Lake Willersinnweiher is situated in the plain of the Upper Rhine Graben (Germany), northwest of Ludwigshafen (49.499950 °N; 8.397138 °E) and covers an area of 17 ha (Figure 2). It is one of four gravel pit lakes and has neither a surface inflow nor outflow, thereby making inflowing groundwater its main source of water and solutes (Wollschläger et al., 2007). Lake Willersinnweiher is composed of a shallower northeastern basin with a maximum water depth of 14 m and a deeper southwestern basin with a maximum water depth of 20 m. The average water depth in the lake is 8 m (Sandler, 2000).

Geochemically, Lake Willersinnweiher can be characterized as an eutrophic hardwater lake with an average water residence time of 3.7 years and experiences seasonal water stratification during summer (stratification period) (Wollschläger et al., 2007). From November/December to March/April, the water column of Lake Willersinnweiher is fully mixed (mixing period). This leads to fully oxic conditions during the mixing period in the lake with O₂ reaching the upper few millimeters of the sediment (Schröder, 2004). With warming temperatures in spring, thermal stratification starts to build up and reaches a maximum in late summer, leading to the formation of a warm, fully oxygenated epilimnion and the anoxic hypolimnion separated by a thermocline at the upper boundary of the metalimnion and a chemocline/oxycline at the lower boundary of the metalimnion. Chlorophyll-a measurements show a peak in algal activity at the thermocline and at the transition from metalimnion to hypolimnion. As thermal stratification weakens in October due to decreasing temperatures, characteristics of mixing are observed throughout the entire water column reflecting the transition to whole lake circulation prevailing during winter.

Sulfate (SO₄ ²⁻) concentrations in the lake are unusually high for a freshwater environment (∼2 mmol L⁻¹) and are the result of sulfate-rich groundwater inflow at the southwestern shore of the lake (Schröder, 2004). Hence, due to high SO₄ ²⁻ concentrations in Lake Willersinnweiher, the potential for sulfate-dependent AOM is high compared to most other limnic environments. The main process of organic matter turnover in Lake Willersinnweiher is degradation via sulfate reduction (Kleint et al., 2021). This results in the production of sulfide (S²⁻) in the lake sediment, causing diffusive release into the bottom water and consequently leading to euxinic conditions in the hypolimnion during the stratification period. Pyrite oxidation in the Quaternary river sediments of the Rhine cause high SO₄ ²⁻ concentrations in the catchment upstream of the lake (Schröder, 2004; Isenbeck-Schröter et al., 2016). A detailed review of geochemical processes in the lake water and sediment of Lake Willersinnweiher can be found in a recent study by Kleint et al. (2021).

Eutrophic conditions in the lake are caused by agriculture and land use in the vicinity of the lake, resulting in the release of nutrients into the groundwater, which ultimately reach the lake (Laukenmann, 2002). Groundwater flow in the area of Lake Willersinnweiher is generally directed from southwest to northeast with low flow velocities due to a nearly horizontal groundwater table. Inflowing groundwater at the southwestern shore has already passed at least one of the adjacent smaller lakes upstream of Lake Willersinnweiher (Wollschläger et al., 2007).

Sampling of the lake water and sediment was performed at three different sites in the southwestern basin. The pelagic sampling site in the center of the lake has a water depth of 16 m, the slope site is 9 m and the littoral site about 1.5 m deep. Groundwater sampling was carried out at three wells surrounding the lake (see Figure 2). The lake water, groundwater and sediment were sampled in July 2020 during the stratification period and in March 2021 during the mixing period.

Changes in lake water parameters (temperature, pH, dissolved oxygen and chlorophyll-a) with depth were recorded using an Exo1 multiparameter probe (Xylem Analytics, Norway). The probe was calibrated for each of the monitored parameters prior to each sampling session.

Samples of the water column were taken at different depth levels using a submersible pump (COMET-Pumpen Systemtechnik GmbH & Co. KG, Germany) and prepared for measurement of CH₄ concentration and isotopic composition using a headspace technique (Kampbell et al., 1989). Samples collected for dissolved ion and dissolved inorganic carbon (DIC) analysis were filtered through a 0.2 μm filter into falcon tubes (Corning, United States). Samples for cation analysis were acidified with 150 μl of 6 M nitric acid.

For pore-water analysis, two sediment cores (core length ∼21–29 cm) were taken at each site with a manually operated gravity corer. Pore-water was extracted from one of the cores immediately after sampling in defined intervals using rhizons (Rhizosphere Research Products, Netherlands) with a pore-size of 0.15 μm. For measurement of sedimentary CH₄ concentration and its isotopic composition, the sediment of the second core was subsampled in the same intervals as the pore-water by transferring 3 ml of lake sediment with a cut-off plastic syringe into glass vials. The sediment was treated with 5 ml of sodium hydroxide (1 M NaOH) and subsequently the vials were crimped with a lid containing a butyl rubber septum and shaken vigorously to impede any further microbial activity. In the laboratory, the sediment samples were shaken for ∼10 min to equilibrate porewater CH₄ and the gas headspace. Afterwards, the headspace was extracted for further analysis. The sediment samples were dried in an oven at 105°C for several days to determine their water content and porosity.

Groundwater wells were sampled using a submersible pump (MP1, Grundfos GMBH, Germany) after pumping until groundwater parameters showed steady values (∼30 min). Groundwater samples were prepared in the same way as lake water samples.

Ebullitive CH₄ was sampled for its isotopic composition in November 2020 and September 2021 by deploying an in-house built bubble trap consisting of inverted plastic funnels. A gravity corer was dropped into the sediment in order to release gas bubbles trapped in the sediment. Released gas bubbles were collected with the bubble traps directly under the lake surface and the accumulated gas was analyzed for CH₄ concentration as well as its carbon and hydrogen isotopic composition. The collection of ebullitive CH₄ via this method was only performed in November 2020 and September 2021 at the littoral and slope sites, whereas at the pelagic site, it was not possible to collect gas bubbles at the surface after dropping the weight into the sediment.

Gas samples for measurement of δ¹³C-CH₄ and δ²H-CH₄ values released to the atmosphere via diffusion were taken between March and September 2021 using a floating chamber. The floating chamber consisted of a plastic body with a volume of 8.6 L, two tubes equipped with three-way valves in order to take samples and a floatable ring made from polyethylene that kept the chamber afloat and the edges of the chamber in the water at a depth between 2 and 3 cm. Samples were collected when the chamber was placed in the water and after 15 and 30 min. All gas samples collected from the water column, sediment, groundwater and via the floating chamber were analyzed for their CH₄ concentrations, δ¹³C-CH₄ and δ²H-CH₄ values in the laboratory.

All laboratory analyses were performed at the Institute of Earth Sciences at Heidelberg University, Germany.

