The DQ-1/ACDL L2A XCO₂ product is used as the active lidar dataset in this study. The retrieval algorithm, error characterization, and quality-control procedure of the product are described in detail by Han et al. (2025). Ascending (Asc) and descending (Desc) observations correspond to daytime and nighttime overpasses, respectively, and are processed separately. Quality filtering retains only valid retrievals with QAflag=1 or 5, where QAflag=1 denotes a normal retrieval and QAflag=5 denotes a normal retrieval with a high signal-to-noise ratio. Because the released ACDL L2A product does not provide a dedicated flag for missing hard targets, QAflag=3, which denotes abnormal retrievals associated with low echo intensity, is used here only as an operational proxy for insufficient return signal rather than as a direct identification of missing hard targets. During June 2022–December 2024, QAflag=3 accounted for 15.60 % of the examined L2A records, with monthly fractions ranging from 13.80 %–17.68 % and no clear recurring seasonal cycle. These records lack valid footprint geolocation in the released L2A product, preventing a robust assessment of their geographical distribution.

The main variables used in this study include XCO₂, XCO₂_uncertainty, Hour, Day_Flag, SurfacePressure, PressureLevel, and the vertical weighting function (WF). Here, XCO₂ represents the column-averaged CO2 dry-air mole fraction for each valid ACDL observation, and XCO2_uncertainty denotes the retrieval uncertainty reported in the product. Hour and Day_Flag are used to determine the observation time and day–night condition. SurfacePressure, PressureLevel, and WF characterize the effective ACDL integration column and its vertical sensitivity, and are used in the correction for XCO₂ column-definition differences in Sect. 2.2.3. Because DQ-1 active lidar observations do not rely on solar illumination, daytime DQ-1 samples are used for the active–passive consistency assessment with passive satellite products, whereas nighttime DQ-1 samples are analyzed separately for the external model-reference diagnosis described in Sect. 2.2.7.

To evaluate the consistency between DQ-1 ACDL XCO₂ and passive NIR/SWIR satellite XCO₂ products, we use XCO₂ products from OCO-2, OCO-3, GOSAT, and GOSAT-2 as comparison datasets. These products mainly retrieve XCO₂ from solar-reflected near-infrared and shortwave-infrared absorption spectra; therefore, the observations generally correspond to daytime clear-sky or near-clear-sky conditions.

OCO-2 and OCO-3 are NASA Orbiting Carbon Observatory missions designed to retrieve XCO₂ from reflected solar spectra using three-channel high-resolution grating spectrometers and full-physics retrieval algorithms (Crisp et al., 2017; Eldering et al., 2017; O'Dell et al., 2018; Taylor et al., 2023). GOSAT and GOSAT-2 carry the Thermal And Near-infrared Sensor for carbon Observation Fourier Transform Spectrometer (TANSO-FTS) and its successor TANSO-FTS-2, respectively. Their instrument characteristics, retrieval algorithms, and XCO₂ products have been described in previous studies (Kuze et al., 2009, 2016; Noël et al., 2021, 2022; Suto et al., 2021; Yoshida et al., 2023). For GOSAT-2, the official land- and ocean-specific empirical bias corrections were applied to the individual XCO2 retrievals following the V02.20 and V02.21 release notes (NIES GOSAT-2 Project, 2026a, b). The official correction coefficients were derived using TCCON GGG2020 as the reference. GOSAT-2 V02.20 was used through February 2024 and V02.21 from March 2024 onward. The empirical bias correction was applied to each quality-controlled individual retrieval before daily 2° aggregation and collocation, whereas the CAMS-based column-definition correction was subsequently applied to the collocated samples. The passive satellite products are provided as individual soundings and provide the XCO₂ observations for comparison with DQ-1. The corresponding quality-control criteria are summarized in Table 2, and the spatiotemporal collocation and column-definition correction are described in Sects. 2.2.2 and 2.2.3. Although all products report XCO₂, their effective column definitions are not identical because the passive products use product-specific prior profiles, pressure weights, and column averaging kernels, whereas DQ-1 ACDL uses its weighting function and effective pressure layers. These differences are accounted for in Sect. 2.2.3.

