Spatially Resolved Isotopic Source Signatures of Wetland Methane Emissions

We present the first spatially resolved wetland δ13C(CH4) source signature map based on data characterizing wetland ecosystems and demonstrate good agreement with wetland signatures derived from atmospheric observations. The source signature map resolves a latitudinal difference of ~10‰ between northern high‐latitude (mean −67.8‰) and tropical (mean −56.7‰) wetlands and shows significant regional variations on top of the latitudinal gradient. We assess the errors in inverse modeling studies aiming to separate CH4 sources and sinks by comparing atmospheric δ13C(CH4) derived using our spatially resolved map against the common assumption of globally uniform wetland δ13C(CH4) signature. We find a larger interhemispheric gradient, a larger high‐latitude seasonal cycle, and smaller trend over the period 2000–2012. The implication is that erroneous CH4 fluxes would be derived to compensate for the biases imposed by not utilizing spatially resolved signatures for the largest source of CH4 emissions. These biases are significant when compared to the size of observed signals.


Introduction
Methane (CH 4 ) is the second most important greenhouse gas after carbon dioxide and is emitted from a variety of natural and anthropogenic sources (Saunois et al., 2016). Natural wetlands are the single largest individual source of CH 4 emissions to the atmosphere, which can vary significantly in time and space due to environmental factors such as temperature and precipitation. Numerous studies have quantified wetland CH 4 emissions through both bottom-up and top-down approaches, often with large disparity, particularly on regional scales (Saunois et al., 2016).
The rate of increase of CH 4 in the atmosphere exhibits strong year-to-year changes due to variations in the strengths of sources and sinks (Saunois et al., 2016). In the 1980s, the CH 4 growth rate was >10 ppb yr À1 , then after 1992, was approximately zero and again resumed at about 6 ppb yr À1 after 2007 (Nisbet et al., 2016). Diagnosing the mechanisms behind these fluctuations continues to generate considerable attention and controversy, in particular for the period after 2007, when CH 4 concentrations began to rise globally after a decade of near stability (Dlugokencky et al., 2009;Nisbet et al., 2016;Rigby et al., 2008). Explanations proposed for the post-2007 rise include increases in tropical wetland emissions (Nisbet et al., 2016), increases in fossil fuel emissions (Hausmann et al., 2016), increases in agricultural emissions (Schaefer et al., 2016), reduction in biomass burning (Worden et al., 2017), and changes to the main atmospheric sink, the hydroxyl radical (Rigby et al., 2017;Turner et al., 2017). These varying conclusions are largely driven by the same or similar sets of observations: measurements of CH 4 mole fraction and observations of the 13 CH 4 isotopologue of CH 4 (hereby expressed as δ 13 C(CH 4 ) = ((R sample /R standard ) À 1) where R = 13 C/ 12 C and the standard is Vienna Peedee Belemnite; Coplen, 2011) at atmospheric monitoring stations around the world. While the atmospheric mole fraction of CH 4 has increased after 2007, atmospheric δ 13 C(CH 4 ) has simultaneously decreased (i.e., become more 13 C-depleted; Nisbet et al., 2016). Measurements of δ 13 C(CH 4 ) are useful for source attribution because fossil fuel, and biological CH 4 sources have distinctive signatures and sink process partition 13 CH 4 and 12 CH 4 to different extents. Accurate characterization of these isotopic "fingerprints" coupled with observations of atmospheric CH 4 and δ 13 C(CH 4 ) enables the diagnosis of drivers of variability in the growth rate of atmospheric CH 4 . However, the accuracy of those diagnoses relies strongly upon accurate characterization of the δ 13 C(CH 4 ) signatures of emission sources.
Previous studies that have utilized δ 13 C(CH 4 ) observations to examine drivers of interannual variability have typically employed a globally uniform isotopic source signature for wetlands of approximately À60‰ (Bousquet et al., 2006;Houweling et al., 2000;Mikaloff Fletcher et al., 2004;Monteil et al., 2011;Quay et al., 1999;Rigby et al., 2012). This simplifying assumption has been made mostly due to the lack of a gridded δ 13 C(CH 4 ) wetland source signature map. A similar approach has been used in studies that analyzed the post-2007 increase in the growth rate of atmospheric CH 4 (Ghosh et al., 2015;Rice et al., 2016;Schaefer et al., 2016;Schwietzke et al., 2016) with the exception of Warwick et al. (2016), who attributed separate δ 13 C(CH 4 ) signatures to high-latitude and tropical wetlands, and Feinberg et al. (2018), who employed a uniform δ 13 C(CH 4 ) signature for the tropics and linearly decreasing δ 13 C(CH 4 ) values for highlatitude wetlands.
Here we develop a wetland δ 13 C(CH 4 ) source signature map based on current understanding of key biogeochemical distinctions between wetland types and the source signatures associated with those types as discussed above.

