Last modified on Sept 10, 2025 08:42

Contributors: M. Reuter (Institute of Environmental Physics (IUP)), B. Fuentes Andrade (Institute of Environmental Physics (IUP)), M. Buchwitz (Institute of Environmental Physics (IUP))

Issued by: Institute of Environmental Physics (IUP), University of Bremen / Maximilian Reuter

Date: 20/11/2024

Ref: C3S2_313a_DLR_WP1-DDP-GHG-v1_ATBD_XGHG_v4.6

Official reference number service contract: 2024/C3S2_313a_DLR/SC1

History of modifications

List of datasets covered by this document

Acronyms

General definitions

Essential climate variable (ECV): An ECV is a physical, chemical, or biological variable or a group of linked variables that critically contributes to the characterization of Earth's climate (Bojinski et al., 2014).

Climate data record (CDR): The US National Research Council (NRC) defines a CDR as a time series of measurements of sufficient length, consistency, and continuity to determine climate variability and change (National Research Council, 2004).

Fundamental climate data record (FCDR): A fundamental climate data record (FCDR) is a CDR of calibrated and quality-controlled data designed to allow the generation of homogeneous products that are accurate and stable enough for climate monitoring.

Thematic climate data record (TCDR): A thematic climate data record (TCDR) is a long time series of an essential climate variable (ECV) (Werscheck, 2015).

Intermediate climate data record (ICDR): An intermediate climate data record (ICDR) is a TCDR which undergoes regular and consistent updates (Werscheck, 2015), for example because it is being generated by a satellite sensor in operation.

Satellite data processing levels: The NASA Earth Observing System (EOS) distinguishes six processing levels of satellite data, ranging from Level 0 (L0) to Level 4 (L4) as follows (Parkinson et al., 2006).

Absolute systematic error or systematic error: Component of measurement error that in replicate measurements remains constant or varies in a predictable manner. Note that "systematic error" refers to the absolute systematic error (in contrast to "relative systematic error" defined below). For satellite GHG ECV products especially the relative systematic error is important.

Relative systematic error, relative accuracy or relative bias: Identical with "Systematic error" but after bias correction and without considering a possible global offset (overall mean bias). Reflects the importance of spatially and temporally correlated errors (spatio-temporal biases). Computed from standard deviations of spatial and temporal biases. 

Bias: Estimate of a systematic measurement error.

Precision: Measure of reproducibility or repeatability of the measurement without reference to an international standard so that precision is a measure of the random and not the systematic error. Suitable averaging of the random error can improve the precision of the measurement but does not establish the systematic error of the observation (CMUG-RBD, 2012).
Note: Precision is quantified with the standard deviation (1-sigma) of the error distribution.

Stability: Term often invoked with respect to long-term records when no absolute standard is available to quantitatively establish the systematic error - the bias defining the time-dependent (or instrument-dependent) difference between the observed quantity and the true value (CMUG-RBD, 2012).
Note: Stability requirements cover inter-annual error changes. If the change in the average bias from one year to another is larger than the defined values, the corresponding product does not meet the stability requirement.

Representativity: Extent to which an average of a set of measured values corresponds to the true average, e.g., over a grid cell. It is important when comparing with or assimilating in models. Measurements are typically averaged over different horizontal and vertical scales compared to model fields. If the measurements are smaller scale than the model it is important. The sampling strategy can also affect this term (CMUG-RBD, 2012).

Threshold requirement: The threshold is the limit at which the observation becomes ineffectual and is not of use for climate-related applications (CMUG-RBD, 2012).

Goal requirement: The goal is an ideal requirement above which further improvements are not necessary (CMUG-RBD, 2012).

Breakthrough requirement: The breakthrough is an intermediate level between the "threshold" and "goal" requirements, which - if achieved - would result in a significant improvement for the targeted application. The breakthrough level may be considered as an optimum, from a cost-benefit point of view when planning or designing observing systems (CMUG-RBD, 2012).

Horizontal resolution: Area over which one value of the variable is representative of (CMUG-RBD, 2012). 

Vertical resolution: Height over which one value of the variable is representative of. Only used for profile data (CMUG-RBD, 2012). 

Observing Cycle (or Revisit Time): Temporal frequency at which the measurements are required (CMUG-RBD, 2012).

XCO₂ (column-averaged dry-air mole fraction of atmospheric carbon dioxide): amount of CO₂, expressed in moles, in the vertical column divided by the amount of dry air, also expressed in moles, in that vertical column.

XCH₄ (column-averaged dry-air mole fraction of atmospheric methane): amount of CH₄, expressed in moles, in the vertical column divided by the amount of dry air, also expressed in moles, in that vertical column.

Column averaging kernel: The column averaging kernel vertical profile represents the sensitivity of the retrieved XCO₂ or XCH₄ to the true mole fraction depending on altitude. Values near one are ideal and indicate that the influence of the a priori is minimal.

A priori profile: The CO₂ or CH₄ a priori profile represents the knowledge of the vertical profile of the dry-air mole fraction of CO₂ or CH₄ before the measurement. See  Rodgers, 2000 for a more detailed explanation.

