Carbon Dioxide Retrieval from TanSat Observations and Validation with TCCON Measurements

: In this study we present the retrieval of the column-averaged dry air mole fraction of carbon dioxide ( XCO 2 ) from the TanSat observations using the ACOS (Atmospheric CO 2 Observations from Space) algorithm. The XCO 2 product has been validated with collocated ground-based measurements from the Total Carbon Column Observing Network (TCCON) for 2 years of TanSat data from 2017 to 2018. Based on the correlation of the XCO 2 error over land with goodness of ﬁt in three spectral bands at 0.76, 1.61 and 2.06 µ m, we applied an a posteriori bias correction to TanSat retrievals. For overpass averaged results, XCO 2 retrievals show a standard deviation (SD) of ~2.45 ppm and a positive bias of ~0.27 ppm compared to collocated TCCON sites. The validation also shows a relatively higher positive bias and variance against TCCON over high-latitude regions. Three cases to evaluate TanSat target mode retrievals are investigated, including one ﬁeld campaign at Dunhuang with measurements by a greenhouse gas analyzer deployed on an unmanned aerial vehicle and two cases with measurements by a ground-based Fourier-transform spectrometer in Beijing. The results show the retrievals of all footprints, except footprint-6, have relatively low bias (within ~2 ppm). In addition, the orbital XCO 2 distributions over Australia and Northeast China between TanSat and the second Orbiting Carbon Observatory (OCO-2) on 20 April 2017 are compared. It shows that the mean XCO 2 from TanSat is slightly lower than that of OCO-2 with an average di ﬀ erence of ~0.85 ppm. A reasonable agreement in XCO 2 distribution is found over Australia and Northeast China between TanSat and OCO-2.


Introduction
Atmospheric carbon dioxide (CO 2 ) along with methane (CH 4 ) and nitrous oxide (N 2 O) are among the longest-lived greenhouse gases, with atmospheric lifetimes of decades [1]. CO 2 exhibits a larger radiative forcing on climate change than other greenhouse gases, which implies the great importance of monitoring global CO 2 sources and sinks. Global atmospheric CO 2 concentrations have increased by~120 ppm over the last 200 years, largely due to human activities, such as fossil fuel combustion and land use changes [1]. Although surface CO 2 monitoring networks have expanded in recent decades, these observations remain insufficient for the limitations of low spatial coverage. These limitations have led to large uncertainties in climate predictions [2].
One of the most effective approaches to improve the spatial coverage and resolution for CO 2 monitoring is to use satellite measurements [3]. The thermal infrared observations of CO 2 from with TanSat measurements. In this paper, we apply the ACOS algorithm to TanSat measurements under nadir mode and evaluate the XCO 2 retrieval quality with the collocated ground-based TCCON measurements. For target mode, we collected TanSat observations of several cases and evaluate the XCO 2 retrieval results with a synchronous Unmanned Aerial Vehicle (UAV) experiment over Dunhuang calibration field (94.3208 • E, 40.1375 • N) and the measurements from ground-based Fourier-Transform Spectrometer (FTS) located in Beijing [29]. To exclude the low quality XCO 2 retrievals with large uncertainties (i.e., high aerosol loading, cloudy or large spectral uncertainties), we developed an a posteriori data filtering and an XCO 2 bias correction method for the bias between different footprints. A case where TanSat and OCO-2 have partly overlapping orbits is also investigated, where the XCO 2 regional distribution over Australia and northeast China between the different sensors are compared and discussed.
The paper is organized as follows: Section 2 describes the TanSat data and the validation datasets used in this work. The ACOS algorithm including the a posteriori data filtering and adjustments especially for TanSat measurements is described in Section 3. In Section 4, we validate the XCO 2 retrieval results under nadir mode using collocated TCCON measurements. The XCO 2 retrievals under target mode are also evaluated. Here, the performance of the bias correction is also discussed. Section 5 compares the XCO 2 spatial distribution over regions where TanSat and OCO-2 have overlapping orbits. Finally, Section 6 gives the conclusions.