We use the Copernicus Atmosphere Monitoring Service (CAMS) global greenhouse gas inversion CO2 product as an external model reference field. The CAMS CO2 inversion product used here is constrained by surface air-sample observations and generated by the PYVAR atmospheric inversion system, which is based on the LMDZ offline global atmospheric transport model. The product provides surface fluxes, model-level CO2 dry-air mole fractions, and column-averaged XCO₂, among other variables (Chevallier et al., 2005, 2010).

CAMS is used in three main ways in this study. First, CAMS column-averaged XCO₂ is used to evaluate the spatial homogeneity and short-term temporal coherence within each 2° candidate grid cell, thereby identifying background regions that are more suitable for inter-satellite comparison. Second, CAMS model-level CO2 profiles are used as a common external profile and are passed through the observation operators of different satellites to construct CAMS-derived XCO₂ values consistent with each satellite's column definition. This allows us to estimate the theoretical differences caused by differences in vertical sensitivity and effective column definition. Third, for nighttime DQ-1 observations, CAMS-derived XCO₂ is used as an external model reference to evaluate the consistency between nighttime DQ-1 XCO₂ and the model reference field. Throughout this study, TCCON is used as the ground-based observational reference for daytime validation, whereas CAMS is used as a model-based common reference for comparison-region selection, column-definition harmonization, and diagnostic analyses. CAMS is not treated as observational truth. The specific uses of CAMS are described in Sects. 2.2.1, 2.2.3, and 2.2.7.

To examine the potential influence of shortwave-infrared surface reflectance on the differences between DQ-1 and passive satellite XCO₂, we use the Aqua MODIS MYD09CMG.061 daily surface reflectance product. MYD09CMG is a Level-3 Climate Modeling Grid product that provides atmospherically corrected surface reflectance in the visible, near-infrared, and shortwave-infrared spectral regions (Vermote et al., 1997, 2002; Vermote and Kotchenova, 2008).

We select MYD09CMG Band 6 (1628–1652 nm) as a proxy for surface reflectance near the 1.6 µm CO2 absorption region. This band is not the actual retrieval channel of any of the XCO₂ sensors and is not used for any XCO₂ correction. Instead, it is used only as a common indicator of surface optical conditions to diagnose whether the bias and RMSE between DQ-1 and passive satellite XCO₂ vary systematically with surface reflectance. The MODIS quality filtering, spatial aggregation, and reflectance binning methods are described in Sect. 2.2.4.

To examine the potential influence of ocean surface conditions on the differences between DQ-1 and passive satellite XCO2, we use hourly 10 m wind data from the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis, ERA5 (Hersbach et al., 2020). ERA5 provides globally complete atmospheric fields on a regular 0.25°×0.25° latitude–longitude grid. We use the 10 m zonal and meridional wind components (u10 and v10) to derive 10 m wind speed. Over the ocean, near-surface wind influences sea-surface roughness and thus the sun-glint reflectance relevant to passive NIR/SWIR observations (Nelson et al., 2020). ERA5 10 m wind speed is therefore used as an auxiliary indicator of ocean surface conditions to diagnose whether the DQ-1–OCO-2/OCO-3 bias and RMSE vary systematically with surface wind conditions.

We use the Total Carbon Column Observing Network (TCCON) GGG2020 data product as a ground-based validation reference. TCCON retrieves the column-averaged dry-air mole fraction of CO2 from ground-based Fourier transform spectrometer measurements of solar near-infrared absorption spectra, and it is widely used for the validation of OCO-2/OCO-3, GOSAT/GOSAT-2, and other satellite XCO₂ products (Noël et al., 2022; Taylor et al., 2023; Wunch et al., 2010, 2011).

Only TCCON XCO₂ observations that pass the official quality control are used in this study. Because TCCON relies on direct solar spectra, it is mainly used for the validation of daytime DQ-1 observations and passive satellite XCO₂ products. The satellite–TCCON collocations analyzed in this study were not used to derive any additional bias correction. The TCCON sites and valid observation periods used for validation are listed in Table A2. The satellite–TCCON spatiotemporal matching method is described in Sect. 2.2.6.