Methane formation and consumption processes are associated with a kinetic isotope effect leading to a change in its isotopic composition. The magnitude of this kinetic isotope effect is expressed in the isotope fractionation factor α. Processes of CH₄ formation can be distinguished by determining the apparent carbon isotopic fractionation factor α_CH4-CO2 between CH₄ and CO₂ according to Eq. 2: α C H 4 − C O 2 = δ C − C O 2 + 1000 13 δ C − C H 4 + 1000 13 (2)

In order to calculate the δ¹³C-CO₂ values from δ¹³C-DIC values the methodology as described by Gonzalez Moguel et al. (2021) was used. Shortly, in a first step the DIC concentrations as well as the pH values in the respective depth were used to calculate the distribution of CO₃ ²⁻, HCO₃ ⁻ and dissolved CO₂. Using this species distribution and the isotope fractionation factors between gaseous CO₂ and dissolved CO₂, HCO₃ ⁻ and CO₃ ²⁻ as reported by Zhang et al. (1995), dissolved δ¹³C-CO₂ values were calculated. An α_CH4-CO2 between 1.050 and 1.060 indicates acetoclastic methanogenesis whilst between 1.060 and 1.090 shows predominance of hydrogenotrophic methanogenesis (Thottathil and Prairie, 2021).

Isotopic fractionation factors ¹³α for carbon and ²α for hydrogen during CH₄ oxidation were determined using the Rayleigh model for closed systems according to Bastviken et al. (2002) (Eq. 3): ln ( 1 − f ) = [ ln ( δ P + 1000 ) − l n ( δ O x + 1000 ) ] [ α − 1 ] (3) where f is the fraction of CH₄ being oxidized, δ P the carbon/hydrogen isotopic value of CH₄ in the near-bottom water and the zone of CH₄ production in the sediment, respectively, and δ O x the carbon/hydrogen isotopic value of CH₄ in the oxidation zone in the aerobic water column or the anoxic sediment, respectively. During CH₄ oxidation, a gradual enrichment of the heavier isotope in the residual CH₄ compared to initial δ¹³C-CH₄ and δ²H-CH₄ values occurs due to kinetic fractionation. The magnitude of this enrichment is expressed by the isotope fractionation ε (Eq. 4). ε = α − 1 (4)

The Keeling plot method was used to determine the δ¹³C-CH₄ and δ²H-CH₄ values of CH₄ released from the water column to the atmosphere (Keeling, 1958). For a detailed description of the Keeling plot method, we refer the reader to Pataki et al. (2003) and Keppler et al. (2016). Briefly, a graphical approach based on the Keeling plot method was used to estimate stable isotope source values of CH₄. Here, the inverse CH₄ mixing ratios of the three individual measurements during sampling of diffusion (x-axis) are plotted against their respective δ¹³C-CH₄ or δ²H-CH₄ values measured via GC-C-IRMS (y-axis). Then a linear regression was employed and the intercept of this linear regression with the y-axis reflects the δ¹³C-CH₄ or δ²H-CH₄ source value. Reported errors are based on the standard error of the linear regression.

A novel stable isotope indicator ∆ ( 2,13 ) was applied, which was introduced by Tsunogai et al. (2020), to characterize sources of CH₄ by correcting for changes in the isotopic composition of CH₄ due to the progression of oxidation (Eq. 5). ∆ ( 2,13 ) = δ H 2 − Λ   x   δ C 13 (5)

The Λ value thereby corresponds to the ratio of stable hydrogen vs. stable carbon isotope fractionation ε H and ε C , respectively, during microbial CH₄ oxidation (Eq. 6), and thus corrects for the kinetic isotope effect associated with oxidation. Λ = ε H ε C (6)

To calculate the ∆ ( 2,13 ) values, the Λ value for Lake Willersinnweiher needs to be known. Hence, a MOx incubation experiment was performed in the month of July 2021 with water from a depth of 6 m (Supplementary Figure S1). Lake water was filled into acid washed and autoclaved vials and incubated without any further treatment for 20 days in the dark at the lake temperature (15°C). Temporal sampling of CH₄ was performed three times in triplicate during the incubation period via the headspace technique (Kampbell et al., 1989). The δ¹³C-CH₄ and δ²H-CH₄ was subsequently analyzed and Λ was then estimated from the slope of the linear regression between the changes in δ¹³C-CH₄ and δ²H-CH₄ values analyzed at the different intervals during the incubation yielding a result of Λ = 9.3 ± 0.3 (Supplementary Figure S1). In order to calculate ∆ ( 2,13 ) , the concentration-weighted mean isotopic value of the lake water samples was used.

Sediment porewater profiles of CH₄ concentrations at the pelagic site showed an increase with greater sediment depth during the stratification period with maximum concentrations ranging around 1 mmol L⁻¹, which were accompanied by δ¹³C-CH₄ values of −80 to −75‰ and δ²H-CH₄ values of −314 to −328‰ (Figure 3D). A brief shift towards more positive isotopic values of CH₄ within a few centimeters in the upper sediment occurred, where δ¹³C-CH₄ values showed a maximum increase of 11‰, however δ²H-CH₄ data is missing for this depth interval due to problems in collecting samples. The upper sediment core at the pelagic site was characterized by decreasing CH₄ concentrations towards the sediment surface. Sulfate concentrations decreased with depth in the upper few centimeters (3–5 cm) of the sediment while simultaneously a rise in S²⁻ concentrations was recorded in the same depth interval (Figure 3E). Also, DIC concentrations in the pore-water increased with depth and showed lowest δ¹³C-DIC values of around −14‰ in the upper part and an enrichment in ¹³C with increasing sediment depth to −9‰ (Figure 3F).

At the slope site an increase in CH₄ concentrations with depth was observed accompanied by δ¹³C-CH₄ values varying from −77 to −69‰ and δ²H-CH₄ values ranging from −338 to −271‰ (Figure 4D). Similarly to the pelagic site, a decrease in SO₄ ²⁻ and an increase in S²⁻ concentration with depth was recorded (Figure 4E), whereas DIC concentrations increased towards the bottom of the sediment core coinciding with an overall decrease in δ¹³C-DIC values (Figure 4F).

At the littoral site, profiles of the sediment porewater showed CH₄ concentrations of up to 1.3 mmol L⁻¹ (Figure 5D). ¹³C-enriched CH₄ values compared to the pelagic and slope sites around −58 to −52‰ were found during the stratification period along with δ²H-CH₄ values ranging from −333 to −256‰ (Figure 5D). Similar to the deeper sites, a shift towards a more positive isotopic signal particularly in δ²H-CH₄ values was recorded in the upper sediment layers, whereas δ¹³C-CH₄ values showed a gradual increase from −57‰ at 3 cm to −51‰ at 9 cm sediment depth.

During the mixing period, porewater CH₄ at the pelagic site showed highly variable δ¹³C-CH₄ values throughout the entire sediment core varying from −39 to −75‰, whereas δ²H-CH₄ showed a rather uniform distribution ranging between −234 and −266‰, respectively (Figures 3J–L). Methane concentrations were at a much higher level than during the stratification period at the pelagic site, increasing to 3.1 mmol L⁻¹ in the lower part of the core. In contrast, the littoral sediment recorded significantly lower CH₄ concentrations around 0.3 mmol L⁻¹ during the mixing period (Figure 5J). For the slope site no CH₄ data is available for the mixing period. Similar to the stratification period, SO₄ ²⁻ concentrations decreased in the upper part of the pelagic sediment and stayed at very low levels in the lower part of the core (Figure 3K). No increase in S²⁻ concentration was observed in the sediment of the three investigated sites during the mixing period. DIC concentrations showed a similar trend as during the stratification period and increased with sediment depth accompanied by increasing δ¹³C-DIC values (Figure 3L).