TanSat Observations
TanSat is a sun-synchronous polar-orbiting environmental satellite, with a local time of ∼13:30, an orbit inclination of 98.16 • and an orbit altitude of approximately 700 km. TanSat operates in three observational modes, including nadir, sun-glint, and target modes. TanSat carries two key instruments: The Atmospheric Carbon dioxide Grating Spectroradiometer (ACGS) and the Cloud and Aerosol Polarization Imager (CAPI). The ACGS was designed to measure solar radiation reflected in three different bands. The O 2 A, ranging from 758 to 778 nm, includes the absorption of molecular oxygen, the weak absorption band of molecular carbon dioxide (WCO 2 ) ranges from 1594 to 1624 nm, and the strong absorption of carbon dioxide (SCO 2 ) band ranges from 2042 to 2082 nm. The spectral resolutions at the three bands defined as the Full Width at Half Maximum (FWHM) are~0.04 nm,~0.0131 nm and 0.171 nm respectively. Within the FWHM, there are at least two samples in the direction of dispersion. The ACGS has a spatial resolution of 2 km × 3 km for nadir mode and nine footprints across the orbit, which makes a swath of~20 km [29].

Validation Datasets
TanSat observations in nadir mode from January 2017 to December 2018 are collected. For nadir observations, all the exposures are used for XCO 2 retrieval. The a posteriori data filtering discussed in Section 4.1 is used to exclude the retrievals with large uncertainties. TCCON measurements are collocated with the TanSat nadir observations. The TCCON measures XCO 2 with an uncertainty lower than 0.25% [30]. The collocation criteria include a spatial distance of less than three degrees in both latitude and longitude direction and a time difference of less than two hours. For target mode observations, the view zenith angle should be smaller than 45 degrees.
The validation of retrievals with target mode is conducted using the ground-based FTS measurements in Beijing. The Beijing site is not part of the TCCON observation network. The site is operated by National Satellite Meteorological Center, China Meteorological Administration. The Bruker FTS 125HR in Beijing is similar to the equipment used at TCCON sites and has made observations since 2016 [31]. The precision of FTS CO 2 column has been reported to be better than 0.2% under clearsky conditions [31]; however, systemic bias needs be removed through continuous comparison withother FTS of TCCON sites. In April 2017, for validation of the TanSat target mode observation, Remote Sens. 2020, 12, 2204 4 of 21 a synchronous UAV experiment was carried out over the Dunhuang calibration field. The CO 2 profile under~5 km measured from Greenhouse Gas Analyzer (GGA) equipped on the UAV together with the CO 2 profile of higher layer obtained from the Carbon Tracker (CT) model [32] are integrated for XCO 2 . The GGA CO 2 measurement uncertainty is smaller than 0.6 ppm and is ±0.08 ppm when averaging over 2000 s [33].

Retrieval Algorithm
The ACOS algorithm described in detail by O'Dell [21] has been developed for CO 2 retrievals with OCO data. Before the launch of OCO-2 it has been successfully applied to GOSAT data. After OCO-2 was launched in 2014, the algorithm has been used for the XCO 2 operational product and validated widely against ground-based measurements [12]. As the design of the ACGS is not exactly the same as of OCO-2, with a different band range, dynamic range and noise model, the algorithm had to be adjusted for the new instrument. When the measured radiances at all wavelengths in bands are included in the measurement vector y, it can be described as where F is the forward transfer model, x is the state vector which contains all the parameters needed to be retrieved, and are the combined uncertainties from both instrument and forward model. To find the state vector that produces the maximum a posteriori probability, we minimize the following standard cost function χ 2 S is the measurement covariance matrix, S a is the a priori covariance matrix, x a is the a priori state vector.
For this nonlinear problem, we use an iterative way to find the solution as follows ∂x is the weighting function matrix, here we use the Levenberg-Marquardt modification of the Gauss-Newton method to find the best estimation of the state vectorx iteratively [34]. γ is the Levenberg-Marquardt parameter, this method reduces to regular Gaussian-Newton minimization when γ = 0. γ is initialized with a value of 10.0 as used for OCO-2 [35].
