Temporal Variations of the Mole Fraction, Carbon, and Hydrogen Isotope Ratios of Atmospheric Methane in the Hudson Bay Lowlands, Canada

We have conducted simultaneous measurements of the mole fraction and carbon and hydrogen isotope ratios (δ13C and δD) of atmospheric methane (CH4) at Churchill (58°44′N, 93°49′W) in the northern part of the Hudson Bay Lowlands (HBL), Canada, since 2007. Compared with the measurements at an Arctic baseline monitoring station, Ny‐Ålesund, Svalbard (78°55′N, 11°56′E), CH4 mole fraction is generally higher and δ13C and δD are lower at Churchill due to regional biogenic CH4 emissions. Clear seasonal cycles in the CH4 mole fraction, δ13C, and δD are observable at Churchill, and their seasonal phases in summer are earlier by approximately 2 weeks than those at Ny‐Ålesund. Using the one‐box model analysis, the phase difference is ascribed to the different seasonal influence of CH4 emissions from boreal wetlands on the two sites. Short‐term CH4 variations are also observed at Churchill throughout the year. The analysis of the observed isotopic signatures of atmospheric CH4 confirmed that the short‐term CH4 variations are mainly produced by biogenic CH4 released from the HBL wetlands in summer and by fossil fuel CH4 transported over the Arctic in winter. Forward simulations of an atmospheric chemistry‐transport model, with wetland CH4 fluxes prescribed by a process‐based model, show unrealistically high CH4 mole fractions at Churchill in summer, suggesting that CH4 emissions assigned to the HBL wetlands are overestimated. Our best estimate of the HBL CH4 emissions is 2.7 ± 0.3 Tg CH4 yr−1 as an average of 2007–2013, consistent with recent estimations by inverse modeling studies.


Introduction
Methane (CH 4 ) plays an important role in global climate change, as well as in atmospheric chemistry, because CH 4 is the second most important anthropogenic long-lived greenhouse gas after CO 2 and its destruction occurs primarily by chemical reactions in the atmosphere. CH 4 is emitted from natural (wetlands, freshwater, wild animals, wildfires, termites, geological processes, ocean, hydrates, and permafrost) and anthropogenic (rice paddies, ruminants, landfills and waste, fossil fuels, and biomass burning) sources. CH 4 is mainly destroyed by reaction with OH radicals in the troposphere and partly by reactions with OH,Cl,and O( 1 D) in the stratosphere and by bacterial consumption in soils. Since the atmospheric CH 4 mole fraction shows large spatiotemporal variations due to unevenly distributed CH 4 sources/sinks and complicated atmospheric transport, an extensive and dense network of observations is required to depict a global picture of atmospheric CH 4 variations. For this purpose, observations of atmospheric CH 4 with grab sampling and continuous measurement techniques have been conducted mainly at ground-based stations since the 1970s (e.g., Aoki et al., 1992;Blake & Rowland, 1986;Cunnold et al., 2002;Dlugokencky et al., 2011;Rasmussen & Khalil, 1981). In the last few decades, the mole fraction of CH 4 showed unpredictable trends; the rate of increase in atmospheric CH 4 slowed down in the 1980s to 1990s, leveled off from 1999 to 2006, and then rose again in Morimoto et al., 2017;Rigby et al., 2008). Such a CH 4 trend was examined in terms of ruminants, boreal and/or tropical wetlands, fossil fuels, or change in OH, but the cause is still controversial (e.g., Kirschke et al., 2013;Nisbet et al., 2016;Patra et al., 2016;Rigby et al., 2017;Schaefer et al., 2016;Turner et al., 2017). It is also known that there is a large discrepancy between CH 4 budgets estimated by top-down (inverse modeling using atmospheric measurements) and bottom-up (direct flux measurement, statistical database, and process-based modeling) approaches, especially for natural sources (Kirschke et al., 2013;Saunois et al., 2016).
Systematic and high-precision observations of carbon and hydrogen isotope ratios (δ 13 C and δD) of CH 4 provide us with additional constraints to understand the contribution of individual CH 4 sources to atmospheric CH 4 variations because each source has its own characteristic isotope ratio (e.g., Quay et al., 1999;Schwietzke et al., 2016;Sherwood et al., 2017;Whiticar & Schaefer, 2007). Their data would also help to close the gap in the CH 4 budget estimation between the top-down and bottom-up approaches through better source apportionment. δ 13 C and δD are commonly defined by Here δ represents δ 13 C or δD and R indicates 13 C/ 12 C or D/H. Subscripts "sample" and "standard" denote the sample and the standard, respectively, and as an international standard scale, VPDB is widely used for δ 13 C and VSMOW for δD. Sherwood et al. (2017) recently reported by compiling a large number of isotope observation data that the biogenic, fossil fuel, and biomass burning CH 4 sources have the respective mean isotope ratios of À61.7 ± 6.2 (±1 standard deviation [σ]), À44.8 ± 10.7, and À26.2 ± 4.8‰ for δ 13 C and À317 ± 33, À197 ± 51, and À211 ± 15‰ for δD. Atmospheric background δ 13 C and δD were also reported to be approximately À47 and À86‰, respectively (Allan et al., 2001;Whiticar & Schaefer, 2007). However, there have only been a few studies on simultaneous and high-precision measurements of atmospheric δ 13 C and δD, which aim at examining atmospheric CH 4 variations (Rice et al., 2016;Röckmann et al., 2016;Tyler et al., 2007;Umezawa et al., 2012;Warwick et al., 2016).
The Hudson Bay Lowlands (HBL), the second largest continuous wetland in the world, is an important natural CH 4 source region in northern latitudes (Glooschenko et al., 1994). Nevertheless, there still remains a large uncertainty in magnitude, seasonality, and spatial distribution of CH 4 emissions in the HBL. Previous estimates of CH 4 emission rates for the HBL wetlands range from 0.2 to 11.3 Tg CH 4 yr À1 (Melton et al., 2013;S. M. Miller et al., 2014Pickett-Heaps et al., 2011;Roulet et al., 1994;Thompson et al., 2017;Worthy et al., 2000). In addition to the regional influence, the HBL area is also affected to some extent by anthropogenic CH 4 released in Europe and boreal Asia due to long-range air transport, especially in winter (Worthy et al., , 2009). There may also be large anthropogenic CH 4 sources in Alberta located to the west of the HBL in association with natural gas production (S. M. Miller et al., 2014;Thompson et al., 2017). It is further pointed out that natural CH 4 sources such as ocean, geological seepages, subsea permafrost, and sea ice exist in the Arctic (e.g., Sapart et al., 2017;Walter Anthony et al., 2012). Therefore, to accurately estimate CH 4 emissions from the HBL wetlands based on the atmospheric CH 4 observations, it is necessary to examine the influence of anthropogenic and other natural CH 4 on its atmospheric variations.
