Freshwaters emit significant amounts of CH4 and CO2 and, as CH4 is the stronger greenhouse gas, understanding how carbon gets mineralized to either gas is important. In theory, under anoxia, methanogenesis coupled to fermentation should produce CH4 and CO2 in a 1 : 1 ratio. Here, we find that this 1 : 1 ratio is rare, with lower ratios of 0.1 : 1 being typical which confounds understanding CH4 in freshwaters. First, using a simple mathematical model we rationalize low ratios as poor methanogenic substrate utilization, including loss to nonmethanogenic processes. Second, we find substrate utilization improves at higher temperatures, especially for hydrogen. This increases CH4 to CO2 production ratios exponentially which could drive higher CH4 to CO2 emission ratios. Hence, we rationalize how warmer freshwaters may emit more methane. Inland freshwaters (e.g., wetlands, rivers, lakes, and rice paddies) are significant players in the carbon cycle (Cole et al. 2007), sequestering large amounts of fixed carbon (0.5 Pg yr−1) in their sediments and soils and mineralizing approximately twice as much (1.2 Pg yr−1) back to CO2 and CH4 (Regnier et al. 2013). In turn, inland freshwaters are responsible for nearly 50% of global CH4 emissions. With CH4 having approximately 80 times the global warming potential of CO2 over 20 yr, there is a clear need to understand the processes and conditions that determine the relative production of CH4 vs. CO2 in aquatic sediments and water-logged soils (Balcombe et al. 2018; Rosentreter et al. 2021). In the top layers of sediments and water-logged soils, and most overlying waters, organic carbon can be respired aerobically to CO2 or, deeper in, where O2 is limiting, also anaerobically to CO2 via any available alternative electron acceptors (e.g., inorganic ions such as Fe3+, NO 3 − $$ {\mathrm{NO}}_3^{-} $$ / NO 2 − $$ {\mathrm{NO}}_2^{-} $$ and SO 4 2 − $$ {\mathrm{SO}}_4^{2-} $$ and/or oxidized organic matter; see Fig. 1). Eventually, when these aerobic and anaerobic electron acceptors are depleted the remineralization of any remaining organic carbon to CO2 and/or CH4 is completed via a combination of fermentation and methanogenesis. First, fermentation produces acetate, CO2 and H2 (Eq. 1) and then methanogenesis utilizes CO2 and H2 (hydrogenotrophic, Eq. 2) to make CH4 and/or acetate (acetoclastic, Eq. 3) to produce CH4 and CO2 (Fig. 1) (Thauer et al. 2008). In addition to acetate and CO2 and H2, a wide variety of simple organics, including methyl-compounds, can fuel methanogenesis, but in anoxic freshwaters for example, anoxic lake sediment or water-logged soils, methanogenesis is dominated by the acetoclastic and hydrogenotrophic pathways (Liu and Whitman 2008). In 1999, however, Conrad proposed that by coupling the complete fermentation of glucose to methanogenesis, CH4 and CO2 would be produced in a 1 : 1 ratio (Eq. 4, which is the sum of Eqs. 1-3) (Conrad 1999). This expectation is based on the idea that one-third of the total CH4 would be produced using H2 derived from the original fermentation, with the remaining two-third coming from the acetate. Hence, in an idealized methanogenic system, both deplete in electron acceptors and where all of the acetate and H2 produced by fermentation are subsequently used in methanogenesis, the ratio of CH4 to CO2 leaving the anoxic sediment and soil layers would be fixed at 1 : 1—regardless of temperature. Despite this broadly accepted 1 : 1 assumption even being used to model CH4 emissions from global wetlands (Chadburn et al. 2020), published ratios from incubations of anoxic sediments and soils often appear far lower (see Amaral and Knowles 1994; Conrad et al. 2011; Kolton et al. 2019 as examples). Furthermore, while we acknowledge that ratios lower than 1 : 1 are recognized (Wilson et al. 2017; Gao et al. 2019), there has been no systematic characterization of how often it occurs or, more importantly, how the CH4 to CO2 ratio might increase toward 1 : 1 in response to warming. To explore this, we compiled data from the Web of Science for CH4 and CO2 production in typical microcosm incubations of sediments or water-logged soils—examples of our search terms are included as metadata with the source data at https://doi.org/10.5281/zenodo.7612326. As we knew this search to be incomplete—for example, omitting the terms “oxidation” and “marine” missed Roden and Wetzel (1996) and Shelley et al. (2015) that both report CH4 and CO2 production, we supplemented our search using the compilations in Yvon-Durocher et al. (2014) and Wilson et al. (2017) or those related to our previous publications (Zhu et al. 2020, 2022). Note, we further excluded any publications where the authors had not stated explicitly that they had accounted for all of the CO2 produced in their incubations, that is, CO2 gas in the headspace plus that dissolved in the water phase (ΣDIC: CO2, HCO 3 2 − $$ {\mathrm{HCO}}_3^{2-} $$ , CO 3 − $$ {\mathrm{CO}}_3^{-} $$ ). Whereas only measuring the incubation headspace would typically capture >95% of any CH4 produced, the same is not true for CO2 which is approximately 100 times more soluble than CH4. Our search yielded 64 publications and a total of 512 measurements of CH4 and CO2 production including: lakes (n = 109), wetlands (n = 276), rice paddies (n = 64), a reservoir (n = 28), rivers (n = 4) and our own incubations of streambed sediments (n = 31, Zhu et al. 2022) for which we previously published just the CH4 data. We extracted the data using WebPlotDigitizer (https://automeris.io/WebPlotDigitizer/) and calculated CH4 to CO2 production ratios. Our compilation (Fig. 2a) clearly shows that Conrad's idealized 1 : 1 ratio is seldom realized in practice, with ratios >0.95 : 1 only appearing in 2% of the 512 incubations and 50% of all incubations producing CH4 to CO2 at a ratio of only 0.1 : 1. Of the 64 publications included here, 47 had very low CH4 to CO2 production ratios (< 0.1 : 1) and, of those, 13 provided data for the concentration of any alternative electron acceptors ( NO 3 − $$ {\mathrm{NO}}_3^{-} $$ , SO 4 2 − $$ {\mathrm{SO}}_4^{2-} $$ , Fe3+, or Mn4+). Using these 13 datasets we estimated P CO 2 − AEA $$ {P}_{{\mathrm{CO}}_2-\mathrm{AEA}} $$ to be only 0.1% or 0.3% (median) through AMO and Rana, respectively, in lake sediment and peatland soil (n = 93, Fig. 2b). Note, varying the density of wet soil from 1250 to 1850 g L−1 would alter P CO 2 − AEA $$ {P}_{{\mathrm{CO}}_2-\mathrm{AEA}} $$ for AMO, from 0.09% to 0.14%, and for Rana, from 0.25% to 0.37%, for the median concentration of the most abundant AEA, that is, 12 μmol SO 4 2 − $$ {\mathrm{SO}}_4^{2-} $$ L−1. Our minor contribution from AEA-induced CO2 agrees with estimates of 0.1–11% through Rana in other peatland soils (Gao et al. 2019) and would unlikely explain the typically low CH4 to CO2 production ratio of 0.1 : 1 reported here (Fig. 2c). Equation 9 shows that the CH4 to CO2 production ratio is (x + 2y)/(2 − x + 2y) and, as proposed by Conrad, if all of the H2 and acetate produced by fermentation is used to make CH4 (i.e., x = 1 and y = 1), the ratio of CH4 to CO2 will be 1 : 1 (Conrad 1999). Conversely, if either substrate escapes or gets used in a nonmethanogenic pathway (i.e., 0 ≤ x < 1 or 0 ≤ y < 1), the resulting ratio will always be less than 1 : 1 (Fig. 3a). Eq. 9 provides a tool to help us rationalize the typically low CH4 to CO2 production ratios by quantifying the effect of variable utilization of acetate and H2 by methanogens. Acetate and H2 are both direct precursors to CH4 and at the median CH4 to CO2 ratios of 0.1 : 1 reported here (Fig. 2a), it appears that a maximum of 11% of any acetate (no hydrogenotrophy and x = 0, Fig. 3a) or 18% of any available H2 (no acetoclasty and y = 0, Fig. 3a) was used to produce CH4. However, whereas we can use the literature values to account for any potential CO2 production through anaerobic respiration of inorganic SO 4 2 − $$ {\mathrm{SO}}_4^{2-} $$ , NO 3 − $$ {\mathrm{NO}}_3^{-} $$ / NO 2 − $$ {\mathrm{NO}}_2^{-} $$ , Fe3+ (as detailed above), we cannot account for anaerobic respiration with organic compounds, hydrogenation, homoacetogenesis, growth, or loss by diffusion (Schütz et al. 1988; Greening et al. 2016; Wilson et al. 2017; Gao et al. 2019). No matter what the nonmethanogenic fate, it appears that only minor proportions of either acetate or H2 are used to produce CH4 constraining the ratios below Conrad's idealized prediction of 1 : 1. As non-methanogenic utilization of acetate and H2, be it anaerobic respiration, hydrogenation etc., would only lower the CH4 to CO2 production ratio, we continue to use Eq. 9 to explore how CH4 to CO2 production ratios would increase with better utilization of acetate or H2. Starting from the typical nonidealized CH4 to CO2 production ratio of 0.1 : 1 with poor substrate utilization (11% for acetate and 18% for H2), if we increase the utilization of acetate (i.e., increasing y from 0.11 to 1), the ratio increases subexponentially to a maximum of 0.5 : 1 (Fig. 3a), that is, Conrad's idealized ratio can never be realized through acetoclastic methanogenesis alone. In contrast, if we increase the utilization of H2 (i.e., increasing x from 0.18 to 1), then the ratio increases exponentially to the maximum idealized ratio of 1 : 1 (Fig. 3a), that is, by using H2 to reduce CO2 Conrad's idealized ratio of 1 : 1 can be realized. Recently we reported that long-term (11 yr) experimental warming of freshwater ponds disproportionately enhanced methane emissions along with an increase in CH4 to CO2 production ratios (Zhu et al. 2020). We argued how such an increase in CH4 to CO2 production ratio could be rationalized by a greater proportion of the available H2 being used to make CH4 and here we have extended that analysis to include acetate (Eqs. 3, 8, and 9). Although the CH4 to CO2 production ratio would increase with greater utilization of either H2 or acetate, the fact that the ratio only increases exponentially with greater H2 utilization provides a clue to answering how CH4 to CO2 production ratios