An eleven year record of XCO 2 estimates derived from GOSAT measurements using the NASA ACOS version 9 retrieval algorithm

. The Thermal And Near infrared Sensor for carbon Observation - Fourier Transform Spectrometer (TANSO-FTS) on the Japanese Greenhouse gases Observing SATellite (GOSAT) has been returning data since April 2009. The version 9 (v9) Atmospheric Carbon Observations from Space (ACOS) Level 2 Full Physics (L2FP) retrieval algorithm (Kiel et al., 2019) was used to derive estimates of carbon dioxide (CO 2 ) dry air mole fraction (XCO 2 ) from the TANSO-FTS measurements collected over it’s ﬁrst eleven years of operation. The bias correction and quality ﬁltering of the L2FP XCO 2 product were evaluated 5 using estimates derived from the Total Carbon Column Observing Network (TCCON) as well as values simulated from a suite of global atmospheric inverse modeling inversion systems which do not assimilate In the ACOS GOSAT XCO 2 results were compared with collocated XCO 2 estimates derived from Orbiting Carbon Observatory-2 using the version 10 (v10) ACOS L2FP algorithm. indicate that the v9 ACOS GOSAT XCO 2 product has improved throughput, scatter, (cid:58) and bias, when compared to the earlier v7.3 ACOS GOSAT product, which extended through mid 2016. Of the 37 million (M) soundings collected by 2020, approximately 20% were selected for processing by the v9 L2FP algorithm after screening for and other artifacts. After post-processing, 5.4% of the soundings (2M M out of 37 M) were a XCO 2 as compared to 3.9% in v7.3 (<1 M out of 24 M). After quality ﬁltering and bias correction, the differences in XCO 2 between ACOS GOSAT v9 and both TCCON and models have a scatter (one sigma) of approximately 1 ppm for ocean-glint observations and 1 to 1.5 ppm for land observations. Similarly, global mean biases

After obtaining the calibrated L1b product from JAXA, the ACOS team converts the files to the format needed as input to the ACOS L2 algorithms. The L2FP algorithm uses a simple average of the S and P linear polarizations to produce an approxima-135 tion of the total measured intensity. Due to cooperation agreements between JAXA and the California Institute of Technology, the distribution of the ACOS GOSAT L1b product is restricted and therefore not publicly available on the NASA DISC. However, the data may be procured by submitting a request to the GOSAT project.
3 The ACOS v9 L2FP XCO 2 retrieval algorithm 140 The ACOS Level 2 full physics (L2FP) retrieval algorithm is well documented, most recently in O' Dell et al. (2018) for v8 and in Kiel et al. (2019) for v9. A Bayesian optimal estimation framework is used to derive estimates of XCO 2 from spectral measurements of reflected solar radiation. A post-processing step assigns a simple good/bad quality flag (QF) to each XCO 2 value based on successful L2FP algorithm convergence and a series of empirically derived filters. An empirical bias correction (BC) to the estimated XCO 2 values, derived from comparisons with TCCON derived XCO 2 and CO 2 fields from a suite of 145 atmospheric inversion systems, is included in the Lite File product. Here we provide a summary of the recent evolution of the ACOS algorithm and discuss retrieval parameters and setup specific to GOSAT. can be found in O'Dell et al. (2018). The trace gas absorption coefficient tables (ABSCO) were updated from v4.2  in ACOS v7 to ABSCO v5.0  in ACOS v8/9. The ACOS v9 L2FP algorithm is unmodified relative to v8 (Kiel et al., 2019). However, changes were made in v9 regarding the sampling of the meteorological prior, which does affect ACOS GOSAT estimates of XCO 2 . The source of the prior meteorology was switched from the European Center for Medium-range Weather Forecast (ECMWF) in ACOS v7, to the NASA Goddard Modeling and Assimilation Of-155 product (Rienecker et al., 2011). However, between v7 and v8/9, an additional stratospheric aerosol layer was introduced, as described in Section 3.1.1 of O'Dell et al. (2018). In addition, the prior value of the aerosol optical depth (AOD) for each 160 retrieved aerosol type was lowered from 0.0375 in ACOS v7 to 0.0125 in ACOS v8/9 based on extensive testing. There was no change in the source of the CO 2 prior from ACOS v7 to v8/9; both versions adopted the prior developed by the TCCON team for use in the ggg2014 algorithm . An additional change from ACOS v7 to v8/9 was a switch from a purely Lambertian land surface model, to a more sophisticated bi-directional reflectance distribution function (BRDF) model. 165 Several important components of the v9 ACOS L2FP retrieval configured for GOSAT have not changed from v7.3; (i) the surface pressure prior constraint remains set at ±2 hPa, (ii) three Empirical Orthogonal Functions (EOFs) are fit in each spectral band (see Section 3.3 in O' Dell et al. (2018) for a full discussion of ACOS EOFs), and (iii) a zero level offset (ZLO) is fit in the state vector to account for non-linearity in the ABO2 signal chain on GOSAT TANSO-FTS . 170 To support comparisons of the ACOS GOSAT v9 XCO 2 product with the OCO-2 v10 product, Table 1 includes the most recent updates to the ACOS v10 L2FP algorithm. For v10, the ABSCO tables were again updated from v5.0 to v5.1 (Payne et al., 2020). The aerosol prior was updated from the MERRA monthly climatology to daily GEOS-FT-IT values, with a tightened prior uncertainty (Nelson and O'Dell, 2019). Finally, the CO 2 priors developed by the TCCON team for use in ggg2014 were updated to a revised set of priors developed for use in ggg2020.