Observations for Model Intercomparison Project (Obs4MIPs, here also OBS4MIPS): is an effort to make observational data more accessible for climate model evaluation, development and research. An Obs4MIPs (or OBS4MIPS) dataset is a dataset technically aligned with climate model data, and following data specifications consistent with the CMIP (Coupled Model Intercomparison Project) standard output. See https://pcmdi.github.io/obs4MIPs/ for more detailed information.

Glint observation mode: Viewing geometry used by some satellite instruments where the detector points toward the direction of the specularly reflected sunlight, i.e. the viewing zenith angle and solar zenith angle are approximately equal. This mode is used for measuring CO₂ and CH₄ over water surfaces (such as the ocean), which have low reflectivity in the spectral region used for the retrieval of these gases. By observing in glint mode, the instrument measures a higher reflected radiance compared to other viewing geometries, enhancing the signal for the gas retrievals.

Inter-algorithm spread (IAS): Algorithm-to-algorithm standard deviation of the grid box averages (for a set of L3 algorithms). It informs about potential regional or temporal systematic uncertainties.

Mean Local Time (MLT): Expression of time given by the hour angle of the mean position of the Sun, plus an offset of 12 hours. 

Executive summary

This document is the Algorithm Theoretical Basis Document (ATBD) for L3 products XCO2_OBS4MIPS and XCH4_OBS4MIPS v4.6, generated in the framework of the Copernicus Climate Change Service (C3S, https://climate.copernicus.eu/). For C3S a large number of satellite-derived Essential Climate Variable (ECV) data products are generated and made available via the Copernicus Climate Data Store (CDS, https://cds.climate.copernicus.eu/).

This document describes how two satellite-derived atmospheric carbon dioxide (CO₂) and methane (CH₄) L3 products have been generated. CO₂ and CH₄ are important greenhouse gases (GHG). The two XCO2_OBS4MIPS and XCH4_OBS4MIPS products are column-averaged dry-air mole fractions of CO₂ and CH_4, denoted as XCO₂ (in parts per million, ppm) and XCH₄ (in parts per billion, ppb), respectively. These two "XGHG" products are generated by the Institute of Environmental Physics (IUP), University of Bremen on behalf of the C3S. In the following this project is referred to as C3S/GHG project. Within this project also mid-tropospheric CO₂ and CH₄ products are generated. These mid-tropospheric CO₂ and CH₄ products are not described in this document but in dedicated separate documents (ATBD MTGHG, 2024, PQAR MTGHG, 2024 and PUGS MTGHG, 2024).

The XCO2_OBS4MIPS and XCH4_OBS4MIPS products are merged multi-sensor XCO2 and XCH4 Level 3 (L3) products with monthly time and 5ºx5º spatial resolution, generated using an ensemble of individual satellite sensor Level 2 (L2) products. The two XGHG data products have been generated from the satellite instruments SCIAMACHY onboard ENVISAT, TANSO-FTS/GOSAT, TANSO-FTS-2/GOSAT-2 (XCO2 and XCH4 products). For product XCO2_OBS4MIPS also Level 2 products from NASA's OCO-2 mission have been used as input products.

These XCO2_OBS4MIPS and XCH4_OBS4MIPS products result from merging the individual L2 input products using the Ensemble Median Algorithm (EMMA). In broad terms, the merging algorithm grids all L2 products to a monthly 10º x 10º grid and selects, for each grid cell, the L2 product that corresponds to the median of the gridded input products. The output of EMMA is a merged L2 intermediate product that contains the soundings of the individual L2 input products that were selected from the merging algorithm, i.e. for each grid cell, one algorithm was selected, and the L2 soundings corresponding to this algorithm become part of the merged L2 product.

The merged L2 product is again gridded to create the L3 OBS4MIPS product. The quality of the L3 OBS4MIPS products is described in PQAR XGHG, 2024.

This document describes the input data and the algorithm used to generate the L3 products. The algorithm has been developed at the University of Bremen, Germany, and has also been used in the past to generated previous versions of these products (e.g. ATBD XGHG main, 2023, PQAR XGHG main, 2023, PUGS XGHG main, 2023).

1. Missions and Instruments

Satellite radiance observations in the Near Infrared / Short Wave Infrared (NIR/SWIR) spectral region in nadir (downward looking) and glint observation viewing modes are sensitive to atmospheric CO₂ and CH₄ concentration changes with good sensitivity down to the Earth’s surface (because solar radiation reflected at the Earth’s surface is observed). These measurements permit to obtain “total column information” but do not permit to obtain (detailed) information on the vertical profiles of CO₂ and CH₄. The CO₂ and CH₄ products derived from these satellites are column-averaged dry-air mole fractions of CO₂ and CH₄ denoted as XCO₂ (e.g., in ppm) and XCH₄ (e.g., in ppb).

In the following, the satellite instruments used to generate XCO₂ and/or XCH₄ data products are briefly described.

Currently data from four instruments – SCIAMACHY/ENVISAT, TANSO-FTS/GOSAT, TANSO-FTS-2/GOSAT-2 and OCO-2 - have been used to generate the XCO₂ and XCH₄ data products described in this document (see Table 1).

Table 1: Overview of the key characteristics of the four satellite sensors used to generate the XCO₂ and XCH₄ data products. All sensors perform nadir observations of reflected solar radiation in the NIR/SWIR spectral region at moderate to high spectral resolution.