CAMS XCO₂ is first averaged to daily fields and then used to evaluate the internal consistency of each 2°×2° grid cell. Because the native horizontal resolution of CAMS is 1°×1°, each 2° grid cell contains up to four 1° subgrid cells. For day d and 2° grid cell g, the spatial dispersion of subgrid XCO₂ relative to the 2° grid-cell mean is defined as: 1σsp(d,g)=1Ng∑k=1Ng(Xd,k-X‾d(g))21/2 where Xd,k denotes the daily mean XCO₂ for the 1° subgrid cell k on day d, X‾d(g) is the daily mean XCO₂ of the corresponding 2° grid cell, and Ng is the number of valid subgrid cells. The quantity σsp(d,g) represents the subgrid heterogeneity within a 2° grid cell on a given day. Over the study period, the median and 95th percentile of σsp(d,g) are denoted as σsp,med(g) and σsp,95(g), respectively, and are used to characterize spatial heterogeneity under typical and highly dispersed conditions.

To evaluate whether short-term temporal variations are consistent among the 1° subgrid cells within the same 2° grid cell, a 30 d moving-mean background is removed from the daily XCO₂ time series of each subgrid cell to obtain a high-pass anomaly series: 2Xd,k′=Xd,k-X̃d,k30 where Xd,k′ denotes the high-pass XCO₂ anomaly for kth subgrid cell on day d, and X̃d,k30 denotes the 30 d moving-mean background. Let P be the set of pairwise combinations of 1° subgrid cells within the 2° grid cell g. The temporal consistency index is then defined as: 3TCI(g)=1NP∑(p,q)∈Pcorrd(Xd,p′,Xd,q′) where corrd denotes the Pearson correlation coefficient calculated from the daily anomaly series. A higher TCI(g) indicates more consistent short-term XCO₂ temporal variations within the grid cell.

To describe whether the relative differences among subgrid cells remain stable over time, the stability of internal spatial differences is defined as: 4SDI(g)=1NP∑(p,q)∈Pstdd(Xd,p-Xd,q) where stdd denotes the standard deviation calculated along the time dimension. Grid cells with fewer than 60 valid days are excluded from the scoring procedure to avoid unstable correlation and percentile statistics caused by overly short time series.

The quantities σsp,med, σsp,95, TCI, and SDI are then normalized using the 5th and 95th percentiles across all valid 2° grid cells and clipped to the range 0–1. Lower values of σsp,med, σsp,95, and SDI indicate higher coherence; therefore, their normalized values are reversed. In contrast, higher TCI values indicate stronger temporal consistency. The final CAMS-based spatiotemporal coherence score is defined as: 5SCAMS(g)=Hsp,med(g)+Hsp,95(g)+CTCI(g)+HSDI(g)4 where Hsp,med(g), Hsp,95(g), CTCI(g), and HSDI(g) are the four normalized components. A higher SCAMS(g) indicates that the CAMS XCO₂ field within the 2° grid cell has lower spatial dispersion, more stable internal spatial differences, and more coherent short-term temporal variability.

To ensure stable multi-satellite observational coverage in the candidate 2° grid cells, we construct a satellite sampling availability score. For each satellite, daily XCO₂ observations after quality control are first assigned to the same 2° grid according to the latitude and longitude of the observation center. Following the grid-based spatial-coverage method of Han et al. (2024) and the path-length-based definition of valid gridded observations described by Han et al. (2025), we do not use the raw number of observations as the only criterion for determining valid gridded observations. Instead, for each sensor, day, and grid cell, we calculate the along-track sampling length by accumulating the great-circle distances between adjacent valid observation centers along the same orbit track. For each sensor and day, only grid cells with an accumulated sampling length greater than or equal to half of the diagonal length of the local 2° grid cell are counted as one valid observation. DQ-1 Asc and Desc are counted separately, and DQ-1 Total (Asc+Desc) is calculated as the direct sum of the two counts. The number of valid observations is then accumulated over the study period and normalized to the range 0–1 using the 95th percentile among grid cells with positive values, yielding the satellite sampling availability score.

On this basis, the mean sampling availability of the main sensors is calculated by averaging As(g): 6Amean(g)=1ns∑s=1nsAs(g) where Amean(g) represents the overall sampling sufficiency of grid cell g, As(g) is the normalized sampling-availability score derived from the accumulated number of valid observations for sensor s, and ns is the number of sensors included in the main score (ns=5). These sensors include daytime DQ-1, OCO-2, OCO-3, GOSAT, and GOSAT-2.

