Sensitivity analysis of the potential impact of discrepancies in stratosphere – troposphere exchange on inferred sources and sinks of CO 2

Introduction Conclusions References

ical Asia of 19, 13, and 49 %, respectively.Conversely, the inversion increased the source of CO 2 from tropical South America by 23 %.We find that the model also underestimates CO 2 in the upper tropical and subtropical troposphere.Correcting for the underestimate in the model relative to HIPPO in the tropical upper troposphere leads to a reduction in the source from tropical South America by 77 %, and produces an estimated sink for tropical Asia that is only 19 % larger than the standard inversion (without the imposed source and sink).Globally, the inversion with the Arctic and tropical adjustment produces a sink of −6.64 Pg C, which is consistent with the estimate of −6.65 Pg C in the standard inversion.However, the standard inversion produces a stronger northern land sink by 0.98 Pg C to account for the CO 2 overestimate in the high-latitude UTLS, suggesting that this UTLS discrepancy can impact the latitudinal distribution of the inferred sources and sinks.We find that doubling the model resolution from 4 • × 5 • to 2 • × 2.5 • enhances the CO 2 vertical gradient in the high-latitude UTLS, and reduces the overestimate in CO 2 in the extratropical lower stratosphere.Our results illustrate that discrepancies in the CO 2 distribution in the UTLS can affect CO 2 flux inversions and suggest the need for more careful evaluation of model errors in the UTLS.

Introduction
The Greenhouse Gases Observing Satellite (GOSAT), the first satellite launched specifically to monitor atmospheric carbon dioxide (CO 2 ) from space, has been providing greater observational coverage of atmospheric CO 2 than is possible from existing surface observation networks.The expectation has been that these data would offer greater constraints on atmospheric CO 2 , and hence improve estimates of regional sources and sinks of CO 2 .However, although global flux estimates from various inversion analyses constrained by GOSAT data have been found to be consistent across the different inversion analyses, and in good agreement with optimized fluxes based on flask CO 2 measurements, regional flux estimates have not been robust (e.g.Maksyutov et al., 2013;Basu et al., 2013;Chevallier et al., 2014;Deng et al., 2014).Deng et al. (2014), for example, found that flux estimates for temperate North America and tropical South America were particularly sensitive to the treatment of the regional bias in the GOSAT data.Chevallier et al. (2014) showed that model errors are another source of discrepancy in the regional fluxes inferred from GOSAT CO 2 data.
Inversion analyses using satellite observations have also produced large differences in the flux estimates from some regions, such as Europe and northern Africa, relative to those inferred from the surface-observing network.Reuter et al. (2014) noted that the satellite-derived flux estimates for Europe are more than a factor of two larger than those obtained from in situ surface data.It is difficult to determine whether the differences between the fluxes inferred from the satellite data and those based on the surface data reflect actual additional information provided by the satellite data or discrepancies in the free troposphere in the models, to which the surface data would be much less sensitive.
Observations from instruments such as GOSAT and the Orbiting Carbon Observatory 2 (OCO-2) are vertically integrated column abundances of CO 2 (referred to as XCO 2 ), and it is expected that inversion analyses using these data will be less sensitive to vertical transport errors, such as mixing in the planetary boundary layer (PBL), than those using in situ surface data.However, Lauvaux and Davis (2014) found that vertical transport errors are still an issue for inversion analyses using column data.Stephens et al. (2007) showed that models that do not correctly capture the vertical transport of CO 2 between the PBL and the free troposphere, and, consequently, overestimate the vertical gradient in CO 2 , and tend to suggest a stronger extra-tropical land sink of CO 2 .It is unclear how sensitive the XCO 2 -based inversions are to model errors in transport in the free troposphere.We examine here the potential impact of discrepancies in CO 2 in the upper troposphere and lower stratosphere (UTLS) on the regional flux estimates inferred from GOSAT XCO 2 data.We focus on the UTLS because this is a region that has been neglected as an important source of error in CO 2 flux inversions, even though it is characterized by strong vertical gradients in the distribu-tion of long-lived tracers and by complex transport processes that occur on a range of spatial and temporal scales that can be challenging for models to reliably capture.
In the extratropics, the latitudinal distribution of CO 2 is strongly influenced by quasi-adiabatic transport that tends to align the CO 2 distribution along the isentropes (although diabatic effects result in cross-isentropic transport) (Miyazaki et al., 2008).This can be seen in Fig. 1, which shows the zonal mean CO 2 distribution on 1 April 2010 estimated using the GEOS-Chem model.Also shown are the isentropic surfaces in the model.In the tropics, convective transport provides a means for fast transport of CO 2 from the lower to the upper troposphere.In the extratropics, isentropic transport plays an important role in the export of air from the PBL to the free troposphere.Parazoo et al. (2012) showed that not properly capturing this isentropic transport of CO 2 could impact CO 2 flux inversions.They conducted an observing system simulation experiment (OSSE) and found that data gaps in satellite measurements due to cloud cover, which is associated with poleward moist transport at mid-latitudes, could produce large biases in regional flux estimates.For example, in their perfect model OSSE, the sampling bias due to the data gaps resulted in a bias of 0.43 Pg C yr −1 for the European flux estimates.Here we focus mainly on transport in the extratropical UTLS, where mixing along isentropic surfaces, such as the 320 and the 340 K surfaces, enables rapid exchange of CO 2 between the high-latitude UTLS and the subtropical and mid-latitude middle and upper troposphere.Miyazaki et al. (2008) showed that in winter and spring, transport by large-scale eddies has a positive tendency on CO 2 in the high-latitude UTLS, transporting air with high CO 2 from the lower troposphere at lower latitudes.In contrast, transport by the mean meridional circulation has a negative tendency on CO 2 in the high-latitude UTLS, due to the transport of low CO 2 air from the tropical upper troposphere and down from the high-latitude stratosphere.Accurately reproducing the observed CO 2 distribution in the UTLS requires models to reliably capture the compensating effects of these transport processes.The CO 2 distribution will also be influenced by discrepancies in the numerical schemes and in the parameterizations of subgrid-scale processes not explicitly represented in the models.
We use observations of CO 2 and ozone (O 3 ) from the HI-APER Pole-to-Pole Observations (HIPPO) campaign to evaluate the GEOS-Chem CO 2 simulation in the high-latitude UTLS.The GEOS-Chem model has been widely used as a tropospheric chemistry transport model (CTM), but it is driven by assimilated meteorological fields from the Global Modeling and Assimilation Office (GMAO) that extend from the surface to 0.01 hPa, providing a full description of the circulation in the stratosphere.The model simulates a source of ozone from the stratosphere to the troposphere of about 500 Tg O 3 yr −1 , which is consistent with the multi-model mean of 550 Tg O 3 yr −1 from Stevenson et al. (2006).However, although the model has been successfully used for stud- ies of tropospheric chemistry and transport, we note the CO 2 flux inversions are particularly sensitive to model errors.As discussed below, we find that the model overestimates CO 2 relative to the HIPPO data in the high-latitude UTLS.We then use the HIPPO CO 2 /O 3 correlations to impose an adjustment to the modeled CO 2 in the high-latitude UTLS and conduct a series of inversion analyses of the GOSAT data, using the GEOS-Chem 4-dimensional variational (4D-var) data assimilation system, to quantify the potential impact of the UTLS adjustment in CO 2 on regional flux estimates of CO 2 .
We begin in Sect. 2 with a brief discussion of the data and the methods.We use the same GOSAT data and 4D-var inversion approach as in Deng et al. (2014).In Sect.3, we present our results, starting with a discussion of the use of the HIPPO CO 2 /O 3 correlations to evaluate the model in the UTLS, followed by results of the 4D-var inversion analyses.Finally, we conclude with a discussion of the implications of our results in Sect. 4.

