Salinity causes widespread restriction of methane emissions from small inland waters

Domain: earth_science
Published: 2024-01-24
Editorial outcome: accept

Abstract
Inland waters are one of the largest natural sources of methane (CH4), a potent greenhouse gas, but emissions models and estimates were developed for solute-poor ecosystems and may not apply to salt-rich inland waters. Here we combine field surveys and eddy covariance measurements to show that salinity constrains microbial CH4 cycling through complex mechanisms, restricting aquatic emissions from one of the largest global hardwater regions (the Canadian Prairies). Existing models overestimated CH4 emissions from ponds and wetlands by up to several orders of magnitude, with discrepancies linked to salinity. While not significant for rivers and larger lakes, salinity interacted with organic matter availability to shape CH4 patterns in small lentic habitats. We estimate that excluding salinity leads to overestimation of emissions from small Canadian Prairie water bodies by at least 81% (~1 Tg yr−1 CO2 equivalent), a quantity comparable to other major national emissions sources. Our findings are consistent with patterns in other hardwater landscapes, likely leading to an overestimation of global lentic CH4 emissions. Widespread salinization of inland waters may impact CH4 cycling and should be considered in future projections of aquatic emissions.

Introduction
Methane (CH4) is a potent greenhouse gas responsible for 16% of current atmospheric radiative forcing1. Inland waters are the largest natural source of CH4, emitting 398.1 (±79.4) Tg CH4 yr−1 2,3. However, this number is largely based on measurements performed in solute-poor waters 2,4–6, despite salt-rich systems representing roughly half of the global inland water volume7 and a fifth of inland water surface area (ref. 8 and references therein). There is clear evidence that salinity, particularly as sulfate (SO42−), inhibits CH4 production through multiple mechanisms, which may lead to lower CH4 emissions from these systems9–12. The paucity of empirical data from salt-rich inland waters raises questions about our current understanding of aquatic CH4 regulation and about the accuracy of global CH4 emissions estimates.

The salinity of aquatic ecosystems shapes microbial communities13, in particular the abundance and distribution of methanogens and methanotrophs14,15. Methanogenesis is the least energy-efficient carbon (C) mineralization process in the redox chain. An abundance of ions favors more energetically efficient reactions, with sulfate (SO42-) and iron (Fe3+) reducers outcompeting methanogens for labile C substrate and hydrogen ions12,16,17. The reduction of SO42−, nitrate (NO3−), Fe3+, and other ions can be coupled to anaerobic CH4 oxidation18–24, further suppressing CH4 concentrations at high salinity. Salinity can also interact with other key CH4 controls, with organic C availability modulating the SO42− inhibition of methanogenesis12,19,25,26, and nutrient availability changing with salt content due to sorption to sediments19,27. Salinity thus integrates multiple pathways of CH4 suppression. The inhibition of CH4 by salinity (especially SO42−) has been demonstrated in coastal and salt-rich wetlands10,11,28–32, as well as in experiments that demonstrated suppression of net sediment CH4 production under elevated exposure to NaCl9,33, suggesting a potentially significant effect of multiple ions on CH4 across salt-rich inland waters. We provide an extensive overview of the mechanisms by which salinity may restrict net CH4 production in inland waters (supporting text S1). Ultimately, the impact of these finer-scale controls on regional and continental CH4 emissions is unknown.

Here we survey 193 aquatic ecosystems, including rivers, lakes, open-water wetlands, and agricultural ponds spanning a wide range in morphometry, hydrology, chemistry, and trophic status in the Canadian Prairies (Fig. S1 and Table S1), a region with the highest density of salt-rich inland waters worldwide34. We support this with a peripheral survey of wetland ponds (fewer environmental parameters, with greater spatio-temporal sampling of CH4) plus high-resolution eddy covariance data from two wetlands representative of fresh- and hardwater wetland habitats on the Canadian Prairies. We show that salinity restricts CH4 emissions in small lentic water bodies, especially through ebullition, leading existing freshwater models to over predict emissions. Regionally scaled, this inaccuracy is highly relevant to the Canadian national emissions budget, as it is comparable to other components of national GHG inventories (e.g., wastewater treatment plant emissions). We show that salinity is a key driver of CH4, interacting with organic matter (OM) content to shape surface CH4 partial pressure (pCH4). Our findings are consistent with data from other global hardwater landscapes, leading us to conclude that salinity likely downregulates emissions worldwide, and current global budgets likely overpredict aquatic CH4 emissions due to overestimates of emissions from hardwater regions.

Results
Salinity–pCH4 link varies across ecosystem types
Across all primary sites where the full suite of limnological parameters was measured, we found clear differences in the predictors of pCH4 among ecosystem types. We used multiple linear regressions to explore the connection between salinity and CH4 while accounting for influences of other known drivers of CH4 cycling, including temperature35–37, and common proxies for organic substrate (DOC and TP4,5,38,39) (Table 1 and Fig. S2). The effect of salinity on pCH4 varied among ecosystem types, from non-significant in rivers and lakes to pronounced control of pCH4 in small lentic systems (surface area <0.1 km2, wetlands and agricultural ponds) (Fig. 1, S2, Table 1). In rivers, salinity, DOC, and nutrient concentrations were highly colinear (Pearson r > 0.6), making salt-rich rivers also highly concentrated in organic matter (elevated DOC and nutrient content), and overriding a potential inhibitory effect of salinity on pCH4. Similarly, there was no significant influence of salinity in larger lakes (surface area >0.1 km2), whereas ionic concentration was a key pCH4 predictor in small, lentic water bodies (surface area <0.1 km2) (Fig. 1a, S2).

Among ecosystem types, contrasting environmental characteristics likely led to differences in salinity–pCH4 relationships (Fig. 1a) between the small lentic systems versus larger lakes and rivers. The importance of salinity in small and shallow water bodies may reflect the closer connection between surface pCH4 and sediment methanogenesis, directly affected by salinity, compared to larger lakes where pCH4 is more susceptible to water column processes like mixing, oxidation, and pelagic production40,41. The concentration of OM, nutrients, and ions often covary due to common catchment sources (e.g., agricultural and urban inputs), hydrological transport, and evapoconcentration34,42–45. Accordingly, the highest salinity, DOC, TP, and TN concentrations were found in lentic water bodies with long water residence time (WRT) favoring solute accumulation, while fast-flowing lotic systems were the most solute-poor (Fig. S1 and Table S1). Site-specific factors can decouple OM cycling and ions, with groundwater inputs, local geology, and atmospheric deposition changing ionic water composition7,34,46. The influence of salinity on pCH4 observed in small lentic water bodies (Fig. 1, S2) has the potential for large-scale impacts as these wetlands and ponds are the most abundant aquatic features in the regional Prairie landscape34,47,48 and a large source of CH4 globally2,3.

Interplay between salinity and OM regulates pCH4 in small lentic systems
We explored the connection between CH4 cycling, salinity, and substrate availability (as DOC content) in small lentic systems (Fig. 1b) in more detail. The positive correlation between pCH4 and the DOC/salinity ratio (R2adj = 0.15, Fig. 1b, S3a) suggests that organic-rich systems (with elevated DOC concentrations) can compensate for the inhibitory effect of salinity on methanogenesis. Similarly, pCH4 correlated with ratios of TN and TP to salinity (Fig. S3b, c), indicating that DOC was a proxy for OM content and ecosystem productivity. As an independent validation of this finding, we sampled a peripheral set of 48 wetland ponds across the three Prairie Provinces (Fig. S1), covering the same environmental gradients, but each was sampled repeatedly throughout the 2021 ice-free season. This independent survey confirmed that the relationship between pCH4 and the ratio of DOC/salinity found here holds at broader spatial and temporal scales (Fig. S4). In line with previous research, the correlation with DOC likely reflects the absence of competition for organic substrate between methanogenesis and other reduction pathways when OM is abundant or when the low concentration of other electron acceptors limits alternative redox processes12,19,25. Conversely, low DOC/salinity ratios may favor other reduction reactions12,16,17 that outcompete methanogens for the limited available OM, enhance anaerobic oxidation of CH4, and restrict net CH4 production through other mechanisms (supporting text S1) thereby lowering pCH4. This inhibitory effect is likely mostly caused by SO42− ions in the wetland systems, which correlated strongly with salinity (Figs. S5 and S6), in line with previous studies of brine composition in Canadian Prairie waters34. For the agricultural ponds, the relationship between pCH4 and SO42− concentration was considerably weaker than for that with salinity (Fig. S6), indicating additional mechanisms independent of ambient SO42− content were relatively more important in restricting net CH4 production (as detailed in supporting text S1). Despite these differences, salinity as a predictor better captured the diverse mechanisms that may restrict pCH4 among small lentic ecosystems.

Using the empirical relationship in Fig. 1b, the modeled response of pCH4 to changes in salt content is non-linear, with the greatest sensitivity at the low end of the salinity gradient (Fig. 1c). Most sampled sites (78%) in the Prairie landscape exhibited moderate salinity <1 ppt (Fig. S1, Table S1), a range within which even modest salinity changes from year to year45,49 could have a substantial effect on CH4 dynamics (Fig. 1c). For example, at the same DOC concentration (10 mg L), a 0.5 ppt increase in salinity at low salinity conditions (0.5 ppt) results in a 35% reduction of pCH4, (710–458 ppm) while a 0.5 ppt increase in salinity from 3.5 to 4 ppt only decreased pCH4 by 8% (207–190 ppm) (Fig. 1c). The non-linear and enhanced effect on pCH4 at the lower end of the range of salinity in our simulation is important, because it shows that increased salinity in solute poor systems may have a stronger effect on CH4 dynamics than in already saline systems. Where anthropogenic pressures result in the salinization of hardwater systems alongside an increased supply of OM and nutrients, the net balance may not be as strong an increase of CH4 emissions as previously anticipated based on nutrients alone (e.g., ref. 39).

Higher salinity was associated with lower CH4 emissions from inland waters in the Canadian Prairies, particularly via ebullition from small lentic systems (Fig. 2). Diffusive CH4 fluxes ranged from 0.11 to 91 mmol m−2 d−1 in small lentic systems (5 ponds and 5 wetlands) (Fig. 2, Table S1), within the global range reported for small (<0.1 km2) water bodies39. Averaged ebullitive CH4 emissions rates, measured over the summer months in 10 individual ponds and wetlands (5 each), spanned 6 orders of magnitude, with 70% of measurements lower than the 1st quantile of globally reported ebullition rates for small lentic systems39. These systems were each sampled in one central location continuously through June, July, and August, thus providing integrated estimates of CH4 emissions. Past work has emphasized the need for detailed spatio-temporal sampling to constrain uncertainties in flux budgets for single-system research50. We highlight that to constrain regional-scale patterns and gradients, more intensive sampling efforts at each site would have added little to our study, given the multiple orders of magnitude of variability in emissions rates that exist between sites, which is already constrained in our current sampling design (see supporting text S2 and Tables S3, S4 for a demonstration of this rationale). Both diffusive and ebullitive flux rates were negatively correlated with salinity (Fig. 2), although the regression slope was much steeper for ebullition than for diffusion (−3.0 vs. −0.7, respectively, on a log10 scale), with a 10-fold increase in salinity (0.1–1 ppt) leading to a 4.5 vs. 1000-fold decline in diffusion vs ebullition, respectively. As detailed in supporting text S1, the stronger influence of salinity on ebullition likely reflects diverse controls that include an impact on sediment CH4 dynamics (CH4 production and anaerobic oxidation), whereas water column CH4 production, consumption, and physical mixing influence surface diffusion and weaken the effect of salinity on this flux pathway.