To better understand the CH 4 cycle around the HBL, we started systematic air sampling at Churchill in 2007, situated in the northern part of the HBL, and analyzed those samples for the CH 4 mole fraction, δ 13 C, and δD. We present long-term, seasonal, and short-term variations of these three variables observed at the site and compare them with those at an Arctic baseline station, Ny-Ålesund, Svalbard (78°55 0 N, 11°56 0 E; Morimoto et al., 2006Morimoto et al., , 2017. We then discuss the potential causes of temporal variations. By comparing the observed atmospheric CH 4 mole fractions with those simulated using an atmospheric chemistry transport model, we further examine CH 4 emissions in the HBL.  Figure 1, together with the land cover map of the HBL and its surrounding areas. Details of air sampling procedures and site description are found at the World Data Centre for Greenhouse Gases (WDCGG) website (https://ds.data.jma.go.jp/gmd/wdcgg/cgi-bin/wdcgg/accessdata.cgi?index=CHL458N00-EC&param=201208150002&select=parameter&parac=observation); thus, a brief explanation is presented here.
Churchill is a small port city on the western shore of Hudson Bay with a population of about 900. The land cover around Churchill is mainly characterized by the Arctic tundra and the boreal forest. Air samples were taken from an intake mounted at the top of a 60-m high tower in the Churchill Northern Studies Centre (https://www.churchillscience.ca/), located 23 km east of the town of Churchill. Each air sample was automatically collected twice a week into a 2-L Pyrex glass flask at a pressure of 0.21 MPa, using a dedicated sampling system consisted of a separated line, a diaphragm pump, and a glass trap submerged in a À80°C methanol bath. The collected samples with a dew point of around À60°C were first analyzed at ECCC for mole fractions of various trace gases such as CO 2 , CH 4 , CO, N 2 O, and SF 6 and then transported to NIPR, Japan, at approximately 0.16-0.17 MPa for isotope analyses of atmospheric CH 4 . At NIPR, each sample was divided into four 100-mL Pyrex glass flasks, two for the analysis of δ 13 C at NIPR and two for δD at TU.
Observations at Ny-Ålesund, Svalbard (78°55 0 N, 11°56 0 E), to be compared with those at Churchill have been described by Morimoto et al. (2006) in detail. Air samples were collected once a week into 800-mL stainless steel flasks at 0.8 MPa and then sent to NIPR and TU for the mole fraction and isotope analyses.
Air samples collected at Churchill were analyzed for the CH 4 mole fraction at ECCC by using a gas chromatograph (Agilent 6890) equipped with a flame ionization detector (GC-FID)  against the WMO-X2004A scale based on a gravimetric method (Dlugokencky et al., 2005, https://www.esrl.noaa.gov/ gmd/ccl/ch4_scale.html). The repeatability of the CH 4 mole fraction analysis was estimated to be better than 2 ppb by analyzing the same sample repeatedly. CH 4 mole fractions of the air samples collected at Ny-Ålesund were determined using the GC-FID (Shimadzu, GC-8A) at NIPR relative to the TU1987 scale (Aoki et al., 1992;Morimoto et al., 2006). The results of the fifth and sixth WMO (World Meteorological Organization) Round-Robin intercomparison programs (https://www.esrl.noaa.gov/gmd/ccgg/wmorr/ wmorr_results.php) showed that the TU2008 scale is higher than the WMO-X2004A scale by 2.5 ± 0.5 ppb on average. The TU2008 scale was also gravimetrically established by the same procedure as the TU1987, but a recently conducted close comparison of the two scales shows that the former provides lower CH 4 mole fractions by about 3.0 ppb than the latter at atmospheric CH 4 levels. Therefore, the difference between the TU1987 and WMO-X2004A scales is about 0.5 ppb. In this study, we compare the data at Churchill and Ny-Ålesund without any scale correction.
δ 13 C of CH 4 was determined by using a gas chromatography-combustion isotope ratio mass spectrometer (  2017). The standard used in this analysis was pure CO 2 calibrated using a dual-inlet mass spectrometer against the TU δ 13 C scale prepared from NBS-19 with δ 13 C VPDB of +1.95‰ (Nakazawa et al., 1993). In the daily δ 13 C analysis, we analyzed a CH 4 -in-air "test gas" with the known value of δ 13 C, stored in a 47-L aluminum cylinder, at least once a day to confirm the long-term stability of our δ 13 C measurements. δD of CH 4 was obtained by using a gas chromatography-pyrolysis isotope ratio mass spectrometer (GC-P-IRMS) based on Delta Plus XP (Thermo Fischer) with repeatability of 2.2‰ ). Our δD scale was established based on VSMOW (δD VSMOW = 0‰) and SLAP (À428‰) using a dual-inlet mass spectrometer with a chromium reduction system at NIPR. To confirm the internal consistency of our δD analyses over a long period of time, we also analyzed a test gas at least twice on a measurement day and then corrected for potential day-to-day fluctuations of the measured δD arisen from changeable conditions of the GC-P-IRMS, assuming that the δD value of the test gas is stable with respect to time . The δD value of the test gas was determined using GC-P-IRMS against a reference gas (purified H 2 ) calibrated by VSMOW and SLAP.
The comparison of our δ 13 C scale with that of the National Institute of Water and Atmospheric Research (NIWA) was carried out in 2004, and the result showed that our scale is 0.33 ± 0.04‰ higher than the NIWA scale (Morimoto et al., 2006(Morimoto et al., , 2017. The comparison of our δD scale with that of the Institute for Marine and Atmospheric Research Utrecht carried out in 2013-2015 showed that our scale is lower by 13.1 ± 0.6‰ than theirs at ambient air levels (Umezawa et al., 2018). More information on the intercomparison of standard scales used in the CH 4 isotope community, including TU and NIPR, has been given in Umezawa et al. (2018).