As ACGS is sensitive to polarized light, the forward model should be able to simulate polarized light. The Lidort model [36] is used to simulate the multi-scattering radiance which is assumed to be unpolarized while the polarized light is simulated with the two Orders of Scattering (2OS) model [37]. Then the elements of the instrument Mueller matrix are used to put the stokes vector of the simulated polarized radiance at the Top Of Atmosphere (TOA) into the simulated radiance measured by the ACGS on the high resolution 0.01 cm −1 wavelength grid. The absorption coefficient spectroscopic database includes all the absorption lines of related gases used in the forward mode for the gas absorption cross-section calculation [35]. It includes the absorption lines in the O 2 A band and CO 2 and H 2 O absorption in the weak and strong CO 2 bands. In the forward model, the atmosphere is divided into 20 layers. Since the absorption cross-sections are nonlinear in both temperature and pressure within each layer, each atmospheric layer is subdivided into ten sub-layers; cross-sections for each are calculated for the interpolated pressure and temperature at the center of each sub-layer, converted to optical depth and then added to obtain the optical depth for each atmospheric layer.
For the modeling of atmospheric scattering, the algorithm retrieves a mixture of profiles of four fixed-type atmospheric scatters, which includes water cloud, ice cloud, dust aerosol, sea salt aerosol and stratospheric aerosol. To find the best combination of the five particles, the Aerosol Optical Remote Sens. 2020, 12, 2204 5 of 21 Depths (AOD) at 755 nm of each component is retrieved in the algorithm. The forward model uses a Lambertian reflection over land and a wind-speed dependent COX-Munk reflectance for the ocean [38].
The retrieval algorithm requires a priori information on surface pressure, temperature profile, water vapor concentration and surface wind speed, which are interpolated from the European Centre for Medium Range Weather Forecasts (ECMWF) high-resolution 10-day forecast analysis data on a 0.125 • × 0.125 • grid. The interpolation is performed with linear interpolation in both time and space. 6-hourly global XCO 2 reanalysis products in 2016 and 2017 from Copernicus Atmosphere Monitoring Service (CAMS) are used as the XCO 2 a priori for the retrieval of 2017 and 2018, respectively. The a priori profiles for CO 2 are obtained by scaling the CO 2 profile derived from a multi-year global run of the Laboratoire de Météorologie Dynamique Zoom (LMDZ) model [39]. The monthly zonal mean is calculated from the model in 10 • latitude bands. An offset is added to all the model values to make the global average surface value approximately equal to the measured value from GLOBALVIEW-CO 2 product (Co-operative Atmospheric Data Integration Project-Carbon Dioxide, 2005, ftp.cmdl.noaa.gov/ccg/co2/globalview/); this offset is updated monthly to reflect the increasing concentration of CO 2 .
The solar irradiance data are obtained through a solar model which consists of two parts: the solar absorption model and the solar continuum model. The solar absorption model calculates the solar lines based on empirical solar line list which covers the 550-15,000 cm −1 spectrum and contains over 18,000 lines. The solar continuum model calculates the solar Planck function which is then multiplied with the solar absorption spectra to obtain the solar spectrum. The solar continuum model is based on a polynomial fit to the near-infrared part of the low resolution extra-terrestrial solar spectrum acquired by the SOLar SPECtrum (SOLSPEC) instrument [40].
The state vector is listed in Table 1.  Table 2 gives the filters used in the TanSat retrieval to exclude retrieval results with large uncertainties, where Albedo_O 2 A and Albedo_SCO 2 are the surface albedo in the O 2 A band and SCO 2 band, respectively.

Retrieval Filters and Bias Correction
As we do not use the cloud mask product to screen out the exposure points contaminated by cloud, nearly 240 thousand exposure points of the TanSat nadir mode measurements are collocated with TCCON measurements and~5.0% of these exposure points can obtain converged retrievals. After applying the filters listed in Table 2, 3320 effective retrievals (~1.5%) are found to be suitable retrievals used in the comparison with TCCON measurements.