In the lake water column, CH₄ concentrations showed a decrease from the hypolimnion towards the surface water accompanied by an enrichment in ¹³C-CH₄ and ²H-CH₄ during the stratification period (Figure 3A). Methane in the bottom water of Lake Willersinnweiher showed δ¹³C-CH₄ and δ²H-CH₄ values of −77‰ and −309‰, respectively, and increased to δ¹³C-CH₄ values of −56‰ and −269‰, respectively, in the surface water layer during the stratification period. Methane concentrations in the surface water ranged from 0.37 to 0.67 µmol L⁻¹ with highest concentrations found at the littoral site (Figure 5A). DIC concentrations rose from 1.4 mmol L⁻¹ in the surface water to 2.6 mmol L⁻¹ in the bottom water, while δ¹³C-DIC showed a decrease from −4 to −12‰ throughout the water column from top to bottom (Figure 3C).

A pronounced zone of low CH₄ concentrations was observed at the pelagic site during the stratification period in the lower metalimnion, showing a maximum decline in CH₄ of 0.52 µmol L⁻¹ from 6 to 8 m water depth (Figure 3A). This minimum in CH₄ concentrations coincided with maximum δ¹³C-CH₄ and δ²H-CH₄ values in the water column.

A local peak in CH₄ concentrations in the oxic upper water column was found at a water depth of 6 m during the stratification period at the pelagic site, showing a maximum increase of 0.56 µmol L⁻¹ compared to surface water CH₄ concentrations during the stratification period (Figure 3A). This was accompanied by an increase in the δ¹³C-CH₄ and δ²H-CH₄ values of about 9‰ and 83‰, respectively, compared to surface water values, resulting in δ¹³C-CH₄ values of −48‰ and δ²H-CH₄ values of −83‰ at 6 m water depth.

The slope site showed similar surface water CH₄ concentrations (0.37–0.39 µmol L⁻¹) and isotopic compositions (δ¹³C-CH₄ of -56‰ and δ²H-CH₄ of -268‰) as the pelagic site and recorded an increase in the concentration with depth up to 0.94 µmol L⁻¹, which was accompanied by an increase in δ¹³C-CH₄ and δ²H-CH₄ values of 17‰ and 136‰, respectively (Figure 4A). The littoral site displayed CH₄ enriched in ¹³C-CH₄ and ²H-CH₄ (δ¹³C-CH₄ and δ²H-CH₄ values of −51 and −263‰) in the surface water (Figure 5A) compared to the pelagic and slope sites.

During the mixing period, distinctively lower CH₄ concentrations around 0.07 µmol L⁻¹ at the pelagic site throughout almost the entire water column were characterized by δ¹³C-CH₄ values of −39‰ and +11‰ for δ²H-CH₄ values (Figure 3G). The bottom water showing CH₄ concentrations of 0.4 µmol L⁻¹ recorded more negative isotopic values of −65‰ and −127‰. The concentration of DIC in the water column stayed at the same level throughout the water column and the carbon isotopic pattern recorded a minor shift towards slightly more positive values from −7 to −5‰ at intermediate water depths (Figure 3I). While CH₄ concentrations and δ¹³C-CH₄ values at the slope and littoral site were similar to those found at the pelagic site, δ²H-CH₄ values were more negative varying around −30‰ (Figures 4G, 5G).

The apparent carbon isotopic fractionation factor α_CH4-CO2 between CH₄ and CO₂ (Eq. 2) in the sediment was determined for sediment depths where CH₄ concentrations were highest, therefore most likely indicating the occurrence of methanogenesis in these depths. The α_CH4-CO2 was found to be lowest at the littoral site (1.047) and rose with increasing lake depth (1.058 at the slope site and 1.066 at the pelagic site) during the stratification period (Supplementary Table S1). During the mixing period, the pelagic and littoral site exhibited a α_CH4-CO2 of 1.070 and 1.047, respectively.

Isotopic fractionation factors associated with CH₄ oxidation (Eq. 3) were determined in the upper sediment layers of the three sampled locations where a zone of decreasing CH₄ was observed. During the stratification period, isotopic fractionation in these zones was found to range from 1.005 to 1.031 for ¹³α and from 1.042 to 1.124 for ²α (Table 1). During the mixing period, ¹³α varied from 1.051 to 1.087 and ²α from 1.015 to 1.169. In the water column, an isotopic fractionation factor was determined for the zone between the upper and the lower metalimnion at the pelagic site in which a decrease in CH₄ concentrations was apparent for the stratification period, where an ¹³α of 1.009 and an ²α of 1.057 was calculated. An isotopic fractionation factor for the mixing period could not be calculated since no changes in the isotopic composition of CH₄ was observed in the water column and similar CH₄ concentrations throughout the entire water column were recorded (Figure 3G).

Methane released via diffusion from the lake surface water into the atmosphere during the stratification period (May to September) recorded similar δ¹³C-CH₄ values at each of the three sampled sites, varying between −52 and −58‰ (Table 2). δ²H-CH₄ values were more variable ranging from −195 to −310‰ at the different sites, whereby the pelagic and slope site showed in July the most positive values during the stratification period (−208 ± 3 and −205 ± 14‰, respectively) and the littoral site in August (−195 ± 22‰). During the mixing period, CH₄ emitted from the lake was considerably enriched in the heavier isotopes at all investigated sites compared to the stratification period. δ¹³C-CH₄ values ranged from −36 to −42‰ and δ²H-CH₄ values from 1 to 26‰.

The concentrations and isotopic composition of ebullitive CH₄ were analyzed for the littoral and slope site of the lake in November 2020 and September 2021 (Supplementary Table S2). Ebullitive CH₄ was not collected for analysis in July 2020 and March 2021 due to logistical reasons. Nevertheless, the stratified lake period is represented by the data from September 2021, whereas the mixing period is represented by the data from November 2020.

In September during thermal stratification, CH₄ concentrations in gas bubbles in the littoral area reached 80.8 ± 4.5%. In November, CH₄ concentrations of ebullitive CH₄ were in the range of 62.1 ± 7.4% and 66.8 ± 3.2% at the littoral and slope site, respectively. δ¹³C-CH₄ values at the littoral site were more negative in September compared to November with −58 ± 1‰ and −50 ± 12‰, respectively. In contrast, δ²H-CH₄ values in September and November at the littoral site were very similar with −323 ± 3‰ and −326 ± 4‰. At the slope site, δ¹³C-CH₄ values were more negative compared to the littoral site with −64 ± 11‰, but δ²H-CH₄ values were in a similar range compared to the littoral site with values of −318 ± 1‰.

