Model simulations of atmospheric methane (1997–2016) and their evaluation using NOAA and AGAGE surface and IAGOS-CARIBIC aircraft observations

Methane (CH4) is an important greenhouse gas, and its atmospheric budget is determined by interacting sources and sinks in a dynamic global environment. Methane observations indicate that after almost a decade of stagnation, from 2006, a sudden and continuing global mixing ratio increase took place. We applied a general circulation model to simulate the global atmospheric budget, variability, and trends of methane for the period 1997–2016. Using interannually constant CH4 a priori emissions from 11 biogenic and fossil source categories, the model results are compared with observations from 17 Advanced Global Atmospheric Gases Experiment (AGAGE) and National Oceanic and Atmospheric Administration (NOAA) surface stations and intercontinental Civil Aircraft for the Regular observation of the atmosphere Based on an Instrumented Container (CARIBIC) flights, with > 4800 CH4 samples, gathered on > 320 flights in the upper troposphere and lowermost stratosphere. Based on a simple optimization procedure, methane emission categories have been scaled to reduce discrepancies with the observational data for the period 1997– 2006. With this approach, the all-station mean dry air mole fraction of 1780 nmol mol−1 could be improved from an a priori root mean square deviation (RMSD) of 1.31 % to just 0.61 %, associated with a coefficient of determination (R2) of 0.79. The simulated a priori interhemispheric difference of 143.12 nmol mol−1 was improved to 131.28 nmol mol−1, which matched the observations quite well (130.82 nmol mol−1). Analogously, aircraft measurements were reproduced well, with a global RMSD of 1.1 % for the measurements before 2007, with even better results on a regional level (e.g., over India, with an RMSD of 0.98 % and R2 = 0.65). With regard to emission optimization, this implied a 30.2 Tg CH4 yr−1 reduction in predominantly fossil-fuelrelated emissions and a 28.7 Tg CH4 yr−1 increase of biogenic sources. With the same methodology, the CH4 growth that started in 2007 and continued almost linearly through 2013 was investigated, exploring the contributions by four potential causes, namely biogenic emissions from tropical wetlands, from agriculture including ruminant animals, and from rice cultivation, and anthropogenic emissions (fossil fuel sources, e.g., shale gas fracking) in North America. The optimization procedure adopted in this work showed that an increase in emissions from shale gas (7.67 Tg yr−1), rice cultivation (7.15 Tg yr−1), and tropical wetlands (0.58 Tg yr−1) for the period 2006–2013 leads to an optimal agreement (i.e., lowest RMSD) between model results and observations. Published by Copernicus Publications on behalf of the European Geosciences Union. 5788 P. H. Zimmermann et al.: Model simulations of atmospheric methane (1997–2016)

The atmospheric CH 4 dry air mole fractions in our model setup without chemical feedback on the reactants are linearly dependent on the source strengths, allowing the source segregated simulation of eleven biogenic and fossil emission categories (tagging), with the aim to analyze global observations and derive the source specific CH 4 steady state lifetimes (τ). Moreover, tagging enables a-posteriori rescaling of individual emissions with proportional effects on respective source segregated methane abundances. A sophisticated optimization procedure ("Solver") was applied to the 25 model results minimizing the Root Mean Square deviation (RMS) from the observations. Under given constraints the 2000 -2006 observed all-station mean dry air mole fraction of 1,780 nmol/mol could be reproduced within an RMS = 0.40 %, associated with a coefficient of determination R 2 = 0.81. With regard to source optimization this implies a reduction in fossil fuel (predominantly coal and gas) related emissions and an increase in biogenic sources such as tropical wetlands and rice paddies. The observed interhemispheric difference between the most northerly and southerly 30 stations was reproduced within 0.76 %.
The CH 4 rise started nearly linearly from 2007 through 2013, explained by an additional emission of 20.47 Tg/y CH 4 .
We explored the contributions of four potential causes, representing biogenic emissions from tropical wetlands (TRO), from agriculture including ruminant animals (ANI) and rice cultivation (RIC), and from anthropogenic (e.g. shale gas fracturing) fossil emissions from North America (SHA), added to the posteriori no-trend period emission distribution. 35 For each source, independently, between 20.36 and 20.64 Tg/y were obtained with the Solver to fit the observed trend with smallest RMS. A statistically most likely combination completely excludes the fossil source SHA in favor of 20.02 Tg/y CH 4 -RIC and a small addition of 0.43 Tg/y CH 4 -TRO.
After 2013 the trend steepened and further assumptions will be needed, not discussed in this study.