Model Simulation of CH 4 Mole Fraction
To interpret temporal variations of CH 4 in the atmosphere at Churchill and to estimate CH 4 emissions from the HBL, forward simulations of atmospheric CH 4 mole fraction were conducted for 2007-2013 using the CCSR/NIES/FRCGC (Center for Climate System Research/National Institute for Environmental Studies/Frontier Research Center for Global Change) AGCM-based Chemistry Transport Model (ACTM) developed at JAMSTEC (Japan Agency for Marine-Earth Science and Technology), with the setup described in Patra et al. (2016). ACTM uses a horizontal resolution of approximately 2.8°× 2.8°(T42 spectral truncation), with 67 pressure-sigma vertical layers. The atmospheric transport and tropospheric OH radical fields used in the model were validated by Patra et al. (2011Patra et al. ( , 2014. Two CH 4 emission scenarios, "P16pri" and "P16pos," were used in this study, which are a priori and a posteriori CH 4 emissions of the global inverse modeling (Patra et al., 2016, corresponding to their "Case 2. CH4ags"). In the P16pri scenario, anthropogenic CH 4 emissions are adopted from EDGAR42FT (2013) and kept constant at the value of the year 2000, except for agricultural soils for which annual emissions are given until 2010 and then the value in 2010 is used repeatedly for 2011-2013. CH 4 emissions from biomass burning are taken from the combination of GISS (Goddard Institute for Space Studies) inventory (Fung et al., 1991) and GFED (Global Fire Emission Database) version 3.1 (van der Werf et al., 2010) after multiplying the GISS inventory by an optimal scaling factor (Patra et al., 2011). Biogenic (wetlands and rice paddies) CH 4 emissions are obtained from a process-based terrestrial ecosystem model, VISIT (Ito & Inatomi, 2012). The P16pos scenario is derived by optimizing the P16pri scenario using ACTM and CH 4 mole fraction observations (Patra et al., 2016). In forward simulations with ACTM and the above mentioned two scenarios, atmospheric CH 4 is destroyed through reactions with OH, Cl, and O 1 (D) and through bacterial consumption in soils. Global OH field obtained by Spivakovsky et al. (2000) is scaled so that ACTM reproduces the observed decay rate of CH 3 CCl 3 in the atmosphere (Patra et al., 2011. The soil sink is prepared by VISIT (Ito & Inatomi, 2012), and stratospheric loss by OH, Cl, and O( 1 D) is calculated using their concentration fields obtained by ACTM's stratospheric model run (Takigawa et al., 1999).
To investigate CH 4 source regions contributing to atmospheric CH 4 variations at Churchill, tagged tracer experiments were also performed using ACTM (Umezawa et al., 2014). In the experiments, the surface CH 4 emission field from the P16pos scenario was used. The global surface was first divided into 17 regions (Figure 2), and the forward simulation was performed for CH 4 released from each region. The region division is slightly different from that in Umezawa et al. (2014). In particular, we divided Boreal North America into four regions to better understand the regional contribution of CH 4 sources around Churchill. We defined the HBL

Results and Discussion
3.1. Variations of CH 4 Mole Fraction, δ 13 C, and δD at Churchill and Ny-Ålesund Figures 3a-3c show temporal variations of the CH 4 mole fraction, δ 13 C, and δD observed at Churchill and Ny-Ålesund for 2007-2014, together with best fit curves to the data and long-term trends obtained using a digital-filtering technique (Nakazawa et al., 1997). In the filtering, an average seasonal cycle of each variable was approximated by fundamental and its first harmonics, and low-pass filters with cutoff periods of 4 and 24 months were adopted to obtain the best fit curve and the long-term trend, respectively. As seen in Figure 3a, the CH 4 mole fraction at Churchill shows a clear seasonal cycle with a prominent minimum in June-July and a broad maximum in late winter, superimposed on an increasing trend. Similar characteristics are also observed at Ny-Ålesund. However, there are noticeable differences between the CH 4 variations at Churchill and Ny-Ålesund: (1) the annual mean CH 4 mole fraction is higher by 3-16 ppb at Churchill than at Ny-Ålesund for 2007-2013, (2) the timing of the seasonal CH 4 minimum is earlier by about 1 week, on average, at Churchill than at Ny-Ålesund (Figure 4a), and (3) episodic high CH 4 mole fractions, sometimes over 2000 ppb, are frequently observed at Churchill throughout the year. A clear seasonal cycle is also observed in δ 13 C and δD at Churchill and Ny-Ålesund, showing the maximum in early summer and the minimum in autumn. From inspection of the observation data at the two sites, it is obvious that (1) the annual means are lower by 0.1-0.2‰ for δ 13 C and 1-4‰ for δD at Churchill than at Ny-Ålesund, (2) the average seasonal maxima of δ 13 C and δD at Churchill precede those at Ny-Ålesund by about 2-3 weeks (Figures 4b and 4c), and (3) anomalously low δ 13 C and δD values, below À48.5‰ for δ 13 C and À115‰ for δD, are often observable at Churchill in the summertime. The differences in annual mean CH 4 , δ 13 C, and δD between the two sites suggest that Churchill is more strongly affected by biogenic CH 4 sources with low δ 13 C and δD than Ny-Ålesund. The seasonal phases of CH 4 , δ 13 C, and δD at the two sites and the events with high CH 4 and low δ 13 C and δD at Churchill are discussed in sections 3.2 and 3.3 in detail, respectively.

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The seasonal cycles of CH 4 and δ 13 C at Churchill and Ny-Ålesund are similar to those observed previously at other northern mid-to-high latitude sites J. B. Miller et al., 2002;Nisbet et al., 2016;Tyler et al., 2007;Warwick et al., 2016). There are a few δD observations for the background atmosphere in northern mid-to-high latitudes (Tyler et al., 2007;Warwick et al., 2016). The seasonal cycles of δD observed by Warwick et al. (2016) at three northern high-latitude sites of Alert (82°N, 63°W), Barrow (71°N, 157°W), and Cold Bay (55°N, 163°W) are generally similar to those at Churchill and Ny-Ålesund.
