Role of emission sources and atmospheric sink on the seasonal cycle of CH 4 and 𝜹 13 - CH 4 : analysis based on the atmospheric chemistry transport model TM5

. This study investigates the contribution of different CH 4 sources to the seasonal cycle of 𝛿 13 C during years 2000– 2012 using the TM5 atmospheric transport model. The seasonal cycles of anthropogenic emissions from two versions of the EDGAR inventories, v4.3.2 and v5.0 are examined. Those includes emissions from Enteric Fermentation and Manure Management (EFMM), rice cultivation and residential sources. Those from wetlands obtained from LPX-Bern v1.4 are also examined in addition to other sources such as ﬁres and ocean sources. We use spatially varying isotopic source signatures for 5 EFMM, coal, oil and gas, wetlands, ﬁres and geological emission and for other sources a global uniform value. We analysed the results as zonal means for 30° latitudinal bands. Seasonal cycles of 𝛿 13 C are found to be an inverse of CH 4 cycles in general, with a peak-to-peak amplitude of 0.07–0.26 ‰. However, due to emissions, the phase ellipses do not form straight lines, and the anti-correlations between CH 4 and 𝛿 13 C are weaker (-0.35 to -0.91) in north of 30° S. We found that wetland emissions are the dominant driver in the 𝛿 13 C seasonal cycle in the Northern Hemisphere and Tropics, such that the 10 timing of 𝛿 13 C seasonal minimum is shifted by ∼ 90 days in 60° N–90° N from the end of the year to the beginning of the year when seasonality of wetland emissions is removed. The results also showed that in the Southern Hemisphere Tropics, emissions from ﬁres contribute to the enrichment of 𝛿 13 C in July–October. In addition, we also compared the results against observations from the South Pole, Antarctica, Alert, Nunavut, Canada and Niwot Ridge, Colorado, USA. In light of this research, comparison to the observation showed that the seasonal cycle of EFMM emissions in EDGAR v5.0 inventory is more 15 realistic than in v4.3.2. In addition, the comparison at Alert showed that modelled 𝛿 13 C amplitude was approximately half of the observations, mainly because the model could not reproduce the strong depletion in autumn. This indicates that CH 4 emission magnitude and seasonal cycle of wetlands may need to be revised. Results from Niwot Ridge indicate that in addition to biogenic emissions, the proportion of biogenic to fossil based emissions may need to be revised. NOAA/GML

