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

Yanmeng BI, PengZHANG*,ZhongdongYANG,QianWANG,XingyingZHANG,Chengbao LIU,

PengmeiXU2,Lizhou HOU2,JunyuKE2, andNaiqiang ZHANG3

1 Innovation Center for Fengyun Meteorological Satellite, Key Laboratory of Radiometric Calibration and Validation for Environmental Satellites, National Satellite Meteorological Center, China Meteorological Administration, Beijing 100081

2 China Academy of Space Technology, Beijing 100081

3 Huayun ShineTek, Beijing 100081

ABSTRACT China’s Fengyun-3D meteorological satellite launched in December 2016 carries the high-resolution greenhousegases absorption spectrometer (GAS) aimed at providing global observations of carbon dioxide (CO2). To date, GAS is one of the few instruments measuring CO2 from the near-infrared spectrum. On orbit, the oxygen (O2) A band suffers a disturbance, and the signal-to-noise ratio (SNR) is significantly lower than the nominal specification. This leads to difficulties in the retrieval of surface pressure and hence a degradation of the retrieval of the column-averaged CO2 dry air mole fraction (XCO2) if a full physics retrieval algorithm is used. Thus, a fast CO2 inverse method, named semi-physical statistical algorithm, was developed to overcome this deficiency. The instrument characteristics, the semi-physical statistical algorithm, and the results of comparison with ground-based measurements over land were introduced in this paper. XCO2 can be obtained from three bands, namely, the O2 A, weak CO2, and strong CO2 bands, with compensation from the Medium Resolution Spectral Imager-2 (MERSI-2) products, ECMWF Reanalysis v5 (ERA-5) data, and Total Carbon Column Observing Network (TCCON) data. The eigenvectors of covariance matrices and the least square fits were used to derive retrieval coefficients and yield cloud-free solutions. In addition to the GAS radiance, some key factors necessary for the accurate estimations of XCO2 were also taken as input information (e.g., air mass, surface pressure, and a priori XCO2). The global GAS XCO2 restricted over land was compared against the simultaneously collocated observations from TCCON. The retrieval algorithm can mitigate the issue caused by the low SNR of the O2 A band to a certain extent. Overall, through site-by-site comparisons, GAS XCO2 agreed well with the average precision (1σ) of 1.52 ppm and bias of -0.007 ppm. The seasonal variation trends of GAS XCO2 can be clearly seen at TCCON sites on the 1-yr timescale.

Key words: carbon dioxide, fast retrieval, Fengyun-3, high-resolution spectrometer

1. Introduction

Carbon dioxide (CO2) is one of the most important greenhouse gases. Human activities such as fossil fuel combustion emit billions of tons of CO2into the atmosphere since preindustrial times. Measuring the global distribution of CO2is 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 CO2can 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 CO2measurements is by collecting observations from satellites. Although these measurements cannot provide CO2profiles, the CO2column concentrations are still very useful because they are much less sensitive to uncertainties in flux modeling. In addition, these satellite CO2columns have much greater sampling densities on regional and global scales. These satellites can provide a large number of observations in regions where groundbased stations are poorly located.

Several satellites have been successfully launched to monitor the global distributions of CO2using near-infrared bands centered at 0.76 μm (O2A band), 1.61 μm(the weak CO2band near 1.61 μm—WCO2), and 2.06 μm(the deeply saturated strong CO2band 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 CO2observation 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 O2and 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 CO2dry air mole fraction (XCO2). O2A band provides the surface pressure, whereas the two CO2bands provide information on the CO2column abundance.XCO2can be defined as the ratio of the column abundance of CO2to the column abundance of dry air:

whereNCO2andNairarethe numberdensitiesofCO2and dry air, respectively.Because theconcentrationofO2is close to 0.20935, which is required to get the CO2amount,XCO2can also be written as follows:

After the TanSat, China launched theFengyun-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 onFY-3D. Unfortunately, the O2A band suffers from some on orbit disturbance induced by solar panel charging. This disturbance makes it difficult to get high-quality observations in the O2A 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 XCO2products 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 O2A band.

2. Greenhouse-gases absorption spectrometer(GAS)

TheFY-3Dmeteorological 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-3Dis to measure the distribution of CO2with precisions of better than 1–4 ppm on regional to continental scales.These CO2products 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 onFY-3D(see also at https://space.oscar.wmo.int/instruments/view/gas).Signal-to-noise ratios (SNR) are very essential for the retrieval of XCO2with low uncertainties. During on-orbit testing, we found that band 1, i.e., the O2A 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 O2A band.The other bands are not obviously affected by the charging. The other basic characteristics of GAS, such as onorbit spectral response, meet our requirements.

Table 1. GAS designed parameters and the tested results on orbit

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.

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 onFY-3Drecords 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 XCO2is 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:

wherea,b, andcare referred to as conversion factors,anddnis the digital number of spectral data. As an example, Fig. 2 shows these factors for the forward scans for the WCO2band. 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.

