On-orbit radiometric calibration of SWIR bands of TANSO-FTS onboard GOSAT

The Greenhouse gases Observing SATellite (GOSAT) was launched on 23 January 2009 to monitor global distributions of carbon dioxide and methane. The Thermal And Near-infrared Sensor for carbon Observation-Fourier Transform Spectrometer (TANSO-FTS) onboard GOSAT measures short-wavelength infrared (SWIR) spectrum, 5 and its radiometric accuracy directly inﬂuences the accuracy of the retrieved green-house gas concentrations. From a 2.5-yr retrieval analysis of GOSAT data, we found that the minimum of the mean-squared value of the residuals (the di ﬀ erence between observed and ﬁtted spectra) and the radiance adjustment factor (one of the ancillary parameter to be retrieved with the gas concentrations for adjusting the radiance level 10 between the bands) changed with time, possibly due to inaccurate degradation correction. In this study, the radiometric degradation of TANSO-FTS was evaluated from the on-orbit solar calibration data and modeled as a function of time and wavenumber for each spectral band. The radiometric degradation of TANSO-FTS Band 1 (centered at 0.76 µm) after the launch was evaluated to be about 4 to 6 %, varying with wavenum-15 ber, whereas the other two bands (Band 2: 1.6 µm and Band 3: 2.0 µm) showed about 1 % degradation and small wavenumber dependency. When we applied the new degradation model in the retrieval analysis, the above-mentioned issues disappeared


Introduction
Atmospheric carbon dioxide (CO 2 ) and methane (CH 4 ) are well-known anthropogenic greenhouse gases.The global monitoring of these gases from space is expected to improve our knowledge of the global distribution and seasonal cycle of the carbon flux (Rayner and O'Brien, 2001;Chevallier et al., 2007Chevallier et al., , 2009;;Hungershoefer et al., 2010;Takagi et al., 2011).
The Greenhouse gases Observing SATellite (GOSAT) was launched on 23 January two instruments: the Thermal And Near infrared Sensor for carbon Observation-Fourier Transform Spectrometer (TANSO-FTS) and the Cloud and Aerosol Imager (TANSO-CAI) (Kuze et al., 2009).The TANSO-FTS is the main instrument to observe CO 2 and CH 4 .It measures solar light reflected from the Earth's surface in the short wavelength infrared (SWIR) region (centered at 0.76, 1.6, and 2.0 µm; TANSO-FTS Bands 1, 2, and 3, respectively) with two orthogonal linear polarizations, designated "P" and "S", as well as thermal radiation from the Earth's surface and atmosphere in the thermal infrared (TIR) region (5.5 to 14.3 µm; TANSO-FTS Band 4).Column-averaged dry-air mole fractions of CO 2 and CH 4 (XCO 2 and XCH 4 ) retrieved from SWIR spectra have been released as the GOSAT SWIR Level 2 product (SWIR L2; Yokota et al., 2009Yokota et al., , 2011)).Other retrieval algorithms have also been developed and applied to the GOSAT SWIR observations (Oshchepkov et al., 2011;Butz et al., 2011;Parker et al., 2011;O'Dell et al., 2012;Crisp et al., 2012;Schepers et al., 2012).One of the major error sources of the retrieved XCO 2 and XCH 4 is the optical path modification due to atmospheric light scattering.The strength of the optical path modification depends not only on the amount of scattering particles but also on the surface reflectance.Therefore, precise radiometric calibration of TANSO-FTS is needed to retrieve accurate XCO 2 and XCH 4 .Currently, most of the GOSAT SWIR retrieval algorithms use the simple degradation model proposed by Kuze at the Japan Aerospace Exploration Agency (JAXA; A. Kuze, personal communication, 2010; Fig. 1).However, this degradation model has been shown to produce large deviations (Kuze et al., 2011(Kuze et al., , 2012)).Further, the degradation of each band is modeled as a function of time, but the model does not take the polarization and wavenumber dependencies into account.From an analysis of 2.5 yr of retrievals using SWIR L2 version 01.xx (Yoshida et al., 2011), we found two time-dependent issues (see next section for details), which may be related to the degradation model.In this study, we re-evaluated the TANSO-FTS degradation using the on-orbit solar calibration data (i.e., the spectral radiances) and clarified the wavenumber and polarization dependencies more precisely.The following two issues were found in the SWIR L2 version 01.xx retrieval results.ISSUE-1: the minimum of the mean-squared value of the residual of TANSO-FTS Band 1 increased with time (Fig. 2a), probably owing to the changes in the baseline shape of the residual spectrum (Fig. 2b).ISSUE-2: the ratio between the radiance adjustment factors (see below for definition) changed with time (Fig. 2c).
Both issues were seen only for the ocean cases.In the SWIR L2 version 01.xx retrieval, the handling of the surface reflectance was different for land and ocean cases (Yoshida et al., 2011).Rough spectra of ground surface albedo in each band were retrieved for the land case, whereas the surface wind speed and radiance adjustment factor were retrieved for the ocean case.A water surface reflectance was calculated based on the slope probability distribution function proposed by Cox and Munk (1954).This assumption provides the water surface reflectance over the entire spectral range with a single parameter of surface wind speed.Because the SWIR L2 version 01.xx retrieval utilizes both Band 1 and 2 spectra, one surface wind speed parameter cannot represent the reflectance levels of the entire TANSO-FTS spectral range if the relative accuracy of the degradation between these bands is inaccurate.The radiance adjustment factor adjusts the radiance level between the bands to avoid a retrieval failure.ISSUE-1 can be explained if the Band 1 degradation has a wavenumber dependency, and ISSUE-2 is directly related to the accuracy of the degradation.