The extensive monitoring of two wetland sites with eddy covariance towers suggests that the link between salinity and CH4 emissions holds at an ecosystem-level and over annual scales. Emissions patterns from both sites aligned with our regression results (Fig. 2). The two wetlands have diverging salinity levels (0.5 vs. 2.3 ppt) and exhibited two orders of magnitude difference in CH4 flux rates (Fig. 2, S7) when integrating all flux pathways (diffusive, ebullitive, and plant-mediated) and over multiple temporal scales (sub-hourly to annual). Mean and median CH4 emissions at the low salinity site were 20.7 and 8.7 mg C m−2 d−1 and at the high salinity site were 0.96 and 0.07 mg C m−2 d−1, respectively. Were salinity not a controlling factor, we would have anticipated consistently high rates of CH4 emissions from both wetland ecosystems, given the hypereutrophic status of both sites and the DOC-rich surface water environments (Table S4). In addition to the role of salinity, differences in CH4 emissions at each wetland may be partly related to other ecosystem features (e.g., open water extent and vegetation features). Future work is needed to fully explain the finer-scale mechanisms and interplay between individual drivers that have led to the large difference in emissions observed here. Overall, our eddy-covariance measurements provide independent support for the Prairies-wide inverse relationship that we observed between salinity and CH4 emissions.

Our meta-analysis showed that the inverse relationship between salinity and CH4 emissions for lentic inland waters exists across the three additional global regions where data were available. Analysis of published data from lakes and ponds from Tibet, Mexico, and India (Fig. 2) show inverse relationships between emissions and salinity. Individually, these relationships are built from limited available data and are of varying strength, but collectively follow a similar trend as the more extensive datasets from the Canadian Prairies (Fig. 2). This further suggests that salinity may restrict aquatic CH4 emissions from hardwater landscapes worldwide (see supporting text S1 for more detail).

Improving the prediction of emissions from salt-rich inland waters
Existing empirical models5,36–38 predicted a portion of the variability in CH4 dynamics in a subset of our primary study systems, and for rates of diffusion and ebullition in particular, deviations from predictions were linked to salinity (Fig. 3). The models we tested were developed based on regional and global data largely from freshwater systems5,36–38, and use typical CH4 drivers including water temperature, lentic surface area, chlorophyll a, TN and DOC concentrations. These models captured a third of the observed variability in pCH4 in our dataset (R2 = 0.32; Fig. 3a), and weakly predicted diffusive and ebullitive emissions from small lentic systems (R2 = 0.15 and 0.03 respectively; Fig. 3b, c). Salinity, which is not included in these models, explained 20%, 24%, and 42% of the deviation from predicted pCH4, diffusion, and ebullition, respectively (Fig. 3d–f). Model deviation was large for ebullitive fluxes in wetlands and agricultural ponds, being on average ~3 orders of magnitude lower than predicted (Fig. 3c, f; in line with results from Fig. 2) reflecting a particularly strong impact of salinity on sediment-related processes. Given the generally weak predictive strength of such empirical models, the inclusion of salinity as a model term represents a simple, but major improvement to our ability to predict aquatic CH4 emissions in Canada (Fig. 3) and likely abroad (Fig. 2).

Salinity impacts large-scale CH4 budgets
By accounting for salinity, the emissions budget for the Canadian Prairies shrinks dramatically as compared to scenarios relying on soft-water model predictions. As a conservative first-order calculation of the potential magnitude of this overestimation, we tested the effect of two salinity levels (0.5 vs. 0.1 ppt). These levels, respectively, correspond to the median salinity value of the small lentic sites that we sampled (Table S1), versus that of typical freshwater systems. We predicted the total CH4 emission rate (diffusion+ebullition) using the relationship from a subset of our primary sampling sites in Fig. 2 (n=10, small lentic sites sampled over three summer months51). This yielded a large difference in flux rate (1.57 vs. 8.42 mmol m−2 d−1, respectively), consistent with the ~3-fold overestimation of total flux rates by existing freshwater models (Fig. 3). The results are within the range of the differences between salt-rich and fresh water sites in our eddy-covariance measurements (Fig. 2, S5). We conservatively applied this simulated difference in emissions to three summer months and used only the areal estimate of small open-water lentic systems in the Canadian Prairies (<0.1 km2, 2869 km2 in total area). This areal estimate is derived from recently completed mapping and represents the best available current estimate of small lentic systems (see the “Methods” section) and is thus a significant advance to scaling Canadian Prairie aquatic emissions. While not included in the scaling estimates, simulations using our peripheral sampling dataset indicated that uncertainties in this cross-province extrapolation stem mostly from spatial coverage, and not enhanced within-site or temporal coverage (Supporting Text S2). This first-order extrapolation exercise resulted in >5-fold lower emissions in the actual salt-rich vs. freshwater scenario (6555 vs. 35,169 Mg CH4 over the 3-month period). This difference (0.97 Tg CO2 equivalents) is regionally significant, equal in magnitude to ~11% of the total C footprint (CO2 + CH4 emissions) of the entire beef cattle industry of the province of Saskatchewan52, or to the entire national emissions budget of the Canadian wastewater treatment sector53. Further, the discrepancy in CH4 emissions in our two calculations is roughly equivalent to the entire N2O budget (in CO2 equivalents) for all US-based Prairie wetlands54. Therefore, as a first-order approximation, our calculation demonstrates the importance of obtaining accurate emissions data for Prairie ecosystems in the context of our national GHG emissions inventory. Inaccuracies in these calculations have far-reaching implications for national emissions mitigation, and how aquatic ecosystems are represented in these budgets. The inclusion of salinity represents a simple but major refinement to estimates of aquatic emissions from hardwater ecosystems in Canada and likely other nations (Fig. 2).

Globally, the use of soft-water-derived models to estimate hardwater CH4 fluxes can lead to an overestimation of emissions, with consequences for planetary budgets. We don’t presently have the data required to determine the rate of CH4 emissions from salt-rich inland waters at the global scale with confidence. However, our observations from a large area of Canada and three other global regions imply that CH4 emissions are restricted in salt-rich lentic water bodies, and these fluxes have likely been overestimated by the traditional methodologies used to scale lentic emissions rates to the globe2. As a first step to resolving this issue, we demonstrate the potential magnitude of this overestimation at the global scale using the same exercise that we applied to the Canadian Prairies, i.e., we compare the difference in scaled fluxes when using CH4 emissions rates of 1.57 vs. 8.42 mmol m−2 d−1 (derived from our mid-salinity and freshwater estimates, respectively). Approximately 12.8% of the global area of small-sized waterbodies are salt-rich (166,120 km2, detailed in the “Methods” section). Using the same conservative 3-month window of time as above, the difference in emissions estimates, when each flux rate is scaled, is 0.38 vs. 2.04 Tg CH4 yr−1, respectively. This 1.7 Tg CH4 yr−1 difference represents a potential overestimation equal to 4% of the most recent estimate of global lentic CH4 emissions (41.6 Tg CH4 yr−1; ref. 55). Using a comprehensive, annual-scale approach and including larger ecosystems would lead to an even larger discrepancy in actual versus currently estimated emissions for hardwater ecosystems. The global lentic ecosystem emissions budget is continually being refined55, and future explicit consideration of salt-rich inland waters may help to constrain this budget and resolve some of the discrepancies between top-down and bottom-up global CH4 emissions estimates56.

Future salinization may impact aquatic emissions
Worldwide, salinization of inland waters is on the rise due to anthropogenic activities (mining, agriculture, urbanization, atmospheric deposition, climate change)32,42,44,57–62, which may further reduce aquatic CH4 emissions32. In the Canadian Prairies, SO42− concentrations have increased in 64% of the 14 monitored lakes for which data are available in Saskatchewan over the past 30 years (Fig. S8). This is consistent with previous findings that, despite high-local variability, many Prairie waters are becoming more saline42,63. This may in part be linked to rapid increases in the application of S-based fertilizers in agricultural landscapes64, which may in turn lead to enhanced SO42− content and salinity in receiving waters (though such a mechanistic link remains unconfirmed). While future global increases in temperature, eutrophication, and DOC content are expected to stimulate CH4 production36,65, the effects may be partially counteracted by increases in salinity. To derive more accurate predictions, future emissions scenarios should consider both ambient salinity, and projected changes in ecosystem salinity alongside other variables. Our study demonstrates that ignoring the link between salinity and CH4 emissions can have major implications for the emissions budgets of individual nations where hardwater ecosystems account for an important fraction of regional surface water.

Methods
Sampling sites in primary and peripheral surveys
The study was conducted in the Canadian Prairie ecozone of the provinces of Alberta, Saskatchewan, and Manitoba, covering 467,029 km2 (Fig. S1). The region is characterized by a cold continental to semi-arid climate66, with extreme seasonal temperature variability (monthly means from ~19 °C in July to ~−18 °C in January34), low annual precipitation, and strong winds67. Land use is largely agricultural, containing >80% of Canada’s farmland area68. The region is known for its generally flat topography34,67, widespread endorheic drainage basins, and high evaporation to precipitation ratio, making hardwater lentic systems (wetlands, ponds, and lakes) largely dominant in the regional aquatic landscape34,47,48. The region exhibits the highest abundance and diversity of salt-rich lakes worldwide34, mostly driven by elevated concentrations of SO42− in lakes and wetlands, with more variable ionic composition in agricultural ponds (Fig. S5, but see supporting text S1)34.

The 193 primary survey sites (Fig. S1) covered a diverse range of system types and sizes, with 23 sample drivers, 17 lakes, 45 wetlands (shallow open water), and 108 agricultural ponds (Table S1), which are common features of the landscape69. Each site was sampled once in the summer (June–August 2011–2021). Peripheral survey sites included a series of 48 Prairie wetlands (16 in Manitoba, 16 in Saskatchewan, and 16 in Alberta) located in the prairie parkland ecozone that were sampled between May and September 2021. For the most part, peripheral survey sites were sampled a minimum of 3–5 times over the course of the open-water season, except for a few sites that dried up shortly after the initial sampling round. Additionally, 2 of the wetland sites in Manitoba were equipped with eddy covariance flux towers and were sampled more frequently (n=10). The general environmental features of each site are provided in Table S4.

Environmental parameters
At each primary survey site, water temperature, dissolved oxygen concentration, pH, and specific conductivity were measured near the water surface using a multiparameter probe. The probes used at each site varied in model but were all either Yellow Springs Instruments (YSI) or Hydrolab DS5 model probes, and all were routinely calibrated before sampling. Salinity was either directly measured by the probe or derived from specific conductivity and temperature using the function ‘swSCTp’ from the package ‘oce’70 in R71. Salinity is reported here as ppt (%), consistent with other limnological analyses, where 1 ppt = 1 PSU. Water samples were collected at each sampling site (at <0.5 m depth) in clean bottles and stored at cold temperatures until analyzed for DOC, TP, and TN concentrations. DOC analyses were performed on water samples filtered to 0.45 μm on site or in the lab (shortly after collection), then acidified (to remove inorganic carbon) before being processed on an organic carbon analyzer (Shimadzu TOC-L or 5000A, or Aurora 1030W). TP was analyzed by spectrophotometry on a Lachat QuickChem 8500 instrument using the standard molybdenum blue technique after persulfate digestion. TN was measured after chemical digestion on an Alpkem analyzer (IO analytical Flow Solution 3100), a Lachat QuickChem 8500, or a Dionex DX600 instrument. For 105 sites, TP and TN analysis were performed on filtered samples (0.45 μm) and thus represent the dissolved rather than the total P and N concentrations. However, where both the dissolved and total concentrations were measured, the dissolved fraction represented the vast majority of nutrient content (mean of 77% and 89% for P and N, respectively). Therefore, we assumed the dissolved fraction to be representative of the total nutrient content in these samples. The small error that this introduces into the data was considered in the interpretation of results, and these assumptions have little impact on our observations over such long nutrient gradients. Chlorophyll a concentration was measured in most lentic systems by spectrophotometry after filtration (on GF/F or GF/C filters) and alcohol extraction. Concentration of SO42− was measured in 118 sites using a SmartChem 200 discrete analyzer or a Dionex DX600 and ICS2500.

