A simple and quick sensitivity analysis method for methane isotopologues detection with GOSAT-TANSO-FTS

Measurements of methane isotopologues can differentiate between different source types, be they biogenic (e.g. marsh lands) or abiogenic (e.g. industry). Global measurements of these isotopologues would greatly benefit the current disconnect between ‘top-down’ (knowledge from chemistry transport models and satellite measurements) and ‘bottom-up’ (in situ measurement inventories) methane measurements. However, current measurements of these isotopologues are limited to a small number of in situ studies and airborne studies. In this paper we investigate the potential for detecting the second most common isotopologue of methane (13CH4) from space using the Japanese Greenhouse Gases Observing Satellite applying a quick and simple residual radiance analysis technique. The method allows for a rapid analysis of spectral regions, and can be used to teach university students or advanced school students about radiative transfer analysis. Using this method we find limited sensitivity to 13CH4, with detections limited to total column methane enhancements of >6%, assuming a desert surface albedo of >0.3.


Introduction Global context
The impact of methane on the environment and its potential for global warming is well documented [1]. Wuebbles and hayhoe [2] state that the increasing levels of methane in the atmosphere significantly affects the levels of ozone, water vapour (in the stratosphere), hydroxyl radicals and numerous other atmospheric compounds which result from the oxidation of methane [3]. All these occurrences lead to detrimental effects on the chemistry of the atmosphere (e.g. the formation of tropospheric ozone, and the depletion of atmospheric methane sinks), as well as the absorption of infrared (iR) radiation causing atmospheric heating [3]. The total global methane budget is not currently well understood, as is exemplified by multiple contrasting theories for the stall of the global methane concentration between 2000 and 2006 after a century of increase, and then a subsequent rise from 2014 [4]. Aydin et al. [5] suggest that the drop in global methane output is due to a reduction in the fossil fuel sources of methane, through observations of global concentrations of ethane, which can be used as a global indicator of anthropogenic methane. however, in a completely contrasting view, Kai et al. [6] assert that the reduction in global methane output is in fact due to a reduction in microbial methane from the Northern hemisphere; while other authors [7][8][9] suggest that fluctuating hydroxyl radical concentrations are a potential cause of global methane variations. it is therefore important to understand how and where methane is released, and to develop more sophisticated methods of methane detection that will allow for greater understanding of the processes behind methane generation, and how they will affect the global environment.
Methane gas may be formed through multiple natural and anthropogenic processes, including microorganism decomposition of cellulose in sediments under reducing conditions, the breakdown of gas hydrates including clathrates, and thawing permafrost in arctic and subarctic conditions. Melting of the permafrost is a topic of particular concern, with the Arctic warming faster than any other part of the Earth. The Arctic, currently a minor source of methane, could become a major source over the coming century due to warming [10]. Methane emissions from the Arctic are a particularly complex issue, with up to 33% of the world's organic carbon stored within the Arctic permafrost [11], and vast reserves of methane being stored in crystalline clathrate structures [12]. Yet there is no consensus on how and when these carbon reserves will enter the atmosphere; new data and methods are required to address these uncertainties. Other important processes include; geological processes in the Earth's crust reaching the surface through features such as mud volcanoes or soil exhalation, catagenesis, metamorphism of coal and dispersed organic matter, as well as during petroleum maturation. Anthropogenic sources such as industry by-products (e.g. leaks from gas plants) and agriculture (e.g. livestock or rice paddy fields) must also be considered as being highly significant [3,13]. industrial by-products imply that fossil fuels can be detected by the type of methane gas given off by their formation and exploitation [14,15]. Towards this end many satellite missions have been focused on trying to measure fossil fuel sources using their methane emissions, including the Japanese Greenhouse Gases Observing Satellite (GOSAT) [16,17], which was designed specifically for this purpose.
Atmospheric methane consists of a number of different isotopologues (molecules that vary according to their isotopic composition), the main four being 12 Ch 4 accounting for roughly 98% of atmospheric methane, 13 Ch 4 making up roughly 1.1% of atmospheric methane and Ch 3 D, present in very small concentrations (roughly 0.06%), with all the other isotopologues present in tiny amounts. UCL

