Mineralization of organic matter in boreal lake sediments: Rates, pathways and nature of the fermenting substrates

The complexity of organic matter (OM) degradation mechanisms represents a significant challenge for developing 10 biogeochemical models to quantify the role of aquatic sediments in the climate system. The common representation of OM by carbohydrates formulated as CH2O in models comes with the assumption that its degradation by fermentation produces equimolar amounts of methane (CH4) and dissolved inorganic carbon (DIC). To test the validity of this assumption, we modeled using reaction-transport equations vertical profiles of the concentration and isotopic composition (δC) of CH4 and DIC in the top 25 cm of the sediment column from two lake basins, one whose hypolimnion is perennially oxygenated and 15 one with seasonal anoxia. Our results reveal that methanogenesis only occurs via hydrogenotrophy in both basins. Furthermore, we calculate, from CH4 and DIC production rates associated with methanogenesis, that the fermenting OM has an average carbon oxidation state (COS) below −0.9. Modeling solute porewater profiles reported in the literature for four other seasonally anoxic lake basins also yields negative COS values. Collectively, the mean (±SD) COS value of −1.4 ± 0.3 for all the seasonally anoxic sites is much lower than the value of zero expected from carbohydrates fermentation. We conclude that carbohydrates 20 do not adequately represent the fermenting OM and that the COS should be included in the formulation of OM fermentation in models applied to lake sediments. This study highlights the need to better characterize the labile OM undergoing mineralization to interpret present-day greenhouse gases cycling and predict its alteration under environmental changes.

methanogenesis. Such interpretation, however, must be validated by investigating other lakes before revising the formulation 65 of the fermenting OM used in diagenetic models in order to improve model predictions of C cycling, including greenhouse gases production and emission from these environments.
In this study, centimeter-scale vertical porewater profiles of the concentrations and of the stable carbon isotope ratios (δ 13 C) of CH4 and dissolved inorganic carbon (DIC), as well as those of the concentrations of EAs were obtained in the hypolimnetic sediments of two additional boreal lake basins showing contrasted O2 dynamics: one whose hypolimnion remains perennially 70 oxygenated and the other whose hypolimnion becomes anoxic for several months annually. Reaction-transport equations are used to quantify the rates of each OM mineralization pathway and estimate the COS of the substrates fermenting in the sediments. Additional insight into the COS of the fermenting OM in lakes is also provided by applying these equations to similar porewater solute concentration profiles gathered from the scientific literature or from our data repository.

Sites and sample collection
This study was carried out in two small, dimictic, oligotrophic and headwater lakes located within 50 km from Québec City, Eastern Canada and having fully forested and uninhabited watersheds (Fig. 1). Lake Tantaré (47°04'N, 71°32'W) is part of the Tantaré Ecological Reserve and has four basins connected by shallow channels and a total surface area of 1.1 km 2 . Lake Bédard (47°16'N, 71°07'W), lying in the protected Montmorency Forest, comprises only one small (0.05 km 2 ) basin. The 80 samples for this study were collected at the deepest sites of Lake Bédard (10 m) and of the westernmost basin of Lake Tantaré (15 m), thereafter referred to as Basin A of Lake Tantaré to remain consistent with our previous studies (e.g., Couture et al., 2008;Clayer et al., 2016). These two sampling sites were selected based on their contrasting O2 regimes ( Fig. 1): Lake Bédard develops an anoxic hypolimnion early in the summer (D'arcy, 1993), whereas the hypolimnion of Lake Tantaré Basin A is perennially oxygenated (Couture et al., 2008). The O2 diffusion depth in the sediments of Lake Tantaré Basin A, as measured 85 with a microelectrode, does not exceed 4 mm (Couture et al., 2016). Sediment porewater samples were acquired by in situ dialysis in October 2015 with peepers (Hesslein, 1976;Carignan et al., 1985) deployed by divers within a 25-m² area at the deepest site of each lake basin. Bottom water O2 concentrations were ~2.5 and < 0.1 mg L −1 in Lake Tantaré Basin A and in Lake Bédard, respectively. The acrylic peepers comprised two columns of 4-mL cells, filled with ultrapure water, and covered by a 0.2-µm Gelman HT-200 polysulfone membrane, which allowed 90 porewater sampling from about 23-25 cm below the sediment-water interface (SWI) to 5 cm above this interface (thereafter referred to as overlying water) at a 1-cm depth resolution. Oxygen was removed from the peepers prior to their deployment, as described by Laforte et al. (2005). Four peepers were left in the sediments of each lake basin for at least 15 d, i.e., a longer time period than that required for solute concentrations in the peeper cells to reach equilibrium with those in the porewater (5-10 d;Hesslein, 1976;Carignan et al., 1985). At least three independent porewater profiles of pH, of the concentrations of CH4, 95 DIC, acetate, NO 3 − , SO 4 2− , Fe and Mn, and of the δ 13 C of CH4 and DIC were generated for the two sampling sites. In Lake https://doi.org/10.5194/bg-2020-5 Preprint. Discussion started: 31 January 2020 c Author(s) 2020. CC BY 4.0 License.
Bédard, samples were also collected to determine three porewater profiles of sulfide concentrations (ΣS(−II)). After peeper retrieval, samples (0.9-1.9 mL) for CH4 and DIC concentrations and δ 13 C measurements were collected within 5 minutes from the peeper cells with He-purged polypropylene syringes. They were injected through rubber septa into He-purged 3.85-mL exetainers (Labco Limited), after removal of a volume equivalent to that of the collected porewater. The exetainers were 100 preacidified with 40-80 μL of HCl 1N to reach a final pH ≤ 2. The protocols used to collect and preserve water samples for the other solutes are given by Laforte et al. (2005).