Introduction 50
The greenhouse gas methane (CH 4 ) is emitted into the atmosphere by various natural and anthropogenic sources, and is removed by photochemical reactions and to a small extent through oxidation by methanotrophic bacteria in soils . The tropospheric mean lifetime of CH 4 due to oxidation by OH has been estimated to be 8-9 years  and its concentration has been growing by about 1 %/y since the beginning of the Anthropocene in the 19 th century (Crutzen, 2002, Ciais et al. 2013. 55 The resulting factor of 2.5 increase in the global abundance of atmospheric methane (CH 4 ) since 1750 contributes 0.5 Wm −2 to total direct radiative forcing by long-lived greenhouse gases (2.8 Wm −2 in 2009), while its role in atmospheric chemistry adds another approximately 0.2 Wm −2 of indirect forcing . Etminan et al. (2016) presented new calculations including the impact of the shortwave forcing and found that the 1750-2011 radiative forcing is about 25% higher (increasing from 0.5 Wm −2 to 0.6 Wm −2 ) compared to the value in the Intergovernmental 60 Panel on Climate Change (IPCC) 2013 assessment. After the strong upward CH 4 trend since the 1960s, by the end of the 1990s the increase had slowed down until sources and sinks quasi balanced for about 8 years, while in 2007 the CH 4 increase resumed unexpectedly (Bergamaschi et al., 2013). The resuming upward trend after 2007 (Dlugokencky et al., 2009;Rigby et al., 2008, IPCC 2014 is not fully understood (Nisbet et al., 2014, Mikaloff-Fletcher andSchaefer, 2019), and causes of the trend changes have been subject of a number of studies, some with contradictory results, highlighting the complexity of the processes that control atmospheric methane in the Anthropocene.
Data analysis (Nisbet et al., 2016, Worden et al., 2017 and inverse modelling studies (Bergamaschi et al., 2013) 70 indicate that global emissions since 2007 were about 15 to 25 Tg CH 4 /y higher than in previous years, possibly caused by increasing tropical wetland emissions and anthropogenic pollution in mid-latitudes of the northern hemisphere. Hausmann et al. (2016), using methane and ethane column measurements, concluded that the increase in CH 4 since 2007 has been between 18 to 73 % (depending on assumed ethane/methane source ratios) due to thermogenic methane.
Further, Helmig et al. (2016) suggested a large contribution of US oil and natural gas production to the increased 75 emissions. A potentially growing source that was identified is hydraulic shale gas fracturing, for instance in Utah, where 6 to 12 % of the natural gas produced may locally leak to the atmosphere (Karion et al., 2013, Helmig et al. 2016.
At first glance the increasing production of fossil fuels may explain the CH 4 trend but it was concluded (Schwietzke et al., 2016) that overall fossil sources have decreased during the last decades owing to industrial efficiency improvements. Based on 13 C/ 12 C isotope ratio analyses for -2011Schaefer at al. (2016 concluded that fossil fuel 80 related emissions are a minor contributor to the renewed methane increase, compared to tropical wetlands and agriculture. According to Nisbet et al. (2016) "since 2007 δ 13 C-CH 4 (a measure of the 13 C/ 12 C isotope ratio in methane) has shifted to significantly more negative values suggesting that the methane rise was dominated by increases in biogenic methane emissions, particularly in the tropics, for example, from expansion of tropical wetlands in years with strongly positive 85 rainfall anomalies or emissions from increased agricultural sources such as ruminants and rice paddies". With regard to biogenic emission sources, e.g. Saunois et al. (2016) conclude that "methane emissions from increasing agricultural activities seem to be a major, possibly dominant, cause of the atmospheric growth trends of the past decade" and "Recent bottom-up inventories estimate an increase in annual agricultural emissions of 3-5 Tg between 2006 and 2012, mostly from Africa and Asia, whereas wetland emissions were estimated to be mostly unchanged between 2006 and 90 2012". In this context Schaefer et al. (2016) state that "after 2006, the activation of biogenic emissions caused the renewed CH 4 rise", thus raising concern about the contribution from rice production versus wetland emissions. The latter are higher in the southern hemisphere, whereas remote sensing shows that CH 4 mainly increased in the northern tropics and subtropics (Houweling et al., 2014). Furthermore, tropical wetlands match the post-2006 δ 13 C-CH 4 perturbation not as well as rice cultivation and C3-fed ruminants (Schaefer et al., 2016). 95 Here we investigate how well, based on source estimates, CH 4 mixing ratios and their changes over the past two decades can be simulated numerically, by accounting for atmospheric dynamical and chemical processes with the ECHAM/MESSy Atmospheric Chemistry (EMAC), which describes the transport, dispersion, and chemistry of atmospheric trace constituents, and allows the online sampling of calculated mixing ratios in four dimensions, mimicking the sampling by observational systems (Jöckel et al., 2010). To evaluate the simulation results we use CH 4 100 measurements at surface stations, i.e. data from NOAA (Dlugokencky et al., 2018) and AGAGE (Prinn et al., 2000) and CH 4 data collected by the CARIBIC (Civil Aircraft for the Regular observation of the atmosphere Based on an Instrumented Container) passenger aircraft (Brenninkmeijer et al., 2007).
Both measurement data sets (i.e. the surface-station and the aircraft based) allow a global approach, with each having its characteristic "footprint". The station data are based on regular measurements at fixed coordinates in both hemispheres. 105 The CARIBIC data are based on monthly flight series (nominally 4 sequential long-distance flights) covering large parts of the globe from a Eurocentric perspective. A summary of all abbreviations is provided in the "Acronyms" table at the end.

