For the slurry incubation experiment, samples were taken on three occasions (in March, April and May 2018) from 12 of the 13 sampling sites within the lake from three transects covering multiple water depths (<50, <100, <125 and <150 cm) (see Fig. 1). On each sampling date, 4 of the 12 sampling sites were chosen randomly as it was not possible to set up the experiment with all samples at once. At the sampling dates, measured air, water and sediment temperatures at the sampling dates were 7.7, 5.6 and 5.2 ∘C (March), 13.8, 15.1 and 10.1 ∘C (April), and 23.9, 23.6 and 13.8  ∘C (May), respectively. Sediment samples were taken in duplicates with a gravity corer (UWITEC, Mondsee, Austria) from a boat in 60 cm long PVC tubes and transported in an insulated box at ∼5 ∘C. The next day, sediment cores were cut with a core cutter in the laboratory in segments of 5 cm thickness (0–5 and 5–10 cm sediment depth). Duplicate samples were homogenized, and then 20 g of each sediment was filled into 120 mL crimp vials containing 20 mL lake water, after which the vials were closed with a butyl rubber stopper and aluminum crimp cap. Samples were flushed with N2 for 30 min in order to remove any remaining oxygen from the water and headspace, and then they were preincubated for one week so they were fully anoxic. They were again flushed with N2 prior to the actual incubation. Slurry incubations were set up in triplicates and maintained at 25 ∘C (corresponding to maximum measured in situ sediment temperatures in summer 2018) in the dark. During each run, one set of parallel samples was incubated at 10 ∘C in order to determine a Q10 value for CO2 and CH4 production rates.

The remaining sample material was freeze-dried (Alpha 1–4 LDplus, Christ, Osterode, Germany), ground with a ball mill (Mixer Mill MM 400, Retsch, Haan, Germany) and used for solid-phase analyses, as outlined below.

Freeze-dried and ground sediment samples were analyzed for total C and N concentrations and stable isotopes using isotope-ratio mass spectrometry (IRMS; EuroVector EA3000 coupled with Nu Instruments Nu Horizon, HEKAtech, Wegberg, Germany) and for OM components using FTIR spectroscopy (Cary 670 FTIR Spectrometer, Agilent, Santa Clara, USA).

For IRMS, 5 mg of sample was weighed out into a tin cup, together with 4 mg of vanadium pentoxide (V2O5). The combustion and reduction furnaces were set to 1000 and 650 ∘C, respectively, and the resultant gaseous compounds were quantified by IRMS. Results are provided in percent (%) by mass for C and N contents (precision <1 % for C and <0.1 % for N) and in per mill (‰) vs. VPDB/AIR (Vienna Pee Dee Belemnite; atmospheric N2) for C and N isotopic signatures (precision <0.05 ‰ for 13C and <0.5 ‰ for 15N). For isotope analyses, appropriate certified reference materials were used: IAEA 600 (δ13C = -27.77 ‰; δ15N = 1.0 ‰) and BBOT (2.5-Bis-(5-tert.-butyl-2-benzo-oxazol-2-yl)thiophen; HEKAtech, Wegberg, Germany), birch leaf, wheat flour and sorghum flour standards (IVA Analysetechnik e. K., Meerbusch, Germany) as working standards covering a range of -27.5 ‰ to -13.68 ‰ for 13C and -0.6 ‰ to 2.12 ‰ for 15N.

Functional groups of OM compounds were identified by FTIR spectroscopy. For this purpose, 2 mg of freeze-dried sample was ground together in a mortar with 200 mg KBr (potassium bromide), pressed into 13 mm pellets and analyzed. Each sample was scanned from 599 to 4000 cm-1 with a resolution of 2 cm-1 and was baseline corrected. Distinct peaks at specific wavelengths were assigned to functional groups according to Artz et al. (2008) and normalized to the peak intensity at 1031–1035 cm-1 (indicative of polysaccharides) in order to obtain intercomparable peak ratios of functional moieties in all samples, as FTIR spectra only provide information about the relative abundance of certain functional moieties in one sample.

Potential CO2 and CH4 productions rates were determined by measuring the increase in concentration of CO2 and CH4 in the incubation vials over time. Concentrations were obtained by analyzing the headspace at the beginning of the experiment (t0) and after 1, 3, 8, 11, 14 and 18 d (t1–t6). Samples were taken from the vial with a 10 mL polypropylene syringe equipped with a three-way stopcock and a 0.6 mm needle. Before each sampling, the pressure inside the vial was determined with a pressure sensor (GMH 3110, Greisinger, Regenstauf, Germany), and the syringe was flushed three times with N2. Then 2 mL of N2 was left in the syringe before the needle was stabbed through the vial's stopper, whereby the N2 was added to the headspace and mixed, and, subsequently, 2 mL of the sample was taken from the vial so that the volume inside the vial remained constant. The gas samples were analyzed for CO2 and CH4 concentrations with a gas chromatograph (8610 GC-TCD/FID, SRI Instruments, Torrance, USA) equipped with a flame ionization detector (FID) and methanizer to simultaneously measure CO2 and CH4. Before every sampling day, the gas chromatograph was calibrated with standard gas mixtures of known concentrations (CO2: 385, 5000 and 50 000 ppmV; CH4: 5, 1000 and 50 000 ppmV).

