TanSat ACGS on-orbit spectral calibration by use of individual solar lines and entire atmospheric spectra

The spectra measured by the Atmospheric Carbon dioxide Grating Spectrometer (ACGS) carried by the China’s global carbon dioxide observation satellite (TanSat) in the band of 0.76μm, 1.61μm and 2.06μm can be used for the retrieval of carbon dioxide (CO2) concentrations by fitting the observations and simulations using the optimal estimation algorithm. Accurately detecting the change of the center wavelength is highly important because of its very high spectral resolution and accuracy 5 requirement for product retrieval. The variations of center wavelength for all three bands of ACGS have been calculated on the locations of the individual solar absorption lines by comparing the solar-viewing measurements and the high resolution solar reference spectrum. The variations with magnitudes less than 10% of the spectral resolution for each band have been detected. The changes are probably caused by vibration and the instrument status difference between the ground and space, especially temperature variation on orbit. In addition to solar lines, the entire atmospheric spectra simulated by radiative transfer model 10 can be used as the reference spectrum to determine the wavelength change by fitting the measured and simulated spectra. The change of wavelength determined by atmospheric spectra is closely consistent with that by solar lines. Both schemes described here can be used not only for monitoring spectral stability but also to gain spectral knowledge prior to the level-2 product processing. These minor temporal changes of wavelength on orbit should be corrected in the product retrieval.

per full width at half maximum (FWHM) in the range of spectrum and to get a better signal-to-noise ratio (SNR), the spectral resolution is decreased to 0.14 nm in WCO2 and 0.18 nm in SCO2 band, which are lower than that of OCO-2 (Frankenberg et al., 2014;Crisp et al., 2017). Table 1 shows the detailed spectral parameters of the TanSat ACGS instrument. 75 The TanSat ILS and wavelength of each pixel in three band were determined by a tunable diode laser before launch (Yang et al., 2018). Figure 1 shows the ILS profiles as examples at some middle pixels for three bands. The wavelength λ p for a single pixel is expressed by a fifth-degree polynomial as follows: where p refers to the pixel number index ranging from the first pixel to the last pixel in each detector. The total number of 80 pixels is shown in Table 1. The c are the dispersion coefficients associating the spectral pixel index with its wavelength. These coefficients, which are different for each FOV within each band, are initially calculated by fitting the spectral pixel index and its associated wavelength at the laboratory before launch. An example of wavelength calculated by this formula at FOV 5 is shown in Figure 2. The accuracy of this parametrization is sufficient for ACGS's spectral calibration requirement that is one tenth of the spectral resolution.

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The reference spectrum is taken from Kurucz solar spectrum atlas with different resolution available for scientific community (Fontenla et al., 1999;Chance and Kurucz, 2010). The Kurucz's spectra with the sampling resolution of 0.001 nm in the three bands are available via the internet (http://Kurucz.harvard.edu/sun). The Fraunhofer lines, which result from the absorption of sun light by elements in the outer layers of the Sun, can be clearly distinguished in the spectrum observed by ACGS pointing the Sun through the diffuser. The resolution of the Kurucz solar spectrum is one order of magnitude higher than that of ACGS.

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Therefore, the Kurucz solar spectrum is suitable for spectral calibration of ACGS on orbit.
In this method, individual solar lines, not the entire solar irradiance, are used as references. Figure 3 shows the Kurucz solar spectrum for each band. The positions of solar absorption lines are well determined in these spectra and can be used as the reference throughout the three ACGS's bands. The spectral calibration method using solar spectrum needs to select the suitable lines with its center position as the reference standard. These lines should be single and possess adequate intensity so that they 95 can be easily distinguished from the spectrum. The wavelength offset with respect to the wavelength measured at ground is caused by the instrumental effects and Doppler effects on orbit. The latter can be calculated based on the relative velocity of the spacecraft and the Sun. The formula for Doppler correction f d is: where c is the speed of light, and f is the raw solar irradiance frequency. The relative velocity V rel of the satellite and the Sun 100 takes a positive value when they are approaching each other. The solar calibration are carried out at about 7kms −1 relative velocity that moves the spectra by ∼ 1/2 spectral resolution of the O 2 A-band. After the Doppler correction is completed, these spectra are merged into one single oversampled solar spectrum. Then, the selected lines are compared to the expected positions to obtain the wavelength offset induced by the instrumental effects.

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According to the criteria for the lines selection, we have selected ten, eight and eight solar lines in the O 2 A-band, WCO2 and SCO2 band, respectively. Figure 3 shows high-resolution reference spectrum in three bands and the positions of the selected lines are also marked. These lines almost evenly distribute across the spectrum. In the phase of TanSat testing on orbit, we used these selected lines as reference for spectral calibration of the ACGS. Then, this method are successfully implemented in the operation monitoring and the raw data to level-1 product processing. The statistics of offsets are calculated for each band, each spatial FOV, and each solar lines. Figure 7 - Figure 9 show the statistics of the offsets between measured solar lines and the reference lines in 2017. The largest standard deviations are observed in the SCO2 band, followed by the WCO2 band, with a much lower standard deviations in the O 2 A-band. The better statistical feature in O 2 A-band is found, which we attribute to the insensitivity to thermal variations in this band. The offset for the SCO2 band is much noisier than the other two bands. Temperature variations have larger effects on the SCO2 bands 125 than that on O 2 A-band and WCO2 band. The O 2 A-band uses the silicon detector to respond to radiance, while the two CO 2 bands use the HgCdTe detector which are more sensitive to minor variations in temperature. These results demonstrate that these solar lines can be used as reference to determine the wavelength offset, although the solar lines are significantly weaker in the three band than those in UV-visible bands.
3 Calibration with entire atmospheric spectra 130