To avoid high scores being dominated by a single sensor, we further calculate the sampling evenness among sensors: 7Esensor(g)=-∑s=1nsps(g)ln⁡ps(g)ln⁡ns8ps(g)=Hs(g)∑s=1nsHs(g) where Esensor(g) is the Shannon evenness calculated from the sensor contribution fractions. It is higher when the contributions from multiple sensors are more balanced and lower when the valid observations are dominated by a single sensor. Here, ps(g) denotes the fraction of valid observations contributed by sensor s in grid cell g, calculated as the accumulated number of valid observations Hs(g) of sensor s divided by the total accumulated valid observation days from all sensors.

The multi-sensor same-day sampling support is defined as: 9Cmulti(g)=min⁡Dmulti(g)P95(Dmulti>0),1 where Cmulti(g) represents the same-day multi-sensor observation support for grid cell g. It is obtained by normalizing Dmulti(g), the accumulated number of days on which at least two main sensors satisfy the valid-observation condition on the same day, using its 95th percentile.

The final satellite sampling availability score is defined as: 10SSAT(g)=Amean(g)+Esensor(g)+Cmulti(g)3 where SSAT(g) accounts for mean sampling sufficiency, sampling evenness among sensors, and same-day multi-sensor observation support.

The final comparison-region score is determined jointly by the CAMS-based spatiotemporal coherence score and the satellite sampling availability score. To ensure both background-field coherence and sufficient multi-satellite sampling, we define the final score as the geometric mean of the two component scores: 11Sfinal(g)=SCAMS(g)SSAT(g) where Sfinal(g) denotes the final score for grid cell g. For the final selection, the 90th percentile of Sfinal is calculated separately for land and ocean grid cells. The 2° grid cells with Sfinal greater than or equal to the corresponding land or ocean threshold are retained as the final comparison regions. The P90 threshold was adopted as a conservative reference criterion. It prioritizes grid cells with relatively high background-field coherence and sufficient multi-satellite sampling. This choice was not intended to imply that P90 is an empirically optimized threshold. To test the sensitivity to this choice, we repeated the inter-satellite comparisons using P80 and P70 thresholds. These thresholds retain approximately the upper 20 % and 30 % of eligible land and ocean grid cells, respectively. All other processing and collocation procedures were kept unchanged. The sensitivity cases and results are presented in Appendix A2.

The quality-control criteria applied to each satellite XCO₂ product are listed in Table 2. Inter-satellite comparisons are based on daily samples aggregated within selected 2° comparison grid cells, rather than on matching individual soundings or footprints. After quality control, valid XCO₂ observations are assigned to the selected 2° comparison grid cells according to the latitude and longitude of their observation centers. For each date and selected grid cell, the daily XCO₂ and mean observation time are calculated using simple arithmetic averaging over all valid observations within the grid cell. A sample pair is considered a candidate pair only when the two products fall within the same selected 2° comparison grid cell on the same date and both satisfy the valid-observation criterion defined in Sect. 2.2.1. Candidate pairs are retained as final paired samples only if the difference between their daily mean observation times does not exceed 4 h. For the pairwise statistics shown in Fig. 4 and Table S3 in the Supplement, bias is defined as XCO₂(y-axis product) - XCO2(x-axis product).

The 2° aggregation was chosen as a common analysis scale for sensors with different footprint sizes and sampling densities. It is also consistent with the CAMS-based coherence analysis, because each 2° grid cell contains up to four native 1° CAMS grid cells. A finer 1° grid would therefore not preserve the same within-cell coherence assessment. The 4 h temporal window was selected to balance temporal representativeness with the availability of valid collocations among satellites with different sampling characteristics. A comparable 4 h criterion has also been used in direct OCO-2/OCO-3 XCO₂ comparisons (Taylor et al., 2023). We therefore retained the 2° grid and tested temporal windows of 3, 2, and 1 h while keeping the P90 spatial criterion fixed. The sensitivity cases and results are presented in Appendix A2. Unless otherwise stated, the inter-satellite comparison results presented in the main text are based on the Main case, which uses the P90 spatial-selection threshold and a maximum temporal difference of 4 h.