Analyses
Concentrations and carbon isotopic composition of CH4 and DIC were measured as described by Clayer et al. (2018). Briefly, the concentrations were analyzed within 24 h of peeper retrieval by gas chromatography with a precision better than 4 % and 105 detection limits (DL) of 2 µM and 10 µM for CH4 and DIC, respectively. The 13 C/ 12 C abundance ratios of CH4 and CO2 were determined by Mass Spectrometry with a precision of ± 0.2 ‰ when 25 µmol of an equimolar mixture of CH4 and CO2 was injected, and results are reported as: where the subscript solute stands for CH4 or DIC and the reference standard is Vienna Pee Dee Belemnite (VPDB). Acetate concentration was determined by ion chromatography (DL of 1.4 µM) and those of Fe, Mn, NO 3 − , SO 4 2− and ΣS(−II), as given 110 by Laforte et al. (2005).

Modeling of porewater solutes and the reaction network
The computer program WHAM 6 (Tipping, 2002) was used, as described by Clayer et al. (2016), to calculate the speciation of porewater cations and anions. The solute activities thus obtained, together with solubility products (Ks), were used to calculate saturation index values (SI = log IAP/Ks, where IAP is the ion activity product). 115 The following one-dimensional mass-conservation equation (Boudreau, 1997): was used to model the porewater profiles of CH4, DIC, O2, Fe and SO 4 2− , assuming steady state and negligible solute transport by bioturbation and advection . In this equation, [solute] and [solute] tube denote a solute concentration in the porewater and in the animal tubes (assumed to be identical to that in the overlying water), respectively, x is depth (positive downward), φ is porosity, D s is the solute effective diffusion coefficient in sediments, α Irrigation is the bioirrigation 120 coefficient, and R net solute (in mol cm −3 of wet sediment s −1 ) is the solute net production rate (or consumption rate if R net solute is negative). D s was assumed to be φ 2 D w (Ullman and Aller, 1982), where D w is the solute tracer diffusion coefficient in water.
The R net solute values were determined from the average (n = 3 or 4) solute concentration profiles by numerically solving Eq. (2) with the computer code PROFILE (Berg et al., 1998). The boundary conditions were the solute concentrations at the top and at the base of the porewater profiles. In situ porewater O2 profiles were not measured in Lake Tantaré Basin A. For modeling this solute with PROFILE, we assumed that the [O2] in the overlying water was identical to that measured in the lake bottom 130 water and equal to 0 below 0.5 cm (based on O2 penetration depth; Couture et al., 2016). This procedure provides a rough estimate of R net O 2 at the same vertical resolution as for the other solutes. The code PROFILE yields a discontinuous profile of discrete R net solute values over depth intervals (zones) which are objectively selected by using the least square criterion and statistical F-testing (Berg et al., 1998). The fluxes of solute transport across the SWI due to diffusion and bioirrigation are also estimated by PROFILE. In order to estimate the variability in R net solute related to heterogeneity within the 25-m 2 sampling area, 135 additional R net solute values were obtained by modeling the average profiles whose values were increased or decreased by one standard deviation. This variability generally ranges between 2 and 10 fmol cm −3 s −1 .
The main reactions retained in this study to describe carbon cycling in the sediments of the two lake basins are shown in Table   1. Once oxidants are depleted, fermentation of metabolizable OM (r1) can yield acetate, CO2 and H2. The partial degradation of high molecular weight OM (HMW OM) into lower molecular weight OM (LMW OM) can also produce CO2 (r2, Corbett 140 et al., 2013;Corbett et al., 2015). Acetoclasty (r3) and hydrogenotrophy (r4) yield CH4. Moreover, CH4 (r5) and OM (r6) can be oxidized to CO2 when electron acceptors such as O2, Fe(III) and SO 4 2− are present. Note that the electron acceptors (EAs) NO 3 − and Mn oxyhydroxides can be neglected in these two lake basins (Feyte et al., 2012;Clayer et al., 2016) as well as the precipitation of metal carbonates whose saturation index values are negative (SI ≤ −1.5) except for siderite (r7) in Lake Bédard (SI = 0.0 to 0.7). Lastly, sulfide oxidation by iron oxides (r8), which can be a source of SO 4 2− and H2 (Holmkvist et al., 2011;145 Clayer et al., 2018), is also considered.
From Table 1, the net rate of CH4 production, R net CH 4 , in the sediments is: where R 3 and R 4 are the rates of acetoclastic (r3) and hydrogenotrophic (r4) production of CH4, respectively, and R 5 is the rate of DIC production due to CH4 oxidation (r5). The net rate of DIC production, R net DIC , can be expressed as: where R 1 , R 2 and R 6 are the rates of DIC production due to complete fermentation of labile OM (r1), partial fermentation of 150 HMW OM (r2) and OM oxidation (r6), respectively, and R 7 is the rate of DIC removal by siderite precipitation (r7). It can also be written that: https://doi.org/10.5194/bg-2020-5 Preprint. Discussion started: 31 January 2020 c Author(s) 2020. CC BY 4.0 License.

