Contributions of the troposphere and stratosphere to CH 4 model biases

Abstract. Inverse modelling is a useful tool for retrieving CH4 fluxes; however, evaluation of the applied chemical transport model is an important step before using the inverted emissions. For inversions using column data one concern is how well the model represents stratospheric and tropospheric CH4 when assimilating total column measurements. In this study atmospheric CH4 from three inverse models is compared to FTS (Fourier transform spectrometry), satellite and in situ measurements. Using the FTS measurements the model biases are separated into stratospheric and tropospheric contributions. When averaged over all FTS sites the model bias amplitudes (absolute model to FTS differences) are 7.4 ± 5.1, 6.7 ± 4.8, and 8.1 ± 5.5 ppb in the tropospheric partial column (the column from the surface to the tropopause) for the models TM3, TM5-4DVAR, and LMDz-PYVAR, respectively, and 4.3 ± 9.9, 4.7 ± 9.9, and 6.2 ± 11.2 ppb in the stratospheric partial column (the column from the tropopause to the top of the atmosphere). The model biases in the tropospheric partial column show a latitudinal gradient for all models; however there are no clear latitudinal dependencies for the model biases in the stratospheric partial column visible except with the LMDz-PYVAR model. Comparing modelled and FTS-measured tropospheric column-averaged mole fractions reveals a similar latitudinal gradient in the model biases but comparison with in situ measured mole fractions in the troposphere does not show a latitudinal gradient, which is attributed to the different longitudinal coverage of FTS and in situ measurements. Similarly, a latitudinal pattern exists in model biases in vertical CH4 gradients in the troposphere, which indicates that vertical transport of tropospheric CH4 is not represented correctly in the models.

Abstract. Inverse modelling is a useful tool for retrieving CH 4 fluxes; however, evaluation of the applied chemical transport model is an important step before using the inverted emissions. For inversions using column data one concern is how well the model represents stratospheric and tropospheric CH 4 when assimilating total column measurements. In this study atmospheric CH 4 from three inverse models is compared to FTS (Fourier transform spectrometry), satellite and in situ measurements. Using the FTS measurements the model biases are separated into stratospheric and tropospheric contributions. When averaged over all FTS sites the model bias amplitudes (absolute model to FTS differences) are 7.4 ± 5.1, 6.7 ± 4.8, and 8.1 ± 5.5 ppb in the tropospheric partial column (the column from the surface to the tropopause) for the models TM3, TM5-4DVAR, and LMDz-PYVAR, respectively, and 4.3 ± 9.9, 4.7 ± 9.9, and 6.2 ± 11.2 ppb in the stratospheric partial column (the column from the tropopause to the top of the atmosphere). The model biases in the tropospheric partial column show a latitudinal gradient for all models; however there are no clear latitudinal dependencies for the model biases in the stratospheric partial column visible except with the LMDz-PYVAR model. Comparing modelled and FTS-measured tropospheric column-averaged mole fractions reveals a similar latitudinal gradient in the model biases but comparison with in situ measured mole fractions in the troposphere does not show a latitudinal gradient, which is attributed to the different longitudinal coverage of FTS and in situ measurements. Similarly, a latitudinal pattern exists in model biases in vertical CH 4 gradients in the troposphere, which indicates that vertical transport of tropospheric CH 4 is not represented correctly in the models.
Published by Copernicus Publications on behalf of the European Geosciences Union.

Introduction
Atmospheric methane (CH 4 ) is the second most important anthropogenic greenhouse gas. Atmospheric CH 4 concentrations began to rise again in 2007 after a decade of nearzero growth (Rigby et al., 2008). Possible explanations for the stability of CH 4 concentrations during 1999-2006 include an increase in anthropogenic emissions and coincident decrease in wetland emissions (Bousquet et al., 2006), decreased Northern Hemisphere microbial sources (Kai et al., 2011), and a combination of decreasing-to-stable fossil fuel emissions and stable-to-increasing microbial emissions (Kirschke et al., 2013). Several possible reasons for the renewed growth of CH 4 concentrations after 2006 have been proposed, including the increase of wetland emissions during 2007 and 2008 in either the tropics, owing to greater than average precipitation, and/or in the Arctic, owing to high temperatures (Dlugokencky et al., 2009); the anthropogenic contribution at the tropics and midlatitudes in the Northern Hemisphere during the period 2007-2010 ; an increase of emissions from oil and gas production and use during 2007-2014 (Hausmann et al., 2016); and from agriculture (Schaefer et al., 2016).