ACOS L2FP algorithm updates
175 Table 2. Accounting of the soundings in the eleven year long GOSAT ACOS v9 dataset at each stage of the data processing chain. The final line summarizes the number of good quality XCO2 soundings used in the evaluation section of this work. 3.2 ACOS GOSAT v9 L2FP sounding selection and convergence GOSAT data from April 20, 2009 through June 30, 2020 were passed through the ACOS L2FP algorithm pipeline, which includes a series of stages where soundings can be rejected or selected for further processing. The throughput of each of these stages for ACOS GOSAT v9 is summarized in Table 2 and Figure 1. The pipeline begins with a series of preprocessing steps, 180 which reject corrupted spectra and screen the remainder to eliminate those with optically-thick clouds and/or aerosols . From the full set of measurements (Panel A of Figure 1), the remaining soundings are accepted by the L2FP algorithm (18.8% of the 37.4 M measured soundings contained in the ACOS GOSAT v9 record) (Panel B of Figure 1) and a retrieval of XCO 2 is attempted. The majority of the selected soundings successfully converge to a valid solution; 87% for ACOS GOSAT v9 (16.4% of the total measured soundings). Soundings can fail to converge for a variety of reasons, including 185 (i) producing non physical values, such as negative gas mixing ratios or surface pressures (3.9% of the selected), (ii) converging too slowly and exceeding a predefined number of iterations (3.2% of the selected), or (iii) having more diverging steps than the predefined maximum (5.9% of the selected). The 6.1 M valid soundings were then run through the quality filtering and bias correction procedure discussed in the next section. 3.3 ACOS GOSAT v9 XCO 2 quality filtering and bias correction All GOSAT soundings that converged to a valid XCO 2 value within the L2FP retrieval were input to the quality filtering and bias correction procedure. A modest fraction (4.5% of the valid soundings) were removed from the final L2Lite product based on screening via the IDP ::::::::::: IMAP-DOAS ::::::::::: Preprocessor :::::: (IDP) CO 2 ratio, which indicated the presence of clouds or aerosols. GOSAT v9 data record (A). The fraction of the total soundings selected to run through the L2FP algorithm (B). The fraction of the total soundings that converged in the L2FP and were assigned a good L2FP QF (C). The sounding density of the good QF data per 2.5 • by 5 • latitude/longitude grid cell (D).
Based on a series of screening criteria derived from comparisons with TCCON and modeled CO 2 fields, each sounding that 195 converged within the L2FP is assigned either a "good" (=0) or "bad" (=1) XCO 2 quality flag. Generally, for global or regional studies, it is recommended that users retain only the "good" quality soundings, as the soundings flagged as "bad" quality are likely to include biases that compromise their utility for some applications. A global map of the ACOS GOSAT v9 "good" XCO 2 sounding density is provided in panels C and D of Figure  A fundamental aspect of the quality filtering and bias correction procedures (QF/BC) is the need for XCO 2 truth metrics with which to compare the satellite derived estimates (O'Dell et al., 2018). The development of ACOS GOSAT v9 used XCO 2 truth metrics derived from both TCCON measurements, and the median CO 2 distributions determined from a suite of four 205 atmospheric inversion systems : , ::::: which ::: do ::: not :::::::: assimilate ::::::: satellite :::: CO 2 :::::::::::: measurements.
TCCON is a well established validation transfer standard for space-based estimates of XCO 2 (Wunch et al., 2011a(Wunch et al., , 2017b. For the ACOS GOSAT v9 QF/BC, estimates of XCO 2 derived from TCCON measurements using the ggg2014 retrieval algorithm were used . Individual GOSAT soundings were compared to TCCON daily mean XCO 2 values. TCCON 210 data were included if: (i) they were flagged good (flag = 0), (ii) they fell within 3 standard deviations of a daily quadratic fit against time (to remove outliers, e.g. due to unscreened cloud), (iii) they covered at least 15 minutes within a given day, (iv) there were at least 3 good soundings within the day, and (v) the standard deviation of the good soundings for the day was less than 3 ppm. In the GOSAT-TCCON comparisons described here, an averaging kernel correction was applied to each TCCON XCO 2 estimate following Nguyen et al. (2014), prior to calculating the daily mean value.
Estimates of CO 2 from atmospheric inversion systems, or models, provide a useful metric for evaluating satellite based estimates of XCO 2 (O' Dell et al., 2018). In this work, a suite of four models (CarbonTracker, CAMS, CarboScope, and Univ. of Edinburgh) were sampled at the GOSAT sounding times and locations. Brief descriptions of each, along with references, are 230 provided in Table 3. The models use a variety of land biosphere prior fluxes, inverse solvers and transport models, and assimilate CO 2 data only from flasks and continuous analyzers on a wide variety of platforms, e.g., observatories, towers, aircraft, and ships. Specifically, no data from GOSAT, OCO-2, or TCCON are assimilated. The CO 2 concentration fields of the models capture the known features of the global atmospheric CO 2 distribution, including seasonality, time trends and inter-annual variability (IAV) due to ENSO. For each GOSAT sounding, the vertical profiles of CO 2 from the corresponding grid box of 235 each of the four models are spatiotemporally interpolated (linear in latitude, longitude, and time) to the GOSAT observation point, and the GOSAT averaging kernel is applied to each vertical profile to produce a modeled XCO 2 as if viewed from the satellite.
For interested readers, the ::: The : explicit formula for application of the ::::: ACOS ::::::: GOSAT ::: v9 correction is provided in Section 2.5.6 of the ACOS GOSAT DUG . For both land H-gain and M-gain, a set of five BC variables are used, while Ocean-Glint uses only 3 variables. The difference between the H-and M-gain bias correction over land is minor. New for ACOS GOSAT v9 is the use of a correction against time, which is made possible with an eleven year data record; the corrections are +0.05 : ppm/yr over land and +0.10 : ppm/yr over water. The source of this spurious drift in the bias-corrected XCO 2  et al., 2020). Soundings falling outside of the data ranges are assigned a bad XCO2 quality flag. The second column identifies variables that were also used for OCO-2 v9 quality filtering, as taken from  is currently unclear and is the subject of on going study. Although there is some commonality in the quality filtering and bias correction variables used for ACOS GOSAT v9 (compare Tables 5 and 6), they do differ somewhat, as is typically the case with each sensor and data version.
285 Table 6 compares the bias correction variables used for ACOS GOSAT v9 with the variables used in the previous ACOS GOSAT v7.3, as well as with OCO-2 v9 and v10. The same few variables have appeared in all recent versions, including L2FP δ ∇ CO2 , L2FP dP , and L2FP DWS for land soundings. For ocean soundings the bias correction variables have evolved, with the only common one being δ ∇ CO2 . 290 Table 7 summarizes the effect of the quality filtering and bias correction on the ACOS GOSAT XCO 2 for v7.3 and v9. For Ocean-Glint soundings, the v9 quality flag is substantially more restrictive compared to v7.3, i.e. 57% pass rate compared to 78%. This is mostly driven by the more extensive latitudinal coverage in the v9 record, which tends to include more soundings with high solar zenith angles (SZA) and low signal to noise ratio (SNR), which are more challenging for the L2FP.