CH4 partial pressure
CH4 concentration in all samples was determined using the headspace technique, however, since the database is a post hoc combination of data collected independently by different research teams, details of the gas sampling method are not uniform. Yet variation introduced by distinct methodologies is expected to be minor relative to the measured range of CH4 content across sites. Overall, water was collected in an airtight container (140 mL plastic syringe or 1.2 L glass bottle or 160 mL Wheaton glass serum bottle). An air headspace was created inside the sealed container, either on-site or in the laboratory (after preserving the water with potassium chloride). The headspace consisted of ambient air at the sampling site or ultra high purity dinitrogen in the laboratory, and the air-to-water ratio varied between 0.05 and 0.25. To equilibrate the gas and water phases, the closed container was shaken for at least 2 min. The gas phase was then extracted and analyzed for CH4 concentration by gas chromatography on a GC Scion 456, a Varian 3800, or a Thermo Trace 1310 instrument, calibrated against multiple standards. The in-situ concentration of CH4 in the water was back-calculated based on the gas solubility (dependent on salinity and water temperature) before and after equilibration, local atmospheric pressure, and the headspace air-to-water ratio.

Calculations of emissions rates
To link CH4 emissions rates to salinity, we used previously published datasets of surface diffusive flux from a subset of the larger primary survey sites, so that we included 139 wetlands and ponds. Published emissions rates for 101 ponds surveyed in 2017 were taken from Webb et al.72 and diffusive flux rates for the remaining 38 agricultural ponds and wetlands were taken from Jensen et al.73. In both cases, the rates of emissions were estimated using the following equation:

F = k (Cw − Ceq) (1)

where F is the CH4 diffusive flux rate, k is the air–water gas transfer velocity, Ceq is the CH4 concentration in the water at equilibrium, and Cw is the CH4 concentration measured in the water. As detailed in both publications, the parameter k was estimated as the average (±1 SD) value of 1.64 (±1.14) m d−1. This value was derived from floating chamber measurements (10 min duration each, n=30) conducted in 2017, on 3 occasions on 10 of the agricultural ponds72. These diffusive flux estimates from small lentic systems were then used to test the applicability of existing empirical emissions models (Fig. 3b, e).

CH4 ebullition flux rates initially published and detailed elsewhere51 were measured at 10 sites (5 natural wetlands and 5 agricultural ponds) that are a subset of the 38 sites for which we used published diffusive flux data73. At each site, bubbles were collected by deploying two inverse funnel traps (0.061 m2 and 27.3 cm diameter), one in the shallow and one in the deep region of the waterbody, sampled from June to August to determine the volume of bubbles emitted. Here we report the seasonally averaged value of ebullition from deep sites because most measurements in shallow sites were lost due to instability of traps in shallow water. The mean value with associated error bars (±1 SD) for each site is shown in Fig. S9. The CH4 content of bubbles upon ascension was determined by perturbing the sediments and collecting freshly emitted bubbles with funnel traps fitted with an airtight plastic syringe. Gas collected in the syringe was injected in 12 mL Labco vials and analyzed for CH4 concentration as above. Summer mean CH4 ebullition rate was calculated for each site as the product of the total volume of bubble emitted and the concentration of CH4 in freshly emitted bubbles, converted to an areal daily flux rate (per m2 of surface water)51.

Eddy covariance measurements
The eddy covariance method was used to take continuous, ecosystem-scale measurements of CH4 flux over two prairie wetland sites of diverging salinity levels over a full year (May 20, 2021 to May 19, 2022). A flux tower was constructed at each of the sites with sensors mounted at ~4.1 m at both sites. These sensors include a 3-dimensional ultrasonic anemometer (RM Young 81000, RM Young Inc.), an open path CO2/H2O infrared gas analyzer (IRGA) (LI-7500A, LI-COR Inc.), and an open path CH4 IRGA (LI-7700, LI-COR Inc.). An LI-7550 analyzer unit housing LICOR’s Smartflux 2 software was installed to collect and process high-frequency (20 Hz) flux data on-site. High-frequency data was subsequently processed into 30-min averages using the Eddypro v7.0.6 software and then filtered to remove bad data and measurements taken under poor atmospheric conditions.

Using the R package REddyProc v2.2.074, moving point tests were used to determine their minimum friction velocity thresholds for each site75. Half-hourly measurements with friction velocities below this threshold were removed for having insufficient atmospheric turbulence to produce good-quality data. Further filtering by stationarity and turbulence conditions was performed through quality checks using the flagging system proposed by Mauder and Foken76. Data flagged as “2” were identified as bad-quality data and removed from the dataset. Spike detection and removal with variance thresholds were also conducted to remove bad data. Finally, CH4 fluxes received when LI-7700 sensor signal strength dropped below 20%, and when winds passed through the flux tower between 330° and 30° wind directions were removed.

Data gaps in meteorological variables were filled by merging data from nearby Environment and Climate Change Canada climate stations, and gaps in CH4 data were filled using the random forest method77. The final datasets used for this study represent the filtered and gap-filled data from each prairie wetland site.

Statistical analyses and mapping
All statistical analyses and map construction were performed in R71. Prior to analysis, data were log10 transformed if necessary to meet normality requirements. The links between pCH4 or flux and other variables were assessed via multiple linear regressions using the function ‘lm’ and verifying the homoscedasticity of the residuals with a Shapiro-Wilk test (function ‘shapiro.test’). The same regression analysis was performed on standardized values (to a standard deviation of one) to compare effect sizes (coefficients) of explanatory variables (Fig. S2). A marginal effect analysis was performed for each system type using the R package ‘sjPlot’78 to visualize the effect of salinity on pCH4 when other variables are held constant (at dataset average). Measured pCH4, diffusive, and ebullitive fluxes were compared to predicted values based on existing literature models. We selected multiple models that use established CH4 predictors measured in our dataset, and that are based on empirical surveys in Canada or at the global scale. Following Rasilo and coauthors, pCH4 was modeled based on water surface area, temperature, and TN concentration for lentic systems (lakes, wetlands, and ponds)37, using a model based on an empirical linear relationship developed from large-scale surveys in eastern Canada37 with the partial pressure (in ppm) estimated as pCH4 = −0.26 − 0.31(log10 Area) + 0.03(Temperature) + 0.66(log10 TN). Predicted CH4 diffusive and ebullitive flux rates were calculated as the mean of two individually modeled values. First, we predicted diffusive emissions using a global model that includes water surface area and Chla concentration5, with rates in mg C m−2 d−1 estimated as log10 CH4 emissions = −0.167(log10 Area) + 0.53(log10 chla) + 0.098(log10 Area) × (−log10 chla) + 0.705. Second, we used a regional East-Canadian model including surface water area and temperature37, with rates also in mg C m−2 d−1 estimated as log10 CH4 emissions = −0.37 − 0.29(log10 Area) + 0.06(Temperature). Likewise, predicted rates of CH4 ebullition were considered as the mean of a global model based on a global relationship with Chla5, where log10 CH4 emissions = 0.758(log10 chla) + 0.752. We also estimated ebullitive flux rates from a regional (Eastern Canadian) model that includes sediment temperature as a predictor36, where log10 CH4 emissions = −1.19 + 0.11(Sediment Temperature). We approximated sediment temperature as our measured surface temperature minus 1 °C. While comparing results to different existing individual models from the literature would be a useful exercise, this was not the objective of our study and instead relied on the use of multiple models to account more completely for the different potential controls on CH4 cycling and reduce the bias associated with any one model.

Spatial upscaling
To estimate the effect of salinity on CH4 emissions at a regional scale, we simulated the CH4 total flux rate using the regression model developed in Fig. 2 as a function of two salinity levels: 0.5 ppt (median of sampled small lentic sites) vs. 0.1 ppt (typical value in fresh waters). The regression model is based on 10 sites (5 wetlands and 5 ponds) with robust data on both diffusive and ebullitive summer fluxes, providing total CH4 emissions from open-water environments (excluding emergent vegetation). The difference in CH4 flux rate between the two scenarios was applied to 3 months of summer (91 days) and to the regional surface area covered by small open-water lentic water bodies. We calculated the lentic surface area of the Canadian Prairie ecozone using a combination of geospatial layers: the Canadian Wetland Inventory (CWI; systems ≥ 0.0002 km2)79, and the Alberta Biodiversity Monitoring Institute/Ducks Unlimited Canada Southern Saskatchewan Moderate Resolution Wetland Inventory (ABMI/DUC 2022; systems ≥ 0.0004 km2)80 for areas outside of the CWI layer coverage (45.9%). We selected only waterbodies of ‘shallow/open-water’ type, excluding marshes (which are distinguished from shallow/open water by having >25% emergent vegetation cover) and filtered out riverine wetlands (to exclude floodplains) to get a conservative areal estimate of lentic waterbodies of 8843 km2, representing 1.9% of regional land cover. We restricted the upscaling exercise to lentic systems <0.1 km2 (totaling 2869 km2) to remain in the size range of our empirical model. The product of this regional aquatic area by the difference in CH4 flux rate in hardwater vs. freshwater scenarios represented the potential overestimation of CH4 emissions from small waterbodies of the Canadian Prairies if these systems were considered as salt-poor (0.1 ppt).

As a first-order approximation of the potential salt effect on CH4 emissions at the global scale, we estimated the global area of salt-rich small lentic systems and calculated their emissions based on our two reported emissions rates from the Canadian Prairies (intermediate salinity versus freshwater rates). The area of 166,120 km2 was derived from the tentative lower-bound estimate of the global area of salt-rich inland waters (538,892 km2)81 multiplied by 0.31, the fraction of small (<0.1 km2) systems based on the global size distribution of lakes82. Using this approach, the fraction of salt-rich to the total area of small lentic systems is 12.8%81,82.

Temporal trends
To explore temporal trends in SO42− concentration in the study region, we used a publicly available (Saskatchewan Water Security Agency), long-term monitoring dataset collected in southern Saskatchewan lentic systems between 1990 and 2020. A subset of sites was selected for long-term trend analysis based on the following criteria: (1) a minimum of 10 observations within the 1990–2020 time period, (2) observations span at least 5 years, (3) at least one recent observation after 2010. Where all three criteria were met, a Sen slope analysis was performed using R package ‘zyp’83 to determine the trends in SO42− over the past 3 decades. For each Sen slope, a 95% confidence interval (CI) was calculated and used to determine the significance of the slope, with trends considered significantly increasing or decreasing if the CI range was entirely positive or negative, respectively (Fig. S8).

