Algorithm update of the GOSAT / TANSO-FTS thermal infrared CO 2 product ( version 1 ) and validation of the UTLS CO 2 data using CONTRAIL measurements

The Thermal and Near Infrared Sensor for Carbon Observation (TANSO)–Fourier Transform Spectrometer (FTS) on board the Greenhouse Gases Observing Satellite (GOSAT) has been observing carbon dioxide (CO2) concentrations in several atmospheric layers in the thermal infrared (TIR) band since its launch. This study compared TANSO-FTS TIR version 1 (V1) CO2 data and CO2 data obtained in the Comprehensive Observation Network for TRace gases by AIrLiner (CONTRAIL) project in the upper troposphere and lower stratosphere (UTLS), where the TIR band of TANSO-FTS is most sensitive to CO2 concentrations, to validate the quality of the TIR V1 UTLS CO2 data from 287 to 162 hPa. We first evaluated the impact of considering TIR CO2 averaging kernel functions on CO2 concentrations using CO2 profile data obtained by the CONTRAIL Continuous CO2 Measuring Equipment (CME), and found that the impact at around the CME level flight altitudes (∼ 11 km) was on average less than 0.5 ppm at low latitudes and less than 1 ppm at middle and high latitudes. From a comparison made during flights between Tokyo and Sydney, the averages of the TIR upper-atmospheric CO2 data were within 0.1 % of the averages of the CONTRAIL CME CO2 data with and without TIR CO2 averaging kernels for all seasons in the Southern Hemisphere. The results of comparisons for all of the eight airline routes showed that the agreements of TIR and CME CO2 data were worse in spring and summer than in fall and winter in the Northern Hemisphere in the upper troposphere. While the differences between TIR and CME CO2 data were on average within 1 ppm in fall and winter, TIR CO2 data had a negative bias up to 2.4 ppm against CME CO2 data with TIR CO2 averaging kernels at the northern low and middle latitudes in spring and summer. The negative bias at the northern middle latitudes resulted in the maximum of TIR CO2 concentrations being lower than that of CME CO2 concentrations, which led to an underestimate of the amplitude of CO2 seasonal variation.


Introduction
Carbon dioxide (CO 2 ) in the atmosphere is a well-known strong greenhouse gas (IPCC, 2013, and references therein), with concentrations that have been observed both in situ and by satellite sensors.Its long-term observation began in Mauna Loa, Hawaii, and the South Pole in the late 1950s (Keeling et al., 1976a(Keeling et al., , b, 1996)).Since then, comprehensive CO 2 observations in the atmosphere have been conducted worldwide in several observatories and tall towers (Bakwin et al., 1998), by aircraft flask sampling (e.g., Crevoisier et al., 2010), and via the AirCore sampling system (Karion et al., 2010) in the framework of research by the National Oceanic and Atmospheric Administration (NOAA).Atmo-N.Saitoh et al.: Validation of TANSO-FTS TIR V1 UTLS CO 2 product spheric CO 2 concentrations have gradually increased at a globally averaged annual rate of 1.7 ± 0.5 ppm from 1998 to 2011, although its growth rate has relatively large interannual variation (IPCC, 2013).Upper-atmospheric CO 2 observations have been made in many areas by several projects using commercial airliners, such as the Comprehensive Observation Network for TRace gases by AIrLiner (CONTRAIL) project (Machida et al., 2008) and the Civil Aircraft for the Regular Investigation of the atmosphere Based on an Instrument Container (CARIBIC) project (Brenninkmeijer et al., 2007).Continuous long-term measurements of CO 2 made by several airplanes of Japan Airlines (JAL) in the CONTRAIL project have revealed details of its seasonal variation and interhemispheric transport in the upper atmosphere (Sawa et al., 2012) and interannual and long-term trends of its latitudinal gradients (Matsueda et al., 2015).
Atmospheric CO 2 observations by satellite sensors are categorized into two types: those utilizing CO 2 absorption bands in the shortwave infrared (SWIR) regions at around 1.6 and 2.0 µm, and those in the thermal infrared (TIR) regions at around 4.6, 10, and 15 µm.The Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY) on the Environmental Satellite (EN-VISAT) first observed CO 2 column-averaged dry-air mole fractions (XCO 2 ) from spectra at 1.57 µm (Buchwitz et al., 2005;Barkley et al., 2006).The Thermal and Near Infrared Sensor for Carbon Observation (TANSO)-Fourier Transform Spectrometer (FTS) on board the Greenhouse Gases Observing Satellite (GOSAT), which was launched in 2009 (Yokota et al., 2009), has observed XCO 2 with high precision by utilizing the 1.6 and/or 2.0 µm CO 2 absorption bands (Yoshida et al., 2011(Yoshida et al., , 2013;;O'Dell et al., 2012;Butz et al., 2011;Cogan et al., 2012).The Orbiting Carbon Observatory 2 (OCO-2) was successfully launched in 2014 and started regular observations of XCO 2 with high spatial resolution.Satellite CO 2 observations at TIR absorption bands have a longer history beginning with the High-Resolution Infrared Sounder (HIRS) (Chédin et al., 2002(Chédin et al., , 2003(Chédin et al., , 2005)).The Atmospheric Infrared Sounder (AIRS) has achieved more accurate observations of middle-and upper-tropospheric CO 2 concentrations (Crevoisier et al., 2004;Chahine et al., 2005;Maddy et al., 2008;Strow and Hannon, 2008).The Tropospheric Emission Spectrometer (TES) has observed CO 2 concentrations in several vertical layers with high accuracy by taking advantage of its high wavelength resolution (Kulawik et al., 2010(Kulawik et al., , 2013)).The Infrared Atmospheric Sounding Interferometer (IASI) has observed upper-atmospheric CO 2 amounts from its TIR spectra (Crevoisier et al., 2009).TANSO-FTS also has a TIR band in addition to its three SWIR bands, and it obtains vertical information of CO 2 concentrations in addition to XCO 2 in the same field of view (Saitoh et al., 2009).Rayner and O'Brien (2001) and Pak and Prather (2001) showed the utility of global CO 2 data obtained by satellite sensors for estimating its source and sink strength, and many studies of CO 2 inversion have been conducted using a huge amount of satellite data since the 2000s.Chevallier et al. (2005) first used satellite CO 2 data, observed with the Operational Vertical Sounder (TOVS), to estimate CO 2 surface fluxes.They reported that a regional bias in satellite CO 2 data hampers the outcomes.Nassar et al. (2011) demonstrated that the wide spatial coverage of satellite CO 2 data is beneficial to CO 2 surface flux inversion through the combined use of TES and surface flask CO 2 data, particularly in regions where surface measurements are sparse.In addition to CO 2 surface inversion results using TIR observations, global XCO 2 data observed with the SWIR bands of TANSO-FTS have been actively used for estimating CO 2 source and sink strength (Maksyutov et al., 2013;Saeki et al., 2013a;Chevallier et al., 2014;Basu et al., 2013Basu et al., , 2014;;Takagi et al., 2014).One of the important things to consider when incorporating satellite data in CO 2 inversion is the accuracy of the data, as suggested by Basu et al. (2013).Uncertainties in satellite CO 2 data should be assessed seasonally and regionally to determine the seasonal and regional characteristics of the satellite CO 2 bias.
The importance of upper-atmospheric CO 2 data in the inversion analysis of CO 2 surface fluxes was discussed in Niwa et al. (2012).They used CONTRAIL CO 2 data in conjunction with surface CO 2 data to estimate surface flux, and they demonstrated that adding middle-and uppertropospheric data observed by the aircraft could greatly reduce the posteriori flux errors, particularly in tropical Asian regions.Middle-and upper-tropospheric and lowerstratospheric CO 2 concentrations and column amounts of CO 2 can be simultaneously observed in the same field of view with TANSO-FTS on board GOSAT.Provided that the quality of upper-atmospheric CO 2 data simultaneously obtained with TANSO-FTS is proven to be comparable to that of TANSO-FTS XCO 2 data (Yoshida et al., 2013;Inoue et al., 2013), the combined use of upper-atmospheric CO 2 and XCO 2 data observed with TANSO-FTS could be a useful tool for estimating CO 2 surface flux.
GOSAT, which is the first satellite to be dedicated to greenhouse gas monitoring, was launched on 23 January 2009.As described above, TANSO-FTS on board GOSAT has been observing CO 2 concentrations in several vertical layers in the TIR band.In this study, we focused on CO 2 concentrations in the upper troposphere and lower stratosphere (UTLS), where the TIR band of TANSO-FTS is most sensitive.We validated these data by comparison with upper-atmospheric CO 2 data obtained in a wide spatial coverage in the CON-TRAIL project.Sections 2 and 3 explain the GOSAT and CONTRAIL measurements, respectively.Section 4 details the retrieval algorithm used in the latest version 1 (V1) CO 2 level 2 (L2) product of the TIR band of TANSO-FTS.Section 5 describes the methods of comparing TANSO-FTS TIR V1 L2 and CONTRAIL CO 2 data.Sections 6 and 7 show and discuss the results of the comparisons between TIR and CONTRAIL CO 2 data.Section 8 summarizes this study.

