In this study, data products are used from the Greenhouse Gases Observing Satellite (GOSAT) and its successor, GOSAT-2. GOSAT was launched on 23 January 2009, through a joint effort by the Japan Aerospace Exploration Agency (JAXA), the Japanese Ministry of the Environment (MOE), and the National Institute for Environmental Studies (NIES). GOSAT was the world's first scientific satellite dedicated to the precise monitoring of CO2 and CH4 concentrations from space (Yokota et al., 2009). Its core scientific mission aims to fill greenhouse gas monitoring gaps over oceans and remote regions via high-frequency global observations, to accurately assess carbon sources and sinks at sub-continental scales, and to improve the understanding of global carbon cycle mechanisms and their impacts on climate change (Butz et al., 2011). GOSAT operates in a sun-synchronous quasi-recurrent orbit at an altitude of approximately 666 km and an inclination of about 98°, with a local equator crossing time at 13:00 ± 15 min and a revisit period of 3 d, ensuring high-frequency coverage for most parts of the Earth.

The primary payload aboard GOSAT is the Thermal and Near-infrared Sensor for Carbon Observation (TANSO), which consists of two components: the Fourier Transform Spectrometer (TANSO-FTS) and the Cloud and Aerosol Imager (TANSO-CAI) (Yokota et al., 2009). TANSO-FTS measures radiation in four spectral bands including the near infrared band at 0.76 µm (oxygen absorption band), two Short-Wave Infrared (SWIR) bands at 1.6 µm (CO2 and CH4 absorption bands) and 2.0 µm (CO2), and a wide Thermal Infrared (TIR) band extending from 5.5 to 14.3 µm. The spectral resolution of the SWIR bands (Bands 1–3) is approximately 0.27 cm-1 (full width at half maximum, FWHM). Spectra of reflected solar radiation and thermal radiation emitted by the Earth-atmosphere system are analyzed and the intensities of characteristic absorption lines are used to retrieve the total columns and vertical distributions of the concentrations of CO2 and CH4. The nadir footprint diameter of TANSO-FTS is approximately 10.5 km (Kuze et al., 2016). TANSO-CAI utilizes four channels with wavelengths ranging from the visible to the near-infrared to simultaneously acquire cloud and aerosol information along the observation path at spatial resolutions of 0.5 to 1.5 km. This information is used to filter out contaminated data and perform atmospheric corrections (Yokota et al., 2009). Over land, the instruments primarily use a nadir observation mode, whereas, over ocean they observe in the sun glint to capture solar specular reflection to improve the signal-to-noise ratio. GOSAT's design objective is to control the relative observation precision of CO2 and CH4 within 4 ppm (approximately 1 %) and 34 ppb, respectively, providing robust scientific data supporting the implementation of global climate agreements and the formulation of carbon emission reduction policies (Butz et al., 2011).

GOSAT-2 was launched on 29 October 2018, and operates in a sun-synchronous quasi-recurrent orbit at an altitude of approximately 613 km with a local equator crossing time at 13:00 and a revisit period of 6 d. GOSAT-2 was developed to continue and enhance the global greenhouse gas observation capability of GOSAT, with improvements in sensor design and observation efficiency and a slightly better signal-to-noise ratio (Suto et al., 2021; Imasu et al., 2023). Its core payload is TANSO-FTS-2, with an expanded spectral coverage of five bands, adding the capability to detect carbon monoxide (CO). The SWIR bands have a spectral sampling interval of 0.2 cm-1, with FWHM values better than 0.4 cm-1 for Band 1 and 0.27 cm-1 for Bands 2 and 3. The mission was designed with target uncertainties of 0.5 ppm for CO2 and 5 ppb for CH4 over a 500 km spatial mesh and with a 1-month observational period (Imasu et al., 2023; ESA eoPortal, 2026).