Methods
We develop a 0.5°resolution wetland δ 13 C(CH 4 ) source signature map based on differences in wetland ecosystems. We evaluate the map against independent observations of regional wetland δ 13 C(CH 4 ) signatures inferred from Keeling plots of atmospheric observations. Using the refined δ 13 C(CH 4 ) source signature map for wetlands, we assess its potential impact on modeling atmospheric δ 13 C(CH 4 ) variability, specifically on spatial and seasonal patterns in δ 13 C(CH 4 ), and trend during the period 2000 to 2012. We show the benefit of using spatially resolved wetland δ 13 C(CH 4 ) signatures for atmospheric inversion studies by quantifying inaccuracies that would result from using a uniform wetland δ 13 C(CH 4 ) source signature.

Distribution of Major Wetland Classes With Distinct Source Signatures
We investigate whether the variability in global wetland source signatures can be captured using four major wetland types: ombrotrophic and minerotrophic wetlands at northern high latitudes (defined as >45°N) and C3 and C4 wetlands in the subtropics and tropics (between 40°N and 40°S). Over 95% of ombrotrophic bogs and minerotrophic fens wetlands exist in the northern high latitudes (Matthews & Fung, 1987). In the region between 40°to 45°N and S, we apply a smooth gradient for each band of longitude. Wetlands located south of 45°S were not considered because their area comprises less than 1% of total wetland area globally (Poulter et al., 2017).
To our knowledge, a high-resolution globally consistent data set delineating ombrotrophic and minerotrophic wetlands currently does not exist. Consequently, we define the areal extent of these wetlands via a soil pH proxy. The fraction of ombrotrophic and minerotrophic wetland in each grid cell is computed using the Harmonized World Soil Database v1.1, which contains soil pH data at 30 arc-second resolution (FAO/IIASA/ISRIC/ISSCAS/JRC, 2009). We test a range of pH thresholds (pH 4.5-5.2) to delineate ombrotrophic and minerotrophic wetlands, validating the resulting distributions against observational peatland data from two high-latitude regions in Canada and Western Siberia (Peregon et al., 2009;Tarnocai et al., 2000). A pH of 5 yields the best fit to observational data (supporting information).
In the tropics, we use the C3 and C4 vegetation distribution map from Still et al. (2003), which is based on a combination of remote-sensing, climate modeling, and ground-based data. Extensive validation of the areal extent of C3-and C4-dominated wetlands in the tropics was limited by poor availability of observational data.

Generation of δ 13 C(CH 4 ) Source Signature Map
The fraction of each wetland type within a 0.5°grid cell is weighted by δ 13 C(CH 4 ) source signatures associated with those wetlands (section 1) to produce the net δ 13 C(CH 4 ) source signature map. The impact of the ranges in δ 13 C(CH 4 ) values for each wetland type is investigated further in section 3. Because multiple wetland flux data sets exist (using different wetland areas), the source signature data file provided in the supporting information contains a source signature value for every grid cell globally. It can therefore be used in conjunction with any flux and wetland area data set. In our analyses, we use wetland fluxes defined over the inundated area data set from Poulter et al. (2017). The inundated fraction associated with rice is removed using the monthly climatology rice map from Portmann et al. (2010).