GOSAT observations
GOSAT is a joint satellite project of the National Institute for Environmental Studies (NIES), Ministry of the Environment (MOE), and Japan Aerospace Exploration Agency (JAXA) for the purpose of making global observations of greenhouse gases such as CO 2 and CH 4 (Hamazaki et al., 2005;Yokota et al., 2009).It was launched on 23 January 2009, from the Tanegashima Space Center, and has continued its observations for more than 6 years.GOSAT is equipped with TANSO-FTS for greenhouse gas monitoring and the TANSO-Cloud and Aerosol Imager (CAI) to detect clouds and aerosols in the TANSO-FTS field of view (Kuze et al., 2009).TANSO-FTS consists of three bands in the SWIR region and one band in the TIR region.Column amounts of greenhouse gases are observed in the SWIR bands, and vertical information of gas concentrations are obtained in the TIR band (Yoshida et al., 2011(Yoshida et al., , 2013;;Saitoh et al., 2009Saitoh et al., , 2012;;Ohyama et al., 2012Ohyama et al., , 2013)).Kuze et al. (2012) provided a detailed description of the methods used for the processing and calibration of level 1B (L1B) spectral data from TANSO-FTS.They explained the algorithm for the version 150.151 (V150.151)L1B spectral data.The TIR V1 L2 CO 2 product we focused on in this study was created from a later version, V161.160, of L1B spectral data.The following modifications were made to the algorithm from V150.151 to V161.160: improving the TIR radiometric calibration through the improvement of calibration parameters, turning off the sampling interval non-uniformity correction, modifying the spike noise criteria of the quality flag, and reevaluating the misalignment between the GOSAT satellite and TANSO-FTS sensor.Kataoka et al. (2014) reported that the biases of TANSO-FTS TIR V130.130L1B radiance spectra based on comparisons with the Scanning High-resolution Interferometer Sounder (S-HIS) spectra for warm scenes were 0.5 K at 800-900 and 700-750 cm −1 , 0.1 K at 980-1080 cm −1 , and more than 2 K at 650-700 cm −1 .Although the magnitude of the spectral bias evaluated on the basis of V130.130L1B data would change in V161.160L1B data, the issue of L1B spectral bias still remains.The spectral bias inherent in TIR L1B spectra would be mainly because of uncertainty of polarization correction.Another possible cause was discussed in Imasu et al. (2010).When retrieving CO 2 concentrations from the TIR band of TANSO-FTS, the spectral bias that is predominant in CO 2 absorption bands should be considered (Ohyama et al., 2013).

