Mapping pan-Arctic methane emissions at high spatial resolution using an adjoint atmospheric transport and inversion method and process-based wetland and lake biogeochemical models

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Introduction
Methane (CH 4 ) is an important long-lived atmospheric trace gas.It is the second most powerful carbon-based greenhouse gas in the atmosphere behind carbon dioxide (CO 2 ) and also plays a significant role in the cycles of ozone (O 3 ), hydroxyl radicals (OH) and stratospheric water vapor (H 2 O) (Myhre et al., 2013;Shindell et al., 2009) The atmospheric burden of CH 4 is now more than factor of 2.5 greater than the preindustrial value of about 700 ppb (Etheridge et al., 1998), mainly due to anthropogenic emissions.Major sources and sinks of CH 4 have been identified (Denman et al., 2007); however their individual strengths and the causes of the observed concentration trends and inter-annual fluctuations are not well known.For instance, scientists have not yet agreed on what caused the leveling off of atmospheric CH 4 since the 1980s (Dlugokencky et al., 2003;Bousquet et al., 2006;Aydin et al., 2011;Kai et al., 2011;Levin et al., 2012;Simpson et al., 2012;Kirschke et al., 2013) and the recent rebounding of its growth since 2007 (Rigby et al., 2008;Dlugokencky et al., 2009;Nisbet et al., 2014).
Given the uncertainty regarding drivers of trends in CH 4 concentrations, much effort has focused on refining estimates of CH 4 sources using one of two types of general approaches for estimating the contribution of individual CH 4 sources or sinks to the overall CH 4 budget: "bottom-up" and "top-down" methods.Bottom-up estimates are scaled up from small scale studies of emissions factors (e.g., CH 4 flux) and activity data (e.g., global area that applies to the particular wetland studied) or from biogeochemical models (e.g.wetlands) with environmental conditions (Fung et al., 1991;Zhuang et al., 2004;Walter et al., 2006;Tan and Zhuang, 2015a, b).In contrast, top-down estimates use in situ and satellite observations of CH 4 that are representative of large spatial scales with a chemical transport model (CTM) to infer strengths of CH 4 sources and sinks (e.g., Enting, 2002;Bergamaschi et al., 2009).In Bayesian theory, a top-down estimate can reduce uncertainty in bottom-up inventories through the use of model and ambient observations.This method, called Bayesian inference, has been successfully employed in numerous studies for estimating the global CH 4 budget at coarse spatial resolutions (over 300 km) (Bergamaschi et al., 2007(Bergamaschi et al., , 2009(Bergamaschi et al., , 2013;;Meirink et al., 2008;Cressot et al., 2014;Houweling et al., 2014;Alexe et al., 2015).Many of these studies have assimilated space-borne observations of atmospheric CH 4 concentrations to constrain CH 4 emissions because they deliver dense and continuous coverage unachievable by surface networks or aircraft campaigns (Bergamaschi et al., 2007).
There are two types of nadir satellite CH 4 retrievals: one from solar backscatter in the Figures
Estimating CH 4 emissions from the Arctic is important for understanding the global carbon cycle because the fast warming of Arctic permafrost, one of the largest organic carbon reservoirs (Tarnocai et al., 2009), could lead to a rapid rise of CH 4 emissions (Zhuang et al., 2006;Walter et al., 2007;Koven et al., 2011).Natural sources dominate the Arctic CH 4 inventory (Fisher et al., 2011), e.g.wetlands (McGuire et al., 2012), lakes (Walter et al., 2006;Bastviken et al., 2011), sea shelves (Shakhova et al., 2013) and oceans (Kort et al., 2012).As the factors governing natural CH 4 production (methanogenesis) and oxidation (methanotrophy) are notoriously heterogeneous, estimates of Arctic CH 4 emissions are still poorly constrained, even with decades of site-level and modeling studies (Zhuang et al., 2004;Bastviken et al., 2011;Schuur et al., 2015;Tan and Zhuang, 2015a, b).And previous CH 4 inversions over the Arctic only assimilated surface measurements that were too sparse to provide constraints for fine-scale CH 4 fluxes.Further, an important consideration is specification of realistic prior fluxes, given the ill-posed nature of trace-gas inversions (Kaminski and Heimann, 2001).While CH 4 emissions from lakes could be of comparable magnitude to CH 4 emissions from wetlands in the Arctic (Walter et al., 2006(Walter et al., , 2007;;Bastviken et al., 2011;Tan and Zhuang, Figures Back Close Full 2015a), this source has not been included in past global or regional inverse modeling studies.
To address these issues, this study uses the adjoint of a 3-D chemical transport model at high spatial resolution (less than 60 km) with the integration of both processbased wetland and lake biogeochemical models and atmospheric CH 4 mixing fractions to improve the quantification of Arctic CH 4 emissions for July 2004-June 2005.For the first time, we include CH 4 emissions from lakes in a high-resolution Bayesian inversion of CH 4 fluxes in the Arctic.As wetland emissions are likely the largest Arctic CH 4 source, this study also considers the sensitivity of our inversion to prior wetland fluxes.Section 2 describes the satellite retrievals and surface CH 4 observations that are used to infer CH 4 fluxes and evaluate posterior estimates.Section 3 describes the details of the biogeochemical models for wetland and lake emissions (Sect.3.1), the Arctic nested-grid chemical transport model and the prior budgets of other CH 4 sources and sinks (Sect.3.2) and the adjoint-based inversion method (Sect.3.3).Section 4 presents the posterior CH 4 emissions and their evaluation.

