Fast CO₂ Retrieval Using a Semi-Physical Statistical Model for the High-Resolution Spectrometer on the Fengyun-3D Satellite

Carbon dioxide (CO₂) is one of the most important greenhouse gases. Human activities such as fossil fuel combustion emit billions of tons of CO₂ into the atmosphere since preindustrial times. Measuring the global distribution of CO₂ is very essential not only for inferring the source and sink of carbon but also for improving our understanding of climate change at much higher levels (Miller et al., 2007; Smith, 2017). Atmospheric CO₂ can be accurately measured by the network of surface sites or tall towers. However, the existing sites are too sparse and lack the spatio-temporal resolution needed to infer carbon flux between the surface and the atmosphere on regional scales.

One way to improve the coverage and resolution of CO₂ measurements is by collecting observations from satellites. Although these measurements cannot provide CO₂ profiles, the CO₂ column concentrations are still very useful because they are much less sensitive to uncertainties in flux modeling. In addition, these satellite CO₂ columns have much greater sampling densities on regional and global scales. These satellites can provide a large number of observations in regions where ground-based stations are poorly located.

Several satellites have been successfully launched to monitor the global distributions of CO₂ using near-infrared bands centered at 0.76 μm (O₂ A band), 1.61 μm (the weak CO₂ band near 1.61 µm—WCO₂), and 2.06 μm (the deeply saturated strong CO₂ band near 2.06 µm—SCO₂). Examples include the Greenhouse gases Observing SATellite (GOSAT; Butz et al., 2011; Yoshida et al., 2013), Orbiting Carbon Observatory-2 (OCO-2; Connor et al., 2008; Crisp et al., 2012; O’Dell et al., 2012), and China’s global CO₂ observation satellite (TanSat; Yang et al., 2020; Hong et al., 2021). These satellites carry high-resolution spectrometers to collect reflected sunlight, which will be absorbed by O₂ and CO₂. These absorption measurements in these three bands are analyzed together with the remote sensing retrieval method to yield the estimation of the column-averaged CO₂ dry air mole fraction (XCO₂). O₂ A band provides the surface pressure, whereas the two CO₂ bands provide information on the CO₂ column abundance. $X_{\mathrm{C}\mathrm{O}_2} $ can be defined as the ratio of the column abundance of CO₂ to the column abundance of dry air:

where $N_{\mathrm{C}\mathrm{O}_2} $ and N_air are the number densities of CO₂ and dry air, respectively. Because the concentration of O₂ is close to 0.20935, which is required to get the CO₂ amount, $X_{\mathrm{C}\mathrm{O}_2} $ can also be written as follows:

After the TanSat, China launched the Fengyun-3D (FY-3D) satellite carrying a high-resolution spectrometer, named greenhouse-gases absorption spectrometer (GAS). FY-3 series satellites are China’s second-generation polar-orbiting meteorological satellites. It is the first time for GAS to be carried on FY-3D. Unfortunately, the O₂ A band suffers from some on orbit disturbance induced by solar panel charging. This disturbance makes it difficult to get high-quality observations in the O₂ A band. Hence, the full physics retrieval (FPR) algorithm, which usually uses the three bands together, cannot be used to retrieve XCO₂. We attempted to develop a new algorithm to obtain XCO₂ products to explore the possible maximum application of GAS in monitoring the distribution of global CO₂. This algorithm must have less sensitivity to the disturbance from the observation in the O₂ A band.

The FY-3D meteorological satellite carrying GAS was successfully launched in November 2017 into a sun-synchronous, 836-km altitude polar orbit with a 13:30 ascending local time. GAS is the first instrument on the FY-3 series satellite to monitor the global distribution of greenhouse gases. The primary purpose of the GAS/FY-3D is to measure the distribution of CO₂ with precisions of better than 1–4 ppm on regional to continental scales. These CO₂ products are expected to be used to estimate emissions and absorptions of greenhouse gases on a subcontinental scale (several thousand square kilometers) more accurately. It may also be used to assist environmental administrations in evaluating the carbon balance of the land ecosystem and making assessments of regional emissions and absorptions. GAS utilizes optical interference to get high spectral resolutions of 0.27–0.6 cm⁻¹. In addition to the three bands mentioned above, it has a fourth narrow band with a center wavelength located at 2.3 μm. This band can provide information on other gases such as methane (CH₄), carbon monoxide (CO), and nitrogen monoxide (N₂O).