CONTRAIL Continuous Measurement Equipment (CME) observations
We used CO 2 data obtained in the CONTRAIL project to validate the quality of TANSO-FTS TIR V1 L2 CO 2 data.CONTRAIL is a project to observe atmospheric trace gases such as CO 2 and CH 4 using instruments installed on com-mercial aircraft operated by JAL.Observations of trace gases in this project began in 2005.Two types of measurement instruments, the Automatic Air Sampling Equipment (ASE) and the Continuous CO 2 Measuring Equipment (CME), have been installed on several JAL aircraft to measure trace gases over a wide area (Machida et al., 2008).This study used CO 2 data obtained with CME on several airline routes from Narita Airport, Japan.CO 2 observations with CME use a LI-COR LI-840 instrument that utilizes a nondispersive infrared absorption (NDIR) method (Machida et al., 2008).In the observations, two different standard gases, with CO 2 concentration of 340 and 390 ppm based on NIES09 scale, are regularly introduced into the NDIR for calibration.The accuracy of CME CO 2 measurements is 0.2 ppm.See Machida et al. (2008Machida et al. ( , 2011) ) and Matsueda et al. (2008) for details of the CME CO 2 observations and their accuracy and precision.
4 Retrieval algorithm of TANSO-FTS TIR V1 CO 2 data 4.1 Basic retrieval settings Saitoh et al. (2009) provided an algorithm for retrieving CO 2 concentrations from the TIR band of TANSO-FTS.The first version, V00.01, of the L2 CO 2 product of the TIR band of TANSO-FTS was basically processed by the algorithm described in Saitoh et al. (2009).The V1 L2 CO 2 product that we focused on in this study also adopted a nonlinear maximum a posteriori (MAP) method with linear mapping, as was the case for the V00.01 product.We utilized the following expressions in TIR CO 2 retrieval: where x a is an a priori vector, S a is a covariance matrix of the a priori vector, S ε is a covariance matrix of measurement noise, K i is a CO 2 Jacobian matrix calculated using the ith retrieval vector xi on full grids, F ( xi ) is a forward spectrum vector based on xi , y is a measurement spectrum vector, and ẑi+1 is the i + 1th retrieval vector defined on retrieval grids.W is a matrix that interpolates from retrieval grids onto full grids.W * is the generalized inverse matrix of W.
The full grids are vertical layer grids for radiative transfer calculation, and the retrieval grids are defined as a subset of the full grids.In the V1 L2 CO 2 retrieval algorithm, linear mapping between retrieval grids and full grids was also applied, but the number of full grid levels was 78 instead of 110 in the V00.01 algorithm.The determination of retrieval grids in the V1 algorithm basically followed the method of the V00.01 algorithm.It was based on the areas of a CO 2 averaging kernel matrix in the tropics, but the retrieval grid levels were fixed for all of the retrieval processing, as presented in Table 1.Averaging kernel matrix A is defined (Rodgers,  A priori and initial values for CO 2 concentrations were taken from the outputs of the NIES transport model (NIES-TM05) (Saeki et al., 2013b).A priori and initial values for temperature and water vapor were obtained from Japan Meteorological Agency (JMA) Grid Point Value (GPV) data.Basically, the retrieval processing of TANSO-FTS was only conducted under clear-sky conditions, which was judged based on a cloud flag from TANSO-CAI in the daytime (Ishida and Nakajima, 2009;Ishida et al., 2011) and on a TANSO-FTS TIR spectrum in the nighttime.

Improvements in the TIR V1 CO 2 algorithm
The following conditions are the improvements made in the TANSO-FTS TIR V1 L2 CO 2 algorithm from the V00.01 algorithm.The V1 algorithm used the CO 2 10 µm absorption band in addition to the CO 2 absorption band at around the 15 µm band; the wavelength regions of 690-750, 790-795, 930-990, and 1040-1090 cm −1 were used in the CO 2 retrieval.We did not apply any channel selection.In these wavelength regions, temperature, water vapor, and ozone concentrations were retrieved simultaneously with CO 2 concentration.Moreover, surface temperature and surface emissivity were simultaneously derived as a correction parameter of the spectral bias inherent in TANSO-FTS TIR V161.160L1B spectra at the above-mentioned CO 2 absorption bands.We assumed that the spectral bias could be divided into two components: a wavelength-dependent bias whose amount varied depending on wavelength and a wavelength-independent bias whose amount was uniform in a certain wavelength region.We tried to correct such a wavelength-independent component of the spectral bias by adjusting the value of surface temperature.Similarly, a wavelength-dependent component of the spectral bias was corrected by adjusting the value of surface emissivity in each wavelength channel.Therefore the matrices of K and S a of expression (1) are as follows: where vectors of surface emissivity in each of the five wavelength regions.The elements of the Jacobian vectors of surface parameters that were defined for each of the five wavelength regions were set to be zero in the other wavelength regions.The values S sT_1 , S sT_2 , S sT_3 , S sT_4 , and S sT_5 and S sE_1 , S sE_2 , S sE_3 , S sE_4 , and S sE_5 are a priori variances of surface temperature and surface emissivity in each of the five wavelength regions, respectively.Simultaneous retrieval of the surface parameters in the V1 algorithm was conducted just for the purpose of correcting the TIR V161.160L1B spectral bias; it had no physical meaning.We estimated the surface parameters separately in each of the five wavelength regions to consider differences in the amount of spectral bias in each wavelength region.The matrices S a for CO 2 , temperature, water vapor, and ozone were diagonal matrices with vertically fixed diagonal elements with a standard deviation of 2.5 %, 3 K, 20 %, and 30 %, respectively.Here, a priori and initial values for ozone were obtained from the climatological data for each latitude bin for each month given by MacPeters et al. (2007).We assumed rather large values as a priori variances of the surface parameters (a standard deviation of 10 K for surface temperature), which could allow more flexibility in the L1B spectral bias correction by the surface parameters.The a priori and initial values for surface emissivity were calculated by linear regression analysis using the Advanced Space-borne Thermal Emission Reflection Radiometer (ASTER) Spectral Library (Baldridge et al., 2009) using land-cover classification, vegetation, and wind speed information.The a priori and initial values for surface temperature were estimated using radiance data in several channels around 900 cm −1 of the TIR V161.160L1B spectra.
In the TIR V1 L2 algorithm, we estimated surface temperature and surface emissivity to correct the spectral bias inherent in the TANSO-FTS TIR L1B spectra (Kataoka et al., 2014).The existence of a relatively large spectral bias around the CO 2 15 µm absorption band in TANSO-FTS TIR L1B spectra (Kataoka et al., 2014) resulted in a decrease in the number of normally retrieved CO 2 profiles.This is probably because the TIR L1B spectral bias in the CO 2 15 µm absorption band was sometimes too large for the L2 retrieval calculation to converse in a limited iteration.The correction of the TIR L1B spectral bias through the simultaneous retrieval of the surface parameters did not affect retrieved CO 2 concentrations in the UTLS regions, which was the focus of this study, but it altered the number of normally retrieved CO 2 profiles.The correction of the TIR L1B spectral bias through the simultaneous retrieval of surface temperature increased the number of normally retrieved CO 2 profiles.This implies that a wavelength-independent component of the spectral bias in CO 2 absorption bands could be reduced by adjusting the value of surface temperature at the bands.In contrast, the spectral bias correction through the simultaneous retrieval of surface emissivity did not increase the number of normally retrieved CO 2 profiles.If the TIR L1B spectral bias has a wavelength dependence, surface emissivity could be effective for correcting such a wavelength-dependent bias.A more effective method of L1B spectral bias correction based on surface emissivity should be considered in the next version of the TIR L2 CO 2 retrieval algorithm if a future version of the TIR L1B spectral data still has a bias.