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For H-gain land observations, the two versions have quite similar QF pass rates ( 35-45%). The QF pass rate for v9 M-gain Land data is 39% when compared against models, but 56% against TCCON. In all cases there is a significant reduction in the scatter of the XCO 2 after application of the QF/BC; by a factor of 2 for Ocean-Glint and Land M-gain, and a factor of 3 for Land H-gain. The QF/BC scatter is always slightly lower for v9 compared to v7.3, although :::: even :::::: though the number of soundings is greater by 1.5 to 10 times for the various scenarios.
300 Table 6. ACOS L2FP bias correction variables by sensor and product version.
Retrieved minus a priori surface pressure -dP frac , dP frac dP frac dP frac Elevation adjusted dP Retrieved minus a priori surface pressure tyear --Time in years  Figure 2 shows the relative magnitudes of the bias correction on the good quality soundings by season, aggregated to 2.5 • latitude by 5 • longitude. The global median bias of -1.8 ppm has been removed for clarity. This highlights gradients and contrasts in the bias correction, which are of importance as gradients in CO 2 concentrations are the primary driver of CO 2 fluxes in atmospheric inversion systems. In general, the bias correction is necessary to remove spurious contrasts between land and ocean-glint XCO 2 values. The strongest relative bias corrections are positive adjustments over the bright land surfaces in The ACOS GOSAT v9 XCO 2 record was characterized in five ways: (i) an analysis of the XCO 2 "good quality" data volume, (ii) a spatiotemporal analysis of the XCO 2 estimates, (iii) a validation against XCO 2 estimates from TCCON, (iv) a comparison of to XCO 2 derived from models, and (v) a comparison with collocated XCO 2 estimates from the OCO-2 v10 product.