The average growth rate of the CH 4 mole fraction at Churchill over 2007-2013 is 3.7 ± 0.5 ppb/yr (±95% confidence interval [C.I.] derived using a residual bootstrap method; Davison & Hinkley, 1997), which is slightly smaller than 4.9 ± 0.5 ppb/yr at Ny-Ålesund. The globally averaged CH 4 growth rate derived from the National Oceanic and Atmospheric Administration/Earth System Research Laboratory (NOAA/ESRL) sites (http://www.esrl.noaa.gov/gmd/ccgg/trends_ch4/#global) for the same period is 5.3 ± 0.3 ppb/yr (1σ), which is comparable to the value at Ny-Ålesund. Dlugokencky et al. (2009) reported that the largest CH 4 increase of 13.7 ± 1.3 ppb/yr was observed at northern polar latitudes in 2007. A similar rapid CH 4 increase of 8.8 ± 3.0 ppb/yr was observed at Ny-Ålesund from 2007 to 2008, while no significant increase was detected at Churchill (1.1 ± 4.5 ppb/yr) for the same period (±95% C.I.). As seen from Figure   . Measured values of (a) the mole fraction, (b) δ 13 C, and (c) δD of atmospheric CH 4 at Churchill (red circles) and Ny-Ålesund (blue circles). Also shown are the best fit curves to the observed data (thin lines) and long-term trends (thick lines), derived using the digital-filtering technique. The observation data are classified into two groups, one is baseline data lying within 3 times the standard deviation (σ) of the residual of the best fit curve (closed circles) and one is outliers that deviate by more than 3σ from the best fit curve (open circles). The outliers are excluded to derive the best fit curves.

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Journal of Geophysical Research: Atmospheres records of the two sites, the growth rate is 3.9 ± 0.7 ppb/yr for Churchill and 4.3 ± 0.6 ppb/yr for Ny-Ålesund, the values being close to each other.
No significant increasing or decreasing trend is found in δ 13 C at Churchill for 2007-2013, with the rate of change of 0.005 ± 0.005‰/yr (±95% C.I.). In contrast to Churchill, a significant decrease of À0.007 ± 0.004‰/yr was observed at Ny-Ålesund for the same period.
The δ 13 C trend at Churchill is probably due to the same reason as the low CH 4 growth rate, but with very low δ 13 C values in the summer of 2007. By excluding the data for 2007, the rate of change in δ 13 C is found to be À0.002 ± 0.006‰/yr, which still shows no significant trend. Schaefer et al. (2016) and Nisbet et al. (2016) reported the secular decrease in δ 13 C after 2006/2007, suggesting that biogenic CH 4 sources are predominantly responsible for the CH 4 increase after 2006. Longterm variations in CH 4 mole fraction and δ 13 C at Ny-Ålesund in 1996-2013 have been discussed in Morimoto et al. (2017) in detail.
The average rates of increase in δD at Churchill and Ny-Ålesund for 2007-2013 are 0.43 ± 0.13 and 0.12 ± 0.10‰/yr, respectively (±95% C.I.). Since the δD data show relatively large interannual variability and its measurement uncertainty is larger than that of δ 13 C, it is difficult to robustly determine the trend; thus, we do not discuss the long-term variations in δD at this stage. However, considering that δD is more sensitive to the chemical reaction of CH 4 with OH than δ 13 C because of the larger kinetic isotope effect associated to the destruction of CH 3 D in comparison with 12 CH 4 and 13 CH 4 , further studies on atmospheric δD are required to improve our understanding of long-term changes and interannual variability in CH 4 sinks (e.g., McNorton et al., 2016;Montzka et al., 2011;Rigby et al., 2017;Turner et al., 2017).

Seasonal Variations in CH 4 Emissions
As mentioned above, the CH 4 mole fraction, δ 13 C, and δD vary seasonally at Churchill and Ny-Ålesund, and the seasonal minimum of CH 4 mole fraction and the seasonal maxima of δ 13 C and δD at Churchill appear about 2 weeks earlier than those at Ny-Ålesund. To examine the contributions of biogenic, fossil fuel, and biomass burning CH 4 sources to the observed seasonal CH 4 cycle at Churchill and Ny-Ålesund, we employed a simple one-box model expressed by the following equations (Tyler et al., 2007;Umezawa, 2009): where C ATM is the observed value of the CH 4 mole fraction in the atmosphere; R C and R D denote the carbon and hydrogen isotope ratios (i.e., 13 C/ 12 C and D/H) of atmospheric (ATM), biogenic (BIO), fossil fuel (FF), and biomass burning (BB) CH 4 , respectively; S indicates the seasonally variable contributions of the three CH 4 sources; and k is the pseudo-first-order rate coefficient for OH + CH 4 . In this analysis, the observed atmospheric monthly values of C ATM , R C_ATM , and R D_ATM are derived by adding the average seasonal cycle to the average annual value for 2007-2013 ( Figure 4). The respective isotopic signatures of BIO, FF, and BB sources (R C and R D ) were assumed to be À61.7 ± 6.2 (±1σ), À44.8 ± 10.7, and À26.2 ± 4.8‰ for δ 13 C and À317 ± 33, À197 ± 51, and À211 ± 15‰ for δD (Sherwood et al., 2017). k was calculated based on the

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TransCom CH 4 settings (Patra et al., 2011), equivalent to the atmospheric lifetime of 10.3 years. KIE C and KIE D are the overall kinetic isotope effects (KIE) for the carbon and hydrogen isotopes in the CH 4 destruction processes. In this model, KIE C and KIE D were set to 1.0067 and 1.275, respectively, by averaging the KIE values for the CH 4 destruction by OH in the troposphere, OH, O( 1 D), and Cl in the stratosphere, and absorption by soils after weighting the respective isotope effects with relevant CH 4 destruction fluxes (see Table S2 in Rice et al. (2016)). The uncertainty ranges (±1σ) of KIE C and KIE D were assumed to correspond to ±20% of the isotope fractionation factor ε (ε = 1/ KIE À 1), that is, ε C = À6.7 ± 1.3‰ and ε D = À216 ± 43‰. The present uncertainty range of ε C is almost consistent with the estimate by Schaefer et al. (2016). The parameters used in this box model analysis are summarized in Table S1 in the supporting information. For uncertainty estimation of this model analysis, we assumed that the respective source isotopic signatures and KIEs distribute normally around their mean values with 1σ and then ran the Monte Carlo simulation 5000 times by randomly sampling the normally distributed isotopic signatures, KIEs, and average seasonal cycles of CH 4 , δ 13 C, and δD ( Figure 4). By using the 5000 pseudo-data sets thus generated, we calculated the median and 68 percentile confidence intervals of the monthly contributions of the respective CH 4 sources (Ss).