First, measured concentrations (in ppmV) were pressure corrected and converted using the ideal gas law: 1n=(p⋅V)/(R⋅T), where n is the amount of substance (in mol), p is the gas partial pressure (in atm), V is the headspace volume (in L), R is the ideal gas constant (0.082 L atm mol-1 K-1) and T is the laboratory temperature (in K).

Total CO2 and CH4 concentrations in the gas and water phase in the incubation vials were calculated from headspace concentrations using Henry's law: 2c=Kh⋅p, where c is the concentration in the water phase (in mol L-1), Kh is the temperature-dependent Henry constant (CO2, 25 ∘ = 0.0339 mol L-1 atm-1; CH4, 25 ∘C = 0.00129 mol L-1 atm-1; Sander, 2015) and p is the gas partial pressure (in atm).

Moreover, CO2 concentrations were pH corrected in order to obtain pH-independent values for total CO2 concentrations using the Henderson–Hasselbalch equation and equilibrium constants according to Stumm and Morgan (1995): 3nΣCO2=nwater⋅10pH-6.4+(nwater⋅10pH-6.4)⋅10pH-10.25, where nΣCO2 is the pH-corrected CO2 amount (in mol) and nwater is the calculated amount of CO2 in the water phase (in mol).

Finally, production rates were calculated by linear regression (R2>0.8 for CO2 and R2>0.9 for CH4) from concentration change in gas and solute phase over time.

To evaluate the effect of temperature on CO2 and CH4 production, we calculated Q10 values, describing the relative increase of production rates with an increase in temperature of 10 K (Fenchel et al., 2012): 4Q10=(R2/R1)[10/(T2-T1)], where R2 is the production rate at T2 (25 ∘C) and R1 is the production rate at T1 (10 ∘C).

In order to calculate the thermodynamic energy yield for hydrogenotrophic and acetoclastic methanogenesis, we measured H2 concentrations at the beginning, after 8 d (t3) and at the end of the experiment, and we measured acetate concentrations at the beginning and at the end of the incubation. The thermodynamic energy yield, expressed as Gibbs free energy, was calculated using the Nernst equation and total dissolved and gaseous concentrations of educts and products in the incubation vials as described in Beer and Blodau (2007): 5ΔGr=ΔGr0+R⋅Tln⁡(Πi(products)vi/Πi(educts)vi).

By calculating the Gibbs free energy (ΔGr), it is possible to evaluate whether these processes are feasible under given conditions. In order for each reaction to occur, a theoretical threshold of ΔGr=-20 to -25 kJ mol-1 had to be exceeded (Schink, 1997; Conrad, 1999; Blodau, 2011).

For H2 concentration measurements, 2 mL of sample was taken from the incubation headspace with a syringe and needle and replaced with the same amount of N2. Samples were analyzed with a reduction gas detector (RGD) hydrogen and carbon monoxide analyzer (ta3000R Gas Analyzer, Ametek, Pittsburgh, USA) that was calibrated with gas standards of 5, 25 and 50 ppmV H2. Measured H2 concentrations were corrected for pressure and converted into dissolved concentrations using Henry's law (Kh(H2, 25 ∘C) = 0.00078 mol L-1 atm-1; Sander, 2015) analogous to CO2 and CH4.

Acetate concentrations were determined through ion chromatography with chemical suppression (883 Basic IC plus, Metrohm, Filderstadt, Germany; A Supp 5 column, Metrohm, Filderstadt, Germany). Aqueous samples were filtered with 0.45 µm nylon plus glass microfiber syringe filters (Simplepure, BGB Analytik, Rheinfelden, Germany) and kept frozen at -21 ∘C until analysis.

To quantify alternative EAs that could support anaerobic respiration and potentially suppress methanogenesis in anoxic incubations, we measured nitrate (NO3-), sulfate (SO42-), ferric iron (Fe3+), and the EAC and EDC of the OM (EACOM and EDCOM) at the beginning and the end of the slurry incubation.

As the analysis of EACOM and EDCOM is only possible on finely ground materials, thus providing potential capacities rather than true in situ capacities, we set up a second set of slurry incubations for a sediment depth of 0–5 cm with samples from 10 sites (all except 3.50 and 3.100) using 0.4 g of the freeze-dried sediment material and 100 mL of Milli-Q^® water. Slurry incubations were set up in six replicates, flushed with N2, preincubated and stored analogously to the first set of slurry incubations. Samples were analyzed at the beginning and at the end of the experiment since at every sampling occasion, three of the replicates had to be sacrificed (destructive sampling). Prior to analysis, samples were transferred into a glovebox (O2 <1 ppm; Innovative Technology, Amesbury, USA) to avoid alteration of the samples' redox state.