1 Introduction 20 Methane (CH 4 ) is a greenhouse gas of which the abundance is severely perturbed by anthropogenic activities. It causes 28 times more radiative forcing than equal emissions of CO 2 when integrated over 100 years. The abundance of CH 4 in the atmosphere has more than doubled since the pre-industrial times (Hartmann et al., 2013). CH 4 is emitted to the atmosphere from thermogenic, pyrogenic, and biogenic sources, which can be of natural or anthropogenic in origin (Saunois et al., 2020).
The processes are highly dependent on climatological and meteorological conditions, such as temperature and precipitation, and cultivation cycles. In contrast, thermogenic sources, such as fossil fuel extraction and distribution, have little month-tomonth variation, although winter emissions may be greater in some regions due to consumption of natural gas for heating (Crippa et al., 2020). Likewise, instantaneous perturbations in emissions may occur due to blowout events from natural gas 30 wells (Kuze et al., 2020;Pandey et al., 2019).
Seasonal variations in wetland CH 4 emissions have been much studied by site-level measurements (e.g. Delwiche et al., 2021;Villarreal and Vargas, 2021), process-based land surface ecosystem models (e.g. Parker et al., 2020), and atmospheric inversions (e.g. Xu et al., 2016;Zhang et al., 2021), but there are still large uncertainties in the magnitude and timing of maximum emissions on continental to regional scales (Warwick et al., 2016;Bergamaschi et al., 2018;Tsuruta et al., 2019). 35 Anthropogenic based thermogenic and biogenic CH 4 emission cycles mainly depend on political decisions. Although some countries report emission magnitudes to e.g. UNFCCC, often only annual values are reported, and emissions from e.g. rice paddies may not properly consider e.g. temperature dependencies and soil properties (Yan et al., 2009). In addition, emissions from livestock (e.g. enteric fermentation and manure management) may have seasonal cycles depending on temperature (Elsgaard et al., 2016). However, again, such information is often not included in the reported emissions, and only few global 40 inventories take the seasonal changes from this sector into account (Crippa et al., 2020, and references therein).
CH 4 has two stable carbon isotopes, 12 C and 13 C, and hydrogen isotopes, 1 H and 2 H. For the carbon isotopes, their process specific isotopic signatures ( 13 C/ 12 C ratio compared to a reference, denoted as 13 C) depend on processes that produce CH 4 (Nisbet et al., 2016). Generally, emissions with pyrogenic origin are most enriched in 13 C, followed by the thermogenic sources.
Sources from biogenic origin are most depleted in 13 C (e.g. Nisbet et al., 2016;Sherwood et al., 2017). Such information has 45 shown to be useful in quantifying CH 4 source distributions (Schwietzke et al., 2016;Thompson et al., 2018;Monteil et al., 2011;Lan et al., 2021), in addition to CH 4 -only atmospheric inversions, which estimates total CH 4 budgets (e.g. Saunois et al., 2020;Houweling et al., 2014). However, the CH 4 flux information derived using the information from isotopic measurements still have large uncertainty as the isotopic measurements are still limited in both spatial and temporal coverage, and partly overlapping signatures makes source division uncertain (Schwietzke et al., 2016). On top of that, the isotopic signature of 50 emissions can vary significantly by locations due to differences in production processes, types of origin or methanogeneisis (Ganesan et al., 2018;Feinberg et al., 2018;Etiope et al., 2019;Brownlow et al., 2017). Ganesan et al. (2018) also warned that the emission quantification, including its seasonality, may lead to erroneous results without fully incorporating detailed spatial The atmospheric sink in TM5 includes off-line chemistry; photochemical reactions with OH, Cl, and O( 1 D). The reaction with OH, the largest sink of atmospheric CH 4 , is calculated based on Houweling et al. (2014). The monthly variations in OH concentrations are based on Spivakovsky et al. (2000), scaled by 0.92 based on an evaluation using methyl chloroform (Huijnen et al., 2010). The first order loss rates for the reactions with Cl and O( 1 D) are considered only in stratosphere and are calculated separately, where the rates are based on ECHAM5 general circulation model (Jöckel et al., 2006). No interannual variation of 90 the photochemical sink processes is included in this study, as interannual variations are often assumed to be small for the study period (Zhao et al., 2019;Turner et al., 2019;Rowlinson et al., 2019). Note also that the purpose of the study is to analyse the seasonal cycle, but not trends and interannual variations in the CH 4 and 13 C.
In addition to the photochemical sinks, we include the sink to dry soils (i.e. a negative flux from atmosphere to soil) in the lowermost layer of TM5. CH 4 is oxidised by bacteria in aerobic mineral soils, and therefore, the sink is dependent on soil moisture, temperature and also soil texture (Spahni et al., 2011). These dependencies lead to the smallest sink in winter and largest sink in summer (Fig. 1). The soil sink can be treated as a pseudo first order reaction = · [CH 4 ], where = /ℎ 100 and ℎ is the thickness of the lowermost layer. The flux at the soil surface is = · [CH 4 ]. The 12 CH 4 soil sink soil,12 is taken from the LPX-Bern v1.4 land ecosystem process model (Lienert and Joos, 2018), and varies interannually and monthly.
The removal rate of 12 CH 4 is then soil,12 = 1/ℎ · soil,12 . The removal rate for 13  where soil,12 is the negative flux of 12 CH 4 at the surface, ℎ is the thickness of the lowermost layer, [ 12 CH 4 ] and [ 13 CH 4 ] are the atmospheric concentrations of 12 CH 4 and 13 CH 4 , and KIE soil is assumed to be 1.0177 (Snover and Quay, 2000).
TM5 has been applied to various CH 4 studies, and initial 3-dimensional (3D) CH 4 fields were readily available from e.g. our previous study by Tsuruta et al. (2017). For 13 CH 4 , spin-up was needed to create 3D mixing ratio fields that are in approximate steady state. We run 40 years of spin-up (running TM5 using emissions and meteorological fields of year 2000 for 40 times), 110 starting from the converted fields, and based on the emissions and isotopic signatures described in Sections 2.2 and 2.3. The spin-up was started by converting the well-mixed CH 4 fields to 13 CH 4 fields based on Eq. 1, and assuming the average 13 C in the lowest model layer is -47 ‰ and that of the uppermost layer (95 Pa <) to be -30 ‰. During the spin-up, the spatial distribution and the shapes of vertical profile changed significantly. The value at uppermost layer increased much during the spin-up, and the stratospheric 13 C increased by ∼20 ‰, reaching to approx. -10 ‰ at the end of the spin-up. The exact value 115 of stratospheric 13 C is unknown due to lack of observations, but -10 ‰ is close to the previous studies (Röckmann et al., 2011;Saueressig et al., 2001). In this study, the focus is in the troposphere and the exact values in stratosphere are not important for our analysis.  maximum in summer, i.e. July -August in the NH and January-February in the Southern Hemisphere (SH) (Fig. 1).
Monthly biomass burning emissions are taken from GFED v4.2 (Giglio et al., 2013). Biomass burning emissions vary strongly from year to year, and the amplitude in the seasonal cycle varies much by year and locations ( Fig. 1 (Tsuruta et al., 2017). The amplitude of its seasonal cycle is relatively small, with a global average of 0.08 CH 4  ecosystems. The isotopic signatures from Feinberg et al. (2018) were originally given on in T42 resolution, and emission from wetlands on 0.5°× 0.5°. We converted those to 1°× 1°resolution by choosing the closest coordinate value and by taking simple grid averages, respectively. Grid cells with missing data are filled with mean values from Thompson et al. (2018). The applied isotopic signatures do not have seasonal or inter-annual variations. This is appropriate if we assume that the spatial distribution of the sources does not change, but only the magnitude. 190 We acknowledge that there are some differences in the spatial distributions of emissions used in e.g. Feinberg et al. (2018) against the EDGAR versions and Ganesan et al. (2018) against LPX-Bern v1.4, i.e. the signatures are not custom-made for our emission fields. Therefore, the corresponding signature values may not be appropriate in all grid cells. However, considering the large range in source signatures (Schwietzke et al., 2016;Nisbet et al., 2016;Sherwood et al., 2017), we assume that our values are a good approximation for examining the cause of 13 C seasonal cycle. There are large uncertainties in the magnitude and spatial distribution of the isotopic signature, and therefore, we performed several spin-up simulations with slightly different isotopic signature to examine the effect in 13 C seasonal cycle. We first examined the filled values (grids with no initial value assigned) by applying the values from Monteil et al. (2011) and Thompson et al. (2018). We also used a weighted mean value, which lead to less negative values of 13 C, i.e. more enriched with 13 CH 4 200 for most of the sources. In contrary to expectation, the different filling values did not affect the seasonality of 13 C, probably  Fig. S3). SPO is an optimal place to evaluate the seasonal cycle of background levels of CH 4 , and there are no major CH 4 sources nearby. In contrast, NWR is located in the front range of the Colorado Rockies, and mainly measures well-mixed background air. NWR measurements influenced by strong anthropogenic sources are filtered out. Finally, ALT is located far away from anthropogenic sources, and samples air that is more influenced by distant wetland fluxes, whereas SPO is located far away from all sources both natural and biogenic.

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Note, none of the stations are located in the TM5 1°× 1°zoom region, and the model values are sampled from 4°× 6°grid using 3D linear interpolation.
For comparison, observations from 2002-2012 are used. The first two years were omitted from the analysis to be comparable to the modelled seasonality (see Section 3.1.1). To obtain detrended data we used curve fitting methods by Thoning et al. (1989).
We calculated the short term smoothed curve and the trend curve. The detrended seasonal cycle is obtained by subtracting the 220 trend curve from the smooth curve. The 13 C observations from 2007 onward have different trends than those in 2002-2006 (Nisbet et al., 2019). However, using the method from Thoning et al. (1989) we can compare years with different trends.