Data sets
We use here the NASA Atmospheric CO 2 Observations from Space (ACOS) GOSAT CO 2 data product (version b2.10) (O'Dell et al., 2012), spanning July 2009 to December 2010.The ACOS retrievals employ an optimal estimation approach to infer profile abundances of CO 2 from the measurements of reflected shortwave infrared (SWIR) solar radiation made by the Thermal and Near-infrared Sensor for carbon Observation Fourier Transform Spectrometer (TANSO-FTS) onboard the GOSAT satellite.The retrieved CO 2 is the total column dry-air mole fraction (XCO 2 ); consequently, when the data were assimilated into the model, the modeled fields are converted to XCO 2 using the reported GOSAT a priori profile, column averaging kernel, and pressure weighting function.The GOSAT data used here are the same as those labeled "RUN_C" in Deng et al. (2014).We use only the "High gain" (H-gain) data, which excludes data over bright surfaces, such as deserts.We also neglect glint observations, which provide coverage over oceans, since the biases in the glint data are not as well-characterized in version b2.10 of the ACOS product.For additional details of the data set we refer the reader to Deng et al. (2014).
To evaluate the model simulation, we use data from the HIPPO aircraft campaign from March-April 2010 (campaign 3).HIPPO-3 sampled the atmosphere across the Pacific Ocean, from near the North Pole to the coastal region of Antarctica, and from the surface to 14 km (Wofsy et al., 2012).The altitudes of the flights were mostly below 9 km, but extended up toward 14 km typically at least at the beginning and end of every flight.We focus here on data from the polar flights on 26-27 March 2010, when there were two profiles that extended up to about 14 km in the Arctic.The data used here are from the 10 s averaged data set.The CO 2 data are from two (harmonized) sensors: the CO 2 Quantum Cascade Laser Spectrometer (CO2-QCLS) and the CO 2 Observations of the Middle Stratosphere instrument (CO2-OMS).The O 3 measurements were made by an ultraviolet (UV) ozone photometer (Wofsy et al., 2011).
We assimilate O 3 data from the Optical Spectrograph and InfraRed Imager System (OSIRIS), which is a Canadian instrument on the Odin satellite.It was launched in February 2001 into a 600 km circular, Sun-synchronous, nearterminator orbit with an inclination of 97.8 • (Llewellyn et al.,  2004).OSIRIS consists of a limb-viewing ultraviolet (UV)visible imaging spectrograph that measures scattered sunlight between 280-820 nm, and a three-channel infrared imager measuring atmospheric airglow emissions near 1.27 and 1.53 µm.Vertical profiles of O 3 are retrieved from OSIRIS measurements using a multiplicative algebraic reconstruction technique (Degenstein et al., 2009), with a vertical resolu-F.Deng et al.: Flux inversion sensitivity to UTLS CO 2 tion of about 2 km from the upper troposphere to 65 km.We use version 5.07 of the O 3 data.As a result of the orbit of the satellite, observational coverage is limited to the summer hemisphere, with near-global coverage during the equinoxes and year-round coverage in the tropics.The mean relative difference between the retrieved O 3 profiles and those from the Stratospheric Aerosol and Gas Experiment (SAGE) II is less than 5 % between 13.5-54.5km, and less than 3 % between 24.5-53.5 km (Adams et al., 2013).The precision is better than 5 % between 25-50 km, but degrades at lower altitudes, increasing to 5-15 % between 10-20 km in the extratropics (Bourassa et al., 2012).
The assimilation of the OSIRIS data is evaluated using observations from the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS), which is a high-resolution Fourier transform spectrometer (Bernath et al., 2005) on the Atmospheric Chemistry Experiment (ACE) satellite (also known as SCISAT).SCISAT was launched in August 2003, into a low Earth orbit at an altitude of 650 km with an inclination of 74 • .ACE-FTS measures infrared radiation between 2.2-13.3µm (750-4400 cm −1 ) with a resolution of 0.02 cm −1 by solar occultation.The retrieval products (Boone et al., 2005) include vertical profiles of numerous trace gases ranging from the mid-troposphere up to 150 km depending on the gas.We use version 2.2 of the ACE-FTS ozone data.Hegglin et al. (2008) found that the version 2.2 ACE-FTS profiles have an effective vertical resolution of 1 km in the UTLS.Validation of the ACE-FTS O 3 data suggested that the relative mean difference between ACE-FTS O 3 data and independent measurements is less than 8 % between 16-44 km.Hegglin et al. (2008) evaluated the data in the UTLS and reported mean differences relative to aircraft and ozonesonde data of about 8 % in the lower stratosphere and a high bias of 18 % in the upper troposphere.We restrict our use of the ACE-FTS data to the lower stratosphere.