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Full proxy CH 4 retrievals from Frankenberg et al. (2011) that provide a weighted column average dry-mole fraction of CH 4 with 10-layer averaging kernels and prior CH 4 profiles.The averaging kernels show near-uniform vertical sensitivity in the troposphere and declining sensitivity above the tropopause (Butz et al., 2010).Some auxiliary data, e.g. the air mass factor A F (A F = 1/ cos θ + 1 cos ξ, where θ is the solar zenith angle and ξ is the viewing angle of the satellite), water column density and dry air column density, are also published with the IMAP-DOAS v6.0 XCH 4 product.The estimated single-retrieval precision is scene-dependent and averages roughly 1.5 % or 25 ppb (Frankenberg et al., 2011).With this order of instrument precision, SCIAMACHY cannot resolve day-to-day variability of emissions but can strongly constrain a multi-year average (Turner et al., 2015).The retrieving algorithm firstly calculates CH 4 total column density Ω CH 4 (molecules cm −2 ): where ω is the true 10-layer sub-column densities of CH 4 (molecules cm −2 ), ω A is the 10-layer prior CH 4 sub-column density (molecules cm −2 ), Ω A is the corresponding a priori CH 4 total column density, and a is an averaging kernel vector that defines the sensitivity of the retrieved total column to each sub-column in ω.To account for the impact of aerosol scattering and instrument effects on the observed light path, Frankenberg et al. (2006) used the CO 2 column density Ω CO 2 as a proxy to normalize and convert Ω CH 4 to a column mixing ratio XCH 4 (ppb): where XCO 2 is the column-weighted mixing ratio of CO 2 .CO 2 is used as a proxy because it is retrieved in a spectrally neighboring fitting window and, relative to CH 4 , its mixing ratio is known with much higher precision.
As general retrieval quality deteriorates after November 2005 due to the dysfunction of two important detector pixels (Frankenberg et al., 2011), only observations  (Bergamaschi et al., 2009;Alexe et al., 2015).This filtering process ensures that the atmospheric columns seen by SCIAMACHY are well represented by the model columns.To avoid spurious outliers that may have a large impact on the inversion, XCH 4 retrievals of less than 1500 ppb or larger than 2500 ppb are discarded (Alexe et al., 2015).Figure S1 in the Supplement shows the SCIAMACHY retrievals (n = 37 989) of the weighted column-average CH 4 dry mixing ratio for July 2004-September 2004 in the pan-Arctic that have passed all quality control tests.

Surface Observations
The NOAA/ESRL Carbon Cycle Cooperative Global Air Sampling Network provides high-precision measurements of surface atmospheric CH 4 dry-air mole fraction (Dlugokencky et al., 2014).CH 4 measurements were calibrated against the WMO X2004 CH 4 standard scale maintained at NOAA (Dlugokencky et al., 2005).Due to the coarse resolution of the GEOS-Chem model, we include only marine and continental background sites and exclude sites that are strongly influenced by sub-grid local sources, as listed in Table S1 in the Supplement.The flask-air samples in the NOAA/ESRL network that were taken from regular ship cruises in Pacific Ocean serve to evaluate simulated surface mixing ratios of global inversions over the remote ocean and downwind the continental sources (Alexe et al., 2015).One Arctic site (Pallas-Sammaltunturi, Finland (PAL)) that was excluded from the assimilation is used to evaluate the nested-grid inversions.

Modeling
Here we describe the prior emissions, forward model, and inversion method used to optimize CH 4 emissions in the pan-Arctic on the basis of SCIAMACHY and NOAA/ESRL observations.

Wetland and lake CH 4 emissions
CH 4 emissions estimated by the inverse modeling method can be sensitive to the choice of prior wetland CH 4 fluxes (Bergamaschi, 2007).To assess this sensitivity, east Asia and Tropical Africa) where extensive floodplains and warm environment coexist.In the Arctic, the modeled annual wetland CH 4 emissions during 2004-2005 were in the range of 11.4-25.6Tg yr −1 (Fig. 3 and Table 3), and their spatial distribution was mainly controlled by the modeled or mapped wetland coverage (Melton et al., 2013).
As shown in Fig. 3 The biogeochemical models involved in the WETCHIMP project have not included CH 4 emissions from lakes.As CH 4 emissions from pan-Arctic lakes could be significant (Walter et al., 2006;Tan and Zhuang, 2015a) and have different drivers relative to wetland emissions, e.g. the supply of labile yedoma permafrost carbon (Walter et al., 2006) and water deep mixing (Schubert et al., 2012), it is necessary to include this source into the Arctic CH 4 inventory.Prior CH 4 emissions from pan-Arctic lakes are simulated with a one-dimension process-based lake biogeochemical model (Tan et al., 2015;Tan and Zhuang, 2015a).The bLake4Me model explicitly parameterizes the control of temperature and carbon substrate availability on methanogenesis, the control of temperature and oxygen level on methanotrophy and the transport of gaseous CH 4 by diffusion and ebullition.The model also includes two thermal modules, governing the heat transport and water phase change in both water and sediments column of lakes.A detailed model description and evaluation is given in Tan et al. (2015).Model estimates of CH 4 emissions from all lakes north of 60

GEOS-Chem model
Atmospheric CH 4 mole fractions are simulated by GEOS-Chem v9-01-03 (http://acmg.seas.harvard.edu/geos/index.html),a global 3-D CTM model (Bey et al., 2001).GEOS-Chem could be driven by either GEOS-4 or GEOS-5 meteorological (met) data from NASA's Global Modeling Assimilation Office (GMAO).As GEOS-5 is available only from December 2003, in this study we use GEOS-4 met data from 1993 to 2005 for inverse simulations when only surface measurements are assimilated and GEOS-5 met data from 2004 to 2005 for inverse simulations when both satellite retrievals and surface measurements are assimilated.Both the GEOS-4 and GEOS-5 met data have horizontal resolution of 1/2 • latitude × 2/3 • longitude and 6 h temporal resolution.There are 55 and 72 hybrid sigma-pressure levels extending from Earth's surface to 0.01 hPa for GEOS-4 and GEOS-5 met data respectively.In contrast to the global GEOS-Chem model, the nested-grid version does not contain algorithms for handling advection near North and South Poles (Lin and Rood, 1996).To avoid polar grid boxes, we crop the native 1/2 • ×2/3 • resolution GEOS-5 met data to a window region (180 Atmospheric CH 4 is mainly removed by tropospheric oxidation initiated by reaction with tropospheric OH, which was computed using a 3-D OH climatology of monthly average concentrations from a previous simulation of tropospheric chemistry (Park et al., 2004).The global mean pressure-weighted tropospheric OH concentration is 10.8 × 10 5 molecules cm −3 .For minor sinks, CH 4 uptake by upland soils is derived from Fung et al. (1991) and CH 4 oxidation in the stratosphere is calculated from the archived CH 4 loss frequency described by Murray et al. (2012).The resulting atmospheric lifetime of CH 4 is about 8.9 years, consistent with the observational constraint of 9.1 ± 0.9 years (Prather et al., 2012).We regrid and crop the anthropogenic and natural CH 4 emissions in EDGAR4.2,GFED3 and Fung et al. (1991) for the nested Arctic domain using the Harvard-NASA Emissions Component (HEMCO) software (Keller et al., 2014), marked as "other" in Fig. 3. Compared to CH 4 emissions from Arctic wetlands and lakes, these sources are relatively small (∼ 3.2 Tg yr −1 ).