1.1. SCIAMACHY onboard ENVISAT

SCIAMACHY (SCanning Imaging Absorption spectroMeter for Atmospheric ChartographY; Burrows et al., 1995; Bovensmann et al., 1999) was a spectrometer on ESA's ENVISAT satellite (2002-2012). It covered the spectral region from the ultra-violet to the SWIR spectral region (240 nm - 2380 nm) at moderate spectral resolution (0.2 nm - 1.5 nm) and observed the Earth's atmosphere in various viewing geometries (nadir, limb, and solar and lunar occultation). ENVISAT was on a sun-synchronous orbit whose descending node crossed the equator near 10:00 hours Mean Local Time (MLT).

For a good general overview on SCIAMACHY see https://www.iup.uni-bremen.de/sciamachy/ and https://earth.esa.int/eogateway/instruments/sciamachy . SCIAMACHY permitted the retrieval of XCO₂ (e.g., Reuter et al., 2011; Schneising et al., 2011) and XCH₄ (e.g., Schneising et al., 2011; Frankenberg et al., 2011) from appropriate spectral regions in the SWIR (around 1.6 µm) and the NIR (O₂ A-band at 760 nm used to obtain the dry-air column using the known dry-air mole fraction of atmospheric oxygen) (see Table 2). The ground pixel size was typically 30 km along track and 60 km across track and the swath width was about 960 km. There were no across-track gaps between the ground pixels but there were gaps along-track as SCIAMACHY operated only part of the time (approx. 50%) in nadir observation mode.

Table 2: SCIAMACHY spectral bands used for the retrieval of XCO₂ and XCH₄.

1.2. TANSO-FTS onboard GOSAT and TANSO-FTS-2 on GOSAT-2

TANSO-FTS is a Fourier-Transform-Spectrometer (FTS) onboard the Japanese GOSAT satellite (Kuze et al., 2009, 2016). The Greenhouse Gases Observing Satellite "IBUKI" (GOSAT) is the world's first spacecraft in orbit dedicated to measure the concentrations of carbon dioxide and methane from space. The spacecraft was launched successfully on January 23, 2009, and has been operating properly since then. GOSAT covers the relevant CO₂, CH₄ and O₂ absorption bands in the NIR and SWIR spectral region as needed for accurate XCO₂ and XCH₄ retrieval (in addition GOSAT also covers a large part of the Thermal InfraRed (TIR) spectral region). The spectral resolution of TANSO-FTS is much higher compared to SCIAMACHY, as can be seen in Table 2 and Table 3, and the ground pixels are smaller (10 km compared to several 10 km for SCIAMACHY). However, in contrast to SCIAMACHY, the GOSAT scan pattern consists of non-consecutive individual ground pixels, i.e., the scan pattern is not gap-free. For a good general overview about GOSAT see also http://www.gosat.nies.go.jp/en/.

GOSAT-2 (Suto et al., 2021) is the follow-on satellite to GOSAT and is very similar to GOSAT. GOSAT-2 was successfully launched October 29, 2018. GOSAT-2 XCO₂ and XCH₄ retrievals are now also included in the C3S GHG CDR. Both GOSAT and GOSAT-2 are on a sun-synchronous orbit whose descending node crosses the equator at 13:00 MLT. 

Concerning XCO₂ and XCH₄ retrieval from GOSAT and GOSAT-2, see also Noël et al., 2022.

Table 3: TANSO-FTS and TANSO-FTS-2 spectral bands used for the retrieval of XCO₂ and XCH₄.

1.3. OCO-2

NASA's Orbiting Carbon Observatory 2 (OCO-2) mission (Crisp et al., 2004; Boesch et al., 2011) has been successfully launched in July 2014. The OCO-2 Project primary science objective is to collect the first space-based measurements of atmospheric carbon dioxide with the precision, resolution and coverage needed to characterize its sources and sinks and quantify their variability over the seasonal cycle. OCO-2 flies in a sun-synchronous, near-polar orbit with a group of Earth-orbiting satellites with synergistic science objectives whose ascending node crosses the equator near 13:30 hours MLT. Near-global coverage of the sunlit portion of Earth is provided by this orbit over a 16-day (233-revolutions) repeat cycle. OCO-2's single instrument incorporates three high-resolution grating spectrometers, designed to measure the near-infrared absorption of surface-reflected sunlight by carbon dioxide and molecular oxygen. OCO-2 covers 3 spectral bands (see Table 4) like SCIAMACHY and GOSAT, but OCO-2 has much smaller ground pixels (km scale) and a much smaller swath width (approx. 10 km) compared to SCIAMACHY. OCO-2 delivers XCO₂ but not XCH₄. Details on OCO-2 are also given on https://ocov2.jpl.nasa.gov/.

Table 4: OCO-2 spectral bands.

2. Input and auxiliary data

2.1. Satellite L2 data

Several different XCO₂ and/or XCH₄ retrieval algorithms exist for SCIAMACHY, GOSAT, GOSAT-2, and OCO-2 which are partially under active further development in order to meet the demanding user requirements for using these data products to obtain source / sinks information, i.e., for making them useful for surface flux inversions. Specifically, we make use of the algorithms and corresponding data products listed in Table 5 and Table 6. These products are used by the Ensemble Median Algorithm (EMMA, explained in Section 3) into a single L2 product, which is then used to generate the gridded L3 product.

