2.1 TROPOMI and Sentinel-5

S5P TROPOMI (Veefkind et al., 2012) was successfully launched into low Earth orbit (LEO) on the 13 October 2017, with the aim to provide global information on air quality, climate and the ozone layer. The key products that are to be published from TROPOMI include, O₃, SO₂, NO₂, CO, CH₄, CH₂O and aerosol properties. These trace gas products are measured through solar backscatter in four separate spectral ranges, ultra-violet (UV), visible (VIS), near-infrared (NIR) and SWIR, which are described in more detail in Table 1 below. The TROPOMI instrument is built upon the heritage of previous missions aimed at studying the products mentioned earlier, namely the Global Ozone Monitoring Experiment (GOME; (Burrows et al., 1997), SCIAMACHY (Bovensmann et al., 1999), the Ozone Monitoring Instrument (OMI; Levelt et al., 2006) and GOME-2 (Callies et al., 2000). TROPOMI provides a significant advance in instrument technology over SCIAMACHY, with finer spatial resolution (7.5×7.5 km vs. 30×240 km) and measurement uncertainty. The first results from TROPOMI are starting to be published (Borsdorff et al., 2018; Hu et al., 2018) and are already providing significant new results to the community.

Sentinel-5 (Pérez Albiñana et al., 2017), due for launch in 2022 on the MetOp second-generation (SG)-A satellite, will complement the results of TROPOMI, providing global information on GHGs and pollutants at high spatial resolution. MetOp-SG-A is the first of a pair of satellites that are designed to complement each other but carry different instruments unlike the current MetOp satellites. The MetOp-SG series of satellites will eventually be comprised of six separate satellites, each with an 8.5-year lifetime. Sentinel-5/UVNS is very similar to TROPOMI, with both missions having similar instrument types and orbit altitudes but differing descending nodes (S5P – 13:30 LT and S5 – 09:30 LT) such that the instruments will capture measurements under differing solar zenith angles. The key differences are the minor variations in the spectral bands and the inclusion of the SWIR1 band, which allows for the retrieval of CO₂ and multiple band retrievals of CH₄; in the UV–VIS range, CHOCHO will be an additional product of Sentinel-5/UVNS not present in the TROPOMI retrieval products. The spectral bands and spectral resolutions of S5P/TROPOMI and S5/UVNS are described in Tables 1 and 2 below.

Table 1Characteristics of S5P/TROPOMI spectral bands. “UVIS” indicates the combination of longwave ultraviolet and visible bands.

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Table 2Characteristics of S5/UVNS spectral bands.

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2.2 RemoTeC

In this work, we apply the well-established RemoTeC retrieval software designed for TROPOMI (Butz et al., 2010; Hu et al., 2016, 2018); RemoTeC is a solar backscatter model based around the radiative transfer model developed by Hasekamp and Landgraf (2002). RemoTeC uses a 36-layer plane-parallel atmosphere and including multiple atmospheric scattering effects and surface reflection physics. RemoTeC is fully described in Butz et al. (2012); Hu et al. (2016), and we refer to these papers for full details about the software. However, we briefly summarise the algorithm here.

RemoTeC infers an atmospheric state vector from spectral measurements in the NIR band (757–774 nm) and the SWIR bands (1590–1675, 2305–2385 nm) via the inversion method known as the Philips–Tikhonov regularisation scheme (Tikhonov, 1963; Phillips, 1962). This scheme is required because the spectral measurements typically do not contain enough information to retrieve all state vector elements independently. Using a non-linear iterative scheme, the state vector is estimated by minimising the following cost function:

where S_y is the measurement error covariance matrix, and x and x_a are the state and priori state vectors. F(x) is the forward model, representing the physical model of the atmosphere. y is the vector containing the measurement. W is a diagonal weighting matrix rendering the side constraint dimensionless and ensuring that only relevant parameters contribute to the norm. γ is the regularisation parameter that is determined through the L-curve method (Hansen, 2000). The regularisation parameter can be modified manually if deemed appropriate.

The state vector x is composed of the following elements:

• CH₄ in 12 vertical layers, a priori values from CTM TM5;

• CO total column, a priori values from CTM TM5;

• H₂O total column, a priori calculated from ECMWF humidity;

• aerosol column, a priori calculated from aerosol optical thickness of 0.1 at 760 nm;

• aerosol size parameter, a priori fixed value;

• aerosol height parameter, a priori fixed value;

• Lambertian surface albedo in the NIR band, a priori maximum of measured reflectance in the NIR;

• first-order spectral dependence of surface albedo in the NIR band, a priori fixed value;

• Lambertian surface albedo in the SWIR band, a priori maximum of measured reflectance in the SWIR;

• first-order spectral dependence of surface albedo in the SWIR band, a priori fixed value;

• spectral shift NIR, a priori fixed value;

• spectral shift SWIR, a priori fixed value;

• fluorescence emission at 755 nm, a priori fixed value; and

• fluorescence spectral slope, a priori fixed value.