The active and passive satellite XCO₂ products do not necessarily share the same effective column definition because they differ in prior profiles, pressure weighting functions, column averaging kernels, and vertical sensitivities. If the retrieved XCO₂ values are compared directly, part of the difference may arise from differences in the observation operators, rather than from real atmospheric CO2 differences. To reduce this effect, we use CAMS 3 hourly CO2 profiles as a common external reference profile and apply the observation operator of each satellite to these profiles to estimate the theoretical difference caused by XCO₂ column-definition differences.

For a given satellite s, the CAMS-derived XCO₂ under the column definition of that satellite is expressed as: 12XsCAMS=Hs(cCAMS) where Hs is the XCO₂ observation operator of satellite s, and cCAMS is the CAMS CO2 profile.

For the passive products from OCO-2, OCO-3, GOSAT, and GOSAT-2, cCAMS is interpolated to the pressure levels of the corresponding product and then used together with the product-specific pressure weights and column averaging kernels to calculate XCO₂: 13XsCAMS=Xsa+∑k=1nsws,kAs,kckCAMS-cs,ka where Xsa is the prior XCO₂ of satellite s, ws,k and As,k are the pressure weight and column averaging kernel for layer k, respectively, cs,ka is the prior CO2 mixing ratio, and ckCAMS is the CAMS CO2 mixing ratio interpolated to the corresponding pressure level ps,k.

For DQ-1/ACDL, the active lidar retrieval uses the weighting function (WF) to describe vertical sensitivity. The CAMS profile is therefore integrated using the DQ-1 WF and the effective pressure thickness: 14XDQ1CAMS=∑k=1mcCAMS(pk)WFkΔpk∑k=1mWFkΔpk where WFk is the DQ-1 weighting function for layer k, and Δpk is the effective pressure thickness of that layer.

For each satellite sample pair satisfying the spatiotemporal collocation criteria, s denote the product under evaluation and r denote the reference product. The theoretical XCO₂ column-definition difference caused by differences in the observation operators is then defined as: 15ΔXr-sdef=XrCAMS-XsCAMS

This definition difference is subsequently added to the observed XCO₂ of the product under evaluation, thereby converting it to the XCO₂ definition of the reference product: 16Xs→rcorr=Xsobs+ΔXr-sdef

This correction only accounts for the theoretical difference produced when the same CO2 profile is represented under different satellite column definitions. CAMS is used only to estimate column-definition differences and is not treated as a truth reference for correcting satellite biases. The term ΔXr-sdef reflects only differences in the observation operators and effective column definitions. The differences after this correction may still include contributions from instrumental errors, retrieval errors, spatiotemporal sampling differences, and uncertainties in the CAMS CO2 profiles.

The MODIS MYD09CMG Band 6 shortwave-infrared surface reflectance is used only to diagnose the influence of surface optical conditions on the DQ-1–OCO-2/OCO-3 XCO₂ differences. It is not used for any XCO2 correction. For the DQ-1–OCO-2 and DQ-1–OCO-3 paired samples that have passed the spatiotemporal collocation and XCO₂ column-definition correction procedures, we extract the mean MODIS Band 6 reflectance within the same selected 2° comparison grid cell on the same day. Only samples with reflectance values between 0 and 1 and with at least 10 valid MODIS subpixels are retained, to reduce the influence of anomalous reflectance values on the statistics.

For each selected 2° grid cell, we then calculate the mean reflectance, mean bias, and RMSE. The RMSE is defined as the square root of the mean squared residuals of all valid paired samples within the same grid cell. Based on these 2° grid-cell statistics, the samples are further binned according to the grid-cell mean reflectance. A reflectance bin width of 0.05 is used for all samples and land samples, whereas a bin width of 0.02 is used for ocean samples to account for the smaller range of shortwave-infrared reflectance over the ocean. Statistics are calculated for a reflectance bin only when it contains at least 10 valid 2° grid cells. Within each reflectance bin, bias and RMSE are reported as the arithmetic means of the grid-cell mean bias values and grid-cell RMSE values, respectively. The error bars indicate the standard deviations of the corresponding 2° grid-cell statistics within the same reflectance bin. The linear least-squares fits and Pearson correlation coefficients shown in Figs. 6 and 7 are calculated from the displayed reflectance-bin means.