Table 5: Satellite-derived L2 input data products used to generate the L3 v4.6 XCO₂ product. The table lists the satellite instrument, the name and version of the L2 algorithm, the institution and related references.

Table 6: Satellite-derived L2 input data products used to generate the L3 v4.6 XCH₄ product. The table lists the satellite instrument, the name and version of the L2 algorithm, the institution and related references.

The basic retrieval principle to obtain the data products listed in  Table 5 and Table 6 is the same:

1.  A satellite instrument measures backscattered solar radiation in near-infrared O₂ and CO₂ or CH₄ absorption bands.
2. A radiative transfer plus instrument model (forward model) is utilized to simulate the satellite measurement for a set of known parameters (parameter vector) and unknown parameters (state vector).
3. An inversion method tries to find the state vector which results in the best agreement between simulated and measured radiances.
4. The retrieved state vector is assumed to represent the true (or most likely) atmospheric state. 

However, when going into more detail, the algorithms have distinct conceptual differences: the algorithms are optimized for different instruments (SCIAMACHY, GOSAT, GOSAT-2, or OCO-2). They are based on different absorption bands, use different inversion methods (optimal estimation, Tikhonov-Phillips, least squares), and are based on different physical assumptions on the radiative transfer in scattering atmospheres. For example, so-called full physics algorithms explicitly account for (multiple) scattering at molecules, aerosols, and/or clouds by having state vector elements such as cloud water path, cloud top height, and aerosol optical thickness. The XCO₂ ACOS and FOCAL algorithms, listed in Table 5, or the XCH₄ RemoTeC-FP and FOCAL-FP algorithms, listed in Table 6, are instances of full-physics retrieval algorithms (references are provided in the corresponding table). Another example is the light path proxy method, which assumes that photon path lengths are modified similarly in the CO₂ and O₂ or CH₄ absorption bands, and that scattering related effects cancel out when dividing the retrieved CO₂ (or CH₄) and O₂ columns to compute XCO₂ (or XCH₄). The XCH₄ UoL-PR, RemoTeC-PR and FOCAL-PR algorithms, listed in Table 6 along with their corresponding references, are instances of proxy-method retrieval algorithms. Additionally, the algorithms use different pre- and post-processing filters (e.g., cloud detection from O₂-A band or from a cloud and aerosol imager).

2.2. Other data

We use the Simple cLImatological Model for atmosphericCO₂ and CH₄ (SLIM) (Noël et al., 2022) as common a priori when harmonizing the different L2 input data sets (Section 3.3).

SLIM CO₂ and CH₄ use model-based climatologies to estimate the spatial distribution and annual cycle of CO₂ and CH₄, respectively. SLIM2024 CO₂ uses CO₂ mole fraction information from CAMS global CO₂ atmospheric inversion v22r1 (Chevallier et al., 2005, 2010; Chevallier, 2013) . SLIM2024 CH₄ has been derived from CAMS global CH₄ atmospheric inversion v22r2 (Segers et al., 2022).

Both SLIM2024 CO₂ and SLIM2024 CH₄ use 20 height layers, defined in such a way that each layer contains the same number of dry-air molecules.

Additionally, SLIM adjusts the used climatologies for the annual growth.

SLIM CO₂ and CH₄ reproduce large-scale features such as inter-hemispheric gradients and seasonal cycles well compared to their underlying models and TCCON (Total Carbon Column Observing Network) (Noel et al., 2022). However, SLIM CO₂ and CH₄ are only empirically extrapolating from past/averaged modelled CO₂ and CH₄ fields. New or changing phenomena cannot be within SLIM CO₂ and CH₄.

Scaling of the reported L2 uncertainties and validation is done with TCCON GGG2020 (Wunch et al., 2010, 2011, 2015, Laughner et al., 2024) as reference data set. TCCON provides XCO₂ and XCH₄ ground-based retrievals which can directly be compared with the corresponding satellite-based retrievals.

3. Algorithms

3.1. Overview

Our current knowledge about the sources and sinks of atmospheric CO₂ and CH₄ is limited by the sparseness of highly accurate and precise measurements of these important greenhouse gases (e.g., Stephens et al., 2007). Due to their potentially near-global coverage and sensitivity down to the surface, satellite based XCO₂ and XCH₄ (column-average dry-air mole fraction of atmospheric CO₂ and CH₄) retrievals in the near infrared are promising candidates to reduce existing source/sink uncertainties if accurate and precise enough (e.g., Rayner and O'Brien, 2001; Houweling et al., 2004; Miller et al., 2007; Chevallier et al., 2007).

At present, several independently developed XCO₂ and/or XCH₄ retrieval algorithms exist for SCIAMACHY (SCanning Imaging Absorption spectroMeter of Atmospheric CHartographY; Burrows et al., 1995; Bovensmann et al., 1999), GOSAT (Greenhouse gases Observing SATtellite; Yokota et al., 2004), GOSAT-2 (Greenhouse gases Observing SATtellite 2; Suto et al., 2021) and OCO-2 (Orbiting Carbon Observatory-2; Crisp et al., 2017); see Table 5 and Table 6 for those used for EMMA v4.6 CO₂ and EMMA v4.6 CH₄, respectively. A history of changes with respect to previously generated datasets can be found in PUGS XGHG, 2024.