Figures 5a and 5b show the calculated monthly contributions of individual CH 4 sources (S BIO , S FF , S BB ) for Churchill and Ny-Ålesund, respectively, together with those of CH 4 destruction by OH. As seen in Figure 5, biogenic sources of CH 4 are the most dominant ones for the seasonal cycle of atmospheric CH 4 observed at Churchill and Ny-Ålesund, with large contributions in summer. This source would be boreal wetlands, since there is a vast amount of wetlands (e.g., bogs, fens, and tundra) in northern high latitudes from which a large quantity of CH 4 is released, showing a strong seasonal variation unlike anthropogenic biogenic CH 4 (e.g., ruminants, landfills, and waste) (Melton et al., 2013, and references therein). The biogenic CH 4 contribution at Churchill begins in May, reaches a maximum in July, and then ceases in November (Figure 5a). This seasonality is probably associated with soil temperature rise and snow melting, the highest soil temperature, and low surface temperatures and snow cover in the respective months (e.g., Pickett-Heaps et al., 2011).
Previous measurements of CH 4 fluxes indicate that the CH 4 emissions from boreal wetlands peak in June-August (e.g., Whalen & Reeburgh, 1992). However, there are large differences in the strength and seasonality of their measured CH 4 fluxes, mainly due to large spatial and temporal variability of CH 4 emissions. Pickett-Heaps et al. (2011) estimated the CH 4 emissions from the HBL using the GEOS-Chem chemical transport model and the atmospheric CH 4 mole fraction data at Fraserdale and Alert, Canada, and found that the seasonal maximum occurs in July. S. M. Miller et al. (2014) also suggested from their regional inversion that CH 4 emissions from the HBL reach a maximum in July. The Bayesian atmospheric inversion model results by Thompson et al. (2017) showed that the CH 4 flux in the HBL increases gradually in spring, reaches a maximum in August-September, and declines rapidly in September-October.
Seasonal variations of the contribution of biogenic CH 4 estimated for Churchill and Ny-Ålesund are slightly different from each other (Figures 5a and 5b). For example, the biogenic CH 4 is discernible at Churchill in May, but there is no appearance of such a contribution at Ny-Ålesund. Moreover, the seasonal maximum of the biogenic CH 4 contribution appears in July at Churchill and in August at Ny-Ålesund. This difference is presumably attributable to the influence of local/regional wetland CH 4 emissions on Churchill and to different latitudes of the two sites. Churchill is located on the northern perimeter of the HBL; thus, CH 4 emitted from HBL wetlands could directly affect the CH 4 mole fraction at Churchill. On the other hand, since

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Ny-Ålesund is far from strong CH 4 sources, seasonal signals of CH 4 emissions from boreal wetlands may reach the site with a time lag. It is also noteworthy that the onset of wetland CH 4 emissions is earlier at lower latitudes due to the latitude-dependent seasonal temperature pattern.
It is also found in Figure 5 that fossil fuel and biomass burning are minor contributors to the seasonal CH 4 cycle. However, more detailed inspection of the results indicates that fossil fuel sources significantly influence the atmospheric CH 4 mole fraction both at Churchill and Ny-Ålesund in early winter. Fossil fuel sources of CH 4 emissions are usually regarded as nonseasonal sources (EDGAR42FT, 2013), but the contribution of fossil fuel CH 4 emissions could be enhanced in winter, especially in northern high-latitude regions. For example, natural gas is consumed in large quantities during the cold season, during which the transport pipelines are pressurized so that a significant leakage of CH 4 may occur (Lowry et al., 2001). In addition to fossil fuel CH 4 emissions, slow vertical air mixing due to the strong inversion layer and weak destruction of CH 4 with OH may strengthen the influence of the fossil fuel CH 4 source on the wintertime increase of atmospheric CH 4 .
Biomass burning is also known to have seasonality in CH 4 emission, mainly due to seasonally varying rainfall and temperature. GFED 3 shows that the maximum CH 4 emissions from biomass burning occur in July in northern high latitudes (>50°N) (van der Werf et al., 2010). However, in this study, only small seasonal variations are detected for CH 4 emissions from biomass burning. Although the summertime maximum of biomass burning CH 4 emissions is detected both at Churchill and Ny-Ålesund, the values are not statistically significant.
We also see at Churchill and Ny-Ålesund that the chemical destruction by OH varies seasonally as large as biogenic CH 4 . Since CH 4 is a longlived species whose atmospheric lifetime is longer than 1 year even in summer, OH in remote areas would play an important role in the observed CH 4 variations both at two sites. Therefore, we used OH concentration and temperature data averaged over 30°-90°N and 700-1000 hPa in the present one-box model analysis. Other CH 4 sinks, such as soil oxidation and stratospheric loss, also contribute to the CH 4 seasonal cycle to some extent. The results of the one-box model analysis are further affected by values adopted for the isotopic signatures of CH 4 sources and KIEs. To inspect the sensitivity of our model analysis results to these variables, we made the one-box model analysis again using the parameters different from the initial set (see Table S1). The results of the sensitivity tests obtained for the two sites, shown in Figures S1-S3, indicate that the seasonal contributions obtained under various conditions are generally consistent to that derived with our initially set parameters.

Short-Term Variations of CH 4 Mole Fraction, δ 13 C, and δD
The CH 4 mole fraction sometimes shows extremely high values at Churchill throughout the year. Similar anomalous data are also found in δ 13 C and δD with extremely low values, although such data are observed only in the summertime. In this study, 596, 605, and 600 data are available for the CH 4 mole fraction, δ 13 C, and δD, respectively. By defining the data deviated from the best fit curve by more than 3σ of the fit as outliers, 50, 41, and 19 data were selected out from the respective records of the CH 4 mole fraction, δ 13 C, and δD.