Methane isotopologues detection with GOSAT-TANSO-FTS
The ability to distinguish spectroscopically between the isotopologues of methane can potentially allow the determination of the nature of the source of methane emissions (either biogenic, thermogenic or abiogenic), by taking the ratio of the concentration of 12 Ch 4 and 13 Ch 4 isotopologues [4,18,19]. This method has been previously used effectively for in situ terrestrial studies and it is this relationship that is the focus of this study. Currently there are limited global measurements of separated methane isotopologues, the majority of measurement sites falling under the National Oceanic and Atmospheric Administration (NOAA) (www.esrl.noaa.gov/gmd/ccgg/trends_ch4/) as well as a small number of other independent organisations [4]. Based on this limited spread of measurement sites, the existence of a satellite instrument that can differentiate between methane isotopologues would expand the global knowledge of methane distributions. it has been achieved in the upper troposphere and lower stratosphere with solar occultation limb viewing instruments [20,21], and is hoped to be achieved with dedicated potential future instruments [22].

GOSAT and measuring radiance
The GOSAT-TANSO-FTS measures solar backscatter radiance, such that solar irradiance passes through the atmosphere, is reflected off the surface of the Earth, and passes back through the atmosphere where GOSAT-TANSO-FTS measures the radiance (i.e. light magnitude). As this light passes through the atmosphere, it is absorbed at specific frequencies determined by the gases the light passes through. Absorbing this light causing the atoms of the specific gas to change energy levels, these jumps are characterised by spectral lines of finite width. Knowledge of the position of spectral lines for methane (or other gases), means it is possible to calculate how much energy was absorbed by these gases, and therefore how much of this gas is in the path the light travelled through the atmosphere [23].
The radiance received at the instrument due to absorption in the Sun-Earth-GOSAT light path is determined by the Beer-Lambert law [24], expressed by the equation where i refers to the intensity of the incident radiation at wavelength λ, given an optical path of thickness x, and i 0 is the intensity of the initial incident light or radiation, C is the density of the light path (or concentration of molecules) and σ is the absorption cross section (or the likelihood of absorption by a given molecule).
A representation of the standard operations of GOSAT is identified in Fig. 1   assumes a constant density across the light path. The density of the atmosphere (C) is not constant, meaning Equation 1 must be separately applied for multiple atmospheric layers, in order to accurately measure absorption over a long distance. Larger particles in the atmosphere (e.g. aerosols) can scatter radiation away from the main light path, meaning the difference between i and i 0 is not purely due to absorption. These absorption and scattering properties vary depending on what region of the electromagnetic spectrum is being observed. Meaning that prior to attempting to measure the concentration of trace gases in the atmosphere, the most optimum portion of the electromagnetic spectrum must be identified.
The aim of this paper is to identify spectral regions where the main methane isotopologues ( 12 Ch 4 and 13 Ch 4 ) can be detected with the existing GOSAT-TANSO-FTS. Such studies are typically performed using the information content (iC) analysis method described in [25], examples of which are also reported in [26][27][28]. iC analysis is a powerful tool, but has several significant challenges associated with its use. Firstly, on its own the iC analysis cannot be used to estimate atmospheric trace gas concentration as it is an analysis method and not a full retrieval algorithm (such as in [28][29][30]). Secondly, there is a substantial step in effort required to convert the iC analysis method into a retrieval tool capable of trace gas estimation (in terms of computation, analysis methods, etc.). The current algorithms used to produce trace gas concentrations from instruments such as GOSAT-TANSO-FTS or the recently launched Sentinel-5P/Tropospheric Monitoring instrument (TROPOMi) are the results of multi-year efforts, built on experience with older instruments [e.g. the SCanning imaging Absorption SpectroMeter for Atmospheric ChartographY (SCiAMAChY) or similar]. Therefore, new research into satellite trace gas retrieval must rely on one of these wellestablished algorithms, or embark on an expensive development programme.
in this paper we propose using a simple residual radiance analysis technique to identify the suitability of GOSAT-TANSO-FTS for detecting 13 Ch 4 , and the ratio of 13 Ch 4 and 12 Ch 4 known as δ 13 C, which is based on the iC analysis method. Although the residual radiance analysis technique is not as sophisticated as the optimal estimation method (OEM) of Rodgers [25], it remains relevant in the context of trace gas detection/retrieval for its ease of use, and quick applicability. Fundamentally, the residual radiance technique is an excellent starting point for becoming familiar with the OEM, and could be an important aspect for advanced school students or university students.
The paper is structured as follows: • Abstract, Statement of Robustness and introduction (three sections); • Description of tools and methods used in study; • Outline of the results; • Discussion of methods and results; • Conclusion.