ACOS GOSAT v9 "good quality" data volume
It is instructive to compare the ACOS GOSAT v9 product to the earlier v7.3 product to highlight similarities and differences 315 in the quality filter screening. A time series histogram of the monthly throughput of the good quality filtered soundings for the v9 product compared to v7.3 is shown in Figure 3. The soundings have been binned by month, with the three GOSAT observation modes displayed by color. The v7.3 product did not contain any Land M-gain data in the L2Lite files (red in the figure) as the quality filtering and bias correction were not developed for that gain mode in v7.3 due to some unreconciled differences. An important feature of the v9 data record is the extension in time, which runs through June 2020, compared to a 320 termination date of June 2016 for v7.3. Even for the overlapping v7.3 and v9 time period (2009 through mid 2016), there are some differences in the data volume for Land H-gain and Ocean-Glint observations. This is due to changes in both the details of the QF procedure, including changes in the variable thresholds used to assign QF=good/bad, and to some differences in the convergence characteristics of the L2FP retrieval. Generally, v9 is producing up to 60% more good-quality data than v7.3 near the end of the overlap period in 2016. There was a substantial increase in the number of good QF soundings from 2010 to 2019, due to the increased latitudinal range of the ocean observations as a result of improvements in the GOSAT pointing strategy, as well as improvements in the sounding selection for ACOS L2FP v9.  Figure 4 shows sounding density Hovmöller plots comparing ACOS GOSAT v7.3 (A) to v9 (B) with the three GOSAT observation modes combined. Again, the extended time period covered by v9 is evident. The increase in sounding density in the SH 330 beginning in 2016 due to optimization of the GOSAT viewing strategy is prominent in the v9 product. This feature is also seen in the spatial maps showing the fraction of good quality soundings and the density per grid box, in panels C and D of Figure 1, which was introduced in Section 3.2. Persistently clear regions, such as the Sahara and western Australia, have as many as 30% of the observations assigned a good quality flag. Large regions of the tropical Pacific and Atlantic also contain a relatively high fraction of good quality soundings. On the other hand, tropical forests and high latitudes in general have low yields of 335 good quality soundings. This is largely a combination of cloud contamination, dark surfaces at shortwave infrared wavelengths, and low solar illumination conditions, all three of which are problematic for retrieving CO 2 from space using reflected sunlight.