Before the retrievals are used to compare with the TCCON measurements, we need to correct possible errors introduced by instruments, meteorology, a priori or retrieved parameters. The correction should be valid for each sounding. From our retrieval tests of the target mode, significant negative Remote Sens. 2020, 12, 2204 6 of 21 biases are found for all nine footprints. The uncorrected XCO 2 retrievals show statistically differences ranging from −2.20 to −5.46 ppm with a Standard Deviation (SD) of 1.01 ppm. The errors arise from the calibration uncertainties in the Level 1 processing depending on the viewing direction in across-flight direction. As the 1st and 9th footprints have the smallest biases, we first correct the XCO 2 retrieval of the 1st and 9th footprints and then correct the retrievals of other footprints based on the corrected XCO 2 retrievals of these two footprints. The retrieval bias of all footprints was found to be related with the reduced χ 2 in all 3 bands. The reduced χ 2 is defined as where N is the number of wavelengths used in the retrieval, DFS is the degrees of freedom, y(i) is the TanSat measurements, F(i) is the simulated radiance and σ i is the uncertainty of the TanSat measurement. Through statistical analysis on two years of globally collocated retrievals with TCCON measurements in 2017 and 2018, it is found that > 1 tends to lead to the high XCO 2 retrievals < 1 tends to lead to relatively low XCO 2 retrievals. Larger χ 2 wCO2 will amplify the bias for the same . We correct the bias of footprint-1 and -9 by where the coefficient k = 0.5 and c = 2.67. The coefficients are derived from the linear regression fit between retrievals and TCCON measurements. Then similar with the grid of CAMS, we divide the Earth into grid cells. The size of each grid cell is 4 • × 4 • . The whole TanSat orbit along the swath direction should be included within a certain grid cell. Then the XCO 2 retrievals with negative biases larger than 10 ppm from the a priori are excluded because they can be contaminated by cloud. But high XCO 2 retrievals are not excluded as it can be caused by an emission source. Then the averages of the XCO 2 retrievals for the 1st and 9th footprint are calculated as the mean XCO 2 of the grid. The correction of XCO 2 of the other footprints is conducted by correcting the mean XCO 2 of each footprint to the mean XCO 2 of the grid. The correction method works well to correct the bias between different footprints when the CO 2 variance in the grid is low. However, when the XCO 2 variance in the grid cell is high because there are both sources and sinks of CO 2 inside the same grid cell, the correction method may not be accurate enough.
Overall, after applying the bias correction method, the biases are largely reduced from −3.85 ppm to 0.27 ppm and the average sounding precisions σ is improved from 4.16 ppm to 2.25 ppm for retrievals Remote Sens. 2020, 12, 2204 7 of 21 over land with the nadir mode. The bias corrections are intended to reduce mainly the instrument calibration biases.

TCCON Validation for TanSat Retrieval of Nadir Mode
In this section, the XCO 2 data retrieved with TanSat are validated against the collocated groundbased measurements at TCCON sites listed in Table 3. Figure 1 shows the comparison results over the two TCCON sites of Saga (130.28824 • E, 33.24096 • N) in Japan and Parkfalls (90.273 • W, 45.945 • N) in the United States of America (USA) with relatively more XCO 2 effective retrievals from TanSat in 2017 and 2018. Though there are some retrievals with relatively large uncertainties, most of the retrievals can represent the XCO 2 seasonal variance of the local areas around the TCCON sites. The bias is defined as the mean difference between the collocated TCCON and TanSat retrievals, the sounding retrieval precision (σ t ) defined as the SD of the difference and the station to station variability (σ s ) defined as the SD of the biases for different TCCON sites. Here only the land retrievals of the nadir view and target view modes are evaluated. It has been reported that the uncertainty of TCCON measurements is around 0.4 ppm for XCO 2 (1-sigma) [30]. For simplicity, in the following, the uncertainties of TCCON measurements are assumed to be consistent over all stations with the variability over the different sites to be zero [42,43].