GOSAT/TANSO-FTS performs discrete grid observations and revisits the same nominal observation points every 3 d, with a three-point cross-track sampling pattern used for routine observations since August 2010 (Japan Aerospace Exploration Agency et al., 2011). In contrast, GOSAT-2/TANSO-FTS-2 has a 6 d revisit cycle and employs a fully programmable pointing system, allowing more flexible spatial sampling. Its intelligent pointing function can redirect the line of sight toward nearby clearer areas when clouds are detected around the scheduled footprint, increasing the number of clear-sky retrievals over land by approximately 1.8 times relative to standard pointing. However, intelligent pointing is switched off over calibration/validation (Cal/Val) sites and user-specified sites in current GOSAT-2 operations to enable repeated observations of the same target locations (Suto et al., 2021).

TCCON (Wunch et al., 2015; Laughner et al., 2024) is a global network of ground-based Fourier Transform Spectrometers (FTS) that measure direct near-infrared solar spectra within the 4000–9000 cm-1 range, with temporal high-resolution. At these wavelengths, adverse effects of high uncertainties associated with scattered light are avoided. These spectra are used to retrieve vertical column densities of a variety of gases, such as CO2, CH4, N2O, HF, CO, H2O, and HDO, using a non-linear least-squares spectral fitting algorithm. Ground-based FTS observations achieve exceptionally high precision; the single measurement precision for XCO2 is approximately 0.15 % (∼0.6 ppm) and for XCH4 it is 0.2 % (∼4 ppb) (Toon et al., 2009). For the GGG2020 retrieval framework underlying the current data release, the estimated error budgets are below 0.16 % (∼0.6 ppm) for XCO2 and below 0.4 % (∼7 ppb) for XCH4 for solar zenith angles below 82° (Laughner et al., 2024). These high-precision observational data serve as a reference for the validation of satellite-retrieved greenhouse gas products such as CO2 and CH4. The TCCON observations used in this study were obtained from the GGG2020.1 data release, a minor update to the GGG2020 product released in June 2026 (GGG2020 Data Changes, 2026).

Established in 2004, TCCON joined the WMO Global Atmosphere Watch (GAW) as a contributing network in 2009. Currently, China hosts two TCCON stations: the Hefei station and the Xianghe station (Hong et al., 2024).

Based on the principles detailed in the introduction, the XCO2 Proxy algorithm retrieves XCH4 by calculating the ratio of the columns retrieved in the 1.65 µm (CH4) and 1.61 µm (CO2) absorption bands to cancel out common optical path errors. The final XCH4 is derived as follows: 1XCH4(Proxy)=XCH4,rawXCO2,raw×XCO2(model) where XCO2 (model) represents the independent XCO2 estimate derived from atmospheric transport models. This model-based value serves as a reliable reference to scale the retrieved ratio into absolute XCH4, while ensuring robustness against scattering interference. XCH4,raw and XCO2,raw represent the directly retrieved column-averaged dry-air mole fractions of CH4 and CO2, respectively.

In this study, four proxy XCH4 products derived from three distinct algorithms were selected: OCPR, SRPR, and FOCAL Proxy, with SRPR products from application to both GOSAT and GOSAT-2 data. The basic specifications of these products are summarized in Table 2. Detailed descriptions of the principles underlying each algorithm are provided in the following subsections.

To evaluate the influence of aerosol loading on the retrieval accuracy of greenhouse gases, AOD data were incorporated in this study as a key auxiliary parameter. The AOD data were obtained from Sun photometers from the SONET site (Li et al., 2018) in Hefei and the AERONET site (Holben et al., 2001, 1998; Li et al., 2007; Xuehua et al., 2015) in Xianghe. Sun photometers provide AOD from direct sun measurements, at a range of wavelengths, every 15 min during daylight hours. Figure 3 presents the daily mean time series of ground-based AOD at 1640 nm for the Hefei (orange) and Xianghe (blue) sites. The Hefei data set suffers from an approximately four-year data gap between 2018 and 2022, while data at the Xianghe station are available for the periods from March 2019 to June 2020 and from July 2022 to December 2023. The Xianghe site is a typical urban/industrial background station, whereas, the Hefei site represents a low-aerosol background. However, during most of the available measurement periods shown in Fig. 3, AOD values at the Xianghe site are generally lower than those at the Hefei site. At Xianghe, high-AOD pollution events are often associated with extensive cloud cover, which can reduce the availability of quality-assured AERONET observations. Consequently, some very high-AOD observations may be excluded by AERONET cloud screening, leading to an underrepresentation of these events in the available data (Eck et al., 2018).