would increase with warming. We would argue that given the higher sensitivity of the hydrogenotrophic over the acetoclastic pathway to temperature (1.4 vs. 1.1 eV; Zhu et al. 2020), the hydrogenotrophic methanogens would respond more rapidly to warming. This is corroborated by the dominance of hydrogenotrophic over acetoclastic methanogenesis observed in warmer lake sediments and peat soils (Conrad et al. 2014; Kolton et al. 2019) and a general selection for hydrogenotrophic genera in naturally warmer environments (Wen et al. 2017). In turn, warming increases the fraction of H2 used to reduce CO2 to CH4 and, as implied in Fig. 3a, increases the CH4 to CO2 production ratio exponentially toward the idealized 1 : 1 ratio. Indeed, if we plot the data in Fig. 2a as a function of each individual incubation temperature (n = 490 for incubations at <40°C, that is, the generally accepted optimal methanogenic temperature in freshwaters; Schulz et al. 1997), the CH4 to CO2 production ratio increases exponentially—regardless of each initial ratio—toward the idealized ratio of 1 : 1, as hypothesized (Fig. 3b, p < 0.001, log-likelihood ratio test). Any such increase in CH4 to CO2 production ratios in warmer sediments or water-logged soils would only be of relevance to Earth's climate if they ultimately drive higher emission ratios to the atmosphere (Fig. 1). Although we compiled 512 production ratios and there are several thousand emission ratios available through FLUXNET (Pastorello et al. 2017; Delwiche et al. 2021), for example, there are—to the best of our knowledge—few paired measurements with which to establish a relationship between the two (Roden and Wetzel 1996; Blodau and Moore 2003; Rinnan et al. 2003; Zhu et al. 2020; Hopple et al. 2020). We used our frequent measurements of CH4 to CO2 emission ratios from our experimental ponds (three times per day) and parallel monthly laboratory incubations for sediment production ratios (Zhu et al. 2020) to look for any correlation between the two. Note, to present any such correlation at in situ temperature, the laboratory sediment production ratios were standardized to the same emission temperature using known temperature sensitivities (E = 0.7 and E = 0.58 eV for apparent activation energies of CH4 and CO2 production, respectively) (Zhu et al. 2020). We also used a further 15 paired measurements available for peatland soils (Roden and Wetzel 1996; Blodau and Moore 2003; Rinnan et al. 2003; Hopple et al. 2020). The positive relationship between production and emission ratios is very clear in Hopple et al. (2020) for peatland soils, as is the increase in CH4 to CO2 emission ratios at higher temperatures. Overall, CH4 to CO2 emission ratios increase at higher production ratios in both our ponds and peatland soils (Fig. 3c, both p < 0.05, log-likelihood ratio test and F-statistic for pond and peatland measurements, respectively). Furthermore, CH4 to CO2 emission ratios are lower than production ratios which is both expected and relatively easy to explain. For example, CH4 can both be consumed before emission due to aerobic and/or anaerobic oxidation of CH4 to CO2 and further diluted by additional production of CO2 (King et al. 1990; Nedwell and Watson 1995) outside of the methanogenic zone (Fig. 1). We acknowledge that the non-linear correlation between emission and production ratios (i.e., the ln-ln plot in Fig. 3c) is complex, but a full discussion lies beyond the scope of our essay. In brief, possible combinations of respiration, anaerobic or aerobic methane oxidation, dissolved oxygen in sediments (Zhu et al. 2020) and water column (Jane et al. 2021) and water table depth (in peatland soils) (Evans et al. 2021) may explain the increase in attenuation of emission ratios at higher production ratios. Nevertheless, we would argue that emission ratios will likely increase as production ratios increase under climate warming and for that connection between production and emission ratios to be far stronger in soils than aquatic sediments as indicated by the 20-fold offset between the two lines in Fig. 3c. Conrad's idealized 1 : 1 CH4 to CO2 production ratio is seldom realized in anoxic sediments and far lower ratios are typical (0.1 : 1). Here, using a simple mathematical model we rationalize the prevalence of these low ratios as only small fractions of any available acetate and H2 being used for methanogenesis, with the remainder suffering a multitude of nonmethanogenic fates. Furthermore, despite the idealized ratio seldom being realized, CH4 to CO2 production ratios increase exponentially at higher temperatures through greater utilization of H2 for CH4 production. Higher CH4 to CO2 production ratios ultimately appear to drive higher CH4 to CO2 emission ratios. As Earth continues to warm, therefore, we expect this mechanism to contribute to higher ratios of CH4 to CO2 emitted to the atmosphere from freshwaters with the potential to further accelerate climate warming. None declared.
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