EACOM and EDCOM were measured using chronoamperometry (CHI1000C, CH Instruments, Austin, USA) by mediated electrochemical reduction (MER) and oxidation (MEO) (Aeschbacher et al., 2010; Klüpfel et al., 2014). The cell consisted of a cylindrical glassy C working electrode, a platinum wire counter electrode in a ceramic glass frit and an Ag/AgCl reference electrode. Cells were filled with 10 mL of 0.01 M MOPS and 0.1 M KCl buffer to stabilize the pH at 7 and were continuously stirred during measurement. To facilitate electron transfer, organic mediators were added to the buffer: 180 µL DQ (diaquat dibromide monohydrate; Sigma-Aldrich) for MER and 180 µL ABTS (2,2′-azino-bis(3-ethylbenzthiazoline-sulfonic acid), Sigma-Aldrich) for MEO at a potential of Eh=-0.69 V and Eh=+0.41 V, respectively (reported vs. the standard H2 electrode but experimentally measured vs. the Ag/AgCl reference electrode). To determine the electron transfer, 100 µL of suspended samples were added to the buffer solution (Lau et al., 2015) which resulted in an increase of the current, recorded as a peak in the analysis software. After ∼30 min, when the baseline was reached again, the next sample was added to the cells. Samples were analyzed in duplicate. The electron transfer was calculated with the Nernst equation and normalized to the C content in the samples (Lau et al., 2015): 6EACOM(EDCOM)=peakarea/(V⋅F⋅C), where V is the sample volume (in µL), F is the Faraday constant (96 485 A sec/mol e-) and C is the C content (in mg L-1) (EACOM and EDCOM in µmol e- gC-1; peak area in µA seconds).

EACOM and EDCOM had to be corrected for either ferric iron (Fe3+) or ferrous iron (Fe2+) and sulfide (S2-) concentrations, respectively, since with the applied potential, Fe3+ would be reduced and Fe2+ and S2- would be oxidized (Lau et al., 2015; Agethen et al., 2018).

Fe2+, Fe3+ and S2- were determined colorimetrically (Gilboa-Garber, 1971; Tamura et al., 1974) with a spectrophotometer (Cary 100 UV-Vis, Agilent, Santa Clara, USA). Because 1,10-phenanthroline can only detect Fe2+, the Fe3+ in the samples was reduced to Fe2+ with 10 % ascorbic acid. Ferric iron was thus determined as the difference of total Fe and ferrous iron in the samples.

NO3- and SO42- concentrations were determined with ion chromatography (IC), as described above. For this purpose, samples were filtered with a 0.45 µm syringe filter, added into micro-centrifuge tubes, retrieved from the glovebox and stored frozen at -21 ∘C until analysis.

Total EAC (EACtot) was calculated as the sum of EACOM and EACinorg (EAC from nitrate, sulfate, ferric iron) considering the respective amounts of electrons transferred during the main pathways of dissimilatory reduction, i.e., assuming a reduction of NO3- to N2, of SO42- to S-2 and of Fe3+ to Fe2+ (Konhauser, 2009): 7EACtot=EACOM+NO3-⋅5e-+SO42-⋅8e-+Fe3+⋅1e-.

Assuming reversibility of electron transfer to and from OM, EACOM and EDCOM correlate with each other. If EACOM decreases, EDCOM increases equivalently as quinones are reduced to hydroquinones; in practice, values of EDCOM are potentially biased as MEO does not only capture EDCOM but may also irreversibly oxidize phenolic moieties, which are sensitive to the slightest changes in pH and potentials (Aeschbacher et al., 2011; Walpen et al., 2016, 2018). The discussion will, therefore, focus on EACOM data.

To obtain ex situ CO2 and CH4 gas fluxes and estimate changes in sediment CO2 and CH4 stocks, intact sediment cores (PVC tubes, 60 cm length, 5.8 cm diameter) were taken in triplicate from 4 out of the 12 sites in November 2017 (1.50, 2.100, 3.125, S.150; see Fig. 1). S.150 was chosen as one site to represent sites 1.150, 2.150 and 3.150 from the same lake depth category. Sediment cores were transported cool and deployed in a climate chamber (CLF Plant Master, CLF Plant Climatics GmbH, Wertingen, Germany) at constant conditions (temperature 20 ∘C, humidity 60 %). Cores were taken to ensure that each tube contained a sediment layer with an average thickness of 35 cm which was covered with a lake water column of 20 cm; in the lab, we created a headspace of ∼150 mL. The cores were equipped with eight sampling ports: one in the headspace, one in the water phase and six in the sediment. Of the ports in the sediment, three were used to sample dissolved gases in the sediment, and three were used for sediment pore water extraction. The gas samplers consisted of gas-permeable silicon tubes of 5 cm length and 0.8 cm diameter equipped with a three-way stopcock, modified based on Kammann et al. (2001). This technique allows for the sampling of dissolved gases in the sediment by diffusive equilibration through the silicon membrane. For pore water sampling, a vacuum was applied with a syringe to suction samplers (Rhizon, Eijkelkamp Agrisearch, Giesbeek, Netherlands) of 5 cm length, 0.25 cm diameter and about 0.1 µm pore size (Seeberg-Elverfeldt et al., 2005). Gas and pore water samplers were deployed in average depths of 5.0±2.8, 15.3±2.9 and 23.6±2.1 cm below the sediment surface.