Inversion method
Atmospheric inversion is a procedure for using observations of atmospheric gases as constraints to estimate surface gas fluxes.The inverse problem can be characterized by solution of By applying Bayesian theorem and assuming Gaussian errors, the inverse problem can be solved by minimizing the cost function, J (y), that measures the model deviations from both prior assumptions and observations: where y is a vector of observations from SCIAMACHY and NOAA/ESRL, F is a model operator that maps emissions to observations, y represents CH 4 emissions to be constrained, y 0 is the a priori estimate of y, C d is the observational error covariance matrix Figures

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Full that includes contributions from model error, representation error (sampling mismatch between observations and the model) and measurement error, and C x 0 is the parameter error covariance matrix (containing the uncertainties of the parameters and their correlations).The regularization parameter γ controls the relative constraints applied by the observational and a priori parts of J (y) (Kopacz et al., 2009).In the adjoint method, γ is not fixed at unity but determined by analyzing its influence on the minimum of J (y) (Henze et al., 2007;Kopacz et al., 2009).Minimization of J (y) yields the following expression for the maximum a posteriori solution for the state vector ( x) and its associated error covariance ( Ĉx ) (Rodgers, 2000): where ∇ x F is the Jacobian matrix of the forward model.J (y) is minimized iteratively through successive forward and backward simulations with the GEOS-Chem model and its adjoint, developed by Henze et al. (2007) and previously applied to CO, CO 2 and CH 4 source inversions (Jiang et al., 2011;Deng et al., 2014;Wecht et al., 2014).
The GEOS-Chem adjoint model is a 4DVAR inverse modeling system that allows optimization of a very large number of parameters using at the same time very large sets of observational data, such as satellite data.Rather than optimizing CH 4 emissions, it optimizes an exponential scale factor e x (e x = ln(x/x 0 )) at each grid cell to avoid negative emissions.For prior emissions, the uncertainties are set as 100 % in each grid box and the spatial correlation is set as an e-folding function with spatial correlation lengths of 500 km at the global coarse resolution ( 4• × 5 • ) and of 300 km at the nested grid resolution (1/2 • ×2/3 • ) (Bergamaschi et al., 2009).Optimization is performed in three steps.First, a global coarse-resolution inversion using the LPJ-WSL wetland scenario is run from 1993 to 2005 using surface measurements only.and the real analysis time is from 1 July to 1 October 2004.As in Wecht et al. (2014), observations in the first week are not assimilated.This time period is selected based on two factors.First, due to snow cover and large solar zenith angle, the quality of SCIAMACHY retrievals in winter is usually low.Second, CH 4 fluxes from pan-Arctic wetlands and lakes are the most pronounced in summer.In all steps, optimization is run iteratively at least 40 times until the reduction of the cost function becomes less than 0.5 % with each successive iteration (Wecht et al., 2014).

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Full chosen because of the co-variation of spectroscopic errors with the sampled air mass and residual aerosol errors (Cressot et al., 2014;Houweling et al., 2014) and specific humidity was chosen because water vapor is the main cause of SCIAMACHY seasonal bias that lags the variations of solar zenith angle (Houweling et al., 2014).Many studies used seasonal and latitudinally varying functions for bias correction because they can represent the changes in both solar zenith angle and climate variables (Bergamaschi et al., 2007(Bergamaschi et al., , 2009(Bergamaschi et al., , 2013)).It is likely that retrieval bias can be better represented if the effects of air mass change and climate system change can be accounted for together.
To test this hypothesis, we compare the performances of three traditional one-proxy methods (latitude ϕ, air mass factor A F , specific humidity H S ) and two new twoproxy methods (latitude + humidity, air mass factor + humidity), listed in Table 1.After constraining the GEOS-Chem model with surface measurements, the bias correction method that gives the smallest difference between the measured and modeled CH 4 column mixing ratios and the lowest Bayesian Information Criterion (BIC) score will be used.Specific humidity is taken from the European Centre for Medium-Range Weather Forecasts (ECMWF)'s ERA-20C reanalysis product (http://apps.ecmwf.int/datasets/data/era20c-daily), averaged by the column between the surface and 3 km altitude (Houweling et al., 2014).The air mass factor and central latitude of CH 4 retrievals are directly available in the SCIAMACHY IMAP v6.0.For bias correction, we first optimize the GEOS-Chem 4-D CH 4 mixing ratios by an inversion using surface measurements and then sample the modeled XCH 4 at the coordinates and time of SCIAMACHY retrievals and with local averaging kernels applied.The difference between SIAMACHY and GEOS-Chem values (Fig. 1a) is regressed with proxy factors to obtain the optimal bias correction.As suggested by Turner et al. (2015), it is more likely that grid squares between 50 • S and 50 • N with residual standard deviation (RSD) in excess of 20 ppb are dominated by model bias in prior emissions.Thus, we exclude such grid squares in regressions.Further, satellite retrievals with low precisions (the ratio of retrieval precision error to retrieval is larger than 3 %) are removed from analysis.
In our experiments, all bias correction functions are updated monthly.Unlike Bergam-Introduction