Method
A fitting method developed by Geffen and van Oss (2003) was applied to the recalibration of GOME spectra. And, Sun et al.
(2017) also proposed the ILS fitting algorithm to characterize the OCO-2 ILS. Briefly, these methods use a high-resolution reference spectrum, i.e., solar spectrum therein, as the reference spectrum. Simulated spectrum is constructed by convolution of the high resolution reference spectrum and the ILS function. Two parameters, a shift α and a squeeze β which are defined 135 with respect to the raw dispersion coefficients, are determined by a best matching between the observed spectrum and the simulated spectrum. The shift applying to the first coefficient in (1) is equal for all pixels , whereas the squeeze applying to the second coefficient is related to the pixel position index. The difference between the measured spectrum and the simulated spectrum can be expressed by a function: where n is the number of pixels in each band; M (i) and S(i, α, β) denotes the measured and simulated spectrum; and δM (i) represent the uncertainty in the measurement. In this study, we use the search routine to find the minimum of equation (3).
In this section, the entire high-resolution atmospheric spectrum, not individual lines, is used as the reference spectrum for the ACGS on-orbit spectral calibration. The reference spectrum is simulated by the radiative transfer model which is the forward model of the TanSat retrieval algorithm for XCO 2 . Reanalysis data from ECMWF is used as the background in the simulation.

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The atmospheric absorption structures are involved in the reference spectrum. There are so large numbers of and complex absorption lines in the earthshine spectrum that the atmospheric absorption lines dominate over the solar absorption features which are obvious on the top of the atmosphere. Hence, the result of this method is independent of solar lines and can be compared with the calibration results shown in section 2.
The earthshine spectra observed by the ACGS are the products of the high-resolution spectrum and the ILS function for 150 each pixels. In the procedure, the high resolution reference spectrum is degraded to the ACGS's resolution with the ILS. The common analytical functions (for example, Gauss-like function) could not fit the measured ILS very well. Figure 1 shows an example of ILS for each band, which is very similar to a normalized Gauss-like function. But at the top of ILS in the two CO 2 bands, the ILS are a little broader than a Gaussian function, and at the bottom of ILS , there are significantly minor irregular structures. Therefore, the preflight ILS were given by lookup tables. Totally, ACGS has 1242×9, 500×9 and 500×9 155 different ILS tables in O 2 A-band, WCO2 and SCO2 band, respectively. The ACGS ILS functions have full widths at half maximum (FWHM) resolutions of 0.04 nm for O 2 A-band, 0.14 nm for WCO2 band and 0.18 nm for SCO2 band (see Table   1). Mathematically, the convolved reference spectrum at a detector pixel with a central wavelength λ is described by where the λ integration is on the full range of the ILS function. The I(λ) is referred to as the reference spectrum for spectral 160 calibration of ACGS on orbit.

Calibration result
This scheme is applied as a complement and verification for the solar calibration because this scheme strongly depends on reanalysis data, which acquisition has a very long delay, at least 1 month from ECMWF. The wavelength shift and squeeze with respect to initial central wavelength are estimated by applying this scheme over the three bands assuming the ILS functions 165 are constant. The initial wavelength from which the calibration starts is the same as that used in the solar calibration, so that the result can be compared with that from solar calibration.
We perform this calibration for many different orbits, and find that the pattern of the variation along one orbit is very similar.
As an example, Figure 10 shows  Table 2 shows the statistics of the shifts for the nine FOVs in each band. The shift variations in the O 2 A-band are more stable than that in the other two bands. Also, the variations are very close and similar for nine FOVs. These statistical features show larger differences for the nine FOVs in SCO2 band.

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The shifts derived from this method agree closely with that calculated from solar spectra. The mean shift is larger than the offset calculated from the solar calibration. The larger shift derived by applying earthshine spectra mainly come from the uncertainties in the simulation using radiative transfer model. For instance, the surface albedo and the optical properties of the atmosphere or aerosols can influence the depths of the absorption lines, and then influence the fitting between the measurement and simulation. Other possible reasons lies in the fact that most of the SNR in the earthshine spectra is lower than that in the 180 solar spectra, particularly for the SCO2 band. Figure 11 shows the example of matching the measurement and simulation spectra by applying shift and applying shift together with squeeze in the O 2 A-band. The measured spectrum is shifted by about 0.005 nm to get a better agreement with the simulated spectrum. This quantity is about 12% of the spectral resolution, while the squeeze term is approximately 0.07%      Figure 11. Example of wavelength calibration of TanSat ACGS for FOV 2. The cyan dashed line denotes the measurement spectra shifted.
The black dashed line reprensents the measurement spectra shifted plus squeezed. The latter overlays the previous due to the very small squeeze.