To quantitatively evaluate the accuracy and reliability of different retrieval algorithms, five key statistical metrics are introduced in this study: mean bias (Bias), root-mean-square error (RMSE), Pearson's correlation coefficient (R), centered root-mean-square error (CRMSE), and Normalized Standard Deviation (NSD). RMSE is used to quantify the overall difference between satellite retrievals and ground-based observations, accounting for both systematic bias and random fluctuations. CRMSE filters out the influence of the mean bias to specifically measure the variability of retrieval values relative to their own mean. These metrics are calculated as follows: 4Bias=1N∑i=1NXproxy,i-XTCCON,i5RMSE=1N∑i=1N(Xproxy,i-XTCCON,i)26σproxy=1N-1∑i=1N(Xproxy,i-X‾proxy)27R=∑i=1N(Xproxy,i-X‾proxy)(XTCCON,i-X‾TCCON)∑i=1N(Xproxy,i-X‾proxy)2×∑i=1N(XTCCON,i-X‾TCCON)28CRMSE=1N∑i=1N[(Xproxy,i-X‾proxy)-(XTCCON,i-X‾TCCON)]29NSD=σproxyσTCCON where N represents the total number of matched data points, Xproxy,i denotes the ith XCH4 retrieved by the satellite proxy algorithm, XTCCON,i is the corresponding TCCON reference data, X‾proxy and X‾TCCON represent their respective arithmetic means and σproxy and σTCCON denote the standard deviations of the retrieved XCH4 and the TCCON reference data.

The validation results are evaluated against the standards defined by the GCOS (GCOS, 2022), which stipulates a target accuracy of 10 ppb for XCH4 products to support climate change studies.

Time series of XCH4 at the Hefei (a–d) and Xianghe (e–h) sites are presented in Fig. 4. The datasets include four satellite retrieval products – OCPR, SRPR, FOCAL Proxy (indicated as FOCAL), all applied to GOSAT, and SRPR (2SRPR) applied to GOSAT-2 – together with ground-based TCCON observations. To capture the long-term evolution and inter-annual fluctuations of XCH4, a non-linear composite regression model was fitted to the data points: 10y(t)=a0+a1×t+a2×sin⁡(2πt+a3), where y(t) denotes the fitted XCH4 concentration at time t, and t is the time in fractional years. a0-3 represent the free fit parameters, which are iteratively determined using the non-linear least squares regression method.

Figure 4 shows distinct seasonal cycles at both sites, with concentrations peaking in summer and autumn and minima in spring and winter. The number of ground-based observations at the Xianghe site is larger than at Hefei, which is attributed to its more advantageous meteorological conditions (Lorente et al., 2022). The methane concentrations at Hefei are larger than at Xianghe. The temporal variations of all four satellite products closely trace those of the TCCON observations, at both sites, but with some clear deviations too. At the Hefei site, the number of matched data samples was small between 2018 and 2021, which renders the evaluation of the data products more sensitive to outliers than in Xianghe, resulting in significant dispersion and larger uncertainty envelopes (shaded areas).

To quantitatively evaluate these observations, site-specific scatter-density plots of the satellite products versus TCCON observations are provided in Fig. 5 and the statistical metrics are provided in Table 3. The scatter-density plots show distinctly different bias at Hefei and Xianghe: all products show a systematic overestimation (positive bias) in Hefei, whereas at the Xianghe site, the bias for all products except OCPR is negative. In particular, the GOSAT OCPR XCH4 is overestimated at the Hefei site (Fig. 4a), with a bias as high as +13.1 ppb and 61.9 % of the data pairs above the GCOS requirement of ±10 ppb (33.5 % within the GCOS requirements), in spite of the high correlation (R=0.937). This systematic offset is clearly visible in Fig. 4 throughout the whole year. At the Xianghe site, the performance of the OCPR algorithm is better, with 50.2 % of the data within the 10 ppb GCOS requirement.