The EMAC numerical model 110
The EMAC model is a chemistry and climate simulation system that includes sub-models describing tropospheric and middle atmosphere processes and their interaction with oceans, land and human influences. The Modular Earth Submodel System (MESSy, www.messy-interface.org) results from an open, multi-institutional project providing a strategy for developing comprehensive Earth System Models (ESMs) with flexible levels of complexity. MESSy describes atmospheric chemistry and meteorological processes in a modular framework, following strict coding 115 standards. The sub-models in EMAC have been coupled to the 5th generation European Centre HAMburg general circulation model (ECHAM5, Röckner et al., 2006), of which the coding has been optimized for this purpose (Jöckel et al., 2006(Jöckel et al., , 2010. The extended EMAC model version 2.50 at T106L90MA resolution was used to simulate the global methane budget. A triangular truncation at wave number 106 for the spectral core of ECHAM5 corresponds to a ~1.1°×1.1° horizontal 120 quadratic Gaussian grid spacing near the equator, and 90 levels on a hybrid-pressure grid in the vertical direction span from the Earth's surface to 0.01 hPa pressure altitude (~80km, the middle of uppermost layer). The vertical resolution near the tropopause is about 500 m. Numerical stability criteria require an integration time step of 1-2 min. With regard to model dynamics, we applied a weak "nudging" towards realistic meteorology over the period of interest, more specifically by Newtonian relaxation of four prognostic model variables temperature, divergence, vorticity and the 125 logarithm of surface pressure towards ERA interim data (Dee et al., 2011) of the European Centre for Medium-range Weather Forecasting (ECMWF).
Apart from the prescribed sea surface temperature (SST), the sea-ice concentration (SCI), and the nudged surface pressure, the nudging method is applied in the free troposphere only, tapering off towards the surface and the tropopause, so that stratospheric dynamics are calculated freely, and possible inconsistencies between the boundary 130 layer representations of the ECMWF and ECHAM models are avoided. Further, in the free troposphere, the nudging is weak enough to not disturb the self-consistent model physics, while this approach allows a direct comparison of the model output with measurement data (without constraining the model physics), and therefore offers an efficient model evaluation.
The EMAC sub-model collection includes "CH4" (Frank, 2018) which is tailored for stratospheric and tropospheric 135 methane chemistry and solves the ordinary differential equations describing the oxidation of methane by OH, O 1 D, Cl and photolysis. The feedback to the hydrological cycle by modification of the specific humidity is optional in CH4 and was switched off in this particular setup for the same reason as applying tropospheric nudging as mentioned above.
The sub-models "SCOUT" and "S4D" enable online sampling of model parameters such as tracer mixing ratio at selected observation sites as well as along aircraft measuring flight routes (http://www.messy-interface.org/ "MESSy 140 Submodels" and Jöckel et al., 2010).

Model setup for Methane budget investigation
As long as the tracers under consideration are not subject to chemical feedback reactions among each other, they can be processed like separate tracers. In this manner, atmospheric methane can be tagged e.g. by the source category which they derive from and can be simulated individually, while their sum exactly fits the simultaneous total CH 4 calculations. 145 In our particular case, no feedback is affecting the prescribed OH distribution neither in the gross nor in the tagged mode. (cf. Sec. 2.3.3). The water that is produced by methane oxidation in the used setup was not added to the hydrological cycle because this is only relevant in the stratosphere.
The sub-models "SCOUT" and "S4D" enable online sampling of model parameters such as tracer mixing ratio at selected observation sites as well as along aircraft measuring flight routes (http://www.messy-interface.org/ "MESSy 150 Submodels" and Jöckel et al., 2010).
Using a priori emission estimates, an initial CH 4 distribution was derived in the course of several spin-up simulations repeated until a steady state global CH 4 mass has settled over the years 1997 through 2006.
The module "Solver" is a spreadsheet optimizer that is bundled with Microsoft Excel (Fylstra et al. 1998) and uses the "Generalized Reduced Gradient method" (GRG) (Lasdon et al. 1978). A "goal function" defined by the user can be 155 optimized under given constraints upon specific parameters.
In this modeling study the Solver is applied to post-process eleven tagged source segregated a priori tracer distributions Anthropogenic and natural methane sources are based on The Global Atmospheric Methane Synthesis (GAMeS), a 165 GAIM/IGBP (http://gaim.unh.edu/) initiative to develop a process-based understanding of the global atmospheric methane budget for use in predicting future atmospheric methane burdens. Emission data for this initiative have been used for the model setup described here. Natural wetland emissions are based on Walter et al. (2000), fossil sources based on EDGARV2.0 and remaining sources as compiled by Fung et al. (1991). Processes with similar isotopic characteristics are aggregated into one group. Oil related sources, for example, comprise mining and processing of 170 crude fuel and all emission classes related to the use of fossil fuel such as residential heating, on/offshore traffic, industry, etc., and also include an estimate of volcanoes (Houweling et al., 1999). Given that methane emissions from boreal/arctic wetlands are quite uncertain, it is reasonable to assume that this source category accounts for permafrost decomposition emissions as well.
The "burning"-part of the GAMeS dataset is replaced by the GFEDv4s statistics (Randerson et al., 2018) in addition to 175 biofuel combustion emissions from the EDGARV2.0 database (Olivier, 2001). The biogenic emissions from bogs, rice fields, swamps and biomass burning are subject to seasonal variability. About 60 % of the total emissions of 580 Tg/y are caused by human activities; the remainder is from natural sources. At northern middle and high latitudes, methane sources predominantly comprise animals (ruminants), bogs, gas and coal production, transmission and use, landfills, and boreal biomass fires. Tropical wetlands (partly in the subtropics) are the world's largest (natural) source of methane 180 together with animals. Minor tropical anthropogenic input is from biofuel combustion. The individual source strengths are partly subject to seasonal variability, and except for inter-annual differences in the ~20 Tg/y biomass burning, are assumed to be inter-annually constant in a reference simulation for the full period 1997 through 2014. More illustrative plots are provided in the supplement, such as Fig. S1a,b, which depicts the total emission distribution in g (CH 4 ) /m 2 /month for Jan. (a) and Jul. (b), in logarithmic scale for better representation, to illustrate seasonal CH 4 changes. 185 A rearrangement among the natural wetland and the anthropogenic landfill-, coal-, gas-, and oil contributions by ~20 Tg(CH 4 )/y (i.e. 3.6 % of the total) in favor of biogenic emissions such as low latitude wetlands and rice paddies has been applied retrospectively under the condition of least RMS deviation between station and model CH 4 mixing ratios.

