The greenhouse gas methane (CH4) plays a key role in anthropogenically driven climate change . Therefore, monitoring of atmospheric CH4 abundances is one of the crucial elements of future Earth observing satellite missions e.g.,. The European Space Agency (ESA) and its national partners have scheduled the Sentinel-5 Precursor (S5P), also known as TROPOMI , and the Sentinel-5 (S5) for launch in 2016 and around 2021, respectively. Both satellites carry spectrometers sensitive to the shortwave infrared (SWIR) spectral range. CH4 absorption in sunlight backscattered from the Earth's surface and atmosphere allows for the retrieval of column-average dry air mole fractions of methane (XCH4). Thereby, the S5P and S5 strategy builds on the pioneering heritage of the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) and the Greenhouse Gases Observing Satellite (GOSAT) demonstrating that highly accurate satellite remote sensing of XCH4 e.g., can be a valuable tool to gain insight into CH4 emissions at the Earth's surface e.g.,.

Estimating such surface–atmosphere fluxes through inverse modeling, however, poses stringent accuracy requirements on the retrieved XCH4. Regionally or temporally correlated biases as low as 1 % can jeopardize the usefulness of the XCH4 satellite records for inverse modeling of surface fluxes . An analogue, potentially even more stringent requirement applies to remote sensing of column-average dry air mole fractions of carbon dioxide (XCO2) e.g.,. Therefore, considerable effort is dedicated to estimating and reducing sources of error for XCH4 (and XCO2) retrievals from solar backscatter measurements. Most studies focus on how to avoid or evaluate errors due to light-path uncertainties in light-scattering atmospheres e.g.,. In particular, assess the residual aerosol- and cirrus-induced XCH4 retrieval errors for an S5P-like observer using a global and seasonal ensemble of simulated S5P measurements. demonstrate the detrimental impact of spectroscopic uncertainties on XCH4 retrievals and on the respective surface flux estimates from SCIAMACHY. They find about 20 % overestimation of the tropical CH4 source (up to 60 ppb) due to a spurious spectroscopic interference between CH4 and water vapor (H2O) absorption in the 1.65 µmCH4 band. In a previous support study for the S5P mission, degrade high-resolution spectra around 2.35 µm wavelength recorded by ground-based Fourier transform spectrometers (FTS) at a midlatitude and a tropical site to the spectral resolution of the S5P instrument. They conclude on a weak dependence of the retrieved XCH4 on spectral resolution and H2O content of the atmosphere pointing at relatively little impact of erroneous spectroscopy on XCH4 retrievals. The spectral fitting residuals in the 2.35 µm band, however, reveal a clearly systematic pattern, which is in particular correlated with H2O absorption lines.

Here, we aim at mapping spectroscopic errors into XCH4 retrieval errors for an S5- and S5P-like observer on the global scale in order to assess whether error patterns are significant in magnitude and whether they are correlated among regional spatial and seasonal temporal scales. Such correlations are particularly detrimental for surface flux inversions since they can be readily mistaken for a regional or seasonal flux pattern, unlike random noise errors that cancel themselves out on the aggregated scales. To this end, the global ensemble of simulated measurements used previously by is revisited by replacing the light-path perturbation through a perturbation due to imperfect spectroscopy. Thereby the spectroscopic perturbation is estimated from fitting residuals to observations of a direct-sun viewing, ground-based Fourier transform spectrometer (FTS) operating at very high spectral resolution. Submitting the perturbed satellite spectra to the retrieval algorithm (which is not aware of the perturbation) allows for assessing the residual XCH4 forward model error due to imperfect spectroscopy.

This paper is organized as follows. Section  describes the retrieval algorithm and the general properties of the S5P and S5 trial ensemble. Section  describes the ground-based FTS measurements and introduces the method – and its assumptions – to generate a spectroscopic perturbation among the satellite trial ensemble. Section  discusses the spectroscopy-induced XCH4 retrieval errors, and Sect.  concludes the study.