Remote Sens. 2020, 12, x FOR PEER REVIEW 7 of 20 the SD of the biases for different TCCON sites. Here only the land retrievals of the nadir view and target view modes are evaluated. It has been reported that the uncertainty of TCCON measurements is around 0.4 ppm for XCO2 (1-sigma) [30]. For simplicity, in the following, the uncertainties of TCCON measurements are assumed to be consistent over all stations with the variability over the different sites to be zero [42,43].  Figure 2 shows the comparison of the 3320 XCO2 retrievals with TanSat against TCCON measurements. The average bias and SD are 0.41 ppm and 3.57 ppm respectively. It seems the retrievals tend to underestimate XCO2 for the lower TCCON measurements around 405 ppm, while overestimate XCO2 for higher XCO2 measurements. That explains partly why the average bias is small. Figure 3 shows the overall comparison between the averaged TanSat retrievals and the   Figure 2 shows the comparison of the 3320 XCO 2 retrievals with TanSat against TCCON measurements. The average bias and SD are 0.41 ppm and 3.57 ppm respectively. It seems the retrievals tend to underestimate XCO 2 for the lower TCCON measurements around 405 ppm, while overestimate XCO 2 for higher XCO 2 measurements. That explains partly why the average bias is small. Figure 3 shows the overall comparison between the averaged TanSat retrievals and the TCCON measurements.      that leads to overestimating XCO 2 and higher retrieval uncertainty. This trend may be related to the range of solar zenith angle and the different land cover types over the different latitudes. In the high latitude area, χ 2 SCO2 is significantly smaller than that in the low latitude area (the averages are 2.26 and 3.46 respectively), and there is little difference in χ 2 O2 . This phenomenon has also occurred in OCO-2, as [42] found there is a tendency for validations over stations in higher-latitude regions showing relatively larger biases in both the Northern and Southern hemispheres.
to the range of solar zenith angle and the different land cover types over the different latitudes. In the high latitude area, is significantly smaller than that in the low latitude area (the averages are 2.26 and 3.46 respectively), and there is little difference in . This phenomenon has also occurred in OCO-2, as [42] found there is a tendency for validations over stations in higher-latitude regions showing relatively larger biases in both the Northern and Southern hemispheres.    According to the XCO 2 bias correction method for TanSat described in Section 4.1, is the main parameter that affect the retrieval performance. The mean values of χ 2 O2 in 2017 and 2018 are 3.9 and 2.9 respectively, while those of χ 2 sCO2 are 2.7 and 2.5 respectively. Compared to the residuals in both bands in 2017, the residuals decreased in 2018. But the residual decrease in O2A band is larger than that in SCO2 band. It leads to the decrease of and the underestimation of XCO 2 in 2018. One possible reason is that the attenuation of O2A band is larger than that of SCO2 band. This phenomenon was also reported for OCO-2 retrievals [64], which show the fast signal degradation due to ice on the Focal Plane Arrays (FPA) leading to low sensitivity to TOA radiation. The fast signal degradation in the O 2 A band is much stronger than in the two CO 2 bands. The correction of the attenuation needs further study.

Case Study for TanSat Observation of Target Mode
The target mode observations of the TanSat were performed over the ground-based FTS in Beijing for one and a half year after its launch. A flight experiment was also carried out at Dunhuang calibration field in April 2017. As the TanSat instrument began to decay in 2018 (mentioned in Section 4.2), we present the TanSat validation results for target mode observations for three typical cases.
Case 1 gives the retrievals over Dunhuang calibration field. The Dunhuang calibration field is located in the Gobi Desert in northwest China, about 35 km west of Dunhuang City, Gansu Province. A synchronous flight experiment was conducted to collocate with the TanSat target observation over Dunhuang calibration field on 27 April 2017. A delta wing airplane with a powered parachute was used to measure the CO 2 profile. An UAV GGA [33] was installed on the plane for continuous CO 2 , CH 4 and water vapor measurements. The flight duration was in the range of 1.7-2.3 h while spiral descent flights between 5 km and 0.1 km were carried out.
Despite the lack of FTS ground observations at the Dunhuang site, a ground-based GGA was installed at Dunhuang site during the experiment, together with a sun photometer to measure aerosol properties. Figures 6 and 7 show the ground-based aerosol optical measurements and microphysical retrievals by Cimel Electronique-318 sun photometer at Dunhuang on 27 April 2017. AODs at 1.60 µm and 0.76 µm are 0.088 and 0.125, respectively. It can be concluded from the size distribution that the aerosol model is a fine-coarse mixture dominated by coarse particles.