To further examine the potential influence of ocean surface conditions on the DQ-1–OCO-2/OCO-3 differences, ERA5 10 m zonal and meridional wind components (u10 and v10) are collocated in space and time with the oceanic paired samples and used to derive 10 m wind speed. For each selected 2° ocean grid cell, the mean wind speed, mean bias, and RMSE are calculated, and the resulting grid-cell statistics are further grouped into wind-speed bins. The mean bias and RMSE within each bin are used to assess whether the active–passive XCO₂ differences vary systematically with near-surface wind conditions. Wind-speed bins have a width of 1 ms-1. Linear least-squares fits and Pearson correlation coefficients are calculated separately for the individual 2° grid-cell statistics and for the wind-speed-bin means shown in Fig. S6 in the Supplement.

TCCON is used as a common ground-based reference for satellite XCO₂ validation. Following the validation approach for DQ-1/ACDL described by Han et al. (2025), we construct a 1°×1° spatial matching window centered on each TCCON site and extract quality-controlled TCCON XCO₂ observations within ±0.5h of the satellite overpass time. If multiple TCCON observations are available within the matching window, their median value is used as the reference. For the matched satellite samples, we estimate and correct the definition difference caused by differences in XCO₂ column definition and vertical sensitivity following Sect. 2.2.3. The corrected satellite XCO₂ is then compared with the TCCON reference value, and bias, RMSE, and the Pearson correlation coefficient (R) are calculated. To assess site-to-site variability and the potential influence of uneven collocation numbers across TCCON sites, we additionally calculated site-level validation statistics. The interstation bias was defined as the standard deviation of the mean biases calculated separately for individual TCCON sites, while the site-mean RMSE was defined as the mean of the site-specific RMSE values, with each TCCON site weighted equally. The 95 % confidence intervals of the pooled bias and RMSE were estimated using a TCCON-site cluster bootstrap with 20 000 resamples, in which contributing sites were sampled with replacement and all collocations from each selected site were retained together.

Because passive shortwave-infrared satellites and TCCON do not provide nighttime XCO₂ observations, CAMS CO2 is used as an external model reference field for evaluating nighttime DQ-1 XCO₂. We first select nighttime DQ-1 L2A observations that pass quality control, are located within the selected comparison regions, and satisfy the valid-observation criterion defined in Sect. 2.2.1. These observations are then aggregated by date and selected 2° comparison grid cell. XCO₂, WF, SurfacePressure, and Hour are averaged arithmetically over the valid observations within each grid cell.

The nearest CAMS CO2 profile is then matched according to the mean DQ-1 observation time. Using the aggregated WF and SurfacePressure, the CAMS profile is converted to XCO₂ under the DQ-1 column definition. The resulting CAMS-derived XCO₂ is finally paired with nighttime DQ-1 XCO₂, and bias, RMSE, and the Pearson correlation coefficient are calculated. The difference is defined as DQ-1 minus CAMS-derived XCO2. This comparison is used to evaluate the consistency and stability of nighttime DQ-1 relative to an external model reference field, and should not be interpreted as an independent absolute validation against observations. As an additional diagnostic of possible day–night retrieval differences, we also compare the zonal-mean daytime–nighttime XCO₂ difference in DQ-1 with the corresponding difference in CAMS-derived XCO2 under the DQ-1 column definition. Because direct spatial overlap between daytime and nighttime ACDL ground tracks is sparse, this analysis is performed at the zonal-mean level rather than using strict point-by-point daytime–nighttime collocation.

Figure S2 in the Supplement compares the spatial distributions of DQ-1, OCO-2, and OCO-3 XCO₂ over the selected 2° comparison grid cells. Overall, the three products show similar large-scale XCO₂ gradients, with higher values mainly over Northern Hemisphere land and lower values over Southern Hemisphere oceans. The high- and low-XCO2 patterns in DQ-1 are broadly consistent with those of OCO-2 and OCO-3, indicating that active IPDA and passive NIR/SWIR XCO₂ products have similar spatial structures over the selected comparison regions.