Remote sensing of atmospheric parameters in general requires a forward model F that relates the retrieval parameters included in the state x (with xj the jth retrieval parameter) with the measurements y (with yi the ith spectral element): y=F(x)+ϵy+ϵF, with ϵy the noise error due to detector noise (for example) and ϵF the forward model error due to approximate description of the relevant physics or due to errors of parameters feeding F (for example). Here, we intentionally introduce a well-defined spectroscopy-related forward model error ϵF as described in Sect. .

The simulated measurements y are spectra of backscattered sunlight in the SWIR spectral range. Thereby, instrument properties are implemented according to the S5 instrument characteristics summarized in Table . S5 covers spectral bands from the UV to the SWIR but here, we focus on the SWIR bands around 1.6 µm (named henceforth SWIR1) and 2.3 µm (named henceforward SWIR3; in the early phase of the mission, SWIR2 had been assigned to a channel around 2.0 µm, which was dropped later). The finite spectral resolution of the spectrometers is modeled by a Gaussian instrument response function (ISRF) with 0.24 nm width (full width at half maximum (FWHM)). Measurement noise is calculated from a parametric model that considers both signal-dependent contributions such as photoelectron shot-noise and signal-independent contributions such as dark-current noise. The typical signal to noise ratio (SNR) is on the order of several hundreds for the SWIR bands. Being S5's precursor, S5P features similar instrument characteristics but does not include of the SWIR1 channel around 1.6 µm.

The forward model F(x) employed here is a variant of the “RemoTeC” algorithm similar to the method used in . RemoTeC is designed to retrieve XCH4 (and XCO2) for solar backscatter spectra in the SWIR spectral range such as collected by GOSAT, the Orbiting Carbon Observatory (OCO-2), S5P and S5. In its standard setup, the algorithm is able to simulate backscattered radiances in particle-loaded atmospheres taking into account light-path modification by scattering. Here, we focus on the evaluation of spectroscopic errors. Therefore, our study uses a variant of RemoTeC that neglects scattering by aerosols and particles, and the measured spectrum depends only on the absorption properties of the target and interfering absorbers described in Table . The estimation of those absorption properties relies on HITRAN-2008 spectroscopic parameters assuming a Voigt line shape. For the water vapor on the SWIR3, the line list described on the reference is used. It should be noticed, however, that for line-shape parameters of CH4 and H2O in the SWIR1 and SWIR3 regions, data in HITRAN-2008 and HITRAN-2012 have significant uncertainty because only a subset of the absorption lines was accurately measured or calculated. We refer to for a detailed description. Neglecting refined line-shape effects (line mixing, speed dependence and Dicke narrowing) could also lead to gas retrieval errors . Furthermore, the SWIR1 region in HITRAN-2008 and HITRAN-2012 is still not fully characterized, for both line positions and line intensities, compared to other longer wavelength regions ; detailed assignment and lower state energy are not known in many cases affecting line intensity calculations at temperatures other than 296 K. Further experimental and theoretical investigations of this spectral region are presently underway .

The spectra modeled by RemoTeC are convolved by the satellite's ISRF, and noise is added as described above to simulate S5- and S5P-like measurements. Section  explains how an extra error due to spectroscopic deficiencies is generated and added to the measurements.

The ensemble of scenes for which we perform retrieval simulations is the same as the one described in detail by Butz et al. (2010, 2012). While our former studies focus on errors induced by aerosol and cirrus scattering, we neglect such effects here; therefore we assume all scenes to be free of scattering particles. The ensemble covers 1 day in each of the following months: January, April, July, and October, respectively, for which we collect atmospheric absorption and surface reflection properties on an ∼3∘×3∘ latitude × longitude grid. Surface albedo in SWIR1 and SWIR3 is assembled from the MODIS land albedo product and a database generated from SCIAMACHY's 2350 nm channel . Meteorological parameters and the abundances of the relevant atmospheric absorbers listed in Table  are taken from models (CarbonTracker for CO2 , TM4 for CH4 and CO , ECHAM5-HAM for H2O, temperature and pressure, ).