For data analyses, we only used measurements that were made more than 50 d after the deployment of the intact sediment core incubations in the climate chamber. This was done in order to ensure the system had adapted to experimental conditions and had reached a steady state. Steady state conditions were indicated by quasi-constant CO2 and CH4 concentrations in the sediment, as identified by repeated monitoring of dissolved gases.

To determine CO2 fluxes, the cores were closed gas tight with a stopper and connected to a laser-based, portable greenhouse gas analyzer (Los Gatos Research, San Jose, USA), which allowed for the measuring of real-time increases in CO2, CH4 and H2O concentrations in the headspace of the cores with a resolution of 1 Hz. As the headspace was too small for the instrument's flow rate, a gas bag with a volume of 150 mL was interposed between the headspace and the analyzer. The headspace was closed for 10 min, and the diffusive CO2 flux was calculated by linear regression (R2>0.8) using the increase in concentration over time and by the ideal gas law corrected for air pressure and temperature and related to the water surface area: 8F=Δc/Δt⋅(p⋅V)/(A⋅R⋅T), where F is the CO2 flux (in µmol m-2 d-1), Δc/Δt is the slope of the linear regression (in ppm d-1), p is the air pressure (in atm), V is the sum of headspace and gas bag volume (in m3), A is the water surface area (in m2), R is the ideal gas constant (8.2×10-5 m3 atm mol-1 K-1), and T is the temperature (in K).

CH4 fluxes were determined by closing the cores with the stopper for 24 h and taking a gas sample right after closing and then again after 24 h with a syringe from the headspace. CH4 fluxes were calculated according to Bastviken et al. (2004): 9FCH4=k⋅Cw-Cfc, where F is the CH4 flux (in mmol m-2 d-1), k is the piston velocity (in m d-1), Cw is the measured CH4 concentration in the water phase (in mmol m-3) and Cfc is the CH4 equilibrium concentration in the headspace at the given CH4 water concentration.

The piston velocity k was determined as follows: 10k=-ln⁡csat-cend/csat-cstart/Δt⋅V/A⋅Kh⋅R⋅T, where csat is the saturation concentration in the chamber headspace at the measured CH4 water concentration, cend is the measured CH4 concentration in the chamber headspace at the end of the flux measurement and cstart is the measured CH4 concentration in the chamber headspace at the beginning of the flux measurement (all in µatm).

The flux was corrected for the nonlinear increase in CH4 concentration in the headspace over time due to saturation and was divided into diffusive and ebullitive proportions based on the piston velocity (k<2= diffusion, k>2= ebullition).

CH4 and CO2 concentrations in the sediment were obtained from gas-permeable silicon tubes, determined by gas chromatography as described above (Sect. 2.2.3) and calculated by Henry's law using temperature-corrected Henry's constants (see Eq. 4). Measured CO2 concentrations were corrected for pH (Eq. 5).

The storage change of CO2 and CH4 in the sediment was calculated for each depth segment between two sampling ports as the difference of CO2 and CH4 concentrations obtained from silicon gas samples at the beginning and at the end of gas flux measurements: 11ΔCO2=cCO2end⋅Vseg-cCO2start⋅Vseg/Δt,12ΔCH4=c(CH4)end⋅Vseg-cCH4start⋅Vseg/Δt, where ΔCO2 (ΔCH4) is the storage change (in mmol d-1), c(CO2)end/start (c(CH4)end/start) is the CO2 or CH4 sediment pore gas concentration at the end/beginning of the flux measurement (in mmol m-3), and Vseg is the volume of the sediment core segment between two samplers (in m3).

After the completion of flux measurements, intact sediment core incubations were eventually cut into 10 cm slices, freeze-dried and ground for solid-phase analyses, as described above.

The C content in the samples was between 2.2 % and 33.2 % with the lowest values at site 3.50 and the highest at site 1.50. C/N ratios ranged from 11.0 at site 1.150 to 19.1 at site 3.100. Neither the C content nor the C/N ratio showed significant changes with sediment or lake depth, but the C/N ratio was significantly higher in samples taken close to the shore (50) than in samples from the lake center (150) (p<0.01) (see Fig. 2a). C and N isotopic values did not vary much between sites and were on average -27.6 ‰ and -0.6 ‰, respectively.

OM quality as identified by FTIR analysis was dominated by strong absorption features of polysaccharides, lignin, humic acids, phenolic and aliphatic structures, aromatic compounds, and fats, waxes and lipids (see Fig. S1 in the Supplement). Except for lignin, which was not identified at sites 2.50, 2.100, 2.125, 3.50 and 3.100, all components were abundant at all sites. Ranges of peak ratios for each component class can be found in Table 2. Overall, the lowest FTIR peak ratios were present at site 3.50 and the highest at site 3.125, corresponding to the highest and lowest CH4 production rates (see below). All peak ratios correlated with each other. They tended to increase (i.e., indicate more decomposed material) with sediment depth and toward the lake center, but this change was not significant (see Fig. 2b).