Groundwater in the area of Lake Willersinnweiher showed highly variable CH₄ concentrations, δ¹³C-CH₄ and δ²H-CH₄ values and was strongly enriched in ²H-CH₄ and ¹³C-CH₄ (Table 3). During the stratification period, inflowing groundwater yielded a CH₄ concentration of 1.01 µmol L⁻¹ with an isotopic composition enriched in ¹³C and ²H (δ¹³C-CH₄ value of −24‰ and δ²H-CH₄ value of +106‰). Outflowing groundwater of the southwestern basin showed slightly lower CH₄ concentrations of 0.95 µmol L⁻¹ along with δ¹³C-CH₄ and δ²H-CH₄ values of +18‰ and +582‰, respectively. CH₄ concentrations of groundwater flowing out of the northeastern basin were 0.77 µmol L⁻¹ during the stratification period accompanied by δ¹³C-CH₄ values of −50‰ and δ²H-CH₄ values of −187‰. Between the two outflowing groundwater wells in the western and eastern part of Lake Willersinnweiher a disparity in CH₄ concentrations and stable isotope values is worth noticing. This observation is probably caused as outflowing groundwater in the western part consists of a mixture of outflowing groundwater from the lake and groundwater with properties similar to inflowing groundwater, that also passed subjacent lakes, due to its location and groundwater flow direction (see Figure 2). During the mixing period, groundwater at the three wells showed CH₄ concentrations of 1.97 and 2.71 µmol L⁻¹ for inflowing and outflowing groundwater of the southwestern basin, respectively, and even 30.89 µmol L⁻¹ for groundwater flowing out of the northeastern basin. Groundwater outflow of the southwestern basin showed a δ¹³C-CH₄ value of −37‰ and a δ²H-CH₄ value of +24‰. The isotopic composition of groundwater at the other two groundwater wells was in the range of values reported during the stratification period (Table 3).

Methanogenesis is the last step in the microbial degradation of organic matter and is performed by methanogenic archaea in the anaerobic environment (Conrad, 2005). However, in presence of other electron donors (such as SO₄ ²⁻), organic matter degradation via sulfate reduction is favored over methanogenesis. This is most likely the case for Lake Willersinnweiher, where sulfate-reducing bacteria are believed to thermodynamically outcompete methanogenic archaea for available carbon compounds and H₂ in the upper sediment due to high SO₄ ²⁻ concentrations in the lake water (Kleint et al., 2021). In aquatic systems with high SO₄ ²⁻ concentrations, anaerobic methanogenesis is therefore restricted to greater sediment depths, where SO₄ ²⁻ concentrations are low (Holmer and Storkholm, 2001; Reeburgh, 2007; Schubert et al., 2011). Methanogenesis in Lake Willersinnweiher is suggested to occur in zones of the deeper sediment where CH₄ in the sediment accumulated (Figures 3D, 4D, 5D). Hydrogenotrophic methanogenesis as the dominant process of CH₄ production in the sediment during the stratification period was indicated by relatively negative δ¹³C-CH₄ values (ranging from around −80 to −75‰) observed in the lower sediment of the pelagic and slope site, where maximum CH₄ concentrations were recorded (Figure 3D). Whereas the associated δ²H-CH₄ values of around −321 to −246‰ were rather negative for this type of methanogenesis (Whiticar, 1999). However, δ²H-CH₄ values in this environment are likely mostly linked to the δ²H value of the source water (Waldron et al., 1999; Douglas et al., 2021) and seem to be less indicative of the methanogenic pathway compared to δ¹³C-CH₄ values as δ²H-CH₄ values are less studied and influenced by more factors. Above that a mixing of the hydrogenotrophic and acetoclastic pathway is possible (Sugimoto and Wada, 1995; Walter et al., 2008). During methanogenesis, hydrogen originating from ambient water is incorporated into the CH₄ molecule, thus δ²H-CH₄ values are mostly dependent on the hydrogen isotopic composition of the water (Sugimoto and Wada, 1995). Plotting sedimentary δ¹³C-CH₄ values against δ²H-CH₄ values and classifying them after Whiticar (2020) indicated an overlap of the two different methanogenic pathways at the pelagic and slope site (Figure 6). For the littoral site, a dominance of acetoclastic methanogenesis seems to be implied due to less negative δ¹³C-CH₄ values compared to the pelagic and slope site.

Furthermore, based on the carbon isotopic shift between CH₄ and CO₂, we determined apparent carbon isotopic fractionation factors associated to anaerobic methanogenesis, which is an indicator to distinguish between the hydrogenotrophic and acetoclastic pathway. At the pelagic site, an α_CH4-CO2 of 1.066 supports the dominance of hydrogenotrophic methanogenesis during the stratification period (Supplementary Table S1). The α_CH4-CO2 decreased towards the littoral site, indicating an increasing contribution of the acetoclastic pathway. Overlapping characteristics were hence especially visible at the slope site, where δ¹³C-CH₄ values around −75‰ point to hydrogenotrophic methanogenesis whereas the calculated α_CH4-CO2 of 1.058 is representative for acetoclastic CH₄ formation. The proposed increasing dominance of acetoclastic methanogenesis from the pelagic towards the littoral area is based on the isotopic values of sedimentary CH₄ observed at Lake Willersinnweiher and might be coupled to changes in sediment temperatures and differences in organic matter availability with varying lake depth (Thottathil and Prairie, 2021). However, further investigations are needed to gain more insight into the occurrence and distribution of the different methanogenic pathways in the sediment of Lake Willersinnweiher.

During the mixing period, the observed α_CH4-CO2 of 1.070 for the pelagic site (Supplementary Table S1) was higher than during the stratification period suggesting a higher dominance of hydrogenotrophic CH₄ formation. This might possibly reflect the limited availability of fresh organic material in the lake. However, higher sedimentary CH₄ concentrations found at the pelagic site during the mixing period compared to the stratification period (Figures 3D,J) seemed to contradict the expected decrease of CH₄ concentrations due to lower primary production in winter and therefore reduced organic matter availability. This indicated that processes other than microbial activity in the sediment must have contributed to the high observed sedimentary CH₄ concentrations and isotopic pattern in the sediment at the pelagic site and highlights the complex interaction of the occurring processes influencing the sedimentary CH₄ cycle. However, we suggest that infiltrating groundwater as a potential CH₄ source might also play an important role at Lake Willersinnweiher since it yielded very high CH₄ concentrations characterized by extremely positive isotopic δ¹³C-CH₄ and δ²H-CH₄ values both for inflowing and outflowing groundwater (Table 3). Mixing of groundwater and lake sediment CH₄ might potentially skew the calculated fractionation factors for the mixing period, hence these have to be considered with caution and can only be used as a preliminary indicator for the methanogenic pathway.