Experimental design and starting assumptions
Methane source isotopologue composition The isotopic composition of atmospheric background methane and methane sources has been studied at some length [4,8,31,32], especially the four key isotopologues 12 Ch 4 , 13 Ch 4 , 12 Ch 3 D and 13 Ch 3 D. These papers effectively describe how the ratios of methane isotopologues (often referred to as 'δ' values) can be used to identify the nature of the source. Normally the metrics δ 13 C and δD are used to define the ratio of isotopologues at the source. The δ 13 C ratio is defined as where δ 13 C is generated by taking the ratio 13 C: 12 C of the gas sample under investigation, and dividing it by a base ratio (or standard ratio) taken from the established literature known as the Vienna Pee Dee Belemnite, which then determines how far the sample in question deviates from the standard [33]. A large negative value indicates that the sample is depleted in 13  Methane isotopologues detection with GOSAT-TANSO-FTS values tend to be associated with biogenic sources of methane, while values closer to 0 are largely from industrial sources.
The methane-to-deuterium-based methane ratio is known as δD and is calculated using a similar method to the calculation of δ 13 C, this ratio divided by an established base ratio taken from the established literature is known as the Vienna Mean Standard Ocean Water. however, as stated earlier, deuterium-based methane is very rare in the atmosphere, and we decided early on to focus solely on 13 Ch 4 as opposed to Ch 3 D.
The main reason for the depletion of the heavier isotopologues in biogenic sources is due to the observation that formation of methane by microorganisms tends to discriminate against 13 C due to kinetic isotope effects (KiEs), accounting for the low δ 13 C values. Different forms of microorganisms will have different rates of KiEs, thus changing the δ 13 C values with respect to the exact source, however, the precise nature of these KiEs is still poorly understood. in addition, specific plants will vary in their 13 C signature due to differing photosynthetic enzymes, partially accounting for the range in δ 13 C values noted in microbial sources [34,35].

Radiative transfer models -SCIATRAN and ORFM
Radiative transfer models (RTMs) are a fundamental aspect of this work, and a key aspect of this study is focused on providing trace gas investigation methods for independent research. it is difficult to perform trace gas research without the use of an RTM. Developing an RTM from scratch for this project fulfils neither of the quick or simple goals, and we therefore decided to use an open source RTM.
in this study we use the SCiATRAN RTM [36], developed by the SCiATRAN working group at the institute of Environmental Physics and the University of Bremen, available from http://www.iup. uni-bremen.de/sciatran/index.html. SCiATRAN is an RTM capable of solving the radiative transfer equation using multiple numerical methods. SCiATRAN can simulate satellite solar backscatter radiative transfer in both clear-sky and aerosol-loaded conditions. SCiATRAN is versatile and can simulate numerous atmospheric effects such as clouds, fluorescence, advanced bidirectional reflectance distribution functions and others for multiple geometry types. For this study, the simulations from SCiATRAN are run at a spectral resolution of 0.01 cm −1 and are convolved with a TANSO-FTS type Gaussian instrument line shape function (iLSF) of 0.27 cm −1 full width half max [16]. All simulations include multiple scattering effects, where all Mie scattering effects assume spherical particles. SCiATRAN has a significant pedigree with previous instruments such as SCiAMAChY, and has been previously used in studies relating to GOSAT previously [37].
SCiATRAN uses a climatological database derived from a two-dimensional (2D) chemistry transport model (CTM) described in [38]. All gases, temperatures and pressures are provided in the altitude range 1-95 km for 10° latitudinal bins for all months in a given year. The isotopologue profiles in SCiATRAN are identical to the Ch 4 profile included in the simulated atmosphere. The difference in abundance between Ch 4 and 12/13 Ch 4 is accounted for in the hiTRAN2016 database, which scales the isotopologue line strengths by abundance figures provided by [39]. The advantage of this method is that the complexity of adding an additional trace gas profile to the forward model is reduced, the disadvantage is that this scaling assumes that this abundance ratio is true for the whole globe (which is unlikely to be true).
Scattering is considered in SCiATRAN, both through Rayleigh scattering and aerosol-induced Mie scattering. Rayleigh scattering is not considered in this study as it is minor in the shortwave infrared (SWiR). For aerosol-related scattering SCiATRAN draws upon the LOWTRAN database [40], which can simulate multiple different aerosol types for different layers of the atmosphere. in this study we assume the standard SCiATRAN/LOWTRAN settings for aerosol loading in SCiATRAN.
The spectral line database used in this study is hiTRAN2016 [41]. hiTRAN2016 builds upon the hiTRAN2012 database, but includes an increase in the number of assigned 13 Ch 4 spectral lines, with Brown et al. [42] indicating a significant jump in the number of and accuracy of 13 Ch 4 (and 12 Ch 4 ) spectral lines in comparison to the previous hiTRAN iteration (hiTRAN 2008; [43]). hiTRAN2016 includes data from recent studies such as [44], which contain numerous additional line assignments in the spectral range of GOSAT-TANSO-FTS band 2. however, it is not suggested that there are any updates to the 13  Methane isotopologues detection with GOSAT-TANSO-FTS in addition to SCiATRAN, we also employ the Oxford Reference Forward Model (ORFM; [45]), developed at the University of Oxford, and available at http://eodg.atm.ox.ac.uk/RFM/. We do not use the ORFM in the residual radiance calculations described in the following sections, but rather to simulate atmospheric transmittance and optical depth. This is because the ORFM allows for quick and easy transmission (and absorption) calculations in all of the wavelengths of interest in this study. ORFM is not used for the residual radiance study as a 'sun' is not included in the radiance calculations, and scattering is not included.