Table 1 shows the parameters of GAS on FY-3D (see also at https://space.oscar.wmo.int/instruments/view/gas). Signal-to-noise ratios (SNR) are very essential for the retrieval of XCO₂ with low uncertainties. During on-orbit testing, we found that band 1, i.e., the O₂ A band, is frequently affected by solar panel charging. This can cause the SNR to decrease to about 100–200 depending on the noise level at the specified radiance in the O₂ A band. The other bands are not obviously affected by the charging. The other basic characteristics of GAS, such as on-orbit spectral response, meet our requirements.

GAS acquiring one interferogram precisely views the earth’s surface with the footprint diameter or instantaneous field of view of 13.2 km with the nadir on the ground. It stares at each footprint for 2.2 s to generate an interferogram. During this period, the satellite flies about 15 km in the along-track direction. The observation schematics of GAS are illustrated in Fig. 1. Both the cross-track and along-track spatial dimensions are undersampled. Unlike the atmospheric carbon dioxide grating spectrometer (ACGS) on TanSat, GAS only uses a single detector with a two-axis pointing mechanism that enables observations toward the surface. In total, GAS provides seven observation points along the cross-track direction. The radiance calibration requirement is 5% (absolute accuracy). This requirement is consistent with those of other instruments, such as OCO-2, TanSat, and GOSAT (Kuze et al., 2012). Another requirement for spectral calibration is a 10% spectral resolution.

Figure 1.  GAS observation patterns. The x direction is the satellite flying direction. The distances between the adjacent footprints are 202 and 117 km in the cross-track and along-track directions, respectively. The swath width is 1212 km.

A next-generation sensor will be carried on FY-3H, which is planned to launch in 2024. GAS on FY-3H used focal plane array detectors of more than 1024 by 1024 pixels. That is, the interferometer is changed to an imaging grating spectrometer, as also used by OCO-2 and TanSat.

GAS on FY-3D records each observation in the form of digital interferograms, which directly display information in the time domain. The preprocessing of GAS is more complicated than that of TanSat’s ACGS, which records observations in the spectra space. The interferogram is converted to the spectra space by the fast Fourier transform (FFT) algorithm on the ground. Before this procedure, saturation detection, zero path difference detection, and phase correction are applied to the raw interferograms. Then, the real and imaginary parts of the spectral data are obtained by the FFT. After converting these to spectral radiance, they are stored as the Level 1B data used in the retrieval of XCO₂. Because XCO₂ is inferred from the ratio between the continuum and line core intensities, the radiometric calibration must consider the nonlinearities of the instrument response. Although GAS has good linearity, it is still described by a quadratic polynomial, which converts signals to radiance to account for any nonlinear effects:

where a, b, and c are referred to as conversion factors, and d_n is the digital number of spectral data. As an example, Fig. 2 shows these factors for the forward scans for the WCO₂ band. GAS was radiometrically calibrated before launch using integrating spheres. It was put into a thermal vacuum chamber (TVC) to remove atmospheric absorption in the testing. An absolute radiometric accuracy of 5% was achieved in the TVC testing. After the launch, the time-dependent variation of the calibration was monitored and corrected through solar measurements using the diffuser plate and through direct deep space measurements. For example, the calibrated spectra are shown in Figs. 3–5.

Figure 2.  The GAS radiance (W cm⁻² sr⁻¹ cm⁻¹) conversion factors for the forward scan mode for the WCO₂ band.

Figure 3.  Example radiance spectra in the O₂ A band observed by GAS in the cloud-free scene.

Figure 4.  As in Fig. 3, but for the WCO₂ band.

Figure 5.  As in Fig. 3, but for the SCO₂ band.

Several missions use the FPR algorithm for their XCO₂ products. Crisp et al. (2012) and O’Dell et al. (2012) described the NASA’s atmospheric CO₂ observations from space XCO₂ retrieval algorithm. GOSAT also uses a similar algorithm for its XCO₂ products. The main inputs are the calibrated radiances for each of the three bands (i.e., the O₂ A, WCO₂, and SCO₂ bands), as well as geometrical and a priori information. The major components of the approach are forward and inverse models. In general, the observation y from a state vector x can be mathematically written as:

where F is the forward model involving the unknown state vector ${\boldsymbol{x}}$ and a set of fixed input parameters ${{\boldsymbol{x}}_0}$, and ${\boldsymbol{\varepsilon}} $ contains instrumental noise and forward model error.