Prediction of the evolution of CH 4 in the atmosphere requires knowledge of the sources and sinks. Inverse modelling is usually used to retrieve fluxes from observations of atmospheric concentrations. The commonly used measurements include surface measurements from global networks, such as the NOAA/ESRL (Earth System Research Laboratory of the National Oceanic and Atmospheric Administration), and total column data from satellites, such as the SCIAMACHY (SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY) or GOSAT (Greenhouse gases Observing Satellite). However, compared to total column data the surface measurements characterise the boundary layer only and CH 4 concentrations in the boundary layer are sensitive to boundary layer height, which is difficult to accurately simulate in a global transport model. The total column measurements are less sensitive to model errors in the vertical distributions of CH 4 . However, they are also only sensitive to broader-scale signatures. Compared to satellite measurements, surface in situ measurements have poor spatial coverage but are more precise and less subject to biases. Total column measurements of CH 4 include a contribution from the stratosphere where the concentrations are influenced by dynamical processes like meridional transport, tropopause variations, and subsidence associated with the polar vortex, and chemistry. If a transport model does not accurately simulate these processes, the retrieved sources and sinks using total column measurements will not be correct (Locatelli et al., 2015a, b). Especially in the polar region, the tropopause height varies strongly and the dynamical processes are complex. Turner et al. (2015) compared GOSAT CH 4 with GEOS-Chem simulations, and found large differences at high latitudes. They proposed that the model bias in total column CH 4 at high latitudes comes from the stratosphere since the validation with TCCON (Total Carbon Column Observing Network), NOAA surface and aircraft measurements, and HIPPO shows good performances of the model in the troposphere. Ostler et al. (2016) assessed accuracies of models in the stratosphere by replacing modelled stratospheric CH 4 with satellite measurements. They found that modelled stratospheric CH 4 shows large scatter and the corrected total columns of CH 4 show improved or degraded agreements with TCCON measurements depending on the used satellites and models. These results imply that satellite-based stratospheric CH 4 is not accurate enough to resolve a possible stratospheric contribution to model biases in total column CH 4 as uncovered by TCCON. TCCONbased measurements could fulfil such a role, as presented in Saad et al. (2016) and this study. Using HF as a proxy, Saad et al. (2016) derived tropospheric CH 4 products and investigated the impact of stratospheric and tropospheric model biases in GEOS-Chem on inversions. They found an increasing stratospheric mismatch with decreasing tropopause altitudes and a phase lag in modelled tropospheric seasonality. A small bias in the modelled CH 4 column could come from counteracting stratospheric and tropospheric model errors. They noted that the tropospheric time lag can produce large errors in posterior wetland emissions at high northern latitudes.
In this study the model biases in the stratosphere and troposphere are assessed with respect to the latitudinal pattern. In order to investigate the accuracy of the models several measurements are used: (i) total, tropospheric, and stratospheric column-averaged CH 4 mole fractions measured at the TCCON Wang et al., 2014), which are used to separate stratospheric and tropospheric contributions to model bias in total columns; (ii) total columnaveraged CH 4 mole fraction measured by GOSAT (Parker et al., 2011) and CH 4 profiles measured by TES (Tropospheric Emission Spectrometer) (Worden et al., 2012); (iii) surface CH 4 measured within the NOAA network (Dlugokencky et al., 1994); and (iv) in situ CH 4 profiles from aircraft campaign HIPPO (HIAPER Pole-to-Pole Observations) (Wofsy et al., 2012). In the following, Sect. 2 presents the measurements, models, and analysis approach, while Sect. 3 presents the results and discussions. Conclusions are drawn in Sect. 4.