Fig. 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.

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

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

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

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

Fig. 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.

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

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

3. Semi-physical statistical retrieval model

3.1 FPR algorithm

Several missions use the FPR algorithm for their XCO2products. Crisp et al. (2012) and O’Dell et al.(2012) described the NASA’s atmospheric CO2observations from space XCO2retrieval algorithm. GOSAT also uses a similar algorithm for its XCO2products. The main inputs are the calibrated radiances for each of the three bands (i.e., the O2A, WCO2, and SCO2bands), as well as geometrical and a priori information. The major components of the approach are forward and inverse models.In general, the observationyfrom a state vectorxcan be mathematically written as:

whereFis the forward model involving the unknown state vectorxand a set of fixed input parametersx0, and εcontains instrumental noise and forward model error.

The core of the forward model simulates the observed intensityIat any wavelength (Boesch et al., 2017):

whereF0is the solar flux at the top of the atmosphere,θ0is the solar zenith angle,Ris the reflectance of the surface, and σmandNm(s) are the absorption cross-section and the number densities of the absorbing gas molecules along an optical paths, respectively. Note thatIis 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 χ2merit function:

whereSεandSaare the observation error covariance matrix and the priori covariance matrix, respectively, andxais the priori state vector. After CO2concentrations for each level are obtained, XCO2can be calculated from the outputxusing Eq. (2).

In principle, GAS XCO2can 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 O2A band plays a crucial role in the FPR algorithm. It provides the O2amounts as the reference gas to derive CO2ratios.However, there are obvious difficulties in this algorithm for GAS XCO2due to the disturbance in GAS O2A 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 CO2concentration 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 XCO2fast retrievals with some remedies for the disturbance in the observation. We will discuss this in detail in Section 5.

3.2 Statistical model

Observations in the O2A, WCO2, and SCO2bands 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 matrixXrepresents the deviation or departure from the average of the observed field:

where the column vectorXnrepresents the deviation of the field acquired at one field of view (FOV). In total, the number of observations ism. 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 λ2is the eigenvalue, anduis the eigenvector or EOF. In practice, the singular value decomposition(SVD) technique can be used to solve the eigenvalue problem. Anyn×mmatrixXcan be decomposed as

where Γ is ann×rmatrix with column singular vector Γ1,···,Γr;Uis anr×mmatrix with column singular vectoru1,···,ur; and Λ is a diagonal matrix withrelements λ1≥λ2≥···λr. Performing an eigenvalue analysis on the data covariance matrix yields the following diagonalization:

The EOFsu1,···,urare 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

whereUandU* are the orthonormal EOFs forVandR,respectively; andAandBare 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 retrieveVfromR. However, obtainingAfromBusing a transformation matrixDis more stable.Using the least squares solution to determine this matrix yields

SubstitutingA=D*Binto theVexpression, we can obtain

where theCmatrix 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.

3.3 Physical factors

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 CO2to XCO2, as described in Eqs. (1) and (2). A priori CO2information was also added to the model for a latitude grid of 10° for each season in 2018. A priori XCO2came 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 CO2values 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:

Table 2. The zonal priori XCO2 (ppm) values for each season (JFM,AMJ, JAS, and OND) in the Northern Hemisphere in 2018

wherer1,r2, andr3represent the observations in the three bands,αandβare the solar and satellite zenith angles, respectively,sis the priori CO2information, andpis the priori surface pressure obtained from the ECMWF Reanalysis v5 (ERA-5) fields.val ues:

Weestablished a regression model to retrieveXCO2

whereCrepresents the regression coefficient matrix.This matrix can be determined by the best fitting of thetraining datasets that include GAS observations and“true” XCO2values 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 XCO2can 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 O2A band, 1594–1618 nm from the WCO2band, and 2047–2076 nm from the SCO2band. Figures 3–5 show examples of the radiance spectra for the three bands in cloud-free scenes. The absorption features made by O2and CO2can be clearly seen. The numbers of spectral channels in the O2A,WCO2, and SCO2bands 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.

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.

3.4 Quality check

The raw data transmitted to the ground were preprocessed to Level-1B data, which may contain some lowquality 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 O2A 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.

3.5 Cloud screening

As is well known, clouds and aerosols can contaminate observations in the three bands and lead to significant uncertainties in XCO2retrieval. 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 XCO2retrieval. 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 byFY-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 XCO2results 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 XCO2results. 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 O2A 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 XCO2data with supplements from ground-based measurements.

4. GAS XCO2 results and validation

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 XCO2and the reconstructed XCO2using 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.

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 XCO2product 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 XCO2over TCCON stations within a distance range of ±1° latitude/longitude. However, this condition is not suitable for GAS XCO2comparisons 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 XCO2data 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 XCO2retrieved by the FPR algorithm shown by Bi et al. (2018).

