In this study, we balanced the methane sources in two basins of the temperate meso-oligotrophic Lake Stechlin in high temporal resolution covering the shift from mixed to stratified water column conditions. We further analyzed the methane budget in two different types of enclosures, both isolated from littoral methane input: in experimental enclosures (1200 m3) where water is periodically exchanged (last time 2 weeks prior to sampling) and in the central reservoir (14,000 m3) where water has not been exchanged since installation in 2011/2012 and is likely nutrient depleted. Comparing the methane budgets in the open water and enclosures allowed us to demonstrate that stratification mainly disconnected SML methane from bottom sediment methanogenesis, that OMP occurred irrespective of littoral influence, and that OMP contributed substantially to the system-wide methane emission of Lake Stechlin’s Northeast (64%) and South basin (50%) exceeding the littoral methane source contribution (32% in the Northeast basin and 45% in the South basin). Finally, combining mass balance results for Lake Stechlin and literature data for other lakes allowed us to develop a predictive model estimating the contribution of OMP to the system-wide methane surface emission as a function of lake morphological parameters, and the model suggests that OMP has important ramifications especially in large stratified lakes.

Mass balance approach has been successfully used by others to study methane dynamics in lakes40, including OMP21,32. However, this approach is sensitive to the accuracy of the individual components of the mass balance. Therefore, to assess the validity and robustness of our mass balance analysis, we evaluated the different components by comparing our measurements with literature values and examined how variabilities of the mass balance components may alter the overall conclusion. The average surface methane emission (F S ) during the stratified period was 0.47 mmol m−2 d−1 (±57% SD) in the Northeast basin and 0.71 mmol m−2 d−1 (±34% SD) in the South basin (taken mainly during calm weather). The larger value in the South basin can be attributed to higher influence from littoral methane sources. However, these emission values are comparable with the global estimate of 0.62 mmol m−2 d−1 for the region 25–54° latitude41 and within the range reported earlier for Lake Stechlin42 (exceeding 4 mmol m−2 d−1 at strong wind; on average 2.6 mmol m−2 d−1 ± 42% SD). Highly variable surface emission has been reported earlier, for some systems standard deviations exceed 100% of mean emission values during summer24,26. In case of the South basin we estimated the emission from wind speed data and the corresponding results are dependent on the gas transfer constant (k 600 ) value used. Our k 600 -wind speed relationship (k 600 [cm h−1] = 1.98 × U 10 [m s−1] + 0.98) was very similar to an earlier report (e.g., Lake Hallwil: k 600 [cm h−1] = 2.0 × U 10 [m s−1]; Donis et al.21). Applying six alternative emission models (based on wind or combined wind and lake size) presented by Vachon and Prairie37, MacIntyre et al.38 and Donis et al.21 to this dataset resulted in an average emission rate between 0.55 and 1.03 mmol m−2 d−1. Applying these alternative emission rates to the mass balance analysis gave an OMP rate between 41 and 185 nmol l−1 d−1, which still translated to a substantial oxic methane contribution (32–68%) to the surface methane emission (details in Supplementary Table 7). In other words, regardless of the method or model used to estimate surface methane emission, it remains that OMP was an important contributor to surface emission.

Comparing the methane data inside the experimental enclosures with that of the open water gave an average lateral methane input (F L ) of 1.4 mmol m−2 d−1 from the littoral sediment. It is within the range of fluxes reported for other temperate water bodies (e.g., Rzeszów Reservoir, Poland43: (mean ± SD) 0.69 ± 0.56 mmol m−2 d−1 in May–Sep; Lake Hallwil, Switzerland21: 1.75 ± 0.2 mmol m−2 d−1 in Sep (Supplementary Note 1); Boltzmann–Arrhenius equation at ca. 20 °C12: ca. 2 mmol m−2 d−1, including Lake Constance (Überlingen basin)/Lake Ammer/Lake Königsegg/Reservoir Schwarzbach in Germany12 with ca. 1.3 mmol m−2 d−1). Even doubling the lateral methane input, what is an unlikely scenario for a meso-oligotrophic lake such as Lake Stechlin, still could not fully explain the observed SML methane in the Northeast basin, and a substantial OMP rate (19 nmol l−1 d−1) would still be required to balance the methane budget. More importantly, within the experimental enclosures, which were isolated from lateral input, the estimated OMP was (mean ± SD) 101 ± 17 nmol l−1 d−1 (Aug 2014 dataset), which was comparable to the estimated average OMP in the open water for both basins (72–88 nmol l−1 d−1) (June/July 2016 dataset).