Validation Against Atmospheric Observations
To provide an independent evaluation of the source signature map, we compare simulated atmospheric δ 13 C(CH 4 ) values at several locations against regional source signatures inferred from atmospheric observations. Regional source signatures were inferred through Keeling plots from Brownlow et al. (2017, Umezawa et al. (2012), and Umezawa et al. (2011) for Alaska, Canada, Scandinavia, Siberia, Costa Rica, Bolivia, Uganda, South Africa, Borneo, and Hong Kong. There are several requirements that need to be met to infer signatures from Keeling plots (Pataki et al., 2003), and these are discussed in the measurement studies. For this study, it is important that wetlands are the sole source of CH 4 emissions in the regions sampled by the observations. These studies have sampled from regions where wetlands were isolated from other CH 4 emission sources.
The source signatures derived through atmospheric measurements are representative of a larger scale (tens of kilometers) than the chamber measurements from which the signatures for each wetland type have been assigned (meters). Any fine-scale heterogeneity, which would not be represented by the flux model or the transport model, is integrated by the atmosphere. The intention of the source signature map is to simulate regional patterns and not to represent fine-scale heterogeneity.
The simulated atmospheric δ 13 C(CH 4 ) at a particular site is the flux and surface sensitivity weighted contributions of source signature from each grid cell in the domain: where i is the grid cell, f i is the 12 CH 4 flux in mol m À2 s À1 , h i is the surface sensitivity in (mol/mol)/ (mol m À2 s À1 ), and δ i is the wetland source signature.
The sensitivity of each observation to fluxes from the surface is derived using the Lagrangian Particle Dispersion Model, NAME (Numerical Atmospheric dispersion Modelling Environment). NAME simulates atmospheric transport using three-dimensional meteorological fields from the Unified Model at approximately 17-km resolution (in 2016; the resolution depends on the year the measurements were made). The model output quantifies the relationship between concentration at a measurement location and time, and surface emissions from each grid cell of the regional domain (e.g., Manning et al., 2011). The mean sensitivity over the period that the samples were collected for the Keeling plot analysis is used for h i in equation (1). For each site, we simulate 1,000 δ 13 C(CH 4 ) values using randomly drawn samples of the source signature from each wetland type and compare this distribution to the observed δ 13 C(CH 4 ). Samples are drawn from a Gaussian distribution with the mean and standard deviation defined by observed values (section 1). The resulting distribution provides an estimate of the uncertainty in the simulated δ 13 C(CH 4 ) values at each site owing to variability in the underlying source signature.

Atmospheric Chemical Transport Modeling of δ 13 C(CH 4 )
We Two scenarios are modeled in which everything is held the same apart from the wetland source signature: Scenario 1 (S1) uses a globally uniform wetland signature of À62‰, and Scenario 2 (S2) uses the wetland source signature map derived in this study. The S1 value is chosen to give the same mean area-and fluxweighted signature for the years 2000-2012 as derived from S2 (equation (2)): where f, A, and δ are the flux, area, and source signature of grid cell i and δ is the global mean source signature.
This approach avoids any significant systematic offset in mean atmospheric δ 13 C(CH 4 ) arising from the different mean values in the two cases. The mean value of S1 and S2 is similar to the value of À60‰ typically used in previous inverse modeling studies. We assess differences between S1 and S2 in the global mean, spatial distribution, seasonal distribution, and trend during the period 2000 to 2012. signature from wetlands is À62.0‰, while the mean boreal signature is À67.8‰ and the mean tropical signature is À56.7‰. In addition to the latitudinal differences, there is significant regional variability. CH 4 emissions from Canadian and Scandinavian wetlands at approximately À75‰ are significantly more 13 C-depleted than the high-latitude mean, while Alaskan wetlands are more 13 C-enriched at À65‰. Regions, such the Okavango Delta, which host significant C4 papyrus wetlands, are more enriched at À50‰. Our mean global source signature is similar to the mean microbial signature of À61.5 ± 0.6‰ reported in Schwietzke et al. (2016), but more negative than the one derived by Feinberg et al. (2018) (approximately À60.5‰), in which a function was fit through samples spanning the tropics and high latitudes. However, the Feinberg et al. (2018) wetland signature function does not capture regional variability in δ 13 C(CH 4 ) source signature, which is a primary aim of our study.