To investigate the cause of the 50 outliers with extremely high CH 4 mole fractions in terms of emission sources, the "Miller/Tans plot" represented by

10.1002/2017JD027972
Journal of Geophysical Research: Atmospheres was applied to the CH 4 mole fraction, δ 13 C, and δD data (J. B. Miller & Tans, 2003;Umezawa et al., 2012). Here C and δ represent the CH 4 mole fraction and corresponding δ 13 C (or δD), respectively, and subscripts obs, BGD, and S denote the observed, background, and source values, respectively. The mean isotope ratio of the source, δ S , can be obtained as a slope of the regression line of C obs δ obs À C BGD δ BGD and C obs À C BGD . In this analysis, the background value for each variable is given by the best fit curve of the related observation data. Figures 6a and 6b show the Miller/Tans plots for δ 13 C and δD, respectively. It is found from the figures that the summertime (May-October) and wintertime (November-April) slopes are significantly different from each other. By applying an ordinary least squares regression to each cluster, the summertime data yield the slopes of À63.3 ± 2.8‰ (±95% C.I; correlation coefficient R = À0.96) for δ 13 C and À327 ± 26‰ (R = À0.92) for δD, while the wintertime data provide the corresponding values of À47.7 ± 4.3‰ (R = À0.96) and À241 ± 48‰ (R = À0.89). The summertime slopes agree well with those expected from biogenic CH 4 sources (e.g., Sherwood et al., 2017;Whiticar & Schaefer, 2007), suggesting the influence of CH 4 emissions from the HBL wetlands. On the other hand, the wintertime slopes result in much heavier isotope ratios than the summertime slopes, the values being close to the isotopic signatures of fossil fuel CH 4 .
Previous studies reported that the δ 13 C and δD values of CH 4 released from wetlands in northern high latitudes range from À60 to À80‰ and from À300 to À420‰, respectively (e.g., Nakagawa et al., 2002;Walter et al., 2008). Our summertime δ 13 C and δD slope values fall in previously reported ranges for the respective variables. Measurements taken by Kuhlmann et al. (1998) for two days at Fraserdale, Ontario, in August 1995 show that the isotopic signature of CH 4 from regional wetlands is À60.0 ± 3.2‰ for δ 13 C and À442 ± 142‰ for δD. These values are consistent with our summertime values within estimated uncertainty limits, although their δD estimate is more negative than ours on average. Worthy et al. (1998Worthy et al. ( , 2009 show that the air is often transported from Siberia and Europe to the Canadian high Arctic region in winter, by which Canada is widely covered with polluted air masses originated in the Eurasian Continent. To investigate the highly elevated CH 4 mole fractions observed at Churchill in winter, a 7-day backward trajectory analysis was conducted using the HYSPLIT model (Stein et al., 2015). In this analysis, each air parcel was released from 500 m above sea level over Churchill at the time when the high CH 4 mole fraction was observed. The results show that the air parcels wander around Churchill in summer, while the wintertime air parcels go back to more distant areas, mainly northern high latitudes (Figure 7). The backward trajectory analysis also shows that some air parcels assigned to high CH 4 mole fractions observed at Churchill in winter originated from Western Canada (Figure 7b)  Journal of Geophysical Research: Atmospheres (2017) reported recently that a large amount of CH 4 is presumably released from Alberta, Western Canada, in association with natural gas production.
There are also other minor natural CH 4 sources, such as ocean, geological seepages, subsea permafrost, and sea ice, in the Arctic region, of which isotopic signatures are close to the values of wetlands and/or fossil fuel sources (e.g., Sapart et al., 2017;Walter Anthony et al., 2012). As mentioned above, the backward trajectory analysis indicates that Churchill is strongly influenced by air masses from the HBL and its surroundings in summer. This suggests that the summertime CH 4 enhancement at Churchill is mainly due to wetlands rather than these minor sources. On the other hand, it is difficult to distinguish anthropogenic fossil fuel origin from natural geologic origin in winter using the backward trajectory analysis. However, some wintertime high CH 4 events at Churchill were found to be coincident with high CO and CO 2 mole fractions, suggesting the influence of human activities.

Model Simulation of Atmospheric CH 4 Variations
To investigate CH 4 emissions from the HBL in more detail, we simulated the atmospheric CH 4 mole fraction at Churchill by using ACTM and two CH 4 emission scenarios, P16pri and P16pos. The atmospheric CH 4 mole fractions simulated for 2007-2013 are shown in Figure 8a, together with the observed values. For comparison, the results for Ny-Ålesund are also shown in Figure 8b. As seen in the figures, CH 4 mole fractions simulated for Ny-Ålesund reproduce general features of the observed CH 4 variations, while obvious discrepancies between the simulated and observed mole fractions are seen at Churchill. The CH 4 mole fractions simulated using both scenarios for Churchill frequently overestimate and underestimate the summertime and wintertime values, respectively. It is also found at the two sites that the model-simulated CH 4 mole fractions based on P16pri are higher than the observations for 2007-2010 as a whole. In this connection, Patra et al. (2016) mentioned that a priori emissions used in their inversion (i.e., P16pri scenario) are too high early in the 2000s. On the other hand, P16pos reproduces fairly well the long-term trends of atmospheric CH 4 at the two sites.
To see the degree of model-observation agreement at each site, the correlation coefficient (R) and the rootmean-square error (RMSE) of the simulated and observed CH 4 mole fractions for each scenario are summarized in Table 1. These statistical parameters were calculated from the respective curves fitted to the simulated and observed data (Nakazawa et al., 1997). R generally indicates the degree of agreement between the model calculation and observation for the seasonal phase of atmospheric CH 4 , since the seasonal CH 4 cycle is larger in amplitude than interannual variations. RMSE is a measure of how well the model reproduces the observed CH 4 variations.