The GEOS-Chem model and assimilation approach
We use the GEOS-Chem (http://geos-chem.org)4D-var data assimilation system (Henze et al., 2007) to infer regional CO 2 flux estimates.The model is driven by assimilated meteorology from the Goddard Earth Observing System (GEOS-5) of the NASA GMAO.The native horizontal resolution is 0.5 • × 0.67 • with 72 vertical levels from the surface to 0.01 hPa, but we degrade the resolution to 4 • × 5 • and 47 vertical layers (with the reduction in vertical resolution in the middle and upper stratosphere).The GEOS-Chem CO 2 simulation is described and evaluated in Nassar et al. (2010).Details of the model configuration and setup of the 4D-Var system are described in Deng et al. (2014).Here we will provide only a brief description of the modeling setup.
In the 4D-Var approach, we iteratively minimize a cost function J as a function of CO 2 fluxes (x), where y o is a vector of GOSAT XCO 2 observations and S o and S a are the observational and a priori error covariance matrices, respectively.H is the forward atmospheric model (y = H (x)), which includes the GEOS-Chem simulation of the CO 2 distribution and the transformation of the modeled CO 2 profile to XCO 2 using the GOSAT averaging kernels and a priori profiles.We solve for monthly mean fluxes of CO 2 using GOSAT observations from March-August 2010.Following Deng et al. (2014), the reported observational XCO 2 uncertainties are uniformly inflated by a factor of 1.175 when the data are ingested into the GEOS-Chem assimilation system.As described in Deng et al. (2014), the prior CO 2 fluxes (x a ) imposed in the model are: (i) monthly national fossil fuel and cement manufacture CO 2 emissions from the Carbon Dioxide Information Analysis Center (CDIAC) (Andres et al., 2011); (ii) monthly shipping emissions of CO 2 from the International Comprehensive Ocean-Atmosphere Data Set (ICOADS) (Corbett and Koehler, 2003;Corbett, 2004;Endresen et al., 2004Endresen et al., , 2007)); (iii) 3-D aviation CO 2 emissions (Kim et al., 2007;Wilkerson et al., 2010;Friedl, 1997); (iv) monthly mean biomass burning CO 2 emissions from the Global Fire Emissions Database version 3 (GFEDv3) (van der Werf et al., 2010); (v) biofuel (heating/cooking) CO 2 emissions estimated by Yevich and Logan (2003); (vi) the flux of CO 2 across the air-water interface based on the climatology of monthly ocean-atmosphere CO 2 flux by Takahashi et al. (2009); and (vii) 3-hourly terrestrial ecosystem exchange produced by the Boreal Ecosystem Productivity Simulator (BEPS) (Chen et al., 1999), which was driven by NCEP reanalysis data (Kalnay et al., 1996) and remotely sensed leaf area index (LAI) (Deng et al., 2006).The annual terrestrial ecosystem exchange imposed in each grid box is neutral (Deng and Chen, 2011).The assumed prior errors (1σ ), specified for each grid box and each month, are 16 % for the fossil fuel emissions, 38 % for the biomass burning emissions, and 44 % for the ocean flux.For gross primary production (GPP) and total ecosystem respiration (TER), we assumed an uncertainty of 22 % in each 3-hour time step and in each model grid box.
The assimilation of the OSIRIS O 3 data into GEOS-Chem uses the same 4D-var approach as described in Eq. ( 1).However, instead of optimizing a model parameter, such as the surface fluxes of CO 2 , we optimize the O 3 distribution at the beginning of the assimilation period (the initial conditions) so that the model better matches the OSIRIS data over the assimilation period.For the results presented here, the assimilation period extended from 20 March to 2 April 2010.The O 3 distribution in GEOS-Chem is simulated with a detailed description of O 3 -NOx-hydrocarbon chemistry in the troposphere, but the version of the model employed here uses a linearized version of the chemistry in the stratosphere, based on the Linoz scheme from McLinden et al. (2000).As mentioned above, with the Linoz scheme, the model simulates a source of tropospheric ozone of about 500 Tg O 3 yr −1 , which is close to the multi-model mean of 550 Tg O 3 yr −1 from Stevenson et al. (2006).We note that degrading the vertical resolution in the stratosphere (from 72 to 47 levels) does not impact the stratospheric source of ozone into the troposphere, suggesting that stratosphere-troposphere exchange (STE) is not influenced by the reduction in levels in the middle and upper stratosphere.Additional details of the configuration of the O 3 simulation in the version of GEOS-Chem used here are described in Zhang et al. (2011).The use of the GEOS-Chem 4D-var system for assimilation of ozone observations is described in Singh et al. (2011).