Case study for TanSat observation of target mode
The target mode observations of the TanSat were performed over the ground-based FTS in Beijing for one and a half year after its launch. A flight experiment was also carried out at Dunhuang calibration field in April 2017. As the TanSat instrument began to decay in 2018 (mentioned in Section 4.2), we present the TanSat validation results for target mode observations for three typical cases.
Case 1 gives the retrievals over Dunhuang calibration field. The Dunhuang calibration field is located in the Gobi Desert in northwest China, about 35 km west of Dunhuang City, Gansu Province. A synchronous flight experiment was conducted to collocate with the TanSat target observation over Dunhuang calibration field on 27 April 2017. A delta wing airplane with a powered parachute was used to measure the CO2 profile. An UAV GGA [33] was installed on the plane for continuous CO2, CH4 and water vapor measurements. The flight duration was in the range of 1.7-2.3 h while spiral descent flights between 5 km and 0.1 km were carried out.
Despite the lack of FTS ground observations at the Dunhuang site, a ground-based GGA was installed at Dunhuang site during the experiment, together with a sun photometer to measure aerosol properties. Figures 6 and 7 show the ground-based aerosol optical measurements and microphysical retrievals by Cimel Electronique-318 sun photometer at Dunhuang on 27 April 2017. AODs at 1.60 μm and 0.76 μm are 0.088 and 0.125, respectively. It can be concluded from the size distribution that the aerosol model is a fine-coarse mixture dominated by coarse particles.

Case study for TanSat observation of target mode
The target mode observations of the TanSat were performed over the ground-based FTS in Beijing for one and a half year after its launch. A flight experiment was also carried out at Dunhuang calibration field in April 2017. As the TanSat instrument began to decay in 2018 (mentioned in Section 4.2), we present the TanSat validation results for target mode observations for three typical cases.
Case 1 gives the retrievals over Dunhuang calibration field. The Dunhuang calibration field is located in the Gobi Desert in northwest China, about 35 km west of Dunhuang City, Gansu Province. A synchronous flight experiment was conducted to collocate with the TanSat target observation over Dunhuang calibration field on 27 April 2017. A delta wing airplane with a powered parachute was used to measure the CO2 profile. An UAV GGA [33] was installed on the plane for continuous CO2, CH4 and water vapor measurements. The flight duration was in the range of 1.7-2.3 h while spiral descent flights between 5 km and 0.1 km were carried out.
Despite the lack of FTS ground observations at the Dunhuang site, a ground-based GGA was installed at Dunhuang site during the experiment, together with a sun photometer to measure aerosol properties. Figures 6 and 7 show the ground-based aerosol optical measurements and microphysical retrievals by Cimel Electronique-318 sun photometer at Dunhuang on 27 April 2017. AODs at 1.60 μm and 0.76 μm are 0.088 and 0.125, respectively. It can be concluded from the size distribution that the aerosol model is a fine-coarse mixture dominated by coarse particles.  The two CO2 profiles are averaged to obtain the mean CO2 profile at the overpass time of TanSat. In order to compare with the CO2 column concentration retrieved by satellite, we interpolate the airplane measured CO2 profiles to the layers used in the TanSat retrieval. The CO2 profile above 5 km is obtained from the CT modelled profile. The CO2 measurements on the ground are obtained from ground-based GGA. Then the XCO2 for the aircraft in situ profile is calculated as follows: i i i X hu (6) where N is the number of layer level boundaries, N−1 is the number of layers, i h′ is the weight function of each pressure layer. Finally, the integrated XCO2 was 407.36 ppm and the uncertainty was estimated to be lower than 0.5 ppm. Figure 9 demonstrates the XCO2 retrievals of the nine footprints of TanSat over Dunhuang. The mean and the SD of each footprint are also shown. We find that the average XCO2 of footprint-5 to footprint-8 are overestimated and the bias range between 0.27 and 3.29 ppm. The average XCO2 of the other footprints are underestimated and the biases range between −1.33 and −0.34 ppm. Except for the significantly high variance of footprint-6 (4.64 ppm), the variances of other footprints range between 0.67 and 1.27 ppm. The average XCO2 of all footprints is 407.43 ppm and the bias was 0.06 ppm. With the exclusion of the footprint-6, the mean variance of the other footprints is 0.79 ppm.  The two CO 2 profiles are averaged to obtain the mean CO 2 profile at the overpass time of TanSat. In order to compare with the CO 2 column concentration retrieved by satellite, we interpolate the airplane measured CO 2 profiles to the layers used in the TanSat retrieval. The CO 2 profile above 5 km is obtained from the CT modelled profile. The CO 2 measurements on the ground are obtained from ground-based GGA. Then the XCO 2 for the aircraft in situ profile is calculated as follows: where N is the number of layer level boundaries, N−1 is the number of layers, h i is the weight function of each pressure layer. Finally, the integrated XCO 2 was 407.36 ppm and the uncertainty was estimated to be lower than 0.5 ppm.