The comparison of the GOSAT SRPR product with the TCCON data shows that the RMSE and SD are similar, the correlation R is higher at Hefei than at Xianghe and there are large differences between the bias and the compliance with GCOS requirements. SRPR significantly overestimates XCH4 in Hefei, with 43.6 % of the observations above the GCOS requirements (42.6 % within), resulting in a positive bias of +7.0 ppb. In Xianghe the compliance with the GCOS requirements is slightly higher (44.0 %), but a large underestimation is observed with 42.1 % of the data points below the GCOS requirements and a negative bias of -6.8 ppb.

The evaluation of the GOSAT FOCAL Proxy product shows that more than 50 % of the data points meet the GCOS requirements at both sites. However, the short time series provide a limited number of observations that precludes robust statistical results and makes it difficult to effectively neutralize random errors through averaging. This product exhibits the lowest correlation (R≈0.8) at both sites.

Overall, the performance of the three GOSAT products is comparable overall, although their performance characteristics vary across different metrics and between the two sites, with no single product consistently outperforming the others at both sites. OCPR shows relatively high correlations but a pronounced positive bias at Hefei, while FOCAL has the highest proportion of data meeting the GCOS requirement at both sites but relatively low correlations. SRPR generally shows intermediate performance among the three GOSAT products across the evaluated metrics.

To further assess the performance differences between GOSAT and GOSAT-2 based on the same SRPR product, Fig. 6 and Table 4 compares GOSAT SRPR with GOSAT-2 SRPR over the common time range at each site. The performance of the GOSAT-2 SRPR is better than GOSAT SRPR, with the lower RMSE (9.7–10.6 ppb), lower SD (9.0–10.3 ppb) and the higher correlation (R≈0.9) at both sites. In Hefei, 75.6 % of the data points fall within the GCOS target; however, a systematic overestimation is observed at Hefei, with 20.7 % of the data pairs above the GCOS requirements and a positive bias of +3.7 ppb. At the Xianghe site 69.9 % of the data points meet the GCOS requirements, but 20.6 % fall below this range, resulting in a negative bias of -2.5 ppb.

This discussion shows that the performance of GOSAT-2 SRPR is overall better than that of the other three products, with lower bias, RMSE and SD. When the matching radius is expanded from ±2.5 to ±5° (Appendix B), the statistical metrics of the products show varying degrees of change (Fig. B2). Nevertheless, GOSAT-2 SRPR still exhibits the best overall performance among the four products, indicating that the relative performance of the products is broadly robust to the choice of matching radius.

The biases of the four Proxy XCH4 products relative to TCCON observations, averaged in XCH4 bins of 25 ppb, are presented in Fig. 7 as a function of the TCCON-reference XCH4. At the Hefei site, the mean biases of the four Proxy XCH4 products generally exhibit a positive offset, with variations primarily concentrated between 0 and 20 ppb, except for SRPR for which the mean bias is slightly negative in the two largest bins. The biases are largest for the lower XCH4 and overall decreases with increasing XCH4. The GOSAT FOCAL Proxy (brown) covers a narrower concentration range, with a notable absence of observation data in the low-to-medium range (<1900 ppb); the error bars are significantly larger at the high concentrations, indicating higher retrieval uncertainty. OCPR (blue) shows an overall higher bias, averaging between 10 and 20 ppb. For GOSAT SRPR (orange) the mean bias variations for XCH4 smaller 1900 ppb are similar to those of OCPR, but decreases toward zero as XCH4 concentrations increase further. The mean bias of the GOSAT-2 SRPR product (magenta) is smaller overall and generally fluctuates around zero.

At the Xianghe site the biases are smaller than at Hefei, as indicated above. The mean bias of all products except GOSAT-2 SRPR decrease with increasing XCH4 and become negative when XCH4 exceeds 1900 ppb, particularly for GOSAT SRPR and the GOSAT FOCAL Proxy. In contrast, the mean bias of GOSAT-2 SRPR generally fluctuates around zero.