Area comparisons
Here, we used the level flight CO 2 data of CONTRAIL CME observations in 2010 to validate the quality of UTLS CO 2 data from the TANSO-FTS TIR V1 L2 CO 2 product.The level flight data obtained from the following eight airline routes of the CONTRAIL CME observations were used in this study: Tokyo-Amsterdam (NRT-AMS) and Tokyo-Moscow (NRT-DME), Tokyo-Vancouver (NRT-VYR), Tokyo-Honolulu (NRT-HNL), Tokyo-Bangkok (NRT-BKK), Tokyo-Singapore (NRT-SIN) and Tokyo-Jakarta (NRT-CGK), and Tokyo-Sydney (NRT-SYD).We merged the level flight data of Tokyo-Amsterdam and Tokyo-Moscow into "Tokyo-Europe", and the data of Tokyo-Singapore and Tokyo-Jakarta into "Tokyo-East Asia".Figure 2 shows the flight tracks of all of the CONTRAIL CME observations in 2010 used in this study.As shown in the figure, we divided the CON-TRAIL CME level flight data into 40 areas following Niwa et al. (2012), and compared them with TANSO-FTS TIR CO 2 data in each area in each season.The amount of level flight data varied depending on the area and season.The largest amount of data was obtained in area 15 over Narita Airport, where 4694-9306 data points were obtained.A relatively small amount of level flight data, 79-222 data points, was obtained in area 1 over Amsterdam.In all 40 areas, we collected sufficient level flight data to undertake comparison analysis based on the average values, except for seasons and regions with no flights.

Comparisons of CME profiles with and without averaging kernels
In comparisons of TIR V1 L2 CO 2 data with the CON-TRAIL CME level flight data, it is difficult to smooth the CME data by applying TIR CO 2 averaging kernels, because CO 2 concentrations below and above the CME flight levels were not observed.Here, we evaluated the impact of considering averaging kernel functions on CO 2 concentrations using the CME profile data.We regarded the CME data obtained during the ascent and descent flights over the nine airports as part of CO 2 vertical profiles, and investigated differences between TIR and CME CO 2 data with and without applying averaging kernel functions in the altitude regions around the CME level flight observations.We assumed the CME ascending/descending CO 2 concentration at the uppermost altitude level to be constant up to the tropopause height, following the method proposed by Araki et al. (2010).We used stratospheric CO 2 data taken from the Nonhydrostatic Icosahedral Atmospheric Model (NICAM)-Transport Model (TM) (Niwa et al., 2011(Niwa et al., , 2012) ) to create whole CO 2 vertical profiles over the airports.The NICAM-TM CO 2 data used here introduced CONTRAIL CO 2 data to the inverse model in addition to surface CO 2 data, and therefore could simulate upper-atmospheric CO 2 concentrations well (Niwa et al., 2012).We determined the stratospheric CO 2 profile by assuming the CO 2 concentration gradients, calculated on the basis of the NICAM-TM CO 2 data above the tropopause height.
To compare these CME CO 2 profiles with TIR CO 2 data, we calculated a weighted average of all the CME CO 2 data included in each of the 28 retrieval grid layers with respect to altitude, and defined the CO 2 data in the 28 layers as "CONTRAIL (raw)" data.Then, we selected TIR CO 2 data that coincided with each of the CONTRAIL (raw) profiles.The criteria for the coincident pairs were a 300 km distance from Narita airport, and a 3-day difference of each other observation.We applied TIR CO 2 averaging kernel functions to the corresponding CONTRAIL (raw) profile, as follows (Rodgers and Connor, 2003): (5) Here, x CONTRAIL (raw) and x a priori are CONTRAIL (raw) and a priori CO 2 profiles.We defined the CONTRAIL (raw) data with TIR CO 2 averaging kernel functions as "CON-TRAIL (AK)" data.