The core of the forward model simulates the observed intensity $I$ at any wavelength (Boesch et al., 2017):

where $ {F_0} $ is the solar flux at the top of the atmosphere, $ {\theta _0} $ is the solar zenith angle, $ R $ is the reflectance of the surface, and $ {\sigma _m} $ and $ {N_m}(s) $ are the absorption cross-section and the number densities of the absorbing gas molecules along an optical path s, respectively. Note that $ I $ is a function of multiple variables such as wavelength, observation zenith and azimuth angle, and the corresponding solar zenith and azimuth angle.

Coupled with the above forward model, an inverse model solves for the state vector that produces the maximum post-priori probability by minimizing the $ {{\boldsymbol{\chi}} ^2} $ merit function:

where $ {{\boldsymbol{S}}_\varepsilon } $ and $ {{\boldsymbol{S}}_a} $ are the observation error covariance matrix and the priori covariance matrix, respectively, and $ {{\boldsymbol{x}}_a} $ is the priori state vector. After CO₂ concentrations for each level are obtained, XCO₂ can be calculated from the output $ {\boldsymbol{x}} $ using Eq. (2).

In principle, GAS XCO₂ can also be retrieved by a similar algorithm because it uses a similar high-resolution spectrometer collecting the reflected sunlight for remote sensing of CO₂. Particularly, the O₂ A band plays a crucial role in the FPR algorithm. It provides the O₂ amounts as the reference gas to derive CO₂ ratios. However, there are obvious difficulties in this algorithm for GAS XCO₂ due to the disturbance in GAS O₂ A band. In addition, this FPR method is very complex in many aspects, such as in aerosol scattering calculation, surface bidirectional reflectance distribution function treatment, and the inverse model. It must resolve the state vectors including CO₂ concentration and a lot of other physical parameters from the radiative transfer equation. All these processes require high-quality observations with reliable and stable SNRs. Therefore, we developed a new algorithm, the semi-physical statistical (SPS) retrieval model, to allow GAS XCO₂ fast retrievals with some remedies for the disturbance in the observation. We will discuss this in detail in Section 5.

Observations in the O₂ A, WCO₂, and SCO₂ bands are the result of the complex interaction between solar radiation, surface, atmospheric absorption, and particle scattering. This process is characterized by many degrees of freedom or modes and high dimensionality. The statistical method aims to find ways to reduce and link these modes to the physics of the system. Empirical orthogonal function (EOF) analysis and principal component analysis have been extensively used in dimensionality reduction and pattern extraction in atmospheric science (Lorenz, 1956; Smith and Woolf, 1976; Hannachi et al., 2007).

Suppose that a data matrix X represents the deviation or departure from the average of the observed field:

where the column vector $ {{\boldsymbol{X}}_n} $ represents the deviation of the field acquired at one field of view (FOV). In total, the number of observations is m. Once the deviation matrix is determined, the sample covariance matrix is given by

EOF analysis aims to find uncorrelated linear combinations of the variables that represent maximum variance. They can be obtained as solutions to the following eigenvalue equation:

where $ {\lambda ^2} $ is the eigenvalue, and u is the eigenvector or EOF. In practice, the singular value decomposition (SVD) technique can be used to solve the eigenvalue problem. Any n × m matrix X can be decomposed as

where $ {\boldsymbol{\varGamma}} $ is an n × r matrix with column singular vector $ {{\boldsymbol{\varGamma}} _1}, \cdots ,{{\boldsymbol{\varGamma}} _r} $; U is an r × m matrix with column singular vector ${u_1}, \cdots ,{u_r}$; and $ \; {\boldsymbol{\varLambda}} $ is a diagonal matrix with $ r $ elements ${\lambda _1} \geqslant {\lambda _2} \geqslant \cdots {\lambda _r}$. Performing an eigenvalue analysis on the data covariance matrix yields the following diagonalization:

where the eigenvalues $\lambda _1^2, \lambda _2^2, \cdots , \lambda _r^2$ of the matrix ${{\boldsymbol{\varLambda}} ^2}$ are sorted in decreasing order.