Simulation setups
We carried out five TM5 simulations using different input emission fields for 2000-2012 ( versions of the EDGAR inventory, v5.0 (SIM_E5) and v4.3.2 (SIM_E432), and those without EFMM seasonal cycle in v4.3.2 (SIM_E432_EFMMNS). In addition, we examined the seasonal cycle in wetland emission by using annual mean emissions (SIM_E5_WETNS) instead of a seasonal cycle. We further examined the 13 C seasonal cycle exclusively caused by the CH 4 sinks by removing the seasonal cycle of all emission sources (SIM_NS). based on Thoning et al. (1989), and the detrended smoothed fit is averaged over 2002-2012 to examine the seasonal cycle. Note that we found that it takes approximately two years for the seasonal cycle of the lower atmosphere to stabilise by changing 235 emission fields to those used in spin-up ( Supplementary Fig. S5). Therefore, in order to remove the effect of initial state, the first two years of the forward simulations are omitted from the analysis. In this section, we focus on the seasonal cycle in Δ 13 C and its relation to ΔCH 4 cycle in Section 3.1.2, as CH 4 cycle has been discussed extensively in previous studies (e.g. Dlugokencky et al., 1997;Javadinejad et al., 2019;Kivimäki et al., 2019;Khalil and Rasmussen, 1983).

Results
We acknowledge that the 13 C cycles are affected by local sources, and can vary spatially at smaller resolution than 30°240 latitudinal bands (Hein et al., 1997;Allan et al., 2001b;Warwick et al., 2016;Fujita et al., 2018;Bergamaschi et al., 2000). In addition, tropical meteorological dynamics such as the positions of the Intertropical Convergence Zone and the South Pacific Convergence Zone affect the seasonality of CH 4 and 13 C, and these variations can not be distinguished by using 30°latitudinal means (Lowe et al., 2004).
3.1.1 Peak-to-peak amplitude and shape of 13 C seasonal cycle 245 Generally, the seasonal cycle of Δ 13 C mirrors the seasonal cycle of ΔCH 4 , such that 13 C has seasonal minimum in winter and maximum in summer in the NH, and vice versa for the SH (Fig. 2). Seasonal variations of both CH 4 and 13 C are larger in the NH than in the SH, mostly because the major emission sources are located in the NH. The seasonal cycle amplitude for ΔCH 4 in our model is the largest in the NH Tropics EQ-30°N (49.7 ppb, SIM_E5), while that for Δ 13 C is the largest at 60°N-90°N (0.26 ‰, SIM_E5). The smallest amplitude is found in the SH Tropics (30°S-EQ) for both ΔCH 4 and Δ 13 C, with 15.1 ppb 250 and 0.07 ‰, respectively (SIM_E5). This is well in line with previous studies (e.g. Allan et al., 2001a;Tyler et al., 1994a). The  N for both ΔCH 4 (63.4 ppb) and Δ 13 C (0.29 ‰), which is an increase of 28 % and 10 % compared to SIM_E5, respectively.
The smallest amplitudes are again found in 30°S-EQ (19.3 ppb and 0.05 ‰). In that latitude band, the Δ 13 C amplitude decreased 25 % compared to SIM_E5, and that of ΔCH 4 shows an 28 % increase. Generally in the NH, the amplitude of ΔCH 4 increased (12-37 %), while the Δ 13 C amplitudes decreased slightly at all latitudes (7-25 %), except for 60°N-90°N, which 260 increased by 10 %. Although wetland emissions have the largest seasonal cycle amplitude in the Tropics (Fig. 1), removing the seasonal cycle resulted in an increase in the ΔCH 4 amplitudes because a compensating effect is eliminated: normally wetland emissions increases (decreases) at the same time as the oxidation capacity increases (decreases). In contrast, the Δ 13 C amplitude at 60°N-90°N increased because normally wetland emissions decreased (increased) when OH concentrations are high (low). The results also indicate that the contribution of the wetland emissions to the Δ 13 C amplitude is equally strong in in the NH (19 %, 30°N-60°N) compared to the SH (≤ −2 %, 30°S-60°S). The largest differences in the shapes of the Δ 13 C seasonal cycles between SIM_E5_WETNS and SIM_E5 are found at latitudes north of 30°S (Fig. 2). In the NH, Δ 13 C in SIM_E5 is increasing in spring towards autumn, while it is decreasing in SIM_E5_WETNS in spring. The depletion of Δ 13 C in autumn is more gradual in SIM_E5_WETNS, and continuously decreasing towards winter. The time when the seasonal 270 minimum occurs is significantly shifted from the end of the year to the beginning of the year by 69-93 days in the NH. The changes in phase of peak maxima are smaller (6-32 days), except for the band 30°N-60°N, which is shifted towards autumn by 67 days. In 30°S-EQ, Δ 13 C is decreasing in the beginning of year in SIM_E5, while it is increasing in SIM_E5_WETNS.
This creates two maxima peaks in SIM_E5_WETNS; one on DOY = 98 and another on DOY = 319, although the latter peak is more than two times larger ( Fig. 2).In south of 30°S, the differences are small, but the timing of the minima and maxima from SIM_E432 shows a clear depletion in spring; it is higher in the beginning of the year, increases for a month or two, and decreases significantly in spring (Fig. 2). The maxima are lower and the depletion in autumn is less significant (Fig. 2), resulting in smaller seasonal cycle amplitudes by 5-29 % in all latitude bands north of 30°S compared to SIM_E5. The seasonal cycle of anthropogenic biogenic sources is driven by EFMM and Rice. Although the emission amplitude of these sources is greater in EDGAR v4.3.2 in 30°N-60°N, the Δ 13 C amplitude is smaller. This is because EFMM and rice emissions in v4.3.2 are 295 high in spring only one month, while for v5.0 rice emissions are high in summer and remain high for three months (Fig. 1). The minimum in SIM_E432 occur earlier by ∼20 days in latitudes 60°N-90°N compared to SIM_E5. For 30°N-60°N, unlike SIM_E5, SIM_E432 has two minima peaks (DOY = 92 and DOY = 294), with spring peak being lower. The largest differences in the timing of the maxima are found in 30°N-60°N, where the SIM_E432 peak occurs 51 days later than that of SIM_E5.
It may look as if the effect of anthropogenic biogenic sources comes without much lag-effect, in contrast to wetland emissions 300 (those emissions are larger in spring and lower in winter in EDGAR v4.3.2 than in v5; Fig. 1), but the Δ 13 C maximum is ∼28 % lower in SIM_E432 (north of 30°N). Less EFMM emissions in winter could explain the earlier minimum and higher Δ 13 C at the end and beginning of the year compared to SIM_E5. Therefore, we suspect that the effect continues for a few months. It is also noted that, the effects of changes in emissions are clearly seen in 60°N-90°N, although anthropogenic emissions and their seasonal cycle in that latitude band are small (Fig. 1). This indicates the strong effect of mid-latitude emissions to the high 305 northern latitudes. When the EFMM seasonal cycle is removed (SIM_E432_EFMMNS), the Δ 13 C seasonal cycle is closer to that of SIM_E5 than to SIM_E432. The spring depletion is not seen, and magnitude of autumn depletion is similar to SIM_E5 (Fig. 2). However, the maximum is lower and the minimum is higher than in SIM_E5, resulting in 11-15 % smaller amplitudes in latitudes north of 30°N. The amplitudes increase at all other latitudes compared to SIM_E5, but with smaller magnitudes (6-15 %). No significant differences in the timing of minima and maxima are found at other latitudes compared to SIM_E5, 310 except for the timing of the maximum at 30°N-60°N, which is 46 days later. Compared to SIM_E432, the maxima are higher, confirming that the high spring EFMM emissions result in lower Δ 13 C in halfway of the year (June-August). In addition, the lower winter EFMM emissions contribute to an increase in Δ 13 C in the beginning of the year, i.e. there is a small lag-effect in how emissions affect Δ 13 C the cycle.