On-orbit solar calibration
The solar radiation reflected by the onboard Spectralon diffuser plate is introduced into the TANSO-FTS when the satellite passes over the northern polar region.Around 35 ∼ 50 scans (about 3 ∼ 4 min converted into the data acquisition time) of solar calibration data were obtained for each orbit (Fig. 3).Both sides of the diffuser plate are used for the solar calibration; the front side is usually exposed to direct solar radiation and the back side is exposed only once a month (Kuze et al., 2011).
In this study, we used the solar calibration data taken with the back side diffuser plate, because it is expected to have suffered less degradation than the front side diffuser (Kuze et al., 2012).Table 1 summarizes the solar calibration data observed by the back side diffuser plate.Furthermore, to discard the data that were contaminated by weak absorption of the terrestrial atmosphere, we selected the solar calibration data with the following criterion.We used the sun-earth-satellite angle θ SES (see Fig. 3) to specify the scan from a series obtained in a single solar calibration.To discover the fine absorption structure, the observed solar spectra were averaged over certain θ SES regions and then their differences were checked (Fig. 4).The absorption structure due to terrestrial atmospheric oxygen can be seen when θ SES is smaller than about 105 degrees.By also considering the data availability (see the range of θ SES in Table 1), we used the data with θ SES just above 105 degrees for each solar calibration in the following analysis.
The general formula of the spectrum observed by TANSO-FTS was a function of the pointing mirror direction.It was expressed as a sum of several Mueller matrices (Eqs.9 and 10 of Kuze et al., 2012).The pointing mirror pointed the diffuser plate and did not move during the solar calibration, and the incident solar irradiance was regarded as non-polarized light.Therefore, the observed spectrum S of the solar calibration can be expressed as where ν is a wavenumber; θ and ϕ are the incident and relative azimuth angles of the incident solar radiation to the diffuser plate, respectively; t is a day after the launch; F SUN is the solar irradiance; R is the distance between Sun and Earth in astronomical units; r is the reflectance of the diffuser plate; OPT is the optical efficiency of the 4715 pointing mirror, TANSO-FTS-mechanism, and after-optics; A is the radiometric degradation of TANSO-FTS; and subscripts "P" and "S" indicate the polarization components.

Incident angle dependency of the diffuser plate
Figure 5a shows the relationship between θ and ϕ for the solar calibration data observed by the back-side diffuser plate.Each curve corresponds to a single solar calibration.Because the requirement θ SES ≈ 105 deg.determines the relationship between θ and ϕ uniquely, ϕ is omitted hereafter.To obtain the θ dependency of the diffuser plate reflectance, a special solar calibration was conducted on 4 March 2009 by rotating the whole satellite (corresponding to the three uppermost data in Table 1 and three longest curves in Fig. 5a; Kuze et al., 2012).In this case, Eq. ( 1) can be written as Therefore, the diffuser plate reflectance normalized by the reference reflectance observed at θ 0 becomes r P/S (ν, θ) In this study, the uppermost data in Table 1 was selected as the reference spectrum; i.e., θ 0 = 33 degree.If the diffuser plate is Lambertian, Eq. (3) becomes unity; however, it showed clear θ dependency (Fig. 6).In addition, the degree of θ dependency varied with wavenumber and polarization.To make a diffuser plate reflectance model, the observed spectrum was first fitted by a cubic-spline curve.Then, the θ dependency was evaluated at each wavenumber point.The diffuser plate reflectance was assumed to be expressed as a second-order polynomial of cosθ, although the validity of this assumption could not be confirmed because of the insufficient number of incident angles.