Modeling of the δ 13 C profiles
The δ 13 C profiles of CH4 (δ 13 C-CH4) and DIC (δ 13 C-DIC) were simulated with a modified version of Eq. 1 (Clayer et al., 160 2018):  (7) where f, the molecular diffusivity ratio, is the diffusion coefficient of the regular solute divided by that of the isotopically heavy solute, α i is the isotope fractionation factor in reaction ri, and δ 13 C i reactant is the δ 13 C of the reactant leading to the formation of the solute (CH4 or DIC) in reaction ri. Input and boundary conditions used to numerically solve Eqs 2 and 7 for where δ 13 C m and δ 13 C s are the measured and simulated δ 13 C values, respectively. The norm of residuals (N res ) varies between 0 and infinity with smaller numbers indicating better fits.

Data treatment of other data sets 175
To better assess the COS of the fermenting OM in lakes, relevant sets of porewater concentration profiles (CH4, DIC, EAs, Ca) available from the literature or from our data repository have been modeled with the code PROFILE, as described in section 2.3, to extract their R net CH 4 , R net DIC and R net Ox profiles. These porewater datasets, described in section S3 of the SI, had been generated by sampling porewater in the hypolimnetic sediments of: i) Lake Bédard and Basin A of Lake Tantaré, at other dates than for this study ; ii) Basin B of Lake Tantaré (adjacent to Basin A; Fig 1), on four occasions (Clayer et 180 al., 2016;; iii) Williams Bay of Jacks Lake (44°41' N, 78°02' W), located in Ontario, Canada, on the edge of the Canadian Shield (Carignan and Lean 1991); iv) the southern basin of the alpine Lake Lugano (46 o 00'N, 3 o 30'E) located in Switzerland, on two occasions . All lake basins, except Basin A of Lake Tantaré develop an anoxic hypolimnion. reduced to produce dissolved Fe. In Lake Bédard, the ΣS(−II) concentrations decrease from the SWI to ~10 cm depth and remain relatively constant below that depth at 0.08 ± 0.06 µM for two of the profiles and at 0.71 ± 0.18 µM for the other one (grey filled triangles in Fig. 2n). 205 The concentrations of CH4 (< 1.5 mM; Fig. 2a and i) are well below saturation at 4°C and in situ pressure (4.4-5.5 mM; Duan and Mao, 2006), implying that CH4 ebullition is a negligible CH4 transport process. The CH4 values increases from < 2 µM in the overlying water to 0.18-0.20 mM at the base of the Lake Tantaré Basin A profiles (Fig. 2a), and from 0.2-0.5 mM to 1.0-1.4 mM in those of Lake Bédard (Fig. 2i). The three CH4 profiles from Lake Tantaré Basin A (Fig. 2a) show a modest concaveup curvature in their upper part, close to the SWI, indicative of a net CH4 consumption, and a convex-up curvature in their 210 lower part, typical of a net CH4 production. Such trends, however, are not observed in Lake Bédard sediments. The CH4 profiles from this lake exhibit a convex-up curvature over the whole sediment column, although more pronounced in its upper part (Fig. 2i).
The DIC concentrations consistently increase from 0.27-0.32 mM and 1.2-1.5 mM in the sediment overlying water to 0.76-0.83 mM and 3. .3 mM at the bottom of the profiles in Lake Tantaré Basin A and Lake Bédard, respectively ( Fig. 2c and 215 k). All DIC profiles show a similar shape with a slight concave-up curvature in their lower segment and a convex-up curvature in their upper portions.

Modeled CH4 and DIC concentration profiles
The modeled [CH4] and DIC profiles accurately fit the average (n = 3 or 4) data points (r 2 > 0.996 and r 2 > 0.998 for CH4 and DIC, respectively; Fig. 2g,h,o and p). The R net CH 4 profiles reveal three zones in each lake basin numbered Z1, Z2 and Z3 from the 220 sediment surface whose boundaries match those defined by the R net DIC profiles. For Lake Tantaré Basin A, Z1 corresponds to a net CH4 consumption and Z2 and Z3 to net CH4 production, with the highest rate in Z2 (Fig. 2g). In contrast, the three zones in Lake Bédard show net CH4 production with the highest rate in Z1 and the lowest in Z3 (Fig. 2o). The R net DIC profiles in both lake basins show a zone of net DIC consumption below two zones of net DIC production with the highest rate values in the Z1 and Z2 for Lake Tantaré Basin A and Lake Bédard, respectively. 225 The R net CH 4 and R net DIC profiles displayed in Figure 2 are, among all the possible solutions, the ones that give the simplest rate profile while providing a satisfying explanation of the averaged solute concentration profile as determined by statistical Ftesting implemented in the code PROFILE (P value ≤ 0.001 except for the R net DIC profile in Lake Bédard whose P value is ≤ 0.005). As an additional check of the robustness of the depth distribution of R net CH 4 and R net DIC provided by PROFILE, we used another inverse model, i.e., Rate Estimation from Concentrations (REC; Lettmann et al., 2012) to model the average CH4 and 230 DIC profiles. Note that the statistical method, implemented in REC to objectively select the depth distribution of the net reaction rates, i.e., the Tikhonov regularization technique, differs from that of PROFILE. Figure S1  (r 2 > 0.983). As expected from the contrasting O2 regimes of the two lake basins, R net Ox values for Lake Tantaré Basin A were one to two orders of magnitude higher than those for Lake Bédard. Note that R net O2 was by far the highest contributor to the value of R net Ox in Lake Tantaré Basin A with values of −290 and −72 fmol cm −3 s −1 in the Z1 and Z2, respectively. The values of R net CH 4 , R net DIC and R net Ox estimated in each zone of each lake basins are reported in Table 2.

