Seasonal variability of stratospheric methane: implications for constraining tropospheric methane budgets using total column observations

Abstract

Global and regional methane budgets are markedly uncertain. Conventionally, estimates of methane sources are derived by bridging emissions inventories with atmospheric observations employing chemical transport models. The accuracy of this approach requires correctly simulating advection and chemical loss such that modeled methane concentrations scale with surface fluxes. When total column measurements are assimilated into this framework, modeled stratospheric methane introduces additional potential for error. To evaluate the impact of such errors, we compare Total Carbon Column Observing Network (TCCON) and GEOS-Chem total and tropospheric column-averaged dry-air mole fractions of methane. We find that the model's stratospheric contribution to the total column is insensitive to perturbations to the seasonality or distribution of tropospheric emissions or loss. In the Northern Hemisphere, we identify disagreement between the measured and modeled stratospheric contribution, which increases as the tropopause altitude decreases, and a temporal phase lag in the model's tropospheric seasonality driven by transport errors. Within the context of GEOS-Chem, we find that the errors in tropospheric advection partially compensate for the stratospheric methane errors, masking inconsistencies between the modeled and measured tropospheric methane. These seasonally varying errors alias into source attributions resulting from model inversions. In particular, we suggest that the tropospheric phase lag error leads to large misdiagnoses of wetland emissions in the high latitudes of the Northern Hemisphere.

Atmos. Chem. Phys., 16, 1400314024, 2016 www.atmos-chem-phys.net/16/14003/2016/ doi:10.5194/acp-16-14003-2016 Author(s) 2016. CC Attribution 3.0 License.

Katherine M. Saad1, Debra Wunch1,2, Nicholas M. Deutscher3,4, David W. T. Grifth3, Frank Hase5,Martine De Mazire6, Justus Notholt4, David F. Pollard7, Coleen M. Roehl1, Matthias Schneider5, Ralf Sussmann8, Thorsten Warneke4, and Paul O. Wennberg1

1Environmental Science and Engineering, California Institute of Technology, Pasadena, California, USA

2Department of Physics, University of Toronto, Toronto, Ontario, Canada

3Center for Atmospheric Chemistry, School of Chemistry, University of Wollongong, Wollongong, NSW, Australia

4Institute of Environmental Physics, University of Bremen, Bremen, Germany

5Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology, IMK-ASF, Karlsruhe, Germany

6Royal Belgian Institute for Space Aeronomy, Brussels, Belgium

7National Institute of Water and Atmospheric Research, Omakau, New Zealand

8Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology, IMK-IFU, Garmisch-Partenkirchen, Germany

Correspondence to: Katherine M. Saad ([email protected])

Received: 7 April 2016 Published in Atmos. Chem. Phys. Discuss.: 10 May 2016

Revised: 24 October 2016 Accepted: 25 October 2016 Published: 11 November 2016

Abstract. Global and regional methane budgets are markedly uncertain. Conventionally, estimates of methane sources are derived by bridging emissions inventories with atmospheric observations employing chemical transport models. The accuracy of this approach requires correctly simulating advection and chemical loss such that modeled methane concentrations scale with surface uxes. When total column measurements are assimilated into this framework, modeled stratospheric methane introduces additional potential for error. To evaluate the impact of such errors, we compare Total Carbon Column Observing Network (TCCON) and GEOS-Chem total and tropospheric column-averaged dry-air mole fractions of methane. We nd that the models stratospheric contribution to the total column is insensitive to perturbations to the seasonality or distribution of tropospheric emissions or loss. In the Northern Hemisphere, we identify disagreement between the measured and modeled stratospheric contribution, which increases as the tropopause altitude decreases, and a temporal phase lag in the models tropospheric seasonality driven by transport errors. Within the context of GEOS-Chem, we nd that the errors in tropospheric advection partially compensate for the stratospheric

methane errors, masking inconsistencies between the modeled and measured tropospheric methane. These seasonally varying errors alias into source attributions resulting from model inversions. In particular, we suggest that the tropospheric phase lag error leads to large misdiagnoses of wet-land emissions in the high latitudes of the Northern Hemisphere.

1 Introduction

Identifying the processes that have driven changes in atmospheric methane (CH4), a potent radiative forcing agent and major driver of tropospheric oxidant budgets, is critical for understanding future impacts on the climate system. Methanes growth rate, which had been decreasing through the 1990s from about 10 to 0 ppb per year, began to increase again in 2006 and over the past decade has averaged 5 ppb per year (Dlugokencky et al., 2011). Developing robust constraints on the global CH4 budget is integral to understanding which processes produced these decadal trends

Published by Copernicus Publications on behalf of the European Geosciences Union.

Seasonal variability of stratospheric methane: implications for constraining tropospheric methane budgets using total column observations

14004 K. M. Saad et al.: Assimilation of total column methane into models

(e.g., Bergamaschi et al., 2013; Wecht et al., 2014a, b; Turner et al., 2015).

One common approach to quantifying changes in the spatial distribution of sources are atmospheric inversions, which incorporate surface uxes estimated by bottom-up inventories as boundary conditions for a chemical transport model (CTM). The modeled CH4 concentrations are compared to observations within associated grid boxes, and prior emissions are scaled to minimize differences with measured dryair mole fractions (DMFs), producing posterior estimates.The accuracy of these optimized emissions depends on how well the CTM simulates atmospheric transport and CH4 sinks, which are generally prescribed.

Pressure-weighted total column-averaged DMFs (Xgas) provide a relatively new constraint and have previously been shown to improve estimates of regional and interhemispheric gradients in trace gases (Yang et al., 2007). Infrared spectrometers can measure CH4 DMFs (XCH4) from ground-based sites, such as those in the Total Carbon Column Ob-serving Network (TCCON) and Network for the Detection of Atmospheric Composition Change (NDACC), and satellites, including SCanning Imaging Absorption spectroMeter for Atmospheric CartograpHY (SCIAMACHY) (Bergamaschi et al., 2007), Greenhouse gases Observing SATellite (GOSAT) (Parker et al., 2011), and the upcoming TROPOspheric Monitoring Instrument (TROPOMI) (Butz et al., 2012). These observations complement surface measurements because they add information about the vertically averaged prole and are sensitive in the free troposphere (Yang et al., 2007). Additionally, they complement aircraft observations by measuring trace gases at higher temporal frequency, although they share the limitation of not measuring in inclement weather. Satellite measurements add global coverage that can ll in gaps where in situ observations are sparse. Fraser et al. (2013) found that assimilating GOSAT CH4 columns into the GEOS-Chem CTM with an ensemble Kalman lter reduced posterior emissions uncertainties by 948 % for individual source categories and by more than three times those of inversions that only assimilated surface data for most regions. Wecht et al. (2014b) determined from their analysis of observing system simulation experiments (OSSEs) that TROPOMIs daily frequency and global coverage performs similarly to aircraft campaigns on sub-regional scales, and could provide a constraint on Californias CH4 emissions similar to CalNex aircraft observations (Santoni et al., 2014; Gentner et al., 2014).

Incorporating total columns into modeling assessments can also be used to diagnose systematic issues with model transport. For example, comparing carbon dioxide (CO2)

from TCCON and TransCom (Baker et al., 2006), Yang et al. (2007) found that most models included in the comparison lack sufciently strong vertical exchange between the planetary boundary layer (PBL) and the free troposphere, thereby dampening the seasonal cycle amplitude of XCO2. The limitations of models to accurately represent vertical transport

can lead to radically different spatial distributions of uxes;

Stephens et al. (2007) found, for example, that the northern terrestrial carbon land sink and tropical emissions were overestimated by 0.9 and 1.7 PgC year1, respectively, when comparing models to aircraft CO2 proles. More recent studies attribute to model transport errors the tendency of simulated CH4 in the Southern Hemisphere to be higher at the surface than the free troposphere, in contrast with measurements (Fraser et al., 2011; Patra et al., 2011).

Tropospheric CH4 typically does not vary radically with height above the PBL; above the tropopause, however, the vertical prole of CH4 exhibits a rapid decline with altitude as a result of its oxidation and the lack of any source beyond advection from the troposphere. Fluctuations in stratospheric dynamics, including the height of the tropopause, change the contribution of the stratosphere to the total column. CH4 proles with similar tropospheric values can thus have significant differences in XCH4 (Saad et al., 2014; Washenfelder et al., 2003; Wang et al., 2014).

