err}}}}}}}}}=\frac{{P}_{{{{{{{{\rm{net}}}}}}}}}-{P}_{{{{{{{{\rm{net}}}}}}}}}^{{\prime} }}{{P}_{{{{{{{{\rm{net}}}}}}}}}};\quad [{{{{{{{\rm{-}}}}}}}}]$$

(6)

where ${P}_{{{{{{{{\rm{net}}}}}}}}}^{{\prime} }$ is calculated using Eq. (1) considering ${F}_{{{{{{{{\rm{a}}}}}}}}}^{{\prime} }={k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}^{{\prime} }\left({C}_{{{{{{{{\rm{w}}}}}}}}}-{C}_{{{{{{{{\rm{sat}}}}}}}}}\right)$, then:

$${P}_{{{{{{{{\rm{net}}}}}}}}}^{{{{{{{{\rm{err}}}}}}}}}=\frac{{F}_{{{{{{{{\rm{a}}}}}}}}}{A}_{{{{{{{{\rm{s}}}}}}}}}}{{P}_{{{{{{{{\rm{net}}}}}}}}}{\forall }_{{{{{{{{\rm{SML}}}}}}}}}}{k}_{{{{{{{{\rm{err}}}}}}}}};\quad [{{{{{{{\rm{-}}}}}}}}]$$

(7)

where F_a is the average measure flux to the atmosphere and ${k}_{{{{{{{{\rm{err}}}}}}}}}=\frac{{k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}^{{{{{{{{\rm{cb}}}}}}}}}-{k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}^{{\prime} }}{{k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}^{{{{{{{{\rm{cb}}}}}}}}}}$ is the error between the mass transfer coefficient obtained from k₆₀₀ parameterization (${k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}^{{\prime} }$) and from chamber measurements (${k}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}^{{{{{{{{\rm{cb}}}}}}}}}$).

Porewater CH₄ concentration and ${\delta }^{13}{{{\mbox{C}}}}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ signature

Littoral sediment cores were taken in most of the lakes, except for LIO where the rocky bottom made it impossible to take a sample. Sampling was performed with a gravity sediment corer (Uwitech, Mondsee, Austria) equipped with an acrylic liner of 70 cm in length and with an internal diameter of 6 cm. 3 mL of sediment was sub-sampled at 1–2 cm depth intervals with headless 3 mL syringes through the pre-drilled holes from the selected depths. The sediment sub-sample was immediately placed into 1 L glass bottle (Duran GmbH, Mainz, Germany) containing 500 mL of lake water previously bubbled with air to reach equilibrium with the atmosphere. The subsequent procedure followed the same as for the water column headspace method. Porewater CH₄ concentrations were back-calculated from the headspace concentrations accounting for dilution of sediment porewater in the lake water (assuming that aerated lake water is in equilibrium with the atmosphere), temperature, headspace ratio, and assuming a porosity of 0.9. The location and depth of each core are shown in Supplementary Fig. 1 and Supplementary Table 4.

Methane benthic fluxes

The littoral CH₄ sediment flux (F_s) at each lake was determined as the average flux provided by two independent methods. On average, three cores above the thermocline depth were taken in the epilimnion on September 2018 and July 2019 (Supplementary Table 4) to estimate the littoral sediment fluxes at each lake.

Porewater method

Methane fluxes at the sediment-water interface were calculated using the CH₄ concentration retrieved from porewater cores and Fick’s 1st Law over the linear top 2–3 cm of the porewater concentration profile.

$${F}_{s}=-\phi {D}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}{\theta }^{-2}\frac{\partial C}{\partial z};\quad [{{{{{{{\rm{mmol}}}}}}}}\,{{{{{{{{\rm{m}}}}}}}}}^{-2}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]$$

(8)

where F_s is the diffusive CH₄ flux at the sediment-water interface, ϕ the porosity of the sediments (assumed as 0.9), ${D}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ the diffusion coefficient for CH₄ in water (1.5 × 10⁻⁵ cm² s^−1 65, θ² the square of tortuosity (1.2)⁶⁶ and ∂C/∂z the measured vertical concentration gradient.

Benthic chamber

Benthic fluxes were measured directly in sediment cores retrieved from the littoral sediment or core liners deployed in situ connected to a portable GHG analyzer (UGGA: Los Gatos Research, Inc.). The core was covered leaving ~5 cm of headspace and ~30–50 cm of water. The lid was connected to a GHG analyzer creating a closed loop and partial pressure of CH₄ (${P}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$) in the headspace was measured over time. Water CH₄ concentrations (C_w) were measured at the beginning and at the end of the deployment. Each deployment lasted about 1 h while the surface water was gently stirred to increase the mass transfer coefficient (k_bc) at the air-water interface without producing sediment resuspension. The sediment flux was calculated using three methods:

• Integrated mass balance: F_s is obtained using the beginning and final air and gas CH₄ concentration and performing a mass balance in the water and the air phase as:

  $${F}_{{{{{{{{\rm{s}}}}}}}}}{A}_{{{{{{{{\rm{bc}}}}}}}}}=\frac{{V}_{{{{{{{{\rm{air}}}}}}}}}}{R{T}_{{{{{{{{\rm{a}}}}}}}}}}\frac{\Delta {P}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}}{\Delta t}+\frac{{V}_{{{{{{{{\rm{w}}}}}}}}}\Delta {C}_{{{{{{{{\rm{w}}}}}}}}}}{\Delta t};\quad [{{{{{{{\rm{mmol}}}}}}}}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]$$

  (9)

  where V_w and V_air are the volume of the water and air phases, respectively. R is the ideal gas constant, T_a is the air temperature and A_bc is the surface area of the chamber.

• Transient mass balance: solving the mass balance over time we obtain that:

  $$\frac{\partial {P}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}}{\partial t}=\frac{aR{T}_{{{{{{{{\rm{a}}}}}}}}}}{b}\left(w{F}_{{{{{{{{\rm{s}}}}}}}}}-\left(w{F}_{{{{{{{{\rm{s}}}}}}}}}-b{k}_{{{{{{{{\rm{bc}}}}}}}}}{C}_{o}\right){e}^{-b{k}_{{{{{{{{\rm{bc}}}}}}}}}t}\right);\quad [{{{{{{{\rm{Pa}}}}}}}}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]$$

  (10)

  where $w={A}_{{{{{{{{\rm{bc}}}}}}}}}/{V}_{{{{{{{{\rm{w}}}}}}}}},\,a={A}_{{{{{{{{\rm{bc}}}}}}}}}/{V}_{{{{{{{{\rm{a}}}}}}}}},\,{C}_{0}={C}_{{{{{{{{\rm{w}}}}}}}}}(0)-{H}_{{{{{{{{\rm{cp}}}}}}}}}{P}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}$ and b = (w − H_cpRT_aa). The sediment flux is estimated fitting k_cb and F_s to the measured $\partial {P}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}/\partial t$ using least square method optimization solver implemented on the curve fit function from Scipy⁶² in Python. The k_bc boundaries were set from 0–40 m d⁻¹ for the fitting.

• Equilibrium mass balance: after ~ 1 h of measurements, we assume that the exponential part of the curve of Eq. (10) becomes negligible. Therefore, F_s can be estimated with the last 5 min of the CH₄ partial pressure as:

  $${P}_{{{{{{{{{\rm{CH}}}}}}}}}_{4}}=\frac{aR{T}_{{{{{{{{\rm{a}}}}}}}}}}{b}w{F}_{{{{{{{{\rm{s}}}}}}}}}t;\quad [{{{{{{{\rm{Pa}}}}}}}}]$$

  (11)

The flux from the benthic chamber was calculated as the average of the results of the three methods described above.

CH₄ bubble dissolution and ebullition rates

The CH₄ dissolution from a single bubble released from the sediment was calculated using McGinnis et al.⁴⁸. For each bubble we considered a diameter of 5 mm and the water column CH₄, CO₂, and O₂ concentrations and temperature profiles. The initial bubble composition at each depth was estimated from a linear interpolation from bubble content obtained following the same methodology as Langenegger et al.¹⁹. The total bubble dissolution rate (R_dis(z)) was calculated considering the contribution from all bubbles released below that depth as:

$${R}_{{{{{{{{\rm{dis}}}}}}}}}(z)=\frac{\mathop{\sum }\nolimits_{{{{{{{{\rm{bottom}}}}}}}}}^{z}{r}_{i}\frac{{F}_{{{{{{{{\rm{eb}}}}}}}},{{{{{{{\rm{SWI}}}}}}}},i}}{{n}_{0,i}}\Delta {A}_{{{{{{{{\rm{sed}}}}}}}},}i}{{A}_{{{{{{{{\rm{p}}}}}}}}}(z)}\quad [{{{{{\rm{\mu}}}}}} {{{{{{{\rm{mol}}}}}}}}\,{{{{{{{{\rm{m}}}}}}}}}^{-3}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]$$

(12)

where r_i is the bubble dissolution from an individual bubble at depth i (μmol bub⁻¹), F_eb,SWI,i is the CH₄ ebullition flux released at the sediment-water interface (SWI) at depth i (mmol m⁻² d⁻¹) and n_0,i is the initial amount of CH₄ in a single bubble (μmol bub⁻¹). ΔA_sed,i is the sediment area between the depth interval i to i + 1 (m²). F_eb,SWI,i was estimated using Langenegger et al.¹⁹’s model. Using a mass balance in the sediment, this model predicts CH₄ ebullition if the following are known: (1) the bubble CH₄ content, (2) the water depth where the bubble was collected and (3) the diffusive CH₄ flux from the sediment. In our study, we used the measured F_s to estimate F_eb,SWI using Langenegger et al.¹⁹ approach. The mass balance model can be described by:

$$\phi {D}_{i}\frac{{\partial }^{2}{C}_{i}(z)}{\partial {z}^{2}}+{W}_{i}(z)=0,\quad 0 \, < \, z \, < \, {z}_{{{{{{{{\rm{eb}}}}}}}},\min }$$