Phase ellipses 315
The seasonal cycle of Δ 13 C with respect to the ΔCH 4 cycle can be examined with a so-called phase ellipse (Bergamaschi et al., 2000;Allan et al., 2001b). In this study, we examine phase ellipses, where the detrended daily averages of CH 4 are plotted against that of 13 C. Fig. 3 shows phase ellipses from the simulations using different emission fields at 30°latitudinal bands. In SIM_NS, the seasonal cycle of the emission components are removed, and the ΔCH 4 to Δ 13 C ratio is only driven by the sinks (atmospheric and soil sinks). The results show high eccentricity of the phase ellipse at south of 60°N, i.e. close 320 to a line, and the correlation 0 ≈ −1 and 2 ≈ 1 (Fig. 3). The effect of the soil sink is small at these latitudes, so probably the seasonal cycle of Δ 13 C is preliminarily driven by the atmospheric sinks at these latitudes. Note that the rotation with respect to the DOY on the NH is anticlockwise, and that on the SH clockwise (Fig. 3).
In addition, we examine the timing (DOY) when the shifted correlations ( ) between ΔCH 4 at time and Δ 13 C at time + are at minimum and maximum. When there are seasonal cycles only in the atmospheric sinks, we expect min = 0 and max 325 = 366/2 = 183, with ( min ) = -1 and ( max ) = 1. We use min = and max = to denote the specific case when there are no surface emissions or sinks affecting the seasonal cycle. The shifts in min and max indicate the differences in ΔCH 4 and Δ 13 C cycles, such that the times when Δ 13 C are in decreasing or increasing phases are earlier or later than phase of ΔCH 4 . In SIM_NS, there is no notable shift in (Supplementary Fig. S4) except for max in 30°S-EQ and 60°N-90°N. In 30°S -EQ, the phase ellipse is close to a straight line, with 0 ≈ −1 and 2 ≈ 1, but max = 116, which is 67 days earlier than .

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There are actually two maxima in the shifted correlations, at DOY = 116 and 270, and on these days is ∼0.5 ( Supplementary   Fig. S4). This corresponds mainly to the OH and temperature cycles (OH reaction rate is strongly depended on temperature), where temperature is at maximum in April, and OH concentration in September. In 60°N-90°N, the correlation 0 = -0.98 and R 2 = 0.96 are not at the minimum or maximum (Fig. 3), and max is shifted approx. by -10 days ( Supplementary Fig. S4). This is probably due to the effect of the soil sink, which has a larger seasonal cycle amplitude in the NH (1.45 Tg CH 4 yr −1 ) than in  When the emissions' seasonality is included, the ellipses' eccentricity decreases and the shape becomes more like a circle 345 (Fig. 3). The correlation 0 becomes weaker, R 2 smaller, and shifts by -97 days the most, indicating the differences in the shape of ΔCH 4 and Δ 13 C seasonal cycles. In SIM_E5, the correlation 0 is weak (-0.57 to -0.56) and R 2 small (0.31-0.32) in north of 30°N (Fig. 3). The phase ellipses in those latitudes show that 1) both Δ 13 C and ΔCH 4 increase at the end and beginning of the year, i.e. there is no inverse relation in Δ 13 C and ΔCH 4 as in SIM_NS.
2) The relative rate of increase in Δ 13 C is slower compared to the relative rate of decrease in ΔCH 4 in spring, and 3) the relative rate of decrease in Δ 13 C is 350 faster compared to the relative rate of increase in ΔCH 4 in autumn. This effect creates a phase ellipse closer to an oval shape with one axis of symmetry (i.e. an egg-like shape), where the near-circle ellipses (i.e. smaller eccentricity) are formed at end and beginning of the year (short-half), and the other half of the ellipses with higher eccentricity (long-half) (Fig. 3). The Δ 13 C seasonal cycle amplitude in 60°N-90°N is ∼37 % larger than the amplitude at 30°N-60°N (0.26 and 0.19 ‰), creating a larger circle at 60°N-90°N compared to 30°N-60°N (Fig. 3). At latitudes north of 30°N, min and max are shifted by approx.