Provided that simulations replicate seasonal and zonal variability of stratospheric CH4 loss, tropopause heights, and vertical exchange across the upper troposphere and lower stratosphere (UTLS), posterior ux estimates from inversions incorporating XCH4 measurements would not be sensitive to stratospheric processes. However, most models do not accurately represent stratospheric transport, producing low age-of-air values and zonal gradients in the subtropical lower stratosphere that are less steep than observations (Waugh and Hall, 2002). The TransCom-CH4 CTM inter-comparison assessment of transport using sulfur hexauoride (SF6) showed a strong correlation between the stratosphere

troposphere exchange (STE) rate and the models CH4 budget, and a weaker correlation between the CH4 growth rate and vertical gradient in the models equatorial lower stratosphere (Patra et al., 2011). These forward model dependencies of CH4 concentrations on vertical transport, both within the troposphere and across the tropopause, have the potential to introduce substantial errors in atmospheric inversions. As temporal and spatial biases in a models vertical prole will alias into posterior emissions, inversions that incorporate total column measurements must ensure that the stratosphere is sufciently well described so as to not introduce spurious seasonal, zonal, and interhemispheric trends in CH4 concentrations and consequently emissions.

In this analysis, we identify systematic model errors in the seasonal cycle and spatial distribution of CH4 DMFs by comparing TCCON total and tropospheric columns (Saad et al., 2014) to vertically integrated proles derived from the GEOS-Chem CTM (Bey et al., 2001; Wang et al., 2004;Wecht et al., 2014a). We assess the impact of errors in the characterization of stratospheric processes on the assimilation of XCH4 and resulting posterior emissions estimates. In

Sect. 2 we describe the TCCON column measurements and GEOS-Chem setup and characteristics. In Sect. 3 we present the results of the measurementmodel comparison. In Sect. 4

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Table 1. TCCON sites, coordinates, altitudes, start date of measurements and locations used in this analysis.

Site Latitude Longitude Elevation Start date Location Data reference( ) ( ) (km)

Bialystok 53.2 23.0 0.18 Mar 2009 Bialystok, Poland Deutscher et al. (2014) Bremen 53.1 8.9 0.03 Jan 2007 Bremen, Germany Notholt et al. (2014) Karlsruhe 49.1 8.4 0.11 Apr 2010 Karlsruhe, Germany Hase et al. (2014)

Orleans 48.0 2.1 0.13 Aug 2009 Orleans, France Warneke et al. (2014) Garmisch 47.5 11.1 0.75 Jul 2007 Garmisch, Germany Sussmann and Rettinger (2014) Park Falls 45.9 90.3 0.47 Jan 2005 Park Falls, WI, USA Wennberg et al. (2014b)

Lamont 36.6 97.5 0.32 Jul 2008 Lamont, OK, USA Wennberg et al. (2014c)

JPL 34.2 118.2 0.39 Jul 2007 Pasadena, CA, USA Wennberg et al. (2014d, a)

Saga 33.2 130.3 0.01 Jul 2011 Saga, Japan Kawakami et al. (2014) Izaa 28.3 16.5 2.37 May 2007 Tenerife, Canary Islands Blumenstock et al. (2014)

Darwin 12.4 130.9 0.03 Aug 2005 Darwin, Australia Grifth et al. (2014a)

Runion Island 20.9 55.5 0.09 Sep 2011 Saint-Denis, Runion De Mazire et al. (2014)

Wollongong 34.4 150.9 0.03 Jun 2008 Wollongong, Australia Grifth et al. (2014b)

Lauder 45.0 169.7 0.37 Jan 2005 Lauder, New Zealand Sherlock et al. (2014a, b)

we compare the base case simulation to one in which emissions do not vary within each year and quantify the sensitivity of source attribution of the biggest seasonal emissions sector, wetlands, to the tropospheric seasonal delay.

2 Methods

2.1 Tropospheric methane columns

TCCON has provided precise measurements of XCH4 and other atmospheric trace gases for over ten years (Wunch et al., 2011a, 2015). Developed to address open questions in carbon cycle science, the earliest sites are located in Park Falls, Wisconsin, United States and Lauder, New Zealand at about 45 north and south, respectively. Since 2004, the ground-based network of Fourier transform spectrometers has expanded greatly. XCH4 are processed with the current version of the TCCON software, GGG2014, to be consistent, and thereby comparable, across sites. Total column retrievals are generated with the GFIT nonlinear least-squares tting algorithm, which calculates the best spectral t of the solar absorption signal to an a priori vertical prole and outputs a scaling factor. The pressure-weighted integration of the scaled a priori prole produces column abundances, which are then divided by the dry air column, calculated using concurrently retrieved oxygen (O2) columns (Wunch et al., 2010, 2011a, 2015). Trace gas a priori proles are derived with empirical models, which are generated incorporating aircraft and balloon in situ and satellite measurements (see Wunch et al., 2015, for a complete list), and for CH4 include a secular increase of 0.3 % per year and an interhemispheric gradient in the altitude dependence of the vertical proles (Toon and Wunch, 2014). These models are t to daily noontime National Centers for Environmental Protection and National Center for Atmospheric Research (NCEP/NCAR) reanalysis

pressure grids (Kalnay et al., 1996), interpolated to the surface pressure measured real-time on site. Because the prole of CH4 drops off rapidly in the stratosphere, the accuracy of the a priori shape, and thus the retrieved column, depends on correctly determining the tropopause.

Tropospheric columns have been shown to represent the magnitude and seasonality of in situ measurements (Saad et al., 2014; Washenfelder et al., 2003; Wang et al., 2014).The tropospheric CH4 column-averaged DMFs (XtCH4) are derived by the hydrogen uoride (HF) proxy method described in Saad et al. (2014), which uses the relationship between CH4 and HF in the stratosphere, derived from ACE

FTS satellite measurements (Bernath, 2005; De Mazire et al., 2008; Mahieu et al., 2008; Waymark et al., 2014), to calculate and remove the stratospheric contribution to XCH4.

The XtCH4 used in this analysis have been processed consistently with the GGG2014 TCCON products, with air-mass dependence and calibration factors calculated for and applied to XtCH4 (Wunch et al., 2010, 2015). Additional details about the tropospheric CH4 measurements can be found in

Appendix A.

With the exception of Eureka and Sodankyl, which are highly inuenced by the stratospheric polar vortex, all TCCON sites that provide measurements before December 2011 are included in this analysis (Fig. 1). Table 1 lists locations and data collection start dates for each of the sites.

2.2 GEOS-Chem model

Model comparisons use the ofine CH4 GEOS-Chem version 9.02 at 4 5 horizontal resolution on a reduced

vertical grid (47L). CH4 loss is calculated on 60 min intervals and is set by annually invariable monthly 3-D elds: hydroxyl radical (OH) concentrations in the tropo-sphere (Park et al., 2004) and parameterized CH4 loss rates

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Figure 1. Map of TCCON sites used in this analysis. Site colors are on a spectral color scale in order of latitude, with Northern Hemisphere sites designated by cool colors and Southern Hemisphere sites designated by warm colors.

per unit volume in the stratosphere (Considine et al., 2008; Allen et al., 2010; Murray et al., 2012). Emissions are released at 60 min time steps and are provided by the GEOSChem development team for 10 sectors: (i) gas and oil, (ii) coal, (iii) livestock, (iv) waste, (v) biofuel and (vi) other anthropogenic annual emissions from EDGAR v4.2 (European Commission Joint Research Centre, Netherlands Environmental Assessment Agency, 2011; Wecht et al., 2014a), (vii) other natural annual emissions from Fung et al. (1991), (viii) rice agriculture (European Commission Joint Research Centre, Netherlands Environmental Assessment Agency, 2011) and (ix) wetland (Pickett-Heaps et al., 2011) monthly emissions, which incorporate GEOS5 annual and monthly mean soil moisture values, and (x) biomass burning daily emission from GFED3 estimates (Mu et al., 2011; van der Werf et al., 2010). Loss via soil absorption (Fung et al., 1991), set annually, is subtracted from the total emissions at each time step.

2.2.1 Model setup

We initialized zonal CH4 distributions with GGG2014 data version a priori proles (Toon and Wunch, 2014) produced at horizontal grid centers, which we adjusted vertically to match the zonally averaged daily mean models tropopause, derived from the National Aeronautics and Space Administration Global Modeling and Assimilation Ofce (NASA/GMAO) Goddard Earth Observing System Model, Version 5 (GEOS5). The model was run from December 2003, the rst month in which GEOS5 meteorological data were available, to June 2004, the beginning of the TCCON time series; we then ran the model repeatedly over the June 2004May 2005 time frame, which allowed us to make comparisons with the TCCON data at Park Falls and Lauder, until CH4 concentrations reached equilibrium. A number of perturbation experiments were run in this way to quantify the sensitivity of CH4 distribution and seasonality to the ofine OH elds, prescribed emissions, and tropopause levels (Table 2). These model experiments are described in greater detail in Appendix B1.