Methane uptake by soils
A small but significant (6.6 % in this study) removal process of methane is its oxidation by methanotrophic bacteria in soils . The MESSy sub-model "DDEP" simulates dry deposition of gas phase tracers and aerosols (Kerkweg et al. 2006). For our CH 4 budget modeling the deposition velocity was derived for a fixed 200 atmospheric-methane mixing ratio of 1800 nmol/mol (Spahni R. et al., 2011, Ridgwell et al., 1999 and is scaled correspondingly. The deposition has a pronounced seasonal cycle in phase with the wetland emissions and depends on soil temperature, moisture content and the land cultivation fraction and varies from 2.4 Tg in January to 4.0 Tg in July.

Methane chemical removal
The chemical removal process of CH 4 is photo-oxidation, predominantly by hydroxyl (OH) radicals. In addition to the 205 reaction with OH in the troposphere and stratosphere, there are minor oxidation reactions with atomic chlorine (Cl) in the marine boundary layer and the stratosphere and with electronically excited oxygen atoms (O( 1 D)) in the stratosphere (Lelieveld et al., 1998;Dlugokencky et al., 2011). In EMAC the methane photolysis and chemical reaction system is numerically solved by the sub-model "CH4". Global distributions of OH, Cl, and O( 1 D) have been pre-calculated from the model evaluation reference simulation S1 (Jöckel et al., 2006), therefore providing internally consistent oxidation 210 fields for the model transport and chemistry of precursors. Monthly averaged fields calculated for the year 2000 have been used in this study.

Observations used for model evaluation
The EMAC model simulates the global distribution of methane from given emission source categories, and produces time series of methane distributions as output. Additionally, model samples during the simulation are recorded for the 215 evaluation of the results at prescribed locations and times. Monthly averaged mixing ratios are computed at the location of selected NOAA and AGAGE sites and about 4,600 CARIBIC flight measuring samples (Brenninkmeijer et al., 1999(Brenninkmeijer et al., , 2007 gathered during more than 350 flights from 1997 through 2014. The station records predominantly serve as a reference for the model-and recursive emission evaluation and help to gain confidence in the CARIBIC flight data analysis and interpretation. 220

NOAA and AGAGE station network
The NOAA Global Greenhouse Gas Reference Network measures the atmospheric distribution and trends of the three main long-term drivers of climate change including methane (CH 4 ), the subject of this study. The Reference Network is part of NOAA's Earth System Research Laboratory in Boulder, Colorado (https://www.esrl.noaa.gov/gmd/ccgg/). The data provided (Dlugokencky et al., 2018) are filtered with respect to synoptic scale pollution events. We take 225 advantage of 16 stations approximately equally distributed over the globe (Fig. 2a) and remote from the major emission areas to ensure comparability with the model results which are not filtered. For the same reason, in case of Cape Grim, Australia (41º S, 145º) we refer to the unfiltered AGAGE records (Prinn et al., 1978(Prinn et al., , 2013. At all stations monthly mean mixing-ratios are compared to respective monthly averaged model samples.

CARIBIC flight observations 230
CARIBIC (Civil Aircraft for the Regular Investigation of the Atmosphere Based on an Instrument Container, Brenninkmeijer et al., 2007) is a European passenger aircraft based atmospheric composition monitoring project that has become part of the IAGOS Infrastructure (www.iagos.org). CARIBIC deploys an airfreight container equipped with about 1.5 tons of instruments, connected to a multi-probe air inlet system. The container is installed monthly for 4 sequential measurement flights from and back to Frankfurt or Munich Airport after which air samples, aerosol samples 235 and data are retrieved. The container houses instruments for measuring ozone, carbon monoxide, nitrogen oxides, water vapor and many more trace gases as well as atmospheric aerosols. Air samples are collected at cruise altitudes between about 10 and 12 km and depending on latitude and season and actual synoptic meteorological conditions represent tropospheric or stratospheric air masses.
Overall the ratio between sampled stratospheric and tropospheric air masses is about 0.5. These air samples are The calibration is carried out using NOAA Methane WMO scale (Dlugokencky et al., 2005) For further information about CARIBIC based studies involving CH 4, we refer to Schuck et al. 2012, and Rauthe-Schöch et al. 2016. For the period 1997-2002, we use data from the first phase of CARIBIC (Brenninkmeijer et al. 1999). In our specific model setup, the oxidation chemistry, neglecting chemical feedback reactions on the oxidants as well as on H 2 O, responds linearly to the emissions, thus allowing the separate tracer simulation of individual sources by tagging. Consequently, the sum of eleven tagged methane tracers exactly reflects the reference total methane distribution, and the CH 4 composition at any grid point in the atmosphere can be attributed to the specific source categories. Furthermore, the tagging retrospectively allows re-scaling the source segregated a-priory global methane 260 distributions with the aim of an optimal station measurement fitting approach -Sect. 4.1.1.