GOSAT-TANSO-FTS
The Japanese Aerospace Exploration Agency (JAXA) launched GOSAT in 2009; GOSAT was the first satellite specifically designed to measure GhG emissions around the globe. The GOSAT project is a joint effort between the Ministry of the Environment (MOE), the National institute for Environmental Studies (NiES) and JAXA [16,46]. GOSAT originally had a 6-year lifespan, but this has since been extended. its replacement GOSAT-2 was launched in October of 2018.
The key instrument on GOSAT is the TANSO-FTS, which measures the radiance of sunlight reflected from the Earth's surface through the atmosphere in three separate bands: the main band of interest in this study is band 2 which measures radiance in the wavenumber range 5814-6410 cm −1 (1.56-1.72 μm), with a sampling interval of 0.2 cm −1 . GOSAT-TANSO-FTS has a fourth band that measures emissions spectra in the thermal infrared (TiR) between 699 and 1799 cm −1 (5.56-14.3 μm) [16,46].
GOSAT has a history of providing reliable estimates of the global distributions of methane and carbon dioxide [30,[47][48][49] since its launch. With its high spectral resolution and high signal to noise ratio (SNR), GOSAT was judged to be a good candidate for detecting methane isotopologues, and therefore prompted this investigation. There are other instruments for measuring methane isotopologues from orbit, for example, SCiAMAChY and TROPOMi. SCiAMAChY has a significantly lower spectral resolution (1.5 cm −1 ) and has been found to have poor single sounding precision. Buchwitz et al. [50] state that SCiAMAChY registers a maximum single sounding measurement precision of 30 ppbv, which is unlikely to be sufficient for the retrieval of 13 Ch 4 , where the total column concentration of 13 Ch 4 is roughly 20 ppbv. The recently launched TROPOMi is a possible candidate for methane isotopologues measurements, TROPOMi contains a push-broom spectrometer and sacrifices spectral resolution (0.45 cm −1 ) for much increased SNR. TROPOMi is likely to be investigated in the future for methane isotopologue detection.

Study structure and methods
The following subsection discusses the structure of the research study. The key aims are to show the following under realistic atmospheric conditions: a) The optimal regions in bands 2 and 4 of the GOSAT-TANSO-FTS for 13 Ch 4 detection. b) Measurable changes in 13 Ch 4 spectral lines over and above the background contaminating gases, and GOSAT-TANSO-FTS instrument noise.
c) The effects of background contaminating gases on any measurable changes.