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Figure 2. Seasonality of the difference between base and aseasonal CH4 for tropospheric, total and stratospheric contribution to total columns. Site colors are as in Fig. 1.

Using CH4 elds for 1 January 2005 from the equilibrium simulation as initial conditions, model daily mean CH4 mole fractions were computed through 2011. These were converted to dry mole fractions, as described in Appendix B2. In addition to the default emissions scheme, an aseasonal simulation setup, in which rice, wetland, and biomass burning emissions were disabled and aseasonal emissions scaled up such that total annual zonal uxes approximate those in the base simulation, was similarly run to equilibrium and used as initial conditions for the 20052011 run. The model infrastructure posed difculties for setting the seasonally varying uxes constant throughout each year; thus we implement this scaling technique as an alternative to assess rst-order impacts of emission seasonality. The resulting changes to the spatial distribution of CH4 emissions are shown in Fig. B1.

For comparisons with column measurements, model vertical proles were smoothed with corresponding TCCON CH4 averaging kernels, interpolated for the daily mean solar zenith angles, and prior proles, scaled with daily median scaling factors, following the methodology in Rodgers and Connor (2003) and Wunch et al. (2010). Averaging kernels and prior proles were interpolated to the models pressure grid, and all terms in the smoothing equation were interpolated to daily mean surface pressures measured at each site.Tropospheric columns were integrated in the same manner as the total columns up to the grid level completely below

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Table 2. Sensitivity experiments.

Simulation name Description CH4 lifetime Final CH4 burden (years) (Tg)

Base Default OH and emissions 9.55 4825 Aseasonal Constant monthly emission rates 9.57 4872 Updated OH Monthly OH elds from standard chemistry + biogenic VOCs 8.53 4828

Figure 3. Smoothed daily mean Xt

CH4 and stratospheric contribution to XCH4 at Park Falls (blue) and Lauder (red) for (a) base equilibrium

simulation and the difference between the base and (b) aseasonal and (c) updated OH simulations.

the daily mean tropopause, consistent with how GEOS-Chem partitions the atmosphere in the ofine CH4 simulation. To test the dependence of our results on the chosen vertical integration level, tropospheric columns were also calculated assuming the tropopause was one and two grid cells above this level. While XtCH4 changed slightly, by a median of about 1 and 5 ppb for a one and two-level increase respectively, shifting the tropopause did not alter the ndings discussed in this paper. A description of the model smoothing methodology and assumptions is provided in Appendix B3. The stratospheric contribution to the total column, which is calculated as the residual between the XtCH4 and XCH4, is the amount by which the stratosphere attenuates XCH4 via stratospheric loss and transport (see Appendix C for the derivation).

2.2.2 Model features

The seasonal amplitude of the differences between base and aseasonal simulations are small within 4 ppb for all ver

tical levels in the Southern Hemisphere (Fig. 2). In the Northern Hemisphere, however, the difference is much larger and primarily impacts the troposphere, where it varies between

10 and +13 ppb. The insensitivity of the stratosphere to

the seasonality of emissions is due to the common source of stratospheric air in the tropics (Boering et al., 1995) and

the loss of seasonal information as the age of air increases (Mote et al., 1996).

Due to the relatively short photochemical lifetime of CH4 in the stratosphere, about 22 months in the base simulation, stratospheric CH4 concentrations stabilize much more quickly than in the troposphere (Fig. 3a). This rapid response time of the stratosphere occurs regardless of perturbations to the troposphere, such as the seasonality of emissions (Fig. 3b) or tropospheric OH elds (Fig. 3c). In both hemispheres the differences between the base and experimental simulations asymptotically approach steady state with seasonal variability over a decade in the troposphere, but oscillate seasonally around a constant mean in the stratosphere. Stratospheric differences between simulations are considerably smaller than the seasonal amplitude of the base run: within 6 and 1 ppb, respectively, vs. a seasonal range of 30 ppb at Park Falls. By contrast, XtCH4 have differences within 30 and 10 ppb, respectively, vs. a seasonal range of 20 ppb at Park Falls. The stratosphere at Lauder is even less sensitive to tropospheric perturbations.

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14008 K. M. Saad et al.: Assimilation of total column methane into models

Figure 4. Daily median TCCON and smoothed daily mean GEOS-Chem base (top) and aseasonal (bottom) DMFs for (a) Xt

CH4, (b) XCH4,

and (c) stratospheric contribution. Site colors are as in Fig. 1. Northern Hemisphere least squares regression equations are in the top left, and Southern Hemisphere least squares regression equations are in the bottom right of each plot. Dashed lines mark the one-to-one lines.

3 Measurementmodel comparison

The TCCON daily median and GEOS-Chem daily mean

CH4 column-averaged DMFs demonstrate a strong inter-hemispheric difference for XtCH4 and XCH4 in both the base and aseasonal simulations (Fig. 4). The Northern Hemisphere XtCH4 slope deviates from the one-to-one line more than the XCH4 slope (0.60 0.02 vs. 0.86 0.03), and the

correlation coefcients are equivalent (R2 = 0.41), which

indicates that the poorer agreement between measurements and models in the troposphere drives the scatter in the total column.

The stratospheric contribution comparison between TC

CON and the base simulation for the Northern Hemisphere sites has an equivalent slope (0.60 0.1) and higher corre

lation coefcient (R2 = 0.68) compared to XtCH4 (Fig. 4c).

GEOS-Chems larger stratospheric contribution to the total column, coupled with lower tropospheric values, depresses XCH4. Because this effect on XCH4 occurs more at higher latitudes, zonal errors in the models stratosphere balances those in the troposphere. The result is better measurement model agreement in the total columns.

The aseasonal simulation produces lower slopes and correlation coefcients for, XtCH4 (slope = 0.42 0.02, R2 =

0.32), XCH4 (slope = 0.60 0.03, R2 = 0.26), and the

stratospheric contribution (slope = 0.52 0.01, R2 = 0.66)

in the Northern Hemisphere. Removing the seasonality of emissions increases both measurementmodel differences and scatter, as we would expect given the seasonality of Northern Hemisphere emissions noted in bottom-up stud-

ies (Kirschke et al., 2013). The aseasonal simulation also reduces the offset between TCCON and GEOS-Chem, whereby modeled XtCH4 and XCH4 are systematically low.

TransCom-CH4 showed that GEOS-Chem CH4 concentrations tend to be lower than the model median, and much lower than the range of other models when using the same OH elds (Patra et al., 2011). The aseasonal emissions used in this analysis likely reduce this documented imbalance with the models tropospheric OH elds.

The XCH4 and XtCH4 regression equations across Southern

Hemisphere sites are nearly equivalent, which suggests that the Southern Hemisphere is not as impacted by the STE errors as the Northern Hemisphere. This consistency between XCH4 and XtCH4 could also be a function of the zonal dependence of the stratospheric error: whereas more than half of the Northern Hemisphere sites are north of 45 N, the most poleward site in the Southern Hemisphere is located at 45 S.

The increased scatter associated with the slightly lower XtCH4

R2 value of 0.63, compared to the XCH4 R2 value of 0.88, does indicate that the Southern Hemisphere is not exempt from model errors associated with emissions, the OH distribution, or transport. The lower XtCH4 slope of the aseasonal simulation (1.1 vs. 1.3) illustrates the inuence of emissions: removing their seasonality leads to better measurement model agreement, evidenced by a slope closer to both the one-to-one line and the zero-intercept. We hypothesize that either the seasonality of Southern Hemispheric emissions is too strong or, more likely, errors in the Northern Hemispheric seasonality of emissions drive measurementmodel mismatch in the Southern Hemisphere via interhemispheric

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Spring

-60 -40 -20 0 20 40 60

Latitude

Figure 5. Zonally averaged ACE minus GEOS-Chem climatological CH4 mole fractions for boreal spring and fall. Black line represents the mean zonal tropopause level. Site colors of squares on the x axis are as in Fig. 1.

transport. If this effect was solely due to a changed emissions distribution, we would expect the XCH4 slope to also change for the Southern Hemisphere sites, if only slightly;

instead the slope is equivalent to the base simulation XtCH4 and XCH4 slopes, and R2 = 0.87, only marginally less than

the base simulation XCH4 correlation coefcient.