In order to apply the software to methane isotopologues, some minor changes were required, primarily in the spectroscopy, which we describe here, but also the state vector, where ¹³CH₄ and ¹²CH₄ replace purely CH₄. RemoTeC primarily draws its spectroscopic data from the high-resolution transmission molecular absorption database (HITRAN) 2008 (Rothman et al., 2009), amongst others. However, these databases were found to be deficient in methane isotopologue spectral lines (mainly ¹³CH₄); therefore, the spectroscopy was updated to HITRAN2012 (Rothman et al., 2013). The HITRAN2012 database includes line parameters for all isotopologues of the same molecule assuming fixed abundance ratios, such that the total CH₄ absorption cross section can be computed conveniently based on the total atmospheric profile (i.e. the sum over all isotopologues). In the case of ¹³CH₄, this scaling is done through a multiplication factor of 0.0111. In the context of this performance study, we can justify keeping this scaling factor since we aim to describe the feasibility of methane isotopologue retrieval and not perform retrievals from current TROPOMI data. All other aspects of the RemoTeC algorithm (state vector parameters, etc.) are as identified in Hu et al. (2016).

Note that the current version of RemoTeC is optimised for the SWIR3 band of TROPOMI and not Sentinel-5/UVNS, and some modifications were made in order to apply RemoTeC to Sentinel-5 simulations. In addition, because RemoTeC has heritage with GOSAT, the additional SWIR1 channel can also be used. This study uses the SWIR3 TROPOMI noise model applied in Hu et al. (2016); in addition, we employ a noise model that is representative of UVNS.

2.3 Synthetic study: the global ensemble

We decided in this study to focus on synthetic measurements since TROPOMI is still in an early mission phase, and methane isotopologues are still an unexploited area. S5/UVNS will not be launched until 2022, and therefore data will not be available until then. Further, because this is a feasibility study, full control of synthetic scenarios along with the known “truth” for verification is a significant benefit.

The synthetic data in this study are effectively the same as those outlined by Butz et al. (2012); Hu et al. (2016) and are described in detail by Hu et al. (2016), though note that in this paper only the SWIR spectra are considered. To summarise, the synthetic database comprises a wide range of realistic conditions that TROPOMI and UVNS are/will be expected to encounter, such as surface types, atmospheric conditions, solar zenith angles, nadir viewing and orbit. The measurements are designed to simulate the four main seasons over the course of a year and include examples of aerosols and cirrus clouds. All measurements in the databases are derived from a combination of chemistry transport models (TM5, ECHAM5-HAM) and satellite products (MODIS and SCIAMACHY). The synthetic data are sampled over the globe on a $\mathrm{2.79}{}^{\circ }\times \mathrm{2.8125}{}^{\circ }$ latitude by longitude grid, with only land surfaces considered.

Aerosol parameters are derived from a sophisticated combination of the ECHAM5-HAM (Stier et al., 2005) global aerosol model and MODIS observations. The ECHAM-HAM model is run at the same spatial resolution and in vertical layers up to the mid-stratosphere and contains five different chemical species on a superposition of seven log-normal size distributions. The aerosol optical depth (AOD) is scaled to match observations from the MODIS satellite instrument in 2007, all of which are considered in the synthetic spectra generation (Butz et al., 2012; Hu et al., 2016). In contrast, the aerosol representation in the retrieval scheme is relatively simple, where only one aerosol type is considered for which the aerosol column amount, aerosol size parameter and aerosol height parameter are derived. Both Rayleigh and Mie scattering are considered in RemoTeC, where only spherical particulates are considered. The result of these differences in the treatment of aerosols between the synthetic database and the retrieval algorithm is the deliberate introduction of systematic errors into the retrieval process through the forward model. This is similar to the spectral sampling approach, where the synthetic spectra are calculated using line-by-line parameters, and the retrieval algorithm is calculated using a correlated k-means method.

Using these simulated scenarios and the LINTRAN forward model (Hasekamp and Landgraf, 2002), we generate 11 041 simulated synthetic spectra. In order to include simulated TROPOMI/Sentinel-5 instrument effects, the synthetic spectra are convolved with a Gaussian instrument line shape function (ILSF) with a full width half maximum (FWHM) of 0.25 nm. The instrument noise models are as described in Hu et al. (2016) for the SWIR3 bands on TROPOMI and UVNS, while the noise model for the SWIR1 band on UVNS is based on characterisation work performed at the European Space Agency (ESA). Both of these noise models include shot noise and inherent instrument noise terms.

In essence, the RemoTeC software is comprised of two distinct elements; the first element is a forward model which takes in the synthetic database of atmospheric profiles and surface conditions, and converts these into top-of-atmosphere radiances (including aerosol and surface albedo effects) and includes ILSF and noise effects. The second element is the retrieval algorithm which then retrieves the trace quantities back from the simulated spectra and is based on the Philips–Tikhonov regularisation scheme. The retrieval forward model allows introduction of deliberate inconsistencies with the synthetic forward model, in order to simulate forward model errors. For example, the synthetic scenario spectra are generated using line-by-line spectroscopy, while the retrieval forward model uses the linear k-means method (only applicable to scattering retrievals; Hasekamp and Landgraf, 2002) as an approximate spectral sample technique, which is quicker than the line-by-line method. Errors in the spectroscopy are not modelled in this study.

Through this paper, we will refer to “latitudinal bands”, which we split in three distinct areas: tropical ($\mathrm{0}-\mathrm{20}{}^{\circ }$), midlatitude ($\mathrm{20}-\mathrm{60}{}^{\circ }$) and high latitude ($>\mathrm{60}{}^{\circ }$). These are typically how model atmospheres are split (e.g. midlatitude summer). Surface conditions will cause the results in these bands to vary, and we identify any regions that show significant deviation.