Simulation results
For the trend period since 2007 we introduced additional emissions to account for the recent CH 4 increase (Kirschke et al., 2013, Miller et al., 2013, Nisbet et al., 2016, Turner et al., 2017. On top of the rescaled "base" emissions from the non-trend years we simulated the effect of four tagged potentially rising biogenic sources: tropical wetlands, ruminant animals, rice cultivation, and a new fossil emission source from North America based on shale gas drilling statistics. 265 Also for this period the smallest RMS (measurement vs model) deviation together with the coefficient of determination R 2 is used as a criterion to evaluate the emission scenarios, while the Solver optimization analysis attributes an overwhelming ~ 99% to biogenic agricultural (see Sect. 4.2 for more details).

The period 1997 through 2006 270
For initialization, a global methane distribution pattern for January was created as mentioned above (Sect. 2.2) and ensures a balanced annual average global CH 4 mass over the entire period with inter-annually constant sources and sinks up to deviations caused by variations in biomass burning. According to prescribed 4-dimensional coordinate tables, calculated CH 4 mixing ratios are recorded and stored at all sampling positions and times at selected (NOAA (Dlugokencky, 2018) and AGAGE (Prinn et al., 2013) observation sites and along the CARIBIC flight tracks 275 (Brenninkmeijer et al., 1999(Brenninkmeijer et al., , 2007 for the years 1997 through 2016 in view of further graphical and statistical evaluation. Additionally, based on the mass conserving sources in the EMAC model simulation, for the entire time period a series of global CH 4 -distributions was produced and stored in 2-day frequency. The linear dependency between source strength and atmospheric abundance in this model setup (see 2.2) ensures that the sum of all tagged tracersas mentioned aboveis equal to the reference tracer comprising the sum of all 280 emissions. Moreover, this numerical property of the model's partial differential equation system allows the redistribution of certain amounts amonge.g. northern and southernemitters without affecting the global budget.
While the global total CH 4 emissions are relatively well-constrained, estimates of emissions by source category range within a factor of two . The global observational networks have shown to be very helpful to derive the emissions at large scales. The CARIBIC observatory provides an additional global constraint of CH 4 285 abundance and variability in the UTLS, not directly affected by emission sources at the surface, while being sensitive to the vertical exchange of air masses between the lower and upper troposphere.
The use of tagged tracers helps to determine the origin of the methane that is sampled. Tagged initial distributions and tagged soil sinks are calculated as ratios between the respective source fluxes and the total. Corresponding sourcesegregated CH 4 station and aircraft samples were calculated the same way as for the reference tracer, but in this case for 290 all categories. Chemical reactions and photolysis were the same for all tagged tracers as for total CH 4 , i.e. the tagged emissions are exposed to the same oxidant environment. Assuming that the sources are inter-annually constant, apart from the variability in the comparably small (3.4 %) biomass burning source, the partial masses of the tagged tracers remain in steady state over the simulation period at roughly proportional amounts to the emission fluxes. However, the exact weighting factors, in terms of the steady-state atmospheric lifetimes, vary somewhat around the integral lifetime τ 295

NOAA/AGAGE stations
Based on the a priori emission assumptions (Table 1,  Consistent with the observations, the simulated CH 4 mixing ratios are largest at BRW (71°N) and decrease with latitude, reaching minimum values south of 40 °S at CRZ (46°S), HBA (76°S), and SPO (90°S). The abundance at AGAGE CGO (41°S) is slightly enhanced and scattered, being exposed to pollution events from the Australian 310 continent, but also well reproduced by the model. The -2006 average observed mean mixing ratios for these stations range from 1,865 to 1,727 nmol/mol and, using a-priori emissions, are simulated within an average percentage RMS = 0.67 %. Northern Hemispheric values however are overestimated, e.g. at BRW by 18.2 nmol/mol (0.98 %) much more than the 5.7 nmol/mol (0.33 %) at SPO (North Pole) and cause an excessive interhemispheric difference (Fig. 3, black crosses vs open blue circles) indicating mismatches in the emission 315 assumptions. Although this imparity could also be caused by erroneous interhemispheric transport, previous analyses (Aghedo et al.2010, Krol et al. 2017 show that the underlying ECHAM5 model reproduce realistically the Interhemispheric transport time. Taking advantage of the Solver (Sect. 2.2) we defined the goal as the minimum RMS deviation between the station measurements and respective model simulations composed of the tagged components multiplied with scaling factors, 320 i.e. the parameters. Likely tolerance intervals (constrains) are available in form of uncertainty specifications along with the a-priori emission assumptions (e.g. Bergamaschi et al., 2013). The largest interval (12%) is allowed for the category gas production.
The a-priori simulation results (Fig. 3, black crosses), as mentioned above, are too high in the Northern Hemisphere The tagged tracers indicate that the atmospheric mixing-ratios over the years 1997 through 2006 are proportional to the respective emission amounts, but influenced by the distance from the source due to the oxidation by OH. Footprints at stations are the result of source and sink interaction (Fig. S5). A shorter distance leads to a reduced atmospheric abundance relative to the source strength and vice versa. This is quantified in terms of "steady state lifetime", defined as the ratio between the global atmospheric trace mass (i.e. atmospheric burden) and the annual emission amount, which 345 is , by definition of steady state, equal the total annual sink. Over the period of relative stagnation 2000 -2006 (Fig. 1) the shortest lifetimes (τ ≌ 7.3 years) were found for fossil methane being emitted predominantly by industrialized countries, from landfills and oil production in the Northern Hemisphere and therefore experiencing the highest OH concentrations (Fig. 6). On the other hand, wetland methane (swamps) is exposed to lower OH concentration, producing a steady state lifetime of τ = 10.08 years (Table 1, col. 5 and Fig. S6a). Biomass burning methane never establishes 350 steady state equilibrium because of the very irregular inter-annual intensity of the fire events (Fig. S6b). Considering that its contribution to the total emissions with ~3.5 % is small, the quantification of the total CH 4 -lifetime τ ≌ 8.45 years appears reasonable.
From 2007 on, when the station records show an upward trend (cf. Fig. 1 representatively for SPO) additional emissions were necessary in order to close the budget if the sink processes are kept unchanged. The simulation for this period is 355 presented in Sect. 4.2.