Spectral region identification
The first step of this study is to make an initial assessment as to where the least contaminated regions for 13 Ch 4 may be found in the SWiR and TiR. The strongest absorption lines for methane in the SWiR are present within the wavebands at 1.6 μm and 2.3 μm [42]. however, the GOSAT-TANSO-FTS sensitivity to methane is limited to 1.6 μm, in band 2. in the TiR region there is a broadband methane absorption feature at 7.7 μm, which is covered by band 4 of TANSO-FTS. We therefore set-up a simulation scenario with ORFM in order to pick out the maximum absorption points for the 13  Methane isotopologues detection with GOSAT-TANSO-FTS interferometer for passive atmospheric sounding (MiPAS) retrievals [51]. An example of the atmospheric profiles of three gases from this model is shown in Fig. 2.
GOSAT-TANSO-FTS measures the column average density of methane and carbon dioxide (XCh 4 , XCO 2 ); therefore, using the pressure profiles captured in the University of Leicester (UoL) MiPAS profile, the column-averaged densities can be calculated.
The strongest absorption regions of the methane isotopologues are then investigated in order to gain further insight into the influence of contaminant gases on the isotopologues. The ORFM includes the options to simulate absorption as well as radiance, thus giving some insight into the presence of spectral lines of interest. The conditions required to calculate a typical 13 Ch 4 atmospheric absorption profile are specified in Table 1.