Spatially Resolved Wetland Source Signatures
To assess the accuracy of this spatially resolved source signature map, we compare simulated and measured atmospheric δ 13 C(CH 4 ) at highlatitude and tropical sites using JULES and a suite of additional models to assess any sensitivity to the flux model (Tables 1 and S2 in the supporting information). For each site and in all models, the mean simulated δ 13 C(CH 4 ) value is broadly consistent with the observed values (for reference, S1 would result in atmospheric δ 13 C(CH 4 ) of À62‰ at all sites). There is typically a larger uncertainty in the modeled values due to the wetland source variability. The observed wetland source signatures further highlight large regional differences even within similar latitude bands. The largest differences between modeled and observed δ 13 C(CH 4 ) values occur in the tropics, suggesting that more studies are needed to either determine fundamental source signatures between C3-and C4-dominated wetlands or to better classify their spatial distribution.

Impact on Atmospheric δ 13 C(CH 4 ) Variability
We assess the impact on atmospheric δ 13 C(CH 4 ) by using the spatially resolved map (S2) presented here rather than a globally uniform wetland signature (S1). This analysis is based on forward modeling, keeping flux fields and source signatures from non-wetland CH 4 sources the same between the two scenarios. We analyze the differences in global mean, spatial distribution, seasonality, and trends during the period 2000 to 2012 between S1 and S2 ( Figure 2). While the numbers presented here are specific to this setup of the forward model, the results of the simulation demonstrate the biases that would result in an inversion analysis by   Fisher et al. (2017). c Umezawa et al. (2012). d Brownlow et al. (2017). *Fossil fuel emissions may influence this site, and this signature has applied a correction. not employing the more accurate spatially resolved map. A direct comparison to observations is out of the scope of this study because we focus on only one component of the global CH 4 budget, whereas uncertainties exist in all components which must be reconciled together.
In both S1 and S2, mean global, NH, and SH CH 4 mole fractions are the same because both scenarios use the same fluxes. The mean global atmospheric δ 13 C(CH 4 ) also is similar in both S1 and S2 because we define the mean global fluxand area-weighted δ 13 C(CH 4 ) wetland signatures to be the same. Therefore, any differences are solely due to the different spatial distributions in δ 13 C(CH 4 ) source signatures. Mean NH and SH δ 13 C(CH 4 ) values are 13 C-depleted and 13 C-enriched, respectively, in S2 compared to S1, by approximately À0.1‰ and 0.1‰, owing to more 13 CH 4 -depleted boreal and more 13 CH 4 -enriched tropical signatures. The interhemispheric difference in δ 13 C(CH 4 ) values is 1.4 times larger in S2 (S2-S1 of À0.2‰), and this magnitude is significant compared to the observed interhemispheric (NH-SH) difference of approximately À0.4‰ (Nisbet et al., 2016). The NH seasonal cycle amplitude in δ 13 C(CH 4 ) is enhanced by a factor of 1.5 in S2 (S2-S1 of 0.25‰), and this difference is important considering that the observed NH amplitude is 0.7‰. The trend in δ 13 C(CH 4 ) is smaller in S2 than S1, due to greater increases in wetland emissions occurring at high latitudes than in the tropical regions in this wetland flux field. The 0.06‰ difference in trend is a significant fraction of the observed change of~0.2‰ that occurred between 2007 and 2014 (Nisbet et al., 2016). This analysis demonstrates that if the uniform δ 13 C(CH 4 ) map, S1, were used in an atmospheric inversion, emissions would be derived to compensate for these biases: Emissions would have greater seasonality, a greater spread between NH and SH emissions and slower growth rate than the true emissions. The setup of this forward model is based on commonly used estimates for source and sink fluxes, and quantification of the difference between S2 and S1 is based on forward model configuration. However, the implication is that the biases imparted from inaccurate spatial distribution in δ 13 C(CH 4 ) can be of significant size compared to observed values.
In addition to the large-scale differences in global and hemispheric means that are broadly due to latitudinal differences in source signature, there also exist large regional variations in atmospheric δ 13 C(CH 4 ) ( Figure 3). In Canada and Western Siberia, simulated δ 13 C(CH 4 ) is more than 0.5‰ too high without using the spatially resolved map of S2. In contrast, in some South American and African wetland areas, simulated δ 13 C(CH 4 ) is 0.5‰ too low. Compared to the surrounding overall latitudinal differences, these regions would still be more than 0.3‰ biased, if one were to use only a simple latitudinal gradient for source signatures. In regional atmospheric inversions assimilating δ 13 C(CH 4 ) observations, differences of this magnitude would impart a significant bias on retrieved sources.