The δ 13 C profiles 240
The δ 13 C-DIC values increase from −28.2 ± 0.4 ‰ and −17.2 ± 0.7 ‰ in the overlying water to −5.1 ± 1.0 ‰ and 3.6 ± 1.7 ‰ at the base of the profiles in Lake Tantaré Basin A and Lake Bédard, respectively ( Fig. 2d and l). Similarly, the δ 13 C-CH4 values in Lake Bédard increase steadily from −82.5 ± 3.3 ‰ in the overlying water to −74.0 ± 1.5 ‰ at 24.5 cm depth (Fig.   2j). Regarding Lake Tantaré Basin A, the CH4 concentrations above 1.5 cm depth were too low for their 13 C/ 12 C ratio to be determined. Starting at 1.5 cm depth, the δ 13 C-CH4 values first decrease from −91.1 ± 11.1 ‰ to −107.0 ± 6.8 ‰ at 2.5 cm 245 depth and then increase progressively to −83.5 ± 1.6 ‰ at the base of the profiles (Fig. 2b). Note that a shift toward more positive δ 13 C-CH4 values upward, generally attributed to the oxidation of CH4 (Chanton et al., 1997;Norði et al., 2013), is only observed in the profiles of Lake Tantaré Basin A (Fig. 2b).
As shown in Fig. S2 (SI), the isotopic signatures of nearly all samples from the two lake basins fall within the ranges reported for hydrogenotrophic methanogenesis, i.e., CO2 reduction, in a δ 13 C-CO2 vs δ 13 C-CH4 graph similar to that proposed by 250 Whiticar (1999). Indeed, the values of δ 13 C-CH4 which are lower than -70 ‰ over the whole profiles in the two lake basins, and the large difference (67 to 92 ‰) between the δ 13 C of gaseous CO2 (δ 13 C-CO2) and δ 13 C-CH4, strongly contrast with the typical δ 13 C-CH4 values (−68 to −50 ‰) and with the difference between δ 13 C-CO2 and δ 13 C-CH4 (39 to 58 ‰) reported for acetoclasty (Whiticar, 1999). The δ 13 C results reported previously for another basin of Lake Tantaré (Basin B; Clayer et al., 2018) show also in the hydrogenotrophy domain in Fig. S2. 255

Modeled δ 13 C profiles
In order to model the δ 13 C profiles with Eq. 6, accurate profiles of [C] and [ C 13 ] need first to be determined by numerically solving Eqs. 2 and 7, respectively. The modeled profiles of [CH4] and DIC obtained with Eq. 2 replicated well the measured profiles of these two solutes when the depth distributions of R net CH 4 or R net DIC provided by PROFILE ( Table 2) and those of D s , α Irrigation and φ were used as inputs in Eq. 2, and when measured CH4 or DIC concentrations at the top and bottom of the 260 profiles were imposed as boundary conditions. Getting a truthful profile of [ 13 C] with Eq. 7 requires, however, accurate values of δ 13 C i reactant , αi, and Ri for each of the reactions given in Table 1, and of f for both CH4 (f-CH4) and DIC (f-DIC). The multistep procedure followed to obtain the best [ 13 C] profiles for CH4 and DIC is described in section S2 (SI). This modeling exercise revealed that R3 = 0 for all the zones in the sediments of both lake basins, thus confirming that practically all CH4 is produced through hydrogenotrophy, as inferred above from the δ 13 C values.
The best fits between the simulated and measured δ 13 C profiles of CH4 and DIC for Lake Tantaré Basin A and Lake Bédard (red lines in Fig. 3) were obtained with the f, αi and Ri values displayed in Table 3. The optimal αi and f values were within the ranges reported in the literature for both lake basins, except for the lower-than-expected value of α2 (0.984) in the Z2 of Lake Bédard. Note that α3 is not given in Table 3 since the modeling of the δ 13 C profiles of CH4 and DIC indicates that R3 = 0 (see section S2.2.2.1 in the SI). Optimal values for α4, α5 and f-CH4 for both lake basins were also similar to those reported in 270 our previous study on Lake Tantaré Basin B .