All retrieval teams find encouraging validation results when comparing with TCCON (Wunch et al., 2010, 2011, 2015, Laughner et al., 2024) ground-based FTS (Fourier transform spectrometer) measurements (see references in Table 5 and Table 6). This goes along with a good inter-algorithm agreement at TCCON sites.

However, the inter-algorithm agreement often declines when remote from validation sites because of differences in the large-scale bias patterns of the individual L2 data sets in such regions. Such biases can be a critical issue for surface flux inversions and the user requirements are demanding; as an example, Miller et al. (2007) and Chevallier et al. (2007) found that regional biases of a few tenths of a ppm can already hamper surface flux inversions. This indicates that assessing an algorithm's quality should not be based on comparisons against TCCON stations only. Many regions of the world present more "complicated" retrieval conditions compared to locations around TCCON stations. In general terms, examples of regions with complicated retrieval conditions are deserts, or regions with high aerosol load or frequent occurrence of subvisible cirrus clouds. High solar zenith angles or viewing zenith angles also make retrievals more complicated in general. However, the specific retrieval difficulties depend on the independent retrieval algorithms. The TCCON network does not cover some of this generally complicated retrieval conditions, leading to a lack of ground truth measurements which could be used to judge the algorithms' performance in these regions.

Diverging model results are common to many scientific disciplines (e.g., Araujo and New, 2007; Rötter et al., 2011) and much attention and effort are devoted to this topic on the subject of weather and climate modelling. Here, the divergence of the model results arises not only from structural differences of the different models, but also from the nonlinearity of the model equations, which can lead to differing results even for one single model when performing multiple realizations with slightly differing initial conditions (Hagedorn et al., 2005; Tebaldi and Knutti, 2007).

Especially in the case of weather forecasting or climate projections, where no ground truth is available for the verification of the forecasts and projections, it is impossible to identify the "best" model and the "perfect" initial conditions. For long-term climate projections, this problem is impaired by the unknown future greenhouse forcing.

This conceptual problem is dealt with by using multi-model, multi-realization, multi-emission-scenario ensembles of simulations, which ideally span the entire range of possible model outcomes and, thus, can be used to estimate the uncertainties of the forecast or projection. 

However, interpreting the ensemble's spread as uncertainty is not the only possible application: some studies indicate that the ensemble mean, weighted mean, or median can outperform each individual model under appropriate conditions (e.g., Kharin and Zwiers, 2002; Vautard et al., 2009).

Here, we take this idea for the Ensemble Median Algorithm (EMMA, Reuter et al., 2013, 2020) which uses data from the retrieval algorithms listed in Table 5 and Table 6, together with TCCON and SLIM data. EMMA generates a database of individual Level 2 (L2) retrievals and takes advantage of the variety of different retrieval algorithms and their independent developments.

The Level 3 (L3) OBS4MIPS format XGHG products are derived from the L2 EMMA products via "gridding". 

The L3 products have a spatial resolution of 5^ox5^o and monthly time resolution. A corresponding algorithm flowchart is shown in Figure 1. As can be seen, the main algorithm steps are the following (see also Reuter et al., 2013, 2020):

• Input data collection: The EMMA algorithm requires collection of all required input data (mainly satellite L2 products but also TCCON XGHG products)
• Harmonization including a priori adjustments (using SLIM model data as common a priori)
• Uncertainty calibration
• Initial gridding
• Offset correction
• Median selection
• Ensemble spread computation
• Generation of results as daily EMMA L2 output files
• Gridding of the EMMA L2 data to generate the final L3 OBS4MIPS format output files

All these processing steps are described in detail in the following.

Figure 1: Flowchart showing the main steps of the EMMA algorithm used to generate the merged L2 EMMA product from the individual satellite-sensor L2 data products. The resulting EMMA L2 product is then gridded to generate the L3 OBS4MIPS format data product.

3.2. Input data collection

The inputs for the EMMA algorithm are described in Section 2.

The main input data are the individual L2 data products listed in Table 5 and Table 6. Additionally, TCCON data version GGG2020 (Wunch et al., 2010, 2011, 2015, Laughner et al., 2024) are used for the uncertainty calibration. SLIM model data (Noël et al., 2022) are used as a common a priori to harmonize the L2 input data.

3.3. Harmonization including a priori adjustments

In order to account for different column averaging kernels, all L2 input data sets are adjusted to a common a priori, namely the Simple cLImatological Model for atmospheric SLIM CO₂ and CH₄ (Noël et al., 2022). We do this as proposed by Wunch et al., 2011, and as described in the textbook of Rodgers, 2000. It should also be mentioned that the adjustment is mostly minor, especially for CO₂ , with adjustments typically on the order of a few tenths of a ppm.

Additionally, we interpolate the column averaging kernels and a priori profiles of the L2 input data sets so that the atmospheric column is split into ten layers defined by an equidistant pressure grid starting at the surface pressure and ending at zero.