Detecting changes in the 13 CH 4 signal
Background simulated radiance values (containing radiance from the main contaminating gases), are subtracted from the radiances generated from a scenario with elevated concentrations of methane. if this calculated residual difference is greater than the noise radiance known as the noise equivalent delta radiance (NEDL) then it suggests that GOSAT-TANSO-FTS could detect this change in methane concentration. This is known as the residual radiance technique, and has been  Volume mixing ratio profiles of the main gases of interest Ch 4 , h 2 O and CO 2 in ppm from 0-120 km altitude [51], adapted from [27].  [52,53] as an effective technique for assessing whether changes in concentrations of trace gases can be detected. Roberts et al. [53] state that spectral residuals are often the first step in full atmospheric inversions. Following the method proposed by [53], the residual radiance technique is used to determine the atmospheric conditions when isotopologue retrieval may be possible. The key question to answer is which combination(s) of methane concentration, water vapour concentration and surface reflectance allow for a residual radiance greater than the instrumental noise. This can be determined from the equation where F d is the detection factor, where any value above 0 suggests that some signal is detectable above the noise limit, and therefore constitutes a detection. L b is the background radiance at the wavelength of the maximum radiance λ m given reflectance A, L e is the atmospheric radiance with elevated methane concentrations (see Table 3) at the wavelength of the maximum radiance λ m given reflectance A and NEDL.
Typically, NEDL can be calculated from knowledge of instrument parameters (dark current etc.), however, these parameters are often kept secret by instrument manufacturers. According to the GOSAT-TANSO-FTS instrument manufacturers at JAXA the GOSAT-TANSO-FTS L1B product [interferograms (L1A data) are converted into radiance spectra via a Fourier transform, including some data screening routines]. They contain two separate elements: real spectra (equivalent to the radiance spectra of interest in trace gas retrieval), and imaginary spectra which are equivalent to noise from FTS theory. The implication of this is that the noise from the spectrum of a particular retrieval can be extracted from the L1B spectra. Therefore, we generate a relationship where the noise profile of GOSAT-TANSO-FTS is estimated given a radiance output from real spectra. The steps for generating this profile are as follows: Extract the real and imaginary spectra from several L1B data GOSAT-TANSO-FTS band 2 products, in order to get variation in radiance output based on the location and surface characteristics of the retrieval. Calculate the root mean square (RMS) of the off-band imaginary spectrum radiance (off-band being the region where the indium gallium arsenide detector is not sensitive to the incident radiation due to an optical band pass filter present in the instrument). This is equivalent to the inherent instrument noise, and the RMS of the on-band (where the detector is sensitive to measured radiance) real spectrum for multiple retrievals. This builds up a profile of how instrument noise varies with received radiance at the detector (dominated by shot noise). The square of the RMS imagery spectrum radiance values is then plotted against the RMS of the real spectrum radiance values; this builds up a profile of how the noise is dependent on the spectral radiance, as well as highlighting what the basic instrument noise is. This allows for a mathematical relationship to be generated, meaning that for any given particular retrieval radiance, a specific noise value can be attributed to it. Using a random selection of 400 GOSAT L1b spectra downloaded from the GOSAT Data Archive Service (https://data2.gosat.nies.go.jp/index_en.html), the relationship was calculated as where L is the received radiance (in W/cm 2 /str/cm −1 ) and C is a conversion factor from internal GOSAT units into radiance units. The value of C is available on the GOSAT data archive website in the TANSO-FTS Radiometric Conversion for Band 1-3 document (https://data2.gosat.nies.go.jp/ doc/document.html#Document). in this study the NEDL is assumed to be a constant value over the whole spectral range, and we assume that the GOSAT spectra are captured under high gain conditions. Equation 3 is based on using individual measurements, which will most likely suffer significantly from noise levels. however, as suggested by Roberts et al. [53], the NEDL can be reduced by averaging multiple spectral measurements focusing on the spectral positions with the most 13 where F d is the detection factor over an averaged number of spectral bands, n is the number of spectral bands for combination, between wavelengths a and b. in the normal operation of GOSAT there is no oversampling of measurement points, until the satellite returns to the same orbital Methane isotopologues detection with GOSAT-TANSO-FTS path (i.e. only one spectrum is captured per sample point). in this case the method proposed in Equation 5 cannot be used, as repeat measurements are captured under different conditions. however, Kuze et al. [54] describe non-standard operational modes, one of which includes three repeat measurements of the same point for 'sun glint and limited calibration and validation site observations'. Although not all GOSAT data will be captured in this way, for simulation purposes, it is justified to investigate the effects of averaging three concurrently captured spectra. indeed, GOSAT has a 'targeted observations' mode, where registered researchers can request observations of specific sites, implying that a large number of concurrently captured spectra could be obtained with this method. The exact details of this mode are not published, and are therefore not modelled in this study. Note that the method described in Equation 5 assumes that errors between spectral points are uncorrelated.
The sensitivity of any 12 Ch 4 and 13 Ch 4 absorption bands to interfering trace gases and different reflectance conditions must also be considered; the methane absorption windows in the SWiR are typically heavily influenced by water vapour, and therefore any absorption by 13 where S f is the sensitivity factor, L res (W s , A) is the residual radiance between background and elevated methane conditions at standard atmospheric conditions between wavelengths, a and b, L res (W e , A) is the residual radiance between background and elevated methane conditions with elevated water vapour concentrations between the wavelengths, a and b, and n is the number of spectral measurements considered. Note that this method applies to any desired target and interfering species.
it is important to define appropriate atmospheric scenarios in order to determine feasible detection factors, with the key factors being methane concentration in the atmospheric profile and surface reflectance. Numerous total column retrieval methods are based on the 'scale' method, where the total column concentration is scaled rather than individual atmospheric layer concentrations modified. Therefore, a range of total column scale factors on which to calculate residuals are specified, appropriate to real world scenarios. The maximum total column XCh 4 values observed from GOSAT tend to be roughly 1900 ppb [48], equating to a column scaling of 10% (w.r.t. to the MiPAS profile). Very large methane values (>1900 ppb) have been observed by GOSAT in fire affected regions [48], suggesting that although >1900 ppb values are possible, they will be found in unique circumstances.
The second key factor, reflectance, can be determined using the online database created by UCL and Noveltis under contract to the European Space Agency (ESA) called 'A surface reflectance Database for ESA's earth observation Missions (ADAM)' available at http://adam.noveltis.com/ [55]. ADAM predicts that the expected Earth's surface reflectance values at 1600 nm range from 0.1 for densely vegetated areas, to 0.6 for desert regions (e.g. in the United States or the Sahara).
Based on this range of values, a series of simulation conditions and scenarios were generated as specified in Table 2.
Applying to GOSAT-TANSO-FTS L1B spectra The final step in this process is to determine whether or not the changes shown in the results from the section Detecting changes in the 13  Methane isotopologues detection with GOSAT-TANSO-FTS spectra as closely as possibly by: 1) Using solar zenith angles and instrument angles identified in the L1B data. 2) Using the geolocation of data capture to inform as to which UoL MiPAS model atmosphere to use. 3) identify surface reflectance values by fitting reflectance values in 0.001 steps linearly to the synthetic spectra sections until the RMSE difference between the synthetic spectra and the L1B spectra were at a minimum. 4) Convolved the synthetic spectra with the GOSAT instrument line shape model available on the data archive service, and resampled to a 0.2 cm −1 grid using a 'Matlab' spline interpolation function. 5) Applied a linear shift to the x axis of the L1B spectra, as the wavenumber axis on TANSO-FTS is variable. The magnitude of the linear shift is defined by wavelength differences between large spectral peaks found in both simulated and measured spectra.
Based on these conditions, direct comparisons between synthetic spectra and L1B spectra were made over known regions of 13 Ch 4 activity in the SWiR spectrum. Several hundred L1B data points from June in 2016 were used in order to provide a wide range of atmospheric and surface conditions.