2.4 Study requirements

Fundamentally, the goal of methane isotopologue retrieval is to differentiate between methane source types. To achieve this, we calculate the δ¹³C value, which is the currently accepted metric used for this differentiation (Rigby et al., 2012; Schaefer et al., 2016). Nisbet et al. (2016) identify that for a given source type δ¹³C values typically vary by up to 1 ‰ over the course of a year, which means that TROPOMI/Sentinel-5/UVNS need to achieve 1 ‰ total uncertainty or better (<0.1 ‰) if seasonal variations are to be observed (Nisbet et al., 2016). However, Buzan et al. (2016), Weidmann et al. (2017) and Malina et al. (2018) identify that with current satellite retrieval techniques, this level of precision is difficult, since this would require total ¹³CH₄ column errors <0.02 ppb, which equates to roughly 0.1 % ¹³CH₄ total column error, assuming that total column ¹³CH₄ VMR is roughly 0.011 % of a total column VMR of CH₄ based on the HITRAN apportionment.

This is not currently possible for instantaneous measurements even for higher-concentration species. However, if the random error is sufficiently low, higher-order precisions could be obtainable with spatiotemporal averaging given the high repeat cycles of S5P/TROPOMI and S5/UVNS (planned). The question then becomes what may be technically possible with current satellite instruments and how such data can be leveraged. Malina et al. (2018) identify a target total uncertainty for δ¹³C of 10 ‰ as a more realistic and potentially achievable value (based on simulations with GOSAT-2). However, further analysis (e.g. Fisher et al., 2017) and discussions suggest that although such variations in δ¹³C between sources may be possible when measured at the surface, it is unlikely to remain true when viewed from space. For this study, we are aiming for a δ¹³C uncertainty of 1 ‰, as of possible benefit to the wider community. Rigby et al. (2017); Nisbet et al. (2016) indicate that the δ¹³C signature of sources can vary by 1 ‰ over the course of the year, and given that S5P and S5 are envisaged to operate for several years, we will aim for this target uncertainty.

2.5 Study structure

The primary aim of this study is to establish the IC (Rodgers, 2000) of ¹³CH₄ in simulated TROPOMI and UVNS retrievals, similar to the study by Malina et al. (2018). Malina et al. (2018) based their study on an optimal estimation routine (Rodgers, 2000) and experimented with a priori covariance matrices for ¹³CH₄. This paper builds on Malina et al. (2018) but is significantly different from Malina et al.'s work, since we are investigating different satellite instruments, in addition to more advanced atmospheric scenarios and scenes. Another fundamental difference between the studies is that RemoTeC is based on the Philips–Tikhonov regularisation scheme, and therefore experimenting with a priori covariance matrices is no longer necessary. In theory, there should be no difference in the results from using the two different methods, but in practice care must be taken to ensure that the algorithms are fully optimised for minor species.

Based on the methods of Hu et al. (2016); Malina et al. (2018); Rodgers (2000), we use the following metrics to identify the IC of ¹³CH₄ from TROPOMI:

• Column-averaging kernels indicate sensitivity of the retrieved state vector to the truth.

• Degrees of freedom of signal (DFS) measure for the number of pieces of information in a retrieval that can be associated with the state vector. It is defined by the trace of the full averaging kernel.

• Total column errors indicate the precision and accuracy of retrievals. In this synthetic study, the errors are defined as the difference between the synthetic “truth” and the retrieved quantity. Therefore, all errors include both precision and systematic errors.

• For fit quality, the (χ²) test is used, outlining quality of retrieval fits (as Galli et al., 2012).

• Jacobians indicate sensitivity of the forward model to state vector changes. The Jacobians are defined as the sensitivity of the forward model to changes in the state vector. In this study, we investigate how the total column Jacobians vary between the isotopologues; however, Malina et al. (2018) give examples of how the Jacobians vary on a profile basis.

These metrics are calculated for the ¹³CH₄ retrievals using the SWIR3 band (TROPOMI and UVNS), SWIR1 (UVNS) and a combination of the SWIR1 and SWIR3 bands (UVNS), under the assumption that retrievals for ¹²CH₄ will exhibit similar values to those shown in Hu et al. (2016).

Following this, we investigate the sensitivity of ¹³CH₄ and δ¹³C retrievals to prior knowledge of the atmospheric state focusing on the following areas:

• A priori methane profile: ideally, the retrieval will be insensitive to the choice of a priori methane profiles. To test this assumption, we investigated the effects of perturbation (±2 %) of the a priori profile, which is otherwise set to the synthetic “truth” in this study.

• A priori water vapour profile: in the same way as methane, we investigate the effects of imprecise knowledge of the water vapour column (±10 %); since water vapour exhibits strong absorption features in this spectral range, it can interfere with methane retrievals especially in the case of focusing on a weak absorber such as ¹³CH₄.

• Pressure: here, we introduce a ±0.3 % error into the a priori pressure profile. Pressure errors can affect the retrieval of methane in two ways: the first is through the retrieved air column which converts the total column concentration of methane into VMRs. The second way is through pressure dependence of the spectroscopy cross sections.

• Temperature: errors in the temperature profile are introduced through the temperature dependence of the spectroscopic cross sections (±2 K).