Overall, production rates decreased from the shore to the center of the lake. Rates for potential CO2 production at 0–5 cm depth ranged from 10.3±0.0 µmol gC-1 d-1 at site 3.125 to 38.5±2.5 µmol gC-1 d-1 at site 2.100. Potential CH4 production was between 7.3±0.1 µmol gC-1 d-1 at site 3.125 and 33.5±7.2 µmol gC-1 d-1 at site 3.50. Production rates at 5–10 cm depth were always lower compared to the upper sediment layer and were between 7.2±0.1 and 14.7±0.4 µmol gC-1 d-1 for CO2 and between 5.4±0.6 and 14.3±0.3 gC-1 d-1 for CH4. Both CO2 and CH4 production rates showed significant differences between sites (Kruskal–Wallis, p<0.001) and were significantly (Dunn's test, p<0.05) higher at the shore (50+100) than in the center of the lake (125+150) (see Figs. 3, S2 and S3).

CO2 and CH4 production rates decreased with time. CO2 production was highest at the beginning, while CH4 production was impeded and highest only after 3 to 8 d of incubation (see Fig. 4, Table 3). The CO2/CH4 amount ratio constantly decreased during the incubation with a maximum value of 62.1±58.4 at the beginning of the incubation at site 1.125 and minimum values of 1.2±0.0 at the end of the incubation at site 2.50, approaching ratios of 1 as expected under strictly methanogenic conditions (see also Table 3).

Q10 values were between 1.6±0.1 and 2.2±0.1 for CO2 production rates and between 2.7±0.5 and 11.4±1.0 for CH4 production rates.

Sampling dates did not have any impact on production rates, as confirmed by a Kruskal–Wallis test (CH4: p=0.17; CO2: p=0.76).

Neither CO2 nor CH4 production rates exhibited significant correlations with C content, the C/N ratio, δ13C or δ15N, but we found significant negative correlations (p<0.01, ρ<-0.6) between all FTIR peak ratios and CO2 and CH4 production rates, as well as of FTIR peak ratios and Q10 values of CH4 production (p<0.05, ρ=-0.82) (see Fig. 5; for test statistics, see Table S1 in the Supplement).

Both H2 and acetate concentrations increased during the incubation. H2 concentrations were between 0 and 1587.4±170.1 nmol L-1, and acetate concentrations ranged from 219.7±104.3 to 1212.7±11.4 µmol L-1 (see Fig. 6). Gibbs free energy for acetoclastic methanogenesis was between -96.3±0.8 and -66.4±0.3 kJ mol-1, and for hydrogenotrophic methanogenesis it was between -62.4±0.9 and -7.4±0.0 kJ mol-1. Energy yields decreased for the acetoclastic pathway and significantly increased (Mood's median; t0–t6: p<0.05, t3–t6: p<0.001) for the hydrogenotrophic pathway throughout the incubation (see Fig. 6). Energy yields did not differ significantly between lake depths except for the acetoclastic pathway at the end of the incubation (p<0.001) when the energy yield was highest in samples from the center of the lake. Significant differences between all sites were found for the acetoclastic and hydrogenotrophic pathways at the beginning (Kruskal–Wallis, p<0.01) and at the end of the incubation for acetoclastic methanogenesis only (Kruskal–Wallis, p<0.01). H2 concentrations at the end of the experiment exhibited a significant positive correlation with average CO2 (p<0.001, ρ=+0.51) and CH4 (p<0.001, ρ=+0.45) production rates (for test statistics see Table S2). Further, Gibbs free energy of acetoclastic methanogenesis exhibited a significant positive correlation with the C/N ratio (p<0.05, ρ=+0.45) at the end of the experiment. Acetate concentration at the end of the incubation exhibited significant negative correlations with FTIR peak ratios and the C/N ratio (p<0.05, ρ<-0.44). Gibbs free energy of hydrogenotrophic methanogenesis exhibited significant positive correlations with FTIR peak ratios of fats, humic acids, phenolics and C content (p<0.05, ρ>0.17); i.e., a high energy yield was associated with low FTIR peak ratios and C content. Correspondingly, H2 concentrations exhibited significant negative correlations with all FTIR peak ratios and C content (p<0.05, ρ<-0.15) (for test statistics see Table S2).

EACOM was between 218.7±97.2 and 545.7±60.3 µmol e- gC-1 at the beginning and decreased on average by 44.9 µmol e- gC-1 until the end of the slurry incubation. The highest values for EACOM were found at site 3.125 corresponding to the lowest measured CH4 production rates at that site. EACinorg was, with values between 2.9±1.0 and 39.2±4.4 µmol e- gC-1, much lower than EACOM and also decreased during the incubation by a mean of 6.4 µmol e- gC-1. EACtot ranged from 250.8±93.9 µmol e- gC-1 at site 3.150 to 551.4±60.3 µmol e- gC-1 at site 3.125 and decreased from the beginning to the end of the incubation by, on average, 51.2 µmol e- gC-1. EDCOM was between 149.5±26.7 and 462.7±18.6 µmol e- gC-1 at the beginning and between 152.9±53.8 and 370.7±196.2 µmol e- gC-1 at the end of the incubation, showing a slight decrease by, on average, 31.4 µmol e- gC-1. The lowest EDCOM at both the beginning and the end of the incubation was found at site 2.100, corresponding to the highest CO2 production rates there (see Fig. 7).

