There is growing interest in developing spatially resolved methane
(CH

Methane (CH

Isotopic tracers, particularly

In addition to variance caused by

In order to use

Using this dataset we applied statistical analyses to address key questions
surrounding the global distribution of freshwater

Hydrogen and carbon isotope ratios are primarily discussed as delta values,
using the generalized formula (Coplen, 2011)

We also refer to the isotopic fractionation factor between two phases, or

To identify datasets we used a set of search terms (methane OR CH

Most samples were associated with geographic coordinates in data tables or
text documentation, or with specific geographic locations such as the name
of a town or city. In a few cases we identified approximate geographic
locations based on text descriptions of sampling sites, with the aid of
Google Earth software. Sampling sites were defined as individual water
bodies or wetlands as identified in the relevant study. In one study where a
number of small ponds were sampled from the same location, we grouped ponds
of a given type as a single site (Bouchard et al., 2015). We divided
sampling sites into six ecosystem categories: (1) lakes and ponds (hereafter
lakes), (2) rivers and floodplains (hereafter rivers), (3) bogs, (4) fens, (5) swamps and marshes, and (6) rice paddies. Most data (seven of eight sites) in the
rivers category are from floodplain lake or delta environments. Swamps and
marshes were combined as one category because of a small number of sites
and because there is no clear indication of biogeochemical differences
between these ecosystems. To make these categorizations we relied on site
descriptions in the data source publications. We also analyzed data in two
larger environment types, inland waters (lakes and rivers) and wetlands
(bogs, fens, swamps and marshes, and rice paddies), which correspond to two
flux categories (freshwaters and natural wetlands) documented by Saunois
et al. (2020). While rice paddies are an anthropogenic ecosystem; they are
wetlands where microbial methanogenesis occurs under generally similar
conditions to natural wetlands, and therefore we included them as wetlands
in our analysis. In some cases the type of wetland was not specified. We did
not differentiate between ombrotrophic and minerotrophic peatlands since
most publications did not specify this difference, although it has been
inferred to be important for

We also categorized samples by the form in which CH

Where possible (78 % of sites),

To estimate

To account for the effects of

For all statistical analyses we use site-level mean isotopic values. This
avoids biasing our analyses towards sites with a large number of
measurements, since there are large differences in the number of samples
analyzed per site (

We perform a set of linear regression analyses

To compare isotopic data (

When comparing

To better understand how latitudinal differences in wetland isotopic source
signatures influence atmospheric

Values for the flux,

Estimates of source-specific fluxes,

To calculate mean

Since fluxes from

To estimate uncertainty in the modelled total source

The dataset is primarily concentrated in the Northern Hemisphere (Fig. 1a)
but is distributed across a wide range of latitudes between
3

Distribution of sites shown

A total of 74 of 129 sites are classified as inland waters, primarily lakes (

As discussed in Sect. 2.2.3, we regressed annual and growing season

Scatter plots of annual or growing season

For inland waters, regression with growing season

Based on these results we combine measured and estimated

We carried out regression analyses of

Scatter plots of

Scatter plots of

Given the similar results when regressing with estimated or measured

Overall, our results are broadly consistent with those of Waldron et al. (1999a), and confirm the finding of that study that

Given that

To further understand the processes controlling the observed freshwater

Scatter plots of

Pure-culture hydrogenotrophic methanogenesis experiments (Gruen et al.,
2018) yield a regression slope that is consistent with a constant

In particular, the

As shown in Fig. 3, there is a large amount of residual variability in

In order to facilitate interpretation of isotopic co-variation, we estimated
approximate vectors of predicted isotopic co-variation for the four
variables being considered (Fig. 6). We emphasize that these vectors are
uncertain, and while they can be considered indicators for the sign of the
slope of co-variation and the relative magnitude of expected isotopic
variability, they are not precise representations of the slope or intercept
of isotopic co-variation. In reality, isotopic co-variance associated with
these processes likely varies depending on specific environmental
conditions, although the sign of co-variance should be consistent. The
starting point for the vectors is arbitrarily set to typical isotopic values
for inferred acetoclastic methanogenesis in freshwater systems (Whiticar,
1999). We based the vectors for differences in the dominant methanogenic
pathway and methane oxidation in Figs. 8, 5, and 10 in Whiticar (1999).
These figures are widely applied to interpret environmental isotopic data
related to CH

Scatter plots of

The vector for isotopic fractionation related to gas-phase diffusion is
based on the calculations of Chanton (2005) and indicates isotopic
change for residual gas following a diffusive loss. Gas–liquid diffusion is
predicted to have a much smaller isotopic effect (Chanton, 2005). The
vector for differences in enzymatic reversibility is based on experiments
where CH

We observe significant positive correlations between

Overall, our results are not consistent with arguments that residual
variability in freshwater

Further research examining intra-site isotopic co-variation, which largely
avoids complications associated with estimating

When analysing all sites together, we found a significant difference in the
distribution of

Boxplots of

Estimates of flux-weighted mean freshwater

Differences in

Our analysis indicates significant differences in the distribution of
freshwater

Boxplots of

Latitudinal differences in

We speculate that latitudinal differences in

When comparing ecosystems, we analyze

The significant difference in the distribution of

As with comparing ecosystems, when comparing sample types we analyze

Boxplots of

We suggest that the higher

Overall, our data imply that isotopic differences between dissolved and gas-phase methane are relatively minor on a global basis, especially in
wetlands. This result could imply that the relative balance of diffusive vs.
ebullition gas fluxes does not have a large effect on the isotopic
composition of freshwater CH

Our mixing model estimates a global source

Comparison of estimates of dual-isotope global source

Our bottom-up estimate of global source

Our bottom-up estimate of global source

Previous studies have argued, on the basis of comparing atmospheric
measurements and emissions source

The uncertainty in our bottom-up estimates, the overall greater uncertainty
associated with isotopic source signatures in our Monte Carlo calculations,
and the apparent discrepancies for

Our analysis of an expanded isotopic dataset for freshwater CH

The dependence of

Our bottom-up estimate of the global

The datasets used in this paper (Supplement Tables S1–S4) are publicly available at

The supplement related to this article is available online at:

PMJD designed the project, assisted with compiling the data, analyzed the data, and wrote the manuscript; ES and JP compiled the data and assisted with analyzing the data and editing the manuscript; DP developed code for mixing model and Monte Carlo calculations and assisted with analyzing the data and editing the manuscript.

The authors declare that they have no conflict of interest.

We thank all of the researchers whose published data made this analysis possible (see Supplement Table S1). We also thank Susan Waldron, Edward Hornibrook, and the anonymous reviewer for constructive feedback.

This research has been supported by the Natural Sciences and Engineering Research Council of Canada (grant no. 2017-03902) and by McGill Science Undergraduate Research Awards.

This paper was edited by Caroline P. Slomp and reviewed by Susan Waldron, Edward Hornibrook, and one anonymous referee.