Level flight comparisons
In this study, we made comparisons between TIR and CON-TRAIL CME level flight CO 2 data in two ways.The first was a direct comparison with original CME CO 2 data, i.e., CONTRAIL (raw) data.The second was a comparison with CONTRAIL (AK) data in the altitude regions around the CME level flight observations that were based on "assumed CO 2 profiles" created at each of the measurement locations of all the CME level flight data.In the first comparison with CONTRAIL (raw) data, the CME level flight data in each of the 40 areas were averaged for each season (MAM, JJA, SON, and JF/DJF).The average altitude of all of the CME level flight data used here was 11.245 km.The airline routes of Tokyo-Europe, Tokyo-Vancouver, and Tokyo-Honolulu contained both tropospheric and stratospheric data in the areas along their routes; therefore, we calculated the average and standard deviation values separately.Here, we differentiated between the tropospheric and stratospheric level flight data on the basis of temperature lapse rates from the JMA GPV data that were interpolated to the CONTRAIL CME measurement locations.The average altitudes of the tropospheric and stratospheric level flight data from the airline route between Tokyo and Europe were 10.84 and 11.18 km, respectively.
In the comparison with CONTRAIL (raw) data, we selected TANSO-FTS TIR V1 L2 CO 2 data that were in the altitude range within ±1 km of the average altitude of the CME level flight data for each area for each season, and we calculated their averages and standard deviations.Similarly, we calculated the averages and standard deviations of the corresponding a priori CO 2 data for each area for each season.For the airline routes of Tokyo-Europe, Tokyo-Vancouver, and Tokyo-Honolulu, the averages and standard deviations of TIR V1 CO 2 data and the corresponding a priori CO 2 data were calculated separately for the tropospheric and stratospheric data.In this calculation, we first selected TIR V1 CO 2 data that were collected in a range within ±1 km of the average altitudes of the CONTRAIL tropospheric and stratospheric CO 2 data for each area.Then, we classified each of the selected TIR CO 2 data points into tropospheric and stratospheric data on the basis of the temperature lapse rates from the JMA GPV data that were interpolated to the TANSO-FTS measurement locations, and we calculated the seasonal averages and standard deviations for the reselected tropospheric and stratospheric TIR CO 2 data.This procedure was required for two reasons: (1) tropopause height at each TANSO-FTS measurement location should differ on a daily basis, and (2) because TIR CO 2 data were selected within the range of 2 km, some tropospheric TIR CO 2 data were selected on the basis of the CONTRAIL stratospheric level flight data, and vice versa.Figure 3 shows the number of TANSO-FTS TIR CO 2 data points that were finally selected in each retrieval layer for each of the airline routes.The TIR CO 2 data used in the comparative analysis were mainly from layers 9 and 10 (from 287 to 196 hPa) for the tropospheric comparison and from layers 10 and 11 (from 237 to 162 hPa) for the stratospheric comparison.
In the second comparison, we assumed a CO 2 vertical profile on the basis of CONTRAIL (raw) data at each of the CONTRAIL CME level flight locations and applied TIR CO 2 averaging kernel functions to the assumed profiles.For this purpose, realistic CO 2 vertical profiles were required along the eight airline routes.In this study, we created a CO 2 profile at each CME level flight measurement location from CarbonTracker CT2013B monthly-mean CO 2 data (Peters et al., 2007).The CarbonTracker CT2013B CO 2 data are available to the public, and therefore readers can refer to the data set that we used as a CO 2 climatological data set.The method for creating a CO 2 vertical profile from the CON-TRAIL (raw) and CarbonTracker CT2013B data is as follows.We first averaged all of the CarbonTracker CT2013B monthly-mean data included in each of the 40 areas to create area-averaged CarbonTracker CT2013B profiles.Then, we shifted the area-averaged CarbonTracker CT2013B profile so that its concentration fit to each of the CONTRAIL (raw) data at CME level flight altitude.Finally, we applied area-averaged TIR CO 2 averaging kernel functions to each of the shifted area-averaged CO 2 profiles and created profiles of CONTRAIL (AK) at all the CME level flight measurement locations.

N. Saitoh et al.: Validation of TANSO-FTS TIR V1 UTLS CO 2 product
We compared the CONTRAIL (AK) data with TIR CO 2 data at the altitude regions around the CME level flight observations for each area in each season.We extracted CON-TRAIL (AK) data that corresponded to the TIR retrieval layers where TIR CO 2 data were compared to CONTRAIL (raw) data, and we averaged them for each area for each season.For the airline routes of Tokyo-Europe, Tokyo-Vancouver, and Tokyo-Honolulu, we separately averaged CONTRAIL (AK) data created from tropospheric and stratospheric CONTRAIL (raw) data and defined the averages as tropospheric and stratospheric CONTRAIL (AK) data, respectively.As shown in Fig. 3, the CONTRAIL (AK) data used for the comparison during flights between Tokyo and Sydney consisted of CO 2 concentrations in layers 9 and 10 of the CONTRAIL (AK) profiles.For the flights between Tokyo and Europe, the CONTRAIL (AK) data used for the tropospheric and stratospheric comparisons were based on CO 2 concentrations in layers 9 and 10 and in layers 10 and 11 of CONTRAIL (AK) profiles, respectively.

Impacts of averaging kernels on CME profiles
Figure 4 shows comparisons of the differences between TANSO-FTS TIR and CONTRAIL (raw) CO 2 data, and the differences between TIR and CONTRAIL (AK) CO 2 data at low (BKK), middle (NRT and SYD), and high (DME) latitudes in layers 9, 10, and 11.At low latitudes, the differences between CONTRAIL (raw) and CONTRAIL (AK) were mostly less than 0.5 ppm in all seasons.This is because the tropopause heights there were much higher than the altitude levels of CONTRAIL CME level flight measurements, and CO 2 concentrations did not change much in the altitude regions where we compared TIR and CONTRAIL CME data.The same was true for other airports at low latitudes.While the differences between CONTRAIL (raw) and CONTRAIL (AK) were larger at middle and high latitudes than at low latitudes, they were in most cases less than 1 ppm in all seasons.In conclusion, the impact of applying the TIR CO 2 averaging kernels on CONTRAIL CME CO 2 data at around the CME level flight altitudes (∼ 11 km) was on average less than 0.5 ppm at low latitudes and less than 1 ppm at middle and high latitudes.