Measurements and models
We work here with near-infrared spectra of TCCON, from which the tropospheric CH 4 is derived using an a posteriori correction method in contrast to the direct profile retrieval (Sepúlveda et al., 2014) being applied to mid-infrared spectra. The tropospheric CH 4 is derived through removing stratospheric contributions in total column CH 4 . The stratospheric contributions are estimated from stratospheric N 2 O columns derived from total N 2 O columns. A calibration of the method against in situ measurements shows an agree-Atmos. Chem. Phys., 17, 13283-13295, 2017 www.atmos-chem-phys.net/17/13283/2017/ Figure 1. Calibration results of FTS-derived tropospheric column-averaged CH 4 mole fractions against in situ measurements. The in situ profiles are smoothed using GFIT CH 4 averaging kernels in the troposphere as described in Wang et al. (2014). The FTS data are averaged for the in situ measurement periods. The IMECC is an aircraft campaign over Europe (Geibel et al., 2012). The Lamont-AirCore measurements are from Greenhouse Gas Group Aircraft Program (http://www.esrl.noaa.gov/gmd/ccgg/aircraft/). The AirCore data at Sodankylä is from the FTS group there. ment within 3.0 ± 2.0 ppb (see Fig. 1). Given the total and tropospheric CH 4 columns, stratospheric column-averaged CH 4 is derived using knowledge of the tropopause pressure. The TCCON sites used in this study are listed in Table 1, the products are all using the GGG2014 version , except for at Ny-Ålesund. The CO 2 proxy retrieval method (Frankenberg et al., 2011) is applied in GOSAT data, which infers dry air columns from the CO 2 columns retrieved from the same spectra as used in the CH 4 retrieval. This method assumes the CO 2 concentra-tions are known and provided by model simulations (the Car-bonTracker model). The GOSAT total column-averaged dryair CH 4 mole fractions used here are version UoL-OCPRv7 and only spectra measured in clear-sky conditions are used (Parker et al., 2011). GOSAT has a ground footprint diameter of about 10.5 km and 4 s exposure duration. The TES instrument measures atmospheric radiances from which atmospheric profiles are inferred using an optimal estimation algorithm subject to a priori constraints. The CH 4 retrieval of TES has a DOFS (degree of freedom for signal) of about 0.8- Vertical gradients of tropospheric CH 4 can be qualitatively calculated by using the comparative tropospheric columnaveraged CH 4 and surface CH 4 . Only long-term timescales are used here, and variations with scales longer than 1.4 years are extracted from the time series of tropospheric and surface CH 4 . TCCON and in situ sites are selected to be located close to one another so that both instruments measure similar air masses. The sites and measurements are listed in Table 3.
The CH 4 measurements during HIPPO 1-5 are those made with a quantum cascade laser spectrometer (QCLS). Calibrations derived through comparisons with NOAA Programmable Flask Package measurements are applied.
The models used in this study are TM3, TM5-4DVAR, LMDz-PYVAR; details are given in Table 2. All the three models are optimised against in situ measurements at the surface through inversions of CH 4 surface emissions. The first two models used a common emission a priori for their inversion runs. Detailed information on the inversion methodology is discussed in Bergamaschi et al. (2015). The LMDz-PYVAR uses different a prior and background stations as constraints, the BG-SP (background network -transport parameterisation scheme) set-up described in Locatelli et al. (2015b). The chemical reactions considered in the models are the oxidation by OH in the troposphere and by Cl, OH, and O( 1 D) in the stratosphere. The fields of the radicals are prescribed monthly with no interannual changes.
Details on the global atmospheric tracer model TM3 can be found in Heimann and Körner (2003) and the inversion method of the Jena CarboScope is described in Rödenbeck (2005). TM5-4DVAR is a four-dimensional data assimilation system for inverse modelling of atmospheric methane emission (Meirink et al., 2008). The system is based on the TM5 atmosphere transport model (Krol et al., 2005). LMDz-PYVAR is a framework that combines the inversion system PYVAR (Chevallier et al., 2005;Pison et al., 2009) with the transport model LMDz (Hourdin et al., 2006).