The variations in the biases of the satellite-retrieved XCH4 as function of the TCCON reference XCH4 data during different seasons are presented for the two sites in Fig. 8. The number of valid matchups (n) for each product and season is also shown in the figure. The sample availability varies among seasons, particularly at the Hefei site, where the number of observations in summer is relatively small for all four products (n=12–32). The data range varies across seasons, reflecting the higher concentrations in summer and autumn than in winter and spring; notably, the mentioned large variations occur during summer. At the Hefei site (Fig. 8a–d), the positive bias of GOSAT OCPR is most prominent with high values across the entire XCH4 range during spring and summer. The various proxy products show smaller fluctuations of the mean bias among the four data sets during autumn and winter. GOSAT-2 SRPR generally exhibits small biases with limited variations across seasons, except at high XCH4 concentrations in summer, where the error bars become notably larger. The relatively small summer sample size may partly contribute to the larger variability represented by these error bars.

At the Xianghe site (Fig. 8e–h), GOSAT OCPR shows positive biases in the low-to-medium concentration ranges, while other products fluctuate around the zero line. Except for GOSAT-2 SRPR, the other products all present a consistent decrease as XCH4 increases, manifesting as negative biases at high concentrations.

The four Proxy products at the Hefei and Xianghe sites are further evaluated through the Taylor diagram plotted in Fig. 9, using the correlation coefficient (R, Eq. 7), the Centered Root-Mean-Square Error (CRMSE, Eq. 8) and the Normalized Standard Deviation (NSD, Eq. 9). The mean bias is excluded from this evaluation to focus on the statistical consistency and precision of the products.

In the Taylor diagram, the distance of the OCPR RMSE to the reference point (star, where R=1 and NSD=1), representing the CRMSE, is relatively small, in spite of having the highest bias value in Table 3. This confirms that the high OCPR RMSE is primarily driven by systematic bias rather than by random fluctuations. At the Xianghe site, all products except GOSAT SRPR are generally distributed close to NSD=1, indicating that their variability amplitudes are comparable to that of the TCCON observations. At the Hefei site, GOSAT FOCAL Proxy (squares) shows lower precision and stability, with an NSD significantly greater than 1.0, indicating substantially larger variability than the TCCON observations. Notably, GOSAT SRPR shows relatively low NSD values at both sites, indicating smaller standard deviations than the TCCON observations.

The four XCO2 proxy algorithms discussed in this paper use different independent estimates of XCO2 for the final calculation of XCH4 (Eq. 1), based on different models as indicated in the algorithm descriptions. In this section, the XCO2 estimates used in the proxy algorithms are evaluated versus TCCON reference data. For the FOCAL proxy, the XCO2 estimates are not directly accessible within the satellite products, therefore only the model results for the other three products are validated.

The time series of the model XCO2 data used in the GOSAT SRPR proxy algorithm is presented in Fig. 10, together with the TCCON XCO2 data at the Hefei and Xianghe sites. Similar time series for the OCPR and GOSAT-2 SRPR products are presented in Fig. A6 (Appendix A). The time series show seasonal variations similar to those of XCH4 in Fig. 4, but with a phase lag of approximately six months. XCO2 peaks by the end of winter and early spring and minima occur by the end of summer and early autumn. This phase shift is attributed to the asynchronous seasonal variations in the sources and sinks of CH4 and CO2: the peak of CH4 emissions occurs in summer due to vigorous microbial methanogenesis from organic matter decomposition (East et al., 2024), whereas the peak of CO2 uptake occurs in summer due to robust photosynthesis, resulting in the observed minimum by the end of summer (Yuan et al., 2019).

At the Hefei site (Fig. 10a), the uncertainties (shaded areas) for both the SRPR modeled XCO2 and the TCCON reference data between 2018 and 2021, as well as in 2023, are much larger than at other times, due to the sparsity of coincident observation points during these periods. The time series show that the model XCO2 are initially slightly larger than the TCCON observations, whereas in later years the TCCON observations are larger. At the Xianghe site (Fig. 10b), the modeled XCO2 data are noticeably smaller than the TCCON reference data, especially during the spring peaks, with gradually increasing differences toward the end of the time series.

The time series at both TCCON sites show the evolution of the model XCO2 resulting in a very pronounced underestimation in 2023. This is primarily attributable to the sharp surge in emissions driven by the rapid recovery of socio-economic activities in the post-pandemic era (Ahmed and Stern, 2023), which was not captured because the CAMS model values used by the SRPR algorithm only extended to 2015 and were subsequently extrapolated year by year using the 2016 growth rate (3 ppm), rather than reflecting actual emission changes (Wu, 2021b).