The calculation of methane diffusive input from the lower water layers (F z ) is dependent on the estimated K z value (diffusivity). Our K z values were comparable to an earlier report for the same lake36. Even in Lake Hallwil, which is 5–10 times larger than the Lake Stechlin basins and is therefore exposed to stronger seiching effects, very similar K z values were observed21 (thermocline minimum about 10−6 m2 s−1). The SML methane in Lake Stechlin was decoupled from bottom sediment methanogenesis during thermal stratification, as it is also indicated by the methane-depth profile of the central reservoir (Fig. 2e) where water has not been exchanged since installation in 2011/2012. Accordingly, methane diffusion from Lake Stechlin’s thermocline water accounted for only 2–5% (likely overestimated) of the SML methane in the open-water sites, and only 1% in the experimental enclosures. Variability in the corresponding mass balance components, therefore, was negligible and would not affect the overall conclusion.

The magnitude of methane oxidation (MOx) varies between seasons44,45,46 and between lakes39. Oxygen concentration47 and light48,49 are important modulating factors for MOx in lake surface waters. In other lakes, MOx rates in oxic surface waters have been reported to range between 4 and 30 nmol l−1 d−1 21,32,50. For our study, we assumed MOx to be equivalent to a constant fraction (30%) of the internal production during the stratified season (see method section for details). The average OMP rates for both basins were 72–88 nmol l−1 d−1, giving a hypothetical MOx rate of ca. 24 nmol l−1 d−1, which is within the range of literature values. Because methane oxidation is parameterized as a loss term in the mass balance analysis, higher MOx would translate to higher OMP, and vice versa. If we consider the extreme scenario by completely ignoring methane oxidation (MOx = 0), the estimated average OMP rate for the South basin would decrease to (mean ± SD) 40 ± 53 nmol l−1 d−1 and would still remain an important SML methane source (32%).

Comparing our measurements and assumptions against literature values shows that our mass balance analysis is reasonably parametrized and robust. The system-wide methane emission from the SML in the Northeast basin was estimated to be 942 mol d−1 in the stratified period, of which 32% from lateral input (372 mol d−1) and 5% from vertical diffusion from the thermocline (56 mol d−1) (Table 1). Similarly, methane emission from the SML in the South basin was 795 mol d−1, and only 45% (423 mol d−1) could be attributed to lateral input and 4% (41 mol d−1) to vertical input from the thermocline. The deficits (plus additional consumption via methanotrophy), therefore, must be compensated for by internal OMP. The estimated OMP rate averaged over the stratified period was (mean ± SD) 72 ± 74 nmol l−1 d−1 (Northeast basin) and 88 ± 75 nmol l−1 d−1 (South basin). An earlier study15 using bottle incubations measured a net OMP rate of up to 58 nmol l−1 d−1 for Lake Stechlin, which corresponds to a hypothetical gross production rate of 75 nmol l−1 d−1 when assuming 30% oxidation. Similar OMP rates have also been estimated for Lake Hallwil, between 76 and 138 nmol l−1 d−1 21 (Supplementary Note 1). Particularly high OMP values, such as what we found in late June (mean ± SD; 236 ± 32 nmol l−1 d−1), have also been reported by others32 (e.g., 230 ± 10 nmol l−1 d−1 in Lake Cromwell, Canada). Overall, by accounting for the different methane sources and sinks in the SML mass balance analysis, we show that OMP is a key contributor to system-wide surface emission in Lake Stechlin. This conclusion is consistent with previously reported OMP rates obtained from bottle incubations15 and is not sensitive to inherent uncertainties in our mass balance approach as shown by the sensitivity analysis.