Remote Sens. 2020, 12, x FOR PEER REVIEW 14 of 20      The comparison of the two cases in Beijing shows that ACOS algorithm performs well on correcting the uncertainty introduced by aerosol scattering. The average bias of the two-day retrieval results over Beijing is 2.09 ppm with similar variance. We also find that the footprint-6 has some significant system deviations compared with other footprints, probably due to the too many bad pixels for this footprint.
The comparison of the two cases in Beijing shows that ACOS algorithm performs well on correcting the uncertainty introduced by aerosol scattering. The average bias of the two-day retrieval results over Beijing is 2.09 ppm with similar variance. We also find that the footprint-6 has some significant system deviations compared with other footprints, probably due to the too many bad pixels for this footprint.

Comparison of the TanSat and OCO-2 Retrieval Results
In order to further evaluate the retrieval accuracy of TanSat nadir mode observations, the simultaneous XCO2 retrieval products with TanSat and OCO-2 are compared. Figure 11 shows the orbital XCO2 products of two satellites with overlapping regions on 20 April 2017. Figure 11a,b show the XCO2 retrievals over Australia and Northeast China, respectively. In Australia, the average XCO2 retrieved from TanSat and OCO-2 are 399.64 ppm and 400.48 ppm respectively, and the variances are 1.52 ppm and 1.17 ppm respectively. In the northeast of China, the mean XCO2 retrieved from TanSat and OCO-2 are 408.52 ppm and 409.36 ppm respectively, and the variances are 3.15 ppm and 2.27 ppm respectively. In the two regions, the mean values of TanSat are slightly lower than OCO-2, with differences of 0.84 ppm and 0.86 ppm over Australia and Northeast China, respectively. And the variances of TanSat are slightly higher than OCO-2 with differences of 0.35 ppm and 0.88 ppm over Australia and Northeast China, respectively. It can be seen from the comparison that TanSat has

Comparison of the TanSat and OCO-2 Retrieval Results
In order to further evaluate the retrieval accuracy of TanSat nadir mode observations, the simultaneous XCO 2 retrieval products with TanSat and OCO-2 are compared. Figure 11 shows the orbital XCO 2 products of two satellites with overlapping regions on 20 April 2017. Figure 11a,b show the XCO 2 retrievals over Australia and Northeast China, respectively. In Australia, the average XCO 2 retrieved from TanSat and OCO-2 are 399.64 ppm and 400.48 ppm respectively, and the variances are 1.52 ppm and 1.17 ppm respectively. In the northeast of China, the mean XCO 2 retrieved from TanSat and OCO-2 are 408.52 ppm and 409.36 ppm respectively, and the variances are 3.15 ppm and 2.27 ppm respectively. In the two regions, the mean values of TanSat are slightly lower than OCO-2, with differences of 0.84 ppm and 0.86 ppm over Australia and Northeast China, respectively. And the variances of TanSat are slightly higher than OCO-2 with differences of 0.35 ppm and 0.88 ppm over Australia and Northeast China, respectively. It can be seen from the comparison that TanSat has relatively larger uncertainties than OCO-2, which may be attributed to signal-to-noise ratio of TanSat being lower than that of OCO-2 for the same retrieval bands. The deviation in retrieval bias between the two satellites is less than 1 ppm, therefore, it can be concluded that the XCO 2 products from two satellites agree well. relatively larger uncertainties than OCO-2, which may be attributed to signal-to-noise ratio of TanSat being lower than that of OCO-2 for the same retrieval bands. The deviation in retrieval bias between the two satellites is less than 1 ppm, therefore, it can be concluded that the XCO2 products from two satellites agree well.