CO 2 /O 3 correlations in the Arctic
Deng et al. ( 2014) compared the a posteriori CO 2 fields from their inversion analysis of the GOSAT data to HIPPO-3 data in the lower troposphere (between 1-5 km) and found that the mean differences between the model and the data were small, less than 0.20 ppm.In Fig. 2, we compare the a posteriori CO 2 fields (defined as our standard inversion here) with the HIPPO-3 data in the upper troposphere (above 5 km).The linear correlation between the HIPPO-3 observations and the modeled CO 2 is high, R 2 = 0.7708, but there is a large bias at high latitudes in the Northern Hemisphere, where the observed CO 2 mixing ratio values are much lower than the modeled CO 2 .The HIPPO data are 10 s averages, and we are aware that at a temporal resolution of 10 s, the HIPPO data will reflect CO 2 on spatial scales that are much smaller than the model resolution.Consequently, representativeness errors associated with the coarse model grid and temporal resolution will contribute to the differences between the model and the data.Xiong et al. (2013) reported the occurrence of a strong stratospheric intrusion over North America on 27 March 2010, which was captured by the HIPPO data.They reported significantly reduced CH 4 values, reflecting stratospheric air that was transported down as low as 550 hPa, which would be consistent with the low CO 2 values of 385 ppm measured by HIPPO (in Fig. 2).Because of the coarse horizontal resolution of the model simulation, it is possible that the model underestimates the stratospheric intrusion (e.g., Lin et al., 2012).
The influx of stratospheric air will be associated with low CO 2 and high O 3 ; therefore, we examined the CO 2 /O 3 correlations in the HIPPO data and in the model.Tracer-tracer correlations have been used extensively to study transport and mixing in the stratosphere (e.g., Plumb and Ko, 1992;Waugh et al., 1997;Hoor et al., 2002;Sankey and Shepherd, 2003;Pan et al., 2004).The correlations, shown in Fig. 3, indicate a clear separation of tropospheric air (with low ozone and high CO 2 ) and stratospheric air (with high ozone and low CO 2 ), with a mixing region in between, with intermediate CO 2 and O 3 values that reflect the mixing between the tropospheric and stratospheric air masses.Shown also are linear fits to the HIPPO data in the stratospheric and mixing regions.Assuming an ozone threshold of 100 ppb as the transition from tropospheric air to stratospheric air (e.g., Pan et al., 2004), the intercept of the stratospheric branch with the 100 ppb ozone threshold suggests a tropopause CO 2 level of about 387 ppm, in the absence of mixing.The modeled correlation agrees well with the data in the tropospheric and stratospheric branches, but the modeled values are displaced to higher CO 2 compared to the aircraft data in the mixing region, suggesting excessive mixing in the model (e.g., Hoor et al., 2002;Pan et al., 2004).We believe that the two clear mixing lines in Fig. 3 reflect the effects of the intrusion reported by Xiong et al. (2013), which the model does not capture.The mixing feature starting at CO 2 and O 3 abundances of 385 ppm and 400 ppb, respectively, corresponds to stratospheric air extending down to 7-8 km, while the feature starting at CO 2 and O 3 abundances of 386 ppm and 300 ppb, respectively, extends down to 5-7 km.Although the model does not capture these features, the correlations suggest that the mean state of the model in the UTLS is characterized by stronger mixing than suggested by the observations.
Examination of the CO and O 3 correlations reveals a similar discrepancy, with the modeled CO and O 3 correlation shifted relative to the HIPPO data, as shown for CO 2 and O 3 in Fig. 3.The HIPPO CO/O 3 correlations also show the influence of the enhanced STE at O 3 values less than 400 ppb, which is not captured by the model.We also examined the CO/O 3 and CO 2 /O 3 correlations in HIPPO-1 in January 2009 and found similar discrepancies between the model and the aircraft data.In a separate study, (MacKenzie et al., 2015) used ACE-FTS CO and O 3 data to evaluate the stratospheretroposphere mixing layer in the GEOS-Chem model.They found that vertical extent of the mixing layer simulated by the model agrees with that derived from ACE-FTS data.However, at high-latitudes the altitude of the mixing layer in the model is biased high relative to that from ACE-FTS, whereas at low-latitudes it is biased low.
Since CO 2 and O 3 are both long-lived tracers in the lower stratosphere, and their distributions largely reflect the influence of transport, we chose to optimize the modeled O 3 distribution and use the observed CO 2 /O 3 correlation to obtain an observation-based adjustment to the modeled CO 2 distribution.To improve the modeled ozone distribution, we assimilated OSIRIS ozone observations using the GEOS-Chem 4D-var system.The 4D-Var assimilation scheme adjusts the initial O 3 conditions to optimize the model trajectory over the assimilation window.If the window is long compared to the lifetime of ozone, the assimilation system is unable to use the information from observations toward the end of the window to adjust the initial conditions, since that information is chemically destroyed.On the other hand, if the window is too short, there are fewer data available to adjust the state.In the high-latitude UTLS, the O 3 lifetime is long, however, in the tropical middle troposphere, the O 3 lifetime is about 3 weeks (Wang et al., 1998).Consequently, we chose a 2-week assimilation window, from 20 March to 2 April 2010.Furthermore, since the Arctic HIPPO measurements were made on 26 and 27 March, we chose the assimilation window so that the timing of the HIPPO data would fall at the midpoint of the window, providing the best constraint on the O 3 distribution at that time.
The changes in the modeled O 3 fields as a result of the assimilation are shown in Fig. 4. The assimilation increased O 3 in the lowermost stratosphere by about 10-20 % and decreased it by as much as 40 % in the tropical and subtropical UTLS.To evaluate the modeled O 3 fields, we compared the a priori and a posteriori ozone fields with data from the ACE-FTS instrument, shown in Fig. 5.The modeled ozone distributions were sampled at the ACE-FTS observation locations and times (we selected the model grid box consistent with the location of the 30 km tangent height).The comparisons shown used 31 ACE-FTS profiles between 55-65 • N and 44 profiles between 65-75 • N during the period 20 March to 3 April 2010.In the Arctic, between 100-20 hPa both the a priori and a posteriori ozone fields agree with the ACE-FTS data to within 10 %.At these altitudes, the a priori bias was −2.7 % between 55-65 • N (Fig. 5a), while the a posteriori bias was 1 %.Between 65-75 • N, the a priori and a posteriori biases were 2.3 % and 4.4 %, respectively.At lower altitudes, the model bias was larger, with the a priori model underestimating ACE-FTS O 3 by as much as 30-40 % near 200 hPa.The assimilation reduced the underestimate to within 15-25 % of the ACE-FTS data.Despite this large residual bias at these levels, the assimilated ozone fields represent a significant improvement over the a priori in the lower stratosphere.It should be noted that because the data from both OSIRIS and ACE-FTS are limb measurements, the information ob- tained from them is more limited at pressures of 200 hPa and higher.
With the optimized stratospheric O 3 , we used the empirical fit between CO 2 and O 3 from the HIPPO CO 2 /O 3 correlations to produce an adjustment to the modeled CO 2 in the lower stratosphere.Examination of CO 2 /O 3 correlations in the model at the locations of the HIPPO data and elsewhere across the modeled Arctic produced negligible differences in the correlations.Consequently, although the HIPPO measurements were localized over the Pacific (over Alaska on 26-27 March 2010), we applied the empirical fit throughout the Arctic to produce a zonal mean adjustment to the modeled CO 2 profile in the Arctic.The zonal mean change in the vertical profile of CO 2 in the Arctic as a result of the HIPPO-derived adjustment is shown in Fig. 6.The HIPPO CO 2 /O 3 correlations suggest a steeper vertical gradient in CO 2 across the tropopause, which is consistent with the results of MacKenzie et al. ( 2015) that showed that the stratosphere-troposphere mixing region in the model is biased high relative to the tropopause at high latitudes.We examined the CO 2 /O 3 correlation throughout the month of March 2010 and found little variations in the correlations, so we applied the adjustment to the CO 2 vertical distribution throughout March.This adjustment was then imposed in the modeled CO 2 fields and we repeated the GOSAT inversion from Deng et al. ( 2014), but only for the growing season, March-August 2010, to assess the impact of this perturbation in CO 2 in the Arctic UTLS on the inferred surface fluxes of CO 2 .This adjustment to the Arctic CO 2 distribution corresponds to a sink in the global mass of CO 2 of 0.6 Pg C in the GOSAT inversion analysis.Ideally, one would use seasonally varying CO 2 /O 3 correlations to obtain the appropriate UTLS CO 2 adjustment over the seasonal cycle.However, there was only one HIPPO campaign (in spring) in 2010.Consequently, as a first step in assessing the potential impact of this discrepancy in the UTLS on the flux estimates we chose to impose a constant adjustment to the CO 2 distribution.It should be noted that if the UTLS discrepancy is due to excessive ver- tical mixing then we would expect it to be larger when the vertical gradient in CO 2 is large.This means that we would expect the discrepancy to be present from March until summer, by July or August, when the summertime drawdown reverses the vertical gradient in CO 2 in the troposphere.