Organic matter mineralization pathways at the sampling sites
The porewater data as well as the combined modeling of carbon isotopes and concentration profiles, allows to highlight key OM mineralization mechanisms and to quantify the relative contribution of methanogenesis and fermentation to OM 275 degradation at both sampling sites The 13 C isotopic signatures, i.e., highly negative values of δ 13 C-CH4 and large differences between δ 13 C-CO2 and δ 13 C-CH4 (section 3.3 and Fig. S2 in the SI), as well as the modeling of the δ 13 C-CO2 and δ 13 C-CH4 profiles (section S2.2.2.1 and Fig S4a and b in the SI) all point to hydrogenotrophy as being the only pathway for methanogenesis in the two lake basins. The dominance of hydrogenotrophy is consistent also with the finding that acetate concentrations were close to or below DL in the porewater samples. Under the condition that acetocalsty is negligible (i.e., 280 x = 1 ), reaction r1 from Table 1 becomes: Methanogenesis was also reported to be essentially hydrogenotrophic in the sediments of Basin B of Lake Tantaré . The absence of acetoclasty in the sediments of the oligotrophic lakes Bédard and Tantaré is consistent with the consensus that hydrogenotrophy becomes an increasingly important CH4 production pathway: i) when labile OM is depleted Chasar et al., 2000;Hornibrook et al., 2000), ii) with increasing sediment/soil depth (Hornibrook et al., 285 1997;Conrad et al., 2009), or iii) with decreasing rates of primary production in aquatic environments (Wand et al., 2006;Galand et al., 2010).
The modelling of concentrations and δ 13 C profiles revealed that oxidative processes occurred essentially in the upper 7 cm of the sediments of the perennially oxygenated Lake Tantaré Basin A, i.e., mainly in the Z1 and, to a lesser extent, in the Z2 (Table   3 and sections S2.1.2.1 and S2.1.2.2 of the SI). Moreover, it showed that methanotrophy was the dominant oxidative reaction 290 in these sediment layers since 75% of the oxidants were consumed through r5 (section S2.2.2.2 of the SI). This outcome is consistent with several studies showing that methanotrophy occurs at higher rates than OM oxidation at low EA concentrations (Sivan et al., 2007;Pohlman et al., 2013;Kankaala et al., 2013;Thottahil et al., 2019). Methanotrophy is also evidenced in the Z1 of this lake basin by the negative R net CH 4 value and by a shift of the δ 13 C-CH4 profiles to more positive values in their upper part ( Fig. 2b and g). Use of Eq. 2 to model the EAs profiles with the code PROFILE predicts that O2 was by far the main EA involved either directly, or indirectly via the coupling with the Fe or S cycles, in the oxidative processes. Indeed, comparing the values of R net O2 and R net Ox (see Section 3.2 and Table 2) shows that O2 accounts for 87% and 70% of the oxidants consumed in the Z1 and Z2 of Lake Tantaré Basin A, respectively. Since O2 penetration in the sediment by molecular diffusion is limited to ⁓4-mm, a significant amount of O2 is predicted by Eq. 2 to be transported deeper in the sediment through bioirrigation. The predominance of O2 among the EAs consumed in the sediments is consistent with our previous study in this basin of Lake 300 Tantaré . Given that methanotrophy is the dominant oxidative process and that O2 is the main oxidant consumed, it is probable that aerobic oxidation of methane prevails over its anaerobic counterpart in this lake basin. This is in line with the common thinking that CH4 oxidation in freshwater lake sediments is carried out by methanotrophs essentially in the uppermost oxic sediment layer (Bastviken et al., 2008 and references therein).
The sharp upward depletion in 13 C-CH4 leading to a minimum δ 13 C-CH4 value at 2.5 cm depth in Lake Tantaré Basin A 305 sediments ( Fig. 3a) was unanticipated since, according to the modeling with the code PROFILE, it occurs in the methanotrophic zone, i.e., where the remaining CH4 is expected to be 13 C-enriched as a result of CH4 oxidation. Marked 13 C-CH4 depletions at the base of the sulfate-methane transition zone, where CH4 is consumed via SO 4 2− reduction, have often been observed in marine sediments (Burdige et al., 2016 and references therein). Such features are generally attributed to the production of CH4 by hydrogenotrophy from the 13 C-depleted DIC resulting from the anaerobic CH4 oxidation, a process referred to as intertwined 310 methanotrophy and hydrogenotrophy (e.g., Borowski et al., 1997;Pohlman et al., 2008;Burdige et al., 2016). Here the modelled δ 13 C-CH4 profile captured the minimum in δ 13 C-CH4 in the Z1 by simply assuming concomitant hydrogenotrophy and methanotrophy in this zone and an upward-increasing α4 value from 1.085 in the Z3 to 1.094 in the Z1 (section S2.2.1 of the SI). These α4 values remain within the range reported for this isotope fractionation factor (Table S1 in the SI). A small variation with sediment depth in the fractionation factor α4 is arguably possible since its value depends on the types of 315 microorganisms producing CH4 (Conrad 2005). The possibility that a depth variation in this isotope fractionation factor could explain some of the minima in δ 13 C-CH4 reported in other studies should be considered.
Indeed, methanogenesis through the coupling of these two reactions yields a R1/R4 ratio of 2 if the fermenting substrate is carbohydrates (COS of 0) and lower than 2 if the fermenting substrate has a negative COS value. We thus attributed the production of the additional DIC to the partial fermentation of HMW OM, an assumed non-fractionating process reported to 325 occur in wetlands (Corbett et al., 2015). The better fitting of the δ 13 C-DIC profile when α2 is set to 0.980-0.984 rather than to 1.000 in the Z2 (compare the blue and red lines in Fig. 4b) suggests that C fractionates during this partial fermentation process. Table 3 displays the depth-integrated reaction rates (ΣRi) over the top 21cm of the sediment column which are given by: https://doi.org/10.5194/bg-2020-5 Preprint. Discussion started: 31 January 2020 c Author(s) 2020. CC BY 4.0 License.
where ∆x j (cm) is the thickness of the zone Zj. In this calculation, we assume that other zones of CH4 or DIC production are absent below 21 cm. Values of ΣRi clearly show that anaerobic carbon mineralization reactions (fermentation and 330 methanogenesis) are important contributors to the overall OM mineralization in the two studied lake basins. Indeed, the sum of the rates of CH4 production (ΣR4), DIC production due to CH4 formation (ΣR1 − ΣR4) and HMW OM partial fermentation (ΣR2) represents 49% and 100% of the total OM degradation rate (ΣR1 + ΣR2 + ΣR5 + ΣR6) in the sediment of lakes Tantaré Basin A and Bédard, respectively. The contribution of anaerobic mineralization for Lake Tantaré Basin A is about 1.6 times higher than the average of 30% reported for this lake basin in a previous study . This significant discrepancy 335 arises because these authors, in the absence of isotopic data to adequately constrain the Ri values, assumed that R4 = 0 in the net methanotrophic zone Z1. Should we make the same assumption in the present study, we would also estimate that fermentation and methanogenesis represent only 30% of the total rate of OM degradation in the oxygenated Lake Tantaré Basin A and we would thus underestimate the importance of methanogenesis. The inclusion of δ 13 C data in the present modeling study thus allowed to better constrain the effective rates of CH4 production (R4). 340 Table 3 indicates that hydrogenotrophy (r4) coupled to the complete fermentation of OM (r1) produces CH4 at higher rates (R4) than DIC (R1 − R4) in the Z1 and Z2 of both lake basins. This outcome is inconsistent with the equimolar production of CH4 and DIC expected from the fermentation of glucose (C6H12O6), the model molecule used to represent labile OM in diagenetic models (Paraska et al., 2014), thus suggesting that the fermentation of this compound is not the exclusive source of 345 the H2 required for hydrogenotrophy. Had OM been represented by C6H12O6 in r1, the rate of H2 production by this reaction would have been twice that of CO2, i.e., 2R 1 . For its part, the rate of H2 consumption through hydrogenotrophy is four times that of the CH4 production, i.e., 4R 4 . Hence, an additional H2 production at rates of up to 212 and 70 fmol cm −3 s −1 , i.e., 4R 4 − 2R 1 , is needed to balance the H2 production rate expected from the fermentation of C6H12O6 and the H2 consumption rate by hydrogenotrophy observed in the sediments of Lake Tantaré Basin A and Lake Bédard, respectively. As discussed by Clayer 350 et al. (2018), this additional production rate of H2 could be provided by a cryptic Fe-S cycle such as r8 (Table1), or by the production of CH4 via the fermentation of organic substrates more reduced than glucose.