The magnitudes of the errors used in the prior knowledge are based on the errors derived by Hu et al. (2016) and Landgraf et al. (2016) from the CTMs used to provide the prior atmospheric data. For methane, TM5 was used; all of the other data are based on ECMWF. Note that the magnitudes in this study are worst case scenarios, and therefore the bias errors indicated in this section will be the maximum. Hu et al. (2016) do not indicate any significant non-linear behaviour in systematic error investigations, suggesting that different magnitude errors in the a priori methane profile will yield similar systematic errors. Typical standard deviations of the CTMs were found to be significantly lower (Landgraf et al., 2016). In addition, when calculating the errors induced in the δ¹³C ratio, errors from calculating the ¹²CH₄ VMR are included, since the methane a priori profile is used for both ¹³CH₄ and ¹²CH₄. In addition to the atmospheric state, we investigate the following instrument/calibration errors:

• radiometric offset (additive): a spectrally constant offset (±0.1 % of the continuum) is added to the synthetic spectrum, with no modification of the state vector; and

• radiometric gain (multiplication): error in the radiometric accuracy is introduced by apply a ±2 % scaling factor to the synthetic spectra.

The magnitudes of the instrument errors are defined as the minimum observation requirements for TROPOMI (Landgraf et al., 2016) and again therefore represent the worst case scenarios for instrumentation errors.

These bias effects are investigated for the SWIR1 and SWIR3 bands individually and are not considered for a combined retrieval. These tests do not cover every possible systematic bias that could be applied (e.g. spectral calibration errors, which can be fitted to reduce errors); however, we deem the above tests sufficient to determine the sensitivity of ¹³CH₄ retrievals to biases in the a priori information and/or the instrument. Note that the magnitudes of the biases applied in this section are identical to those applied in Hu et al. (2016).

Finally, we investigate the validity of the light path error cancellation assumption by comparing the calculated δ¹³C values for scattering and non-scattering cases. δ¹³C is defined as follows:

where VPDB refers to the international standard ratio of ¹³CH₄ and ¹²CH₄ based on the marine fossil Vienna Pee Dee Belemnite, which has a value of 0.0112372. Sherwood et al. (2016) indicates that biological methane sources such as wetlands typically have δ¹³C values of $<-\mathrm{60}$ ‰, while industrial sources are typically $>-\mathrm{30}$ ‰.

This comparison will allow us to determine if any bias is present between the calculated values. Errors caused by scattering are not random in nature but systematic (Inoue et al., 2016). Because this is a synthetic study not based on real data, we can compare the δ¹³C values for scattering and non-scattering scenarios using noiseless data. By performing retrievals without instrument noise, we remove all random components to calculate the δ¹³C ratio and are left with bias.

2.6 Filtering criteria

Since we are considering a non-scattering environment, with no clouds or aerosols, there are no filtering criteria applied to the retrievals performed on the synthetic data, in relation to optical depth. All retrievals that fail to converge are filtered, as well as all retrievals which exhibit DFS values lower than unity. All retrievals that show total uncertainties of >3 ppb are also excluded.

3.1 Example spectral fit

First, we provide a typical example (shown in Fig. 1) of the spectral fit output from RemoTeC with ¹³CH₄ set as the target species. The target species in RemoTeC is retrieved as a profile in 12 pressure equidistant vertical layers; the interfering species (¹²CH₄, H₂O, CO₂) are retrieved as total column density scalar profiles, assuming a fixed profile shape (temperature and pressure are typically not retrieved).

Figure 1Example spectral fit from RemoTeC, assuming the SWIR1 of S5/UVNS. (b) Example fit at simulated coordinates 32.09^∘ N 112.5^∘ W for a day in October 2015 (black line is synthetic “measured” spectra; red dashed line is retrieved modelled spectra). Panel (a) shows the spectral residual between modelled and measured spectra, with the red dashed lines indicating the noise level based on the SNR. Panel (c) shows the total column Jacobians of ¹²CH₄ (red) and ¹³CH₄ (black).

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The spectral fit quality is good, with a χ² value equal to 1.17, and all large spectral residuals are limited to random high-frequency components. However, there are some points which could be interpreted as not due to random noise, where the retrieval seems to disagree with the “truth”, notably the methane lines between 1645 and 1650 nm. However, upon further investigation, we found that these features do not consistently appear in spectral residuals. Therefore, the disagreement shown in Fig. 1 is random in nature.

3.2 Averaging kernels

Here, we show the column-averaging kernel (cAK) for when ¹³CH₄ is the target of RemoTeC, in Fig. 2 below. We also show the cAKs for when ¹²CH₄ is the target of RemoTeC.

Figure 2Example column-averaging kernels from synthetic retrievals of ¹³CH₄ (a) and ¹²CH₄ (b), from the SWIR1 channel of S5/UVNS. The blue plot is an example retrieval over the Sahara, the red plot is over Siberia (high latitude), the green plot is over the Amazon rainforest (tropical), and the black plot is temperate Europe (midlatitude). Metadata associated with each retrieval are highlighted in the legend.

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Figure 2 shows a tight spread of cAKs which generally do not reach a value of unity in the lower atmosphere, which suggests reduced sensitivity of ¹³CH₄ in the lower atmosphere. The cAKs suggest there is significant IC available in total column retrievals of ¹³CH₄, but there still may be some noise components present in the retrievals, especially in the lower atmosphere where cAK values are the lowest. The uniformity of the cAKs with respect to surface type suggests insensitivity to changing atmospheric or retrieval conditions.

The ¹²CH₄ cAK exhibits the typical behaviour of CH₄ cAKs (e.g. Hu et al., 2016), which is expected since ¹²CH₄ makes up 98 % of atmospheric CH₄. However, the ¹³CH₄ cAK exhibits behaviour closer to that of CO (Landgraf et al., 2016). Given that ¹³CH₄ makes up ∼1.1 % of atmospheric CH₄, the retrieval column loses sensitivity in the lower atmosphere, where H₂O dominates. Borsdorff et al. (2014) show that in the case where sensitivity is low in the troposphere, the cAK values are enhanced at other altitudes. This is apparent in the cAKs of ¹³CH₄ in Fig. 2, where cAK values larger than those of ¹²CH₄ are observed.