Passive tracer experiments
To help understand the potential impact of the adjustment to CO 2 in the Arctic UTLS shown in Fig. 6, we conducted forward sensitivity analyses using a passive CO 2 -like tracer in the model.As mentioned above, the Arctic UTLS adjustment leads a total atmospheric CO 2 mass decrease of 0.60 between March-August 2010, so for the passive tracer experiment we imposed an equivalent source.This way, the source matches the change in CO 2 in the UTLS shown in Fig. 6.As in the inversion analysis, we impose the adjustment across the whole Arctic, but here it is a source, whereas it is a sink in the in- version analysis.The zonal mean distribution of the passive tracer is shown in Fig. 7 for March and June 2010.Within the first month, there is significant transport of the stratospheric CO 2 down into the mid-latitude and subtropical troposphere.In summer, there is transport to the Southern Hemisphere in the tropical UTLS, as described by Miyazaki et al. (2008).By June the tracer has been transported south as far as 30 • S (Fig. 7b), and by August, the tracer distribution extends as far as 60 • S (not shown).
In Fig. 8 we have plotted the distribution of the tracer in terms of the column averaged dry mole fraction (XCO 2 ).We have sampled the tracer distribution at the GOSAT observation locations and times and applied the GOSAT averaging kernels to smooth the tracer in a manner that is consistent with the vertical sensitivity of the GOSAT retrievals.Although the imposed source is located mainly in the stratosphere, its impact on the CO 2 column, as reflected in the XCO 2 values, is not negligible.By June, the perturbation in XCO 2 exceeds 0.5 ppm in the mid-and high-latitudes of the Northern Hemisphere.As a result of the inter-hemispheric transport in the tropical UTLS, we see small corrections of about 0.1-0.2ppm in XCO 2 in the southern tropics and subtropics.In June, the XCO 2 changes are confined to equatorward of 30 • S, reflecting the southern extent of the tracer transport in the upper troposphere (Fig. 7b).However, by August, the influence of the Arctic source is reflected in the XCO 2 values across all of South America and Australia.We note that even though the tracer is accumulating in the troposphere over the course of the run, the impact on XCO 2 in the Southern Hemisphere in August is still small, about 0.1-0.2ppm.The results in Fig. 8 are interesting, nevertheless, as they demonstrate that the perturbations in CO 2 in the UTLS can have a noticeable impact on XCO 2 values, which have implications for interpreting differences in inversion analyses using XCO 2 and in situ surface data.