The stratospheric contribution regression equations differ only slightly between the base and aseasonal simulations: (0.64 0.02)x + 14, R2 = 0.68, vs. (0.62 0.02)x +

15, R2 = 0.67. The insensitivity of both the stratospheric

contribution and the total columns in the Southern Hemisphere to perturbations in the seasonality of tropospheric emissions could be driven by the smaller vertical gradient across the UTLS that results from the inuence of Northern Hemispheric air both in the free troposphere (Fraser et al., 2011) and the stratosphere (Boering et al., 1995). This effect would also support the interpretation of Northern Hemispheric emission errors driving disagreement between observations and the model in the Southern Hemisphere.

In the troposphere, CH4 increases from south to north; the stratospheric contribution of CH4, however, increases from the Equator to the poles due to the zonal gradient in tropopause height. In the Northern Hemisphere total column, the zonal gradient largely disappears: at high latitudes, the larger tropospheric emissions balances the larger stratospheric contribution. By contrast, zonal gradients in the Southern Hemisphere troposphere and stratosphere are additive, and greater south to north differences are apparent in the total column.

Figure 5 illustrates how the model differs from ACE

FTS CH4 measurements in the stratosphere over boreal spring (MarchAprilMay) and fall (SeptemberOctober November). Except above the tropical tropopause, CH4 is considerably lower in the ACE-FTS climatology (v. 2.2, Jones et al., 2012) compared to GEOS-Chem. The difference varies both with altitude and latitude, especially in the North-

Fall

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ern spring poleward of 40 N. The vertical gradient is the least pronounced in Lauder, where the stratospheric contributions of TCCON and GEOS-Chem fall most closely to the one-to-one line (Fig. 4). The low CH4 in the tropical mid and upper stratosphere in GEOS-Chem could be a result of too-weak vertical ascent to the stratosphere; however, the ACEFTS data gaps in the tropical troposphere make this hypothesis difcult to test.

3.1 Dependence on tropopause height

In the Northern Hemisphere, the measurementmodel mismatch of the stratospheric contribution increases as the tropopause altitude shifts downward (Fig. 6). As the models stratospheric portion of the pressure-weighted total column increases, the error in stratospheric CH4 is amplied, causing a larger disagreement with measurements. Because the tropopause height decreases with latitude, and this gradient increases during winter and spring, this introduces both zonal and seasonal biases. The disagreement exhibits a large spread for relatively few tropopause pressure heights because the models effective tropopause, that is, the pressure level at which the model divides the troposphere from the stratosphere in GEOS-Chem, is dened at discrete grid level pressure boundaries.

The tropospheric mismatch ([Delta1]XtCH4), by contrast, decreases with tropopause height for the majority of days and exhibits a much weaker correlation to tropopause height, 0.099 vs. 0.22 for the stratospheric contribution. Thus, as expected, the tropopause height explains less of the variance in the measurementmodel mismatch in XtCH4: the upper troposphere is generally well-mixed, and chemical loss does not vary with altitude as much as in the lower stratosphere. This weaker relationship also demonstrates that the choice of tropopause used in the tropospheric prole integration does not strongly impact [Delta1]XtCH4.

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Stratospheric contribution

y = (-0.055

0.003)x+9 R2 = 0.22

100 200 300 400 500

-40 0 GEOS-Chem tropopause height (hPa)

Figure 6. TCCON minus GEOS-Chem CH4 column-averaged DMFs as a function of the effective GEOS-Chem tropopause height, shown for Northern Hemisphere sites. Site colors are as in Fig. 1.

The relationship between [Delta1]XtCH4 and tropopause height has a clear zonal component that indicates that the correlation is instead a result of another parameter that varies with latitude. The tropospheric slope is dominated by high-latitude sites; the subtropical sites exhibit a much weaker correlation. At Izaa, which is in the sub-tropics at an altitude of2.4 km, the correlation between [Delta1]XtCH4 and tropopause position is weak: the slope of 0.035 0.03 is nearly at within

error, and R2 is 0.025. By contrast, the stratospheric relationship at Izaa corresponds more closely with the other Northern Hemisphere sites: the slope is 0.088 0.02, and

R2 = 0.36.

3.2 Seasonal agreement

The tropospheric difference between TCCON and GEOS

Chem, [Delta1]XtCH4, has a periodic trend indicating that the model error has a strong seasonal component in the troposphere.

To isolate stable seasonal patterns from the cumulative inuence of emissions, we calculate the detrended seasonal mean column-averaged DMFs for each site. In the Southern Hemisphere, the measurements and model agree well. Across the Northern Hemisphere sites, however, the seasonality differs (Fig. 7). The seasonal amplitude of GEOS-Chem XtCH4 is about equal to that of TCCON, but the TCCON XtCH4 seasonal minimum is in June/July while the GEOS-Chem seasonal minimum is in September/October. Additionally, while TCCON XtCH4 begins to decrease in January, GEOS-Chem shows some persistence into the spring.

The seasonal delay also appears in comparisons of GEOS

Chem surface CH4 with National Oceanic and Atmospheric

Administration (NOAA) surface ask measurements at the

LEF site in Park Falls (Fig. 8). The seasonality of GEOSChems surface is regulated more by emissions than transport: CH4 peaks in the summer, when wetland emissions are highest (Fig. 10). This contrasts with the ask measurements, which reach a minimum in the summer (Fig. 8). The season-

Tropospheric column

40

30

20

10

0

-10

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-30

-20

100

80

~CH 4(ppb)

~CH 4(ppb)

Bialystok Bremen Karlsruhe Orleans Garmisch Park Falls Lamont JPLSaga Izaa

60

40

20

0

y = (-0.072

0.007)x+52 R2 = 0.099

-40 0 100 200 300 400 500

GEOS-Chem tropopause height (hPa)

ality covaries remarkably closely with respect to other features: the late winter decrease, spring persistence, and local minimum in October. The spring plateau lasts twice as long as seen in observations, however, and matches XtCH4, indicating that feature is not the result of vertical transport between the PBL and free troposphere.

Not surprisingly, a time lag does not occur in the stratosphere; the TCCON stratospheric seasonal amplitude is less than half but in phase with that of GEOS-Chem (Fig. 7). The vertical inconsistency of the seasonality produces unusual features in the model total column. From January through April, the TCCON and GEOS-Chem XCH4 are consistent because the models bias in the troposphere is balanced by the larger stratospheric contribution. Starting in May, however, the model diverges from the measurements as the higher tropopause limits the stratospheres inuence, and the phase lag in the troposphere dominates. This balancing effect is also demonstrated by the greater variance across sites in the model XtCH4 and stratospheric contribution compared to measurements, but about the same variance in XCH4.

For the aseasonal simulation, the tropospheric seasonal cycle amplitude and variance across sites increase (Fig. 7). The greatest model differences, from August through October, are a result of dampening the large wetland uxes in the base simulation that balance higher OH concentrations. The seasonal amplitude does not increase as drastically in the sub-tropics, where the total emissions are not as impacted by seasonally varying sources, leading to the greater variance across sites. The second largest difference between simulation amplitudes occurs in the spring, and OH loss could potentially be contributing to the discrepancy in these months also. The aseasonal simulation spreads the wetland uxes so as to introduce emissions in the winter and spring, when the OH concentrations are lowest. Another possibility is that the model could be subject to errors that are in phase with the base simulation seasonal emissions, which would then have an ameliorating effect that produces the reasonable sea-

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J F M A M J J A S O N D

Troposphere

TCCONBase GEOS-Chem Aseasonal GEOS-Chem

Total column

Stratospheric contribution

20

20

20

Seasonal CH 4(ppb)

10

10

10

0

0

0

-10

-10

-10

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J F M A M J J A S O N D

J F M A M J J A S O N D

Figure 7. Detrended seasonality of TCCON (black diamonds), GEOS-Chem base (red circles), and GEOS-Chem aseasonal (blue squares) CH4 column-averaged DMFs, averaged across Northern Hemisphere sites, excluding Saga, which has less than one year of measurements prior to 2012. Error bars denote the 1 standard deviation across sites.

40 Park Falls, WI (46N) NOAA Flask

GEOS-Chem

the Northern Hemisphere phase shift also occurs in simulations performed with large changes in OH (Fig. B3, in Appendix B1). Transport is thus the most likely driver of these tropospheric trends in the model.