3.3 DFS spread

The next logical step from checking the cAKs is to view the seasonal and geographical distribution of DFS over the synthetic database. This is achieved by plotting the DFS for each retrieval over global maps, as shown in Fig. 3 below. The seasonal dependence will be brought to the fore since we filter out all cases where DFS does not reach unity.

In Fig. 3, midlatitude highly reflective surfaces show the highest DFS, and the high-latitude/“green” regions show the lowest DFS values. In general, high information content is achieved with the SWIR1 band; indeed, DFS values greater than unity (passing the filtering criteria) are achieved over the Amazon forest regions of Brazil and for some of the high-latitude regions.

Figure 3Global spread of DFS based on the RemoTeC synthetic data ensemble, with ¹³CH₄ as the target for retrievals. The four main seasons in the synthetic database are represented in this figure by 1 d in the months of January, April, July and October. The far right panel in the figure outlines the spread of DFS values over the entire dataset in the form of a boxplot indicating median and upper and lower quartile values, with the mean value and the total number of measurements indicated at the bottom; the circles are outlier values.

Figure 4Global spread of total error based on the RemoTeC synthetic data ensemble, with ¹³CH₄ as the target for retrievals. The four main seasons in the synthetic database are represented in this figure by 1 d in the months of January, April, July and October. The far right panel in the figure outlines the spread of error values over the entire dataset, with the mean value and the total number of measurements indicated at the bottom; the circles are outlier values.

3.4 Total errors

Section 3.3 suggests that there is enough information in the total column to retrieve ¹³CH₄; however, this is irrelevant if the retrieval errors are so large as to make assessing δ¹³C impossible. The assessed errors from the synthetic database are shown in Fig. 4 below.

Note that the errors in Fig. 4 are remarkably uniform across the seasons and locations (apart from the high-latitude regions), suggesting that SNR is not the limiting factor in the SWIR1 band. Typically, the midlatitude errors have values <0.5 ppb, equating to roughly <2.5 % of the total column, which we assume to be 20 ppb for ¹³CH₄, as indicated in the requirements. The analysis shows that the SWIR1 band results in mean values of 0.68 ppb. Some very high errors in excess of 20 ppb were found in high-latitude regions (when the DFS >1 and uncertainty <3 ppb filters were removed), typically within the Arctic Circle, but also surprisingly within the southeast Asia region. Typically, the largest errors are found in coastal regions where there is likely low albedo causing large errors. An investigation showed that these retrievals are all captured under low SNR conditions, largely driven by solar zenith angle (SZA) and albedo, thus leading to high uncertainty.

Figure A1 in the Appendix shows that the overall majority of the uncertainty can be attributed to precision, with (when considering the mean uncertainty value) 0.08 ppb uncertainty associated with systematic errors. However, this figure makes it clear that the systematic error is larger than the target of 0.02 ppb total uncertainty, meaning that systematic error must be accounted for before making any judgements on ¹³CH₄ retrievals.

3.5 Systematic prior knowledge errors

The previous section deals with errors associated with precision and other systematic errors present in the retrieval approach. In this section, we investigate the effects of imprecise knowledge of a priori and ancillary information and instrument calibration errors on the retrieved column of ¹³CH₄; for example, Fig. 5 below indicates the differences when applying a 2 % bias to the a priori methane column.

Figure 5Comparison of retrieved ¹³CH₄ (a) and δ¹³C (b) before and after a priori modification by applying a 2 % bias on the methane. The red line is a line of best fit, and the statistical characteristics (coefficient of correlation, gradient, intercept and standard deviation of the difference) are indicated in the legend.

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We show the biases for both ¹³CH₄ and δ¹³C, since the δ¹³C ratio is expressed in permil and is therefore highly sensitive to any change, in addition to the fact that errors from ¹²CH₄ are also included in the δ¹³C ratio. In the case of the SWIR1 band, we note that a 2 % bias in the a priori methane column has no effect on the retrieved a posteriori ¹³CH₄ and δ¹³C ratio values. Using a similar analysis to that shown in Fig. 5, the bias metrics for the systematic error scenarios described in Sect. 2.5 are summarised in Table 2 below.

Table 3Effects of errors in a priori databases and instrument calibration errors on test retrievals of SWIR1 ¹³CH₄ and δ¹³C; the metrics displayed in this table are as described in Sect. 2.5.

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The systematic errors indicated in Table 3 suggest that uncertainty in the a priori state vector does not adversely affect δ¹³C calculations; however, uncertainty in the pressure and temperature ancillary data does have a notable impact, which translates to large biases in δ¹³C values. This impact could be reduced when averaging over monthly periods, since pressure and temperature errors are unlikely to be systematically offset over a long period. We therefore assume that pressure errors are of lesser relevance. However, the 2 K temperature error still results in a bias of roughly −30 ‰ and scatter of roughly 26 ‰. This amount of bias renders the usefulness of retrieving the δ¹³C ratio considerably. Reuter et al. (2012) describe how the lower state energy (E₀) of molecular transitions fundamentally controls the temperature sensitivity for each molecule in relation to carbon dioxide isotopologues. The HITRAN2012 database shows that the E₀ values for ¹³CH₄ are typically several times lower than the main methane isotopologue and therefore will be affected by a temperature shift to a greater degree than the main methane isotopologue. The exponential relationship between the lower state energy and the line strength (Eq. 3) suggests that molecules with lower E₀ values (such as ¹³CH₄) are much more affected by temperature shifts in the cross sections, as opposed to molecules with higher E₀ values such as ¹²CH₄. An et al. (2011) show that for a given temperature difference, the change in line intensity can be expressed as

where S(T) is the line intensity, Q(T) is the total partition function of the absorbing molecule, and T is temperature. Note that RemoTeC includes the option for fitting a temperature offset; the results of including this option in the retrieval process are shown in Fig. 6 below.