Further Development
There are several areas in which this map could be used to inform future studies. First, the source signature map is a static map and it is likely that wetland source signatures exhibit some seasonal variations, although such temporal differences are expected to be smaller than spatial variations driven by wetland type Fisher et al., 2017;Hornibrook, 2009). There currently is a scarcity of measurements spanning full annual cycles both in the δ 13 C(CH 4 ) flux measurements needed to develop a time-varying map and the atmospheric δ 13 C(CH 4 ) data required to validate such a map. Second, we have assimilated the data that currently exist in the literature, but more field studies characterizing δ 13 C(CH 4 ) emissions from tropical wetlands are required. Third, we have not included potentially important alterations to wetland signatures based on emission pathways such as trees Figure 2. Comparison of atmospheric δ 13 C(CH 4 ) (‰) using the spatially resolved wetland source signature distribution (S2, solid lines) versus the common assumption of globally uniform signature (S1, dashed lines). The black lines correspond to the global mean, the blue lines to the northern hemisphere means, and the red lines to the southern hemisphere means. Figure 3. Difference in spatial distribution of atmospheric δ 13 C(CH 4 ) (‰) derived using the spatially resolved wetland source signature distribution and a globally uniform signature (S2-S1). (Pangala et al., 2017). Finally, while we have used mean δ 13 C(CH 4 ) signatures from each wetland type, there exists variability likely linked to fundamental physical processes such as emission pathway and substrate isotopic composition. When this variability is better quantified, the δ 13 C(CH 4 ) source signature map can better incorporate fundamental processes.

Conclusions
This work demonstrates the need for accurate, spatially resolved δ 13 C(CH 4 ) source signature information to make better use of atmospheric measurements of δ 13 C(CH 4 ) for source and sink characterization. We present a spatially resolved wetland δ 13 C(CH 4 ) source signature map based on data that have been collected on fundamental differences in δ 13 C(CH 4 ) emissions between wetland types. We have validated this map against regional-scale atmospheric observations of wetland δ 13 C(CH 4 ) signatures. The δ 13 C(CH 4 ) source signature map represents broad features, such as latitudinal gradient, in observed atmospheric δ 13 C(CH 4 ), and includes important regional variations. The map provides more accurate regional-scale δ 13 C(CH 4 ) source signatures that should be used in atmospheric inversions. We have demonstrated that significant biases would result in flux estimates derived through atmospheric inverse modeling by using a globally uniform wetland δ 13 C(CH 4 ) source signature rather than the spatially resolved map presented here.