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Full  2009), we do not further optimize bias correction functions in the inversion cycle because such an optimization could make bias correction account for the uncertainties that should not be dealt with by correction, e.g.unaccounted model errors or even the sources and sinks (Houweling et al., 2014).As listed in Table 1, the "latitude only" correction performs the best within three single proxy correction methods and only slightly worse than the best correction method "latitude + humidity" in our test.This implies that the latitude polynomial correction used in most previous CH 4 inversions is appropriate.As the "latitude + humidity" method performs the best, it is applied for satellite bias correction in this study.After bias correction, we estimated the error variances of SCIAMACHY observations (Fig. 1b) using a relative residual error (RRE) method described by Heald et al. (2004).Figure 1d indicates that the correction greatly reduces model-satellite differences in tropical areas of America, Africa and South Asia and also reduces the difference in Australia and some areas of the United States.As shown in Fig. 1c, the agreement between GEOS-Chem and SCIAMACHY XCH 4 is also improved at the global scale.However, because the model-data difference in East Asia has an opposite latitude dependence to that in other areas of the same latitudes (Fig. 1a), the correction deteriorates the model-satellite agreement there (Fig. 1d).
The observational error of the NOAA/ESRL CH 4 mixing ratios is estimated as the sum of measurement error (∼ 0.2 %) and representation error.Similar to satellite retrievals, the representation error of surface measurements is defined as the standard deviation of the difference of CH 4 residuals between NOAA/ESRL measurements and GEOS-Chem.And the CH 4 residuals are calculated by subtracting the simulated or observed CH 4 mixing ratios by a fitted polynomial trend (Masarie and Tans, 1995).Introduction

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Full finding of inter-hemispheric δ 13 CH 4 is questionable (Levin et al., 2012), it is uncertain whether this declined tropical source is in the Northern Hemisphere.
The posterior global CH 4 emissions using both NOAA/ESRL and SCIAMACHY observations and different prior wetland scenarios are shown in Fig. 5 and also listed in Table 2. Since total emissions are constrained by the atmospheric burden of CH 4 and the CH 4 lifetime, while the prior CH 4 fluxes in six scenarios are different in a wide range of estimates (471.5-627.8Tg CH 4 yr −1 ), the posterior global CH 4 emissions converge into a very narrow zone (496.4-511.5 Tg CH 4 yr −1 ).This suggests that the surface observations are of sufficient density to constrain the global emissions.However, there are still not enough high-precision measurements at regional scales, resulting in large differences between the posterior emissions in the TransCom3 land regions (Table 2).
There have been many studies that assimilated surface and/or satellite observations into a CTM inverse model to constrain global CH 4 fluxes, see Kirschke et al. (2013) for review.For instance, using the same observations suite, Bergamaschi et al. (2009)  The renewed growth of atmospheric CH 4 since 2007 has been observed by several studies (Rigby et al., 2008;Dlugokencky et al., 2009;Nisbet et al., 2014).According to Nisbet et al. (2014), the global growth rate was about 6 ppb yr −1 from 2007 to 2012.Assuming 1 ppb equivalent to 2.75 Tg CH 4 in the entire atmosphere (Khalil et al., 2007) and the lifetime of atmospheric CH 4 constant, the estimated global CH 4 emissions during 2010-2011 should be at most 49.5 Tg larger than the estimated during 2004-2005.The higher CH 4 emissions after 2007 were also demonstrated by other top-down studies: 539 Tg CH 4 yr −1 during 2009-2011 (Turner et al., 2015) and 538 ± 15 Tg CH 4 yr −1 during August 2009-July 2010 (Cressot et al., 2014).When comparing the estimate of Alexe et al. (2015) for 2010-2011 with our estimates (Table 2), the difference is in the range of 29-44.1 Tg CH 4 (Table 2), consistent with these independent studies.Our estimates also agree well with the inference of Houweling et al. (2014) 2).They probably underestimated the emissions during this period because the calculated increase from 2004 to 2009 is too low (∼ 10 Tg CH 4 yr −1 ).
As shown in Fig. 5a, the highest CH 4 fluxes are located in the Amazon, China, Southeast Asia, North America and Europe where extensive wetlands or large population exist.Our inversions indicate that the Eurasian temperate regions, including China, North America and Europe, emitted much more CH 4 than other regions (Table 2) the dominance of anthropogenic sources in the global CH 4 inventory.As presented in Fig. 5c, our inverse model reduces the CH 4 emissions from China, the Amazon basin and Eurasian boreal region (scale factor < 1) but enhances the emissions in Europe and Southeast Asia (scale factor > 1) relative to the prior.This adjustment could be primarily driven by the constraints of the surface measurements and satellite retrievals and secondarily by the satellite bias correction.