Organic substrates for methanogenesis at the sampling sites
The progressive downward increases in dissolved Fe and SO 4 2− (Fig. 2e, f, m and n) below ~5 cm depth and decrease in ΣS(−II) ( Fig. 2n) observed in the porewaters support a production of H2 from r8 in both lakes. However, modeling the appropriate solute profiles with the code PROFILE indicates that the production rates of dissolved Fe (<10 fmol cm −3 s −1 ) and SO4 2-(<1 355 fmol cm −3 s −1 ) and the consumption rate of ΣS(−II) (<1 fmol cm −3 s −1 ) are about one order of magnitude too low to explain the missing H2 production rate in both basins. Moreover, in the Z1 and Z2 of Lake Tantaré Basin A, the rate of solid Fe(III) reduction (<3 fmol cm −3 s −1 ; calculated from Liu et al. 2015) is much lower than that required from r8 (i.e., 1 to 2 times the https://doi.org/10.5194/bg-2020-5 Preprint. Discussion started: 31 January 2020 c Author(s) 2020. CC BY 4.0 License. additional H2 production of 4R 4 − 2R 1 ; 70-424 fmol cm −3 s −1 ) to produce sufficient amounts of H2 to sustain the additional hydrogenotrophy. Given these results, we submit that a cryptic Fe-S cycle, if present, would contribute only minimally to the 360 missing rate of H2 production, and that the fermentation of reduced organic compounds could provide a better explanation to the imbalance between the H2 production and consumption rates.
Since CH4 is produced by hydrogenotrophy in the two lake basins (χ H = 1), Eqn. S15 (section S2.2.2. of the SI) describing the COS of the fermenting organic substrate CxHyOz simplifies as: where χ M is the fraction of oxidants consumed through methanotrophy. Combining Eqs. S7 and S5 of the SI with Eq. 11, we 365 obtain: Introducing the values of R net CH 4 , R net DIC , R net Ox and R 2 (Table 2 and 3) into Eq. 12, we calculate COS values of −3.2 and −0.9 for the Z1 and Z2 of Lake Tantaré Basin A, respectively, and of −1.0 to −1.1 for the Z1 of Lake Bédard, respectively. Note that we were unable to constrain with Eq. 12 the COS for the Z2 of Lake Bédard since we had to assume a COS value to estimate R2 and the COS has no influence of the modelled δ 13 C profiles (section S2.2.2.3 of the SI). Negative COS values between −0.9 370 and −1.1 suggest that fermenting OM in the sediments of the two lake basins would be better represented by a mixture of fatty acids and fatty alcohols than by carbohydrates, as suggested by Clayer et al. (2018) for the sporadically anoxic Lake Tantaré Basin B. For its part, the highly negative COS value of −3.2 calculated for the Z1 of Lake Tantaré Basin A is unreasonable, and the inaccuracy of the COS determination in this lake basin is discussed in section 4.3.