3.4. Uncertainty calibration

The uncertainty calibration consists of a potential scaling of the reported uncertainty for the individual L2 soundings. This scaling factor is such that the average reported uncertainty is consistent with the standard deviation of satellite minus TCCON ground-based validation data differences.

3.5. Initial gridding

Due to entirely different samplings (different satellites, different filtering strategies, etc.) of the L2 input data, the EMMA data product inter-comparison is based on aggregated data (L3), namely monthly averages on a 10°×10° grid.

In order to get statistically robust results, we only use, for each algorithm, those grid boxes with more than five soundings and for which the standard error of the mean (SEOM) is estimated to be less than 1 ppm and 12 ppb for XCO₂ and XCH₄, respectively. The SEOM is defined 

with \( \sigma_i \) the (scaled; see Section 3.4) XCO₂ or XCH₄ uncertainty of the i-th out of  \( n \) soundings. This takes the individual retrieval precisions into account so that the minimum number of soundings needed to build the average of a grid box can vary from retrieval to retrieval and grid box to grid box.

Figure 2 and Figure 3 show examples of the calculated monthly XCO₂ or XCH₄ averages, respectively.

First of all, one can see many large-scale similarities such as the north/south gradient. However, with visual inspections, one can find some potential outliers for several algorithms. The relatively high XCO2 values in Malaysia in the GOSAT UoL-FP v7.3 product (Figure 2) may serve as example.  Often the observed systematic deviations (of L3 data) are larger than expected from instrumental noise, i.e., they are dominated by specific algorithm effects. Because L3 data are always calculated, for each grid cell, from multiple individual L2 soundings (ideally) sampled all over the given grid box, we here assume sampling and representation errors to be lower than the observed deviations. Therefore, sampling and representation errors are not discussed further in this context.

Figure 2: Monthly gridded XCO₂ averages and inter-algorithm spread (defined in Section 3.8) for the example of August 2018 for EMMA CO₂.  Gray areas indicate that there is no gridded L3 data in the corresponding grid cell. The magenta triangles in the Inter-Algorithm (IAS) spread map (bottom right) indicate the locations of TCCON stations. Additionally, the IAS values of the grid cells containing TCCON stations are shown above the colorbar.

Figure 3: Monthly gridded XCH₄ averages and inter-algorithm spread (defined in Section 3.8) for the example of September 2019 for EMMA CH₄. Gray areas indicate that there is no gridded L3 data in the corresponding grid cell. The magenta triangles in the Inter-Algorithm (IAS) spread map (bottom right) indicate the locations of TCCON stations. Additionally, the IAS values of the grid cells containing TCCON stations are shown above the colorbar.

3.6. Offset correction

We correct for potential offsets between the individual data products by adding a constant global offset for each L2 product. The global offset applied to each product is computed using SLIM as a reference. SLIM reproduces basic features well as it is constructed from state of the art models and the NOAA annual growth rates. However, other models would also work as reference.

Figure 4 and Figure 5 show the influence of the global offset correction.

Only grid boxes with the maximum number of overlapping algorithms (see Figure 6 and Figure 7) are considered for the global bias adjustment.

 
Figure 4: Global monthly average bias for XCO₂ in common grid boxes relative to SLIM CO₂ before and after global bias correction.

Figure 5: Global monthly average bias for XCH₄ in common grid boxes relative to SLIM CH₄ before and after global bias correction.

3.7. Median selection

XCO₂ or XCH₄ averages (one for each algorithm) are calculated within each grid box. However, we are aiming to use the ensemble not only to assess regional and temporal uncertainties, but also to create a data set which is potentially less influenced by regional or temporal biases. This could be achieved, for example, by building the average, a weighted average, or the median in each grid box. 

Outliers are data points that differ significantly from the other observations, i.e., making them unlikely to belong to the same statistical distribution. In this context, the median has advantages: outliers are assumed to be rare, and grid boxes most likely contain none or only one outlying algorithm. Unlike the mean, the median is not directly influenced by extreme values at the high or low end of the distribution, making it less sensitive to occasional outliers. Additionally, the median does not calculate a new quantity; instead, it selects a specific ensemble member. Therefore, it allows us to trace L3 averages back to individual L2 sounding.

There are five scenarios for median calculation within a grid box:

1. All algorithms perform well and scatter slightly around the true XCO₂ or XCH₄ value. In this case the median will help to reduce scatter.
2. A minority of algorithms produce outliers, affecting the median only marginally.
3. Most algorithms produce outliers in different directions. In this case it is still likely that the median falls on a well performing algorithm in the "middle".
4. The majority of algorithms produce outliers in the same direction. This is the only case where the median is a bad choice, because it could select an outlier and ignore a well performing algorithm. However, we consider this unlikely to happen often, since we assume that the algorithms within one grid box are often realistic with uncorrelated occasional outliers.
5. If all algorithms are outlying, the median could be better or worse than selecting any other ensemble member.

For a grid cell to be assigned a valid value, the following criterion has to be fulfilled: a minimum number of data products having a standard error of the mean (SEOM) of less than 1 ppm for XCO₂ and 12 ppb for XCH₄, have to be available (see grey area in Figure 6 and Figure 7 ). For an even number of values, we define the median as the value closest to the mean.

