The pre-processing step collects and prepares all data required for the processing. This step especially includes the measured GOSAT and GOSAT-2 spectra, as well as geolocation and matching meteorological and topographic information (from ECMWF ERA5 and GMTED2010). Furthermore, some initial filtering (especially for clouds) is performed. The cloud filtering method is based on the derivation of an effective albedo and a water vapour absorption filter from the spectral data as described in . This makes use of the facts that clouds are usually bright and are located above the surface such that the amount of water vapour above the cloud is low.

For the new FOCAL products, two filter limits of the pre-processing have been relaxed to increase the final data yield: we now use a maximum solar zenith angle (SZA) of 90∘ and also latitudes up to ±90∘. In v1.0, both limits were set to 70∘. Note that these limits are applied for pre-processing; further filtering is done later during post-processing, depending on the different products (see Sect. ). All other filtering (including the cloud filter) is unchanged compared to v1.0. The main difference in pre-processing to v1.0 is, therefore, that for v3.0 high latitudes are not necessarily filtered out before processing. This allows for more flexibility in the definition of product-specific post-processing filters by taking into account different sensitivities of each product. Furthermore, as mentioned above, we now use SLIMCO2 and SLIMCH4 data as a priori data for XCO2 and XCH4.

Both v1.0 and v3.0 processing versions use the FOCAL algorithm described in . FOCAL is a full-physics retrieval method, which approximates scattering in the atmosphere by a single layer. With this, the forward model to simulate radiation can be expressed as an analytical formula, which allows for a high computational speed. The v3.0 updates to FOCAL include the use of a modified version of FOCAL, which assumes isotropic instead of Lambertian scattering at the scattering layer, and we also fit H2O in the NIR band (see Table ).

The FOCAL retrieval is based on an optimal estimation algorithm , taking as main input measured calibrated spectra and their uncertainties. The quantities to be retrieved are collected in the state vector, and secondary inputs to the retrieval algorithm are corresponding a priori values and their uncertainties in the form of an a priori error covariance matrix. The main output of the FOCAL retrieval is the values and uncertainties of the elements of the state vector. The state vector elements of v3.0 (see Table ) are almost the same as in v1.0; however, we increased the degrees of the background polynomials to improve the fit residuals such that now all fitted polynomials are of degree 3 except for the small solar-induced fluorescence (SIF) windows where we use a degree of 1 and the XN2O window where a degree of 4 is used. The latter is done because the sensitivity of XN2O to surface effects turned out to be larger than for the other products. All quantities in the state vector are retrieved simultaneously. For CO2, CH4 and H2O, we derive profiles on five layers which are then converted to total column averages.

δD, XCO and XN2O are derived via scaling factors. The XCH4 proxy product is derived after the retrieval from these full-physics products (see below). In the case of GOSAT-2, all scattering parameters as well as methane, water vapour and δD are only fitted in windows 1 to 6 (i.e. those spectral ranges which are also available for GOSAT). This is done to provide consistent products for the two sensors.

As in v1.0, for GOSAT – but not GOSAT-2 – we compute a spectral correction factor to account for changes in the spectral calibration with time. In v3.0 the factor is obtained from the spectral difference of Fraunhofer lines in the solar irradiance and measured radiance in the SIF window, which is more stable than the least-squares fitting procedure used in v1.0. This new method only corrects for shifts on the scale of one spectral sampling interval (0.2 cm-1); this, however, is sufficient, as additional spectral shift and squeeze factors are determined in the later retrieval for both versions.

We also use a noise model to correct the uncertainties of the GOSAT and GOSAT-2 spectra estimated during pre-processing and consider possible forward model uncertainties in the retrieval. This noise model is the same as in v1.0, but we recomputed the parameters for all fitting windows based on an input data set consisting of 1 d per month in 2019 for both GOSAT and GOSAT-2. The resulting parameters are, however, similar for v1.0 and v3.0.