The EOFs $ {u_1}, \cdots ,{u_r} $ are orthogonal, and they provide a complete basis for the data matrix. Using orthonormal EOFs, the expansions of both the atmospheric variable and the radiance observed by satellite can be expressed as

where U and U* are the orthonormal EOFs for V and R, respectively; and A and B are the corresponding expansion coefficients. Typical high-resolution spectra have too many channels that are beneficial for reducing random retrieval errors. However, the variability of these spectra is caused by limited parameters such as atmospheric states, surface states, and optical paths. The reduction of the degrees of freedom of the atmospheric variables and radiances is expected to be effective. Therefore, they can be expressed by the above two equations.

We aim to retrieve V from R. However, obtaining A from B using a transformation matrix D is more stable. Using the least squares solution to determine this matrix yields

Substituting A = D*B into the V expression, we can obtain

where the C matrix is given by the quantity in braces. Compared with the ordinary least squares regression method, this solution is less sensitive to the noise levels of the observations.

Many previous studies demonstrated that statistical models can be used to retrieve atmospheric parameters or constituents (Zhang et al., 2014). Bril et al. (2017) used a regression algorithm to retrieve GOSAT XCO₂. Du et al. (2018) successfully employed an SVD statistical method to retrieve solar-induced chlorophyll fluorescence using the radiance from TanSat observations at a global scale. The purpose of statistical models is to find a new set of variables that represent most of the observed variance from the raw observation through linear combinations of the original variables. Following this idea, we designed the SPS model to retrieve GAS XCO₂.

Some key parameters also used in FPR were added to this retrieval model. For one observation, we first combined key geometric parameters, the solar and satellite zenith angles, into this model because these geometric parameters represent the gas optical depth. In addition, a priori information on surface pressure was also added to transform the total column amount of CO₂ to XCO₂, as described in Eqs. (1) and (2). A priori CO₂ information was also added to the model for a latitude grid of 10° for each season in 2018. A priori XCO₂ came from the OCO-2 Level 3 data products (https://hpc.niasra.uow.edu.au/oco2level3/), which are predicted on a regular 1° × 1° grid. We then average these grid CO₂ values every 10° latitude interval for each season to get the zonal XCO₂. Table 2 shows the priori values used in our retrieval algorithm in the Northern Hemisphere. It should be noted that this table should be updated annually. Thus, the observed quantities are supplied by important parameters that are also used in the FPR and can be represented by the following column vector:

where r₁, r₂, and r₃ represent the observations in the three bands, α and β are the solar and satellite zenith angles, respectively, s is the priori CO₂ information, and p is the priori surface pressure obtained from the ECMWF Reanalysis v5 (ERA-5) fields.

We established a regression model to retrieve ${\boldsymbol{X}}_{\mathrm{C}\mathrm{O}_2} $ values:

where C represents the regression coefficient matrix. This matrix can be determined by the best fitting of the training datasets that include GAS observations and “true” XCO₂ values that come from the Total Carbon Column Observing Network (TCCON) measurements. In this study, the training data were about 30% of the total data, passing data quality controls and cloud screenings. The remaining 70% were used for retrieval and validation. The coefficient matrix was derived by using the eigenvectors of covariance matrices technique and the least square fit method on the basis of the training datasets as mentioned in Section 3.2. Once the coefficient matrix is obtained, the XCO₂ can be retrieved from the supplied radiance directly.

Compared with the grating technology adopted by OCO-2 or TanSat, the advantage of the interference technology is that it can obtain a wider spectrum coverage with nearly the same spectral resolution. This allows users to select subwindows of spectra according to their requirements. For our applications, we selected the windows of 764–770 nm from the O₂ A band, 1594–1618 nm from the WCO₂ band, and 2047–2076 nm from the SCO₂ band. Figures 3–5 show examples of the radiance spectra for the three bands in cloud-free scenes. The absorption features made by O₂ and CO₂ can be clearly seen. The numbers of spectral channels in the O₂ A, WCO₂, and SCO₂ bands are 450, 350, and 450, respectively, giving a total number of about 1250 for the retrieval. The number of eigenvalues is limited by the total number. Figure 6 shows the spectra of the leading 50 eigenvalues for the covariance matrix of the training dataset.

Figure 6.  Eigenvalue spectrum (%) of the covariance matrix of the training dataset. The first eigenvalue is greater than 90% and the variations of the leading 50 eigenvalues are not shown clearly.