Some algorithms, like the NASA or FOCAL OCO-2 algorithms, may provide significantly more L2 data than others. To avoid over-weighting these algorithms, we limit the maximum number of data points per grid box. To do so, we calculate the standard error of the mean of each successfully determined average. The idea behind this is that the lower the standard error of the mean, the larger the potential constraint on an inverse model becomes. The standard error of the mean of the selected algorithm in a grid box is compared to the standard error of all other algorithms available in this grid box. If it falls below the threshold value \( \frac{1}{\sqrt{2}} \)  times the 25% percentile of the standard error of the other algorithms, soundings of the selected algorithm are randomly rejected until its standard error exceeds the threshold. In this way, the number of data points can still be rather different but the potential constraint on an inverse model becomes similar. 
EMMA selects for each month and each 10º × 10º grid cell exactly one product (i.e. the product corresponding to the median) of the available individual L2 input products and then transfers all relevant information for inverse modelling (i.e., XCO₂ or XCH₄ and their uncertainty, related averaging kernels, a priori profiles, geo-location, time, etc.) from the selected harmonized and uncertainty calibrated L2 data into the corresponding daily EMMA L2 file. This ensures that most of the original information from the selected individual product is also contained in the merged product.

Figure 6: EMMA input data availability (colored bars) and minimum number of used algorithms (gray) for median calculation for CO₂.

Figure 7: EMMA input data availability (colored bars) and minimum number of used algorithms (gray) for median calculation for CH₄.

3.8. Ensemble spread computation

In addition to the L2 information of the selected data products, EMMA stores a set of diagnostic information for each selected sounding:

• the identifier for the selected L2 algorithm,
• the Inter-algorithm spread (IAS), defined as the algorithm-to-algorithm standard deviation of the grid box averages, which  informs about potential regional or temporal systematic uncertainties,
• the portion of the inter-algorithm spread (IAS) expected from measurement noise, defined as

where SEOM_i refers to the SEOM, computed according to Equation 1, of the i-th algorithm in a given grid cell, and N is the number of algorithms in the grid box,

• potential spatio/temporal biases estimated from TCCON co-locations (as defined in PQAR XGHG, 2024), and
• the number of L2 algorithms contributing to the median calculation.

Due to independent algorithm developments, different physical approaches and assumptions, different pre- and post-processing filters, and due to the different instruments, we expect relatively independent bias patterns. This is supported by Figure 2 and Figure 3, which show (uncorrelated) outliers in various regions, i.e., it seems unlikely that all algorithms produce the same bias within one grid box. This implies that similar averages within one grid box can give us more confidence in the individual retrievals within this grid box. 

On the other hand, large inter-algorithm spreads indicate regions with more difficult and uncertain retrieval conditions. Therefore, we interpret the ensemble spread, i.e., the standard deviation, as uncertainty due to regional retrieval biases. An example is given in Figure 8 and Figure 9 showing larger inter-algorithm spreads for XCO₂ and XCH₄ in the tropics and in Asia (mostly remote from TCCON sites). This pattern is temporally more or less stable, i.e., similar also for sub-periods.

 Figure 8: Average inter-algorithm spread (01/2003 – 12/2023) (top) and expected average inter-algorithm spread due to measurement noise (bottom) for EMMA CO₂.

Figure 9: Average inter-algorithm spread (01/2003 – 12/2023) (top) and expected average inter-algorithm spread due to measurement noise (bottom) for EMMA CH₄.

3.9. Generation of daily EMMA L2 files

The EMMA L2 data products consist of individual soundings retrieved by algorithms which can change from grid box to grid box and month to month.

Figure 10 shows the relative data weight (RDW) and the number of soundings per month for XCO₂ and XCH₄, respectively. How the RDW is defined is explained in detail by Reuter et al., 2013. In short, the RDW is defined as the relative number of soundings weighted with the corresponding (square of the inverse) uncertainty. More specifically, the RDW is computed from the integrated data weight for each month m and L2 product p, IDW_m,p, as

where σ_i is the (scaled) individual sounding error of each sounding i in month m and for product p. The RDW is the IDW_m,p normalized by the maximum value of the IDW for all months and L2 products. The RDW is an unitless quantity.

RDW is high if a (relatively) large number of soundings contribute to the EMMA product and if these soundings have (relatively) low uncertainty compared to the other contributing products. The RDW of a product is a measure of how much information on XCO₂ or XCH₄ this product contributes to the EMMA product relative to the other contributing products. As can be seen from Figure 10 and Figure 11, the SCIAMACHY BESD and SCIAMACHY WFMD products are the only products for XCO₂ and XCH₄, respectively, until early 2009, when the GOSAT time series starts. As can also be seen in Figure 10, OCO-2 dominates in terms of RDW and number of soundings from 2015 onwards for XCO₂. This is because OCO-2 provides much more data with typically better uncertainty compared to the other (GOSAT) product.

For April 2019, Figure 12 shows the EMMA XCO₂ (top) and XCH₄ (bottom) values as well as the corresponding selected median algorithm (product).

Figure 10: EMMA normalized relative data weight proportional to ∑1/σ_i² and number of soundings per contributing L2 data product (algorithm) and month for XCO₂.