The main changes between v1.0 and v3.0 occur in the post-processing step. The overall concept of our new approach is that we tried to establish a generic, mostly automated, procedure that provides reproducible results and thus can be applied to all gases under consideration. However, it still allows for an optimisation for each product.

The following post-processing steps are in general applied to all products:

basic filtering,

The XCH4 proxy product is computed during post-processing from 1XCH4proxy=XCH4retrievedXCO2aprioriXCO2retrieved. This means we normalise the retrieved full-physics XCH4 by the retrieved full-physics XCO2 (both without bias correction) and use as reference the a priori XCO2. Note that this is different to, for example, the SRON XCH4 proxy product , which is derived from a dedicated non-scattering retrieval using a different wavelength region (6045–6138 cm-1). The uncertainty of the proxy product is then determined via error propagation. The XCH4 proxy product is then treated in post-processing as the other products.

The general advantage of proxy products see also is that they are less sensitive to light-path effects like scattering. They therefore usually have a larger coverage. However, they usually depend on a model reference, which is in our case SLIMCO2 (see Appendix ). The uncertainty of the XCH4 proxy product is also larger than for the full-physics product, because it includes the uncertainty of the derived XCO2.

For each of the different data products, an example map comprising a mean for April 2019, gridded to 5∘× 5∘, is shown in Figs.  to for GOSAT and GOSAT-2. In all maps, grid points that were only based on a single measurement have been omitted to avoid outliers. The spatial patterns of XCO2, methane, water vapour and δD look very similar for GOSAT and GOSAT-2. GOSAT-2 data show in general fewer gaps over the oceans but with smaller latitudinal coverage. The latter is due to the currently applied RSR filtering for GOSAT-2, which especially removes data over water surfaces. Note that over the year the spatial range of valid data varies according to solar illumination conditions.

The XCO2 data show higher values in the Northern Hemisphere than in the Southern Hemisphere as expected during springtime. This is because plants absorb more XCO2 during growing season (i.e. hemispheric summer and autumn).

For methane, the known source regions in the USA, Africa and Asia are clearly visible, as well as the inter-hemispheric gradient. The spatial coverage of the proxy product is much larger than for the full-physics product, especially at higher latitudes. This is due to the relaxed filtering for the proxy product.

Water vapour (XH2O) also shows the expected behaviour: large values in the tropics and lower values at higher latitudes. The observed spatial distribution of δD is in line with the maps shown in . All δD values are in the expected range (about 0 to -300 ‰); they also decrease from the tropics to higher northern and southern latitudes. This is because water vapour generated in the tropics by strong evaporation is transported to higher latitudes, during which the heavier HDO decreases more rapidly via precipitation than H2O.

For GOSAT-2, there are also data for carbon monoxide (XCO) and XN2O. In the XCO map the expected source regions in China, Indonesia and Africa (fossil fuel combustion, biomass burning) are apparent over the otherwise quite smooth and constant background. The transport of XCO from the equatorial African fire regions to the west over the Atlantic Ocean due to the trade winds is clearly visible, as is some transport from Asia to the Pacific.

The XN2O product shows an overall decrease of the background XN2O from the tropics to higher latitudes on the order of 15 ppb. Such gradients were also observed by the IASI (Infrared Atmospheric Sounding Interferometer) instrument on Metop ; however, we see larger differences. This could be related to the sampling of the XN2O data.

Furthermore, the IASI data shown in refer to the mid-troposphere over the ocean only, whereas the GOSAT-2 FOCAL data are total column averages over all surfaces. The latitudinal XN2O gradient can, in principle, be explained by the variation of the tropopause height. As most of the XN2O is contained (and well mixed) in the troposphere, the total column average is larger in the tropics (where the tropopause is high) than at higher latitudes. We also see increased XN2O over central Africa. This is also visible in IASI data and probably related to convection see.

Time series of all GOSAT FOCAL data products for different latitudinal regions are depicted in Fig. . These plots show the expected temporal behaviour: a seasonal cycle is visible in all data sets; amplitudes and/or phase differ for northern and southern latitudes with usually more variability in the north.