The amount of variance accounted for by an eigenvector is the corresponding eigenvalue. The eigenvectors are sorted in a decreasing order such that the first eigenvector explains the largest amount of the variance, whereas the other eigenvectors represent the residual variance. Figure 7 shows the first three eigenvectors of the covariance matrix from the training GAS radiance. These eigenvectors can be thought of as describing various degrees of oscillation. From this figure, one can see that the first eigenvector has the lowest amplitude of oscillation, whereas the third has the highest. In fact, the first eigenvector has a very small oscillation, one order smaller than those of the other two eigenvectors, which looks like a straight line.

Figure 7.  The first three eigenvectors of the GAS radiance covariance from the training dataset.

The raw data transmitted to the ground were preprocessed to Level-1B data, which may contain some low-quality radiance. During the preprocessing, the data with certain known problems can be checked out using attached quality flags. However, some quality problems cannot be easily found. The saturation of interferograms can occur and cannot be explicitly detected and corrected near real time. This can lead to incorrect spectral radiances and can be screened from the radiance out of the band coverage. For the O₂ A band, the signals are disturbed by the solar panel charging. Additionally, satellite and point mechanism microvibrations can slightly affect the signals on the three bands. All these lead to incorrect radiances or lower SNRs. The affected data or lower quality spectra of the three bands were filtered by using the quality check program.

As is well known, clouds and aerosols can contaminate observations in the three bands and lead to significant uncertainties in XCO₂ retrieval. GAS has a footprint with a diameter of about 13 km, which is much larger than those of OCO-2 or TanSat. More than 80% of the GAS observations will be contaminated by clouds. Hence, cloud screening must be performed before XCO₂ retrieval. For the GAS cloud screening, we used cloud and aerosol products generated by the Medium Resolution Spectral Imager-2 (MERSI-2), which is also carried by FY-3D. MERSI-2 is an upgraded version of MERSI carried by the FY-3A satellite launched in 2008. For more details, please refer to Yang et al. (2012). The pixels of MERSI-2 have a spatial resolution of 1 km with a swath of nearly 2500 km. Typically, a GAS point at nadir includes more than 100 MERSI-2 pixels. If 80% of the pixels of MERSI-2 in a GAS point contain obvious clouds or certain aerosol information (e.g., haze), this GAS point will be eliminated from the observations. With this threshold, about 80% of all GAS scenes are cloudy observations.

We believe that unfiltered clouds or aerosols may influence the XCO₂ results because cloud and aerosol changes are very complex and because our cloud screening cannot completely eliminate the influence of clouds or aerosols existing in the GAS footprints. However, the degree of influence of clouds depends on whether the unfiltered clouds in the training and retrieval datasets have consistent physical and optical properties. If they are consistent, the unfiltered clouds will not obviously bias the XCO₂ results. In GAS retrieval, they are consistent because the same cloud screening provided by MERSI-2 was used for the training and retrieval datasets. From the global validation over TCCON sites, obvious biases have not been found in GAS retrieval (see Section 4). Therefore, to some extent, the SPS algorithm can tolerate certain cloud effects.

In summary, this algorithm considered the key physical insights on the behavior of the observation system and used these insights to eliminate contaminated measurements and find adequate physical factors to link the observations and the required XCO₂. The function of the O₂ A band is supplied by the reanalysis ERA-5 and MERSI-2 products. Therefore, we call this algorithm the SPS retrieval model. To some extent, this model can get some useful XCO₂ data with supplements from ground-based measurements.

In this study, we empirically selected the leading 100 eigenvalues that can provide an accurate fit of the original radiance spectra observed by GAS. Figure 8 shows the scatter plot between the TCCON XCO₂ and the reconstructed XCO₂ using the leading 100 eigenvectors on the training dataset. The root-mean-square error (RMSE) is 1.14 ppm without obvious biases. This is an acceptable accuracy, and increasing the number of eigenvectors (e.g., 120 eigenvectors) does not improve the accuracy.

Figure 8.  The scatter plot between the true XCO₂ and the reconstructed XCO₂ using the leading 100 eigenvectors based on the training dataset.