ACOS GOSAT v9 XCO 2 spatiotemporal analysis
There has been a steady increase in the atmospheric burden of CO 2 since the onset of the industrial age due mainly to the 340 burning of fossil fuels (e.g., Keeling et al., 1995). In May of 2009, at the beginning of the GOSAT mission, the mean global value of XCO 2 reported by the NOAA Global Monitoring Laboratory was 387.95 ppm, while by May of 2020, the mean global value had risen to 413.81 ppm (Dlugokencky and Tans, 2021). This yields a secular increase of 2.35 ppm/yr. For comparison, This small disagreement in secular trend of approximately 2% is understandable, given the significant differences in the spatiotemporal sampling of the two data sets. For the interested reader, a thorough comparison of satellite and surface-derived growth rates in atmospheric CO 2 is given in Buchwitz et al. (2018). Grid cells with less than 10 GOSAT soundings are not colored.

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Land M-gain observations have near zero bias (µ=-0.02 ppm and +0.02 ppm for SS and OPM, respectively), and scatter similar to that for Ocean-Glint (σ=1.09 and 0.84 ppm for SS and OPM, respectively), likely driven by lower variability in surface topography and brightness compared to Land H-gain observations, as well as higher SNRs over these bright land surfaces.
Knowledge of the average XCO 2 seasonal cycle can be used to disentangle the CO 2 growth rate from the seasonal variability, 440 as well as for quantifying potential seasonal biases between satellite and ground-based XCO 2 estimates. Lindqvist et al. (2015) fitted a skewed sine wave (See Eq. 1 of Lindqvist et al., 2015) to the ACOS GOSAT v3.5 XCO 2 time series and the TCCON estimates of XCO 2 at 16 stations, spanning April 2009 through December 2013. They found that ACOS GOSAT v7.3 captured the seasonal cycle within approximately 1 ppm of the TCCON estimates for all but the European sites, and that the satellite and ground-based CO 2 growth rates agreed generally better than 0.2 ppm per year. Here, we provide an update to those results using 445 the eleven year ACOS GOSAT v9 XCO 2 data record. For this part of the analysis, a slightly more restrictive set of collocation criteria were implemented, compared to that described in Section 3.3 for the BC/QF procedure and to that used to generate  disagreement of a few tenths of a ppm, with TCCON showing a slightly higher fitted peak XCO 2 value during the spring maximum phase, compared to GOSAT. This is similar to the results for this site reported in (Fig. 4 of Lindqvist et al., 2015). The time series of the calculated difference in satellite and ground-based estimated XCO 2 (GOSAT -TCCON), shown in (C), highlights the magnitude of the scatter about the mean bias, and suggests that there is no observable time-drift in the data at this site. A summary of the data from each station that met the seasonal cycle collocation criteria is provided in Table 9. In addition, the full complement of plots are presented in Appendix A. Overall, the seasonal cycle analysis at most sites is in agreement, to within the estimated uncertainties. The standard deviation of the mean XCO 2 biases for the 26 sites is 0.41 ppm for the ACOS GOSAT v9 record. This compares to a value of 0.51 ppm at 23 stations for ACOS GOSAT v7.3, suggesting an improvement in 465 the quality of the v9 XCO 2 product.

ACOS GOSAT v9 XCO 2 versus models
The collocation and calculation of the multi-model-mean (MMM) was described in Section 3.3. Although the model data used for evaluation was very similar to that used in the QF/BC procedure, some minor version updates and extensions in time were 470 included, as indicated in Table 4. It is important to be aware that there can be a considerable time delay between performing Table 9. Evaluation of the daily mean bias corrected ACOS GOSAT v9 XCO2 (all viewing modes combined) against collocated TCCON estimates for individual stations. There were 7547 days total for the 25 stations. The following sites/instruments were excluded from this part of the analysis due to inadequate timeseries or seasonal cycle coverage; Eureka, Four Corners, Indianapolis (Influx), JPL2007, Lauder1, Lauder3, Manaus, and Ny Ålesund. The mean, standard deviation, and Pearson correlation coefficient (µ, σ, R 2 ) of the linear fit between GOSAT and TCCON are given in columns 3-5. The remaining columns quantify the seasonal cycle fit following the methodology described in Lindqvist et al. (2015). The bottom row provides mean summary statistics for the linear fit. the QF/BC procedure and the full generation of the final product, during which time the models are often updated.