We further found significant differences for EACOM and EACtot (ANOVA, p<0.001) between all sites with the highest average values at site 3.125 and the lowest at sites 1.125 (t0) and 3.150 (t6) (see Fig. S4). Average CO2 and CH4 production rates exhibited a significant negative correlation with initial EDCOM (p<0.05, ρ=-0.7), whereas we did not find any significant correlation between the production rates and EAC, electron exchange capacity (EEC; sum of EAC and EDC), or the EAC / EDC ratio, although low CH4 production rates were associated with high EAC. Acetate concentration exhibited significant negative correlations with EACOM and EACtot (p<0.01, <0.001, ρ<-0.38). Gibbs free energy of hydrogenotrophic methanogenesis exhibited significant positive correlations with EACOM and EACtot (p<0.05, ρ=0.43). We did not find any significant correlations between EAC or EDC and OM quality parameters except for EDCOM and the FTIR peak ratio indicative of fats, waxes and lipids (p<0.05, ρ=-0.76). Of the inorganic EAs, only total S content in the sediment exhibited a significant negative correlation with CO2 production rates (p<0.05, ρ=-0.45) (for test statistics see Table S1).

Calculated potential CO2 production from prevalent organic and inorganic EAs was always lower than the measured CO2 production in slurry incubations and was between 110.5 and 586.4 µmol CO2eq. gC-1 (see Fig. 8), which could explain 38 % to 91 % of measured CO2 production, whereof 4 % to 51 % were explained by EACOM alone.

Results from the slurry incubation experiment showed that both CO2 and CH4 production rates were – despite its small size - highly variable within the examined lake. CH4 production rates were within the range of previously reported values from lakes in central Sweden, a reservoir in Brazil and in sediments from lakes Stechlin and Geneva in Germany and Switzerland, respectively (Duc et al., 2010; Fuchs et al., 2016; Grasset et al., 2018). CO2 production rates were high compared to rates found in Lake Kinneret in Israel and in the Pantanal and Amazon regions in Brazil, exceeding reported values by a factor of 7 to 100 (Schwarz et al., 2008; Conrad et al., 2011) and supporting the assumption that small lakes generally have higher C turnover rates compared to larger ones.

In all samples, production rates were higher at the beginning of the experiment than toward the end. While CO2 production rates were highest right after the start and then constantly decreased until reaching a plateau around day 8, CH4 production rates peaked after 3 to 8 d and then slowly decreased afterwards, approaching a 1 : 1 CO2:CH4 production ratio. This typically observed three-phase pattern (Yao et al., 1999) might be among other things due to thermodynamic constraints, such as end-product accumulation in the sample vials and subsequent inhibition of respiration and methanogenesis (Beer and Blodau, 2007; Blodau et al., 2011; Bonaiuti et al., 2017). The observed delay in notable CH4 production was expected as prevalent alternative EAs (NO3-, Fe3+, SO42-, humic substances) likely suppressed methanogenic activity (Lovley et al., 1996; Yao et al., 1999; Fenchel et al., 2012).

Both CO2 and CH4 production rates were higher in the topmost sediment layer compared to the 5–10 cm sediment depth, which suggests that the first centimeters of the sediment play a major role in GHG production as a consequence not only of temperature but also of microbial community distribution and changes in OM quality (Falz et al., 1999; Sobek et al., 2009; Wilkinson et al., 2015). This finding corresponded with decreasing C/N ratios and increasing FTIR peak ratios with sediment depth. While sediment age typically increases with depth, the OM quality and, thus, reactivity usually decreases with sediment depth as recalcitrant compounds are not being completely mineralized but are instead residually enriched, buried and preserved in the sediment (Avnimelech et al., 1984; Burdige, 2007; Sobek et al., 2009).

Similar to den Heyer and Kalff (1998), we found higher production rates in samples close to the lake shore in contrast to lower production rates in the center, which suggests either that the input of OM (quantity) in the sediments is higher at the shore sites or that the OM quality is more labile and, therefore, more easily degradable. As we did not find any correlations between CO2 or CH4 production rates and sediment C content as proposed, for example, by Conrad et al. (2011) and Romeijn et al. (2019), we instead suggest that the OM quality rather than quantity might be the determining factor for CO2 and CH4 production.

C/N ratios are frequently used to characterize the degradation state of OM, but we did not find correlations between C/N ratios and CO2 and CH4 production rates in the slurry incubations. Although OM of autochthonous origin was found to fuel higher degradation rates than allochthonous OM (West et al., 2012; Grasset et al., 2018), we found evidence of predominant inputs of allochthonous (terrestrial) material at sites with higher production rates close to the shore (higher C/N ratios), whereas sites with lower production rates in the lake center received mainly autochthonous (aquatic) OM, as indicated by lower C/N ratios (Meyers, 1994). On the other hand, high C/N ratios also indicate a lower degradation state and, therefore, higher degradation potential, whereas low C/N ratios are usually typical of highly decomposed OM having a lower CO2 and CH4 production potential (Malmer and Holm, 1984; Kuhry and Vitt, 1996). These two possibilities of interpreting C/N ratios might be the reason for apparently contradictory findings and the missing relationship between C/N ratios and CO2 and CH4 production rates.