Figure 5 further shows the spatial distributions of the mean DQ-1–OCO-2 and DQ-1–OCO-3 differences, together with the corresponding zonal-mean results. Spatially, most DQ-1–OCO-2 and DQ-1–OCO-3 differences are within approximately ±1ppm, with no clear global-scale systematic bias. Local positive differences occur mainly over several oceanic sampling bands, Australia, and some low- and middle-latitude land regions, whereas negative differences are scattered over North Africa, Eurasia, and parts of the tropical oceans. Although most grid-cell differences remain within approximately ±1ppm, several regional features are evident (Fig. 5). Over Australia, the mean DQ-1–OCO-2 and DQ-1–OCO-3 biases are +0.76 and +0.57ppm, respectively, compared with +0.46 and +0.15ppm over all selected land grid cells. The tropical Pacific shows a different pattern. For DQ-1–OCO-2, the regional mean bias is +0.58ppm, slightly higher than the all-ocean value of +0.51ppm, whereas for DQ-1–OCO-3 the regional mean bias is +0.30ppm, lower than the corresponding all-ocean value of +0.40ppm. Thus, an enhanced regional mean bias is not common to both tropical-Pacific comparisons. In contrast, the mean grid-cell RMSE values are 1.27 and 1.26 ppm, respectively, both 0.06 ppm higher than the corresponding all-ocean values of 1.21 and 1.20 ppm (Table S4 in the Supplement). These regional differences are examined further in Sects. 3.4.2 and 3.4.3 using CAMS-derived XCO₂, surface reflectance, and ocean wind-speed diagnostics.

The zonal-mean results show that DQ-1 and OCO-2/OCO-3 have broadly consistent meridional XCO₂ variations, with higher values in the Northern Hemisphere mid-latitudes and lower values in the Southern Hemisphere. The zonal-mean values of DQ-1 and OCO-2 are approximately 420.15 and 419.74 ppm, respectively, corresponding to a mean difference of about 0.41 ppm. For the DQ-1–OCO-3 comparison, the corresponding values are approximately 419.17 and 419.00 ppm, with a mean difference of about 0.17 ppm. In most latitude bands, the DQ-1–OCO-2/OCO-3 differences are close to zero, with only small positive or negative deviations in some low- and middle-latitude regions. Overall, DQ-1 is consistent with OCO-2 and OCO-3 in both spatial distribution and meridional structure, indicating that the residual differences between active and passive XCO₂ products are generally small after applying unified filtering, aggregation, collocation, and column-definition correction.

To further diagnose these regional differences, DQ-1 and OCO-2/OCO-3 were independently compared with CAMS-derived XCO2 using exactly the same collocated samples (Figs. S3–S4 and Table S5 in the Supplement). Over Australia, DQ-1 shows small positive biases of +0.22 and +0.23 ppm relative to CAMS-derived XCO₂ for the OCO-2 and OCO-3 collocations, respectively, whereas OCO-2 and OCO-3 show negative biases of -0.53 and -0.35ppm. Thus, the positive DQ-1–OCO differences over Australia are accompanied by opposite-signed departures of DQ-1 and the OCO products from the common CAMS-derived reference. A site-based comparison with TCCON at Darwin and Wollongong provides an independent regional diagnostic and likewise shows a positive DQ-1 bias, although only 10 DQ-1 collocations are available (Fig. S5 in the Supplement). Over the tropical Pacific, the DQ-1–CAMS-derived XCO2 RMSE values are 1.09 and 1.08 ppm, compared with 0.41 and 0.42 ppm for OCO-2 and OCO-3, respectively. In contrast, over the Sahara, both DQ-1 and the OCO products show RMSE values below 1 ppm relative to CAMS-derived XCO₂, and the contrast between the two products is much smaller than that over the tropical Pacific (Table S5). Over the tropical Pacific, the substantially larger DQ-1 RMSE relative to the common CAMS-derived reference indicates that the enhanced scatter is more evident on the DQ-1 side under these collocated conditions. This differs from Australia, where DQ-1 and the OCO products show opposite-signed mean departures from CAMS. CAMS is used here only as a common diagnostic reference rather than as observational truth; these comparisons therefore help identify relative product behavior but do not uniquely attribute retrieval errors.