Optimized Arctic CH 4 emissions
In contrast to the global CH 4 inversions, total posterior CH 4 emissions from the Arctic nested-grid inversions span a wide range: 14.6-30.4Tg CH 4 yr −1 (Table 3).It reflects a strong influence from both the priors (Fig. 3) and the nested-grid boundaries (Berchet et al., 2015) on the posteriors (Fig. 6).Across six Arctic inversions, the range of the posterior is not smaller than the range of the prior (25.7-39.9Tg CH 4 yr −1 ) and the mean departure of the posterior from the prior is 10.1 Tg CH 4 yr −1 .This divergence implies that due to uncertain boundary conditions (Berchet et al., 2015), the surface and satellite observations in the Arctic cannot provide sufficient constrains to reduce the estimate uncertainty.Further, as presented in Table 3 and Fig gions, e.g.Northeastern Europe and Central Siberia, and ( 2) we only use one lake prior scenario in the inversions.The exception of the ORCHIDEE inversion could be explained by that the ORCHIDEE model simulates very high wetland CH 4 fluxes in Canadian Shield, West Siberia Lowlands and East Siberia Coastal Lowlands where high CH 4 fluxes from lakes are also possible (Fig. 3).For CH 4 emissions from Arctic lakes, our estimates, 5.4-7.9Tg CH 4 yr −1 , are close to the lower bound of the estimate (7.1-17.3Tg CH 4 yr −1 ) in Bastviken et al. (2011) with upscaling site-level observations.
Even if the lake source is reduced, on average, by 40 % by the inversions, the remaining amounts are still much higher than the previous estimate of ∼ 4 Tg CH 4 yr −1 in Gao et al. (2013).This emphasizes the importance of including pan-Arctic lakes in the carbon cycle.When the ORCHIDEE scenario is excluded, annual CH 4 emissions from lakes in Alaska, northern Canada, northern Europe and northern Siberia are, on average, 1.0, 3.1, 0.6 and 2.8 Tg CH 4 yr −1 , respectively.These estimates correspond to 1.2, 5.0, 0.  (Bastviken et al., 2011), our estimate of 3.1 Tg CH 4 yr −1 from Canadian lakes should not be considered a large overestimate, as indicated in Tan and Zhuang (2015b).
In contrast to Arctic wetlands, scientists have not reached a consensus on the importance of Arctic lakes to the global CH 4 cycle because only a limited number of Arctic lakes have been observed and their characteristics (e.g., morphology, eutrophication and carbon input) are more heterogeneous.In this study, as the constraints of observations are limited, we only optimize total CH 4 emission in each grid cell and fix the weight of each source during our inversions.Since wetlands and lakes are usually spatially neighbored, this operation could attribute a fraction of lake emissions incorrectly to wetlands or vice versa.To verify the possibility of large CH 4 emissions from pan-Arctic lakes, we conducted a nested-grid inversion in the Arctic based on the DLEM scenario that did not include CH 4 emissions from lakes as a comparison.The DLEM scenario was chosen because as presented in Fig. 3 its simulated wetland emissions are less spatially overlapped with the simulated lake emissions.This no-lake inversion shows that there are low CH 4 fluxes in the East Siberia Coastal Lowlands, a region with extensive high-flux yedoma lakes (Walter et al., 2006).In comparison with the original test, this no-lake inversion produces a larger mean difference between the observed and simulated posterior SCIAMACHY XCH 4 , 27.4 ppb vs. 26.5 ppb.The 0.9 ppb difference is impressive considering the influence of nested-grid model boundaries.For instance, Berchet et al. (2015), even using high-precision surface measurements collected from eight West Siberian Plain sites, only reduced the difference of the observed and simulated posterior GOSAT XCH 4 by 1.5 ppb in a Eurasian-scale inversion.Another sign that SCIAMACHY XCH 4 can be much better represented by including lake emissions is that the no-lake inversion only reduces the simulated prior SCIAMACHY XCH 4 deviation by 0.1 ppb.Thus, the no-lake scenario probably misses some significant CH 4 emissions in the coastal lowlands.Because 56 % of the water-inundated landscapes (i.e., lakes, wetlands and rivers) in this region are lakes (Lehner and Döll, 2004), lakes, especially yedoma lakes, could have contributed a large fraction of the missed CH 4 emissions.Introduction

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Method evaluation
Figure 8 shows the difference between the modeled and observed CH 4 mixing ratios at NOAA ship board sampling stations and aircraft vertical profile sites under different wetland scenarios before and after the global scale inversions.For most scenarios, inversion improves the representation of CH 4 mixing ratios in GEOS-Chem at both marine and inland boundary layers and free troposphere.Specifically, the CLM4Me scenario performs best in the evaluation by reducing the difference by more than 10 ppb.Because this scenario also produces global and wetland CH 4 fluxes consistent with earlier studies (as described in Sect.4.1), it is likely that the spatial pattern of CH 4 fluxes simulated by the CLM4Me model is more realistic than the other scenarios at the global scale.Figure 9 compares the modeled and observed CH 4 mixing ratios at the PAL surface station, in Finland and the PFA aircraft vertical profile site, in Alaska before and after the nested grid inversions.These two stations are near the main CH 4 sources in northern Europe and Alaska, respectively.For PFA, the nested-grid inversions perform better than the nested-grid forward run but do not have clear advantage over the global inversions.The reason for this could be that CH 4 emissions from Alaska can be well constrained by three NOAA/ESRL surface sites in Alaska (BRW, CBA and SHM) and the CH 4 mixing ratios at PFA are representative of the interior of Alaska as was pointed out in Sweeney et al. (2015).