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OCO-2 takes measurements of reflected solar radiation in the Oxygen A-band (0.76 µm), and the weak and strong carbon dioxide bands (1.6 and 2.0 µm, respectively), which are used to estimate XCO 2 using the ACOS L2FP retrieval algorithm O'Dell et al., 2018). However, due to differences in the orbit parameters of the two sensors, e.g., a 3 day repeat cycle for GOSAT versus a 16 day repeat cycle for OCO-2 (see Table 2 of Kataoka et al., 2017), the number of collocated soundings is somewhat limited. Therefore, some criteria must be defined in order to identify soundings that can be compared 515 in a meaningful way. The underlying assumption of the collocation is that on scales of a few hundred kilometers and several hours, the natural variance in XCO 2 is not detectable in satellite derived estimates from the ACOS L2FP algorithm.
For this study, the coincidence criteria to match OCO-2 soundings to individual GOSAT soundings were those: (i) falling within 2 • latitude and 3 • longitude, (ii) with a maximum spatial separation of 300 km, and (iii) acquired within ±2 hours. Due 520 to the dense nature of the OCO-2 soundings relative to the sparseness of the GOSAT soundings, there are typically between zero and several hundred matched OCO-2 soundings per GOSAT footprint. A lower limit of 10 and an upper limit of 100 (randomly selected) OCO-2 soundings that meet the coincidence criteria were set in order to retain the GOSAT sounding for analysis. The individual L2FP quality flags are applied for both GOSAT and OCO-2 during the collocation procedure, and then the mean value of XCO 2 from the 10 to 100 collocated OCO-2 soundings is calculated and subtracted from the corresponding 525 GOSAT XCO 2 to produce ∆XCO OCO-2 2 .
Here we compare ACOS GOSAT v9 against OCO-2 v10 (rather than to the deprecated v9), since we assume that science users will adopt the newest OCO-2 product. Major updates to the version 10 ACOS L2FP algorithm include (i) an upgrade of ABSCO spectroscopic parameters from v5.0 to v5.1 (Payne et al., 2020), (ii) an improved solar continuum 530 model, (iii) improved aerosol priors using GEOS5-FP-IT daily means with tighter constraints (Nelson and O'Dell, 2019), (iv) updated CO 2 priors similar to the forthcoming TCCON ggg2020 values, (v) a quadratic fit for land surface albedos, and (vi) a loosened constraint for the solar induced chlorophyll fluorescence prior. These differences were summarized , ::::: were :::::::: discussed in Section 3.1.
Currently, the underlying cause of these disagreements is unknown, and could stem from instrument calibration or sampling related issues, differences in retrieval algorithm versions, or even collocation issues.

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The disagreement in XCO 2 for Ocean-Glint between ACOS GOSAT v9 and OCO-2 v10 is highlighted in Panel A of Figure   here is that the overall variability is larger compared to the Ocean-Glint data, which we attribute to biases introduced by variations in both topography and surface albedo. A slightly positive (red) signal is observed during the September to December months in the SH, especially in 2014, 2018, and 2019. Although, additional investigation into such signals is warranted, it is beyond the scope of the current work.

Summary
The v9 ACOS GOSAT XCO 2 product, spanning February 2009 through June 2020, has been compared to XCO 2 estimates from TCCON, a suite of atmospheric inversion systems (models), and with collocated OCO-2 v10 data. The ACOS GOSAT v9 product is an improvement over ACOS GOSAT v7.3 relative to these standards. The v9 product provides a significant extension 585 of the data record and contains data in M-gain viewing mode over bright land surfaces.

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Global estimates of CO 2 derived from satellite measurements provide coverage in traditionally data sparse regions where ground-based measurements are difficult. The assimilation of satellite XCO 2 into atmospheric inversion systems to quantify the spatiotemporal variations of carbon fluxes is a promising, but challenging, area of research. This research continues to benefit from various improvements in transport models, atmospheric inversion systems, and satellite retrievals. The role of the GOSAT record in this field remains unique due to its exceptional 11 year length and its coverage of nearly 5.5 years of the 620 carbon cycle prior to the launch of OCO-2. The ACOS GOSAT v9 L2Std and L2Lite file products are both available on the NASA GES DISC (OCO-2 Science Team et al., 2019b, a).