Given the simulated measurements y, RemoTeC uses an inverse method based on Philipps–Tikhonov regularization e.g., to estimate the state vector x from Eq. (). The state vector elements are the 12-layer vertical profiles of CH4 (and CO2 partial column concentrations when SWIR1 band is covered), the total column concentrations of the interfering absorbers H2O, and CO, and surface reflection parameters (per channel). To find x, the inverse method minimizes the cost-function J given by J(x)=Sy-1/2(F(x)-y)2+γ‖W(x-xa)‖2, where xa is the a priori state vector, Sy is the diagonal error covariance matrix, W is the regularization matrix, and γ is the regularization parameter chosen such that it allows for about 1 degree of freedom for the CH4 (and CO2) vertical profiles. The regularization matrix W=LTL is assembled from the discrete first-order difference operator L for the CH4 (and CO2) vertical profiles and vanishes for all other state vector elements.

Once the state vector solution x^ is found it may be written in linear approximation as a combination of the true state xtrue, the a priori, and the error contributions, x^=Axtrue+(I-A)xa+Gϵy+GϵF, where A is the averaging kernel and G is the contribution or gain matrix . For our simulations the true state is identical to the a priori (xtrue=xa) and Eq. () reduces to x^=xtrue+Gϵy+GϵF. Defining an operator hT that selects the CH4 partial columns from the state vector, adds them up and divides by the total dry air column yields the retrieved dry air mole fraction XCH4=hTx^=hTxtrue+hTGϵy+hTGϵF=ctrue+Δcy+ΔcF. Since the true state (xtrue and ctrue) and the noise realization (ϵy and Δcy) are known, we can evaluate the targeted XCH4 forward model error ΔcF by retrieving XCH4 from the simulated measurements and subtracting ctrue and Δcy.

The first step in generating the spectroscopic forward model error for the satellite retrieval simulations is selecting a set of spectra recorded by the ground-based, direct-sun viewing FTS located at the Darwin (Australia) TCCON station and operated by University of Wollongong. The instrument, Bruker 125HR, provides spectral coverage in all absorption bands relevant here (see Table ). Such ground-based FTS measurements have been used in previous studies for validating other ground-based instruments and for comparisons to satellite retrievals of XCH4 and XCO2 e.g.,. The FTS-measured atmospheric transmittance spectra are iteratively fitted by a variant of the RemoTeC algorithm. Essentially, our approach follows the methods and analyses in . Details can be found there. The approach is conceptually analogous to regularly operated TCCON stations and verified by a comparison between the GFIT algorithm and RemoTeC. The adjusted parameters include the vertical profiles of CH4 and the relevant interfering species such as H2O, CO2, CO, and a background baseline transmittance. Assuming that the residual spectra (difference between the measured and the iteratively adjusted modeled spectrum) are dominated by spectroscopic errors, the residual spectra serve as forward model error perturbation ϵF for the satellite retrieval simulations.

The methodology we introduce here assumes that the perturbation Δτ derived from the FTS residuals is dominated by deficiencies of the employed spectroscopic parameters and models. This assumption appears justified by the use of state-of-the-art instrumentation and retrieval techniques with a proven performance record. Further, the FTS residuals represent only a fraction of the actual spectroscopic errors, i.e., those which cannot be compensated by the free parameters of the FTS fitting routine such as CH4 and H2O abundances. In that sense, the estimated perturbation is an optimistic interpretation of spectroscopic errors.