Further discussion
As described in Sect.4, there are still several issues limiting the accuracy of our estimates.First, although the stronger zonal and weaker vertical transport characteristics of northern high latitudes is thought to help transport flux information to the pan-Arctic sites (e.g., Shemya, Barrow and Cold Bay), CH 4 sources in some regions of the Arctic, lite retrievals, it is possible to refine our estimates by incorporating site measurements near Siberia, such as the Surgut site of National Institute for Environmental Studies (NIES) (Machida et al., 2001).The uncertainty of SCIAMACHY retrievals likely also needs to be revisited.The assumed 1.5 % minimum uncertainty for SCIAMACHY retrievals in this study could be somewhat overestimated (Bergamaschi et al., 2007), which limits their potentials to provide constraints on CH 4 fluxes.The treatment of the SCIAMACHY bias could be an important uncertainty source for our estimates, as suggested by Houweling et al. (2014).Future top-down studies could benefit from a more reasonable bias correction method, even for low bias satellite products, e.g.GOSAT (Alexe et al., 2015).
Second, the attribution of CH 4 fluxes to spatially overlapped sources, e.g.wetlands and lakes, could be a problem for even high-resolution inversions.Carbon isotope measurements (δ 13 CH 4 ) are widely used to separate biogenic and geologic CH 4 sources (Langenfelds et al., 2002) but are not useful for two biogenic sources with similar carbon isotope ratios (Walter et al., 2008;Fisher et al., 2011).One possible solution is to constrain the flux ratio of wetlands to lakes using very fine resolution geographical information.For instance, the flux ratio should be well constrained by the area ratio of these two landscapes.Another possible solution is to jointly constrain CO 2 and CH 4 fluxes in a nested-grid inversion.As known, although both wetlands and lakes are CH 4 sources, wetlands are a CO 2 sink and lakes are a CO 2 source (Zhu et al., 2013;Walter Anthony et al., 2014).This opposite correlations of CH 4 and CO 2 emissions could possibly be used to constrain the optimization of the flux ratio in inverse models.
Our Arctic inversions did not include natural CH 4 sources (e.g., CH 4 emissions from subsea permafrost of East Siberian shelf) other than wetlands and lakes in the Arctic.It could lead to more uncertainties in our estimates.But our study also suggests that it is unlikely that CH 4 emissions from sea shelf are as large as 17 Tg CH 4 yr  Full    Full Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | we use wetland CH 4 emissions simulated by six well-known wetland biogeochemical models (CLM4Me, DLEM, LPJ-Bern, LPJ-WSL, ORCHIDEE and SDGVM) to setup our inverse model.All wetland CH 4 simulations follow the same protocol of WETland and Wetland CH 4 Inter-comparison of Models Project (WETCHIMP) (Melton et al., 2013; Wania et al., 2013).Melton et al. (2013) demonstrated that the difference of these estimates primarily arises from the model distinction in CH 4 biogeochemistry and wetland hydrology.These models estimated that the annual global CH 4 emissions from wetlands during 2004-2005 were in the range of 121.7-278.1 Tg yr −1 (Fig. 2 and Table 2) and wetland CH 4 emissions are the highest in tropical regions (e.g., Amazon, South-Discussion Paper | Discussion Paper | Discussion Paper | • N are described by Tan and Zhuang (2015a, b).On average, the estimated CH 4 emissions from pan-Arctic lakes during the studied period are approximately 11 Tg CH 4 yr −1 , see Fig. 3Discussion Paper | Discussion Paper | Discussion Paper | and 80-56 • N) for the Arctic nested grid.Boundary conditions for nested grid simulations are produced for the same period with GEOS-Chem 4 • × 5 • resolution global scale forward runs at 3 h intervals.The GEOS-Chem CH 4 simulation was originally introduced by Wang et al. (2004) and updated by Pickett-Heaps et al. (2011).As described by Wecht et al. (2014), the prior anthropogenic sources, including oil/gas production, coal mining, livestock, waste treatment, rice paddies, biofuel burning and other processes, are extracted from Emission Database for Global Atmospheric Research v4.2 (EDGAR4.2) with 0.1 • ×0.1 • resolution and no seasonality (European Commission, Joint Research Centre/Netherlands Environmental Assessment Agency, 2009).CH 4 emissions from termites and biomass burning are obtained from the study of Fung et al. (1991) and daily Global Fire Emissions Database Version 3 (GFED3) (van der Werf et al., 2010), respectively.CH 4 emissions from wetlands and lakes are from the model simulations described in Sect.3.1Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | aschi et al. ( As shown in Fig.4, the posterior global and regional CH 4 emissions exhibit a strong seasonal variability during 1993-2005, which is mainly driven by the sensitivity of methanogenesis in natural sources to temperature (e.g., wetlands).During this period, there are prominently positive CH 4 emission anomalies in 1994 (+27.4 Tg CH 4 ) and 1998 (+34.6 Tg CH 4 ), and prominently negative anomalies in 1997 (−18.4Tg CH 4 ), 2001 (−20.5 Tg CH 4 ) and 2005 (−22.3Tg CH 4 ).The 1998 CH 4 emission peak has been documented in many studies (e.g.,Dlugokencky et al., 2001;Rigby et al., 2008).Dlugokencky et al. (2001)  attributed this anomaly to an increase in the imbalance between CH 4 sources and sinks equal to ∼ 24 Tg CH 4 , suggested to be caused by an increase of wetland emissions in both tropical regions (13 Tg CH 4 ) and the Northern Hemisphere (11.6 Tg CH 4 ) and a severe fire year in boreal regions (5.7 Tg CH 4 ).However, according to Fig.4, wetlands only contributed a small amount of emission increase during 1998 (9.1 Tg CH 4 ) and most of the increase was from other sources (e.g., biomass burning) in both tropical and high-latitude regions.Our findings are consistent with the claim ofLangenfelds et al. (2002) that two CH 4 emission pulses in 1994 and 1998 could be linked with large biomass burning events in tropical and boreal regions.During 1993During  - 1996, the , the  annual mean of global CH 4 emissions was 534 Tg CH 4 yr −1 , slightly lower than the estimate (549 ± 7 Tg CH 4 yr −1 ) of Dlugokencky et al. (1998).During 1993-2005, there are no visible trends for wetland emissions in tropical, northern mid-latitude and northern high-latitude regions.Also, the annual mean of global CH 4 emissions did not change between 1993 and 2004, coinciding with the leveling off of CH 4 growth rate since the 1990s (Dlugokencky et al., 1998 & 2003).Kai et al. (2011) claimed that the evolution of CH 4 mixing ratios in the recent decades was a result of long-term reduction in agricultural emissions (i.e.rice paddies) or landfills emissions within the Northern Hemisphere.In Fig. 4b, the long-term decline of CH 4 emissions from tropical non-wetland sources seems to provide some support to this argument.But as the 32485 Discussion Paper | Discussion Paper | Discussion Paper | estimated that in 2004, CH 4 emissions in global, tropical (30 • S-30 • N), northern extratropical (30-90 • N) and southern extratropical (90-30 • S) zonal areas were 506.7, 323.5, 172.8 and 10.4 Tg CH 4 yr −1 , respectively.These large-scale estimates are consistent with our calculations: 284.5-319.6Tg CH 4 yr −1 (tropical), 165.3-206.6Tg CH 4 yr −1 (northern extratropical) and 10.0-13.9Tg CH 4 yr −1 (southern extratropical).This agreement reflects that GEOS-Chem adjoint and TM5-4DVAR are consistent in the atmospheric transport, chemistry and inverse modeling methods.In contrast to Bergamaschi et al. (2009), our inversions tend to allocate more emissions to extratropical regions.As a result, the tropical total (SATr + NAF + SAF + TrA) of the six inversions is in the range of 114.1-169.7 Tg CH 4 yr −1 , which is much lower than their estimate of 203.2 Tg CH 4 yr −1 .The most likely reason for this discrepancy from Bergamaschi et al. (2009) is that we use a much larger correction to the SCIAMACHY data in tropical regions.The posterior CH 4 emissions from wetlands in our four scenarios (Bern, CLM4Me, SDGVM and WSL) are close to the estimate (∼ 161 Tg CH 4 yr −1 ) of Bloom Discussion Paper | Discussion Paper | Discussion Paper | et al. (2010) for 2003-2007 based on CH 4 and gravity spaceborne data to constrain large-scale methanogenesis.Our estimates are also close to the inferred CH 4 emissions (175 ± 33 Tg CH 4 yr −1 ) from natural wetlands by Kirschke et al. (2013).By using artificial neural networks, Zhu et al. (2013) estimated that from 1990 to 2009, annual wetland CH 4 emissions from northern high latitudes (> 45 • N) are in the range of 44.0-53.7 Tg CH 4 yr −1 , agreeing with the estimates of the Bern, CLM4Me and SDGVM scenarios.