Conclusions
TanSat is China's first satellite specially used to detect CO 2 concentrations using near-infrared hyperspectral observations. The main on-board instrument ACGS can perform hyperspectral measurements in O 2 A band, CO 2 weak absorption band and CO 2 strong absorption band. Its design parameters are similar to those of OCO-2, and the observations can be obtained in nadir, target and glint modes. The ACOS, which is the CO 2 retrieval algorithm of OCO-2, has been successfully applied to OCO-2 and GOSAT. In this work, we apply the ACOS algorithm to TanSat measurements and evaluate the XCO 2 retrieval performance with various types of validation measurements. The ACOS retrieval system is adjusted according to the instrument parameters and signal-to-noise ratio model of TanSat. Since we do not use the cloud detection product of TanSat to filter the cloud-contaminated observation before retrieval, we set strict post filter conditions to ensure the effectiveness of the retrieval. In nadir observation mode, we have collocated two years' TanSat observations and the ground-based TCCON measurements from 2017 to 2018. We obtained about 0.24 million matches,~5% of all these observations reach converged retrievals. After applying the filter, 3320 effective retrievals (~1.5%) are considered as effective retrievals and used in the validation.
The average bias and SD are 0.41 ppm and 3.57 ppm respectively. If we average the retrievals of the same scene, 120 scenes are obtained. Then the average bias and SD decreased to 0.27 ppm and 2.45 ppm respectively. The bias of each TCCON station as a function of station latitude is also studied. It is found that the XCO 2 tends to be overestimated for regions north of 36 • N in latitude while underestimated south of this latitude. The averaged bias and SD of various sites with latitude north of 36 • N are 1.30 ppm and 2.69 ppm respectively, while those of sites south of 36 • N are −1.34 ppm and 2.22 ppm respectively. The average bias of all stations is 0.66 ppm in 2017 and −0.27 ppm in 2018 respectively. The possible reason is that the attenuation in all three bands of TanSat intensified in 2018 and the attenuation in O 2 A band is much stronger than that of the two CO 2 bands. It leads to relatively low sensitivity to the variance of CO 2 amount.
The analysis of the validation results of the target mode observations show that, the XCO 2 retrievals of the various TanSat footprints are underestimated. Based on the correlation between the retrieval error and the reduced χ 2 in all three bands, we propose a bias correction method. After applying the correction method, the bias is highly improved from −3.85 ppm to 0.27 ppm and the average variation is improved from 4.16 ppm to 2.25 ppm for land retrievals in nadir mode.
Three typical cases are investigated to validate the XCO 2 retrieval with TanSat target mode observations. In April 2017, the Dunhuang synchronous aircraft experiment showed that the retrieved XCO 2 is slightly overestimated with an average bias of all nine footprints being 0.06 ppm. Leaving out footprint-6, the mean variance of all footprints was 0.79 ppm. In 2018, two validation cases around the ground-based FTS in Beijing showed that the average biases are −2.24 and −0.15 ppm on 4 and 31 May respectively. On 4 May, the bias was obviously higher, probably because the AOD at 500 nm reached 0.63, which was much higher than the general retrieval condition (AOD < 0.3). The retrieval accuracy was influenced by the strong aerosol scattering. All the three cases show that the variance of footprint-6 is significantly larger than those of other footprints, and the detector of this footprint is apparently of lower quality.
In order to evaluate the regional distribution of the TanSat XCO 2 , the simultaneous XCO 2 inversion products with TanSat and OCO-2 on 20 April 2017 are cross-compared. The comparison shows that the mean values of TanSat are slightly lower than OCO-2, with differences of 0.84 ppm and 0.86 ppm over Australia and Northeast China, respectively. And the variances of TanSat are slightly higher than OCO-2 with differences of 0.35 ppm and 0.88 ppm. It can be seen that TanSat retrievals show greater uncertainty than OCO-2, which may be due to a lower signal-to-noise of TanSat in the same band. The small deviation in XCO 2 products between the two satellites (less than 1ppm) show that the XCO 2 products from the two satellites agree well.