Data availability
All data used in this study are openly available from multiple sources. Aquatic biogeochemical data from published articles are openly available as linked to published manuscripts or from the Government of Saskatchewan Water Security Agency by request. New data or published sources from primary and peripheral survey sites are available in the Federated Research Data Repository (https://doi.org/10.20383/103.0848). Eddy covariance and associated data are available at the Ameriflux website by accessing sites CA-EM1 (Newdale Manitoba; https://ameriflux.lbl.gov/sites/siteinfo/CA-EM1) and CA-EM2 (Shoal Lake Manitoba; https://ameriflux.lbl.gov/sites/siteinfo/CA-EM2). Hydrometric data for rivers are openly available at https://wateroffice.ec.gc.ca/search/historical_e.html with corresponding station codes for primary sampling sites listed in supporting data.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review of research article “Salinity causes widespread restriction of methane emissions from inland\nwaters”, submitted by C. Soued et al. for publication consideration in Nature Communications.\nThe key hypothesis of their research is that the exclusion of salinity (namely sulfate, SO42-) from\nmethane emission models from inland waters may cause an overestimation of emission estimates. The\nauthors estimate that excluding salinity effects may lead to an overestimate of emissions from small\nwaterbodies by ~80%. This could become more relevant in future climate scenarios if salinity increases\ndue to changes in precipitation and anthropogenic activities. The authors used data collected from\ninland waters in a Canadian Prairie region, including rivers, lakes, rivers and ponds. Additionally, they\npresent methane emission data from two wetlands of varied salinity using the atmospheric eddy\ncorrelation technique. In this case, the saltier system clearly had lower methane emissions than the less\nsalty system. The authors also show that CH4 ebullitive emissions were reduced in more saline\nwaterbodies. In fact, it seems based on their data and interpretation that sulfate inhibits sediment\nmethane formation, which suppresses fluxes at the sediment water interface – either diffusive or\nebullitive. However, the sulfate does not appear to suppress the methane production in the water\ncolumn of (larger) lakes, which could point to other mechanisms of CH4 formation, i.e. processes related\nto “oxic methane production”.\nThe data set is extensive; however, I had a difficult time following the data, how they were obtained, the\nenvironmental setting and the implementation, resulting in multiple readings of the manuscript. I have a\nfew issues (and questions) with the manuscript. The fact that sulfate suppresses methane production\n(and thus fluxes) is well known (especially in the oceanographic community), but perhaps less known is\nthe number of brackish (i.e. sulfate-rich) lakes – which the authors use in their estimates. However,\nthe authors’ key message that emission models should include salinity (that is sulfate, I disagree with using\nsalinity as a parametrization here) could be a solid message, however, it is still unclear how this could be\napplied, and in which cases.\nThroughout the manuscript, I question the use of Salinity as this does not necessarily imply sulfate and\ncould result in considerable error in the authors’ correlations. In fact, they measured SO42- in a lot of the\nstudy sites, so I do not understand why this was not used as the key parameter. While the Fig S3 is\nsomewhat convincing relating Log of sulfate to Log of salinity, since it is on a log-log scale I suspect there\nis substantial error here. My point, is salinity really an appropriate measure here? I understand it is the\neasiest to measure, but perhaps the actual electron acceptor that outcompetes the methanogens would\nbe a much more solid analysis.\nThe data collection on the various lakes (inland waters) is vague and needs to be expanded. Specifically,\nthe data for the individual lakes/ponds, their properties (depth, area, etc), ancillary data, dates of data\ncollection. I believe these data must anyway be supplied should the paper be published. One concern is\nthat the lakes could be overturning while sampling occured, which significantly affects surface methane,\nsalinity and DOC – especially if the lake is experiencing an anoxic hypolimnion. In fact, the authors state\nthat each lake was sampled 3 – 5 times, however no statistics or at least mean and STD are given.\nA final point, I think that rivers should be excluded in this analysis, as these are completely different\nsystems than lakes and ponds (high flow rate, turnover, rapid surface gas exchange), etc.\nMy suggestion would be, including the above comments, include only data where sulfate was measured,\nand only include lakes and ponds. The fact that these two systems respond oppositely in terms of CH4 to\nincreasing SO42- (though the correlation for CH4 and SO42- for lakes is very weak) deserves much more\ndescription and investigation. I question the use of CH4 concentrations in these types of studies, as there\nare some many parameters that can affect concentration in the surface waters (wind exposure, oxidation\nrates, light penetration, etc). I think using rates (i.e. fluxes) is much more robust and revealing. This is a\nnice data set, and potentially nice story. Using only the waterbodies where CH4 flux, concentrations\nand SO42- are all measured would make for a interesting, and very applicable study – especially when\nvalidating the data versus the methane modeling approaches.\nI have specific comments below:\nThe use of “core” study site is ambiguous, as I often think of sediment core. Suggest changing to\n“primary”.\nLine 40 – it would be interesting (if possible) to know how salt-rich lakes are currently represented\nproportionately in the database used to estimate current global estimates of inland water emissions.\nLine 42 – it is very well known that SO42- inhibits CH4 production. Check the oceanographic and coastal\nresearch literature.\nLine 50 – you list SO42- and Fe3+ as energetically favorable electron acceptors. How important are other\nEAs in these systems? The relevant ones should be listed here.\nLine 60 – the authors survey 193 freshwater systems. As a reader, I have an issue interpreting these\nresults without more information on the individual waterbodies.\nLine 78 – define “full suite of limnological parameters”.\nLine 81 – I am not clear why the authors present river systems in this paper, as these systems are\nsubstantially different than the ponds and lakes. I would suggest omitting the rivers from this study, and\ndiving deeper into the fact that salinity affects CH4 in small systems (i.e. ponds), and not lakes. It would\nbe interesting to know where the bathymetric cutoff would be. They touch on this point in line 88, but\nthink that this could be further explored.\nLine 94 – It would be helpful to the reader if the authors could present upfront the global representation\nof wetlands and ponds in general, and the fraction that are brackish – or better yet, the ones with\nelevated SO42-. A table here quantifying the global setting would be appropriate.\nLine 100 – why not show the relationship between CH4 and TN/TP ratios? This can easily be added to the\nsupplemental.\nLine 204 – the authors state “Existing empirical models” are used to compare the model results with\ntheir measured data. As this is such a key component of the study, I suggest that the model details be\npresented so that the reader doesn’t have to search for them in the literature.\nLine 208 the model is driven by chlorophyll a, I would be curious how the data presented here correlate\nwith CHLa – could this be a main driver?\nGeneral comment\nConfirm that tables and figures (including supplement) are listed in order.\nFigure 1a – This figure is very hard to read. As this is a key figure for the message of the paper, I make the\nfollowing suggestions. Remove the River data (from the study in general), and present the lake, ponds\nand wetland data in individual panels with the data behind (mean and std for each site). The correlation\nfor the wetlands and ponds is excellent – it would be great to see with the actual data. It is interesting\n(while very weakly correlated) why the methane increases with salinity in the lakes. In my opinion, this\ndeserves a more detailed focus within this paper, as it is contrary to the authors’ key hypothesis. That is,\nif the salinity decreases the methane in ponds and wetlands, is this compensated by an increase in\nmethane production with salinity in lakes?\nFigure 1b – Again, I strongly suggest removing rivers from this analysis. Overall, this correlation is very\nweak and I find this unconvincing. Esp. including all the different water types in a single correlation. I\nsuggest developing the individual correlation for each waterbody type. This correlation however is the\nbasis for the model shown in Fig. 1c. I question if this can be applied in the manner it has been here.\nFor the first thing, since Fig. 1a shows an inverse relationship between salinity and methane, I am unclear\nhow these data can be used to infer the model. The separate contributions of DOC and salinity in the\nmodel in Fig. 1c could be better explained.\nFigure S2. This figure shows the effect size and the confidence of the regression analysis on the various\nparameters driving the concentrations of dissolved pCH4. It seems that the salinity only negatively\nimpacts methane in the small lentic systems. While the effect size is shown to be large for lake (salinity)\nmethane, it seems to be neutral which I don’t fully understand. The strongest effect is the area – which I\nfeel should be discussed in more detail. Statistics aren’t my strong point, but I have trouble\nunderstanding what this figure actually means. Also, in this figure, the salinity only really seems to have a\nstrong effect on small lentic systems. Also, DOC seems to have the largest (positive) effect on methane,\nbut this is not seen in the individual class systems (i.e. lakes vs rivers vs small lentic). How is this\nexplained?\nMethods – Sampling time: How does that effect outcome due to changing climate (June – August).\nSites were sampled 3-5 times, it would be useful to know the range of values and variability in salinity\n(i.e. sulfate), pCH4 and DOC during these times.\nMethods – Line 147, which type of multiparameter probe? Only surface, or were profiles used?\nMethods – Line 393, how was the wind measured at each site? What is the justification for using\nK600 parameterization from Cole and Caraco, 1998? That study used tracers to estimate k600, and has since\nbeen shown to underestimate k600. My suggestion, since the authors performed direct chamber\nmeasurements on 10 ponds, calculate the k600 directly from their data and compare with other\nparameterizations that may be better suited, e.g. MacIntyre et al. 2010 Geo Res Lett.\nMethods – Line 398, The authors should provide more details on how bubble ebullition was measured.\nHow were the instruments (funnels) deployed to ensure that they did not disturb the underlying\nsediments? It would be interesting to see the maps of the ponds, depths of deployment and data.", "reviewer_2": "The article by Soued, Bogard and others, explores the controls of salinity on methane emissions in inland\nwaters. There are multiple studies showing the importance of salinity on methane emissions, but this\nstudy leverages a uniquely large dataset across many systems to provide a landscape level assessment of\nthe role of salinity in freshwater methane emissions. The article is well written and except some issues\nthat I detail below, the analysis is compelling and supports the story well. Below I detail the bigger issue I\nhave with the study and then some minor issues that could be addressed in a future revision.\nMAIN ISSUES\nThe biggest issue I have with this study is how all different aquatic systems (rivers, lakes, ponds and\nwetlands) are combined in the analysis. The breadth of systems is a strength of the manuscript, but the\nway it is used may not be fully accurate. This is because in some systems (rivers and large lakes) salinity is\nnot that important relative to other factors according to their analysis, and therefore the conclusions and\nsubsequent analysis should reflect that. The title “Salinity causes widespread restriction of methane\nemissions from inland waters” promises that salinity is THE driver across all systems and is widespread,\nwhile the analysis doesn’t fully support it. I will pull a couple of examples to better illustrate the problem,\nand then suggest a way to address it.\n-In the opening sentence of the results and discussion (L79) states: “Across all core sites where the\nfull suite of limnological parameters were measured, salinity had a strong negative effect on pCH4 in a\nmultiple linear regression that also included temperature33–35, and common proxies for organic\nsubstrate (DOC and TP4,5,36,37) (Table S2 and Fig. S2)”. Here I am not sure if they refer to the multiple\nlinear regression including all data, or the system specific linear regression. If the former, I am not sure is\nstatistically sound to include all these different aquatic systems in the same analysis, without including\nthe system as a factor in the model. If the latter, it is not correct given that the MLR for lakes and rivers\nshow in fact a positive effect of salinity on methane emissions (table S2).\n-In the important analysis of Figure 1. Is the regression in panel b on all data, including big lakes and\nrivers? If so, is it meaningful when they behave so different than ponds in wetlands? The analysis in\npanel c depends on the relationship in panel b, and given the conflicting patterns between lakes/rivers vs\nponds/wetlands (shown clearly as the marginal effects in panel a), it may be a bit misleading to use all\ndata to build a model of DOC/salinity vs CH4, which is then used to do some nice and clean lines of\nsalinity and CH4 across DOC (panel c). I don’t dispute these results, but that it may not hold as cleanly for\nrivers/lakes as for the other systems based on the data provided.\nThe authors are clear about the fact that salinity is not a first-order control across all systems (lines 83-\n90), show the data in the multiple linear regressions (Table and figure S2) and the marginal effects in\nfigure 1a. But then in some other cases the authors use all data lumped together to do some broader\nanalysis and claims, that to the reader it may appear that they are applicative across all inland waters\nwhile they are not for larger lakes and rivers (again based on this dataset). I would suggest two ways to\naddress it:\n-Solution 1: The authors have done a much more extensive effort on the aquatic systems that have a\nstrong effect of salinity, with a regional survey of ponds and some eddy covariance data for wetlands,\ngreat work! Given this, maybe the work should have an initial assessment across all systems as follows:\n“we sampled all those systems, seems like the effect of salinity is stronger in wetlands and ponds\nbecause X, in lakes and rivers its non-significant and even positive because of Y. We then proceed with a\ndetailed analysis and landscape relevance of salinity controlling CH4 emissions in ponds and wetlands”.