Figure 6Comparison of retrieved ¹³CH₄ (a) and δ¹³C (b) before and after a priori modification by applying a 2 K bias on the temperature, where temperature shift is retrieved as a part of the state vector. The red line is a line of best fit, and the statistical characteristics (coefficient of correlation, gradient, intercept and standard deviation of the difference) are indicated in the legend.

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Figure 6 shows that including the temperature shift reduces the temperature sensitivity bias of the δ¹³C retrievals to −0.31 ‰ but comes at the cost of reducing valid retrievals by 50 %, which fits within the set requirements of this study. However, note that the scatter on the temperature-fitted retrieval is significant (>7 ‰), suggesting that temporal and/or spatial averaging is required. The preferable solution here is to improve knowledge of the ancillary information, rather than rely on longer-term spatiotemporal averaging.

In addition to the errors in the a priori and ancillary profiles, we note that the apparent sensitivity to radiometric offset errors, where ±0.1 % causes a δ¹³C bias of up to 4.41 ‰, is highly significant. This is likely an effect of the high SNR achievable in the SWIR1 band.

Figure 7As Fig. 1 but focused on the TROPOMI/UVNS SWIR3 band.

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3.6 Summary of SWIR1

The results shown for the planned SWIR1 band in UVNS indicate a difficult but positive outlook for the future. The SWIR1 band shows global DFS and errors are uniform across the globe, aside from high-latitude regions, with high reflectance regions such as the Sahara desert showing similar patterns in DFS and total errors to lower reflectance regions such as the Amazon in South America. For a mean error of 0.68 ppb (or 0.57 ppb for precision), a daily repeat cycle could theoretically lead to the desired precision of 0.02 ppb in 2–3 years, assuming instantaneous measurements. This is not useful, but given the planned high spatial resolution of S5/UVNS, it would be easy to expand the spatial averaging in order hit the target precision within 1 year of averaging. Further, some of the midlatitude regions already have errors that have low precision errors <0.2 ppb, and theoretically the target of 0.02 ppb errors could be achieved with 1 month of averaging with a larger spatial sample, which would be helpful to monitor the annual change of δ¹³C within a specific region.

However, the sensitivity of ¹³CH₄ retrievals to temperature and instrument errors will likely mean that total δ¹³C uncertainty is significantly higher, and assessments on the accuracy of the temperature and pressure will likely be required to make judgements on the required level of spatial and/or temporal averaging required. The instrument sensitivity can be assessed after launch and removed from the spectra prior to full retrievals and thus remove ¹³CH₄ sensitivity to instrument errors (accepting that this will be challenging). Generally, the SWIR1 band looks to be suited to ¹³CH₄ retrieval, with some potential to track δ¹³C over the course of a year once systematic and a priori bias corrections are applied.

4.1 Example spectral fit

Following the same format as that shown in Sect. 3., an example of a spectral fit in the SWIR3 band is shown in Fig. 7 below.

The quality of the fit shown in Fig. 7 is similar to that shown in Fig. 1, with the residual radiance showing similar values based on the χ² value. However, it is important to note that the spectral lines for both the simulated spectra and retrievals are based on Voigt line shapes, which, although resulting in good fits in simulated scenarios, may not be adequate in reality and could cause worse fits. This also applies to other errors that may be present in the fitting process (e.g. ILSF or similar). Note that the radiance magnitudes in this spectral region are significantly lower than the equivalent radiances in Fig. 1, which is not unexpected since solar irradiance and surface albedo in this waveband are significantly lower than in SWIR1. This is best indicated by the SNR shown in Fig. 7a, which is several times smaller than the equivalent in Fig. 1. Reuter et al. (2010) note that measurements of CO₂ in the SWIR1 spectral region with SCIAMACHY tend to have SNR values between 279 and 1950.

The Jacobians in Fig. 7c suggest more ¹³CH₄ spectral lines in this waveband as compared to SWIR3 (Fig. 1 above). However, the Jacobians in Fig. 7 appear to be more dominated by ¹²CH₄, since this spectral range is closer to a methane continuum than to a collection of individual spectral lines, as is found in SWIR1.

4.2 Averaging kernels

Hu et al. (2016) show an example of a total cAK for CH₄ retrievals from TROPOMI, with the values remaining close to unity for the total column, thus implying that the TROPOMI SWIR methane retrievals maintain high sensitivity throughout the total column. Here, we show the equivalent column-averaging kernel for when ¹³CH₄ is the target of RemoTeC, in Fig. 2 below. We also show the equivalent cAKs for when ¹²CH₄ is the target of RemoTeC. ¹²CH₄ cAKs should show similar behaviour to the cAKs of Hu et al. (2016).

Figure 8As Fig. 2 but focused on the Sentinel-5/5P SWIR3 band.