Reduced organic compounds as methanogenic substrates in lake sediments 375
In order to better appraise the COS of the fermenting OM in lakes, relevant datasets of porewater solute concentration profiles were gathered from our data repository and from a thorough literature search. To be able to obtain by reactive-transport modeling the R net solute required to calculate the COS with Eq. 12, the datasets had to: (i) comprise porewater concentration profiles of CH4 and DIC and, ideally, those of the EAs; (ii) reveal a net methanogenesis zone, and iii) enable the carbonate precipitation/dissolution contribution to the DIC concentrations to be estimated. Detailed information on the origin and 380 processing of the 17 selected datasets, acquired in 6 different lake basins from one sub-alpine and three boreal lakes sampled at various dates and/or depths, is given in section S3 of the SI. The CH4 and DIC porewater profiles determined at hypolimnetic sites of these lake basins and their modeling with the code PROFILE are shown in Fig. 4 Table 4. The value of χM was assumed to be alternately 0 and 1 to provide a range of COS values. The only exception was Lake Tantaré Basin A in October 2015 for which χM is known to be 0.75 (section S2.2.2.2 of the SI). Note that although Eq. 12 was derived with the assumption that methanogenesis was hydrogenotrophic (χH = 1), assuming that CH4 was produced by 390 acetoclasty (χH = 0) would yield the same expression.
According to Table 4 the COS values are systematically negative at all dates for Lake Tantaré Basin B, Lake Bédard, Jacks Lake and the two sites of Lake Lugano, and they vary generally between −0.9 and −1.9, with the exception of a value of −2.5 obtained for Lake Tantaré Basin B in July 2007. This latter value is likely too low to be representative of fermenting material and should be rejected. The mean (± SD) COS values are −1.7 ± 0.4 for Lake Tantaré Basin B, −1.4 ± 0.4 for Lake Bédard, 395 −1.4 ± 0.2 for Jacks Lake and −1.4 ± 0.3 for Lake Lugano. These COS values, representative of a mixture of fatty acids (COS of −1.0 for C4-fatty acids to about −1.87 for C32-fatty acids) and of fatty alcohols (COS = −2.00), strongly supports the idea that methanogenesis in boreal lakes sediments, as well as in the sediments of other types of lakes, is fueled by more reduced organic compounds than glucose. Lipids such as fatty acids and fatty alcohols with similar COS are naturally abundant in sediments to sustain the estimated rates of CH4 and DIC production during fermentation (Hedges and Oades, 1997;Cranwell, 400 1981;Matsumoto, 1989;Burdige, 2006). As discussed by Clayer et al. (2018) the most labile organic compounds (i.e., proteins and carbohydrates) can be rapidly degraded during their transport through the water column and in the uppermost sediment layer, leaving mainly lipids as metabolizable substrates at depths where fermentation and methanogenesis occurs. This interpretation is consistent with thermodynamic and kinetic evidences that proteins and carbohydrates are more labile and are degraded faster than lipids (LaRowe and Van Cappellen, 2011). 405 The COS values determined for the perennially oxygenated Basin A of Lake Tantaré (mean of −0.6 ±1.1; range of −3.2 to 2.1; Table 4) are much more variable than for the five other lake basins which undergo seasonal anoxia. Moreover, the COS values Cappellen 2011) and tend to be degraded in the water column (Burdige 2007) or oxidized compounds, such as ketones, aldehydes and esters, known to be quickly reduced to alcohols. These observations indicate that the COS determination in this lake basin is unreliable. The misestimation of the COS can probably not be explained by the presence of O2 itself at the sediment surface of Lake Tantaré Basin A. Indeed, the sediment surface was also oxic at the sites Melide and Figino of Lake Lugano in March 1989 (Table 4) Lazzaretti-Ulmer and Hanselmann, 1999).
Despite this, the COS values determined for the two sites of Lake Lugano appear to be realistic and coherent with those calculated for Lakes Tantaré Basin B, Bédard and Jacks. However, we know that benthic organisms are present in Lake Tantaré Basin A (Hare et al., 1994) but lacking at the two sites of Lake Lugano, as shown by the presence of varves  https://doi.org/10.5194/bg-2020-5 Preprint. Discussion started: 31 January 2020 c Author(s) 2020. CC BY 4.0 License. and the absence of benthos remains in the recent sediments at these sites (Niessen et al., 1992). Clayer et al. (2016) provided 420 evidences that sediment irrigation by benthic animals is effective in Lake Tantaré Basin A and that it should be taken into account in modeling the porewater solutes profiles. However, these authors also point out the difficulty to properly estimate the magnitude of solute transport by bioirrigation. The term used in Eq. 2 to calculate this contribution, i.e., φαirrigation ([solute]tube -[solute]), is indeed an approximation of intricate 3-D processes (Meile et al. 2005). And, in the conceptualization of this bioirrigation term, it was notably assumed that benthic animals continuously irrigate their tubes to maintain solute 425 concentrations in their biogenic structures ([solute]tube) identical to those in the water overlying the sediments. But microbenthic animals are generally reported to irrigate the sediments in a discontinuous manner and the solute concentrations in their biogenic structures may be highly variable with time (Boudreau and Marinelli 1994;Forster and Graf 1995;Riisgård and Larsen 2005;Gallon et al. 2008). Hence, owing to the imperfection of the representation of bioirrigation in Eq. 2, COS values estimated for the sediment of Lake Tantaré Basin A should be treated with caution, especially in the Z1 where the 430 bioirrigation coefficient takes the highest value. Another potential bias in the estimation of COS values for the oxygenated basin is the possibility of DIC production through HMW OM fermentation (reaction r2; Corbett et al. 2013). Note that fitting with Eq. 6 the experimental δ 13 C data does not allow partitioning the production of DIC between r1 and r2 since the two processes share the same value of fractionation factor (α1 = α1 = 1.000). It was possible to attribute unequivocally the excess of DIC production rate over that of CH4 production in the Z2 of Lake Bédard in October 2015 (Table 4  respectively. The above discussion underlines several factors that can explain the unreliability in the actual COS estimation 440 for the perennially oxic Lake Tantaré Basin A, and further research is needed to better assess the importance of these factors.
However, it does not dismiss that the substrate for methanogenesis in this lake basin may have a negative COS value.