Comparisons during level flight
The airline route between Tokyo and Sydney covered a wide latitude range from the northern middle latitudes (35 • N) to southern middle latitudes (34 • S). Figure 5 shows comparisons among CONTRAIL (raw), CONTRAIL (AK), TANSO-FTS TIR, and a priori CO 2 data during flights between Tokyo and Sydney in northern hemispheric spring.In this case, we averaged CO 2 data mainly from layers 9 and 10 of the TIR retrieval layer levels.The 1σ values of the av- erages show the variability of CO 2 concentrations in these UTLS layers.The average of the TIR CO 2 data agreed better with the averages of the CONTRAIL (raw) and (AK) CO 2 data than the a priori CO 2 data at all latitudes.The differences between CONTRAIL (raw) and CONTRAIL (AK) were approximately 0.5 ppm, which is consistent with the result shown in Fig. 4, despite the fact that CONTRAIL (AK) data here were evaluated on the basis of CarbonTracker monthly-mean data.In the Southern Hemisphere, the average of the TIR CO 2 data was within 0.1 % of the averages of the CONTRAIL (raw) and CONTRAIL (AK) CO 2 data.In the Northern Hemisphere, the average of the TIR CO 2 data agreed with the averages of the CONTRAIL (raw) and CON-TRAIL (AK) CO 2 data to within 0.5 %, although the agreement was slightly worse there than in the Southern Hemisphere.
Along the airline route between Tokyo and Europe, both tropospheric and stratospheric CO 2 data were obtained in the CONTRAIL CME observations.Therefore, we were able to validate the quality of TANSO-FTS TIR CO 2 data for this route both in the upper troposphere and lower stratosphere using the UTLS CME CO 2 data.Here, we averaged CO 2 data mainly from layers 9 and 10 for the uppertropospheric comparison and from layers 10 and 11 for the lower-stratospheric comparison.As shown in Fig. 6, the differences between CONTRAIL (raw) and CONTRAIL (AK) were again approximately 0.5 ppm when CONTRAIL CME data were divided into the upper troposphere and lower stratosphere, which is consistent with the result shown in Fig. 4. Figure 6b and c shows that the differences between the upper-tropospheric and lower-stratospheric CO 2 concentrations of CONTRAIL CME data were approximately 2-3 ppm in winter (maximum of 4.24 ppm in area 14).The upper-tropospheric and lower-stratospheric CO 2 concentrations from TANSO-FTS TIR V1 data also clearly differed, while the upper-tropospheric and lower-stratospheric CO 2 concentrations from a priori data were similar.The uppertropospheric TIR CO 2 concentrations were in a good agreement within 1 ppm with the corresponding CONTRAIL (raw) and CONTRAIL (AK) data (Fig. 6b).In the lower stratosphere in winter (Fig. 6c), the averages of the CON-TRAIL (raw), CONTRAIL (AK), TANSO-FTS TIR, and a priori CO 2 data were all within 0.5-1 ppm of each other.
The left panels of Fig. 7 show that the agreements between TIR and CONTRAIL (raw) and CONTRAIL (AK) CO 2 average data were worse in spring and summer than in fall and winter in the Northern Hemisphere in the upper troposphere.The differences between TIR and CONTRAIL (raw) and CONTRAIL (AK) CO 2 data were on average within 1 ppm in fall and winter in the northern troposphere.At 0-40 • N in summer, in contrast, the TIR and a priori CO 2 average data were 2.3 ppm lower than the CONTRAIL (AK) CO 2 average data.At 20-40 • N in spring, the differences between TIR and CONTRAIL (AK) CO 2 average data were 2.4 ppm, although the TIR CO 2 data had a better agreement with CONTRAIL CME CO 2 data than a priori CO 2 data.On the other hand, the averages of the TIR CO 2 data were within 0-0.7 ppm of the averages of the CONTRAIL (AK) CO 2 data in the Southern Hemisphere in all seasons, as in the comparison in northern hemispheric spring shown in Fig. 5.
In the lower stratosphere, the agreements between the average TANSO-FTS TIR and CONTRAIL CME CO 2 data did not have a smaller seasonality than in the upper troposphere.The averages of TIR and CONTRAIL (raw) and CONTRAIL (AK) CO 2 data agreed with each other within 0.5 % in all seasons.