4 Discussion

The stratospheric insensitivity to changes in emissions and tropospheric loss has signicant implications for ux inversions. Model inversions use the sensitivity of trace gas concentrations at a given location to perturbations of different emission sources to adjust those emissions so as to match observations at that location. The response of modeled CH4

DMFs to changing emissions depends on the models transport and chemical loss, as well as assumptions about the seasonal and spatial distribution of emissions relative to each other. Thus the model sensitivity kernel, the linear operator that maps emissions to CH4 concentrations, implicitly includes uncertainties in these terms. The models stratospheric response to emission perturbations differs from that of the troposphere and is subject to different transport and loss errors. Because the tropospheric transport errors covary with emissions, they alias into the resulting source attribution.

Comparing measurement and model stratospheric CH4 as a fraction of the total column provides a normalized comparison that isolates differences in the vertical structure from those caused by initial conditions and unbalanced sources and sinks. Figure 9 illustrates the error associated with the normalized stratospheric column and the associated stratospheric contribution to XCH4 at Park Falls. Although the stratosphere accounts for less than 30 % of XCH4, a relatively small error can produce signicant seasonal differences; the springtime error of 4.5 1017 molecules cm2 (23 ppb) is

more than twice the seasonal cycle amplitude. Winter and spring are also when XtCH4 is least sensitive to seasonal emissions; by contrast, the error is about 15 ppb in the summer, when seasonal emissions have the greatest inuence (Fig. 9, top panel). The seasonality of the stratospheric error will therefore distort the inversion mechanism and thus posterior emissions estimates.

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30

Seasonal CH 4(ppb)

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10

0

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-40 J F M A M J J A S O N D

40 Baring Head, NZ (41S)

30

Seasonal CH 4(ppb)

20

10

0

-10

-20

-30

-40 J F M A M J J A S O N D

Figure 8. NOAA surface ask (black) and GEOS-Chem surface level (red) seasonality of CH4 DMFs over 20052011 at Park Falls,

WI, USA and Baring Head, NZ. Lower and upper bounds denote the 25th and 75th percentiles, respectively, of detrended data for each month.

sonal cycle amplitude. The stratospheric contribution does not change, however, further demonstrating that the stratosphere is insensitive to perturbations to Northern Hemisphere emissions.

The impact of a static stratosphere and changing tropo-sphere is to make the seasonality of the aseasonal simulation XCH4 bimodal: the October local minimum in the base simulation becomes a fall absolute minimum. The aseasonal XCH4 agrees with TCCON in late winter, masking the greater disagreement in the troposphere. Notably, the main tropospheric features of the base simulation, the seasonal phase lag and spring persistence, are still apparent. Thus, the seasonality of emissions prescribed in the forward model is not the driver of the discrepancies between measurement and model XtCH4 seasonalities. OH is not likely the driver of these features, as

14012 K. M. Saad et al.: Assimilation of total column methane into models

0 1 4 7 10

0.5

CH4 (Gg)

Fraction seasonal emissions

90 Wetland emissions

10

0.4

0.3

60

8

0.2

30

0.1

6

0

Latitude

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CHcolumn (10moleccm)

4

17-2

Stratospheric model error Tropospheric dependence on emission seasonality

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CH 4DMF (ppb)

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-90 J F M A M J J A S O N D

-4

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70

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60

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50

Latitude

40

0

30

Figure 9. Top: Seasonally averaged fraction of model emissions from seasonally varying sources, north of 40 N. Bottom: Seasonally averaged normalized model stratospheric column error (teal)

and the difference between base and aseasonal simulation tropospheric columns (orange) at Park Falls.

Additional bias is introduced by differences in the seasonal patterns of [Delta1]XtCH4 and [Delta1]XCH4. Wetlands are the largest seasonal source of CH4 in models and the largest natural source in ux inventories, and their emissions are very uncertain: estimates range between 142 and 284 TgC year1 for the 2000

2009 time period (Kirschke et al., 2013). A priori GEOSChem CH4 emissions from northern high-latitude wetlands are extremely variable, with large uxes in June, July and August, moderate uxes in May and September, and almost no uxes the remainder of the year (Fig. 10a). Surface CH4 concentrations in models depend on the assumed seasonally varying emissions. Patra et al. (2011) found that correlations between the seasonal cycles of the forward model averages and in situ observations of CH4 DMFs at the surface varied for a given site by up to 0.78 0.4 depending on wetland

and biomass burning elds used. Model inversions that scale emissions in a given grid box based on the incorrect seasonality will invariably change the posterior attribution of seasonal emissions. Fraser et al. (2013) found that optimized wetland emissions from inversions that assimilate surface data only are smaller than the priors, while those from inversions that assimilate GOSAT total columns are larger, even if surface measurements are also assimilated. From this we infer that the transport errors in the models free troposphere lead to an optimization of the prior uxes of opposite sign to that of the emission errors that the inversion attempts to correct.

A two- to three-month shift in the phase of the XtCH4 seasonality will produce a strong under- or over-estimation of posterior wetland uxes in late spring through early fall. In an inversion, prior emissions are adjusted in proportion to the deviation of the models CH4 DMFs from observed val-

(a)

20

10

0

-10

J F M A M J J A S O N D

(b)

Figure 10. (a) GEOS-Chem monthly zonal mean wetland emissions, in Gg. (b) The Northern Hemisphere sensitivity of GEOSChem wetland emission attribution caused by a 3-month lag for each 1 ppb increase of CH4 in the tropospheric column, in Gg.

ues. Attribution of these posterior emissions to different sectors depends on a priori information and assumptions about how they vary in time and location relative to one another.Thus, an increase in posterior emissions relative to the prior in the northern mid- and high latitudes during winter will not change emissions from wetlands. For example, Fig. 10b illustrates the sensitivity of posterior wetland emissions to a three-month lag in the Northern Hemisphere. The change in posterior emissions is derived by calculating the total emissions required to produce an increase of 1 ppb of CH4 in each tropospheric column and scaling those emissions according to the a priori contribution of wetlands, estimated as the fractional contribution of wetlands to the total monthly mean emissions. The difference between this change in wetland emissions and the value in the same location three months prior produces the sensitivity of wetland emissions to the tropospheric phase lag. This approach provides an alternative to the computationally expensive calculation of the gain matrix over the entire time series but does not include information about model transport.

The tropics and subtropics are less sensitive to a phase shift, but polewards of 40 N, both the magnitude and seasonality of the difference are signicant. Large differences between measured and modeled XtCH4 are concurrent with low emissions from seasonal sources. The adjustments to prior emissions produced by larger measurementmodel disagreement that occur when seasonal sources are a small fraction of total emissions will overestimate posterior emissions

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K. M. Saad et al.: Assimilation of total column methane into models 14013

from aseasonal sources. Thus these seasonal errors will bias source apportionment toward emissions that do not vary on timescales shorter than annually.

5 Conclusions

Assimilation of total column measurements into CTMs can improve constraints on the global CH4 budget; however, the models treatment of stratospheric chemistry and dynamics must be carefully considered. This work has compared TCCON and GEOS-Chem pressure-weighted total and tropospheric column-averaged CH4 DMFs, XCH4, and XtCH4 respectively, parsing out the seasonality of the troposphere and stratosphere and the resulting impacts on XCH4 (Fig. 9a).

The Southern Hemisphere measurementmodel agreement is robust to changes in emissions or tropospheric OH. In the Northern Hemisphere the models stratospheric contribution is larger than that of the measurements, and the mismatch increases as the tropopause altitude decreases. The result is greater model error at high-latitude sites, with the magnitude of this error varying seasonally. Moreover, in the Northern Hemisphere the GEOS-Chem XtCH4 exhibits a 23 month phase lag. The combined tropospheric and stratospheric errors smooth the model XCH4 such that they may agree with total column measurements despite having an incorrect vertical distribution.

Model transport errors coupled with spatial and seasonal measurement sparsity can limit the accuracy of the location and timing of emissions scaling. The differences in the seasonality mismatch across vertical levels amplify the error uncertainty because the timing of optimized uxes will be especially susceptible to limitations in model transport. The stronger inuence of the stratosphere at higher latitudes due to lower tropopause heights, together with the higher temporal variability of the stratospheric fraction of the total column due to the stronger seasonal cycle of the tropopause, also impacts the seasonality of the meridional gradient of XCH4.