The respective correlation coefficients obtained for the P16pri and P16pos scenarios are 0.22 and 0.36 for Churchill and 0.57 and 0.95 for Ny-Ålesund (Table 1). The results of Ny-Ålesund show that the observed seasonality of atmospheric CH 4 is reproduced fairly well by the model for either scenario and that the agreement between the model and observation is much improved by employing P16pos rather than P16pri. RMSE is also decreased by replacing P16pri with P16pos, suggesting an improvement of the model-observation agreement. On the other hand, the two statistics, R and RMSE, for Churchill indicate that there is no appreciable improvement even if the scenario is altered. It should be noted that the P16pos scenario was derived from the inversion calculation by including the CH 4 mole fraction data observed at Zeppelin Station, Ny-Ålesund, but with no observation data around the HBL (Patra et al., 2016). Therefore, the model with P16pos shows a much better agreement with observed CH 4 variations at Ny-Ålesund rather than at Churchill.
To improve the agreement between the model-simulated and observed seasonal CH 4 cycles at Churchill, we first examined the cause for this discrepancy. The average seasonal CH 4 cycle at Churchill and Ny-Ålesund, Journal of Geophysical Research: Atmospheres derived by applying the digital filtering technique to the observed and model-calculated CH 4 mole fractions, is plotted in Figure 9 after adding the average CH 4 mole fraction over 2007-2013 at the respective sites. Since the OH fields and the atmospheric transport of ACTM are validated (Patra et al., 2011, the difference between the observed and model-generated seasonal CH 4 cycles could be mainly attributable to CH 4 emissions adopted in model simulations. Figure 9c shows the difference between the average seasonal CH 4 cycles at Churchill and Ny-Ålesund (defined as ΔCH 4 ) for each scenario or the observation. Since the variations at Ny-Ålesund are representative of northern high latitudes, ΔCH 4 would be closely related to CH 4 emissions around Churchill. The observations yield the maximum ΔCH 4 of approximately 15 ppb in late July and December-January. On the other hand, model simulations show the maximum ΔCH 4 of up to 40-60 ppb in late July, which is 3 to 4 times the observational result. This suggests that both P16pri and P16pos scenarios overestimate the summertime CH 4 emissions around Churchill. As shown in Figure 5, we found at Churchill and Ny-Ålesund that CH 4 emissions from biogenic and fossil fuel sources dominate the CH 4 mole fractions in summer and winter, respectively, and biomass burning is not important for the seasonality of atmospheric CH 4 . Therefore, the summertime and wintertime maxima of ΔCH 4 are likely associated with the respective emissions of CH 4 from wetlands and fossil fuels around Churchill.
Since the model-observation disagreement is remarkably larger in summer than in winter, we focus our discussion on the summertime events. To clarify which regions contribute to the summertime overestimated CH 4 mole fractions, we conducted tagged tracer experiments as described in section 2.2. The calculated contributions of the respective regions to the average seasonal CH 4 cycles at Churchill and Ny-Ålesund are shown in Figure 10. Also shown in the figure are the observed and model-simulated (P16pos) average seasonal CH 4 cycles.
It is obvious from Figure 10 that the HBL (rg14), Western Canada/Alaska (rg11), and Europe (rg02) have a large influence on the seasonal CH 4 cycle at Churchill. However, the model-generated seasonal CH 4 cycles for the HBL and Western Canada/Alaska are quite different from the observed result, particularly in seasonal phase. CH 4 originated in these regions are emitted mostly from boreal wetlands. Therefore, the reproduction of the observed seasonal CH 4 cycle by the model can be greatly improved by reducing the summertime CH 4 emissions, especially from the HBL. In this regard, the forward simulations with the P16pos scenario can reproduce relatively well the CH 4 mole fractions at Alert (82°N, 63°W), Barrow (71°N, 157°W), Cold Bay (55°N, 163°W), and Estevan Point (49°N, 127°W) (Patra et al., 2016), which suggests that the CH 4 emissions around the four background sites (Western Canada/Alaska) are constrained fairly well.

CH 4 Emissions From the HBL Wetlands
Assuming that the seasonal CH 4 cycle at Churchill is strongly affected by nearby CH 4 sources in the warm months, we made a rough estimation of CH 4 emissions from the HBL. In this estimation, (1) the seasonality of CH 4 emissions from the HBL for May-October was set so as to follow the seasonal variations in biogenic CH 4 sources derived by the one-box model analysis and (2) the annual CH 4 emission strength of the HBL was adjusted to minimize the RMSE between the modeled and observed seasonal CH 4 cycles at Churchill over 2007-2013, based  on the forward simulation of ACTM with the emission scenario modified above ("P16pos_rev" in Table 1 and Figure 9). To keep the global CH 4 emissions unchanged, the same amount of CH 4 as the reduced summertime emission for the HBL was added to the Province of Alberta (Region 12) as nonseasonal CH 4 emissions. This method is based on the results of the previous studies that the anthropogenic CH 4 emissions in Alberta could be underestimated in EDGAR4.2FT (S. M. Miller et al., 2014;Thompson et al., 2017). As mentioned above, the model simulations with P16pos made for Churchill underestimate the observed CH 4 mole fractions in winter. Additional CH 4 emissions in Alberta would contribute to improving this discrepancy.
The best agreement between the observed and model-simulated CH 4 variations is obtained by reducing the HBL CH 4 emissions for May-October to 30%, as an average for 2007-2013, of their original values given by the P16pos. This reduction corresponds to a fall to 39% of the original annual emission given by the P16pos scenario (6.9 ± 0.4 Tg CH 4 yr À1 ). The result yields 2.7 ± 0.3 Tg CH 4 yr À1 as the average HBL CH 4 emission for 2007-2013. Note that this emission value includes CH 4 released not only from wetlands but also from other sources such as human activities and biomass burning. However, total CH 4 emissions from sources other than wetlands could be very small (~0.2 Tg CH 4 yr À1 ), since the a priori P16pri indicates that wetland CH 4 emissions account for 94% of the total in the HBL. With respect to the reduction in CH 4 emissions for May-October in our results, the resultant percent value could be an upper limit in the estimation of CH 4 emissions from the HBL, since the summertime CH 4 mole fractions observed at Churchill are affected not only by the HBL but also by the other regions to some extent.