The time series observations are confirmed by the scatter density plots of the XCO2 model data used in the GOSAT SRPR XCH4 retrieval algorithms versus the TCCON reference data presented in Fig. 11 for both the Hefei and Xianghe sites. Results for other products are presented in Fig. A5 (see Appendix A). The data for the Hefei site (Fig. 11a) show two clusters, one for low XCO2 (402–409 ppm) where the estimates used in SRPR are slightly overestimated, as in Fig. 10a at the beginning of the time series, and one for higher XCO2 (415–421 ppm) where the estimates used in SRPR are underestimated, resulting in an overall bias of -0.49 ppm. At the Xianghe site only one cluster is observed and the model XCO2estimates used in SRPR are underestimated resulting in an overall bias of -2.40 ppm. The fraction within the GCOS requirements is low at both sites. The RMSE at the Hefei site (2.25 ppm) is smaller than at the Xianghe site (3.66 ppm). These discrepancies contribute to the uncertainty in the retrieval process.

Density scatterplots for the OCPR and GOSAT-2 SRPR XCH4 retrieval algorithms and TCCON reference data in Fig. A5 show somewhat different characteristics which vary across algorithms and by site. Like SRPR, OCPR shows two clusters at the Hefei site and a single cluster at the Xianghe site, with a small overestimation in both cases. The GOSAT-2 SRPR algorithm does not show a clear under- or overestimations (Fig. A5b and d), resulting in a small positive bias at Hefei (0.68 ppm) and a small negative bias at Xianghe (-1.12 ppm). The fractions within the GCOS requirements (54.6 % at Hefei and 36.8 % at Xianghe) are larger than for other data products.

Time series of the XCH4/XCO2 ratios determined using the GOSAT SRPR CO2 proxy algorithm are presented in Fig. 12, together with ratios determined from the TCCON observations. Results for GOSAT-2 SRPR (2SRPR) and OCPR products are presented in Fig. A6 (see Appendix A). XCH4/XCO2 ratios cannot be directly extracted from the FOCAL proxy product datasets. The time series in Figs. 12 and A6 show a distinct seasonal variation with maxima in summer and autumn and minima in winter and spring, similar to the XCH4 time series in Fig. 3. XCH4 governs the seasonal variation of the ratio time series because the relative amplitudes are much larger for XCH4 than for XCO2. The data in Fig. 12 show that the large uncertainties observed at the Hefei site between 2018 and 2022 are primarily due to the small number of valid Satellite – TCCON matchups, mainly due to the limited availability of TCCON observations within the ±2 h temporal collocation window.

It is evident that the ratios used in the SRPR XCO2 proxy algorithm are systematically larger than the ratios derived from the TCCON reference observations. This is also clearly observed in the density scatter plots between the ratios of the retrieval results and the TCCON reference data in Fig. 13. Results for other products are presented in Fig. A7 for both sites separately (see Appendix A). These density scatterplots confirm the substantial and consistent systematic positive biases at both sites, for all three proxy XCH4 products. The bias at the Hefei site (0.066 ppbppm-1) is somewhat larger than that at the Xianghe site (0.053 ppbppm-1). Despite the systematic overestimation, the SRPR product shows extremely high correlation with the TCCON reference data (R of 0.911 and 0.918, respectively), and its data fluctuation characteristics are highly synchronized with those of the reference data. Furthermore, the data in Fig. A7 show that the OCPR and GOSAT-2 SRPR algorithms are consistent with GOSAT SRPR in terms of retrieval trends and bias characteristics.