Results
Absorption assessment SWIR Using the atmospheric conditions specified in Table 1, ORFM was used to focus on the 1600-1700 nm region. Figure 3 indicates that it will be challenging to resolve 13 Ch 4 absorption lines in this spectral region, suggesting that pinpointing 13 Ch 4 absorption above background gases will be difficult. The strongest/most dense 13 Ch 4 lines appear to be at 1658-1659 nm and 1670-1671 nm. Focusing on these two spectral regions, the optical depth is explored to determine the effect of background absorbers at these specific wavelengths. Figure 4 makes clear that both of the 13 Ch 4 spectral regions indicated have similar optical depth values to those of all of the remaining gases, implying that the majority of absorption in these spectral regions is due to 13 Ch 4 . however, the spectral line in the 1658-1659 nm wavelength range clearly shows the least interference from background contaminating gases, therefore suggesting that it is more suited for    Methane isotopologues detection with GOSAT-TANSO-FTS retrieval. in spite of this, it is obvious that the optical depth of the 13 Ch 4 lines in this region is very low, and it will therefore be challenging to detect any changes to 13 Ch 4 in this wavelength range.

TIR
Focusing on the TiR band of GOSAT, we perform a repeat analysis of the SWiR. Comparing the strength of 13 Ch 4 absorption in the TANSO-FTS TiR wavelength range shown in Fig. 5 against that in the SWiR shows a number of striking differences, primarily in the magnitude of the absorption. With the strongest of the 13 Ch 4 TiR lines having absorption strengths ×40 of their SWiR equivalents. Despite this, background interference is still strong, dominated by water vapour continuum absorption. We now focus on the optical depth of two regions, the 7700-7800 nm region due to the strength of 13 Ch 4 absorption in this region, and the 8050-8150 nm range due to the lower background absorbance.
The optical depth survey shown in Fig. 6 demonstrates magnitudes far in excess of the SWiR optical depth in Fig. 4 (especially Fig. 6(a), where the atmosphere is opaque), but as shown in Figs 5 and 6, the background interference on the 13 Ch 4 signal is significant, with only minor impacts from the 13 Ch 4 spectral lines. This leaves us with the unenviable position of small optical depth but low background interference in the SWiR, and high optical depth but high levels of interference in the TiR. Figure 6 suggests that 12 Ch 4 and other background gases will dominate the residual radiance method for the TiR. Therefore, for this reason, and because measurements in the TiR are often more uncertain than SWiR measurements, exemplified in multiple studies [56][57][58], we decided to focus on the SWiR in this study. in addition, it has been shown that the SNR on the methane absorption regions in GOSAT are significantly lower than in the SWiR [56,59], suggesting that the

Methane isotopologues detection with GOSAT-TANSO-FTS
TiR is not ideal for methane retrieval with GOSAT. TiR instruments are heavily based on measuring thermal contrast between atmospheric layers, and because of the lack of such contrast in the lower troposphere, therefore have limited sensitivity near the surface [60,61]. This suggests that measurements in the SWiR are far more likely to capture methane fractionation at the surface than in the TiR. There are cases with global scenes with high thermal contrast, which will allow for sensitivity to the surface for TiR instruments, however, we believe that the low SNR of TANSO-FTS band 4 is the more important issue, as opposed to surface sensitivity.

CH 4 detectability under standard conditions
Based on the simulation conditions specified in Table 2, consideration is given as to whether or not the individual peaks highlighted in Fig. 4 will exceed the NEDL. Figures 7 and 8 show example results for two different surface albedos, for all the proposed methane concentration levels.