For a ground-based, direct-sun viewing observer in a plane-parallel atmosphere, the monochromatic atmospheric transmittance Tgb recorded can be written, Tgb(τ)=Igb(τ)ES=exp⁡-τcos⁡αgb, where Igb is the observed radiance, ES is the solar irradiance at top-of-the-atmosphere, αgb is the solar zenith angle of the ground-based sounding, and τ is the molecular absorption optical thickness integrated along the zenith direction (i.e., along the vertical). For simplicity, we neglect scattering processes due to molecules and particles. The processing chain of the ground-based FTS measurements provides a best fit Tgb, mod to the observed transmittance spectra Tgb, true. The corresponding mismatch ΔT=Tgb, true-Tgb, mod is termed the FTS fitting residual to be used for perturbing our simulated satellite retrievals. Figures  and  show the FTS measured transmittance T and the fitting residual ΔT. Our study uses 50 different FTS spectra recorded at different humidity conditions . The FTS operates at very high spectral resolution such that the measured residual ΔT is approximately equal to the monochromatic residual. Further assuming that the FTS fitting residual is caused by errors in spectroscopic parameters, we can evaluate Eq. (), ΔT=exp⁡-τtruecos⁡αgb-exp⁡-τmodcos⁡αgb=Tgb, modexp⁡-Δτcos⁡αgb-1, with Δτ=τtrue-τmod. Thus, given the FTS residual ΔT, the FTS transmittance Tgb, mod, and the FTS solar zenith angle αgb, we can calculate a perturbation Δτ of the vertical absorption optical thickness Δτ=-cos⁡αgbln⁡ΔTTgb, mod+1. In the next step, the perturbation derived from the ground-based spectra needs translation into a perturbation of the satellite observations. In a non-scattering atmosphere, the reflectance Rsat observed from a downward-looking space-borne observer is given by Rsat(τ)=Isat(τ)ES=Acos⁡αsatπexp⁡τcos⁡αsat+τcos⁡θsat, where Isat is the reflected radiance, A is the ground albedo, αsat is the solar zenith angle and θsat is the satellite viewing zenith angle (assumed θsat=0∘, nadir-viewing in our simulation exercise). Replacing the absorption optical thickness τ in Eq. () by a perturbed optical thickness τper=τmod+Δτ yields the perturbed satellite measurement.

Up to here we assume monochromatic light, but in order to introduce the perturbed satellite measurement in the retrieval algorithm we have to take in account the satellite spectral resolution. Therefore, if the satellite retrieval is not aware of this perturbation, the spectroscopic forward model error ϵF amounts to ϵF=(R⋅Fsat)(τper)-(R⋅Fsat)(τ), where (R⋅Fsat) represents the convolution of the reflectance by the satellite's ISRF (Fsat). The forward model error ϵF results in the XCH4 retrieval error ΔcF to be evaluated.

Figures  and  reveal variability in Δτ derived from the two different FTS measurements. Typically, the fitting residuals are larger for wetter than for dryer days. To take into account the dependence on water vapor within the ensemble, the perturbation Δτ for each simulated scene is estimated by interpolating linearly between the perturbations derived from the 50 FTS measurements Δτ(XH2O), where the interpolation variable is the total column water vapor concentration XH2O. The effect of the different viewing geometries is implicitly taken into account by attributing the spectroscopic perturbation to the vertical absorption optical thickness. Figures  and  show how XH2O and the air mass factor (AMF) vary among our trial ensemble. AMF for the satellite geometry is defined as AMFsat=1cos⁡αsat+1cos⁡θsat=1cos⁡αsat+1, while the AMF for the ground-based FTS measurements is defined as AMFgb=1cos⁡αgb. The satellite soundings are assumed nadir-viewing (θsat=0∘) with solar zenith angles up to αsat=70∘, i.e., AMFsat ranges between 2 and 3.9. The XH2O range covered by the FTS measurements is reasonably large (factor 14 between the low and the high value) that we are confident extrapolating to the actual XH2O value of the simulated scene. Dependencies of Δτ on other geophysical variables such as the CH4 and CO2 concentrations are neglected, in particular since these concentrations show comparatively little variability in the atmosphere.