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The cAKs in Fig. 8 shows very similar total column shapes to the SWIR1 cAKs, i.e. weaker in the lower atmosphere and stronger in the upper atmosphere. The shape of the cAKs is almost the mirror image of the example cAK shown by Hu et al. (2016); however, the cAKs of CO retrieval shown by Landgraf et al. (2016) show similarly shaped cAKs, suggesting that weak atmospheric absorbers struggle for information content in the lower atmosphere (where spectroscopy effects such as pressure broadening likely make it difficult for weak absorbers). In addition, the SWIR1 cAKs typically have higher magnitudes, suggesting higher information content in the retrievals and less impact by pressure broadening and similar effects.

4.3 DFS spread

The global spread of DFS values for the SWIR3 band is shown in Fig. 9 below.

Figure 9As Fig. 3 but focused on the Sentinel-5 SWIR3 band.

Figure 9 suggests that DFS values of unity or better can be expected for midlatitude regions in all seasonal conditions; however, high-latitude regions such as Antarctica or Greenland may not achieve DFS values of unity in winter and autumn most likely due to a combination of low surface reflectance and high SZAs. In addition, we see that the highest DFS values typically occur in desert regions such as the Sahara or Arabian Peninsula, and the Amazon rainforest tends not to achieve unity values at most times of year.

The differences in measurement densities indicated in both Figs. 3 and 9 show that the SWIR1 band has almost 3000 additional valid retrievals that pass the filtering criteria as opposed to SWIR3. These additional valid retrievals represent roughly 30 % of the total ensemble and are therefore a significant proportion.

Figure 10As Fig. 4 but focused on the Sentinel-5/5P SWIR3 band.

Table 4Effects of errors in a priori databases and instrument calibration errors on test retrievals from SWIR3 of ¹³CH₄ and δ¹³C; the metrics displayed in this table are as described in Sect. 2.5.

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The results in Table 4 typically show that the included systematic biases for most of the considered parameters have similar magnitudes, with two notable exceptions: pressure and temperature. The 0.3 % pressure bias induces up to roughly 6 ‰ bias in the δ¹³C values, thus making the 10 ‰ target more challenging. However, the main issue is the sensitivity to temperature, with a 2 K error resulting in biases of over 60 ‰ δ¹³C. The reasons for this temperature sensitivity likely stem from Eq. (3), shown in Sect. 3.5 above. The temperature bias effects can be reduced if a temperature shift is included in the state vector, the results of which are shown in Fig. 11.

4.4 Total errors

The global spread of total retrieval errors is shown in Fig. 10 below.

As expected (for non-scattering scenarios), Fig. 10 shows that the minimum errors occur in the high-DFS regions shown in Fig. 9. These regions show that total errors typically range between 0.5 and 1.0 ppb (although some cases where errors >3 ppb, normally in tropical/subtropical regions when filters were removed), which equates to roughly between 2.5 % and 5 % total column error, which is remarkable for such a minor species. The plot of the spread of errors suggests a mean value of ∼1 ppb over the entire year, considering all surface types. When we removed the unity DFS filtering criterion, our investigation found some regions had errors exceeding 20 ppb, typically in high-latitude/low-albedo regions such as Greenland.

The precision error map shown in Fig. A2 indicates similar levels of systematic error in the SWIR3 when compared to the SWIR1 band.

4.5 Systematic prior knowledge errors

Following the methods laid out in Sects. 2.5 and 3.5, the following section investigates the effects of uncertainty in the prior state vector and ancillary information on ¹³CH₄ retrievals in the SWIR3 band. Like in Sect. 3.5, we show the biases for both ¹³CH₄ and δ¹³C, due to their differences in sensitivity to the perturbations. These are highlighted in Table 4 below.

Figure 11As Fig. 5 but including a 2 K temperature bias in the retrieval process and setting RemoTeC to account for temperature offsets.

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Comparing the results in Fig. 11 with those shown in Table 4 shows a significant improvement in the bias, but this has come at a cost of the quality of the fits where we found that ∼50 % of the synthetic scenarios failed to converge, as compared to 99 % convergence before enabling the temperature fitting. However, even with this improvement in bias, the magnitude of the bias (13.9 ‰) is still greater than the desired magnitude of the total error on the δ¹³C metric. Again, like in the SWIR1 band, the preferable solution would be to have more accurate knowledge of temperature. Therefore, at this time, the current RemoTeC algorithm needs more accurate knowledge of temperature (and pressure) profiles before meaningful values of δ¹³C can be generated in this spectral band. It could be argued that it may be possible to average out this temperature bias over time, since it is unlikely that the temperature profile will be systematically offset as much as ±2 K over a period of time, but this is very difficult to predict and is not a solution to rely upon. An additional difficulty with this temperature dependance, as Reuter et al. (2012) identify, is that such temperature sensitivity can add significant uncertainty to the light path at which point the light path proxy method becomes a much less effective method for removing scattering effects.

Radiometric offset errors are less significant in the SWIR3 as opposed to the SWIR1 band. Radiometric offset errors typically lead to underestimation in the surface reflectance estimate in the absence of aerosols/clouds (Kuze et al., 2014). Given that the SWIR1 operates at a higher radiance magnitude than the SWIR3, any minor errors in the surface reflectance estimate will likely lead to larger errors in the calculated radiance, as opposed to the true radiance, thus leading to larger errors in the SWIR1.

Figure 12As Figs. 2 and 8 but focused on a combination of the SWIR channels from Sentinel-5.