\nThis would still provide a compelling work and with a bit more rigour, maybe you should leverage in the\nintroduction then that across all inland waters, wetlands are the largest source of CH4 and that small\nponds the most uncertain one.\n-Solution 2: Use literature data to expand the analysis for lakes and rivers. There is a large new database\nof river methane data that includes conductivity data (https://essd.copernicus.org/preprints/essd-2022-\n346/), and a new global estimate of lakes\n(https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022JG006793 ) and reservoirs\n(https://doi.org/10.1029/2021JG006305 ) with supplementary data. This would be more work and I am\nnot sure the lentic products have salinity data, but it could be crossed with other chemical databases.\nThis would be more work, but if you prefer to maintain the focus across all inland waters more data is\nneeded to support the role of salinity in other aquatic systems besides ponds and wetlands.\nMINOR ISSUES\n-L 41: Instead of freshwater volume, what is relevant in this article is the surface area from an\nemission perspective.\n-L60: Here the number of sampled sites is a bit confusing, I would rephrase to: “Here we survey 193\naquatic systems, including rivers, lakes, open-water wetlands, and agricultural ponds and spanning…”.\n-L94: Maybe worth noting that small lentic water bodies are the largest source of uncertainity in aquatic\nmethane emissions, both in rates and the total global surface area.\n-L113: Here is unclear what aquatic systems you are speaking about. Is it all of them? Ponds?\n-L124-L133: This paragraph is quite short and technical. Maybe it can be clarified a bit. Two suggestions\nhere:\n-L128: Instead of giving specific changes in ppm of CH4, all of that could be simpler by saying “For\nexample, at the same DOC concentration (10 mgL), a 0.5 ppt increase in salinity at low salinity conditions\n(0.5 ppt) results in a 50% reduction of CH4, while a similar increase in modest salinities (4 ppt) only\ndecreased CH4 by 11% (Figure 1c)”.\nThen at the end is missing a take home message. For example a quick draft of one: “Thus, increased\nsalinity in solute poor systems may have a stronger effect on methane dynamics than in already saline\nsystems, given anthropogenic pressures that result in salinization of freshwater systems (ref) but also in\nan increased supply of OM and nutrients, the net balance may not be an increase of methane emissions\nas previously anticipated (ref).”\n-L150: Ecosystems means ponds here right?\n-L176: You could even say that the low salinity wetland has three times more DOC than the high one to\nfurther support this result. Take it or leave it.\n-L199: For the Mexican pond data, If 0, how is it shown in the plot and the regression line calculated?\nAlso, there is a study of Spanish saline lakes that could be worth to include in this figure\nhttps://www.mdpi.com/2073-4441/9/9/659\n-L204: Here and in figure 3, it is all based on published empirical models but these models are not\npresented in the results. For transparency, I would include the models in the methods, and how they\nperform in the supplement materials. These results further strengthen my main issue above, given that\nthe model for rivers does OK (with an offset, but these are different systems form the model) and also\nfor lakes. This analysis would be stronger and more compelling if restricted to ponds and wetlands.\n-L177: The regional upscaling is sound and compelling. In the global attempt though, the authors are\ncautious enough so it is ok, however I find more interesting to highlight that both the area and total\nemissions are heavily uncertain for ponds, and this study provides an important mechanism that could\nrefine global estimates. This is because global estimates from most inland waters are still quite bad from\na mechanistic perspective, so maybe no need yet to quantify biases if salinity is not included.\n-L342: Does eddy covariance need to be in caps?\n-L 358: Would be helpful to know what was the norm and the exception. Any number to say what % of\nsites that were filtered or not?\n-L367: links or reference to the data sources?\n-L369: While still being in Canada, that relationship is from another biome that changes those\nhydraulic scaling relationships. I would rather use a larger assessment such as Raymond et al 2012 L&O Fluids and\nEnvironments (https://doi.org/10.1215/21573689-1597669)\n-L392: I am not a wetland person, but is it common to use a lake based model of gas exchange for\nwetlands?\n-Table S2: Would be interesting to see here whether each given parameter is significant or not in the\nregression. Instead of using gray formatting for the whole equation, it could be used for that, or using an\nasterisk .\n-Now seeing fig S1 I see that most rivers sampled are in Alberta, could there be some regional patterns\nhere of salinity in inland waters, rather than a system difference? Just wondering, no need to do a full\nanalysis on this.\n-Figure S2: Typo in “Small lent.” Top right corner"}, "author_response": "Responses to Reviewer Comments.\nReviewer Comments:\nWe thank both reviewers for their careful reading of our paper and thoughtful comments that\nhave guided us in making the paper better. We hope that the explanations below that detail our\n our\nchanges to the manuscript, or justifications/clarifications where we retained certain methods or\ninterpretations bring the paper up to a satisfactory level of quality. Please note that in some cases\nthe comments have been re-arranged and grouped based on themes. This was done to facilitate\nan easier evaluation of our responses.\nReviewer #1:\nIssues with data reporting and analysis\nWe thank Reviewer #1 for their detailed review and thoughtful comments. We have very carefully\nconsidered each point and note that these comments have led to a deeper exploration of the\nliterature, that has provided us an opportunity to better explain our findings and expand on our\ninterpretations. While in numerous cases we have not made the changes that were requested, we\nhope that it is clear that we have very carefully considered each point and chosen the approach\nthat best suits the aims of our study.\nThe data set is extensive; however, I had a difficult time following the data, how they were\nobtained, the environmental setting and the implementation, resulting in multiple readings of the\nmanuscript. I have a few issues (and questions) with the manuscript.\nAs detailed below, based on the feedback from both reviewers, we have made significant\nchanges to the reporting of data collection, the use of data, and the results. We hope that these\nchanges help Reviewer 1 follow the approach and findings that we’ve used in this study.\nThe data collection on the various lakes (inland waters) is vague and needs to be expanded.\nSpecifically, the data for the individual lakes/ponds, their properties (depth, area, etc), ancillary\ndata, dates of data collection. I believe these data must anyway be supplied should the paper be\npublished.\nWe will supply these data for evaluation and now added a data availability section noting\nwe will provide open access to the database that contains relevant information. We also note the\npublications where existing data came from. We have revised the gas flux calculations section of\nthe methods in great detail and note that now our use of these data comes from only three\npublished sources (two articles and one thesis). The bulk of the paper relies on these data and\nthey have also been extensively detailed in those publications.\nOne concern is that the lakes could be overturning while sampling occured, which significantly\naffects surface methane, salinity and DOC – especially if the lake is experiencing an anoxic\nhypolimnion.\nAs detailed in the methods section, sampling was restricted (in a system that may have\nbeen stratified) to peak summer periods in the survey of primary sites, to eliminate issues such as\nthe one raised here (effects of overturn). Therefore, we are as confident as we can be that this is\nnot a confounding issue in the dataset.\nIn fact, the authors state that each lake was sampled 3 – 5 times, however no statistics or at least\nmean and STD are given.\nFor the subset of sites (peripheral wetland survey) where this sampling was conducted,\nall the statistical reporting can be found in supporting tables 3 and 4 and are discussed in\nsupporting text S2. There were already extensively described in the previous version.\nOf the 193 primary survey sites, they represent 1 sample per site in summer, so no\nstatistics of this kind are presented.\nFor the ebullition data we have clarified now that we present repeated sampling from one\nlocation, which we now summarize in figure S9 where we have added error bars to the salinity\nversus ebullition rate figure seen in the paper (Fig. 2), but for which the error bars would be too\nmuch clutter to add to an already busy figure.\nA final point, I think that rivers should be excluded in this analysis, as these are completely\ndifferent systems than lakes and ponds (high flow rate, turnover, rapid surface gas exchange), etc.\nBased on this comment and those from Reviewer 2, we remove rivers from the bulk of our\nanalyses and title in this revised version of the paper. We did retain the rivers in only 2 key locations\n(table 1, and figure 1 a) because we feel it is important to present the differences between system\ntypes. In our opinion it is a strength of the paper that we explored these patterns across diverse\necosystem types, found distinct relationships, and present the correlation in figure 1b (accounting\nfor DOG and salinity differences) that helps to explain the broad differences in the system types that\nmay lead to the observed trends in figure 1a. The Reviewer is correct to point out the river systems\nare different, but we don’t think this is a reason not to include the data. We feel that underreporting\nnull results would be doing a disservice to the scientific community.\nLine 81 – I am not clear why the authors present river systems in this paper, as these systems are\nsubstantially different than the ponds and lakes. I would suggest omitting the rivers from this\nstudy, and diving deeper into the fact that salinity affects CH4 in small systems (i.e. ponds), and\nnot lakes. It would be interesting to know where the bathymetric cutoff would be. They touch on\nthis point in line 88, but think that this could be further explored.\nWe hope that in responding to this and the comments from Reviewer 2, that we have\nfound the right balance between refocusing the paper on lentic systems, especially the small\nones, but also presenting valuable information about the rivers that highlights these systems are\nindeed not a place where this salinity mechanism is relevant. We have detailed above all the\nsteps that we have taken to deemphasize the rivers and are hoping that this addresses Reviewer\n1’s concerns. Unfortunately, we do not have extensive bathymetric information of most of these\nsites, and have considered such a question as an important point to explore in future research.\nFigure 1b – Again, I strongly suggest removing rivers from this analysis. Overall, this\ncorrelation is very weak and I find this unconvincing.\nWe have removed rivers from the analyses as outlined above and below, but we have\nretained them in the paper simply to demonstrate that the relationship is indeed unconvincing as\nReviewer 1 notes. We feel that it is important to communicate this basic message to readers,\nsince there is great interest in the broader aquatic community to understand methane dynamics\nin rivers, and salinization is a topic that is highly relevant in rivers.\nIssues with the use of salinity as a predictive metric\nThe fact that sulfate suppresses methane production (and thus fluxes) is well known (especially\nin the oceanographic community), but perhaps less known is the number of brackish (i.e. sulfate-\nrich) lakes – which the authors use in their estimates.\nWe respectfully point out that knowledge from oceanographic research and marine settings,\nthough supplying limnologists with basic intuitive knowledge, is not in itself sufficient to understand\nand account for inland water biogeochemical processes. Oceanographers have indeed known\nabout the relationship between methane and salinity for a long time (Reviewer 1 speaks specifically\nabout sulfate, which we address in a separate point). In limnology, this is a very common intuition\nthat many people have on many topics in our field. However, knowing about a possible\nrelationship, and quantitatively demonstrating its importance in an entirely different ecosystem type\n(inland waters) at a different spatio-temporal scale (ecosystem to regional emissions) are two very\ndifferent things. The latter has not been done for salinity and methane flux for inland waters at a\nbroader regional or global scale. Herein lies the value of our paper, and the cutting-edge nature of\nour discoveries. We stated from the beginning and were up front about the fact that the fine-scale\nmicrobial processes have received attention, but nowhere has anybody fully accounted for the\necosystem-scale impacts of these mechanisms on emissions from inland waters in the ways that we\nhave here. Had this been established, we would already see salinity or some equivalent integrated\ninto the emissions models that people use (e.g., see Beaulieu et al. 2019, another recent and\nrelevant paper on the topic in Nat. Comm). Generating these findings is a critical step that takes\nthis topic from intuition and opinion into a quantitative realm.\nAs an extension of this last point, we note that salinity as we use it here is integrating\nmore than sulfate alone (see below response to next point). This observation further\ndistinguishes processes found here from marine work focusing on sulfate cycling alone.\nLastly, we also appreciate that Reviewer 1 has noted the novelty in our presentation of the\nnew pond and wetland surface area dataset we use to scale emissions to the Canadian Prairies.\nSurface water extent is indeed not well known and quantified here, so the use of this product is a\nmajor advance for national emissions estimates. Being the first paper to use this for emissions\nscaling, our paper is making a very important contribution to understanding emissions from the\nvast (>780,000 km2) Prairie Pothole Region.