Saitoh et al. (2009) provided an algorithm for retrieving CO2 concentrations from the TIR band of TANSO-FTS. The first version, V00.01, of the L2 CO2 product of the TIR band of TANSO-FTS was basically processed by the algorithm described in Saitoh et al. (2009). The V1 L2 CO2 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 CO2 retrieval: z^i+1=W∗xa+G[y-F(x^i)+KiW(W∗x^i-W∗xa)]G=[WTKiTSε-1KiW+(W∗SaW∗T)-1]-1WTKiTSε-1, where xa is an a priori vector, Sa is a covariance matrix of the a priori vector, Sε is a covariance matrix of measurement noise, Ki is a CO2 Jacobian matrix calculated using the ith retrieval vector x^i on full grids, F(x^i) is a forward spectrum vector based on x^i, y is a measurement spectrum vector, and z^i+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 CO2 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 CO2 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, 2000) as A=GKW. Figure 1 shows typical averaging kernel functions of TIR V1 L2 CO2 retrieval. The degrees of freedom (DF) in these cases (trace of the matrix A) were (a) 2.22, (b) 1.81, and (c) 1.36. The seasonally averaged DF values of TIR V1 CO2 data ranged from 1.12 to 2.35. At the low and middle latitudes between 35∘ N and 35∘ S, the CO2 DF values were around 2.0 or more; this means that observations by the TIR band of TANSO-FTS can provide information on CO2 concentrations in more than two vertical layers, one of which we focused on in this study.

A priori and initial values for CO2 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.

The following conditions are the improvements made in the TANSO-FTS TIR V1 L2 CO2 algorithm from the V00.01 algorithm. The V1 algorithm used the CO2 10 µm absorption band in addition to the CO2 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 CO2 retrieval. We did not apply any channel selection. In these wavelength regions, temperature, water vapor, and ozone concentrations were retrieved simultaneously with CO2 concentration. Moreover, surface temperature and surface emissivity were simultaneously derived as a correction parameter of the spectral bias inherent in TANSO-FTS TIR V161.160 L1B spectra at the above-mentioned CO2 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 Sa of expression (1) are as follows: K=KCO2KH2OKO3KTksT_1ksT_2ksT_3ksT_4ksT_5ksE_1ksE_2ksE_3ksE_4ksE_5, Sa=SCO2            SH2O              SO3                   ST                                               SsT_1                                SsT_2                        0                                      SsT_3                 0                       SsT_4                                                 SsT_5                                                       SsE_1                                                             SsE_2                                                                    SsE_3                                                                          SsE_4                                                                                  SsE_5, where KCO2, KH2O, KO3, and KT are Jacobian matrices of CO2, water vapor, ozone, and temperature on full grids, respectively, and SCO2, SH2O, SO3, and ST are a priori covariance matrices of CO2, water vapor, ozone, and temperature on full grids, respectively. The vectors ksT_1, ksT_2, ksT_3, ksT_4, and ksT_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 ksE_1, ksE_2, ksE_3, ksE_4, and ksE_5 are the Jacobian 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 SsT_1, SsT_2, SsT_3, SsT_4, and SsT_5 and SsE_1, SsE_2, SsE_3, SsE_4, and SsE_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 V161.160 L1B 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 Sa for CO2, 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 V161.160 L1B 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 CO2 15 µm absorption band in TANSO-FTS TIR L1B spectra (Kataoka et al., 2014) resulted in a decrease in the number of normally retrieved CO2 profiles. This is probably because the TIR L1B spectral bias in the CO2 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 CO2 concentrations in the UTLS regions, which was the focus of this study, but it altered the number of normally retrieved CO2 profiles. The correction of the TIR L1B spectral bias through the simultaneous retrieval of surface temperature increased the number of normally retrieved CO2 profiles. This implies that a wavelength-independent component of the spectral bias in CO2 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 CO2 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 CO2 retrieval algorithm if a future version of the TIR L1B spectral data still has a bias.

Here, we used the level flight CO2 data of CONTRAIL CME observations in 2010 to validate the quality of UTLS CO2 data from the TANSO-FTS TIR V1 L2 CO2 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 CONTRAIL CME level flight data into 40 areas following Niwa et al. (2012), and compared them with TANSO-FTS TIR CO2 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.

In comparisons of TIR V1 L2 CO2 data with the CONTRAIL CME level flight data, it is difficult to smooth the CME data by applying TIR CO2 averaging kernels, because CO2 concentrations below and above the CME flight levels were not observed. Here, we evaluated the impact of considering averaging kernel functions on CO2 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 CO2 vertical profiles, and investigated differences between TIR and CME CO2 data with and without applying averaging kernel functions in the altitude regions around the CME level flight observations. We assumed the CME ascending/descending CO2 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 CO2 data taken from the Nonhydrostatic Icosahedral Atmospheric Model (NICAM)–Transport Model (TM) (Niwa et al., 2011, 2012) to create whole CO2 vertical profiles over the airports. The NICAM-TM CO2 data used here introduced CONTRAIL CO2 data to the inverse model in addition to surface CO2 data, and therefore could simulate upper-atmospheric CO2 concentrations well (Niwa et al., 2012). We determined the stratospheric CO2 profile by assuming the CO2 concentration gradients, calculated on the basis of the NICAM-TM CO2 data above the tropopause height.

To compare these CME CO2 profiles with TIR CO2 data, we calculated a weighted average of all the CME CO2 data included in each of the 28 retrieval grid layers with respect to altitude, and defined the CO2 data in the 28 layers as “CONTRAIL (raw)” data. Then, we selected TIR CO2 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 CO2 averaging kernel functions to the corresponding CONTRAIL (raw) profile, as follows (Rodgers and Connor, 2003): xCONTRAIL(AK)=xa  priori+AxCONTRAIL(raw)-xa  priori. Here, xCONTRAIL  (raw) and xa  priori are CONTRAIL (raw) and a priori CO2 profiles. We defined the CONTRAIL (raw) data with TIR CO2 averaging kernel functions as “CONTRAIL (AK)” data.