Inversion analyses
Using the inversion approach of Deng et al. (2014), we assimilated the ACOS GOSAT XCO 2 from 1 March-31 August 2010, with the reduction in UTLS CO 2 in the Arctic.Deng et al. (2014) showed that the GOSAT data suggest that the bottom-up biospheric fluxes used in this version of GEOS-Chem underestimate the summertime sinks of CO 2 .For example, their GOSAT-derived estimate for the June sink of CO 2 for temperate North America was −0.5 Pg C compared to their a priori of about −0.3 Pg C. Since, as shown in Fig. 6, much of the perturbation in CO 2 in the Arctic UTLS is transported down in the troposphere, the imposed reduction in UTLS CO 2 during the growing season requires weaker surface sinks to bring the model into agreement with the GOSAT data.In the experiment here, the largest changes are obtained for the mid-latitude flux regions in North America and Europe, due to transport of the lower stratospheric adjustment down, along the isentropes (shown in Fig. 4), into the middle and upper troposphere of the mid-latitudes and subtropics.We believe that the large change obtained for the tropical Asian flux may be due to the influence of STE associated with the Asian monsoon (e.g.Postel and Hitchman, 1999;Shuckburgh et al., 2009).
In general, the inversion results show that reducing the CO 2 mixing ratio in the Arctic UTLS decreased the sinks in most northern land regions and increased the sources in the tropics.As mentioned above, the decreased northern land sinks are due to the fact that the imposed UTLS sink compensates for the summertime uptake at the surface.We believe that the increased tropical sources are due to the fact that the UTLS sink exacerbates the underestimate of CO 2 in the model in the tropical upper troposphere.Figure 2 shows that there is a residual negative bias in CO 2 , relative to the HIPPO data, in the upper troposphere in the northern tropics and subtropics in the standard inversion.As shown by the transport pattern in Fig. 7b, the imposed reduction in the UTLS CO 2 will exacerbate this bias, forcing the inversion to compensate by increasing the tropical sources.This underestimate in tropical CO 2 is consistent with the argument that the lowermost stratospheric bias shown in Figs. 3 and 6 is due to excessive mixing across the tropopause in the subtropics.Excessive STE would result in enhanced CO 2 (and reduced O 3 ) in the extratropical lowermost stratosphere and reduced CO 2 (and enhanced O 3 ) in the tropical upper troposphere.Indeed, assimilation of the OSIRIS data, as shown in Fig. 4, increased ozone in the extratropical lowermost stratosphere and decreased it in the upper tropical troposphere.Consequently, the imposed reduction in CO 2 in the Arctic UTLS should be accompanied by an increase in CO 2 in the tropical and subtropical upper troposphere.
Unlike the extratropical UTLS, use of the CO 2 /O 3 correlations in the tropical UTLS to adjust the CO 2 distribution is challenging because of the effects of convective transport and the chemical production of O 3 on the tracer-tracer relationship in the tropical upper troposphere.Therefore, as a first step, we chose to impose a uniform source of CO 2 of about 0.25 ppm between 8-20 • N and about 5-8 km, to remove the mean bias between the model and the HIPPO CO 2 data in this region.This constant 0.   9, shown are the results from using the standard inversion (denoted Standard), with an imposed sink in CO 2 in the Arctic UTLS (denoted Adjusted N), and with the addition of uniform source in the upper troposphere in the northern tropics (denoted Adjusted N + T). estimated as −6.64 Pg C with the combined Arctic sink and tropical source, a 0.01 Pg C difference from −6.65 Pg C obtained in the standard inversion.The flux estimates for the three most northern land regions were relatively unchanged with the tropical adjustment.Europe, for example, was estimated as a sink of −1.39 Pg C with the combined source and the sink compared to −1.36 Pg C with just the Arctic sink.Small changes were obtained from northern temperate regions.Temperate North America, for example, was inferred as a sink of −1.22 Pg C with the combined Arctic and tropical adjustments compared to −1.08 Pg C with just the Arctic adjustment.Although the global land sink with the Arctic and tropical adjustment was consistent with that estimated in the standard inversion, we found that the total northern land sink (for March-August) was 0.98 Pg C weaker with the Arctic and tropical adjustment than in the standard inversion.This large latitudinal change in the land sink is due to the fact that a stronger extratropical drawdown during the growing season is required to account for the high-latitude UTLS bias in the standard inversion.
As expected, the largest relative differences with the addition of the tropical source were for the tropical regions.For tropical South America, the flux estimate increased by 23 % with only the Arctic sink, whereas it was reduced by 77 % with the combined Arctic sink and tropical source.For northern Africa, where the fluxes are small for March-August, the flux estimates changed sign, going from 0.06 Pg C with the Arctic sink to −0.13 Pg C with the combined Arctic sink and tropical source.With only the Arctic sink, we found that the flux estimate for tropical Asia was reduced by a factor of two.However, the addition of the tropical source compensated for the influence of the Arctic sink on this region, producing a flux estimate of −0.30Pg C, which is a slightly stronger sink than that inferred in the standard inversion (−0.26 Pg C).Despite the apparent consistency between the tropical Asian flux estimates from the standard inversion and from the inversion with the combined source and sink, the transition from being a source to a sink for CO 2 is impacted by the specification of the tropical source.The standard inversion suggested a weak source for March, which shifted to a sink in April.However, the inversion with the combined source and sink produced a weak sink in March, which became a weak source in April, before strongly transitioning to a sink in June.Because the a posteriori flux uncertainties are largest in the tropics, the differences in the flux estimates can be small relative to the a posteriori uncertainties for the tropical regions.This is particularly the case for tropical Asia.For northern Africa, the largest absolute flux difference obtained with the tropical source and Arctic sink, compared to the standard inversion, is for July, and that exceeds the flux uncertainty.In contrast, in the extratropics, for temperate North America, for example, with the Arctic sink the changes are larger than the flux uncertainties for March through June.With the combined source and sink, the temperate North American flux changes are larger than the uncertainties in June, when the sink is at a maximum.Although the relative flux differences are small for some regions, the discrepancies represent significant spatially dependent biases, which have implications for the latitudinal distribution of the estimated sources and sinks.

Impact of model resolution
To assess the potential impact of model resolution, we doubled the model resolution to 2 • × 2.5 • and repeated the forward model simulation from 1 July 2009 to 31 December 2010.Because of the large number of iterations required for minimizing the cost function, it is computationally expensive to carry out the global inversion analysis at the 2 • × 2.5 • resolution.As a result, we focus here on a comparison of the forward model simulation.Shown in Fig. 11 is the zonal mean vertical profile of CO 2 at 75 • N on 1 April 2010.The model configuration used to produce the results in Fig. 11 is similar to, but not identical to that used for the results in Figs.1-3 and 6.Here we use the a posteriori scaling factors (the ratio of the a posteriori to a priori fluxes) from the standard CO 2 inversion to scale the fossil fuel, biofuel, ocean, and biospheric CO 2 fluxes, but the biomass burning emissions are not scaled.As shown in Fig. 11, the higher resolution simulation produced a steeper gradient in CO 2 than the low-resolution simulation, which is consistent with excessive vertical mixing in the 4 • × 5 • simulation.Examination of the latitudinal distribution in the UTLS, shown in Fig. 12 reveals more CO 2 in the upper tropical and subtropical troposphere and less CO 2 in the high-latitude lower stratosphere in the 2 • × 2.5 • run compared to the 4 • × 5 • run; the latitudinal gradient in the Northern Hemisphere UTLS is weaker in the low-resolution simulation.
In Table 1 we have listed the mean differences between the standard a posteriori CO 2 and the HIPPO data above 8 km, binned into four latitudinal bins.As discussed above, the largest biases are in the polar region, with a positive bias of 1.72 ppm between 60-90 • N. In the lower latitudes the model is biased low, with a bias of −0.09 ppm between 0-15  higher by 0.55 ppm, which is almost a third of the high bias between the low-resolution simulation and the HIPPO data.In the tropics (0-15 • N), the difference between the 4 • × 5 • and 2 • × 2.5 • simulations is equivalent to the differences between the 4 • × 5 • simulation and the HIPPO data.