There still remain large differences in CH 4 emissions estimated for the HBL region. For example, the ABLE-3B/NOWES airborne and ground observation campaign, conducted in the summer of 1990, estimated annual CH 4 emissions as 0.5 ± 0.3 Tg CH 4 yr À1 for the HBL . The inverse approach based on the atmospheric CH 4 observations at Fraserdale and Alert estimated the annual CH 4 emissions as 0.2-0.5 Tg CH 4 yr À1 (Worthy et al., 2000), similar to the result obtained by Roulet et al. (1994). On the other hand, Pickett-Heaps et al. (2011) calculated CH 4 emissions from the HBL as 2.3 Tg CH 4 yr À1 using a chemical transport model and surface observations of atmospheric CH 4 . A process model intercomparison project (The Wetland and Wetland CH 4 Intercomparison of Models Project; WETCHIMP) showed CH 4 emissions from the HBL at the range of 2.2-11.3 Tg CH 4 yr À1 (Melton et al., 2013). Wetland CH 4 emissions calculated by VISIT, used as a priori flux to derive the P16pos scenario, yield 5.7 ± 0.5 Tg CH 4 yr À1 for the HBL region, which lies near the middle of the nine results from WETCHIMP. Recently, two inversion studies based on atmospheric CH 4 data reported the HBL CH 4 emissions as 2.4 ± 0.3 Tg CH 4 yr À1 (S. M. Miller et al., 2014) and 2.7-3.4 Tg CH 4 yr À1 (Thompson et al., 2017), which are lower than the results of most process model studies but close to the estimate by Pickett-Heaps et al. (2011). Our estimate of 2.7 ± 0.3 Tg CH 4 yr À1 is also comparable to the results of these top-down studies and to the lower values of WETCHIMP.
As mentioned above, CH 4 emissions reduced in the HBL were transferred to the Province of Alberta. By this additional amount of CH 4 , the annual emissions of 2.6 ± 0.3 Tg CH 4 yr À1 allocated by P16pos to Alberta is now increased to 6.9 ± 0.5 Tg CH 4 yr À1 in the P16pos_rev scenario. Thompson et al. (2017) estimated the CH 4 flux in Alberta to be 5.0-5.8 Tg CH 4 yr À1 based on their Bayesian inversion, which is smaller than our estimate by 1.1-1.9 Tg CH 4 yr À1 . By adopting P16pos_rev instead of P16pos, we found that the CH 4 mole fractions observed at two continental tower sites operated by ECCC, Lac La Biche (55°N, 113°W) and East Trout Lake (54°N, 105°W) (http://ds.data.jma.go.jp/gmd/wdcgg/wdcgg.html; also see Figure 1a), are better reproduced by the ACTM forward simulation; the two towers are located in and near the Alberta region, defined as  50°-60°N and 110°-120°W in this study. It is also seen in Figure 9a that not only the summertime minimum but also the wintertime maximum of the average seasonal CH 4 cycle at Churchill is simulated well by P16pos_rev rather than by P16pos. Consequently, our analyses support the results of S. M. Miller et al. (2014) and Thompson et al. (2017) that EDGAR42FT underestimates the anthropogenic CH 4 emissions in the Province of Alberta.

Summary and Conclusions
We measured the mole fraction, δ 13 C, and δD of atmospheric CH 4 at Churchill (58°44 0 N, 93°49 0 W) on the northern perimeter of the Hudson Bay Lowlands (HBL), Canada, from a grab sampling method for 2007-2014. Compared to the measurements at Ny-Ålesund, Svalbard (78°55 0 N, 11°56 0 E), which is away from regional CH 4 sources, the CH 4 mole fraction is generally higher and δ 13 C and δD are lower at Churchill, suggesting CH 4 emissions from regional/local boreal wetlands around the site.
The seasonal cycle of CH 4 (δ 13 C) is clearly observable, with the maximum value in January-February (May) and the minimum in June (October). δD also shows high values in June and low values in cold months of September to March. The summer minimum (maximum) of the CH 4 mole fraction (δ 13 C and δD) appears approximately 2 weeks earlier at Churchill than at Ny-Ålesund. The simple mass balance analysis with the one-box model indicates that the seasonal maximum of biogenic CH 4 influence at Churchill precedes the maximum at Ny-Ålesund, contributing to the phase difference of atmospheric CH 4 , δ 13 C, and δD between the two sites.
Short-term variations in the CH 4 mole fraction are observed throughout the year at Churchill, with higher values especially in the summertime. By inspecting the relationship between the short-term variations of the CH 4 mole fraction and isotope ratios, δ 13 C and δD of related CH 4 sources are estimated to be respectively À63.3 ± 2.8 and À327 ± 26‰ for the summertime (May-October) and À47.7 ± 4.3 and À241 ± 48‰ for the wintertime (November-April). These values indicate that short-term CH 4 variations observed at Churchill are produced mainly by biogenic CH 4 emissions from wetland in summer and fossil fuel sources in winter.
To investigate the seasonal cycle of atmospheric CH 4 in terms of CH 4 sources, we simulated the atmospheric CH 4 mole fractions using ACTM with two CH 4 emission scenarios and then compared them with the observed results at Churchill and Ny-Ålesund. ACTM overestimates the CH 4 mole fraction at Churchill in summer, although the seasonal CH 4 cycle at Ny-Ålesund is reproduced well. Tagged tracer experiments indicate that the summertime high CH 4 mole fractions at Churchill are mainly caused by the air transported from the HBL. This implies that the wetland CH 4 fluxes prescribed for the region in the ACTM simulations are overestimated. By adjusting the CH 4 fluxes prescribed for the HBL in ACTM so that the seasonal CH 4 cycle observed at Churchill is reproduced well, average CH 4 emission from the HBL for 2007-2013 is estimated to be 2.7 ± 0.3 Tg CH 4 yr À1 , which is in good agreement with the results of previous modeling studies based on atmospheric CH 4 observations. This study shows that simultaneous and high-precision measurements of the mole fraction, δ 13 C, and δD provide us with valuable information on CH 4 sources. It is also shown from the model-observation comparison that systematic observations of the atmospheric CH 4 mole fraction in nearby source regions are important for assessing the local/regional CH 4 emissions. Inclusion of δ 13 C and δD into the model analysis would provide additional strong constraints on a better understanding of CH 4 sources and sinks. For this purpose, further efforts are needed not only to increase systematic observations of δ 13 C and δD but also to undertake an extensive intercomparison program of δ 13 C and δD scales among related institutes.