Figure 11: EMMA normalized relative data weight proportional to ∑1/σ_i² and number of soundings per contributing L2 data product (algorithm) and month for XCH₄.

Figure 12: EMMA L2 XCO₂ (top) and XCH₄ (bottom) and corresponding selected algorithm (right) for April 2019.

3.10. Gridding of the EMMA L2 data to generate the final L3 OBS4MIPS format output files

The L3 data products XCO2_OBS4MIPS and XCH4_OBS4MIPS are generated by spatial (5°x5°) and temporal (monthly) gridding of the corresponding EMMA L2 databases. The gridding is based on arithmetic unweighted averaging of all soundings falling in a grid box. For each grid box, we compute the standard error of the mean by

where  \( n \) is the number of soundings within the grid box and  \( \sigma_i \)  the (corrected) reported stochastic uncertainties of the soundings. In order to reduce noise within the level 3 product, we filter out grid boxes with  \( n ≤ 1 \)  and  \( \sigma > 1.6 \) ppm for XCO₂ or  \( \sigma > 12 \) ppb for XCH₄, respectively.

Beside XCO₂ or XCH₄, the final level 3 product also includes the number of soundings used for averaging, the average column averaging kernel, the average a priori profile, the standard deviation of the averaged XCO₂ or XCH₄ values, and an estimate for the total uncertainty

Here, \( \sigma_s \) represents the inter-algorithm spread computed by EMMA averaged over the soundings within a grid box. For cases including only one algorithm,  \( \sigma_s \)  is replaced by quadratically adding the estimate of the spatial and seasonal accuracy determined from the TCCON validation (see PQAR XGHG, 2024). This is only the case during the SCIAMACHY-only period at the beginning of the time series (see Figure 4 and Figure 5).

4. Output data

The output data products are column-averaged dry-air mole fractions of CO₂ and CH₄, denoted XCO₂ (in parts per million, ppm) and XCH4 (in parts per billion, ppb) plus related quantities such as uncertainty,  averaging kernels and a priori profiles, among others.

Table 7 provides an overview of the L3 XCO₂ and XCH₄ data products. The product format is described in the Product User Guide and Specification (PUGS) document (PUGS XGHG, 2024).

Table 7:  Overview XCO₂ and XCH₄ OBS4MIPS data products. The sensors used for the input L2 products are listed in the second column. The third column shows the product version numbers, dates and periods covered by the products, and the dates in which each of the products has become available in the Copernicus Climate Data Store.

These L3 products have been generated by gridding the corresponding L2 EMMA product.

The L2 EMMA products are intermediate products that contain, for each single satellite footprint (ground pixel), the main parameter (e.g., XCO₂ or XCH₄), its uncertainty, its averaging kernel and its a priori profile in addition to other information (most notably geolocation and time information: latitude, longitude, time).

The XCO2_OBS4MIPS and XCH4_OBS4MIPS products consist of monthly, 5°x5° gridded L3 XCO₂ or XCH₄ data computed from the corresponding EMMA databases. Additionally, the output files include gridded information about the number of averaged soundings, column averaging kernels, a priori profiles, standard deviation of XCO₂ or XCH₄, and an estimate of the total uncertainty accounting for measurement noise plus potential spatial and/or temporal biases. For details on the product format see PUGS XGHG, 2024. 

For the example of August 2015, Figure 13 shows XCO₂ (top) and XCH₄ (bottom) as well as the corresponding total uncertainty, which is also provided in the data product files.  

Figure 13: Top: XCO2_OBS4MIPS for August 2015 (left) and its uncertainty (right) computed from the retrieval noise and EMMA’s inter-algorithm spread. Gray areas indicate the absence of data (light gray = ocean, dark gray = land). Bottom: Same for XCH4_OBS4MIPS.

Acknowledments

We acknowledge previous funding by the European Space Agency (ESA) via Climate Change Initiative (CCI) project GHG-CCI. This funding significantly enhanced the quality of the retrieval algorithms and related documentation. This resulted in more mature data products as needed for an operational project such as the Copernicus Climate Change Service (C3S). We also acknowledge the availability of GOSAT and GOSAT-2 data products via the ESA GOSAT Third Party Mission (TPM) archive.

We are also very grateful to the GOSAT/GOSAT-2 teams in Japan comprising the Japan Aerospace Exploration Agency (JAXA), the National Institute for Environmental Studies (NIES), and the Ministry of the Environment (MOE) for providing access to the GOSAT and GOSAT-2 Level 1 and Level 2 data products. 

We also acknowledge the availability of OCO-2 Level 1 and Level 2 (XCO2) data products from NASA, which have been used for the generation of the XCO2_OBS4MIPS product. This product also includes OCO-2 XCO2 retrieved at Univ. Bremen with the FOCAL algorithm. The FOCAL activities would not have been possible without funding from University of Bremen, from the EU H2020 projects CHE (grant agreement ID: 776186) and VERIFY (Grant agreement ID: 776810), from ESA via project GHG-CCI+ and from EUMETSAT project FOCAL-CO2M.

The TCCON data were obtained from the TCCON Data Archive hosted by CaltechDATA at https://tccondata.org

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