For evaluation of the models, we interpolate the simulations in time, latitude, longitude, and pressure to match the measurements. For the total and tropospheric columnaveraged CH 4 the model profile is integrated taking the a priori and averaging kernel into account according to Rodgers and Connor (2003) using Eqs. (9) and (14) from Wang et al. (2014). In contrast to FTS and GOSAT the transformation of model CH 4 profiles to the counterpart of TES is done in logarithms of a prior and model quantities. The thermal tropopause calculated using the ERA-Interim reanalysis data is used in all calculations, and would not be so accurate for the TM5 and LMDz models, especially for LMDz, which predicts its own meteorology fields through nudging to reanalysis data.

Comparison between measurements and models
The CH 4 column meridional distribution is sensitive to the latitudinal distribution of CH 4 sources and sinks, tropopause altitudes, inter-hemisphere transport in the troposphere, and the residual circulation in the stratosphere. Assessing latitudinal variabilities of biases of a model could reveal how well these processes are represented in the model. Another important concern of this study is to determine which of the tropospheric or stratospheric components contributes more to the model biases in the total column. The model to FTS comparison covers the period 2007-2011 when FTS measurements are available and the comparison to GOSAT is for the period 2009-2011. The latitudinal behaviour of the model bias in total column-averaged CH 4 mole fractions is revealed by comparisons to FTS and GOSAT measurements as presented in Fig. 2, similarly to previous work (Monteil et al., 2013). CH 4 is emitted mainly in the Northern Hemisphere, destroyed mainly in the tropics by OH, and has a slow interhemisphere transport with a temporal scale of approximately 1 year. CH 4 is transported into the stratosphere mostly in the tropics and back to the troposphere in the extratropics by the residual circulation. In the troposphere, CH 4 concentrations are higher in the Northern Hemisphere than in the Southern Hemisphere with a gradient throughout the tropics. In the stratosphere, CH 4 has a more or less symmetrical distribution between the two hemispheres. In Fig. 2  With FTS-derived tropospheric and stratospheric columnaveraged CH 4 (Wang et al., 2014), it is possible to examine how the tropospheric and stratospheric partial columns contribute to the model bias in the total column-averaged CH 4 . The partial columns are represented as the tropospheric and stratospheric column-averaged mole fractions scaled by the fraction of the partial air column. Figure 3 shows yearly and seasonal median model biases in the troposphere and stratospheric partial columns. It is clear that model biases in the tropospheric partial column exhibit a north-south gradient with positive values at northern high latitudes during all seasons for all models. The model biases in the stratospheric partial column do not present any clear latitudinal pattern that persists throughout the whole year and shows significant seasonal variabilities for TM3 and TM5-4DVAR. This is consistent with the fact that stratospheric CH 4 distributions cycle between summer and winter hemispheric states. In the case of LMDz-PYVAR there is a permanent pattern in the stratospheric partial column biases that is more negative in the south. This pattern is consistent with the north-south gradient in the total column biases. Compared to Fig. 2 one can see that the latitudinal pattern of model biases in total column-averaged CH 4 results from both the stratosphere and troposphere for LMDz-PYVAR, but arises from the troposphere for TM3 and TM5. The model biases change signs yearly and seasonally; therefore it is more appropriate to use the amplitudes (absolute model to FTS differences) to evaluate the contributions of the troposphere and stratosphere. The medians of model bias amplitudes over all FTS sites and years are 7.4 ± 5.1 ppb in the tropospheric partial column and 4.3 ± 9.9 ppb in the stratospheric partial column for TM3, 6.7 ± 4.8 and 4.7 ± 9.9 ppb for TM5-4DVAR, and 8.1 ± 5.5 and 6.2 ± 11.2 ppb for LMDz-PYVAR.