The GOSAT FOCAL XCO2 results are shown in Fig. a. The overall increase of XCO2 from around 380 ppm in 2009 to about 415 ppm in 2020 is clearly visible, as well as an overlaying seasonal variation, which is most pronounced in the Northern Hemisphere with a minimum in summer due to vegetational growth. In the Southern Hemisphere, the seasonality of XCO2 is shifted by 6 months but much lower since there are less land masses than in the north. The global variation is very similar to the tropical one.

The methane full-physics and proxy products show a similar temporal variation with increasing XCH4 due to larger anthropogenic contributions (about 10 ppb per year, which is in line with recent annual changes from NOAA ground-based measurements; see https://gml.noaa.gov/ccgg/trends_ch4/, last access: 11 January 2022). Small differences between the average XCH4 full-physics and the proxy products can be explained by the broader spatial coverage of the proxy product.

For water vapour (XH2O), the seasonal cycles in the Northern Hemisphere and Southern Hemisphere are shifted by about 6 months, in line with the seasonal shift of the intertropical convergence zone (ITCZ). On the global scale, these seasonal variations largely average out. Some change in the seasonal cycle of XH2O is seen after 2015. This is probably related to the increased number of GOSAT data (especially over ocean) after 2015 (see Fig. ), which changes the sampling. Taking this into account, no clear trend is visible in the GOSAT water vapour data from 2009 to 2020, although there is some indication for a slow increase with time. This is in line with results from other data sets see e.g.and references therein.

Average values of δD vary between about -180 ‰ and -120 ‰. As for water vapour, seasonal variations are small in the global average, but year-to-year variations in the seasonal cycle are larger for δD. Especially note that the peaks in July 2012 in the Southern Hemisphere and in December 2018 in the Northern Hemisphere are due to very few data in these regions in these months.

The GOSAT-2 time series (see Fig. ) show similar temporal variations to the GOSAT data, but of course, they only cover the years 2019 and 2020.

Across different latitudes, GOSAT-2 XCO shows similar values and seasonal variations, except in the Southern Hemisphere where XCO is on average about 30 ppb lower than in the Northern Hemisphere, probably because most sources are around the Equator or in the Northern Hemisphere extra-tropics.

The GOSAT-2 XN2O also shows some seasonal variations of up to about 8 ppb peak-to-peak. However, this seasonality is at least partly a sampling effect. The background XN2O, as shown in Fig. b, comprises larger values in the tropics than at higher latitudes. Because of the varying latitudinal coverage of GOSAT-2 ocean data throughout the year, the regions outside the tropics are not covered during all seasons, which introduces an apparent variation in the averages. This effect in principle applies to all data, but it is especially pronounced for XN2O, for which other spatial variations are low. In the tropics, the XN2O data are always high, and the variations are much smaller. In fact, we see a slight increase in XN2O of about 1 ppb per year, which is about what is expected from ground-based measurements (see growth rate plots on the NOAA Global Monitoring Laboratory website; https://gml.noaa.gov/hats/combined/N2O.html, last access: 30 June 2021). This result is also in line with IASI data .

To assess the quality of the data, for each GOSAT and GOSAT-2 FOCAL product we perform a comparison with TCCON data using the same procedure as in ; see also and for details.

For most gases, we also use the same collocation criteria: a maximum time difference of 2 h, a maximum spatial distance of 500 km and a maximum surface elevation difference of 250 m between satellite and ground-based measurement. However, for water vapour and carbon monoxide these limits are reduced to 1 h time difference and 150 km spatial distance to account for their higher variability. We only include stations with a minimum of 50 data points.

For XCO2 and XCH4, we also perform comparisons with other available GOSAT products from SRON, the University of Leicester, NASA (ACOS v9) and NIES.

From the comparisons, we derive the following main quantities related formulas are given in:

The first is mean station bias, defined as the mean of all biases at each station; this can be interpreted as a global offset to all stations.