Figures 6 and 7 show, respectively, the relationships between MODIS Band 6 shortwave-infrared surface reflectance and the bias and RMSE of DQ-1 relative to OCO-2 and OCO-3. Spatially, MODIS reflectance is substantially higher over land than over ocean, especially in arid and semi-arid regions such as North Africa–the Middle East, Australia, and Central Asia, whereas ocean reflectance is generally low and has a narrower range. In contrast, the spatial distribution of bias is more heterogeneous, with positive and negative residuals spatially mixed and no clear correspondence with the reflectance field. The RMSE distribution also does not simply follow the regions of high reflectance. Higher RMSE values occur not only over some high-reflectance land areas and regions with complex surface conditions, but also over parts of the Southern Hemisphere oceans, the tropical Pacific, and coastal regions. Because the ocean residuals cannot be explained consistently by surface reflectance alone, we further examine whether they covary with ERA5 10 m wind speed.

To further diagnose the influence of surface reflectance on the residuals, we calculate reflectance-binned statistics for the bias and RMSE of DQ-1–OCO-2 and DQ-1–OCO-3. For all samples, the linear relationship between bias and reflectance is weak, with correlation coefficients of approximately R=-0.22 for DQ-1–OCO-2 and R=-0.24 for DQ-1–OCO-3. This indicates that, when all samples are considered, reflectance is not the dominant factor controlling the mean bias. For samples over land, the DQ-1–OCO-2 bias increases slightly with reflectance, with R=0.42, whereas the DQ-1–OCO-3 bias shows a weaker relationship with reflectance, with R=-0.21. For samples over ocean, the correlations are stronger, but the two comparison pairs show opposite trends: the DQ-1–OCO-2 bias increases with reflectance, with R=0.77, whereas the DQ-1–OCO-3 bias decreases with reflectance, with R=-0.77. Thus, surface reflectance is clearly associated with the oceanic bias statistics, but the direction of the association is pair dependent: positive for DQ-1–OCO-2 and negative for DQ-1–OCO-3.

RMSE shows a similar pattern. For all samples, the correlations between RMSE and reflectance are weak for both DQ-1–OCO-2 and DQ-1–OCO-3, with correlation coefficients of approximately R=-0.24 and R=-0.35, respectively. The correlations remain limited for samples over land, with R=-0.17 and R=-0.42, respectively. By contrast, the RMSE–reflectance relationships are more pronounced for samples over ocean, but again show opposite trends for the two comparison pairs: the RMSE of DQ-1–OCO-2 over ocean increases with reflectance, with R=0.64, whereas that of DQ-1–OCO-3 decreases with reflectance, with R=-0.78. The corresponding RMSE relationships show the same pair dependence. Taken together, the ocean results indicate pronounced but opposite-signed reflectance associations rather than a common reflectance response across the two OCO comparisons.

The ERA5 wind-speed analysis reveals different behavior at the individual-grid-cell and binned levels (Fig. S6). At the individual 2° grid-cell scale, the correlations with wind speed are weak, with R=-0.16 and -0.29 for bias and R=-0.03 and -0.08 for RMSE for DQ-1–OCO-2 and DQ-1–OCO-3, respectively. After grouping the grid cells into 1 ms-1 wind-speed bins, however, both the bin-mean bias and RMSE decrease with increasing wind speed, with R=-0.97 and -0.81 for DQ-1–OCO-2 and R=-0.94 and -0.89 for DQ-1–OCO-3, respectively. The strong binned relationships, together with the large spread of individual grid cells within the bins, indicate a systematic change in the mean residual statistics with wind speed, while substantial grid-cell variability remains.

The tropical Pacific has slightly higher mean wind speeds than the selected ocean samples as a whole, but its mean grid-cell RMSE is also slightly higher (Table S4). Thus, the elevated tropical-Pacific RMSE cannot be explained simply by stronger near-surface winds. Moreover, ERA5 10 m wind speed is only an indirect indicator of sea-surface roughness and does not describe the instantaneous sun–sensor glint geometry of individual OCO observations. The present diagnostics therefore indicate that ocean-surface conditions are associated with the residual statistics, but they do not identify a single reflectance- or wind-related mechanism that explains the tropical-Pacific differences.