CARIBIC flights
The spatio-temporal distribution of the CARIBIC CH 4 sampling is quite different from that of the surface stations. 360 Measurements were taken over relatively short time intervals and more than 96 % of the samples are from the NH. In contrast to the monthly average station data, the CARIBIC individual methane observations in the UTLS are based on air sampling over 20 minutes (i.e. ~300 km) for CARIBIC-1 and about two minutes (i.e. ~30 km) for CARIBIC-2 and compared to the stations appear to be much more variable. The sequence of sampling is irregular in time, i.e. the same destinations are reached through different flight routes (Fig. 2b), and take place during different times of the year. Thus 365 the following statistics are not comparable to the station observations. Between 2000 and 2006, all CARIBIC observations average at 1,786 nmol/mol. Corrected with respect to the aposteriori emission data based on the station analysis, the simulation average comes as close as 1,788 nmol/mol. The whole period is fairly well reproduced within an RMS deviation of 1.01 % and a coefficient of determination R 2 = 0.65 (Table 3, rows C1-4). The scattered sampling positions cannot be accurately reproduced by the grid model EMAC, 370 because of its limited resolution. The observed CH 4 variability features short-duration events like the interception of methane plumes or alternatively relatively clean air episodes and especially stratospheric air, however, the patterns are rather well reproduced (Fig. 7). The model appears to capture the variations well, even those which are subject to intercepting upper tropospheric and lowermost stratosphere at mid and higher latitudes.
The amplitudes of the model time series, however, are smaller due to the relatively coarse vertical grid spacing of the 375 model, which represents the UTLS at a vertical resolution of about 500mcompared to ~45m near surface. In contrast to background station measurements, for the CARIBIC time series local maxima and minima are not only related to season but also to vertical gradient effects, especially due to the strong concentration changes across the tropopause.
The scatter plot (Fig. 8, upper left) shows a regression slope of 0.57, i.e. well below 1, which quantifies the evident underestimation of the calculated CH 4 variability in the graphs of Fig. 7, suggesting that the vertical resolution of the 380 model grid is not optimal to resolve the fine structure in the tropopause region. The slope is compensated by a corresponding offset up to 766 nmol/mol, explaining the good congruence between simulations and observations in Fig.   7.
For further analysis, according to the definition in Sect. 3.2 (Fig. 2b), we grouped the data records in Fig. S7  best agreement between model and observations in terms of RMS is achieved over low-latitude regions such as IND with 0.80 % and SAN/SAS ≤ 0.75. Here the effect of stratospheric air is least. At the same time, observations over continental areas in the mid latitude NH still could be simulated within a RMS range of 1.23 % (EUR) and 1.24 % (FAE). It appears that the variance of the CARIBIC measurements with R 2 > 0.60 is fairly well reproduced everywhere and most accurately over EUR with R 2 = 0.82 (Fig. 8). AFR is not discussed here because of the sparse number of 390 samples of 4.7 % of all. The statistics are summarized in (Table 2, rows C1-5).