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-55 and -63 days compared to SIM_NS ( Supplementary Fig. S4). As Fig. 2 shows, this indicates that the minimum of Δ 13 C is ∼60 days earlier than the maximum of ΔCH 4 . In addition, the time of the increasing Δ 13 C and decreasing CH 4 period differ by 39 and 16 days at 30°N-60°N and 60°N-90°N, respectively. This is the effect of changes in the ratio of biogenic and fossil based emissions. At EQ-30°N, the SIM_E5 phase ellipse is closer to a line, especially for the mid-year, compared to that of north of 30°N (Fig. 3). Although eccentricity is smaller for the beginning and the end of the year (short-half), and Δ 13 C and 360 ΔCH 4 are almost always negatively correlated at other days, with min and max shifts of only -24 days. The SIM_E5 phase ellipse at 30°S-EQ forms an irregular shape, with weak negative correlation 0 = -0.35 and R 2 = 0.13 ( Fig. 3). As illustrated in Fig. 2 (Fig. 3). After approx. DOY ≥ 200, ΔCH 4 and Δ 13 C are anti-correlated, where the slope of the phase ellipse is close to that of SIM_NS. Compared to SIM_NS, the ( max ) is higher, with shift in max by -30 days, and the second peak is much smaller (Supplementary Fig. S4). In contrast, the correlation ( min ) is much weaker than the correlation of SIM_NS. In this latitude band, wetlands and biomass burning are the main contributors to the emission seasonal cycle. Wetland emissions maximize in February-March, while biomass burning maximizes in September-October (Fig. 1). Thus, although the CH 4 cycle is preliminary driven by OH, differences in the isotopic signatures of the emissions significantly affect the anti-correlation with 13 C cycle.
At latitudes south of 30°S, the SIM_E5 phase ellipses' eccentricities are very high (Fig. 3) compared to the ellipses found in the NH. The strong correlation 0 ≤ −0.94 and R 2 ≥ 0.88, with shifts in min and max by only ∼-20 days ( Supplementary   Fig. S4), indicating that the 13 C cycle with respect to the CH 4 cycle is preliminary driven by the sinks and little affected by 375 the seasonal cycle of the emissions.
In SIM_E5_WETNS, the phase ellipses are closer to that of SIM_NS than to SIM_E5 at all latitudes except 30°S-EQ (Fig.   3). Δ 13 C and ΔCH 4 are mostly anti-correlated in SIM_E5_WETNS, such that the eccentricity of the short-and long-halves of the ellipses do not differ much, and the correlations are strong ( 0 ≤ −0.94) and R 2 are high (≥ 0.88 ) at all latitude except 30°S -EQ. This indicates that much of the Δ 13 C cycle with respect to ΔCH 4 is driven by wetland emissions. Wetland emission 380 has the largest seasonal cycle amplitude among the emission sources ( Fig. 1), and is a main driver for the shape of the Δ 13 C cycle (see Section 3.1.1). However, for ΔCH 4 , the seasonal cycle is mainly driven by OH, such that the ΔCH 4 cycles do not vary significantly by changes in the emission fields (Fig. 2). At 30°S-EQ the phase ellipse is closer to that of SIM_E5 than to SIM_NS (Fig. 3). The shape of the SIM_E5_WETNS Δ 13 C seasonal cycle in the beginning of the year is closest to that of SIM_NS, while it is closer to SIM_E5 in the second half of the year (Fig. 2). However, the Δ 13 C increasing and decreasing 385 rates in the beginning of the year (∼50 < DOY < 100 and 100 < DOY < 200) are smaller than that of SIM_NS (Fig. 2), creating the phase ellipse offset from the SIM_NS line (Fig. 3). This indicates that, at this latitude band, biomass burning emissions also contribute significantly to the Δ 13 C cycle with respect to ΔCH 4 cycle.
The phase ellipses using EDGAR v4.3.2 (SIM_E432, SIM_E432_EFMMNS) generally form circles with smaller radius compared to those of SIM_E5 (Fig. 3) due to smaller Δ 13 C peak-to-peak amplitudes (Fig. 2). The shapes of SIM_E432_EFMMNS 390 ellipses at north of 30°N are closer to those of SIM_E5 compared to SIM_E432. This is expected, as the Δ 13 C seasonal cycle is close to that of SIM_E5 (Section 3.1.1). The Δ 13 C cycle at EQ-30°N is closest to that of SIM_WETNS (Fig. 2), which is also reflected by the phase ellipse being closest to SIM_WETNS. The phase ellipses of SIM_E432 at latitudes north of 30°N are unique, such that they form an extra circle in the beginning of the year (∼DOY < 75), outside the oval shape. This results in the weakest anti-correlation ( 0 = -0.25) and smallest R 2 = 0.06 at 60°N-90°N. These 0 and R 2 statistics from SIM_E432 395 are among the smallest at other latitude bands as well.