The shift to more positive δ¹³C-CH₄ and δ²H-CH₄ values partially observed in the upper sediment layers during the stratification period was most likely caused by the anaerobic oxidation of CH₄ coupled to SO₄ ²⁻reduction. The occurrence of sulfate-dependent AOM in Lake Willersinnweiher was described in a recent study by Kleint et al. (2021) and we therefore refer the reader to this study for more detailed discussion on this process at Lake Willersinnweiher. Here we want to give a brief summary on sulfate-dependent AOM at Lake Willersinnweiher and discuss the associated isotopic effects of this process. In the sediment, upward rising CH₄ and downward diffusing SO₄ ²⁻ meet in the so-called sulfate-methane transition zone (SMTZ), where anaerobic methanotrophic archaea in syntrophic association with sulfate-reducing bacteria are able to reverse methanogenesis and oxidize CH₄ using SO₄ ²⁻ (Boetius et al., 2000). In most freshwater environments, low SO₄ ²⁻ concentrations usually preclude sulfate-dependent AOM, whereas in the oceans, sulfate-dependent CH₄ oxidation is a widely described and common process due to high SO₄ ²⁻ concentrations in the ocean water (Knittel and Boetius, 2009). Since Lake Willersinnweiher shows high SO₄ ²⁻ concentrations, compared to other lakes, as a result of sulfate-rich groundwater input, sulfate-dependent AOM is possible.

Indicative of AOM might furthermore be the observation of DIC enriched in ¹²C in the upper lake sediment compared to the lower sediment during the stratification period since ¹²C-CH₄ is preferably oxidized by the microorganisms, thereby providing HCO₃ ⁻ relatively enriched in ¹²C to the sedimentary DIC pool (Schubert et al., 2011). With increasing sediment depth, microbial hydrogenotrophic CH₄ production caused a depletion in isotopically light DIC, thus leading to DIC enriched in ¹³C-DIC in the sediment pore-water.

Zones in the lake sediment where sulfate-dependent AOM was presumed to take place were not always characterized by a clear shift towards less negative δ¹³C-CH₄ and δ²H-CH₄ values (Figures 3J, 5D), as one might typically expect for CH₄ oxidation or restrained to a few centimeters within the upper sediment at the investigated sites of Lake Willersinnweiher. Plotting sedimentary δ¹³C-CH₄ values against δ²H-CH₄ values shows a progression of the littoral sediment data of the mixing period within a predicted CH₄ oxidation line between a ratio of C:D of 1:5 and 1:10 (e.g., Wang et al., 2016; Whiticar, 2020), referring to an enrichment of CH₄ in hydrogen isotopes 5–10 times more than in carbon isotopes during AOM (Figure 6). This observation is in good accordance with previously reported C:D ratios during AOM ranging between 6.4 and 10 (Martens et al., 1999; Holler et al., 2009; Feisthauer et al., 2011; Rasigraf et al., 2012). However, this trend was less pronounced at the other two sites, limiting the use of carbon and hydrogen stable isotopes of CH₄ to characterize AOM in the lake sediment. Nevertheless, carbon and hydrogen isotopic fractionation factors ¹³α and ²α were also determined to identify the occurrence of potential AOM in the respective zones of the sediment. The calculated carbon isotopic fractionation factors ¹³α values for the observed enrichment in ¹³C-CH₄ and ²H-CH₄ and associated with AOM in the sediment (1.002–1.019, Table 1) were on the lower end of ¹³α values determined for AOM in marine and brackish environments and in laboratory studies (1.009–1.039, Whiticar and Faber, 1986; Holler et al., 2009; Knittel and Boetius, 2009). The hydrogen isotopic fractionation factors ²α (1.033–1.057) determined for Lake Willersinnweiher were substantially lower than ²α modelled for aquatic environments and found in in vitro experiments (1.109–1.315, Whiticar and Faber, 1986; Alperin et al., 1988; Holler et al., 2009). It is important to mention that natural systems might differ significantly from modelled conditions and in vitro experiments, thus leading to discrepancies in isotopic fraction factors. Furthermore, it must be noted that isotopic fractionation factors of AOM determined from in situ isotopic signatures, as in the case of Lake Willersinnweiher, have to be considered with caution since AOM and methanogenesis might overlap in the sediment and carbon isotope equilibrium effects caused by forward and backward AOM influence the isotopic composition of the CH₄ pool in opposite ways (Holler et al., 2009; Yoshinaga et al., 2014; Chang et al., 2019). A study by Wegener et al. (2021) furthermore showed, that the accumulation of ¹³C and ²H-depleted CH₄ in zones of AOM was driven under low sulfate conditions (similar to SO₄ ²⁻ concentrations found in lake Willersinnweiher) because of intracellular reactions associated with the enzymatic AOM mechanism. They found that the reactions in the enzymatic AOM pathway became more reversible and thus closer to equilibrium at low SO₄ ²⁻ conditions driving the formation of ¹³C and ²H depleted CH₄. The lack of a clear enrichment in the heavier isotopes of CH₄ in sediment zones where AOM is presumed to occur in Lake Willersinnweiher might therefore be resulting from the above-mentioned isotopic effects.

Due to AOM in the lake sediment, the diffusive release of CH₄ at the sediment-water interface is reduced in Lake Willersinnweiher (Kleint et al., 2021). Our concentration depth profiles of CH₄ in the sediment show a decreasing gradient towards the sediment water interface, caused by CH₄ diffusion into the bottom water and most likely AOM. Significant decreases in sedimentary CH₄ concentrations observed particularly at the slope and littoral site were suggested to be related to AOM as they coincided with an enrichment in ¹³C-CH₄ and ²H-CH₄ (Figures 4D, 5D). Methane diffusion from the sediment into the bottom water significantly elevated hypolimnic CH₄ concentrations (up to 74 µmol L⁻¹ at the pelagic site). The negative isotope values of hypolimnic CH₄ of −77‰ and −309‰ for δ¹³C-CH₄ and δ²H-CH₄ values, respectively, during the stratification period (Figure 3A) fell well within the range of δ¹³C-CH₄ and δ²H-CH₄ values found in sediment depths where anaerobic methanogenesis is presumed to occur, hence suggesting anaerobic CH₄ production in the sediment as its origin.

During the mixing period, shifts towards more positive δ¹³C-CH₄ and δ²H-CH₄ values in the upper sediment at the pelagic and littoral site suggested the occurence of AOM in the sediment (Figures 3J, 5J). Furthermore, decreasing CH₄ concentrations and increasing SO₄ ²⁻ concentrations towards the sediment surface might be indicative of the occurrence of sulfate-dependent AOM (Figures 3J,K, 5J,K). The apparent lack of S²⁻ accumulation in the sediment might be caused by re-oxidation of sulfide to sulfate via manganese oxides in the sediment pore-water as described by Kleint et al. (2021). The determined fractionation factors associated to AOM during the mixing period (1.051–1.087 for ¹³α and 1.015–1.169 for ²α, Table 1) do not reflect typical fractionation factors for AOM, however as discussed above, these fractionation factors have to be considered cautiously as different isotopic effects can influence the isotopic composition of CH₄ in the SMTZ. Furthermore, a mixture with other CH₄ sources, e.g., groundwater CH₄ input, might affect the carbon and hydrogen isotopic composition of sedimentary CH₄ since mixing of groundwater and sedimentary CH₄ might lead to an increase in sedimentary δ¹³C-CH₄ and δ²H-CH₄ values due to the very enriched ¹³C and ²H isotopic composition of groundwater CH₄. AOM most likely reduced the release of CH₄ at the sediment-water interface, however diffusion from the uppermost sediment layers into the bottom water layer caused elevated CH₄ concentrations in the bottom water.