In the analysis of the ratios, all proxy XCH4 products exhibited a pronounced and systematic positive bias across both sites. Consequently, we conducted a separate analysis on the XCH4,raw and XCO2,raw values (referred to hereafter as raw XCH4 and raw XCO2, respectively), the directly retrieved quantities used to form the proxy ratio in Eq. (1); the time series of GOSAT and GOSAT-2 SRPR are presented in Figs. A8 and A9 of Appendix A, while the respective scatterplots are displayed in Figs. A10 and A11. Both GOSAT and GOSAT-2 SRPR raw XCH4 exhibit a slightly positive bias, which is notably more pronounced at the Xianghe site. For the raw XCO2 of the GOSAT SRPR product, a systematic negative bias is observed, which gradually decreases in magnitude as TCCON XCO2 increases. Conversely, GOSAT-2 SRPR exhibits a distinct positive bias that increases with increasing TCCON XCO2. Furthermore, both satellite generations show a stronger seasonality than the TCCON references across both sites, with large uncertainties. These findings indicate that the persistent overestimation observed in the proxy ratios is predominantly governed by the deviations in raw XCH4. Consequently, the fundamental assumption underlying the application of the XCO2 Proxy method – that scattering-induced errors cancel out between the two species – is not fully fulfilled in real-world observations. Hence, empirical post-retrieval corrections based on TCCON observations are indispensable for delivering accurate final products. Additionally, since the raw comparisons reveal a distinct time dependence (as shown in Figs. A8 and A9), the bias corrections must be adjusted and updated regularly.

Time series of relative bias (defined below, Eq. 11) for XCH4, model XCO2, and the XCH4/XCO2 ratio at the Xianghe site are presented in Fig. 15 and for the Hefei site they are presented in Fig. A12 (Appendix A). The relative XCH4 bias is defined by Eq. (11): 11relative bias=Xproxy-XTCCONXTCCON×100% where Xproxy and XTCCON represent the XCH4 values retrieved from the satellite and the TCCON ground-based observations, respectively. The relative bias provides a normalized metric to assess the percentage deviation of satellite retrievals from the ground-based benchmark and is used here to facilitate a comparison between the three data products used in the XCH4 proxy algorithm (Eq. 1). To elucidate the origins of the retrieval errors, the contributions of different components to the results from each algorithm are quantitatively assessed using linear decomposition. Using Eq. (1), the impact of each component on the final retrieval accuracy can be quantitatively assessed through the linear decomposition of relative biases: 12δXCH4≈δXCO2+δratio where δX represents the relative bias of X. Higher-order terms are neglected here.

For the GOSAT OCPR product (Fig. 15a), the ratio bias generally fluctuates around zero, whereas the model XCO2 bias becomes predominantly positive after approximately 2020. During the same period, the final XCH4 bias is also mainly positive. The short-term variations in XCH4 generally resemble those of the ratio bias, while the model XCO2 bias varies more smoothly.

For the GOSAT SRPR algorithms (Fig. 15b), the model XCO2 bias is generally negative, whereas the ratio bias remains positive during most of the time series. Between 2018 and 2022, the two components have opposite signs and partially compensate for each other, resulting in a final XCH4 bias that remains close to zero. From late 2022 onward, the negative model XCO2 bias increases markedly, reaching approximately -1.0 % to -1.5 %, while the ratio bias remains positive but smaller in magnitude. Consequently, the final XCH4 bias also becomes markedly negative during this period. This pronounced decrease is attributed to the limited temporal availability of the model data.

For GOSAT-2 SRPR (Fig. 15c), the biases of both components are generally smaller in magnitude than those of GOSAT SRPR. The model XCO2 bias is mainly negative, whereas the ratio bias is generally close to zero or moderately positive. During 2021–2022, the biases of both components are relatively small, and the final XCH4 bias are therefore also close to zero. In 2023, the negative model XCO2 bias increases, accompanied by a negative bias in the final XCH4. Around 2024, the positive ratio bias increases, while the magnitude of the negative final XCH4 bias decreases. Toward the end of the time series, all three relative biases gradually approach zero.

Overall, the comparison shows that the negative bias at the Xianghe site around 2023 is mainly associated with the substantially negative bias in model XCO2 during the same period. Overall, the final Proxy XCH4 bias is related not only to the magnitudes of the biases in the retrieved XCH4/XCO2 ratio and model XCO2, but also to whether the two components compensate or reinforce each other. A small final bias may therefore arise either from small biases in both components or from cancellation between biases of opposite signs.