that global CH 4 emissions in 2004 were close to 500 Tg CH 4 yr −1 and the emissions rose by 27-35 Tg CH 4 yr −1 after July 2006.In contrast, the ensemble Kalman filter assessment in Fraser et al. (2013) involving GOSAT observations and GEOS-Chem is 510.6 ± 18.4 Tg CH 4 yr −1 for the period June 2009-December 2010 (Table Discussion Paper | Discussion Paper | Discussion Paper | . 6, this lack of constraint from the observations mainly occurs in Siberia and causes large uncertainties in the estimates of Siberian wetland CH 4 emissions (2.0-12.7 Tg CH 4 yr −1 ).In comparison with the inverse modeling ofMonteil et al. (2013), we estimate that the annual total CH 4 emission from the pan-Arctic (> 60• N) is 29.2-60.8% of their estimate (50 Tg CH 4 yr −1 ) for CH 4 emissions in the northern high latitudes (> 50 • N).Because all inversions estimate lower CH 4 emissions than the priors, it is possible that CH 4 emissions from Arctic wetlands, lakes and other sources are overestimated by the biogeochemistry models and EDGAR dataset.In contrast to other sources, the estimated CH 4 emissions from Arctic lakes are less divergent in the nested-grid inversions except for the ORCHIDEE scenario, as presented in Fig. 7 and Table 3.There are two reasons for this convergence: (1) CH 4 fluxes from lakes are low in those poorly constrained re-Discussion Paper | Discussion Paper | Discussion Paper | 6 and 5.0 Tg CH 4 yr −1 in Tan and Zhuang (2015a) without optimization.The posterior CH 4 emissions from lakes in northern Canada are closer to the estimate of 2.6±0.4Tg CH 4 yr −1 in Tan and Zhuang (2015b) because thermokarst lakes in northern Canada can be better identified by a high-resolution landscape evolution model in Tan and Zhuang (2015b) than by coarse-resolution geographic datasets in Tan and Zhuang (2015a).The posterior lake emissions from northern Siberia are much smaller than the modeled (Tan and Zhuang, 2015a, b).There are two possible reasons for the larger estimates of the lake model: (1) the model overestimates thermokarst active zone of yedoma lakes; and (2) four high-flux yedoma lakes that are used for calibration are not good representative of all yedoma lakes.For European lakes, Saarnio et al. (2009) estimated that they are a CH 4 source of 1.48 Tg CH 4 yr −1 .This means that CH 4 emissions from lakes in northern Europe (> 60 • N) could constitute 40 % of CH 4 emissions from all European lakes.By upscaling site observations to northern Canada, Laurion et al. (2010) found that annual diffusive CH 4 emission from Canadian thaw ponds was 1.0 Tg CH 4 .Since ebullition could be much stronger than diffusion in transporting CH 4 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |Arctic tundra is regarded as an important source of CH 4 in northern high latitudes.By using process-based models and atmospheric CH 4 observations,McGuire et al. (2012) estimated that Arctic tundra was a source of 25 Tg CH 4 yr −1 to the atmosphere during 1990-2006.By using the TM5-4DVAR inverse model with SCIA-MACHY and NOAA/ESRL observations,Alexe et al. (2015) estimated that CH 4 emissions from Arctic wetlands were 18.2 Tg CH 4 yr −1 for 2010-2011.A similar estimate of 16 ± 5 Tg CH 4 yr −1 was also made by Bruhwiler et al. (2014) with using the CarbonTracker-CH 4 assimilation system.Our estimates of 8.8-20.4Tg CH 4 yr −1 encompass the estimates of Alexe et al. (2015) and Bruhwiler et al. (2014) but are lower than that of McGuire et al. (2012).As discussed, the uncertainty mainly arises from CH 4 emissions from Siberian wetlands.Regionally, when the ORCHIDEE scenario is excluded, annual CH 4 emissions from wetlands in Alaska, northern Canada, northern Europe and northern Siberia are, on average, 1.0, 3.3, 4.2 and 5.8 Tg CH 4 yr −1 , respectively.The estimated total CH 4 emission from Alaskan wetlands is much lower than the inferred value of 4.1 Tg CH 4 yr −1 for the Alaskan Yukon River basin during 1986-2005 using the modeling of process-based CH 4 biogeochemistry and largescale hydrology(Lu and Zhuang, 2012) and also much lower than the inferred value of 3 Tg CH 4 yr −1 for the whole of Alaska(Zhuang et al., 2007).As wetlands in Europe are predominantly located north of 60 • N, our estimate of wetland emissions from northern Europe is very close to a European-scale estimate of 3.6 Tg CH 4 yr −1 by Saarnio et al. (2009).The posterior CH 4 emissions from Siberian wetlands show a wide range (2.0-12.7 Tg CH 4 yr −1 ), which are much smaller than the estimate of 21.63 ± 5.25 Tg CH 4 yr −1 by Kim et al. (2012) for the annual mean CH 4 emissions from Siberian wetlands during 2005-2010.Assimilating in situ CH 4 measurements collected at 13 Eurasian sites in Siberia, Finland, Mongolia, China and South Korea, Berchet et al. (2015) estimated that CH 4 budget on the West Siberian Plain was 5-28 Tg CH 4 for 2010.It is also larger than our estimate but shows a similar large uncertainty.Discussion Paper | Discussion Paper | Discussion Paper | e.g.Siberia, are still poorly constrained by the assimilated measurements.In theory, because surface and aircraft measurements have much lower uncertainties than satel-Discussion Paper | Discussion Paper | Discussion Paper | −1 as suggested by Shakhova et al. (2013) because the posterior CH 4 emissions from Arctic wetlands are no more than 20.4 Tg CH 4 yr −1 .Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Tan, Z. and Zhuang, Q.: Arctic lakes are continuous methane sources to the atmosphere under warming conditions, Environ.Res.Lett., 10, 054016, doi:10.1088/1748-9326/10/5/054016,2015a.Tan, Z. and Zhuang, Q.: Methane emissions from pan-arctic lakes during the 21st century: an analysis with process-based models of lake evolution and biogeochemistry, in review, 2015b.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 1 .Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 6 .Figure 7 .Figure 8 .Figure 9 .
Figure 1.Comparison of column averaged CH 4 mole fractions from SCIAMACHY with those from GEOS-Chem model calculated with prior emissions.(a, b) show the mean bias and residual standard deviation of the satellite-model difference, (c) shows the comparison of the model (x axis) and satellite (y axis) XCH 4 after applying the "latitude + humidity" correction from the linear regression (weighted R 2 is shown inset and the red 1 : 1 line is also shown), and (d) shows the satellite-model difference after bias removal.
during the period of January 2003 to October 2005 are used.The quality of SCIA-MACHY observations is controlled by a filtering scheme that selects only daytime, over land and with cloud free or partially cloud scenes and good fitting accuracy (http://www.temis.nl/climate/docs/TEMIS_SCIA_CH4_IMAPv60_PSD_v2_6.pdf).Further, a surface elevation filter is applied to filter out observations that are different from the model grids at surface altitude by more than 250 m Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Turner et al. (2015)lexe et al., 2015)s correction functions and initial conditions for the next set of inversions.Next, we run six global coarse-resolution inversions using the wetland CH 4 scenarios described in Sect.3.1 at two time windows: January 2004-December 2004 and July 2004-June 2005.In these global inversions, both surface measurements and satellite retrievals are assimilated.The inverse modeling at the 1st time block servers as a spin-up period and the analysis time period is from July 2004 to June 2005(Deng et al., 2014;Alexe et al., 2015).Besides optimizing global CH 4 fluxes, the global inversions also provide boundary conditions for our nested grid inversions.FollowingTurner et al. (2015), we construct time-dependent boundary conditions for the nested simulations of the adjoint model from the forward model at 4 Wecht et al. (2014)Discussion Paper | Discussion Paper | Discussion Paper | • × 5• horizontal resolution using the posterior emissions from a global inversion performed first.This is different from the method ofWecht et al. (2014)where both emissions and boundary conditions were optimized by minimizing two separate cost functions iteratively.The last step is thus to run nested grid inversions in the Arctic at 1/2• × 2/3• resolution to optimize Arctic CH 4 emissions.The modeling period is from 24 June to 1 October 2004