During the stratification period, a strong increase in the isotopic composition of CH₄ (δ¹³C-CH₄ values of −35‰ and δ²H-CH₄ values of −72‰, Figure 3A) along with a decrease in CH₄ concentrations at the bottom of the oxycline in the water column compared to surface water CH₄ suggested MOx of sedimentary released CH_4. The enrichment in the δ¹³C-CH₄ and δ²H-CH₄ signal is caused by the preference of methanotrophic organisms to metabolize light atoms ¹²C and ¹H of CH₄, leading to an enrichment in ¹³C-CH₄ and ²H-CH₄ of the remaining CH₄ (Silverman and Oyama, 1968; Barker and Fritz, 1981; Coleman et al., 1981). From the 2-dimensional isotope plot it can be inferred that MOx occurs in the metalimnion during the stratification period since the metalimnic stable isotope data are distributed along a gradient showing a stronger enrichment of ²H compared to ¹³C during MOx with a C:D ratio of 9.5 (Figure 7). This observation fits well within similar reported C:D ratios during MOx ranging between 5.9 and 14.9 (Coleman et al., 1988; Kinnaman et al., 2007; Powelson et al., 2007; Feisthauer et al., 2011; Wang et al., 2016). In comparison, epilimnic water samples plot did not show this progression, hence implying that δ¹³C-CH₄ and δ²H-CH₄ values there are most likely not or less affected by MOx.

The carbon isotopic fractionation factor ¹³α of 1.009 determined for the observed enrichment in Lake Willersinnweiher furthermore suggested the occurrence of MOx at this depth as it is in the range of ¹³α determined for MOx in experimental studies (1.003–1.039; Templeton et al., 2006). The estimated ²α of 1.057 on the other hand is substantially lower than values determined for MOx in closed cultures (1.103–1.325; Alperin et al., 1988). However, a higher ²α than ¹³α (factor of ∼9.5) at Lake Willersinnweiher confirms the larger isotopic fractionation generally observed for stable hydrogen isotopes compared to stable carbon isotopes during microbial oxidation. The isotopic partitioning between hydrogen isotopes is greater than between carbon isotopes because of a larger mass difference between ²H and ¹H than between ¹³C and ¹²C (e.g., Wang et al., 2016). This leads to a stronger enrichment in hydrogen isotopes than in carbon isotopes during oxidation.

The zone of MOx at the oxic-anoxic interface in Lake Willersinnweiher during the stratification period acts as a barrier and effectively limits the release of sedimentary produced CH₄ into the surface mixed water layer to minimum concentrations (Kleint et al., 2021). The occurrence of MOx at the bottom of the oxycline indicated by maximum δ¹³C-CH₄ and δ²H-CH₄ values suggests that CH₄ oxidizing bacteria are most active at low O₂ levels and their presence is restricted as O₂ concentrations rise in the upper water body (Schubert et al., 2010; Thottathil et al., 2019). At the littoral site, the isotopic composition of the water column agrees well with sedimentary δ¹³C-CH₄ and δ²H-CH₄ values, suggesting that MOx did not occur here. The apparent absence of MOx at the littoral sampling site might be caused by fully oxygenated conditions in the shallow water column. Another controlling factor of MOx might be the availability of light in the photic zone of the water column. Murase and Sugimoto (2005) showed that MOx was inhibited under light conditions, whereas a linkage between a light driven supply of O₂ through photosynthesis and MOx was found in a study by Oswald et al. (2015), implying that MOx is dependent on light availability.

MOx leads to the formation of CO₂, which is converted to HCO₃ ⁻ according to the bicarbonate buffer system due to a prevailing pH of 8.5–7.3 in the water column of the lake. This contributed to an increase in DIC concentrations in the metalimnion, which was accompanied by decreasing δ¹³C-DIC values (Figure 3C) caused by CH₄ oxidizing organisms and their preference for ¹²CH₄ consumption leading to the production of ¹²C enriched DIC. However, increased DIC concentrations might also originate from the degradation of organic matter. Organic material is generally characterized by relatively negative δ¹³C values, consequently causing the trend to more negative δ¹³C-DIC values with depth as degradation proceeds and inorganic carbon is released from the sediment into the water column.

During the mixing period, constant CH₄ concentrations as well as similar δ¹³C-CH₄ and δ²H-CH₄ values in the water column, except between a depth of 12 and 15 m, where stable isotope values of CH₄ became more enriched, did not suggest MOx (Figure 3G). Since almost the entire water column was fully oxygenated, this might have prevented efficient MOx as methane oxidizing bacteria were found to be sensitive to high O₂ concentrations (Thottathil et al., 2019). However, MOx could still have occurred in the lake water column in the absence of O₂, δ¹³C-CH₄ and δ²H-CH₄ gradients due to mixing and thus might contribute to CH₄ enriched in ¹³C and ²H during the mixing period compared to the stratification period. Plotting δ¹³C-CH₄ values against δ²H-CH₄ values further suggests the occurrence of MOx during the mixing period as the data points show a distribution along the gradient of isotope enrichment (Figure 7). Beyond this the enrichment in ¹³C and ²H of lake water CH₄ during the mixing period (δ¹³C-CH₄ values of −39‰ and δ²H-CH₄ values of +11‰) compared to lake water values from the stratification period, the enrichement might also have originated from the input of groundwater CH₄ since inflowing and outflowing groundwater recorded extremely positive δ¹³C-CH₄ and δ²H-CH₄ values (Table 3). Groundwater CH₄ might therefore have constituted an important source to lake water CH₄ during the mixing period and contributed to the shift towards more positive δ¹³C-CH₄ and δ²H-CH₄ values of lake water during the mixing period, when CH₄ concentrations in the water column were much lower compared to the stratification period and the relative importance of groundwater on lake water CH₄ thus increases.

During the stratification period, fully oxygenated conditions in the epilimnion of Lake Willersinnweiher likely prevented efficient MOx in the upper water column, thus leading to the accumulation of CH₄ in the surface mixed water layer. The surface water of Lake Willersinnweiher with CH₄ concentrations ranging from 0.3 to 0.6 µmol L⁻¹ during the stratification period was oversaturated compared to the atmosphere, since water in equilibrium with the atmosphere shows CH₄ concentrations of ∼3 nmol L⁻¹ (Wiesenburg and Guinasso, 1979).

During the stratification period, the δ¹³C-CH₄ and δ²H-CH₄ values of CH₄ in the pelagic surface water were around −56‰ and −270‰, respectively. These values were significantly different from hypolimnic δ¹³C-CH₄ values of −77‰ and δ²H-CH₄ values −323‰. This difference raises the question for the source of CH₄ supersaturation in the surface water layer (Figure 8A). The isotopic signatures of surface water CH₄ is likely altered by the mixing of different CH₄ pools, e.g., through littoral and vertical input, ebullition, groundwater interactions and internal oxic CH₄ production (e.g., Tang et al., 2016; Hartmann et al., 2020).