In this study, we made comparisons between TIR and CONTRAIL CME level flight CO2 data in two ways. The first was a direct comparison with original CME CO2 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 CO2 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 CO2 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 CO2 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 CO2 data and the corresponding a priori CO2 data were calculated separately for the tropospheric and stratospheric data. In this calculation, we first selected TIR V1 CO2 data that were collected in a range within ±1 km of the average altitudes of the CONTRAIL tropospheric and stratospheric CO2 data for each area. Then, we classified each of the selected TIR CO2 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 CO2 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 CO2 data were selected within the range of 2 km, some tropospheric TIR CO2 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 CO2 data points that were finally selected in each retrieval layer for each of the airline routes. The TIR CO2 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 CO2 vertical profile on the basis of CONTRAIL (raw) data at each of the CONTRAIL CME level flight locations and applied TIR CO2 averaging kernel functions to the assumed profiles. For this purpose, realistic CO2 vertical profiles were required along the eight airline routes. In this study, we created a CO2 profile at each CME level flight measurement location from CarbonTracker CT2013B monthly-mean CO2 data (Peters et al., 2007). The CarbonTracker CT2013B CO2 data are available to the public, and therefore readers can refer to the data set that we used as a CO2 climatological data set. The method for creating a CO2 vertical profile from the CONTRAIL (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 CO2 averaging kernel functions to each of the shifted area-averaged CO2 profiles and created profiles of CONTRAIL (AK) at all the CME level flight measurement locations.

We compared the CONTRAIL (AK) data with TIR CO2 data at the altitude regions around the CME level flight observations for each area in each season. We extracted CONTRAIL (AK) data that corresponded to the TIR retrieval layers where TIR CO2 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 CO2 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 CO2 concentrations in layers 9 and 10 and in layers 10 and 11 of CONTRAIL (AK) profiles, respectively.

Figure 4 shows comparisons of the differences between TANSO-FTS TIR and CONTRAIL (raw) CO2 data, and the differences between TIR and CONTRAIL (AK) CO2 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 CO2 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 CO2 averaging kernels on CONTRAIL CME CO2 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.

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 CO2 data during flights between Tokyo and Sydney in northern hemispheric spring. In this case, we averaged CO2 data mainly from layers 9 and 10 of the TIR retrieval layer levels. The 1σ values of the averages show the variability of CO2 concentrations in these UTLS layers. The average of the TIR CO2 data agreed better with the averages of the CONTRAIL (raw) and (AK) CO2 data than the a priori CO2 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 CO2 data was within 0.1 % of the averages of the CONTRAIL (raw) and CONTRAIL (AK) CO2 data. In the Northern Hemisphere, the average of the TIR CO2 data agreed with the averages of the CONTRAIL (raw) and CONTRAIL (AK) CO2 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 CO2 data were obtained in the CONTRAIL CME observations. Therefore, we were able to validate the quality of TANSO-FTS TIR CO2 data for this route both in the upper troposphere and lower stratosphere using the UTLS CME CO2 data. Here, we averaged CO2 data mainly from layers 9 and 10 for the upper-tropospheric 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 CO2 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 CO2 concentrations from TANSO-FTS TIR V1 data also clearly differed, while the upper-tropospheric and lower-stratospheric CO2 concentrations from a priori data were similar. The upper-tropospheric TIR CO2 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 CONTRAIL (raw), CONTRAIL (AK), TANSO-FTS TIR, and a priori CO2 data were all within 0.5–1 ppm of each other.

Figure 7 shows the results of all of the comparisons among CONTRAIL (raw), CONTRAIL (AK), TANSO-FTS TIR, and a priori CO2 data in the upper troposphere (left) and lower stratosphere (right) for each season. We divided the data for all four data sets in each of the 40 areas into six latitude bands: 40–20∘ S (areas 30 and 31), 20–0∘ S (areas 21, 28, and 29), 0–20∘ N (areas 16, 17, 20, 22, 23, 26, and 27), 20–40∘ N (areas 15, 18, 19, 24, 25, and 37–40), 40–60∘ N (areas 1, 2, 14, and 32–36), and 60–70∘ N (areas 3–13). As for the lower stratosphere, we showed the results at northern latitudes of 40∘ N where an adequate amount of data was obtained. Overall, the black and gray lines (TIR average minus CONTRAIL (raw) average, and TIR average minus CONTRAIL (AK) average) were closer to zero than the green lines (a priori average minus CONTRAIL (raw) average), which means that TIR CO2 data agreed better with CONTRAIL CME CO2 data than a priori CO2 data.

The left panels of Fig. 7 show that the agreements between TIR and CONTRAIL (raw) and CONTRAIL (AK) CO2 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) CO2 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 CO2 average data were 2.3 ppm lower than the CONTRAIL (AK) CO2 average data. At 20–40∘ N in spring, the differences between TIR and CONTRAIL (AK) CO2 average data were 2.4 ppm, although the TIR CO2 data had a better agreement with CONTRAIL CME CO2 data than a priori CO2 data. On the other hand, the averages of the TIR CO2 data were within 0–0.7 ppm of the averages of the CONTRAIL (AK) CO2 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 CO2 data did not have a smaller seasonality than in the upper troposphere. The averages of TIR and CONTRAIL (raw) and CONTRAIL (AK) CO2 data agreed with each other within 0.5 % in all seasons.