In addition to known knowledge gaps in the global methane dynamics22,23, OMP has not been considered as source of uncertainty in global assessments1,2,22,23. Because both oxic and anoxic methane sources in lakes can be modulated by multiple factors and processes (Supplementary Fig. 7), some of which are still poorly understood, it would be premature to construct a mechanistic model to fully describe methane dynamics in lakes. Instead, we developed empirical models as useful tools to predict the contribution of OMP to the system-wide emission (OMC) in stratified meso-to-oligotrophic lakes in the temperate region based on a set of simple lake morphological parameters (Fig. 4, Supplementary Fig. 6). The first model using littoral sediment area (A sed ) and SML volume (∀) as proxy explains nearly the entire variance in the dataset (R2 = 0.95, p ≪ 0.01) making it a powerful predictive model to estimate OMC from A sed and ∀. For cases where A sed and ∀ data are unavailable, OMC can be related to easily accessible lake surface area (Supplementary Fig. 6). With an average accuracy of 91.4% (standard error = 8.6%) this model also provides reliable OMC estimates. Both empirical models predict the importance of OMP for atmospheric emission to increase with lake size.

The system-wide contribution of the anoxic methane sources is mainly controlled by littoral sediment flux and the corresponding littoral sediment area. Trophic state51,52 and temperature12,53 are important drivers of the methane flux from sediments. Higher sediment methane fluxes in eutrophic systems and in warmer climate zones compared to our dataset of stratified meso-to-oligotrophic lakes in the temperate region could shift the curve of the empirical models to the right (Fig. 4, Supplementary Fig. 6). However, sediment methane fluxes vary in a rather narrow range by a factor of 26 between oligotrophic and eutrophic lakes52 (e.g., 0.2–5.2 mmol m−2 d−1). Likewise, reported average OMP rates varied by a factor of 6 in stratified lakes15,21,32 (40–230 nmol l−1 d−1 including this study). In comparison, our predictive model covers lake surface area that varies by a factor of 190,000. The OMC prediction, therefore, may vary mainly for small lakes which have been reported to cause less methane emission on a global scale compared to large lakes28 (<0.01 versus >1 km2). It shall be noted that the model predictions based on A sed and ∀ will be more reliable than based exclusively on lake surface area due to sediment steepness, aspect ratio and total depth modulating the littoral sediment area at constant lake surface area.

Methane emission from lakes has been identified as a key contributor of this powerful greenhouse gas to the atmosphere22. It is therefore a legitimate question to ask: how important is OMP in this context on a global scale? To get a first-order estimation, we applied our empirical model to the global lake size distributions based on satellite data, which covers lakes ≥0.01 km231. The result suggests that globally, an average of 66% of lake methane emission may have originated from oxic production (Supplementary Note 4, Supplementary Table 8). Such a surprising finding justifies the need for further investigation of OMP in lakes worldwide with different geological histories, trophic states, climates, and physical (e.g., lake color, stratification patterns or with strong in-/out flow) and chemical characteristics (e.g., alkaline versus acidic) (Supplementary Fig. 7). By increasing data resolution in our empirical models, the models can then be used to further improve the global methane emission assessments.

Unlike the anoxic methane production driven by anaerobic methanogens with enzymes that are oxygen-sensitive54, OMP in lake waters has been attributed to novel biochemical pathways involving photoautotrophs15,34,55. Our system-wide methane mass balance demonstrates that without OMP a substantial methane source is missing when balancing Lake Stechlin’s SML methane sources and sinks. The estimated OMP rates agree very well with earlier results from bottle incubation experiments15 and account for ≥50% of the system-wide methane emission. Following our model, OMC is predicted to be the major methane source for the system-wide emission in lakes >1 km2. In the light of global warming and widespread lake eutrophication, stratification periods will extend56,57 and phytoplankton production in the SML is expected to increase worldwide58, which may increase OMP and its contribution to methane emission to the atmosphere. To understand and predict future climate change scenarios, it is crucial to consider lake water OMP in the global methane assessment and how it responds to environmental perturbations.