Additionally, three processing steps are carried out. First we determine a small spectral shift between the ground-based and the satellite spectra by comparing the FTS transmittance Tgb to simulated satellite soundings at very high instrument resolution. Second, all the FTS measurements are interpolated to the same spectral grid with a resolution of 0.007 cm-1. Third, to avoid spurious large values of Δτ in the vicinity of optically thick absorption lines (Tgb→0 in Eq. ), we adopt a minimum for Tgb equal to the 1-σ noise level of the FTS spectra.

This section discusses the spectroscopic XCH4 retrieval errors (ΔcF) for the three retrieval configurations (SW1, SW3, SW1+3) introduced in Table . Thereby, SW3 (covering SWIR3 only) can be considered representative for the S5P setup, SW1+3 (covering SWIR1 and SWIR3), and SW1 (covering SWIR1 only) are possible strategies for S5. Figures  through show the residual XCH4 retrieval errors when introducing the spectroscopic perturbation in our global trial ensemble covering 1 day in each of the following months: January, April, July, and October, respectively. Overall the induced retrieval errors are in the range of a few tens ppb, which is relevant in the view of S5's and S5P's error budget.

The SW1 configuration (Fig. ) yields an overall overestimation of the true XCH4 over the tropics, while in midlatitudes it yields slight underestimation. The retrieval errors are consistently around 0.7 % larger in the tropics than in mid-to-high latitudes, and the latitudinal pattern of the bias persists over all seasons but is less pronounced for July when the sun is high in the sky. The observed latitudinal correlation appears driven by the dependence of the AMF on latitude and season. Similar patterns have been detected in real XCH4 retrievals from SCIAMACHY's SWIR1 band though SCIAMACHY exhibited much coarser spectral resolution than the soundings simulated here. , for example, assume a latitudinal and monthly bias correction for SCIAMACHY XCH4 to reconcile their source estimates driven by the satellite retrievals and by in situ flask samples. The SW3 configuration (Fig. ) yields XCH4 errors that are spatially and temporally variable between roughly -0.3 and 1.2 %. The error patterns are less correlated with the variation in AMF but tentatively correlate with the variation of total column water vapor XH2O. Persistently dry scenes such as the desert areas show very small XCH4 errors while the seasonally humid midlatitudes reveal regionally and seasonally variable errors. The tropics, however, show overall small variability of spectroscopy-induced XCH4 errors. The combined configuration SW1+3 (Fig. ) yields XCH4 error patterns that combine the characteristics observed for SW1 and SW3. The latitudinal dependence of residual errors shows up through a general overestimation of XCH4 in the tropics. In the midlatitudes, a pronounced dependence on the water vapor column overwrites the latitudinal signal.

To illustrate the dependence of the XCH4 errors on XH2O, Fig.  shows the correlation between the simulated errors and the water vapor content of the scene. The correlation confirms the above observation that SW1 yields XCH4 that is less affected by interference from XH2O than SW3 but still dry scenes over Siberia and humid ones over the tropics correlate with XCH4 errors. SW3 retrievals, however, suffer from a strong interference from water vapor, which results in underestimation of XCH4 for very dry scenes, an increasing overestimation for increasingly humid case and then, a decreasing interference from very humid cases. The complicated structure of overlapping CH4 and H2O absorption lines in SWIR3 (Fig. ) renders such interferences likely. Their detailed mapping on XCH4 retrieval errors, however, largely depends on the choice of the spectral windows and the spectral resolution of the instrument. The SW1+3 retrievals correlate with water vapor abundances for dry and moderately humid cases but show less dependence on very humid conditions.

These results are consistent with the current status of CH4 and H2O spectroscopy in HITRAN-2008/2012. For both SWIR3 and SWIR1, the situation is very challenging for line-shape parameters, namely line broadening. The SWIR3 region being more intense, and given the large number of CH4 and H2O lines in this region, satellite retrievals from SWIR3 are more affected by air-broadening errors than retrievals from SWIR1. A second reason that may explain the differences between SWIR1 and SWIR3 is that, for SWIR1, there are dedicated studies providing effective Voigt line-shape parameters which lead to the smaller transmittance residuals shown in Fig.  compared to Fig. .