The inuence of stratospheric variability on emissions is not unique to the model chosen for this analysis. Bergamaschi et al. (2013) ran TM5-4DVAR inversions using SCIAMACHY column and NOAA surface measurements and found that the mean biases between the optimized CH4 proles and aircraft measurements differ between the PBL, free troposphere, and UTLS. Seasonal emissions from wet-lands and biomass burning vary by 10 and 7 TgCH4, re

spectively, from year to year, and the zonal partitioning of posterior emissions is sensitive to the wetland priors chosen. Moreover, the larger changes to emissions and sensitivity to assumptions in the Northern Hemisphere indicate that TM5 is also subject to the strong hemispheric differences found in GEOS-Chem. The TransCom-CH4 model comparison found that the interhemispheric exchange time in GEOS-Chem was near the model median over the 1996 2007 time series (Patra et al., 2011), which suggests that

GEOS-Chems interhemispheric transport, and thus associated errors, is not particularly distinct. Ostler et al. (2016) found that atmospheric CTM (ACTM) and other CTMs used in TransCom-CH4 are subject to transport errors that impact emissions optimization. Furthermore, ACTM proles show a similar over-estimation of stratospheric CH4, zonally varying measurementmodel mismatch dependent on tropopause height.

In this analysis we have used TCCON XtCH4 derived with the HF-proxy method; however, XtCH4 calculated using other stratospheric tracers such as nitrous oxide (N2O) (Wang et al., 2014) would provide an additional constraint on models representations of the stratosphere, as N2O is not subject to the spectral interference with water vapor that impacts HF. Information about the vertical tropospheric CH4 prole directly retrieved from NDACC spectra (Seplveda et al., 2014) can also be used to assess whether transport errors differ at different levels of the free troposphere. Ideally, information from these tropospheric products could be integrated to overcome the limitations of each: the sensitivity of XtCH4 to prior assumptions of STE and the sensitivity of prole retrievals to UTLS variability (Ostler et al., 2014).

A limitation of the aseasonal simulation was that the distribution of emissions was not identical to that of the base simulation due to the scaling approach we employed. Ideally, the aseasonal emissions for each sector would have been uxes calculated for each grid box from the base simulation annual emissions. The robustness of the models tropospheric phase shift, which was apparent regardless of the emissions used, demonstrates that this feature is not a product of the chosen emissions elds. However, more nuanced analysis on smaller spatial scales would benet from simulations that prescribe the annual mean for each of the seasonal sources.The most recent version of GEOS-Chem has a much more exible emissions scheme (Keller et al., 2014) that allows these more nuanced experiments to be performed and analyzed.

The insensitivity of model stratospheres to tropospheric change allows for a straightforward solution: prescribed stratospheric CH4 elds based on satellite observations from

ACE-FTS, MIPAS (von Clarmann et al., 2009), or a compilation of remote sensing instruments (Buchwitz et al., 2015). As the representation of tropical convection and exchange across the UTLS advances in models and reduces stratospheric isolation, chemical loss and transport mechanisms would need to be improved. The output from more accurate stratospheric models over the time period of interest could be used to set the stratospheric component in the ofine CH4 simulation. For instance, the Universal troposphericstratospheric Chemistry eXtension (UCX) mechanism, which has been added to more recent versions of GEOS-Chem, updates the stratospheric component of the standard full chemistry simulation such that CH4 has more sophisticated upwelling, advection, and chemical reaction

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14014 K. M. Saad et al.: Assimilation of total column methane into models

schemes (Eastham et al., 2014). Models that account for interannual variability in both stratospheric and tropospheric dynamics can then assimilate total column measurements to develop more accurate global CH4 budgets.

6 Data availability

The citations for the TCCON measurements in Table 1 are for the data les themselves and have individually assigned DOIs. They can be found at http://tccon.ornl.gov/

Web End =http://tccon.ornl.gov/ .

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Appendix A: Updates to tropospheric methane data

The TCCON XtCH4 data used in this analysis were developed as in Saad et al. (2014) with several adjustments to both the parameters used and the methodology.

The HF-proxy method for determining XtCH4 incorporates the relationship between CH4 and HF in the stratosphere, which is calculated using ACE-FTS data. These CH4-HF slopes now use updated ACE-FTS version 3.5 measurements with v.1.1 ags (Boone et al., 2013; Sheese et al., 2015). The data quality ags are provided for prole data on a 1 km vertical grid, which uses a piecewise quadratic method to interpolate from the retrievals (Boone et al., 2013). Additionally, the CH4 and HF measurement errors are now considered in the pressure-weighted linear regression that determines the slopes. All other data processing to produce the CH4-HF slopes followed methods described in Saad et al. (2014). Figure A1 shows the updated annual zonal values used to calculate XtCH4 with Washenfelder et al. (2003) and MkIV (re

trieved from http://mark4sun.jpl.nasa.gov/m4data.html

Web End =http://mark4sun.jpl.nasa.gov/m4data.html ) values included for reference (cf. Saad et al., 2014, their Fig. 2).These updates altered XtCH4 for the sites and time period cov

ered in this paper by less than 2 ppb.

The derivation of the tropospheric column in Washen-felder et al. (2003), Saad et al. (2014), and Wang et al. (2014) implicitly assumed that the CH4 prole is continuous across the tropopause; however, the boundary condition for stratospheric CH4 is rather set by tropospheric air transported through the tropical tropopause (Brewer, 1949;Dobson, 1956). Boering et al. (1996) showed that the concentration of CO2 directly above the tropopause can be approximated by introducing a two-month phase lag to the average concentration at northern and southern tropical surface sites: Mauna Loa, Hawaii (MLO) and Tutuila, American Samoa (SMO), respectively. As the CH4 entering the stratosphere originates in both hemispheres (Boering et al., 1995), stratospheric CH4 exhibits a smaller interhemispheric gradient than in the troposphere: about 20 ppb, as calculated from ACE-FTS measurements, vs. about 50 ppb, taken as the difference at MLO and SMO. To calculate the stratospheric boundary condition for CH4 we remove the seasonal component of the mean of CH4 DMFs at MLO and SMO, which are made available through 2014 by the NOAA Earth System Research Laboratory (ESRL) Global Monitoring Division (Dlugokencky et al., 2016). To capture the interhemispheric gradient observed in ACE stratospheric CH4 measurements, we add and subtract 10 ppb, in the northern and southern extratropics respectively, the limits of which we choose as the Tropic of Cancer (23 N) and the Tropic of Capricorn (23 S). A constant value is chosen in each hemisphere to reect the rapid mixing time of air from the extra-tropics in the region directly above the tropopause, which Boering et al. (1996) found to be less than one month. Within the tropics, we interpolate the boundary condition as a linear function of altitude such that xCH4(P t) = xsCH4 + 1023 , where xCH4(P t) is

1976 1980 1984 1988 1992 1996 2000 2004 2008 2012

-850

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MkIV 6090 N 3060

N

030 N

030 S 3060 S

CH 4-HF slope

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2004 2006 2008 2010 2012

Washenfelder et al. 2003 MkIVACE-FTS

Figure A1. Long-term CH4HF slopes from Washenfelder et al. (2003), MkIV, and updated ACE-FTS measurements. Inset: Time series of zonal pressure-weighted ACE-FTS slopes ( ) used to calculate X

tCH4, with error bars denoting the 2 standard error. Zonal

slopes are offset each year for visual clarity.

the boundary condition at the tropopause, xsCH4 is the mean DMF of CH4 at the surface, and is the latitude of the site.