As analyzed in Sect. 3.1, extending the spatial domain to a broader ±5° spatial extent introduces substantial spatial variation, and therefore we adopted a ±2.5° spatial extent. While Table 3 provides the mean bias averaged over the ±2.5° validation area, spatial variability may still persist inside this spatial extent. Therefore, the influence of this localized spatial variation within the selected spatial extent on the overall comparison results was evaluated. To this end, the study area was partitioned into 0.1°×0.1° latitude-longitude grids. Individual residuals, obtained by subtracting the corresponding TCCON measurements from each matched satellite observation, were projected into the grid cells based on their geographic coordinates. To eliminate random noise from individual observations and represent the overall bias level of the region, the median value of all matched data point residuals within a single grid cell was calculated as the representative value for that grid cell. These values were then plotted using a color scale representing the XCH4 bias. The spatial distributions of the biases for the four XCH4 products at the Xianghe site are presented in Fig. 16, and for the Hefei site in Fig. A13 (Appendix A).

The data in Fig. 16a shows the occurrence of the largest positive biases for the OCPR XCH4 product around the Xianghe site and especially to the south, with median values ranging between +10 and +30 ppb. While Table 3 provides an overall mean bias of 6.3 ppb for the validation area, Fig. 16a demonstrates that this single statistical value masks significant intra-region variability. Specifically, the strong overestimation over the southern regions is partially offset by the negative biases distributed across the northern parts of the domain. The GOSAT SRPR XCH4 bias is generally negative near the site but transitions to overestimation in the southern region. The GOSAT-2 SRPR XCH4 product around Xianghe is distributed over a closer range to the TCCON site, with an overall negative bias. The data coverage of the GOSAT FOCAL Proxy XCH4 product is sparse and generally shows a negative bias to the northwest of the site, while to the southwest the biases are mostly positive. The distinct spatial heterogeneities and the shift toward positive biases observed in the southern areas across these products are likely due to the strong spatial gradients of XCH4. Compared with the other products, OCPR may include more observations over urban or potentially methane-enhanced areas to the south of the Xianghe site, where satellite footprints may capture higher XCH4 concentrations than those measured at the TCCON site, contributing to its extensive positive biases. This spatial discrepancy primarily reflects the inherent representation errors between the localized TCCON point measurements and the larger footprints of satellite observations within the matching domain. Notably, the spatial consistency of the GOSAT-2 product is significantly improved compared to the other GOSAT products. As detailed in Sect. 2.3.2, the GOSAT-2 b parameter (0.00158) is smaller, which minimizes the influence of surface albedo variations on XCH4 retrieval results.

Similar plots of the spatial variation of the biases at the Hefei site are presented in Fig. A13. These data show that positive biases dominate in the inland areas to the west of the site, whereas slightly negative biases are found in the coastal regions to the northeast.

Statistical analysis in Sect. 3.1 reveals a significant systematic discrepancy in XCH4 retrieval biases between the two sites: a prevalent overestimation at the Hefei site and a general underestimation at the Xianghe site (with the exception of OCPR). Given its proximity to anthropogenic emission sources in the North China Plain, the TCCON measurements at Xianghe likely exceed the regional background levels captured by satellite sampling (Yang et al., 2020), leading to a negative offset. At the Hefei site, the satellite tracks primarily pass over the western inland areas, where methane concentrations are relatively high (Fig. 2). Due to this geographic offset, satellite observations capture the higher concentrations to the west rather than matching the local TCCON reference levels, leading to an overestimation.

These spatial differences indicate that regional and local methane emissions may affect the representativeness of satellite–TCCON comparisons at both sites. As the satellite observations used in this study were not acquired in target mode over Hefei and Xianghe (Suto et al., 2021), the ±2.5° matching domain includes measurements from different locations that may be influenced by different emission and transport conditions. The uneven distribution of anthropogenic methane emissions produces spatial variations in atmospheric CH4 concentrations, particularly in urban and emission-intensive regions of northern China (Han et al., 2025). Methane emitted from urban and other emission-intensive areas can be transported and dispersed by atmospheric processes, with variations in wind fields, vertical atmospheric motions, and terrain influencing the spatial distribution of methane enhancements (Gao et al., 2026; Zheng et al., 2026). These processes may contribute to spatial differences in XCH4 between satellite footprints and TCCON observations.