The goals of Sentinel 5 and the Sentinel 5 Precursor concerning XCH4 retrievals demand a total accuracy better than 2 % (around 30 ppb) in order to allow for successful source and sink estimates on regional and seasonal scales . Uncertainties due to noise are expected to be in the range of 0.1 % (around 2–3 ppb). Forward model errors are present due to imperfect correction of light-path modification driven by particle scattering . The direct consequence is that additional forward model errors (e.g., due to spectroscopic deficiencies) can jeopardize the desired performance. Our assessment estimates such spectroscopy-induced XCH4 retrieval errors for a global and seasonal ensemble of simulated S5- and S5P-like satellite soundings.

The key assumption of our approach is that a realistic spectroscopic perturbation can be derived from spectral fitting residuals of a ground-based, direct-sun viewing FTS. This assumption can be criticized in two ways: (1) the FTS fitting residual contains only that part of the spectroscopic errors that cannot be accounted for through the free parameters of the FTS fit, i.e., only the part of the spectroscopic errors that are in the null-space of the FTS retrieval; (2) the fitting residual contains errors due to other sources than spectroscopy. While flaw (1) would generate overly optimistic XCH4 errors, flaw (2) would generate overly pessimistic error patterns or an attribution to the wrong error sources. Since the FTS operates at a spectral resolution that allows for fully resolving the atmospheric absorption lines, we expect flaw (1) to be small. Flaw (2) is battled by using an FTS instrument and data reduction methods with demonstrated state-of-the-art performance. Ground-based FTS records such as those exploited here, have been used in the past to evaluate spectroscopic parameters e.g.,.

Translating the ground-based FTS fitting residuals into our satellite sounding ensemble, we consider dependencies on the air mass factor and atmospheric water vapor content but neglect dependencies on other variables such meteorological variables or the CH4 abundance itself. This choice renders parameter space treatable and largely follows previous studies that found water vapor interferences and latitudinal biases (potentially driven by viewing geometry dependencies) to be the dominating error patterns in XCH4 from space-borne sensors.

However, our study only examines the standard configurations currently foreseen for CH4 retrievals from S5 and S5P. The residual spectroscopic errors found here might be mitigated by selecting narrower spectral windows to avoid spectroscopic interferences. For example, we conducted a sensitivity study that omits the CH4 Q-branch in SWIR-1 from the retrievals. The Q-branch (at about 6005 cm-1) consists of a manifold of densely spaced absorption lines that are hard to separate in order to determine spectroscopic parameters and line shapes. Cutting the Q-branch, however, shifts the residual XCH4 errors in the SW1 configuration to negative values (underestimation), but the range of errors is not reduced substantially. A further strategy to avoid H2O absorption interfering with the targeted CH4 lines could be to retrieve the vertical profile of H2O instead of the total column. The retrieved H2O profile would be unrealistic, but the retrieval would gain freedom to compensate wrong H2O spectroscopy by vertical oscillations. Since H2O is not the target parameter a wrong H2O profile shape would do no harm to S5 and S5P's goal to accurately estimate CH4 concentrations. Since such an assessment would imply major changes to our inverse method, we defer it to future studies.

Our retrieval simulations indicate that the spectroscopy-induced XCH4 retrieval errors are significant, both in magnitude and in their spatiotemporal correlation structure. While retrievals from the SWIR1 band (SW1) show a moderate correlation with latitude and water vapor, XCH4 retrievals from SWIR3 suffer from interferences with water vapor absorption. The observed correlated error patterns generally amount to a few tens ppb, which would jeopardize the usefulness of the XCH4 retrievals for inverse modeling of sources/sinks at the surface.