Comparison to surface observations
In this analysis, we focus on the evaluation of SIM_E5, SIM_E432 and SIM_E432_EFMM to examine which emission cycle best matches the observed seasonal cycle in 13 C. The peaks and amplitude of the observations are calculated from 30-day moving averages of the detrended data because the variations in the observations are high even after the smooth-fitting (Fig.   400 4).
At the SPO station, the observations of Δ 13 C show a small enrichment in the early months of the year, after which a gradual depletion is observed until SH spring (NH autumn) (Fig. 4).  shows depletion during DOY ∼50 to 120. This suggests that the EFMM emission cycle in EDGAR v4.3.2 causes the depletion in spring, as was shown in the zonal mean estimates (see Section 3.1.1). In addition, the model reaches the Δ 13 C maximum and minimum ∼20 days later than the observations. Modelled ΔCH 4 has smaller amplitudes (SIM_E5 31.6 ppb, SIM_E432 37.8 ppb, SIM_E432_EFMM 34.5 ppb) than the observations (50.1 ppb). ΔCH 4 is smaller than observed for approx. DOY < 100. Observed ΔCH 4 reaches its maximum at approx. DOY = 50 in spring, but the modelled ΔCH 4 maximum is 75 days 420 later. The observed ΔCH 4 reaches its minimum at approx. DOY = 200, but the modelled ΔCH 4 at approx. DOY = 240. In addition, the increase in modelled ΔCH 4 remains smaller compared to observations.The shape of the ΔCH 4 cycle is closest to the observations in SIM_E5, while the amplitude is closest to SIM_E432. In general, when the modelled Δ 13 C is lower than the observations, the modelled ΔCH 4 is higher than the observations, except during approx. DOY = 25-100 when both Δ 13 C and ΔCH 4 are lower than observations. The differences between the model estimates and observations may be due to 425 smaller magnitude of wetland CH 4 emissions (higher values of 13 C and lower magnitude of CH 4 ) or smaller magnitude of OH sink (higher values of 13 C). However, increasing wetland CH 4 emissions in summer would cause larger discrepancies in CH 4 abundance in summer-autumn (Warwick et al., 2016), and therefore, the magnitude of wetland CH 4 emissions are probably not only the cause for the observed discrepancies between model and observations. In addition, higher OH concentrations during spring and early summer, and lower OH concentrations in autumn could lead to a better match with the observations. Note that 430 changes in the emissions affect the modelled CH 4 and 13 C with some lag (see Section 3.1.2), but changes in OH would lead to an instantaneous effect.
At NWR (Fig. 4)  to fossil based (less depleted) emissions source especially during summer. The differences in SIM_E432 in spring suggest that the biogenic EFMM emissions are probably overestimated. However, although the seasonal cycle of EFMM emissions is removed, the spring discrepancies remain (SIM_E432_EFMMNS). In addition, the differences in both ΔCH 4 and Δ 13 C in winter suggest underestimation of biogenic emissions from all simulations.

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In this section, we examine the seasonal cycle in the zonal mean of Δ 13 C in the stratosphere, similarly to Section 3.1.1, averaged over the eight top most layers of TM5 (corresponds to levels with pressure between approx. 88-0 hPa). The stratospheric chemistry and transport are important such that those also affect the seasonal cycle in the troposphere to some extent. Note however, 13 C observations in the upper atmosphere is limited to validate the modelled seasonal cycles, so this is simply a summary of the model results. Nevertheless, the model is able to simulate realistic ΔCH 4 and 13 C profiles for the stratosphere 460 compared to e.g. Röckmann et al. (2011) (Fig. not shown).
In the spin-up simulations, we could see that the seasonal cycle of 13 C in the tropical stratosphere is influenced by the transport of air from the troposphere. The timescale for reaching a stable 13 C seasonal cycle was therefore similar to that in the troposphere, i.e. ca. 2 years ( Supplementary Fig. S5). Therefore, we consider the detrended seasonal cycle from 2002-2012 for the analysis. The temperature inversion in the stable stratified stratospheric air leads to slow vertical transport, with 465 transport timescales of a few years. The slow transport caused the seasonal cycle of 13 C to stabilize in less time in mid and high latitudes than in the tropics (Figure not shown) in the spin-up simulations. Therefore, the timescale for chemistry is shorter than for transport, and the 13 C is less influenced by the tropospheric air masses and the 13 C corresponds to the KIE of the stratospheric sinks.
The photochemical sinks in the stratosphere together with the Brewer-Dobson circulation causes the amplitudes in the 470 seasonal cycle of both ΔCH 4 and Δ 13 C to become much larger in the stratosphere (47-103 ppb, and 0.53-1.28 ‰) than in the troposphere. The shape of the Δ 13 C seasonal cycles is again generally mirroring the cycle of ΔCH 4 . This is expected, as the KIE of all sinks (OH, Cl and O( 1 D)) in the stratosphere is larger than 1.
The phase shifts are less clear in the stratosphere (correlation 0 ≤ 0.96 and 2 ≥ 0.92), indicating that the effect of emissions on Δ 13 seasonality is small (Supplementary Fig. S6). This is in line with the conclusion from the spin-up simulations described 475 above. This also results in negligible differences in Delta 13 seasonality between the simulations that differ in their surface emissions (figure not shown).
The phase ellipse at 60°S-90°S yet does not form a straight line, such that the increase in Δ 13 C in the beginning of the year is relatively slower than the decrease in ΔCH 4 compared to the second half of the year (Supplementary Fig. S6). This is probably due to seasonal effect of the transport as well as seasonal changes in the species that contribute to the sink. At high

Isotope signatures
The seasonality of 13 C depends on by the isotopic signature of the emissions. Ganesan et al. (2018) showed that changing the source signatures by about ±13 ‰ affects the modelled 13 C more than ± 0.5 ‰. Furthermore, our spin-up tests also indicate 490 that changing the isotopic signature by ± 1 ‰ can reduce/increase the 13 C seasonal cycle amplitude by 1.5-7 times, and the timing of minima/maxima by 7-130 days at 30°latitudinal bands ( Supplementary Fig. S7). Considering that our results agree well with the observations at the South Pole, we could assume that the currently used isotopic signatures are correct in a broad sense, and that more detailed and a better spatial and temporal distribution of the signature values would improve the agreement with observations.