Table 3. Statistical results for available TCCON sites

Figures 10–12 show the time series of GAS XCO2at 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 CO2emissions. The surface vegetation land cover, varying from season to season, has obvious impacts on the time series of the CO2variations. 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 XCO2over this site. We found that CO2retrieved 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 XCO2appears. At this site, we used a larger box span because the geographical variations in XCO2in the Southern Hemisphere are lower than those in the Northern Hemisphere(O’Brien and Mitchell, 1992) and to increase the collocated GAS XCO2points.

Fig. 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.

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

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

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

Fig. 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.

Over these typical TCCON sites located in different areas, the trends of XCO2variations on 1-yr timescales can be easily seen. Also, the temporal variations of GAS XCO2agree very well with those of TCCON XCO2.

Figure 13 displays the global distributions of GAS XCO2over land. In January, the winter for the Northern Hemisphere, there are little data at high latitudes greater than 40°N. The level of XCO2magnitude in the Northern Hemisphere is greater than that in the Southern Hemisphere. In the equatorial region, little XCO2data 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 XCO2against the distribution in winter; that is, XCO2in the Northern Hemisphere is lower than that in the Southern Hemisphere. Overall, these figures show reasonable information on XCO2on broad spatial and temporal scales. However, some spuriously high GAS XCO2was 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 XCO2in this area because of the lack of this type of collocated GAS and TCCON observations in the training datasets.

5. Discussion

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 CO2is 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 CO2sources.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 XCO2global coverage and spatial sampling. This will significantly decrease the cloud influence in a footprint and allow the detection of small CO2sources, such as power plants. Over oceans, the nadir observation mode cannot provide useful observations because of the lower SNR in these bands. Thus, the sunglint mode should be adopted to 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-2 or TanSat, thus increasing the data processing time.

We noted that the FPR method is very time-consuming because of the huge computational expense of highspectral-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 CO2remote 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 CO2information taken from the FPR algorithm. The SPS algorithm was successfully applied to processing GAS observations with very fast computational speeds and obtained reasonable XCO2results 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 XCO2strongly depends on the number densities of O2associated with O2A band observations. The absorption by O2molecules in this band can provide estimates of atmospheric parameters such as surface pressure and surface albedo using certain retrieval algorithms. Previous studies showed that O2A 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 O2A 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 O2A band of the GAS instrument causes difficulties in the inversion of surface pressure, which in turn lowers the accuracy of the XCO2calculations in near real time data processing. It also reduces the sensitivity of the O2A band measurements to clouds and small aerosol particles. Thus, GAS O2A band measurements cannot be used to screen cloud-contaminated measurements that must be rejected in XCO2retrievals. Therefore, discussing in detail how this SPS algorithm remedies the disturbance in the O2A band of GAS on orbit is helpful.

First, the lack of surface pressure, which cannot be obtained by using GAS O2bands, 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 XCO2retrieval, we extracted the surface pressure from the ERA-5 reanalysis field as a priori information to supplement the O2A band observations. This decreased the algorithm dependence on the observations of the O2A band and could get reasonable results when this surface pressure is applied to transform total CO2molecular 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 O2A 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 O2A 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 O2A band, the effectiveness of this approach is reduced because of insufficient SNRs in the O2A band. Thus, an alternative method for cloud screening is using a cloud product generated by the MERSI-2 also carried byFY-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 CO2information is necessary for the retrieval of XCO2if the FPR algorithm is used. Therein, the forward model needs this CO2information and other atmospheric state parameters to simulate the observation acquired by the satellite. A priori XCO2values are also explicitly included in the SPS retrieval model to get accurate XCO2estimations. XCO2is assumed to only have latitudinal variations at a global scale and is computed by a latitude grid of 10°. A priori XCO2value 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 CO2profile along with temperature, humidity, and other factors. We calculated the differences for a priori and retrieved GAS XCO2to evaluate the dependence of the retrieval results on a priori information. Figure 14a shows the histograms of the differences between a priori and true XCO2over 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 XCO2displayed in Fig.14b show that the retrieved XCO2has 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 XCO2using the SPS retrieval.

Besides a priori XCO2, the SPS algorithm also needs high-quality XCO2as known quantities in the training datasets. The regression coefficients for retrieving CO2amounts are derived using these training sets. Here, we used TCCON XCO2values as the known “true” values because of their high precision, accessibility, and extensive usage.

6. Conclusions

The first-generation GAS sensor was launched on theFY-3Dsatellite into a sun-synchronous polar orbit. The disturbance in the O2A band makes it difficult to use an FPR algorithm. A fast SPS algorithm was developed for GAS XCO2retrieval 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 O2A band. The regression coefficients linking the measurements and the XCO2were 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 O2A band. This algorithm is applied to GAS global observations over land in 2018.The GAS-retrieved XCO2generally 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 XCO2meet our product requirements. The time series of GAS XCO2over 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 XCO2are 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.