\nHowever, the authors’ key message that emission models should include salinity (that is sulfate, I\ndisagree with using salinity as a parametrization here) could be a solid message, however, it is\nstill unclear how this could be applied, and in which cases. Throughout the manuscript, I question\nthe use of Salinity as this does not necessarily imply sulfate and could result in considerable error\nin the authors’ correlations. In fact, they measured SO42- in a lot of the study sites, so I do not\nunderstand why this was not used as the key parameter. My point, is salinity really an appropriate\nmeasure here?\nWe maintain that a focus on sulfate alone is a more narrow and incomplete exploration of\nthe factors limiting methane production. In this sense, we appreciate this advice from Reviewer 1,\nbut feel that it would be a sub-optimal exploration had we narrowed down to only looking at sulfate\nrelationships to methane. Undoubtedly, these are questions that other readers would have, so it\nprompted us to compile an extensive supplement text section explaining the potential reasons why\nsalinity is a broader, and more integrative predictor than any individual ion.\nThe assumption that sulfate alone is responsible for the patterns underlying salinity-\nmethane trends worldwide is incorrect, and we now detail our reasoning in an extensive\nsupplemental text section that we hope can alleviate the concerns raised in the first round of\nreview. Importantly, salinity as a master variable is integrating more than DIRECT sulfate effects\nalone, and is indeed an important predictor of emissions patterns from hardwater systems at the\nbroadest scale. As Reviewer 1 points out, sulfate is the best known and probably most important\nion that sets redox conditions that favour alternate processes over methanogenesis. However, there\nare many other ions (nitrate, manganese, iron, organic matter etc) that are also interacting with\nthe cycling of methane in complex ways (that we do not fully appreciate yet), and these ions change\nin availability with increasing salinity. We do not belabour the point here as it is detailed in the\nsupplement. Instead, we present two figures that, as discussed in the supplement, provide clear and\nindependent evidence that we hope the editorial board finds compelling. If, as stated as a reason\nbehind the initial rejection, the salinity-methane connection is strictly dependent on sulfate, we\nwould not see clear effects of other salt manipulations on methane. In reality, even NaCl additions\nalone induce complex biogeochemical effects that suppress net methane production in sediments\n(note that we use the term “net” because effects lowering the rate of methanogenesis, or enhancing\nanaerobic oxidation, or some mix of both effects could yield these observed trends). We present\nfindings from two regions, distinct in their geochemical features from our study region, where non-\nSO 42--based manipulations yielded suppressed net methane flux:\n[Redacted]\nExample taken from NaCl additions and dilutions for lake sediments in Camacho et al. Water,\n2017, 9, 659.\n[Redacted]\nExample taken from NaCl additions to wetland sediments in Baldwin et al. Wetlands, 2006, 26,\n455-464.\nAll of this shows that a focus on sulfate alone is incomplete in the context of our study\nbecause it does not reflect the bigger picture effects of salinity on methane cycling that underly\nour empirical observations. We stress the point that this is not a question of which metric is the\nbetter one to predict methane cycling, but that using salinity (akin to other important metrics like\ntotal phosphorus concentrations or dissolved organic carbon content) captures the broadest\nrelationships, while investigations using individual ions like sulfate provide finer-scale and\ncomplimentary information. In this context, the critique of our use of salinity is equivalent to\ncriticizing a paper for using total phosphorus, total nitrogen, or other bulk chemical properties\nas predictors that establish global empirical relationships in place of metrics that capture a\nsmaller subset of the element (e.g., requesting that we only use soluble reactive phosphorus, or\nammonium or nitrate, or even aromatic carbon forms, to establish trends). We elaborate on this\nin the new supplement.\nIn summary, salinity is indeed reflecting distinct relationships between ions and methane\nthat undoubtedly vary regionally or between system types. This is not a flaw and should not\npreclude using salinity to establish patterns at the broadest scales. We make it clear, we hope,\nthat salinity is a useful metric in regions with diverse geochemistries. The two examples pasted\nabove in response to comments from the Editor clearly demonstrate this point (we elaborate on\nthis in the supplement). Further, our meta-analysis shows inverse relationships in all the regions\nwhere data exist, despite wide ranging geochemistries.\nWhile the Fig S3 is somewhat convincing relating Log of sulfate to Log of salinity, since it is on\na log-log scale I suspect there is substantial error here.\nThis is one strong indicator why sulfate alone is not as comprehensive as salinity as a\npredictor. This considerable variability in the SO4/salinity relationship implies that using sulfate\nconcentrations as predictor does not always reflect ecosystem salinity, even in our study region.\nThe new figure S6 in the supplement showing that the use of SO4 and salinity as predictors\n(standardized by amount of DOG) yields different correlation strengths is particularly important\nwhen we consider the agricultural ponds, where SO4 alone doesn’t reflect the underlying\nrelationship between salinity and methane as well as in wetlands, but when combined salinity and\nSO42- content yield comparable correlations at the larger scale. We have explained above and in\nthe paper why this proposed use of SO42- alone is a more narrow focus than what we wanted to\ntake in the paper, though follow up work looking at individual ions is an important next step.\nI understand it is the easiest to measure, but perhaps the actual electron acceptor that\noutcompetes the methanogens would be a much more solid analysis.\nAs we detail in the supplement, there is a lot more going on in hardwaters than a\nsuppression of methanogenesis alone by direct effects of SO4 concentration increases. Therefore,\nwhile this is obviously an important mechanism of suppression of rates of methanogenesis, it is not\nthe only mechanism that leads to a restriction of net methane production in sediments. For these\nreasons, our goal of predicting methane trends in hardwaters at the broadest scale leads us to\ndisagree with the reviewer statement that their proposed approach would be a more solid analysis.\nMy suggestion would be, including the above comments, include only data where sulfate was\nmeasured, and only include lakes and ponds. The fact that these two systems respond oppositely\nin terms of CH4 to increasing SO42- (though the correlation for CH4 and SO42- for lakes is\nvery weak) deserves much more description and investigation.\nPlease see above responses to use of salinity versus sulfate more broadly. We agree it\nwould be nice to expand on the contrast between small and large systems, though given the\nalready-long manuscript and focus on other key issues that we feel take priority here, we believe\nthat this important issue is one we need to follow up on in future research.\nI question the use of CH4 concentrations in these types of studies, as there are some many\nparameters that can affect concentration in the surface waters (wind exposure, oxidation\nrates, light penetration, etc). I think using rates (i.e. fluxes) is much more robust and revealing.\nThis is a nice data set, and potentially nice story. Using only the waterbodies where CH4 flux,\nconcentrations and SO42- are all measured would make for a interesting, and very applicable study\n– especially when validating the data versus the methane modeling approaches.\nThe use of concentrations for some portions of the paper was deliberate because we did\nnot want to introduce yet more noise in the patterns and broad comparisons through the need to\naccount for yet more physical differences and potential errors. We feel that for the purpose of\ncomparisons in figure 1, table 1, and associated supporting info., comparing concentrations is\nmore appropriate.\nHowever, we note that we are already extensively discussing emissions patterns for 139 of\nthe 193 primary survey sites (in figures 2, 3, and in the scaling calculations later in the\nresults/discussion), so we are essentially already doing what Reviewer #1 requests in the bulk of\nthe paper. We note that exploration of emissions was restricted to these sections because we were\nmore confident in the emissions calculations and data for this subset of the paper, and feel the\nresults are stronger using this approach. Finally, Reviewer #1 mentions using SO42-\nconcentrations here, though we have explained our rationale for not doing so in detail above.\nLine 42 – it is very well known that SO42- inhibits CH4 production. Check the oceanographic\nand coastal research literature.\nWe do not dispute this statement from Reviewer 1. In fact, we cited important marine and\ncoastal papers in this sentence, as well as inland water papers, one of which clearly demonstrates\nthat another form of salinity (NaCl) also suppresses methane production. To make sure that other\nreaders do not take the sentence as a claim that the inhibition of methane production is not well\nestablished, we’ve reworded that sentence to say that there “is clear evidence”. However, as\nnoted above, there is a very important difference between intuitively assuming that a mechanism\ndemonstrated in marine habitats extends to inland waters and demonstrating ecosystem to\nregional scale ramifications of such a process. The sentence immediately following the one\nhighlighted here emphasizes this knowledge gap and makes it clear where oceanographic\nknowledge reaches its limits of application.\nOther specific comments\nThe use of “core” study site is ambiguous, as I often think of sediment core. Suggest changing to\n“primary”.\nWe agree and have changed this terminology throughout the paper.\nLine 40 – it would be interesting (if possible) to know how salt-rich lakes are currently represented\nproportionately in the database used to estimate current global estimates of inland water emissions.\nWe agree and were not able to find such data associated with past research. This is\nsomething that the research community will hopefully establish once our work is publicly\navailable to stimulate interest in this topic.\nLine 50 – you list SO42- and Fe3+ as energetically favorable electron acceptors. How important\nare other EAs in these systems? The relevant ones should be listed here.\nWe now elaborate on this quite extensively in the supplemental text S1. We hope that this\nprovides the context needed to understand and appreciate the issue.\nLine 60 – the authors survey 193 freshwater systems. As a reader, I have an issue interpreting\nthese results without more information on the individual waterbodies.\nWe hope that the provision of the data file will give readers the context needed to\nunderstand the features of individual water bodies (see data availability statement after main text).\nWe have revised the methods section to make it clear how we subset the data for the use of sites\nwith emission data and make more clear reference to the fact that three detailed publications have\nalready elaborated on these study systems. We hope that this clarifies the issue.\nLine 78 – define “full suite of limnological parameters”.\nWe now present table 1 immediately after this paragraph, which provides a list of the\nparameters included in models.\nLine 94 – It would be helpful to the reader if the authors could present upfront the global\nrepresentation of wetlands and ponds in general, and the fraction that are brackish – or better yet,\nthe ones with elevated SO42-. A table here quantifying the global setting would be appropriate.\nWe are unaware of such information that we could present here and note that the global\nextent of such small systems is an active area of research, with wide ranging estimates of area\nthat are error prone. We did add to the introduction half a sentence noting hardwater systems\nmake up a fifth of the global inland water surface area. We also hope that other changes we have\nmade give some context on the geochemical features/differences among global regions. We now\nadded a supporting figure detailing the relationship between SO42- and Cl- in diverse hardwater\nsystems from around the globe (Fig. S10) and discuss in detail in the supporting text S1 the\ndifferences in SO42- to Cl- concentration ratios in our region versus other regions. We also cite\nliterature sources detailing metal and trace metal content along salinity gradients. We hope that\nthese revisions provide more global context on aquatic geochemical differences.\nLine 100 – why not show the relationship between CH4 and TN/TP ratios? This can easily be\nadded to the supplemental.\nWe have added the relationship between methane and both TN and TP to the supplement\nas fig. S3. We think that the comparison to each nutrient concentration, rather than the ratio of\nthe two nutrients, is a better indicator of trophic state, so have taken a slightly modified form of\nthis advice to hopefully clarify this section.\nLine 204 – the authors state “Existing empirical models” are used to compare the model results\nwith their measured data. As this is such a key component of the study, I suggest that the model\ndetails be presented so that the reader doesn’t have to search for them in the literature.\nWe have added a more comprehensive explanation of the models and our use of them in\nthe methods section (see ‘statistical analyses’ section).\nLine 208 the model is driven by chlorophyll a, I would be curious how the data presented here\ncorrelate with CHLa – could this be a main driver?\nWe agree with Reviewer #1 that the model using chla as a predictor assumes that system\nproductivity or trophic status is the main driver of ebullitive emissions. This seems to work well in\nother systems, though clearly doesn’t hold here. We agree that the lack of relationship with chla\nand CH4 is an important reason for the differences in observed and predicted emissions in figure\n3. We felt that this was pretty clear in the manuscript but present the figure summarizing chla\nversus average ebullitive flux here for the interest of Reviewer #1. As the figure indicates, the\npatterns are not clear, though there may almost be a negative relationship if we ignore a few\npoints. At any rate we do not want to overinterpret the figure. We would consider adding it if\nReviewer #1 feels it is important, though held off as we already have quite an extensive\nsupporting information file.\n[Redacted]\nConfirm that tables and figures (including supplement) are listed in order.