Evaluations of the models at the surface using in situ measurements, which are assimilated into the models, show smaller biases than the tropospheric column-averaged CH 4 . The amplitudes are mostly below 10 ppb in the Northern Hemisphere except for a few outliers and below 5 ppb in the Southern Hemisphere (not shown). The model biases at the surface do not show any significant latitudinal dependence that is present in the model biases of both the tropospheric partial column and column-averaged CH 4 (see Fig. A1). It is not clear how the model biases at the surface appear in the regions where no measurements are assimilated. However, it could be true that the overestimation of the tropospheric column-averaged CH 4 meridional gradient is due to model biases in the middle and upper troposphere. That would mean that vertical distributions of CH 4 in the troposphere are not represented correctly in the models. Figure 4 presents a comparison of modelled and measured vertical gradients of tropospheric CH 4 , as qualitatively represented by the difference between the tropospheric columnaveraged CH 4 and the surface CH 4 . The vertical gradient is influenced by surface emissions, transport, and OH fields. Generally there are negative vertical gradients in the Northern Hemisphere and positive vertical gradients in the Southern Hemisphere (except for over the southern continents in locations with strong emissions). Here we refer to decreasing CH 4 mole fractions with altitude as a negative vertical gradient, while increasing CH 4 with altitude is a positive vertical gradient. This occurs because most CH 4 is emitted in the Northern Hemisphere and mixed into the southern hemispheric Hadley cell, the southward branch of which prevails in the middle and upper troposphere. In the troposphere, surface emissions cause decreasing CH 4 with altitude, while OH oxidation causes a negative vertical gradient. The model biases in the tropospheric vertical gradient are mostly positive at middle and high northern latitudes, and negative at other latitudes. So the overestimated tropospheric CH 4 at middle and high northern latitudes could not originate from overestimated emissions, which should result in a more negative vertical gradient in the troposphere. Figure 5 shows a comparison between model simulations and HIPPO measurements. The results are longitudinally av-Atmos. Chem. Phys., 17, 13283-13295, 2017 www.atmos-chem-phys.net/17/13283/2017/ eraged for all five HIPPO missions within grids of 4 • latitude and pressure increments of 10 hPa. A significant feature is an overestimation of CH 4 in the lowermost stratosphere over latitudes higher than 30 • S/N, much larger than the biases in the troposphere. It is not clear whether the overestimation arises from the residual transport in the stratosphere, which appears to be too strong, a too high tropopause, an incorrect vertical CH 4 gradient across the tropopause or a misrepresentation of stratospheric chemistry. Underestimations dominate in the upper southern troposphere, consistent with the results in Fig. 4 that modelled gradients of tropospheric CH 4 are negatively biased as revealed by FTS and surface measurements. There are no significant patterns for the vertical gradient bias in the northern troposphere. Unlike for the FTS, the model biases in the tropospheric column-averaged CH 4 revealed by HIPPO do not show a significant latitudinal trend (Fig. 6, only TM3 are shown there since other models gives similar behaviour). This could be because the FTS-measured tropospheric column-averaged CH 4 is defined differently to the mean mole fraction between the surface and thermal tropopause. In deriving the FTS tropospheric CH 4 , the stratospheric CH 4 is removed via its linear correlation with N 2 O. The tropopause in the FTS data therefore has a chemical definition. It is not clear how different from each other the two kinds of tropopause are during this period. A sensitivity test was conducted by shifting the thermal tropopause 200 hPa upward to include the lower stratosphere where CH 4 is overestimated by the models. The model biases compared against HIPPO then become closer to those against FTS. However, this difference of 200 hPa between the chemical and thermal tropopause is unrealistically large. In addition, the FTS-measured tropospheric columnaveraged CH 4 agrees well with in situ measurements in Fig. 1 where the thermal tropopause is applied.