Conclusions
Our results show that fermentation and methanogenesis represent nearly 50% and 100% of OM mineralization in the top 25 cm of the sediments at the hypolimnetic sites in Lake Bédard and in Basin A of Lake Tantaré, respectively and that methane 445 is produced only by hydrogenotrophy at these two sites. An earlier study reached similar conclusions about the pathways of methanogenesis and the contribution of this process in OM mineralization in Basin B of Lake Tantaré ).
Reactive-transport modelling of porewater solutes from three boreal lakes, i.e., Bédard, Tantaré (Basin B) and Jacks, as well as of the sub-alpine Lake Lugano (Melide and Figino sites) consistently showed that the main substrates for sediment methanogenesis at deep seasonally anoxic hypolimnetic sites have a mean COS value of −1.4 ± 0.3. Mineralization of the most labile compounds during OM downward migration in the water column and in the uppermost sediment layers likely explains why reduced organic compounds fuel methanogenesis in these sediments.
The current representation of the fermenting OM, i.e., CH2O, in process-based biogeochemical models entails a significant risk of misestimating sedimentary CH4 and CO2 production and release to the bottom water and, to a certain extent, of mispredicting evasion of these greenhouse gases to the atmosphere under transient environmental scenarios. To better constrain 455 CH4 and CO2 production within sediments, we suggest taking specifically into account the COS of the fermenting OM in formulating the reactions of methanogenesis associated with fermentation in these models. For example, the rates of CH4 (R CH 4 ) and DIC (R DIC ) production during fermentation coupled to hydrogenotrophy can be expressed as: Given these rate expressions, the stoichiometric formulation of a typical fermentation reaction producing methane becomes: . Note that the same stoichiometric formulation would be obtained for acetoclastic 460 methanogenesis.
The approach used to estimate the COS of the fermenting OM, although successful for the seasonally anoxic basins, failed to produce reliable COS values when applied to the perennially oxygenated Basin A of Lake Tantaré. We attribute this peculiarity to a misestimation and/or misrepresentation of the benthic irrigation and to the impossibility to partition the DIC production between reactions r1 and r2 which share the same fractionation factor value. Similar problems would likely be encountered 465 also in other lake ecosystems such as epilimnetic sediments and wetlands where solute transport processes remain ill-known.
Indeed, these shallow aquatic environments are subject to enhanced benthic activity (Hare 1995), to plant-mediated transport of CH4 and O2 (Chanton et al. 1989;Wang et al. 2006), as well as to turbulence (Poindexter et al. 2016) which complicates the estimation of CH4 and CO2 production and consumption rates. Hence, the remaining challenge resides in the robust estimations the COS of the fermenting OM in epilimnetic sediments and shallow freshwater environments (e.g., ponds, wetlands), since 470 these environments were shown to be the main contributors to freshwater CH4 release to the atmosphere (Del Sontro et al., 2016, Bastviken et al., 2008. One potential solution is to investigate trends in the oxygen isotope signatures in the sedimentary DIC in addition to δ 13 C values since it is also influenced by the source of the OM undergoing degradation (e.g., Sauer et al., 2001).

Data availability: 475
Upon acceptance, readers will be able to access the data at this url: https://www.hydroshare.org/resource/38e069761d7b4cf4abe3cbcaaac06016/. A proper reference with a DOI will be made available to cite this dataset if the present paper is accepted.

Author contribution:
Conceptualization All.

(circles) in Lakes Tantaré Basin A (a-d) and
Basin B (a-h), Bédard (i), Jacks Lake (j-k) and Lake Lugano (l-o) at various sampling dates. The thick red lines represent the net solute reaction rate ( ).