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Although we have used a recently published spatial distributions of source signatures where available, there are still large uncertainties in the modelled 13 C values due to e.g. the vegetation types, especially tropical wetlands (Ganesan et al., 2018).
Tropical wetlands are more enriched with C-13 compared to high-latitude wetlands partly because warmer wetlands have often a thicker oxic layer, and in part because of differences in methanogenic communities, and in part because of different plant material; high-latitude wetlands precursor plant material is C3, which is depleted in C-13, while in the Tropics the dominant 500 plant material is C4 (Fisher et al., 2011).
The coal source signatures vary depending on coal types, depths, coalification processes, type of mining and coal rank (Zazzeri et al., 2016), but only limited measurements and country-level data for coal mining types are available, and may be misreported (Feinberg et al., 2018) as the coal source signature can also vary within in a country (Zazzeri et al., 2016).
EFMM source signatures are dependent on types of feed (Feinberg et al., 2018;Chang et al., 2019;Levin et al., 1993), and 505 therefore isotopic signature can be determined by the fraction of major vegetation types (Chang et al., 2019), i.e. C4 and C3 plants (Still et al., 2003). However, the vegetation distribution in a region may not correspond to the livestock diet. Ruminant C3 diet leads to more depleted values of 13 C emissions (Brownlow et al., 2017). Manure management isotopic source signatures depend on manure type; liquid manure is more depleted in 13 CH 4 , than manure pile emissions (Levin et al., 1993).
Rice cultivation methods also affect the source signatures. Mulching cultivation leads to higher values of 13 C compared to 510 traditional cultivation, and to lower CH 4 total emissions (Zhang et al., 2017). In this study, we used a global uniform value of -62.1 ‰ for RICE emissions, but measured values vary between approximately -45 ‰ and -65 ‰ at three different rice fields in China (Zhang et al., 2017). The seasonality of 13 C is determined by cultivation method, tillage and Nitrogen (N) fertilization, but is also controlled by drainage. For instance, permanently flooded rice fields have enriched 13 C values at the beginning of the crop season followed by a rapid depletion in 13 CH 4 and towards end of the season 13 C values become enriched again 515 (Zhang et al., 2017). In double harvest fields, the 13 CH 4 values are depleted immediately after drainage (Zhang et al., 2017).
Biomass burning emissions have strong 13 CH 4 seasonality due to burning activity and vegetation types, especially in African Savannah, (Brownlow et al., 2017). C4 plants in African Savannah are abundant, and during the burning period, usually between December and March, 13 C is shifted towards less negative (Brownlow et al., 2017). Pine forest burns in southeastern USA are more depleted with 13 CH 4 (-21 ‰ to -29.5 ‰) compared to African grassland burning (-16.6 ‰ to -26.1 ‰), while African 520 woodland burns produce methane with -30 ‰ (Chanton et al., 2000). The 13 CH 4 signature of biomass burning varies during different phases, i.e., the smouldering phase it produces more depleted methane compared to flaming phase (Chanton et al., 2000). However, the main factor determining 13 C is plant type C3 or C4 (Quay et al., 1991).
In addition, we acknowledge that KIE of soil sinks varies among soil types. Snover and Quay (2000) Reeburgh et al. (1997) measured values between 1.022-1.025 in boreal forest in Bonanza Creek, Alaska, USA. Those may also vary with temperature and CH 4 concentration due to variation of biological KIE (Tyler et al., 1994b). processes (Fisher et al., 2017). Forested bogs have larger temporal variations of 13 C emissions compared to poor fen, and the CH 4 emitted from fen is more enriched with C-13 compared to bog emissions (Kelly et al., 1992).
Rice cultivation source signatures also have temporal variations (Tyler et al., 1994a;Bergamaschi, 1997). The exact reasons for the variations are unclear, but possible explanations include changes in the methanogensis pathway (Whiticar et al., 1986), changes in the relative rates of production and oxidation of CH 4 with time (Kelly et al., 1992) and a temperature dependence 535 of the isotope effects in the production of methane (Blair et al., 1993).
As ruminant source signatures are dependent on feed type, the source signatures may have a seasonal cycle and annual variations when the cattle diet changes (Lopez et al., 2017). Seasonal changes in manure management may be affected similarly, but the exact values are yet not well quantified.

Seasonal cycle of CH 4 emissions 540
The modelled 13 C cycle is found to be mostly affected by wetland emissions, and therefore, 13 C measurements could be used to evaluate CH 4 emission magnitude and seasonal cycle of wetland emissions. Wetland CH 4 emissions at high latitudes (north of 50°N) estimated by process-based models (Melton et al., 2013;Bloom et al., 2017) find a maximum in May-August, and inverse models (Bousquet et al., 2011) find a maximum in July. Studies based on 13 C measurements indicate that the highlatitude CH 4 emissions likely peak in August. (Warwick et al., 2016;Fujita et al., 2018;Thompson et al., 2018). Thompson  (Saunois et al., 2020). However, Warwick et al. (2016) showed that the emission magnitude should be approximately doubled to resolve the 555 13 C amplitude as observed in e.g. ALT. It may be unrealistic to assume that wetland emissions in high northern latitudes are underestimated so significantly, but spatial distribution of the emissions (reference), the other natural biogenic emissions, such as those from inland water systems (Rosentreter et al., 2021) and the effects of the upland soil sink on 13 C (Oh et al., 2020) may well be reasons for the underestimation of the 13 C amplitude at high latitudes in this study.
In the Amazon, the climatological monthly biogenic CH 4 flux based on column budgeting (difference of the CH 4 column 560 content is due to the sum of fluxes along the air parcel path) displays two peaks, one in February and another in September-October (Basso et al., 2016). An inversion study over Brazil suggests wetland emissions peak in February and March (Tun-  nicliffe et al., 2020). Our 30°S-EQ averaged wetland emission also shows a high peak in February. However, the peak in September-October is not present. However, results from SCHIAMACHY (Bloom et al., 2012) over the Amazon show that in SH Tropics, the peak is likely to appear in December-February and near the equator the peak is in February-April and a 565 bit to the north in June-August. These differences in wetland emission timing between NH and SH Tropics correspond to the LPX-Bern results used in this study. In addition, the ENSO phase also affects the inter-annual variability of wetland emissions in tropical wetlands, enhancing tropical wetland emission during La Niña (Pandey et al., 2017;Zhu et al., 2017).
Other important emissions in the Tropics is from the fires. Fires in the Amazonian region occur in August-December, with a peak in November (Basso et al., 2016), in line with the GFED emissions used in this study.