Conclusions
We have evaluated the GEOS-Chem CO 2 simulation in the extratropical UTLS using aircraft observations from the HIPPO-3 campaign in March 2010 and found that the model overestimates CO 2 in the lowermost stratosphere in the Arctic.Comparison of the modeled and observed correlations between CO 2 and O 3 , suggest a discrepancy in mixing in the UTLS in the model.To obtain an observation-based adjustment to CO 2 in the model, we assimilated O 3 data from the OSIRIS instrument to improve the stratospheric O 3 in the model and then used the assimilated O 3 together with the HIPPO CO 2 /O 3 correlation to infer an adjustment to the modeled CO 2 in the Arctic.The HIPPO-based adjustment to the modeled CO 2 resulted in an increase in the vertical gradient in CO 2 across the Arctic tropopause.
To assess the potential impact of these changes in CO 2 on regional CO 2 flux estimates, we conducted inversion analyses using GOSAT XCO 2 data, with and without the CO 2 adjustment in the Arctic UTLS.Because of the lack of data to evaluate the CO 2 /O 3 correlations over the seasonal cycle, the adjustment in the Arctic UTLS was assumed to be constant over the assimilation period, from March-August 2010, representing a total sink of 0.60 Pg C in the Arctic UTLS.We found that this adjustment in Arctic CO 2 resulted in a reduction in the inferred flux of CO 2 from temperate North America and Europe during the growing season of 19 and 13 % respectively, compared to the standard inversion (without the imposed sink).For tropical Asia, there was a factor of two reduction in the estimated flux.
If the bias in CO 2 reflects the influence of excessive STE, one would expect the overestimate in CO 2 in the extratropi- cal lower stratosphere to be accompanied by an overestimate in CO 2 in the tropical and subtropical upper troposphere.Indeed, we find that the modeled CO 2 is biased low relative to the HIPPO data in these regions.Also, relative to the OSIRIS data, the modeled O 3 is biased low in the extratropical lower stratosphere and high in the tropical and subtropical upper troposphere, which is consistent with excessive STE.We conducted a sensitivity experiment in which we corrected the underestimate in CO 2 in the low-latitude upper troposphere by imposing a uniform source of CO 2 of 0.55 Pg C (an adjustment of 0.25 ppm) for March-August 2010 in the tropical upper troposphere to remove the mean difference between the HIPPO data and the a posteriori CO 2 from the standard GOSAT inversion.With the extratropical sink and tropical source in the UTLS, the CO 2 source inferred from tropical South America was reduced by 77 %.In contrast, with only the Arctic sink it was increased by 23 %.For tropical Asia, the total estimated flux with extratropical sink and tropical source in the UTLS was close to the estimate in the standard inversion.Although the imposed sources and sinks were ad hoc, due to the lack of data to better quantify the evolution of the model errors over the seasonal cycle, the results here illustrate that discrepancies in the CO 2 distribution in the UTLS can impact the regional CO 2 flux estimates using satellite data, and point to the need to better characterize model errors in the UTLS.Inversion analyses using GOSAT XCO 2 data tend to produce stronger sinks in the extratropical Northern Hemisphere and weaker sources in the tropics compared to those using the surface flask data (Houweling et al., 2015).In our analysis we found that with the combined Arctic and tropical adjustment, the March-August sink in northern lands was 0.98 Pg C weaker than in our standard inversion, even though the estimated total global sink in the two inversions were similar.Our results suggest that the high-latitude UTLS discrepancy could result in a latitudinal redistribution of mass in flux inversions, and we would expect the XCO 2 inversions to be more sensitive to the UTLS discrepancies than the flask inversions.Because we have assumed that the adjustments are constant over the assimilation period, the changes in the flux estimates reported here might be an upper limit for the impact of these discrepancies, but we need to better characterize the spatio-temporal evolution of the UTLS biases to properly quantify their impact.
As we noted in the introduction, the CO 2 distribution in the extratropical UTLS in winter and spring represents a balance between a positive tendency associated with largescale eddies and a negative tendency due to the transport by the mean meridional circulation (Miyazaki et al., 2008).The meridional circulation is, in part, driven by the large-scale eddies, and the balance between the two tendency terms will vary from model to model.It is possible that the inability of GEOS-Chem to reproduce the HIPPO CO 2 /O 3 correlations in the extratropical UTLS may be due to discrepancies in either the large-scale eddies or the meridional circulation in the model.On the one hand, GEOS-Chem is driven by assimilated meteorological fields, so it is expected that the model will capture the large-scale eddies well.On the other hand, it is known that CTMs, which are driven by reanalyses, capture vertical transport in the UTLS less well than free running general circulation models because the data assimilation systems introduce imbalance between the temperature and wind fields (Douglass et al., 2003).It is because of this that CTMs generally underestimate the mean age of air in the stratosphere.
Other potential sources of discrepancy in the CO 2 distribution are the numerical scheme used in the model and the resolution of the model simulation.Prather et al. (2008) compared the CO 2 simulations from two CTMs using the same meteorological fields and CO 2 fluxes, but with different numerical schemes.One model, the Global Modeling Initiative (GMI) CTM, used the numerical transport scheme by Lin and Rood (1996), whereas the other model, the University of California, Irvine (UCI) CTM, used the Second-Order Moments (SOM) scheme by Prather (1986).At a resolution of 5 • × 4 • , the GMI model, with the Lin and Rood (1996) scheme, was more diffusive, producing a weaker seasonal cycle in CO 2 and higher CO 2 values in the stratosphere.Prather et al. (2008) found that doubling the resolution of the models to 2 • × 2.5 • reduced the discrepancies, but the GMI model still had numerical errors that were twice as large as those in the UCI model.We found that doubling our model resolution to 2 • × 2.5 • increased the vertical gradient in CO 2 in the high latitudes, and reduced the CO 2 loading in the highlatitude lower stratosphere.The 4 • × 5 • simulation overestimated the Arctic CO 2 (averaged 60-90 • N and above 8 km) by 0.55 ppm, relative to the 2 • × 2.5 • simulation which is almost a third of the high bias between the low-resolution simulation and the HIPPO data.In the tropics (0-15 • N), the difference between the 4 • × 5 • and 2 • × 2.5 • simulations is equivalent to the differences between the 4 • × 5 • simulation and the HIPPO data.In contrast, the 4 • × 5 • was biased low by 0.23 ppm relative to the 2 • × 2.5 • simulation between 15-45 • N, which is equivalent to the differences between the 4 • × 5 • simulation and the HIPPO data, suggesting that the mixing is excessive in the low-resolution simulation.
There has been a number of studies looking at the impact of transport discrepancies in the UTLS on the distribution of O 3 and other long-lived tracers, using aircraft, balloon, and satellite observations (e.g., Considine et al., 2008;Strahan and Polansky, 2006).But additional attention is needed to understand the impact of these discrepancies in the context of CO 2 flux inversions.We expect that the discrepancies identified here will be more of an issue for inversion analyses using satellite data than those using surface data, since all thermal infrared and shortwave infrared, nadir satellite retrievals have sensitivity to CO 2 in the UTLS.Based on our results, it is unclear the degree to which further increases in the spatial resolution of the model simulation will mitigate the biases in the UTLS.Additional studies using GEOS-Chem at higher spatial resolution, such as at the native resolution of 0.5 • × 0.67 • would be helpful.Also, additional data are needed to better evaluate the model performance in the UTLS.High-resolution CO 2 profile measurements across the UTLS would be useful.Simultaneous satellite measurements of CO 2 , O 3 and other long-lived tracers from instruments such as limb sounders, would enable us to better exploit tracer-tracer correlations to evaluate model transport in the UTLS in the context of the CO 2 flux inversions.For example, CO 2 vertical profiles have also been retrieved from ACE-FTS (Sioris et al., 2014); however the data are currently sparse due to the initial cloud filtering method used, and thus were not used in the current work.Efforts are underway to retrieve profiles down to cloud tops, so that fewer profiles are lost, which could aid in future analyses.