After the retrieval matrix coefficients were determined for retrieval, the SPS algorithm processed GAS sounding over land in 2018. These retrievals restricted to observations over TCCON sites were used to evaluate the SPS error performance. The training dataset was not included in the comparisons. For XCO₂ product comparisons, previous studies chose different temporal and spatial conditions to limit the comparisons. Bi et al. (2018) used relatively tight criteria to select OCO-2 XCO₂ over TCCON stations within a distance range of ±1° latitude/longitude. However, this condition is not suitable for GAS XCO₂ comparisons because GAS has sparse observation grids on the surface. We extended the box centered around the TCCON site, which spans 5° in latitude and 10° in longitude, on the same day as a TCCON measurement. This coincidence criteria, also employed by Wunch et al. (2017), significantly increases the number of coincident points for comparisons.

In total, up to about 1800 measurements from 21 sites were chosen to validate the GAS XCO₂. Figure 9 shows the GAS XCO₂ data comparisons with coincident TCCON FTS (Fourier Transform Spectrometer) data. These data display a better linear relationship. Table 3 shows the statistical characteristics of GAS XCO₂. The precisions or standard deviations are less than 2 ppm except for Reunion Island and Tsukuba, Japan. The average standard deviation over all sites is 1.520 ppm. The maximum bias is found over the station of Pasadena, California, USA, with a value of −1.23 ppm. Still, the average of the biases over all sites is about −0.0070 ppm, indicating no obvious biases existing at a global scale. These uncertainty characteristics of the SPS algorithm are comparable with those of OCO-2 XCO₂ retrieved by the FPR algorithm shown by Bi et al. (2018).

Figure 9.  Comparisons between the GAS XCO₂ and the coincident TCCON FTS data in 2018. The solid blue line is a one-to-one line. The two dashed red lines denote ±2-ppm lines against the one-to-one line. The error bars show the standard deviations over each site.

Figures 10–12 show the time series of GAS XCO₂ at three sites: Lamont, Sodankyla, and Wollongong, respectively. The Lamont site is located at northern mid latitudes with relatively uniform surface properties and is not affected by anthropogenic CO₂ emissions. The surface vegetation land cover, varying from season to season, has obvious impacts on the time series of the CO₂ variations. These seasonal variations can be clearly seen in Fig. 10. The Sodankyla site is located at very northern high latitudes with regular snow cover. It challenges the retrieval algorithm because of its high solar zenith angles and snow cover. The SPS algorithm successfully retrieved the GAS XCO₂ over this site. We found that CO₂ retrieved mainly from March to October presents obvious seasonal variations at this site. The TCCON Wollongong station is located in the Southern Hemisphere where a slight seasonal variation of XCO₂ appears. At this site, we used a larger box span because the geographical variations in XCO₂ in the Southern Hemisphere are lower than those in the Northern Hemisphere (O’Brien and Mitchell, 1992) and to increase the collocated GAS XCO₂ points.

Figure 10.  The time series XCO₂ (DOY: day of year) of the retrieved GAS and TCCON FTS in 2018 at Lamont, Oklahoma, USA.

Figure 11.  As in Fig. 10, but for Sodankyla, Finland.

Figure 12.  As in Fig. 10, but for Wollongong, Australia.

Over these typical TCCON sites located in different areas, the trends of XCO₂ variations on 1-yr timescales can be easily seen. Also, the temporal variations of GAS XCO₂ agree very well with those of TCCON XCO₂.

Figure 13 displays the global distributions of GAS XCO₂ over land. In January, the winter for the Northern Hemisphere, there are little data at high latitudes greater than 40°N. The level of XCO₂ magnitude in the Northern Hemisphere is greater than that in the Southern Hemisphere. In the equatorial region, little XCO₂ data can be retrieved because of the frequent clouds in the atmosphere. In July, the summer for the Northern Hemisphere, we can find a contrary global distribution of XCO₂ against the distribution in winter; that is, XCO₂ in the Northern Hemisphere is lower than that in the Southern Hemisphere. Overall, these figures show reasonable information on XCO₂ on broad spatial and temporal scales. However, some spuriously high GAS XCO₂ was observed in North Africa, especially in April. The land surface over this area was very bright, and the type of aerosol and its scattering effects might be different from those in other areas. Our current SPS model could not accurately retrieve XCO₂ in this area because of the lack of this type of collocated GAS and TCCON observations in the training datasets.