Radiometric degradation of TANSO-FTS
From Eq. ( 1), the relative degradation of TANSO-FTS can be written as S P/S (ν, θ 0 , t 0 ) r P/S (ν, θ 0 ) The reference spectrum is the same as that in previous section; i.e., t 0 = 40 (4 March 2009) and θ 0 = 33 degree.By performing a similar fitting process to that in the previous section, we evaluated the radiometric degradations of TANSO-FTS at specific wavenumbers (Fig. 7).These results are roughly consistent with those of Kuze et al. (2012).However, we obtained several new findings because they did not consider the wavenumber and polarization dependencies.
The sensitivity degraded exponentially for all bands except in the higher wavenumber region (> 5050 cm −1 ) of Band 3P.The reason for this unexpected sensitivity increase was unclear.Among the GOSAT SWIR retrievals (Yoshida et al., 2011;Oshchepkov et al., 2011;Butz et al., 2011;Parker et al., 2011;Crisp et al., 2012;Schepers et al., 2012), none were used in this wavenumber region for greenhouse gas retrieval, al- observed signal level at this wavenumber region and the noise level, the priority of accurate radiometric calibration in this spectral range is not so high.Therefore, we do not discuss this Band 3P issue further in this paper.
The difference in degradation within the band was largest for Band 1 (∼ 2 %) and relatively small for Band 2 and 3S (< 0.5 %).For Band 1, the degradation of the higher wavenumber region (> 13 150 cm −1 ) was smaller than that of other wavenumber regions.Because the wavenumber-independent degradation correction was applied in the SWIR L2 version 01.xx retrieval, the observed Band 1 spectrum in this wavenumber region suffered excess degradation correction; i.e., the corrected spectrum showed a higher radiance level than the true level and the residual spectrum was expected to have positive value.This tendency coincided with ISSUE-1 (Fig. 2b).Although the actual time constants of degradation for all bands looked similar (Fig. 7), the time constant of Band 1 used in the SWIR L2 version 01.xx retrieval was one-fifth that of Bands 2 and 3 (Fig. 1).To compensate this difference, the ratio of the retrieved radiance adjustment factor could be considered to change with time (ISSUE-2; Fig. 2c).
The degradation for each wavenumber point and polarization was modeled as There were several periods that showed slightly large deviation from the exponential form (Fig. 7).These periods corresponded to large incident angle θ, perhaps owing to the assumption of a second-order polynomial for the modeled θ dependency of the diffuser plate reflectance (Eq.4).Here, data with θ larger than 35 degree were not used when the coefficients d , e, and f were evaluated.The evaluated coefficients are summarized in Table 3. Figure 8 shows the TANSO-FTS degradation over 5.5 yr (the lifetime of GOSAT was designed to be 5 yr) calculated from the evaluated degradation model in this study.

Retrieval test using the evaluated degradation model
We performed a retrieval test using the evaluated degradation model.For the absolute value of the TANSO-FTS degradation, we used the vicarious calibration campaign results (Table IV of Kuze et al., 2011).Here, we focus on whether the time-dependent issues were solved or not.We do not discuss the retrieved XCO 2 and XCH 4 values because this subject is beyond of the scope of this paper, and the impact of the degradation correction on the retrieved XCO 2 and XCH 4 depends on the retrieval setting.
Figure 9 shows the updated retrieval results.Both the minimum of the mean-squared value of the Band 1 residual and the ratio between the radiance adjustment factors flattened in time, and the Band 1 residual spectra for different years showed a similar baseline shape.Therefore, the root cause of the time-dependent issues in the SWIR L2 version 01.xx was concluded to be the accuracy of the degradation model.

Conclusions
The radiometric degradation of TANSO-FTS was evaluated from the on-orbit solar calibration data.The radiometric sensitivity degraded exponentially for all bands except for the higher wavenumber region of Band 3P, and the time constant of degradation depended on the wavenumber and polarization.Band 1 showed the largest degradation (about 6 % at the end of 2011) and had the largest wavenumber dependency within the bands.A new degradation model was constructed from the evaluated results.The predicted degradation after 2012 from this new degradation model is expected to be smaller than 1 % for all bands.By applying the new degradation model to the retrieval, we eliminated the time-dependent issues seen in the SWIR L2 version 01.xx retrieval.
The new degradation model is expected to suppress a possible time-dependent bias error in the retrieval results.
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1Figure 4 . 5 Fig. 4 .5
Figure 4.An example of the averaged solar spectrum over the specified SES range 2 (purple) and their differences (red and blue).As for the reference, transmittance of the 3 terrestrial atmospheric oxygen (black) is also shown.4 5

Table 1 .
On-orbit solar calibration data observing with the back-side diffuser plate.On 30 July 2009, the data suitable for the analysis was not available.