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CH 4 emissions from rice follow the rice growing calendar (Cao et al., 1996). Cao et al. (1996) modelled CH 4 emission from rice with a maximum in July-September north of 20°N, and in December-February in the south of 10°S, while near the equatorial regions emissions are high throughout the year, peaking in August. Zhang et al. (2016) also estimated global rice CH 4 emissions to peak in July-August. Measurements performed during the growing season (Bergamaschi, 1997;Tyler et al., 1994a) agree with these estimates. CH 4 emissions from rice cultivation, provided by EDGAR v5.0 correspond better to these 575 estimates and numbers than emissions from EDGAR v4.3.2.
The seasonal cycle of CH 4 emissions from the EFMM sector also varies consideraby between the EDGAR versions. A study based on dairy cows and ewes in New-Zealand showed that the seasonal changes follow the different amounts of feed intake and seasonal variation in milk production for dairy cows compared to ewes (Ulyatt et al., 2002

Atmospheric sinks
OH is the largest CH 4 sink in the atmosphere, and it removes 12 CH 4 faster than 13 CH 4 . The seasonal cycle of OH is affected by humidity, clouds, temperature and forest fires, and Rohrer and Berresheim (2006) estimated that ∼23 % of long-term variations in OH concentrations can be explained by seasonality. Lowe et al. (2004) speculated that their underestimation of 600 the 13 C seasonal cycle amplitude in the Tropics may be associated with the OH sink, while Allan et al. (2001b) suggested the overestimation of CH 4 seasonal cycle in the model is associated with an overestimate of OH sink by more than 28 %. We examined the 13 C seasonal cycle by changing the seasonal cycle amplitude of the OH concentrations by ± 10 %, but the effect on the tropospheric 13 C seasonal cycle with respect to CH 4 was insignificant even in the Tropics (figure not shown).
Marine boundary layer Cl is thought to have a non-negligible contribution in CH 4 sink, with estimates 5-25 Tg yr − 1 in 605 range (Allan et al., 2001b(Allan et al., , 2007. Due to its stronger fractionation compared to that of OH, underestimation of tropospheric Cl will likely lead to underestimation of the 13 C seasonal cycle amplitude in the troposphere, assuming that Cl concentration has similar seasonality as OH (Allan et al., 2007;Wang et al., 2019). In this study, we did not include the tropospheric Cl sink, but could nevertheless reproduce the CH 4 and 13 C seasonal cycle measured at the South Pole reasonably well. As emission seasonality affects this site only marginally, the seasonality at the SPO is mostly driven by atmospheric sinks. Although it 610 has been shown that marine BL Cl concentration is the highest in the Tropics (e.g. Hossaini et al., 2016), our results support the recent study by Gromov et al. (2018) who suggested that the contribution of the tropospheric Cl sink to atmospheric CH 4 budgets are small. Our model results show that the CH 4 to 13 C ratio does not follow the theoretical KIE line at the southern high latitude, similarly to the observation based study by Allan et al. (2001b). They argued that the kinetic isotope fractionation at a site in the SH extratropics require an CH 4 oxidation pathway by Cl.

Summary and conclusions
We performed a global analysis of how different CH 4 emission sources influence the 13  Seasonal cycles in Δ 13 C are reverse of ΔCH 4 cycles in general, with a significant anti-correlation. However, due to the effects of the emissions, the phase ellipses do not form a straight line, but rather oval shapes, especially in the NH. At 30°625 S-EQ, the phase ellipse forms an irregular shape due to the effect of wetland and biomass burning emissions, which have distinct isotopic signatures and emission cycles. We also found that the effect of sinks other than OH contribute to the Δ 13 C cycle in relation to ΔCH 4 cycle. The phase ellipse did not become a straight line in 60°N-90°N even when seasonality of the emissions is removed, suggesting the effect of soil sink, and the KIE-line slope in the deep SH (90°S-60°S) did not exactly follow those when only the OH sink is considered.

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Compared to INSTAAR observations at the South Pole station, Antarctica, the model is able to reproduce the Δ 13 C seasonal cycle well, indicating that seasonality of the sinks and to a lesser extend in the emissions in the model are at the right level. For 13 C observations closer to the emission sources, at Alert, Canada and Niwot Ridge, USA, the moel estimates using EDGAR v5.0 are in closer agreenment to the observations than those using v4.3.2. The seasonal cycle of EFMM causes a 13 C depletion in spring in Alert and Niwot Ridge, which is not in the observations, suggesting that the seasonal cycle of EFMM is not correct 635 in EDGAR v4.3.2. In addition, the modelled Δ 13 C seasonal cycle amplitude is underestimated and maximum and minimum for Δ 13 C are around 20 days later than the observations in Alert. The cause of these discrepancies may be underestimation of wetland CH 4 emissions in the northern high latitudes in summer, although some other factors, e.g. timing of wetland emission peak, seasonal cycle of OH, and isotopic signatures could also affect the simulated seasonal cycles.
Seasonal cycle amplitudes of both Δ 13 C and ΔCH 4 are much larger in the stratosphere than in the troposphere. The effect 640 of emissions is negligible in the stratosphere, and the 13 C seasonality is therefore driven by the atmospheric sinks. However, due to lack of 13 C observations at high altitudes, it is difficult to evaluate whether our estimated seasonal cycles are realistic.
Here, we have focused on the effects of emissions and their source signatures on the simulated seasonal cycle of 13 C. There is an increasing number of studies examining the spatial and temporal distributions of emission signatures, but further research at regional to global scales is needed to examine global changes of 13 C. Furthermore, a step forward to better understand the 645 different source contributions would be to build an atmospheric inversion, and will be the scope of our next study.
Code and data availability. The source code of TM5 used in this paper is available from https://doi.org/10.23729/966bb3fa-6c15-43d d-94d2-e80c5f7ce2f7. The data presented will be provided on request from the corresponding author. The atmospheric CH 4 and 13 C measurements are available from NOAA/GML data server https://www.esrl.noaa.gov/gmd/dv/data/