\nWe have gone through the paper and made edits to the figures, tales, and supplemental\nmaterials. We hope there are no mistakes now and will further correct any potential oversights if\nthey exist.\nFigure 1a – This figure is very hard to read. As this is a key figure for the message of the paper, I\nmake the following suggestions. Remove the River data (from the study in general), and present\nthe lake, ponds and wetland data in individual panels with the data behind (mean and std for\neach site). The correlation for the wetlands and ponds is excellent – it would be great to see with\nthe actual data.\nWhile we have elected to keep this figure as is, we hope we have addressed this issue in\nseveral other ways. We keep this figure as is because we feel it is important to show the differences\nbetween the systems as a first step (we explain why it is important to show the ‘null results’above).\nYet now we first introduce the global multiple regression equations for each system type and the\ncombined lentic systems in the new Table 1. This is the global context and equations needed to\nunderstand the marginal effects derived from multiple regressions in figure 1a. We make specific\nreference in the caption to table 1, so readers should be able to draw a direct line between the two.\nWe also point readers to figure S2 for a visual summary of regression equations to help those who\nlike visual learning over tables. We have also added figure S6, which breaks apart these\nrelationships by individual system type and when combined, because we agree with Reviewer 1 that\nit is nice to show the data behind the regressions. We hope that this addresses these concerns.\nIt is interesting (while very weakly correlated) why the methane increases with salinity in the\nlakes. In my opinion, this deserves a more detailed focus within this paper, as it is contrary to the\nauthors’ key hypothesis. That is, if the salinity decreases the methane in ponds and wetlands, is\nthis compensated by an increase in methane production with salinity in lakes?\nAs we mention above, we have devoted the bulk of the paper to detailing relationships in\nthe systems where these trends are most important. While the differences between large and\nsmall lentic systems is interesting, we feel that to properly explore this issue would require a\ndifferent study design that is not a great match to this dataset and study design (specifically\nplanned to explore the themes we focus on here). To explore the topic that Reviewer 1 proposes,\nwe would need to follow up with a more sophisticated and detailed survey of methane dynamics\nacross depth transects of systems of increasing depth or size.\nEsp. including all the different water types in a single correlation. I suggest developing the\nindividual correlation for each waterbody type. This correlation however is the basis for the\nmodel shown in Fig. 1c. I question if this can be applied in the manner it has been here. For the\nfirst thing, since Fig. 1a shows an inverse relationship between salinity and methane, I am unclear\nhow these data can be used to infer the model. The separate contributions of DOC and salinity in\nthe model in Fig. 1c could be better explained.\nAs per comments from both reviewers. Figure 1c now does not include all system types\nand we exclude rivers in all subsequent analyses. We hope that the removal of rivers throughout\nthe rest of the paper, the inclusion of regression statistics in the new table 1, and addition of\nfigure S6 provides the context Reviewer 1 is looking for.\nFigure S2. This figure shows the effect size and the confidence of the regression analysis on the\nvarious parameters driving the concentrations of dissolved pCH4. It seems that the salinity only\nnegatively impacts methane in the small lentic systems. While the effect size is shown to be large\nfor lake (salinity) methane, it seems to be neutral which I don’t fully understand.\nPlease note that we have revised figure S2 following other comments and have removed the\nrivers from this analysis, and focus on the individual lentic systems, and small lentic systems\ncombined that are now the focus of figure 1c. We have also added figure S6 to show the data behind\nthe individual and combined lentic system relationships that we focus on in figure 1. Reviewer #1\nnoted that the salinity effect is negative in the small systems. We now emphasize this in the paper. For\nthe larger lakes, this relationship is non-significant, so while the salinity relationship with methane is\nnegative, it is non-significant. This non-significance is reflected in the use of the dashed line and\nmassive error bars in figure 1a for larger lakes, and we have now placed table 1 at the\nbeginning of the results/discussion section to better guide readers through the interpretation of\nfigure 1. In table 1 we show that the larger lakes model is non-significant, so this should\nhopefully provide the context needed to understand figure S2.\nThe strongest effect is the area – which I feel should be discussed in more detail. Statistics aren’t\nmy strong point, but I have trouble understanding what this figure actually means. Also, in this\nfigure, the salinity only really seems to have a strong effect on small lentic systems. Also, DOC\nseems to have the largest (positive) effect on methane, but this is not seen in the individual class\nsystems (i.e. lakes vs rivers vs small lentic). How is this explained?\nHere, as we have mentioned in response to other comments above, the multiple regression\nfor larger lakes is nonsignificant overall, so we are hesitant to say too much about the relationship\nbetween pCH4 and surface area. We agree that the salinity effect is restricted to small systems\nand have revised the paper to emphasize this point. We have also explored the patterns with DOC\nin more focused detail by system type and focus, as requested, on the small lentic systems (see\nsupporting text figures S3 and S6, and revised figure 1b). We discuss the system differences in\ndetail at the beginning of the results & discussion. We hope that these changes help to clarify the\nissues raised by Reviewer #1.\nMethods – Sampling time: How does that effect outcome due to changing climate (June –\nAugust). Sites were sampled 3-5 times, it would be useful to know the range of values and\nvariability in salinity (i.e. sulfate), pCH4 and DOC during these times.\nWe agree that sampling time in general is an important consideration, and this is\nprecisely why we conducted such an extensive analysis of the variance associated with our\nperipheral wetland survey sites (summarized in supporting information text S2). This supplement\nhas already summarized our evaluation of the importance of multiple sampling per site, timescales\n(monthly to less frequent, i.e., seasonally,), and inter-regional spatial scales, in terms of inducing\nvariability in our dataset for pCH4. This analysis demonstrates very clearly that by capturing the\nlong environmental gradients reflected in our inter-regional survey, we capture most of the\nvariance in pCH4 that may be induced by wide ranging environmental conditions, and that\nwithin-site variations in conditions, or those induced by shorter-term variation, are much less\nimportant than the spatial gradients that we capture with the survey. We are therefore as\nconfident as reasonably possible that a compilation of summer samples is a reasonable way to\nevaluate the drivers of methane cycling in hardwaters, even with the comparatively small ranges\nin environmental conditions that may be induced with a June-August sampling window. We now\nnote that it was the peripheral dataset that was sampled 3-5 times (for the purpose of this\nanalysis), so that readers are not confused with the primary survey sites.\nMethods – Line 147, which type of multiparameter probe? Only surface, or were profiles used?\nWe now note that we use surface measurements in our analyses, and that “The probes used at\neach site varied in model, but were all either Yellow Springs Instruments (YSI) or Hydrolab\nDS5 model probes, and all were routinely calibrated before sampling.”.\nMethods – Line 393, how was the wind measured at each site? What is the justification for using\nK600 parameterization from Cole and Caraco, 1998? That study used tracers to estimate k600, and\nhas since been shown to underestimate k600. My suggestion, since the authors performed direct\nchamber measurements on 10 ponds, calculate the k600 directly from their data and compare with\nother parameterizations that may be better suited, e.g. MacIntyre et al. 2010 Geo Res Lett.\nPlease note that we have revised this section to more accurately reflect the calculation of\nflux rates. In essence, we use only published and already detailed emissions rates that were\nderived from chamber flux measurements, averaged across sites and time, and applied to all\nponds and wetlands (as reported in Webb et al. 2019 Biogeosci, and Jensen et al. 2023 JGR-B).\nAs these data were already reviewed and published, we are hesitant to recalculate emissions rates\nwith other models that each have their own strengths and limitations. For instance, earlier work\nhas shown that for a small to mid sized lake, averaging chamber based CH4 flux estimates made\nover 24hr periods yields near identical K600 estimates as using averaged wind speed data in the\nCole and Caraco 1998 model (Bogard et al. 2014 Nat Comm), so there are clearly instances\nwhere the Cole and Caraco model works extremely well. Plenty of other examples like this exist in\nthe literature, so given the wide range in potential model options and related outcomes, we are\nhesitant to go in the direction of comparing gas transfer models, as this really is not the focus of\nthe paper and would lead to an overly complicated and off-topic discussion.\nMethods – Line 398, The authors should provide more details on how bubble ebullition was\nmeasured. How were the instruments (funnels) deployed to ensure that they did not disturb the\nunderlying sediments? It would be interesting to see the maps of the ponds, depths of deployment\nand data.\nWe now clarify bubble trap details in methods section on estimating flux rates. We also\nmention where extensive information on the sites has already been published (Jensen et al. 2023\nJGR-B), and where the ebullition data were initially reported (Jensen M.Sc. thesis). We note that\nJensen et al. (2023) provide considerable information on the sites, including the map and example\nphotos that we provide below.\n[Redacted]\nFigure from Jensen et al. 2023 JGR-B. This paper reports the diffusive emissions data from the 5\nwetlands and 5 agricultural reservoirs (ponds) included in our paper, plus an additional 30.\nReviewer #2:\nThe biggest issue I have with this study is how all different aquatic systems (rivers, lakes, ponds\nand wetlands) are combined in the analysis. The breadth of systems is a strength of the manuscript,\nbut the way it is used may not be fully accurate. This is because in some systems (rivers and large\nlakes) salinity is not that important relative to other factors according to their analysis, and therefore\nthe conclusions and subsequent analysis should reflect that. The title “Salinity causes widespread\nrestriction of methane emissions from inland waters” promises that salinity is THE driver across all\nsystems and is widespread, while the analysis doesn’t fully support it. I will pull a couple of\nexamples to better illustrate the problem, and then suggest a way to address it.\nWe thank both Reviewers for raising this point and have revised the paper to focus on\nsmall systems. We explain above why we retain river and large lake data in select locations but\nnote that the vast majority of the paper has now been focused to patterns in small lentic systems.\nIn the opening sentence of the results and discussion (L79) states: “Across all core sites where the\nfull suite of limnological parameters were measured, salinity had a strong negative effect on pCH4\nin a multiple linear regression that also included temperature33–35, and common proxies for\norganic substrate (DOC and TP4,5,36,37) (Table S2 and Fig. S2)”. Here I am not sure if they refer\nto the multiple linear regression including all data, or the system specific linear regression. If the\nformer, I am not sure is statistically sound to include all these different aquatic systems in the\nsame analysis, without including the system as a factor in the model. If the latter, it is not correct\ngiven that the MLR for lakes and rivers show in fact a positive effect of salinity on methane\nemissions (table S2).\nWe have now revised this analysis to remove the combined regression, so this comment is\ngenerally not applicable to the current version of the paper anymore. To make it more clear to\nreaders what we are presenting, we have now included table 1 (initially in the supplement) and\nexplain it in the text before moving on to figure 1. We have revised table 1, figure 1b,c (relying on\nthe regression model), and supplemental materials all so that the rivers and ‘global MLR model’\npresentations are removed from the bulk of the paper. We retain rivers in figure 1a for reasons\noutlined in response to Reviewer #1 comments.\nIn the important analysis of Figure 1. Is the regression in panel b on all data, including big lakes\nand rivers? If so, is it meaningful when they behave so different than ponds in wetlands? The\nanalysis in panel c depends on the relationship in panel b, and given the conflicting patterns\nbetween lakes/rivers vs ponds/wetlands (shown clearly as the marginal effects in panel a), it may\nbe a bit misleading to use all data to build a model of DOC/salinity vs CH4, which is then used to\ndo some nice and clean lines of salinity and CH4 across DOC (panel c). I don’t dispute these\nresults, but that it may not hold as cleanly for rivers/lakes as for the other systems based on the\ndata provided.\nWe agree with the assessment here. We keep rivers in panel 1a (and table 1) because we\nfeel it is important to first point out that these differences appear to exist between system types.\nThis is a very novel observation even if it is not the core focus of the rest of the paper. We have\nrevised figure 1b,c based on this comment so that it only represents patterns for the small lentic\nsystems.