Vertical input of CH₄ from the sediment is strongly reduced in the lower metalimnion through MOx (Figure 3A). However, sedimentary CH₄ might still migrate into the upper water layer and become enriched in ¹³C and ²H through MOx, resulting in less negative surface water δ¹³C-CH₄ and δ²H-CH₄ values compared to hypolimnic values. Transport of CH₄ from the littoral sediment to pelagic lake areas comprises an important source especially in small lakes with organic rich littoral zones, where CH₄ deriving from the sediment can be distributed in the surface water layer of the entire lake through turbulences, e.g., induced by wind activity (Tang et al., 2014). As thermal stratification builds up in the Lake Willersinnweiher, around 0.3 µmol L⁻¹ higher CH₄ concentrations can be observed in the littoral area of Lake Willersinnweiher than in the epilimnion of the pelagic and slope sites during the stratification period. Sediments in the littoral zone are usually not isolated through thermal stratification from the overlying water column compared to pelagic sites, thus often resulting in higher CH₄ concentrations in littoral waters (Loken et al., 2019). Higher sediment temperatures and disruption by waves fuel CH₄ production and release in the littoral zone during summer (Hofmann et al., 2010). A similar pattern of spatiotemporal CH₄ distribution was observed in other lakes and highlights the importance of the littoral area considering CH₄ emission to the atmosphere (Wang et al., 2006; Tsunogai et al., 2020). During maximum stratification, the isotopic CH₄ pattern of littoral surface water showed a δ¹³C-CH₄ value of −51‰ which is different from the values observed for the pelagic and slope sites (δ¹³C-CH₄ value of −56‰), whereas δ²H-CH₄ values were rather similar around −265‰, suggesting that sources of CH₄ in the surface water might differ between the littoral and deeper sites (Figure 8A). However, it is possible that mixing of littoral and vertical CH₄ input caused the observed more negative isotopic values of surface water CH₄ in the pelagic zone of the lake compared to the littoral area. A further potential source of CH₄ in the surface water layer of aquatic system is oxic CH₄ production despite the long-standing paradigm defining methanogenesis as a process occurring only under anoxic conditions (Grossart et al., 2011; Tang et al., 2014, 2016; Donis et al., 2017; Günthel et al., 2019; Hartmann et al., 2020; Thottathil et al., 2022). In Lake Willersinnweiher, CH₄ in the oxic upper water column peaked at a water depth of 6 m during the stratification period, which was accompanied by an increase in the δ¹³C-CH₄ and δ²H-CH₄ values to −48‰ and −183‰, respectively, compared to surface water δ¹³C-CH₄ values of −57‰ and δ²H-CH₄ values of −269‰ (Figure 3A). Although the isotopic signature of CH₄ produced in the oxic water column is hitherto unknown, Hartmann et al. (2020) proposed that oxic CH₄ production might cause an enrichment in ¹³C in the CH₄ pool in the lake surface layer. More recently, δ¹³C mass balance estimates by Thottathil et al. (2022) supported this finding by stating that CH₄ produced from oxic sources is relatively enriched in ¹³C compared to anoxic sources with δ¹³C-CH₄ values ranging between −64 and −38‰. More positive δ¹³C-CH₄ values in the surface mixed layer compared to sedimentary δ¹³C-CH₄ values have also been found in other oxic lakes such as Lake Stechlin (−50‰; Tang et al., 2014), Lake Cromwell (−40‰; Bogard et al., 2014) and Lake Lugano (−55‰; Blees et al., 2014). These isotopic values are in line with the observed increase in δ¹³C-CH₄ values to around −48‰ in the upper metalimnion during the stratification period in Lake Willersinnweiher. The slight enrichment in ¹³C might be due to different precursors and pathways of in situ oxic CH₄ production compared to anoxic methanogenesis and/or an interplay of co-occurring MOx. (Donis et al., 2017). Beyond δ¹³C-CH₄ values, better constraints on δ²H-CH₄ values of oxic CH₄ production would assist in the characterization of in situ produced CH₄ in the oxic environment as well as the possible influence of MOx in the observation of enriched stable isotope values of CH₄.

The exact pathways of CH₄ formation in the oxic water column are not fully understood to date. However recently, Ernst et al. (2022) suggested a reaction mechanism for CH₄ formation associated to the interaction of reaction oxygen species with free iron and methylated sulfur and nitrogen compounds occurring on a cellular level across all living organisms and that increasing the level of oxidative stress enhanced the production of CH₄. Moreover, it has been discovered that cyanobacteria produce CH₄ (Bižić et al., 2020b) and that light as well as temperature yield a significant control over oxic CH₄ production rates by influencing phytoplankton communities (Klintzsch et al., 2020). Furthermore, the role of submerged macrophytes for oxic methane production has so far been ignored, but might also contribute significantly (Hilt et al., 2022). Hence, oxic CH₄ production is most likely closely coupled to primary production, potentially contributing to an increase in CH₄ concentrations in the surface water layer during the stratification period as it was also observed at Lake Willersinnweiher. A peak in chlorophyll-α co-occurring with maximum CH₄ concentrations in the upper metalimnion at Lake Willersinnweiher might support a linkage between CH₄ production and algal activity as proposed already in other studies (Grossart et al., 2011; Bogard et al., 2014; Tang et al., 2016; Hartmann et al., 2020; Thottathil et al., 2022). Nevertheless, Donis et al. (2017) suggested that the accumulation of CH₄ at the thermocline can be caused by physical processes in the water column and the highest production rates of CH₄ can be found in the surface water layer.

Beyond the 2-dimensional stable isotope approach, we applied a novel stable isotopic indicator ∆ ( 2,13 ) introduced by Tsunogai et al. (2020) which corrects for fractionation effects caused by CH₄ oxidation, to isotopically characterize different sources of CH₄ to the lake and disentangle the sources of CH₄ to the lake surface water layer. Since the Δ(2,13) indicator has been introduced only recently more research is necessary to reliably assess its strengths and weaknesses to constrain CH₄ sources and sinks in aquatic systems. Hence, we only briefly discuss the application of this parameter in this section (for a more detailed description see Supplementary Annotations A1). ∆ ( 2,13 ) values of the surface water layer showed good agreement at the pelagic and slope site (266 ± 4‰ and 260 ± 5‰, respectively) but differed distinctively from the littoral water column and sediment (214 ± 2‰ and 219 ± 33‰) (Supplementary Figure S2A). This might imply a different CH₄ source to the pelagic and slope surface water layer compared to the littoral site, making littoral input as the main CH₄ source in the entire lake surface water layer unlikely and potentially indicating internal oxic CH₄ production as an important source during the stratification period. However, it is important to note that ∆ ( 2,13 ) only corrects for the fractionation effects caused by CH₄ oxidation and does not account for fractionation due to mixing of different CH₄ sources. Hence, mixing of vertically migrating sedimentary CH₄ and littoral CH₄ input might cause the observed shift in the epilimnic ∆ ( 2,13 ) values of the pelagic and slope site compared to the littoral site.