Assuming hydrostatic equilibrium, the tropospheric column of CH4, ctCH4, can be calculated as the integral of the vertical prole, xCH4 xCH4(P ), from the surface, P s, to the

tropopause, P t:

ctCH4 =

P s

[integraldisplay]P t

xCH4 d

P

gm = XtCH4

P s P t gt m

, (A1)

where P is the pressure height, g is the gravitational acceleration, gt is the pressure-weighted tropospheric value

of g, and m is the mean molecular mass of CH4 (Washen-felder et al., 2006). The prole of CH4 in the stratosphere can be expressed as a linear function of pressure altitude, xCH4(P ) = xCH4(P t) + P , where = dxCH4dP is the strato

spheric loss of CH4. This stratospheric loss term is estimated by the HF-proxy method to produce the retrieved tropospheric column-averaged DMF, XtCH4, such that

XtCH4

P sg m =tCH4 =

P s

[integraldisplay]0

xCH4 d

P gm

P t

[integraldisplay]0

P

dP

gm, (A2)

where g is the pressure-weighted column average of g. The

stratospheric boundary condition can thus be related to the retrieved tropospheric column as

P t

[integraldisplay]0

xCH4 d

P gm =

P t

[integraldisplay]0

xCH4 P t

[parenrightbig]

dP

gm tCH4 +

P s

[integraldisplay]0

xCH4 d

P

gm. (A3)

Given that the total column integration is the sum of the tropospheric and stratospheric partial columns, and substi-

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14016 K. M. Saad et al.: Assimilation of total column methane into models

tuting Eq. (A3),

P s

[integraldisplay]P t

1875

1850

xCH4 d

P gm =

P s

[integraldisplay]0

xCH4 d

P gm

P t

[integraldisplay]0

xCH4 d

P

gm (A4)

1825

=

P s

[integraldisplay]0

xCH4 d

P gm

P t

[integraldisplay]0

xCH4(P t) d

P

gm +tCH4,

TCCON XCH 4TR (ppb)

1800

1775

1750

P s

[integraldisplay]0

xCH4 d

P

gm, (A5)

1725

1700

=tCH4

P t

[integraldisplay]0

xCH4 P t

[parenrightbig]

dP

gm, (A6)

XtCH4

1675

P s P t gt m =

XtCH4

P s g m

xCH4 P t

[parenrightbig]

P t g0 m

Figure A2. Calibration curve of TCCON Xt

CH4 (cf. Wunch et al.,

2015, their Fig. 8). Site colors are as in Fig. 1. Aircraft campaigns are described in Table 6 of Wunch et al. (2015).

Air-mass-dependent artifacts were derived for updated values consistently with the total column CH4 (Wunch et al., 2015). Removing these artifacts, the XtCH4 was then calibrated with in situ aircraft proles using the same methodology described in Wunch et al. (2010) and including the updates delineated in Wunch et al. (2015) to produce a calibration correction factor of 0.9700 (Fig. A2). The covariance between the difference between the calibrated TCCON and aircraft XtCH4 and several parameters were assessed to ensure biases were not introduced into the measurements. These differences had an uncertainty-weighted correlation coefcient of 0.1 for solar zenith angle and uncertainty-weighted correlation coefcients of less that 0.02 for tropopause and surface pressures, year, and season. Measurement precisions and errors were determined as in Saad et al. (2014), with the additional uncertainties mentioned in this section included. Individual TCCON sites have median XtCH4 precisions in the range of 0.10.8 %, and mean and median precisions are 0.3 and 0.2 %, respectively, for all sites through May 2016.

, (A7)

where g0 is the pressure-weighted average of g from the

tropopause to the top of the atmosphere. While the molecular mass of air changes as a function of water vapor and thus altitude and gravity changes as a function of both altitude and latitude, assuming constant values of g and m changes XtCH4 by less than 2 ppb. Thus, to good approximation these variables can be canceled out:

XtCH4

P s P t[bracketrightbig]= XtCH4 P s xCH4(P t) P t, (A8)

XtCH4 =

XtCH4 P s xCH4 P t

P t P s P t

[parenrightbig]

. (A9)

The surface pressure is measured at each site, and the tropopause pressure is calculated from the TCCON prior temperature proles. The uncertainties associated with the interpolated value of the tropopause height are determined by calculating XtCH4 for 30 % of P t and adding these condence intervals in quadrature to the precision error of XtCH4.

The aforementioned deseasonalization of xCH4(P t) is an approximation that adds another uncertainty. The signal of the tropospheric seasonal cycle of a trace gas entering the stratosphere is apparent directly above the tropopause and both dampens in amplitude and shifts in time with increasing altitude (Mote et al., 1996). Thus, the stratospheric boundary condition is not truly constant throughout the column, but rather the pressure-weighted sum of these attenuated signals. Calculating xCH4(P t) without removing the seasonality, which provides the maximum impact of this uncertainty, decreases XtCH4 by an average of 1 and 4 ppb in the Northern and Southern Hemispheres, respectively, and does not alter the seasonal cycle of XtCH4. Moreover, as described below, the mismatch between the calibrated TCCON XtCH4 and the in situ aircraft XtCH4 does not correlate with season (R2 = 0.017). Thus, we retain the simpler computation of

deseasonalized xCH4(P t) in Eq. (A9).

1700 Aircraft XCH4 TR (ppb)

1725 1750 1775 1800 1825 1850 1875

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Appendix B: GEOS-Chem simulations

B1 Equilibrium sensitivity experiments

All equilibrium runs for a given simulation have identical meteorology, emissions, and OH elds over June 2004May 2005. Initial conditions for each year are set by the restart les of the previous run. To calculate columns at each site, GEOS-Chem monthly mean mole fractions are adjusted for the monthly medians of the sites daily mean surface pressures and smoothed with the monthly median scaled prior proles and averaging kernels, interpolated using the monthly medians of the daily mean solar zenith angles. Because Park Falls and Lauder are the only TCCON sites that had started taking measurements over this time period, they are the only sites used to generate smoothed columns for the comparisons to the experimental simulations.

Emissions in the aseasonal simulation were derived by running a two-dimensional regression on the annual emissions to determine the scale factors that would produce the smallest residual of total emissions and the interhemispheric gradient. Figure B1 illustrates the difference in total emissions between the base and aseasonal simulations for each zonal band.

The updated OH simulation used OH output from a 2012 GEOS-Chem standard chemistry simulation with extensive updates to the photochemical oxidation mechanisms of biogenic volatile organic compounds (VOCs), described in Bates et al. (2016) and references therein. These were converted to 3-D monthly mean OH concentrations to conform to the infrastructure of the GEOS-Chem ofine CH4 tropospheric loss mechanism. The OH was then scaled by 90 % to keep the lifetime above 8 years, and emissions were scaled by 112 % to maintain the same balance between sources and sinks in the base simulation. Figure B2 provides zonal averages of the difference between the base and updated OH columns.

The full list of simulations run is provided in Table B1, with descriptions and the CH4 emissions, tropospheric OH, and total chemical loss lifetimes. Figure B3 shows each simulations seasonality of XtCH4 at Park Falls, with TCCON seasonality plotted for reference, as well as the seasonality of the difference between the base and each simulation.

B2 Derivation of dry gas values

Versions of GEOS-Chem prior to v.10 have inconsistencies in wet vs. dry denitions of pressure, temperature, and air mass, which propagate into model diagnostics and conversions calculated using these terms. As a consequence, CH4 concentrations are output assuming air masses that include water vapor but calculated with the molar mass of dry air.For all comparisons in this analysis CH4 DMFs are calculated taking into account the GEOS-5 specic humidity, qs

-90 J F M A M J J A S O N D

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~CH4 (Tg mo

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60

1

30

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0

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Figure B1. Monthly averages of the difference in total CH4 emissions between the base and aseasonal GEOS-Chem simulations, summed over each zonal band, in Tg mo1.

~OH (10 molec cm )

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-5

-90 J F M A M J J A S O N D

Figure B2. Zonal averages of the difference in total column OH (molecules cm2) between the base and updated monthly OH elds.

(in units of gH2O kg1air), such that

xCH4,dry =

xCH4

1 qs 103

(B1)

where xCH4 is the model prole in mole fractions. Dry air proles were derived by subtracting the water vapor mole fraction, also calculated from the GEOS-5 specic humidity, from the total air mass at each pressure level, as in Wunch et al. (2010) and Geibel et al. (2012).

B3 Model smoothing for measurement comparisons

Base and aseasonal daily runs were initialized using CH4 elds from their respective 34th equilibrium cycles. Daily CH4 mole fractions averaged over both 24 h and 10:0014:00 local time were output to test whether TCCONs daytime-only observations would introduce a bias in the comparisons. Measurementmodel differences were not sensitive to averaging times. Comparison of measurements to model

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14018 K. M. Saad et al.: Assimilation of total column methane into models

Table B1. List of sensitivity experiments.