Simulating the recent methane trend
The measured methane increase, depicted by the blue lines in Fig. 9a for the NOAA background station data SPO (90°S) and in Fig. 9b for the CARIBIC flight records, cannot be reproduced by the model (red lines) based on interannually constant emissions. Between 2007 and 2013 the slope appears nearly linear (Fig. 1) Enhanced precipitation in the boreal summer season (Nisbet et al., 2016;Bergamaschi et al., 2013) is considered as a possible cause of growing tropical wetland emissions. To create a "fracking" map we relied on the publicly available database maintained by the national hydraulic fracturing chemical registry (FracFocus, 2016). ANI and RIC source regions are assumed to be the same as for the pre-2007 years. Fig. S2 depicts the geographical distribution of the global 410 CH 4 mixing ratios near the surface, logarithmically scaled for better visibility, marking the respective hypothetical sources. At the same intensity SHA and RIC emissions are more spatially concentrated compared to TRO and ANI.
Large areas of ANI cover the same region over India as RIC which may be an uncertainty factor in the source attribution analysis. The stronger vertical transport intensity of TRO compared to SHA, leading to reduced altitude gradients (Figs. S3), is related to the proximity to the ITCZ. 415 We used the same upper limit emission of 28 Tg/CH 4 /y to be added in order to fit the upward trend between 2007 and 2013. Separate tagged simulations of TRO, ANI, RIC, and SHA were performed with these sources starting in Jan.
2007. Applying the Solver, the specific annual emission amounts were optimized with respect to RMS deviation from the observations. Except for ANI the coefficient of determination R 2 varies consistently, in a sense that lower RMS deviation is associated with higher R 2 . The relatively reduced R 2 of ANI may be due to the neglect of a seasonal 420 distribution.
Consistent with recent δ 13 C-CH 4 studies (Schaefer at al., 2016, Schwietzke et al., 2016 biogenic emissions and especially those from rice cultivation (RMS = 0.44 %) best explain the trend observed at the sixteen NOAA stations considered here. Any attempt to find an optimal combination of fractional amounts would be strongly dependent on empirical constraints to be imposed on the individual source strengths and would be rather theoretical. Applying the 425 Solver with "open" limits (1 ≥ e x ≤ 0) imposed on the emission sources e x where x = ANI, TRO, SHA, RIC, preventing tagged source amounts from becoming larger than the total increment or becoming negative, results in a pure biogenic, 98 % RIC and 2 % TRO composition. In the following three sensitivity studies are presented: In order to consider the suggestion by Turner et al. (2016) with respect to enhanced U.S. methane emissionssee above -we applied a conservative lower limit of 9.0 Tg/y (30 %) to SHA in our statistical evaluation. This is at the expense of 430 RIC (-14.8 Tg/y) and favors TRO (+ 5.9 Tg/y). The RMS (-1.4 %) as well as R 2 (+0.5 %) deteriorate.
The longitudinal dependency of northern hemispheric anthropogenic fossil CH 4 emissions was investigated based on two options: one with the North American source redistributed to East Asia (FAE: 25° N -50° N, 100° E -150° E) and another to Europe (EUR : 45°N -60°N, 0° -26°E). While no significant trend impact could be assigned to EUR, statistically a hypothetical FAE contribution cannot be excluded. No evidence in favor of SHA or FAE can be detected 435 at one of the stations in the northern hemisphere mid-latitudes, presumably related to the effect of synoptic scale disturbances, the relatively intense latitudinal mixing and the >8 year lifetime of CH 4 . Furthermore, when the assumed agricultural emissions include a larger ruminant contribution of 10 Tg/y (same as RIC), the RMS deteriorates by -1.9 % and R 2 by +0.3 %.
Note that in this work we focus on the source strengths and neglect inter-annual changes in global OH, which are 440 assumed to be small (Nisbet et al., 2016). Changes in the removal rate of methane by the OH radical have not been seen in other tracers of atmospheric chemistry, e.g. methyl chloroform (CH 3 CCl 3 ) (Montzka et al., 2011;Lelieveld et al. 2016) and do not appear to explain short-term variations in methane. Based on numerical analyses Turner et al. (2017) found that a combination of decreasing methane emissions overlaid by a simultaneous reduction in OH concentration (the primary sink) could have caused the renewed growth in atmospheric methane. However, they could not exclude 445 rising methane emissions under time invariant OH concentrations as a consistent solution to fit the (rising) observations.
Changes of the order of 3-5% per year over an 8 year period appear very unlikely.
In the next sections, more detailed analyses are presented to evaluate the emission scenarios.