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4.6 Summary of SWIR3

We find that, in principle, retrieval of ¹³CH₄ using the SWIR3 band of TROPOMI/UVNS is feasible, with all regions of the globe showing DFS in the region of unity, exemplified by uniformity in the cAKs, which show typical responses for weak absorbers. Errors vary significantly but are typically at their minimum over desert or high-reflectance scenes and maximum over “green” scenes or high-latitude regions, indicating that the quality of the retrievals is heavily dependent on SNR. Individual retrieval errors are too high to hit the basic error target of 0.02 ppb; however, as with SWIR1, the precision error can be reduced through temporal averaging. The low-error regions (typically <0.5 ppb) can achieve a precision of 0.02 ppb with roughly 1–2 years of instantaneous measurements (assuming none are corrupted by clouds or similar). However, if we consider mean error values of 1 ppb, the target precision of 0.02 ppb becomes harder to achieve, with multi-year datasets required, even if spatial averaging is taken into account. Note that these values are very optimistic, since they do not take into account errors in the retrieval of ¹²CH₄ or the fact that retrievals may fail due to the presence of aerosols. Hu et al. (2016) estimate that approximately 50 % of the synthetic measurements are not valid due to high aerosol optical depth, which means that we effectively have to double our temporal averaging period. However, all of these points are moot when considering the high systematic error caused by poor knowledge in the temperature profiles. Therefore, while there is enough information content in the total column retrievals of ¹³CH₄, and the precision errors could be low enough to make calculating δ¹³C a worthwhile task, very accurate prior knowledge of the state vector and ancillary elements is required. When comparing with the SWIR1, we find a reduced performance, thus implying SNR is a more important factor in ¹³CH₄ retrieval than spectral resolution (when comparing with Malina et al. (2018), who investigated methane isotopologue retrieval assuming GOSAT-2/TANSO-FTS-2 characteristics of spectral resolution 0.2 cm⁻¹). The key reasons for the lower SNR in the SWIR3 band as opposed to SWIR1 are the lower solar irradiance and surface albedo at these wavelengths.

5.1 Averaging kernels

The cAKs for the combined SWIR1 and SWIR3 bands are shown in Fig. 12 below.

The results in Fig. 12 show characteristics most closely aligned with the SWIR1 band considered on its own. In general, however, the cAKs shown in Figs. 2, 8 and 12 are all similar, and there are only minor variations between the example retrievals and bands.

5.2 DFS spread

The global spread of DFS values generated by combining the SWIR1 and SWIR3 channels is shown in Fig. 13 below.

Spread and magnitude are very similar to those for SWIR1 alone (Fig. 3), again suggesting that the information content from the SWIR1 channel dominates the dual-band retrieval. Note that the mean DFS value for the dual-band method is lower than that for the SWIR1 band alone; however, the dual-band method includes additional valid retrievals in the higher-latitude regions, which likely account for the lower mean DFS.

Figure 13As Figs. 3 and 9 but focused on a combination of the SWIR channels from Sentinel-5.

5.3 Total errors

The total errors for the dual-band retrieval are shown in Fig. 14 below.

The total errors show a minor improvement in the total column ¹³CH₄ errors, with a mean value 0.08 ppb lower than for the SWIR1 band on its own. Similarly to Fig. 13, this minor improvement is caused by higher IC but tempered by the additional valid retrievals in the high latitudes, not present in the SWIR1 band, and which typically have larger errors. In general, these differences are minor, and it is clear that the dual-band retrieval has only a small effect on the retrieval errors. The benefits are very likely to vanish when considering the combination of the systematic errors indicated in Tables 3 and 4, and other instrument or physical errors associated with a dual-band retrieval.

The dual-band retrieval precision errors shown in Fig. A3 indicate that systematic error magnitudes are similar to those for each band considered separately.

Figure 14As Figs. 4 and 10 but focused on the Sentinel-5 SWIR1 and SWIR3 bands.

6.1 SWIR1

Figure 16 above shows that there is no significant global bias between the scattering and non-scattering cases. The bias appears to be small: a global mean value of roughly −4 ‰, which is small in comparison to the uncertainties shown in the sections above but also largely uniform across the globe with some notable exceptions (e.g. high-latitude regions, Hudson Bay in Canada and in the Pacific Ocean). These regions are not known for having significant aerosol errors. This suggests that the apparent systematic bias is not due to the presence of aerosols or caused by scattering.

6.2 SWIR3

We note that the δ¹³C ratio differences represented in Fig. 17 are very similar to those shown in Fig. 16, including the pronounced spike in systematic error over Hudson Bay in Canada and in the Pacific. The mean difference is roughly −4 ‰, again similar to Fig. 16. The SWIR3 band is known to be less affected by scattering than the SWIR1 band and should therefore exhibit lower systematic bias than Fig. 16 if the differences are caused by scattering. This suggests that scattering is not responsible for the biases present in Fig. 17.

Figure 18As Figs. 16 and 17 but focused on dual-band UVNS.

6.3 SWIR1 and SWIR3

Figure 18 shows similar results to those for SWIR1 and SWIR3 considered individually. A global systematic bias is present of roughly similar magnitude to those shown in Figs. 16 and 17. However, note that some of the localised systematic biases (e.g. Hudson Bay) are no longer apparent. Again this suggests that this global systematic bias is not related to atmospheric scattering.

Within Figs. 16, 17 and 18, we can identify several individual retrieval points where there is significant deviation between the scattering and non-scattering cases. These points are clearly linked with the high uncertainty points identified in the error figures (Figs. 4, 10 and 14), which will cause deviations between the scattering and non-scattering cases.