Simulation name Description CH4 lifetime (years) with respect to Final CH4 Emissions Tropospheric OH Total Loss Burden (Tg)

Base Default OH and emissions 9.6 10.7 9.7 4825 Aseasonal Constant monthly emission rates 9.6 10.7 9.7 4872 Updated OH Monthly OH elds from standardchemistry + biogenic VOCs, scaled

down by 10 %

8.5 9.4 8.6

4828

Unscaled updated OH Monthly OH elds from standard chemistry + biogenic VOCs

7.7 8.4 7.8 4917

90 % OH Default OH scaled down by 10 % 10.5 11.9 10.7 5296 110 % OH Default OH scaled up by 10 % 8.8 9.7 8.8 4425 Scaled rice emissions Rice emissions increased by 20 % 9.6 10.7 9.6 4780 No wetlands Wetland emissions turned off 10.7 10.6 9.5 3768 Scaled livestockEmissions

Scale livestock emissions by 50 % 9.6 10.7 9.6 4359

MERRA MERRA meteorology elds 9.6 10.7 9.6 4849 Tropopause level Set top of troposphere 2 vertical levelshigher

9.6 10.6 9.6 4855

Aseasonal

Updated OH

90 % OH

110 % OH

Unscaled updated OH

20

20

20

20

20

Seasonal CH 4(ppb)

-20

10

10

10

10

10

0

0

0

0

0

-10

-10

-10

-10

-10

-20

-20

-20

-20

J FM A M J J A SO N D

J FM A M J J A SO N D

J FM A M J J A SO N D

J FM A M J J A SO N D

J FM A M J J A SO N D

No wetlands

Scaled livestock emissions

Tropopause level

MERRA

20

Scaled rice emissions

TCCON XtCH GEOS-Chem XtCH Base-simulation X tCH

20

20

20

20

Seasonal CH 4(ppb)

-20

10

10

10

10

10

0

0

0

0

0

-10

-10

-10

-10

-10

-20

-20

-20

-20

J FM A M J J A SO N D

J FM A M J J A SO N D

J FM A M J J A SO N D

J FM A M J J A SO N D

J FM A M J J A SO N D

Figure B3. Seasonality of tropospheric methane (Xt

CH4) at Park Falls for TCCON (black solid line), GEOS-Chem (red solid line), and the

difference from the base simulation (dotted red line) for each of the sensitivity experiments, in ppb.

columns produced using the 24 h and 10:0014:00 LT averages produce equivalent slopes and only slightly different intercepts and correlation coefcients. The seasonality of 10:0014:00 LT column-averaged DMFs does not differ, except for the fall seasonal maximum of the adjusted troposphere and stratospheric contribution at Park Falls in October, one month later than the 24 h column-averaged DMF seasonality.

CH4 dry vertical proles for each grid box associated with a TCCON site, xmCH4, were smoothed with corresponding

FTS column averaging kernels, aCH4, and scaled priors for each day and vertically integrated using pressure-weighted levels:

XsCH4 = CH4 XaCH4 + aCH4 [parenleftBig]

xmCH4 CH4xaCH4[parenrightBig]

(B2)

where XsCH4 is the smoothed GEOS-Chem column-averaged DMF, CH4 is the TCCON daily median retrieved prole scaling factor, and xaCH4 and XaCH4 are respectively the a priori prole and column-integrated CH4 DMFs (Rodgers and

Connor, 2003). The pressure weighting function, h, was applied such that X = hT x. TCCON priors were interpolated

to the GEOS-Chem pressure grid, and GEOS-Chem pressure and corresponding gas proles were adjusted using daily mean surface pressures local to each site (Wunch et al., 2010;Messerschmidt et al., 2011). The averaging kernels were in-

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K. M. Saad et al.: Assimilation of total column methane into models 14019

terpolated for the local daily mean solar zenith angle and the GEOS-Chem pressure grid so that it could be applied to the difference between the GEOS-Chem and TCCON proles as ax =

PN

i=1aihixi from the surface to the highest level, N, at i pressure levels (Connor et al., 2008; Wunch et al., 2011b). Figure B4 shows how the smoothed column compares to the column that only uses the dry gas correction.

Appendix C: Derivation of stratospheric contribution

Considering the CH4 prole integration as in Eq. (A4), and substituting the prole of CH4 in the stratosphere, xCH4(P ) = xCH4(P t) + P , described in Appendix A, the

total column is calculated as:

P s

[integraldisplay]0

xCH4 d

P gm =

P s

[integraldisplay]P t

xCH4 d

P gm +

P t

[integraldisplay]0 [bracketleftbig]x

CH4 P t

1900 Tropospheric column

Dry CH 4 (ppb)

[parenrightbig]

+ P

[bracketrightbig]

dP

gm, (C1)

XCH4 P s = XtCH4

P s P t

[bracketrightbig]

+xCH4 P t

[parenrightbig]

Smoothed CH 4(ppb)

1650

P t + c CH4, (C2)

where c CH4 is the pressure-weighted column average of CH4 loss in the stratosphere. Rearranging terms, Eq. (C2) becomes:

hXCH4 XtCH4[bracketrightBig]

P s = [bracketleftBig]

xCH4 P t

[parenrightbig]

XtCH4

1850

1800

1750

1700

iP t + c CH4, (C3)

XtCH4 XCH4 = [bracketleftBig]

XtCH4 xCH4 P t

[parenrightbig][bracketrightBig]

P tP s

1650 1700 1750 1800 1850 1900

c CH4

Dry CH 4 (ppb)

Smoothed CH 4(ppb)

1650

P s , (C4)

such that the difference between the tropospheric and total column-averaged DMFs is a function of the two terms governing the stratospheric contribution to the total column: the gradient across the tropopause, xCH4(P t)XtCH4, and stratospheric CH4 loss, c CH4. The stratospheric contribution is thus a proxy for the impact of stratospheric variability on the total column of CH4: given a constant tropospheric column, as the stratospheric contribution becomes larger the total column-averaged DMF becomes smaller.

1900 Total column

Dry ~ CH 4 (ppb)

1850

1800

1750

1700

1650 1700 1750 1800 1850 1900

125 Stratospheric contribution

Smoothed ~CH 4(ppb)

100

75

50

25

0 0 25 50 75 100 125

Figure B4. GEOS-Chem smoothed vs. dry integrated CH4 DMFs for base simulation tropospheric columns, total columns, and stratospheric contribution. Site colors are as in Fig. 1. Dashed lines mark the one-to-one lines.

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14020 K. M. Saad et al.: Assimilation of total column methane into models

Acknowledgements. This work was supported by NASA Headquarters under the NASA Earth and Space Science Fellowship Program grant NNX14AL30H and NASAs Carbon Cycle Science program. Park Falls, Lamont, and JPL are funded by NASA grants NNX14AI60G, NNX11AG01G, NAG5-12247, NNG05-GD07G, and NASA Orbiting Carbon Observatory Program; we are grateful to the DOE ARM program and Jeff Ayers for their technical support in Lamont and Park Falls, respectively. Darwin and Wollongong are funded by NASA grants NAG5-12247 and NNG05-GD07G and the Australian Research Council grants DP140101552, DP110103118, DP0879468, and LP0562346, and Nicholas Deutscher is supported by an Australian Research Council Fellowship, DE140100178; we are grateful to the DOE ARM program for technical support in Darwin. Bremen, Bialystok, and Orleans are funded by the EU projects InGOS and ICOS-INWIRE and by the Senate of Bremen.Runion Island is funded by the EU FP7 project ICOS-INWIRE, the national Belgian support to ICOS and the AGACC-II project (Science for Sustainable Development Program), the Universit de la Runion, and the French regional and national organizations (INSU, CNRS). From 2004 to 2011 the Lauder TCCON program was funded by the New Zealand Foundation of Research Science and Technology contracts CO1X0204, CO1X0703, and CO1X0406. We thank Shuji Kawakami for his technical support in Saga. We thank Peter Bernath, Kaley Walker, and Chris Boone for their guidance using the ACE-FTS data, which were obtained through the Atmospheric Chemistry Experiment (ACE) mission, primarily funded by the Canadian Space Agency. We are grateful to Geoff Toon for his continuous efforts developing the GGG software, for providing the MkIV data, and his input on the manuscript. We thank Arlyn Andrews for providing the LEF surface ask data, which were generated by NOAA-ESRL, Carbon Cycle Greenhouse Gases Group. Baring Head NIWA surface data were provided courtesy of Gordon Brailsford, Dave Lowe, and Ross Martin. We also acknowledge the contributions of in situ vertical proles from the AirCore, HIPPO, IMECC, INTEX, Learjet, and START08 campaigns. We are grateful to Kelvin Bates for providing monthly OH elds for the GEOS-Chem Updated OH sensitivity experiments. Lastly, we thank the three anonymous reviewers who provided feedback and suggestions.

Edited by: P. JckelReviewed by: three anonymous referees

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Atmos. Chem. Phys., 16, 1400314024, 2016 www.atmos-chem-phys.net/16/14003/2016/