NOAA and AGAGE stations
The methane emissions scenarios defined above affect Northern-as well as Southern Hemispheric observations. Under 450 the influence of deep convection in the tropics and subsequent global transport, the characteristic seasonality of tropical emissions could significantly influence the CH 4 time series worldwide. Shale gas associated emissions (SHA) from the Northern Hemisphere, however, need a relatively longer time period to influence CH 4 at southern hemispheric stations like South Pole (SPO, 90° S). The agricultural emissions from ruminants (ANI) cover parts of both hemispheres, and the North American SHA emissions are assumed to be seasonally independent. We use the model results together with 455 the measurement data to estimate to which extend possible increases in these tropical and extratropical CH 4 sources can provide a plausible explanation for the observed recent trend.
After introducing the additional a priori emissions of 28 Tg-CH 4 /y from 2007 on, the CH 4 increments are calculated at all ground stations for the scenarios TRO, ANI, RIC, and SHA). An obvious overall offset suggests a gross overestimation together with a mismatch in ΔNH/SH, depending on latitudinal source distributions. The latter, 460 compared to the observed 133.84 nmol/mol, varies a priori between 143 (SHA) and 128 (TRO). A suitably downgraded best fit, in the same way as for the no-trend period, can be found by applying the Solver to combinations of the four scenarios. The Solver-optimization procedure suitably reduces the emission amounts for all scenarios to 20.47 Tg CH 4 /y on average, in agreement with Kirschke et al. (2013) who suggested 17-22 Tg/y. Small differences between -0.17 and +0.11 are due to varying exposure to OH oxidation. The all-station percentage RMS deviation with 0.44 % indicates a 465 best fit for the RIC scenario, followed by ANI (0.46 %), TRO (0.47 %) and SHA (0.48 %). With ΔNH/SH = 133.76 nmol/mol, RIC optimally fits the interhemispheric difference, whereas TRO with low 128.56 corroborates Schaefer et al. (2016), stating that CH 4 increased mainly in the northern tropics and subtropics. According to Houweling et al. (2014) the TRO input is larger in the southern hemisphere. The match of the observed variability expressed by R 2 , with 0.870 is also best for RIC, followed by TRO (0.865), ANI (0.862), and SHA (0.859). All indicators all are 470 comparatively close to each other, however, indications about the role of fossil vs. agricultural emissions, and the latter vs. tropical wetlands, agree with those in the literature based on independent considerations such as δ 13 C-CH 4 studies (Schaefer at al., 2016). See Table 3 for a summary of all statistical measures.
The optimal combination, with 98 % RIC and 2 % TRO emissions, performs 0.004 % RMS better than RIC alone. together with the respective no-trend simulations (black crosses) and the Solver-optimized (RIC + TRO) increment (red dots). The respective scatter plots at selected NOAA stations (Fig. 11) indicate good correlation between the observed and calculated station monthly means. NOAA stations records are displayed in Fig. 12, continuing the 1997 through 2006 course (Fig. 5) with optimized (RIC + TRO) increment.

CARIBIC flights 480
Under the assumptions adopted to explain the station trend, the post-2006 CARIBIC-2 methane measurements appear to be realistically simulated by the EMAC model as well. In Fig. 13 Fig. 17a (red dashed thick vs red dashed thin) is obvious, but with 1.0 % on average still relatively small in 2008. The source segregated rice paddy-methane (green, left ordinate) dominates the pattern of the total CH 4 and the R 2 = 0.65 implies that 0.65 % of the observed CH 4 variability along this special flight track can be explained by rice paddy emissions. Largest mixing ratios in excess of 1,850 nmol/mol were recorded in the upper troposphere between 50° and 75° E. Trajectory calculations as well as methane 510 isotope and other chemical tracer analyses Baker et al., 2012) corroborate that these air masses carry emissions from South and Southeast Asia and can be explained by the trapping of air masses (Rauthe-Schöch et al., 2016) from South Asia in the Upper Troposphere Anticyclone (UTAC), a persistent phenomenon during the monsoon and centered over Pakistan and northern India (Garny and Randel, 2013). This is also qualitatively illustrated in Fig. S9a dominates the pattern but is not correctly in phase with CARIBIC in terms of an R 2 = 0.38. Rice fields east of 136°E contribute relatively strongly.
A more systematic study of the source segregated composition of all 327 CARIBIC flights over the years 1997 through 2014 with special emphasis on the developing trend beyond will be subject of continued investigation. 530

Conclusion and Outlook
We analyzed the atmospheric methane budget by means of EMAC model simulations and comparing the results with data from NOAA and AGAGE surface stations and CARIBIC aircraft data. Source tagging is used to analyze the emission distribution and to optimize the respective amounts in relation to the observations. We found that, compared to 535 our a priory assumptions, a larger natural, biogenic methane source with a concomitant reduction in NH fossil emissions is required to explain the measurements and especially the observed interhemispheric gradient.
Additional methane emission categories such as agriculture, notably rice cultivation (RIC) and ruminant animals (ANI), We realize that there is no unique solution for the sourcereceptor relationship. We optimized the size of emissions, the most uncertain aspect of the methane budget, while thecomparably less critical -geographical distribution offers good criteria for optimization, e.g. the interhemispheric difference and the variability. 545 Therefore, the emissions applied in this work should rather be considered as representative of latitudinal sources than from specific locations. Nevertheless, the degree of freedom in the choice of sources is limited and our scenario realistically represents the north-south gradient of CH 4 , being a critical constraint.
In view of the additional global CH 4 source since 2007, a sourcesink equilibrium has not yet been established after the 8 years of emissions considered. A 2 nd order polynomial exactly fits the course from 2007 through 2013 and the 550 extrapolation predicts steady state after 13 years, assuming that the emissions remain unchanged, which, however, does not seem realistic in view of the observed development after 2013/14 (Fig. 1) and further investigation is needed.
NOAA/AGAGE station data of methane are updated annually so further observational data can be expected. CARIBIC flight measurements have been resumed (after a one-year break). We plan to continue the study of these data, supported with EMAC model simulations, also taking advantage of the most recent and future CARIBIC flights. A larger 555 coverage of Southern Hemispheric sampling routes would be desirable to extend the database and help explain the ongoing, and possibly accelerating upward methane trend.
2) merged in one category "oil related" by 1) 3) all EDGAR emission classes related to the use of fossil fuels such as residential heating, onshore traffic, 800 industry, 4) GFEDv4s statistics (Randerson et al., 2018) 5) EDGAR2.0 database (Olivier, 2001  1) Difference between most northern and southern stations Table 3: Statistical evaluation of rising-methane scenariosbest match underlined.  Table 1 for names and coordinates).