Figure 13.  The global distributions of GAS XCO₂ over land in (a) January, (b) April, (c) July, and (d) October 2018.

The spatial sampling of the current GAS instrument cannot provide global coverage very well. Part of the reason is that the reflected signals in the near-infrared bands can only work during the day time. It also cannot provide data during the nighttime. Another reason is that it has too large footprints, which are easily contaminated by clouds. Meanwhile, GAS collects spectral soundings at a rate of 2.2 s, which is too low to provide a large number of observations. A next-generation high-resolution spectrometer for the remote sensing of CO₂ is being developed, funded by the National Satellite Meteorological Center, China Meteorological Administration. This instrument will be carried by FY-3H, which may be launched in 2024. It is designed to have a similar spectral resolution to that of GAS, whereas the swath and the spatial resolution will be significantly improved to 100 and 2 km, respectively. That is, there are nearly 50 footprints within the 100-km swath in the cross-track direction. This allows the detection of typical CO₂ sources. Also, the high spatial resolution allows the detection through cloud gaps even in cloudy areas. Therefore, this feature of large swath width can improve the XCO₂ global coverage and spatial sampling. This will significantly decrease the cloud influence in a footprint and allow the detection of small CO₂ sources, such as power plants. Over oceans, the nadir observation mode cannotprovide useful observations because of the lower SNR inthese bands. Thus, the sunglint mode should be adoptedto provide useful observation. The mentioned aspects, such as width, spatial resolution, and ocean glint mode, will increase the data more to about tens of times than that of OCO-2or TanSat, thus increasing the data processing time.

We noted that the FPR method is very time-consuming because of the huge computational expense of high-spectral-resolution data. The radiative transfer equation must be calculated thousands of times to resolve the spectral information acquired by satellites. Therefore, it will be a great challenge if the FPR is used to process FY-3H GAS observations. Thus, new and fast algorithms are very essential for future missions of CO₂ remote sensing. The SPS algorithm developed in this paper combines the statistical regression algorithm with key physical factors such as observation geometry, surface pressure, and a priori CO₂ information taken from the FPR algorithm. The SPS algorithm was successfully applied to processing GAS observations with very fast computational speeds and obtained reasonable XCO₂ results at global scales.

The primary advantage of the FPR approach is its intrinsic accuracy because it fully considers all of the physics of atmospheric and surface processes that can contribute to the absorption and scattering of the solar spectrum. We can see from Eq. (2) that this approach of deriving XCO₂ strongly depends on the number densities of O₂ associated with O₂ A band observations. The absorption by O₂ molecules in this band can provide estimates of atmospheric parameters such as surface pressure and surface albedo using certain retrieval algorithms. Previous studies showed that O₂ A band observations can estimate surface pressure with an accuracy of ~1 hPa (O’Dell et al., 2011). This accuracy requirement for surface pressure requests very high SNRs in the measurements of the O₂ A band. For example, OCO-2 and TanSat have SNRs of 310 and 360, respectively, under the conditions of 5% albedo and 60° solar zenith (Stephens and Heidinger, 2000; Bi et al., 2015; Yang et al., 2018). The lower SNR of the O₂ A band of the GAS instrument causes difficulties in the inversion of surface pressure, which in turn lowers the accuracy of the XCO₂ calculations in near real time data processing. It also reduces the sensitivity of the O₂ A band measurements to clouds and small aerosol particles. Thus, GAS O₂ A band measurements cannot be used to screen cloud-contaminated measurements that must be rejected in XCO₂ retrievals. Therefore, discussing in detail how this SPS algorithm remedies the disturbance in the O₂ A band of GAS on orbit is helpful.

First, the lack of surface pressure, which cannot be obtained by using GAS O₂ bands, can be provided by reanalysis fields. It is well known that reanalysis data generated by models have very high accuracies in atmospheric states. In our fast XCO₂ retrieval, we extracted the surface pressure from the ERA-5 reanalysis field as a priori information to supplement the O₂ A band observations. This decreased the algorithm dependence on the observations of the O₂ A band and could get reasonable results when this surface pressure is applied to transform total CO₂ molecular numbers to XCO₂. However, one obvious drawback is that the process must wait until reanalysis data are available, which usually takes 3 months later after the raw satellite measurements are acquired. Fortunately, the timeliness requirement of the data process is not very high for climate applications.