Supplement related to this article is available online at doi:10.5194/acpd-15-32469-2015-supplement. Introduction
In this study, we use a nested-grid high-resolution chemical transport inverse model in the Arctic domain to constrain CH 4 emissions from Arctic wetlands, lakes and anthropogenic sources.The sensitivity of the method to different prior wetland CH 4 fluxes is also tested.When assimilating NOAA/ESRL and SCIAMACHY observations, we estimate that during July 2004-June 2005, global total CH 4 emission is in the range of 496.4-511.5 Tg CH 4 yr −1 , with wetlands contributing 130.0-203.3TgCH 4 yr −1 .Both of these estimates are consistent with some widely accepted expert assessments.The nested-grid inversions demonstrate that biogeochemical models tend to overestimate CH 4 emissions from natural sources of the Arctic (e.g., wetlands and lakes).The posterior CH 4 emissions from Arctic lakes from July 2004 to June 2005 are 5.4-7.9TgCH 4 yr −1 , a significant contribution to the Arctic CH 4 cycle.CH 4 emissions from lakes in Alaska, northern Canada, northern Europe and northern Siberia, on average, are estimated to be 1.0, 3.1, 0.6 and 2.8 Tg CH 4 yr −1, respectively.Except for the emissions from northern Siberia, other estimates are consistent with the lake biogeo-Evaluation with independent datasets shows that the global inversions and the Arctic inversions with a nested approach improve estimates of methane mixing ratios in boundary layer and free troposphere.The high-resolution inversions provide more details about the spatial distribution of methane emissions in the Arctic, which helps understand the CH 4 cycle in this climate sensitive region.Figures chemical model simulations.The posterior CH 4 emissions from Arctic wetlands from July 2004 to June 2005 are 8.8-20.4Tg CH 4 yr −1 .CH 4 emissions from wetlands in Alaska, northern Canada, northern Europe and northern Siberia are, on average, 1.0, 3.3, 4.2 and 5.8 Tg CH 4 yr −1 , respectively.The nested-grid inversions indicate that CH 4 emissions from northern Canada, Alaska, Scandinavia and East Siberia Coastal lowlands are better constrained by the inversions than from other Arctic regions, e.g.most of Siberian wetlands.Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | The

Table 1 .
Summary of bias correction methods and of mean absolute satellite-model difference (ppb) for 2003-2005 before and after applying bias correction.∆BIC is the BIC score increase of a bias correction method when referring to the latitude only method.Air mass factor + Humidity p 0 + p 11 A F + p 21 H S 0 + p 11 ϕ + p 12 ϕ 2 + p 21 H S 6.230 −7

Table 3 .
Summary of the prior and posterior CH 4 emissions (Tg CH 4 yr −1 ) from the Arctic from Jul 2004 to Jun 2005.The priors are the range of the initial CH 4 emissions given by the six scenarios.