Figure 1 .
Figure 1.Zonal mean CO 2 from GEOS-Chem on 1 April 2010, as a function of latitude and altitude (left) and latitude and potential temperature (right).In the latitude/altitude plot (left), the white lines indicate the zonal mean potential temperature in Kelvins (K).The thick black line in both plots denotes the location of the tropopause in the model.

Figure 2 .
Figure 2. Comparison of modeled a posteriori CO 2 mixing ratios in the upper troposphere from our GOSAT inversion analysis (in red) with HIPPO observations (in blue) between 70 • S to 84 • N and above 5000 m in altitude.These a posteriori CO 2 fields are from the inversion denoted as our standard inversion.

Figure 3 .
Figure 3. CO 2 /O 3 correlations from GEOS-Chem (red) and HIPPO-3 (green) for 26-27 March 2010, poleward of 60 • N. The high O 3 and low CO 2 values are characteristic of stratospheric air, whereas the low O 3 and high CO 2 values indicate tropospheric air.The values in the UTLS represent a mixture of stratospheric and tropospheric air.The red diamonds represent the GEOS-Chem CO 2 /O 3 correlations obtained after assimilation of the OSIRIS O 3 data in the stratosphere.The two thin black lines show the fit to the HIPPO data in the stratospheric branch and in the mixing region.The vertical dashed line indicates the 100 ppb threshold for O 3 , below which the air is considered tropospheric in origin.

Figure 4 .
Figure 4. Zonal mean change in the GEOS-Chem O 3 distribution as a result of the assimilation of OSIRIS O 3 data.The assimilation was conducted for 20 March-2 April 2010.As in Fig. 1, the white lines indicate the zonal mean potential temperature in Kelvins (K) and the thick black line denotes the location of the tropopause in the model.

Figure 5 .
Figure 5. Relative difference between the a priori and a posteriori modeled O 3 and ACE-FTS O 3 data.Shown are the mean differences for latitudes between 55-65 • N (a) and between 65-75 • N (b).

Figure 6 .
Figure 6.The mean profile of CO 2 in the Arctic before (in blue) and after (in red) the adjustment in CO 2 in the UTLS based on the HIPPO-3 CO 2 /O 3 correlations.

Figure 7 .
Figure 7. Monthly averaged, zonal mean distribution of a passive tracer with a constant source equivalent to the CO 2 adjustment in the Arctic UTLS for March-August 2010.

Figure 8 .
Figure 8. Monthly mean distribution of a passive tracer with a constant source equivalent to the CO 2 adjustment in the Arctic UTLS for March-August 2010.The tracer distribution was sampled at the GOSAT observation locations and times and vertically integrated, using the GOSAT averaging kernels, to produce XCO 2 values.

Figure 9 .
Figure 9. Regional CO 2 flux estimates for March to August 2010 inferred from GOSAT XCO 2 using the standard inversion approach (denoted Standard), with an imposed sink in CO 2 in the Arctic UTLS (denoted Adjusted N), and with the addition of uniform source in the upper troposphere in the northern tropics (denoted Adjusted N + T).
25 ppm adjustment corresponds to a total source of 0.55 Pg C for March-August 2010, and almost balances the imposed Arctic sink.The inversion results with the combined UTLS sink in the Arctic and the tropical source are shown in Figs. 9 and 10.The global land sink was

Figure 10 .
Figure 10.Monthly mean CO 2 flux estimates and their uncertainties for (a) temperate North America, (b) tropical Asia, (c) northern Africa, and (d) tropical South America.As in Fig. 9, shown are the results from using the standard inversion (denoted Standard), with an imposed sink in CO 2 in the Arctic UTLS (denoted Adjusted N), and with the addition of uniform source in the upper troposphere in the northern tropics (denoted Adjusted N + T).

Figure 11 .
Figure 11.Zonal mean profiles of CO 2 at 75 • N on 1 April 2010 from the GEOS-Chem 4 • × 5 • and 2 • × 2.5 • simulations.The simulations began with the same initial conditions on 1 July 2009.The fossil fuel, biofuel, ocean, and biospheric fluxes used in the simulations were scaled based on the a posteriori scaling factors from the GOSAT XCO 2 inversion.The biomass burning fluxes, however, were not scaled.