Infiltrating groundwater might further contribute to CH₄ supersaturation in the surface water layer of Lake Willersinnweiher and most likely influenced lake water CH₄ during the entire year due to the lake’s direct accessibility to the upper aquifer and high groundwater CH₄ concentrations around 1 µmol L⁻¹ (Wollschläger et al., 2007). Possibly, groundwater CH₄ yielding less negative δ¹³C-CH₄ and δ²H-CH₄ values could also have contributed to the observed enrichment in ¹³C and ²H at the upper thermocline. So far the origin of the groundwater CH₄ remains unclear and different possibilities have been proposed to explain the source of CH₄ in the inflowing groundwater and its unusually positive isotopic signature including CH₄ production in a contamination site through oxidative biodegradation of hydrocarbons such as volatile chlorinated organic compounds, in organic-rich sediments from old branches of the Rhine river or in aquifers located upstream of Lake Willersinnweiher (Wollschläger et al., 2007; Kleint et al., 2021). Only limited data about groundwater CH₄ concentrations and δ¹³C-CH₄ values are available to date and groundwater that enriched in ¹³C-CH₄ and ²H-CH₄ seems to be only a rare occurrence (Schloemer et al., 2016). The highly enriched isotopic values of infiltrating groundwater might point to intense AOM since the groundwater is suboxic. The oxidation might therefore be coupled to the reduction of other electron acceptors such as nitrate, nitrite, manganese and iron (Kleint et al., 2021). Methane oxidation causing the highly enriched isotopic composition of groundwater CH₄ might also be supported by the 2-dimensional isotope plot, revealing a distribution of inflowing and outflowing groundwater along the gradient of CH₄ oxidation at Lake Willersinnweiher (Figure 7).

Mixing of lake and groundwater might lead to a change towards more positive isotope values in the lake water column, however the impact of groundwater CH₄ on lake water CH₄ is hard to estimate based on the current dataset and more detailed research concerning groundwater CH₄ in the area of Lake Willersinnweiher is desirable. Due to lower primary productivity and lower CH₄ concentrations in the lake during the mixing period we suggest that groundwater input might be an important source of CH₄ to the lake especially during the mixing period. This might also contribute to the less negative isotopic composition of lake water CH₄ observed during the mixing period (Figures 3G, 4G, 5G).

Supersaturation of CH₄ in the surface water leads to CH₄ release into the atmosphere during the stratification period. Additionally, the surface water was also oversaturated with CH₄ during the mixing period (70 nmol L⁻¹, Figures 3G, 4G, 5G), highlighting that Lake Willersinnweiher emits CH₄ all year round. Methane can be emitted via plant-mediated processes, diffusion or ebullitive transport (Bastviken et al., 2004), however since plant-coverage at Lake Willersinnweiher is negligible, plant-mediated release of CH₄ to the atmosphere is considered to be of minor importance. Methane emitted via diffusion from the surface water into the atmosphere showed a great range in the isotopic composition over 1 year with most positive values found at the three investigated sites during the mixing period (δ¹³C-CH₄ of −42 to −37‰ and δ²H-CH₄ of +1 to +26‰) and distinctively lower values observed during the stratification period (δ¹³C-CH₄ of −59 to −51‰ and δ²H-CH₄ of −310 to −195‰, Table 2). These isotopic values reflect the isotopic composition of lake surface water, which is enriched in the heavier isotopes during the mixing period. Especially during the mixing period, ¹³C-CH₄ and ²H-CH₄ were much more enriched compared to previously reported values (e.g., from Thottathil and Prairie, 2021 ranging from −58.8‰ to −43.5‰), highlighting the potential impact and importance of diffusive CH₄ emissions from lakes with similar properties, such as high sulfate concentrations, for regional and/or global isotope source apportionment studies.

We found that in Lake Willersinnweiher, δ¹³C-CH₄ and δ²H-CH₄ values of CH₄ released via ebullition displayed temporal and spatial disparities (Figure 8). At the deeper sampling site, CH₄ transported via ebullition yielded more negative δ¹³C-CH₄ values (−64 ± 11‰) when compared to δ¹³C-CH₄ values at the littoral site (−50 ± 12‰ during the mixing period in November 2021). These differences in the isotopic composition were most likely induced by CH₄ formation taking place mainly via the hydrogenotrophic and acetoclastic pathways at the slope and littoral sites, respectively, as discussed above. Ebullition plays a particularly important role in the littoral area of aquatic systems since the potential for CH₄ transported via gas bubbles rises to reach the surface water with decreasing water depth. In particular, CH₄ release to the atmosphere via ebullition likely represents an important pathway and has been found to vary significantly spatially and temporally (West et al., 2016; Thottathil and Prairie, 2021). Interestingly, δ²H-CH₄ values only show small differences between the littoral and slope site at Lake Willersinnweiher (326 ± 4‰ for the littoral site and 318 ± 1‰ for the slope site, Figure 8B). In previous studies, changes in the δ²H-CH₄ values of CH₄ emitted via ebullition were attributed to changes in the δ²H values of water (e.g. due to evaporation in shallow lakes), which is a hydrogen source for methanogens (Wik et al., 2020). As Lake Willersinnweiher is a distinctively deeper lake (average depth of 8 m), this effect might only play a minor role and therefore have a smaller influence on δ²H-CH₄ values. However, Douglas et al. (2021) showed that even though the δ²H-H₂O values highly influenced δ²H-CH₄ values, other processes such as methane oxidation and the type of the methanogenic pathway might also contribute to the isotopic composition of CH₄. Furthermore, sulfate-dependent AOM in the sediments of lake Willersinnweiher might play an important role regarding the isotopic composition of CH₄ released via ebullition and therefore might affect δ¹³C-CH₄ values and to a lesser extent δ²H-CH₄ values (Wegener et al., 2021). However, the influence of AOM is hard to estimate as AOM most probably takes place heterogeneously throughout the sediment. In November, when there is less organic matter input than in September (which is also indicated by the lower CH₄ concentrations within the gas bubbles, Supplementary Table S2), pockets of CH₄ within the sediment might be subject to heterogeneously occurring AOM, which might contribute to the relatively high variability of δ¹³C-CH₄ values. During the uprise of gas bubbles in the water column, CH₄ partly dissolves into the water (e.g. McGinnis et al., 2006). However, isotope fractionation associated with dissolution of CH₄ was found to be small and most likely lower than the variability of the measured isotope values (Fuex, 1980; Bergamaschi, 1997). Additionally, the surface water layer showed isotopic values enriched in ¹³C and ²H compared to the gas bubbles (δ¹³C-CH₄ of −56‰ and δ²H-CH₄ of −270‰ for lake surface water and δ¹³C-CH₄ of −64 ± 11‰ and δ²H-CH₄ of −318 ± 1‰ for ebullitive CH₄). We therefore conclude that ebullition is not the main source of surface water CH₄ supersaturation in the pelagic area of the lake.