The abundance of recalcitrant OM compounds (lignin, aromatics, humics, phenols and lipids), as indicated by FTIR peak ratios, proved to be a more suitable explanation for observed CO2 and CH4 production patterns, as indicated by strong significant negative relationships between peak ratios and production rates. All FTIR peak ratios indicative of more refractory components increased toward the lake center, which indicated an increasing predominance of more recalcitrant OM with greater distance from the lake shore and corresponded with decreasing production rates from lake shore to center. At first sight, this was unexpected as allochthonous material is known to be richer in recalcitrant compounds like lignin or aromatics compared to autochthonous biomass and, therefore, is effectively buried in lake sediments (Sobek et al., 2009). However, before reaching the sediment, the internally produced material in the lake center must pass through a deeper water column while undergoing degradation processes such that more decomposed OM reaches the sediment (Meyers, 1994; Torres et al., 2011). As this process might not be of the same importance in shallow lakes compared to deeper lakes, we additionally suggest that the more decomposed OM in the lake center might have undergone degradation processes during resuspension and focusing of small particles as a result of wind-induced bed shearing (Mackay et al., 2011). The less decomposed OM close to the shore might further originate from labile aquatic plant substrates growing at the shoreline (Wetzel, 1992; Cole et al., 2007).

To summarize, the OM degradability does not necessarily depend on its origin, and the OM of terrestrial origin is not necessarily more recalcitrant to degradation by aquatic microorganisms in this study. Sites closer to the shore probably received higher rates of terrestrial OM matter that was less decomposed, whereas autochthonous production in the lake center was overall low due to the low nutrient status of the lake and was already undergoing degradation during sedimentation; this likely led to more recalcitrant OM in the sediment. Earlier studies by West et al. (2012) and Grasset et al. (2018) that found allochthonous material to be less decomposable compared to autochthonous matter were conducted in larger lakes where the influence of the watershed was overall much lower than in our case because larger lakes have a lower perimeter to volume ratio. We hypothesize that in small and nutrient-poor lakes, the pattern might be reversed as the system adapts to overall low productivity and a simultaneously high input of terrestrially produced OM.

In accordance with previous studies (den Heyer and Kalff, 1998; Sobek et al., 2009; Gudasz et al., 2015), we found that with a temperature increase of 10 ∘C, production rates of CO2 doubled, and those of CH4 were even 2 to 11 times higher. Q10 values for CO2 were within the range of earlier reported values by Liikanen et al. (2002) and Bergström et al. (2010), whereas Q10 values for CH4 production were slightly higher than values found by Duc et al. (2010). The large observed range of Q10 values, especially for CH4, implies that responses to temperature increases might not be homogeneously distributed within a lake. The observed negative correlation between Q10 values and FTIR peak ratios further suggests that sites with more labile OM are more susceptive to increasing temperatures in terms of CH4 production, whereas at sites with more recalcitrant OM, the inherent quality of this recalcitrant OM may limit the degradation processes. We, therefore, assume that sediment GHG production – particularly CH4 production – in small and shallow lakes might in the course of global warming increase to a larger extent than in deeper lakes with respect to the fact that shallow waters, as opposed to deeper lakes, do not develop a stable stratification in summer, and thus shallow sediments warm much faster (Jankowski et al., 2006).

The high measured variability in production rates proves (1) that it is necessary to sample lake sediments from different locations in one lake in order to obtain potentials of CO2 and CH4 production representative of the whole lake and (2) that upscaling production rates based on single point measurements may be highly biased. Considering only sediment production rates and based on findings from other studies, it seems that the observed spatial variability of CO2 and CH4 emissions from lakes might to a large extent be controlled by variability in sediment GHG production (Schilder et al., 2013; Bastviken et al., 2015; Natchimuthu et al., 2016; Natchimuthu et al., 2017; Spafford and Risk, 2018). Yet still, as sediment production and emission patterns have so far only been considered separately, other factors driving actual emissions might have been neglected. Therefore, in Sect. 4.2, we further discuss the relationships between CO2 and CH4 production and actual emissions, as assessed in the intact sediment core incubation, and relate them to respective sediment properties.

To make methanogenesis a profitable reaction for microorganisms, theoretical thresholds of -10.6 kJ mol-1 for the hydrogenotrophic pathway and -12.8 kJ mol-1 for the acetoclastic pathway must be exceeded (Hoehler et al., 2001). Except for a few samples at the beginning of the incubation for the hydrogenotrophic pathway, the theoretical thresholds were always exceeded, suggesting that both pathways could potentially contribute to CH4 production during the whole experiment. Still, this approach does not allow us to evaluate which of the pathways is actually dominant.