(13)

$$\phi {D}_{i}\frac{{\partial }^{2}{C}_{i}(z)}{\partial {z}^{2}}+{W}_{i}(z)-E(z)\frac{{K}_{{{{{{{{\rm{H}}}}}}}},i}{C}_{i}(z)}{P}=0,\quad z \, > \, {z}_{{{{{{{{\rm{eb}}}}}}}},\min }$$

(14)

where W_i(z) (mol m⁻³ d⁻¹) is the gas production rates as a function of the sediment depth (assumed exponential for CH₄ and zero for the other gases), ${z}_{{{{{{{{\rm{eb}}}}}}}},\min }$ the depth of a nonebullitive layer at the top of the sediment. D_i the molecular diffusion corrected by tortuosity, C(z) is the dissolved concentration (mol m⁻³), E(z) the total gas ebullition per bulk volume (mol m⁻³ d⁻¹), K_H,i is Henry’s law volatility constant (Pa m⁻³ mol⁻¹), and P is the local critical gas pressure (Pa).

Sensitivity analysis of ebullition

We calculated the CH₄ ebullition fluxes needed (F_eb,need) to compensate the P_net rates. We selected P_net rates for BRE and NOI for June 2018, where we estimated the percentage of F_eb that is dissolved in the SML (β) using McGinnis et al.⁴⁸’s model assuming a bubble diameter of 5 mm. Then F_eb,need was estimated using Eq. (15) and the results are summarized in Supplementary Table 5.

$${F}_{{{{{{{{\rm{eb}}}}}}}},{{{{{{{\rm{need}}}}}}}}}=\frac{{P}_{{{{{{{{\rm{net}}}}}}}}}{V}_{{{{{{{{\rm{SML}}}}}}}}}}{\beta {A}_{{{{{{{{\rm{sed}}}}}}}}}};\quad [{{{{{{{\rm{mmol}}}}}}}}\,{{{{{{{{\rm{m}}}}}}}}}^{-2}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]$$

(15)

Vertical diffusive CH₄ flux from/to hypolimnion

To estimate the transport of CH₄ into the SML via turbulent diffusion we applied Fick’s First Law as:

$${F}_{{{{{{{{\rm{z}}}}}}}}}=-{K}_{{{{{{{{\rm{z}}}}}}}}}\frac{\partial C}{\partial z};\quad [{{{{{{{\rm{mmol}}}}}}}}\,{{{{{{{{\rm{m}}}}}}}}}^{-2}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]$$

(16)

where F_z is the average vertical CH₄ diffusive flux, z is depth (m), $\frac{\partial C}{\partial z}$ is the vertical gradient measured at 1 m depth resolution approximately. The vertical diffusivity (K_z) was determined at each lake for each campaign (Supplementary Fig. 16) from temperature CTD profiles (sampling rate 4 Hz) and the Osmidov method⁶⁷ as:

$${K}_{{{{{{{{\rm{z}}}}}}}}}={\gamma }_{{{{{{{{\rm{mix}}}}}}}}}{L}_{{{{{{{{\rm{T}}}}}}}}}^{2}N;\quad [{{{{{{{{\rm{m}}}}}}}}}^{-2}\,{{{{{{{{\rm{d}}}}}}}}}^{-1}]$$

(17)

where γ_mix is the mixing efficiency (assumed 0.15, Wüest & Lorke⁶⁸), N is the Brunt-Väisälä buoyancy frequency and L_T is the Thorpe scale estimated from the maximum displacement length (${L}_{\max }$) as Lorke & Wüest⁶⁹:

$${L}_{{{{{{{{\rm{T}}}}}}}}}=\frac{\sqrt{2}}{7.3}{L}_{\max };\quad [{{{{{{{\rm{m}}}}}}}}]$$

(18)

This estimation was tested using microstructure profiles measured with a self-contained autonomous microstructure profiler (SCAMP; PME, Inc.) during the summer of 2021 in BRE, NOI, and CHA (Supplementary Fig. 17), where turbulence profiles were resolved after Kreling et al.⁷⁰.

Contribution to total diffusive CH₄ emissions

We studied the importance of each source contribution (SC) to the diffusive surface flux by computing:

$${{{\mbox{SC}}}}_{i}=\frac{{S}_{i}}{{\sum }_{j}{S}_{j}}\cdot 100;\quad [\%]$$

(19)

where S_i is each source term (mol d⁻¹) such as bubble dissolution (R_dis∀_SML), sediment flux (F_sA_s), net production (P_net∀_SML), and vertical diffusive fluxes (F_zA_z). If S_i ≤ 0 then S_i = 0 where i is each source term.