\nThe authors are clear about the fact that salinity is not a first-order control across all systems (lines\n83-90), show the data in the multiple linear regressions (Table and figure S2) and the marginal\neffects in figure 1a. But then in some other cases the authors use all data lumped together to do\nsome broader analysis and claims, that to the reader it may appear that they are applicative across all\ninland waters while they are not for larger lakes and rivers (again based on this dataset). I would\nsuggest two ways to address it: Solution 1: The authors have done a much more extensive effort on\nthe aquatic systems that have a strong effect of salinity, with a regional survey of ponds and some\neddy covariance data for wetlands, great work! Given this, maybe the work should have an initial\nassessment across all systems as follows: “we sampled all those systems, seems like the effect of\nsalinity is stronger in wetlands and ponds because X, in lakes and rivers its non-significant and even\npositive because of Y. We then proceed with a detailed analysis and landscape relevance of salinity\ncontrolling CH4 emissions in ponds and wetlands”. This would still provide a\ncompelling work and with a bit more rigour, maybe you should leverage in the introduction then\nthat across all inland waters, wetlands are the largest source of CH4 and that small ponds the\nmost uncertain one. Solution 2: Use literature data to expand the analysis for lakes and rivers.\nThere is a large new database of river methane data that includes conductivity data\n(https://essd.copernicus.org/preprints/essd-2022-346/), and a new global estimate of lakes\n(https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022JG006793 ) and reservoirs\n(https://doi.org/10.1029/2021JG006305 ) with supplementary data. This would be more work and\nI am not sure the lentic products have salinity data, but it could be crossed with other chemical\ndatabases. This would be more work, but if you prefer to maintain the focus across all inland\nwaters more data is needed to support the role of salinity in other aquatic systems besides ponds\nand wetlands.\nWe thank Reviewer #2 for taking the time to note a few potential solutions to the issue. We\nhave opted generally for solution #1, as we have laid out in our responses above to comments from\nboth Reviewers. We note that we have already summarized in the text that we saw between-system\ntype differences, but improve this by making the transition from the all-system comparison (now\nfigure 1 a) to the focal systems (small lentic, now figures 1b,c, 2 and on). We now state at the start of\nthat section that we focus on the small lentic systems where salinity appears to have the most\nimportant effect on these systems (based on fig 1a). We modified the figure caption to reflect this.\nSpecific comments\nL 41: Instead of freshwater volume, what is relevant in this article is the surface area from an\nemission perspective.\nAdded reference to Duarte. Et al. 2008 JGR-B and note that they make up ~20% of inland\nwater surface area. Obviously, the uncertainties linked to the area of small systems (as this\nReviewer has noted) should be considered here, so this is what we say it is approximate.\nL60: Here the number of sampled sites is a bit confusing, I would rephrase to: “Here we survey\n193 aquatic systems, including rivers, lakes, open-water wetlands, and agricultural ponds and\nspanning...”.\nChanged as suggested.\nL94: Maybe worth noting that small lentic water bodies are the largest source of uncertainity in\naquatic methane emissions, both in rates and the total global surface area.\nChanged as suggested.\n-L113: Here is unclear what aquatic systems you are speaking about. Is it all of them? Ponds?\nWe now make it clear that it is the small lentic systems by adding a header here and\nrevising text. Subsection is now “Interplay between salinity and OM regulates pCH4 in small\nlentic systems”.\nL124-L133: This paragraph is quite short and technical. Maybe it can be clarified a bit. Two\nsuggestions here: L128: Instead of giving specific changes in ppm of CH4, all of that could be\nsimpler by saying “For example, at the same DOC concentration (10 mgL), a 0.5 ppt increase in\nsalinity at low salinity conditions (0.5 ppt) results in a 50% reduction of CH4, while a similar\nincrease in modest salinities (4 ppt) only decreased CH4 by 11% (Figure 1c)”.\nThen at the end is missing a take home message. For example a quick draft of one: “Thus,\nincreased salinity in solute poor systems may have a stronger effect on methane dynamics than in\nalready saline systems, given anthropogenic pressures that result in salinization of freshwater\nsystems (ref) but also in an increased supply of OM and nutrients, the net balance may not be an\nincrease of methane emissions as previously anticipated (ref).”\nWe have modified this section as suggested. Please note that the simulation is now based\non model output from the revised fig. 1b, so values have changed slightly, but the same general\nobservations and interpretation remain.\n-L150: Ecosystems means ponds here right?\nPonds and wetlands. 5 each. Clarified now.\nL176: You could even say that the low salinity wetland has three times more DOC than the high\none to further support this result. Take it or leave it.\nThis is a nice observation, though we decided to leave it as is and will dig into the details\nin a follow up paper.\nL199: For the Mexican pond data, If 0, how is it shown in the plot and the regression line\ncalculated? Also, there is a study of Spanish saline lakes that could be worth to include in this\nfigure https://www.mdpi.com/2073-4441/9/9/659\nFor the Mexican ponds, we make this line a dashed one to make it clear it is not significant.\nFor the study cited here, we had already included the paper as a reference in the text and note that\nthe data reported in this paper are only for sediment incubations (not ambient data from surface\nwaters), so unfortunately, we cannot add this since it is inconsistent with our other systems. To our\nknowledge we are unaware of companion papers that may include such measurements from these\nlakes.\nL204: Here and in figure 3, it is all based on published empirical models but these models are not\npresented in the results. For transparency, I would include the models in the methods, and how\nthey perform in the supplement materials. These results further strengthen my main issue above, given\nthat the model for rivers does OK (with an offset, but these are different systems form the model)\nand also for lakes. This analysis would be stronger and more compelling if restricted to\nponds and wetlands.\nWe now report the models used in the methods section (statistical analysis subsection).\nWe have restricted this to the lentic systems as well. We were not quite sure what Reviewer #2 was\nrequesting regarding model performance, since the statistics and residual deviation etc. is\nprovided in the paper. We would gladly provide more information if needed, with more specific\nrequests.\nL177: The regional upscaling is sound and compelling. In the global attempt though, the authors\nare cautious enough so it is ok, however I find more interesting to highlight that both the area and\ntotal emissions are heavily uncertain for ponds, and this study provides an important mechanism\nthat could refine global estimates. This is because global estimates from most inland waters are\nstill quite bad from a mechanistic perspective, so maybe no need yet to quantify biases if salinity\nis not included.\nWe agree with the comment raised here by Reviewer #2 and think that we have captured\nthis general interpretation in later sections of the paper where we discuss implications of our\nobservations. For instance, where we state “Therefore, as a first-order approximation, our\ncalculation demonstrates the importance of obtaining accurate emissions data for Prairie\necosystems in the context of our national GHG emissions inventory. Inaccuracies in these\ncalculations have far reaching implications for national emissions mitigation, and how aquatic\necosystems are represented in these budgets. The inclusion of salinity represents a simple but\nmajor refinement to estimates of aquatic emissions from hardwater ecosystems in Canada and\nlikely other nations (Fig. 2)”. We think that this captures the spirit of the comment but can revise\nas needed with further guidance.\nL342: Does eddy covariance need to be in caps?\nChanged as suggested.\nL 358: Would be helpful to know what was the norm and the exception. Any number to say what\n% of sites that were filtered or not?\nWe now report that we calculated total nutrients for 105 sites.\nL367: links or reference to the data sources?\nData availability statement now added at end of main text. The final datasets will be\nuploaded once the paper is accepted, and no further revisions are required (to the FRDR, which\nis routinely used for all Bogard lab publications).\nL369: While still being in Canada, that relationship is from another biome that changes those\nhydraulic scaling relationships. I would rather use a larger assessment such as Raymond et al\nRivers have been removed from this portion of the paper, so comment no longer applicable.\nL392: I am not a wetland person, but is it common to use a lake based model of gas exchange for\nwetlands?\nPlease note that we have revised this gas flux calculation section to reflect the use of\nchamber-derived k600 values. In response to Reviewer 1 comment above, we also provide some\ncontext about choosing different models of k600 in the context of this study.\nTable S2: Would be interesting to see here whether each given parameter is significant or not in\nthe regression. Instead of using gray formatting for the whole equation, it could be used for that,\nor using an asterisk .\nPlease note that this is now table 1. Given the small number of sites in this portion of the\ndataset, we hesitate to read too far into the relationships underlying each predictor (as we\nexplained in several responses to Reviewer #1). Both sets of comments are indeed issues that\ninterest us as follow up questions/explorations.\nNow seeing fig S1 I see that most rivers sampled are in Alberta, could there be some regional\npatterns here of salinity in inland waters, rather than a system difference? Just wondering, no\nneed to do a full analysis on this.\nWe agree that this is an interesting and outstanding question. We will follow up on this in\nfuture work because we do not know at present whether some regional effect is lurking that alters\nthe relationships in rivers. This is doubtful, and they probably are quite different from lentic\nsystems (the relationships probably would hold with more data). But we need to explore this in\nfuture work.\nFigure S2: Typo in “Small lent.” Top right corner\nChanged as suggested.\nREVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nEvaluation of the Revised Manuscript Titled “Salinity Causes Widespread Restriction of Methane\nEmissions from Small Inland Waters” by C. Soued, M. Bogard, et al. submitted for publication\nconsideration to Nature Communications.\nI've carefully reviewed the updated manuscript and the authors' responses to the comments from the\ntwo reviewers. Overall, I believe the authors have effectively addressed the reviewers' concerns. The\nnarrative is now much clearer. I offer two additional suggestions for consideration, but the final decision\non their inclusion remains with the editor and the authors.\nData Availability: I'm uncertain about Nature Communications' data availability policy. However, I\nunderstand that it typically mandates that readers should be able to replicate the procedures detailed in\nthe manuscript. To facilitate this, I suggest that all data utilized in the authors' analyses be made\naccessible in a repository. This would enable the reproduction of the manuscript's calculations and plots.\nFor our publications, we provided all data used in plots, calculations, etc., in an accessible database with\na DOI. This promotes transparency and prevents others from having to search through publications for\nthese data.\nInclusion of River Systems: I noted that the authors have chosen to retain some river data, specifically in\nTable 1 and Figure 2. However, I reiterate that I believe the clarity and focus of the manuscript would be\nenhanced if the river data were omitted entirely. Its presence detracts somewhat from the core\nmessage. Nonetheless, the ultimate decision rests with the editor(s) and the authors.\nReviewer #2 (Remarks to the Author):\nThe authors have successfully addressed all issues raised by me and the other reviewer, and the\nmanuscript has substantially improved on what was already a great work. I have read through all\nmaterials and found just a couple of small things. The new text S2 is a bit lengthy and maybe an overkill,\nbut is a useful content to have regardless.\nBelow a couple of typos I found:\n-L171: Maybe is clearer saying ”in 5 ponds and 5 wetlands”\n-L1082-1084. Here with the superscripts for chemical elements, the citations are confusing. Rather\npresent the citations as (ref. xx)\nResponses to Reviewer Comments\nPlease note that below we provide responses to reviewer comments in blue, italicized text,\nimmediately after the initial comment, listed in standard black text.\nReviewer Comments:\nWe thank both reviewers again for another careful reading of our paper.\nReviewer #1:\nData Availability: I'm uncertain about Nature Communications' data availability policy. However,\nI understand that it typically mandates that readers should be able to replicate the procedures\ndetailed in the manuscript. To facilitate this, I suggest that all data utilized in the authors' analyses\nbe made accessible in a repository. This would enable the reproduction of the manuscript's\ncalculations and plots. For our publications, we provided all data used in plots, calculations, etc.,\nin an accessible database with a DOI. This promotes transparency and prevents others from having\nto search through publications for these data.\nPlease see the revised data availability statement – all data are accessible.\nInclusion of River Systems: I noted that the authors have chosen to retain some river data,\nspecifically in Table 1 and Figure 2. However, I reiterate that I believe the clarity and focus of the\nmanuscript would be enhanced if the river data were omitted entirely. Its presence detracts\nsomewhat from the core message. Nonetheless, the ultimate decision rests with the editor(s) and\nthe authors.\nThis is an entirely fair point that the Reviewer makes. We have opted to keep this line of inquiry\nbecause we feel that it is the best way to foster open science and avoid contributing to a positivity\nbias in the field. While the story may be cleaner without the river data included, we believe that\nreaders should see the river results, even though they are non-significant with respect to the\nmethane-salinity relationship. This is also the first exploration of its kind for rivers (to our\nknowledge), so we feel that this is important knowledge that others will likely find useful. We deem\nthe pros to outweigh the cons here, so have elected to keep the data in the paper.\nReviewer #2:\nBelow a couple of typos I found:\n-L171: Maybe is clearer saying ”in 5 ponds and 5 wetlands”\nChanged as suggested.\n-L1082-1084. Here with the superscripts for chemical elements, the citations are confusing. Rather\npresent the citations as (ref. xx)\nChanged as suggested."}]

Decision letter