Second, the ability to perform cloud detection using the O₂ A band may be provided by other cloud products. As mentioned above, clouds must be identified and rejected in the retrieval of XCO₂. High-resolution spectra in the O₂ A band would provide adequate information on absorption and scattering to identify cloud contamination in the FOVs of the satellite sensor (O’Dell and Taylor, 2014). This method was employed in the OCO-2 cloud screening algorithm (Wang et al., 2017). However, for the GAS O₂ A band, the effectiveness of this approach is reduced because of insufficient SNRs in the O₂ A band. Thus, an alternative method for cloud screening is using a cloud product generated by the MERSI-2 also carried by FY-3D. The required work is matching the FOVs between MERSI-2 and GAS. As with the process here, Hong et al. (2021) also successfully applied cloud products provided by the Cloud and Aerosol Polarization Imager (CAPI) for cloud screening of the TanSat ACGS observation. CAPI is also carried by TanSat and is designed to detect clouds and aerosols.

A priori CO₂ information is necessary for the retrieval of XCO₂ if the FPR algorithm is used. Therein, the forward model needs this CO₂ information and other atmospheric state parameters to simulate the observation acquired by the satellite. A priori XCO₂ values are also explicitly included in the SPS retrieval model to get accurate XCO₂ estimations. XCO₂ is assumed to only have latitudinal variations at a global scale and is computed by a latitude grid of 10°. A priori XCO₂ value is given in four seasons. This means that there are the same a priori value for one season in one latitude grid. This is a relatively weak a priori condition compared with that in the FPR algorithm, where each spot has a priori CO₂ profile along with temperature, humidity, and other factors. We calculated the differences for a priori and retrieved GAS XCO₂ to evaluate the dependence of the retrieval results on a priori information. Figure 14a shows the histograms of the differences between a priori and true XCO₂ over TCCON sites. The distributions of the differences indicate that the peak of the number is biased about 1 ppm in the a priori XCO₂. The histograms of the differences between the retrieval and the true XCO₂ displayed in Fig. 14b show that the retrieved XCO₂ has no bias and that the distribution is much closer to a Gaussian distribution, especially in the bottom of histograms. Comparisons between the two plots of differences show the improvements from the priori XCO₂ using the SPS retrieval.

Figure 14.  Histograms of the difference (a) between a priori and true XCO₂ (a priori – true value; ppm) and (b) between the retrieval and true XCO₂ (retrieval – true value; ppm) over TCCON sites.

Besides a priori XCO₂, the SPS algorithm also needs high-quality XCO₂ as known quantities in the training datasets. The regression coefficients for retrieving CO₂ amounts are derived using these training sets. Here, we used TCCON XCO₂ values as the known “true” values because of their high precision, accessibility, and extensive usage.

The first-generation GAS sensor was launched on the FY-3D satellite into a sun-synchronous polar orbit. The disturbance in the O₂ A band makes it difficult to use an FPR algorithm. A fast SPS algorithm was developed for GAS XCO₂ retrieval with reduced sensitivity to the disturbance in the observations. This model combines the spectral radiance observed by the GAS instrument and key physical factors, including solar and satellite zenith angles. Accurate surface pressure from the reanalysis fields and the MERSI-2 cloud product were necessary to compensate the GAS observation for its deficiency in the SNR of the O₂ A band. The regression coefficients linking the measurements and the XCO₂ were derived on the basis of training datasets of collocated GAS and TCCON measurements. To some extent, the SPS algorithm solved the low SNR problem of the O₂ A band. This algorithm is applied to GAS global observations over land in 2018. The GAS-retrieved XCO₂ generally agreed well with coincident TCCON data at global scales, with a standard deviation of about 1.5 ppm and without obvious average bias. The precision and accuracy of the XCO₂ meet our product requirements. The time series of GAS XCO₂ over TCCON sites can reveal the seasonal changes of CO₂. Differences between the Northern and Southern Hemispheres in different seasons can also be clearly seen from the global map of distributions of GAS XCO₂. Spurious local XCO₂ are also found in North Africa, where the lack of training data, including the effects of the bright surface and aerosol scattering, may be the cause of abnormal retrieval, which requires further investigations.

Acknowledgments. The TCCON data are obtained from the TCCON data archive hosted by CaltechDATA at https://tccondata.org. The authors thank two anonymous reviewers for their comments and suggestions.