Against our expectations, Gibbs free energy of acetoclastic methanogenesis at the end of the incubation was significantly lower (i.e., higher energy yield) in the center of the lake, and ΔGr exhibited a significant positive correlation with the C/N ratio. Considering that we found the most decomposed material (following peak ratios from FTIR analyses and low C/N ratios) in the lake center and that low C/N ratios in this case indicate OM of high recalcitrance, whereas the acetoclastic pathway is thought to predominate with high-quality substrates, we would have expected a reverse pattern (Liu et al., 2017; Berberich et al., 2019). Concomitantly, Gibbs free energy of hydrogenotrophic methanogenesis exhibited significant positive correlations with some FTIR peak ratios indicative of higher contributions of recalcitrant OM compounds, although we expected that a high abundance of recalcitrant OM compounds would make hydrogenotrophic methanogenesis more feasible (Liu et al., 2017). Acetate and H2 concentrations, on the other hand, both exhibited significant negative correlations with some FTIR peak ratios. While this seemed reasonable for acetate concentrations (less acetate available in strongly decomposed OM), this result again proved to be against our expectations in terms of H2 concentrations. This suggests that more recalcitrant material in general slows fermentative processes, delivering both acetate and H2, as a rate-determining step, and all fermentation products are thus kept at low levels.

The average EACOM measured in our experiment (302.8±124.6 µmol e- gC-1) was slightly lower but on the same order of magnitude compared to values found by Lau et al. (2015) and Gao et al. (2019) in other lake sediments or peat soils, respectively. Given that C contents in the study by Gao et al. (2019) were much higher than in our study (46.2 %–49.4 %; Agethen and Knorr, 2018) and that Lau et al. (2015) fully oxidized their samples prior to analyses (C content 11.0 %–27.4 %), our measured capacities seem reasonable.

We found that both organic and inorganic EAs decreased during the experiment, indicating that all EAs become similarly depleted with time as they are being reduced by microorganisms. Nevertheless, both absolute EACOM and EACinorg values and relative changes were rather low, which might have been caused by the 1-week preincubation, during which a majority of the reducible organic and inorganic compounds might have already been depleted. Klüpfel et al. (2014) showed that the EAC of oxidized humic acids already strongly declined after 1 d of anoxic incubation and did not change much afterwards. Inorganic EAs were also shown to decrease exponentially during anoxic incubation (Yao et al., 1999). The high CO2 production rates (91.5 µmol gC-1 d-1) at the beginning of the slurry incubation are an indication of these processes.

Sites with higher EACtot had lower CH4 production rates and vice versa as an increased concentration of oxidized humic substances would suppress methanogenic activity on longer timescales, supporting the findings of Agethen et al. (2018) and Gao et al. (2019). Although the relationship between EAC and CH4 production was not significant – probably due to the low number of samples and the sensitivity of the measuring method – a trend was observable.

Non-methanogenic CO2 production could by 38 % to 91 % be explained by prevalent organic and inorganic EAs, whereas organic EAs alone were able to explain up to 52 % of measured CO2 production in slurry incubations. Similar contributions were observed in previous studies from freshwater systems and peatlands, where up to 70 % and 95 % of non-methanogenic CO2 production was explained by total EAC and 25 % to 55 % by decreases in EACOM alone (Lau et al., 2015; Agethen et al., 2018; Gao et al., 2019). The authors suggest several possible reasons for the gap between calculated and experimentally measured CO2 production. Fermentation processes could explain excess CO2, but in this case reduced equivalents of fermentation products such as H2 would be expected to accumulate. Moreover, decarboxylation processes that occur in oxygen-rich, labile OM might occur. Further, the assumption of a nominal oxidation state of C of zero – as assumed in our approach – might be wrong so that when assuming a higher oxidation state, measured changes in EACOM might explain a higher share of CO2 production (Gao et al., 2019). As we did not observe the accumulation of fermentation products and as the sediment under study was not strongly oxidized, we assume these processes are of minor importance and instead suggest that the proportion of unexplained CO2 production can be explained by unknown consumed inorganic EAs during the slurry incubation. In this case, this was most likely solid-phase iron which we found to comprise 2 %–3 % (=^53–137 mg Fe gC-1) of our samples, but we were not able to draw conclusions about its speciation. We suppose this concentration is high enough to reach a closed budget of measured CO2 production and calculated EA turnover; if, on average, 7.8 % (4 %–18.7 %) of solid-phase iron were present as ferric iron, this would suffice to close the CO2 budget.

The large range (4 % to 52 %) of the contribution of organic EAs to CO2 production shows that a distinct small-scale in-lake variability of terminal electron-accepting processes and their contribution to CO2 formation exists in the sediment of Lake Windsborn. Interestingly, the contribution of EACOM was highest at site 3.125 where we observed the lowest CO2 production rates and highest OM recalcitrance. Given that both the absolute C content in the incubation vials and the C:Fe ratio were highest at this site, this supports the findings of Lau et al. (2015), who stated that the contributions of EECOM to total EEC increase with the OC:Fe ratio, indicating more peat-like material.