Discussion
As shown in Fig. 7, TANSO-FTS TIR V1 L2 CO 2 data had a negative bias of 2.3-2.4 ppm against CONTRAIL CME CO 2 data at the northern low and middle latitudes in spring and summer.Uncertainties in surface parameters and temperature profiles could affect CO 2 retrieval in thermal infrared spec-tral regions.As described above, retrieving surface parameters simultaneously instead of using initial surface parameters did not affect CO 2 concentrations in the UTLS regions in the TIR V1 CO 2 retrieval.We compared simultaneously retrieved temperature profiles with a priori JMA GPV temperature profiles in the UTLS region and did not find any difference between the two which could explain the largest TIR CO 2 negative bias at the northern low and middle latitudes in spring and summer.In the UTLS regions, temperature variability is relatively large, and therefore comprehensive validation analysis of both the a priori and retrieved temperature profiles should be required using reliable and independent temperature data such as radiosonde data.
Uncertainty in a priori data could result in uncertainty in retrieved CO 2 data.Here, we arbitrarily decreased the a priori concentration by 1 % in a test TIR CO 2 retrieval and then compared the retrieved CO 2 concentrations with those retrieved using the original a priori data.At the northern low and middle latitudes in spring and summer where the DF values of TIR V1 CO 2 data were around 1.8 and more, a 1 % negative bias in a priori data could yield up to a 0.7 % negative bias in retrieved CO 2 concentrations in the altitude regions where we did comparisons between TIR and CON-TRAIL CME data, although the magnitude of the bias varied depending on retrievals.As shown by the green lines in Figure 7, a priori CO 2 concentrations were underestimated by 2-4 ppm at the northern low and middle latitudes in spring and summer.The test TIR CO 2 retrieval demonstrated that the negative bias of a priori CO 2 data against CONTRAIL CME data is a possible cause of the TIR CO 2 negative bias in the UTLS regions at the northern low and middle latitudes in spring and summer.
In general, the information content of CO 2 observations made by TIR sensors is higher at middle and high latitudes in spring and summer than in fall and winter because of the thermal contrast in the atmosphere, with less seasonal dependence at low latitudes.Therefore, in spring and summer, retrieved CO 2 data contain more measurement information and are less constrained by a priori data at all latitudes.However, as shown in Fig. 7, the retrieved TIR CO 2 data at the northern low and middle latitudes did not sufficiently reduce the negative bias of the a priori CO 2 data in the UTLS regions in spring and summer.This implies the existence of factors that worsened CO 2 retrieval results other than the a priori data, especially in spring and summer.Another possible factor that worsened CO 2 retrieval results is the uncertainty in the calibration of TIR V161.160L1B spectra.As reported in Kataoka et al. (2014), TANSO-FTS TIR V130.130L1B radiance spectra had a wavelength-dependent bias ranging from 0.1 to 2 K.Although the characteristics of the spectral bias in V161.160L1B data used in TIR V1 L2 CO 2 retrievals are still under investigation, we assumed the same degree of bias in V161.160L1B spectra and evaluated the effect of the L1B spectral bias on the TIR CO 2 retrieval using the following equation: Here, G CO 2 is a gain matrix for CO 2 retrieval, d spec is a spectral bias vector based on the evaluation by Kataoka et al. (2014), and d CO 2 is a vector of bias errors in retrieved CO 2 concentrations attributable to the spectral bias.The result showed that a wavelength-dependent bias comparable to V130.130 L1B spectra could yield up to 0.3 and 0.5 % uncertainties in retrieved CO 2 concentration in the UTLS regions at the northern middle latitude in spring and at the northern low latitude in summer, respectively.Uncertainty in the radiometric calibration of TANSO-FTS L1B spectra causes the spectral bias inherent in TIR L1B spectra.The temperatures of the internal blackbody on board the TANSO-FTS instrument partly reflect the environmental thermal conditions inside the instrument.The temperatures of FTS mechanics and aft optics on the optical bench of the TANSO-FTS instrument are precisely controlled at 23 • C. The difference in temperature between the environment inside the instrument and the optical bench could cause the uncertainty in the radiometric calibration of TANSO-FTS L1B spectra.Thus, the temperatures of the internal blackbody on board the TANSO-FTS instrument could be a parameter used to evaluate the TANSO-FTS TIR L1B spectral bias.
Figure 8 shows the averages of the partial degree of freedom of TANSO-FTS TIR V1 L2 CO 2 data for each of the areas along the airline routes between Tokyo and Europe in the upper troposphere (a) and the lower stratosphere (b) for each season.The partial DF is defined as the diagonal element of the averaging kernels corresponding to TIR CO 2 data that were compared to CONTRAIL CME level flight data, which is equal to the 9th, 10th, or 11th diagonal element of matrix A. As shown in Fig. 8, the average values of the partial DF of TIR lower-stratospheric CO 2 data were clearly lower than those of TIR upper-tropospheric CO 2 data for all of the fights between Tokyo and Europe.TIR uppertropospheric CO 2 data were from layers 9 and 10, and TIR lower-stratospheric CO 2 data were from layers 10 and 11, as shown in Fig. 3, which led to a clear difference in partial DF values between the TIR upper-tropospheric and lowerstratospheric CO 2 data.The partial DF values of TIR uppertropospheric CO 2 data were 0.13-0.20 in all of the areas for all seasons.In contrast, the partial DF values of TIR lowerstratospheric CO 2 data in spring, fall, and winter were ∼ 0.05 in almost all of the areas, although they were as high as 0.1-0.14 in summer.From the results shown in Figs.6c and 8, we conclude that TIR CO 2 retrieval results in the lower stratosphere in winter were constrained to the relatively good a priori CO 2 data due to the low information content and consequently had a good agreement with CONTRAIL CME CO 2 data.The comparisons in the areas during the airline route between Tokyo and Europe were included in the comparison results of 60-70 • N in the right panels of Fig. 7.In this region, the average differences between a priori and CON-TRAIL (raw) data were 1-2 ppm in summer and fall, while they were less than 0.5 ppm in spring and winter.In summer, TIR CO 2 retrievals had a relatively high information content compared to the other seasons, which led to an agreement between TIR and CONTRAIL (raw) and CONTRAIL (AK) CO 2 data of within 0.5 ppm.In fall, TIR CO 2 retrieval results in the lower stratosphere were more constrained to the a priori CO 2 data and therefore had a negative bias of approximately 1-2 ppm against CONTRAIL (raw) and CON-TRAIL (AK) CO 2 data.In conclusion, the quality of TIR V1 CO 2 data in the lower stratosphere depends largely on the information content compared to the upper troposphere.
In the case of high-latitude measurements, TIR V1 lowerstratospheric CO 2 data are only valid in summer.
We investigated the differences between TIR and CON-TRAIL CO 2 comparison results in layers 9-11 with and without applying averaging kernel functions over the nine airports where CO 2 vertical profiles were observed during ascent and descent.At the northern middle latitudes in spring (NRT in Fig. 4), CONTRAIL (AK) was on average 0.2 and 1.2 ppm lower than CONTRAIL (raw) in layers 9 and 10.In contrast, the tendency was the opposite at the southern mid- dle latitudes in spring (SYD in Fig. 4); CONTRAIL (AK) was on average 1.1 and 0.4 ppm higher than CONTRAIL (raw) in layers 9 and 10.This means that CO 2 concentrations in layers 9 and 10 were more affected by stratospheric air with relatively low CO 2 concentrations at the northern middle latitude in spring, when considering averaging kernels.This is consistent with the result of Sawa et al. (2012) showing that the difference between upper-tropospheric and lower-stratospheric CO 2 concentrations was larger in the Northern Hemisphere in spring.
Using CONTRAIL CME level flight observations that covered wide spatial areas allowed us to discuss the longitudinal differences in the characteristics of TIR UTLS CO 2 data.In the comparison results of the airline routes of Tokyo-Europe (Fig. 6) and Tokyo-Vancouver (not shown here), the magnitudes of the differences between TIR and CON-TRAIL (raw) and (AK) CO 2 data did not have a clear longitudinal dependence.Table 2 summarizes the latitudinal dependence of the magnitudes of the differences between TIR and CONTRAIL (AK) CO 2 data.In the upper troposphere within 0-60 • N, negative biases in TIR CO 2 data against CONTRAIL CME CO 2 data ranged from 1.2 to 2.4 ppm in spring and summer when applying averaging kernels to the assumed CME CO 2 profiles created based on Carbon-Tracker CT2013B monthly-mean profiles.It is the negative biases at the northern low and middle latitudes that we should in particular be concerned about when using TIR V1 L2 CO 2 data in any scientific analysis.In the upper troposphere at the northern middle latitudes, CO 2 concentrations reach the maximum from spring through early summer.The negative biases in TIR CO 2 data resulted in the maximum TIR CO 2 concentrations being lower than that of the CONTRAIL CME CO 2 concentrations, which led to an underestimate of the amplitude of the CO 2 seasonal variation when using TIR CO 2 data without taking their negative biases into account.