Another possible explanation is that HIPPO sampled the atmosphere mostly in the region 150 • E-110 • W, over the Pacific Ocean. Apart from Izaña and Ny-Ålesund, the northern FTS sites are located inland. The longitudinal dependence of model biases is investigated with TES-measured CH 4 mole fractions at 215, 464, and 680 hPa (the lower panel in Fig. 6). Because the TES profiles have limited vertical resolution, the concentrations at the three levels are not independent. The weighting function of CH 4 at 215 hPa peaks around 200 hPa in the tropics and around 300 hPa higher than 50 • N/S. The measurements at 464 hPa show the largest sensitivity around 500-600 hPa, and those at 680 hPa have similar vertical sensitivity but fewer weights above 400 hPa. The comparisons are separated into a region representing HIPPO sampling (referred as region I) and the remaining longitudes (referred as region II). Differences between the model biases in the two regions occur northward of 45 • N most significantly at the level 215 hPa. Increases in the model biases continue in region II but decrease in region I, which is more or less similar to the differences between model biases revealed by FTS and HIPPO at these latitudes. Consistent with FTS the model-TES difference also shows a north-south gradient northward of 50 • S. However, it is not clear whether the latitudinal pattern comes from the TES retrieval or model errors. Validation of TES tropospheric CH 4 with HIPPO gives near-zeros biases except for latitudes 40-60 • N where the TES biases vary within −10 to −20 ppb (Herman et al., 2014).

Conclusions
In this study, three inverse models for CH 4 are evaluated using different observations that cover different scales. The aim is to determine whether most of the model biases are from the stratosphere or troposphere. With FTS stratospheric and tropospheric column-averaged CH 4 derived from the FTS total column measurements, it is shown that model bias amplitudes are 7.4 ± 5.1, 6.7 ± 4.8, and 8.1 ± 5.4 ppb in the tropospheric partial column for TM3, TM5-4DVAR, and LMDz39-PYVAR. The corresponding stratospheric partial column biases are 4.3 ± 9.9, 4.7 ± 9.9, and 6.1 ± 11.2 ppb. The tropospheric partial column model bias exhibits a northsouth gradient northward of 50 • S with an overestimation at northern high latitudes for all models. There is no persistent latitudinal pattern with season in the stratospheric partial column model bias for TM3 and TM5-4DVAR.
The evaluation of the models at the surface shows a smaller bias compared to the tropospheric column-averaged CH 4 . We assume that the tropospheric model biases are mainly located in the middle and upper troposphere, although comparisons at the surface are only limited to sites where the measurements have been assimilated into the models. A comparison with HIPPO in the troposphere does not show the same latitudinal pattern in model biases as in the comparison with FTS. Two possible reasons are suggested: (i) the difference between the thermal tropopause and that in the FTS tropospheric CH 4 product, and (ii) the latitude patterns of model biases are dependent on longitude. Using an assessment of model biases relative to TES satellite measurements, we propose that the longitudinal dependence of the model performance contributes to the difference between HIPPO and FTS. However, the tropopause altitude could cause differences during short temporal scale processes, e.g. strato-Atmos. Chem. Phys., 17, 13283-13295, 2017 www.atmos-chem-phys.net/17/13283/2017/ spheric intrusions where the stratospheric air can sink below the thermal tropopause. Stratospheric air can also detach from the stratosphere completely and enter the troposphere. If the detached air parcels still have stratospheric properties, e.g. CH 4 correlates with N 2 O as in the stratosphere, the FTS-measured tropospheric CH 4 excludes these air parcels; however, direct integration from the surface to the thermal tropopause, such as that used for the models and in situ profiles, will include these in the tropospheric CH 4 . More confusing situations could occur where there is strong mixing across the UTLS (the upper troposphere and lower stratosphere) and both thermal and chemical tropopause are not well defined. Future work will be devoted to clarifying the realistic content in FTS tropospheric column-averaged CH 4 and to defining a reasonable approach when comparing it with in situ and model products in these situations. Appendix A Figure A1. Latitudinal dependences of yearly averaged model biases in the tropospheric partial column (black) and the tropospheric column-averaged mole fraction (red). The three models are represented by plus (TM3), circle (TM5-4DVAR) and multiplication (LMDz-PYVAR) signs.