Summary
In this study, we conducted a comprehensive validation of the UTLS CO 2 concentrations from the GOSAT/TANSO-FTS TIR V1 L2 CO 2 product.The TIR V1 L2 CO 2 algorithm used both the CO 2 10 and 15 µm absorption bands (690-750, 790-795, 930-990, and 1040-1090 cm −1 ) and simultaneously retrieved vertical profiles of CO 2 , water vapor, ozone, and temperature in these wavelength regions.Because the TANSO-FTS TIR V161.160L1B radiance data used in the TIR V1 L2 CO 2 retrieval had a spectral bias, we simultaneously derived surface temperature and surface emissivity in the same wavelength regions as a corrective parameter, other than temperature and gas profiles, to correct the spectral bias.The simultaneous retrieval of surface temperature greatly increased the number of normally retrieved CO 2 profiles.
To validate the quality of TIR V1 upper-atmospheric CO 2 data, we compared them with the level flight CO 2 data of CONTRAIL CME observations along the following airline routes in 2010: Tokyo-Europe (Amsterdam and Moscow), Tokyo-Vancouver, Tokyo-Honolulu, Tokyo-Bangkok, Tokyo-East Asia (Singapore and Jakarta), and Tokyo-Sydney.For the CONTRAIL data obtained during the northern high-latitude flights, we made comparisons among CONTRAIL, TIR, and a priori CO 2 data separately in the upper troposphere and in the lower stratosphere.The TIR upper-tropospheric and lower-stratospheric CO 2 data that were compared were mainly from layers 9 and 10 (287-196 hPa) and from layers 10 and 11 (237-162 hPa), respectively.In this study, we evaluated the impact of considering TIR CO 2 averaging kernel functions on CO 2 concentrations using the CME profile data over the nine airports; the impact at around the CME level flight altitudes (∼ 11 km) was on average less than 0.5 ppm at low latitudes and less than 1 ppm at middle and high latitudes.
In the Southern Hemisphere, the averages of TANSO-FTS TIR V1 upper-atmospheric CO 2 data were within 0.1 % of the averages of CONTRAIL CO 2 data with and without TIR CO 2 averaging kernels for all seasons, from the limited comparisons made during flights between Tokyo and Sydney, while TIR CO 2 data had a better agreement with CON-TRAIL CO 2 data than a priori CO 2 data, with the agreement being on average within 0.5 % in the Northern Hemisphere.The northern high-latitude comparisons suggest that the quality of TIR lower-stratospheric CO 2 data depends largely on the information content.At high latitudes, TIR lower-stratospheric CO 2 data are only valid in summer, when their information content is highest.Overall, the agreements of TIR and CONTRAIL CME CO 2 data were worse in spring and summer than in fall and winter in the Northern Hemisphere in the upper troposphere.TIR CO 2 data had a negative bias up to 2.4 ppm against CONTRAIL CO 2 data with TIR CO 2 averaging kernels at the northern low and middle latitudes in spring and summer.This is partly because of the larger negative bias in the a priori CO 2 data.The spectral bias inherent to TANSO-FTS TIR L1B radiance data could cause a negative bias in retrieved CO 2 concentrations, particularly in summer.TIR sensors can make more observations than SWIR sensors.When using the TIR UTLS CO 2 data, the seasonally and regionally dependent negative biases of the TIR V1 L2 CO 2 data presented here should be taken into account.

Figure 2 .
Figure 2. Flight tracks of all of the CONTRAIL CME observations in 2010 used in this study.The number next to each box area indicates its area number.

Figure 3 .
Figure 3.The number of GOSAT/TANSO-FTS TIR CO 2 data points compared to the CONTRAIL CME level flight data for each retrieval grid layer level for each flight.The numbers of TIR CO 2 data points in the troposphere ("T") and stratosphere ("S") are shown separately for the Tokyo-Europe (NRT_DME_AMS), Tokyo-Vancouver (NRT_YVR), and Tokyo-Honolulu (NRT_HNL) flight routes.

Figure 6 .
Figure 6.Same as Fig. 5 but for flights between Tokyo and Europe (NRT_DME_AMS) in winter (JF).(a) All of the data, (b) only data in the troposphere, and (c) only data in the stratosphere.See the text for the classification of tropospheric and stratospheric data.

Figure 8 .
Figure 8. Partial degree of freedom (DF) for GOSAT/TANSO-FTS TIR CO 2 data in the upper troposphere (a) and the lower stratosphere (b) for each area of the flight between Tokyo and Europe (NRT_DME_AMS).The means and their 1σ standard deviations of the partial DF data were calculated in spring (MAM), summer (JJA), fall (SON), and winter (JF), as shown by the pink, red, light blue, and blue lines, respectively.
and K T are Jacobian matrices of CO 2 , water vapor, ozone, and temperature on full grids, respectively, and S CO 2 , S H 2 O , S O 3 , and S T are a priori covariance matrices of CO 2 , water vapor, ozone, and temperature on full grids, respectively.The vectors k sT_1 , k sT_2 , k sT_3 , k sT_4 , and k sT_5 are the Jacobian vectors of surface temperature in the wavelength regions of 690-715, 715-750, 790-795, 930-990, and 1040-1090 cm −1 , respectively.The vectors k sE_1 , k sE_2 , k sE_3 , k sE_4 , and k sE_5 are the Jacobian Figure1.Averaging kernel functions of GOSAT/TANSO-FTS TIR V1 CO 2 retrieval in the 28 retrieval grid layers shown in Table1: (a) low latitudes in summer, (b) middle latitudes in spring, and (c) high latitudes in winter.Solid orange, yellow, and green lines indicate averaging kernel functions of each of the three layer levels: 9, 10, and 11, respectively.

Table 2 .
Bias values of GOSAT/TANSO-FTS TIR V1 CO 2 data against CONTRAIL (AK) CO 2 data for each season and each latitude region in the upper troposphere and lower stratosphere in units of parts per million (ppm).Significant bias values larger than ±2 ppm are indicated by boldface.