Figure 7
Residual radiance plots based on the simulation conditions highlighted in Table 3

Methane isotopologues detection with GOSAT-TANSO-FTS
The results in Figs 7 and 8 suggest that detecting changes in concentration of 13 Ch 4 using individual peaks is unlikely to succeed, with only the highest methane concentrations at the highest albedo levels giving a positive detection and all other residual radiance calculations falling below the NEDL line. however, if we assume the GOSAT sampling pattern which takes three concurrent measurements of the same area [54], by applying Equation 5, and using the mean of 13 Ch 4 residual radiance peaks, the NEDL is reduced by √3. These are summarised in Table 3.
Considering the results outlined in Table 3 it is clear that the feasibility of detecting any change in 13 Ch 4 concentration above the NEDL is going to be difficult. The results indicate that the minimum requirements for measuring 13 Ch 4 concentration with any certainty are a methane source of at least 10% higher concentration than background total column value, with a high surface albedo of 0.3. Although such a combination of conditions is possible, it would likely be limited to wildfire regions such as [48]. Note that the detection factors between the two regions of interest are very similar.
We note in the section GOSAT and measuring radiance that hiTRAN2016 includes an intensity adjustment for methane isotopologues that accounts for natural atmospheric abundance. We now investigate if the detection factors indicated in Table 3 change, if we assume the standard δ 13 C value is −70‰ as opposed to 0‰. To achieve this, we modified the isotopologues intensity in hiTRAN2016, by assuming Vienna Pee Dee Belemnite is 0.0010326 as opposed to 0.0011031. Then we reran the scenarios shown in Table 2; the results for the albedo = 0.3 case are shown in Fig. 9.   Figure 9 is interesting because it shows that the 13 Ch 4 peak at 1658.6 nm is highly sensitive to changes in the assumed δ 13 C value, to the point where changes of the methane column concentration has practically no impact on the residual radiance. While the spectral lines at 1670.4 is not as sensitive to the change in δ 13 C value, and as indicated in Table 4, actually shows an increase in the magnitude of the detection factors.
The hiTRAN2016 database suggests that the 13  in addition to the simulations for the δ 13 C values of 0‰ and −70‰, we also performed an analysis for δ 13 C values of −35‰. Based on the detection factors for the range of δ 13 C value shown in this study, we can plot these variables and determine the conditions where GOSAT can detect differences in δ 13 C values. Tables 3 and 4, and given similar results from an analysis of δ 13 C values of −35‰. We can plot a relationship between the detection values and the surface albedo for a given δ 13 C value.

Figure 9
As Figs 7 and 8, with surface albedo increased to 0.3, assuming the standard δ 13 C value is −70‰ as opposed to 0‰.  Methane isotopologues detection with GOSAT-TANSO-FTS Figure 10 is interesting as it shows that the 1658 nm band has more sensitivity to changes in surface reflectance, and total column methane concentration than the 1670 nm band. But only in the case where δ 13 C is assumed to be equal to zero. For the other δ 13 C cases shown in Fig. 10, there are no examples where the detection factor is greater than 0. For the 1670 nm band, although the detection factors are lower in magnitude, the sensitivity to changes in the δ 13 C are minor. These results imply (focusing on the 1670 nm band), that given a significant enhancement in the total methane column, and a high enough surface reflectance, it may be possible to detect changes in the δ 13 C of the measurement. As the detection factor can be related back to a total methane column value, δ 13 C values could be directly estimated. Assuming some knowledge of 12 Ch 4 . Figure 10 suggests that the lowest possible surface albedo of 0.35, requires an enormous methane enhancement of 8% in order to achieve a detection of !3 Ch 4 , while the highest surface albedo of 0.6 requires an enhancement of 5% or 6%.
The required surface conditions to achieve the above values are not common. Using the aforementioned ADAM dataset (http://adam.noveltis.com/), we can indicate how much of the Earth's land surface has surface albedo values of at least 0.3. The database suggests that a significant proportion of the Earth has >0.3 surface albedo. Significantly the biomass burning regions indicated in [48] have the required surface albedo, thus suggesting that in the scenarios observed in [48] it would be possible to detect 13 Ch 4 signals with GOSAT using the methods described in this paper.

CH 4 detectability under high water vapour conditions
Using Equation 6 we can interpret the potential effects of varying water vapour concentration on the spectral averaging factor, given the high water vapour concentration conditions specified in Table 3. Based on the sensitivity factors indicated in Table 5, it is clear that both of the spectral bands we investigate in this paper are affected by the increase in loading of water vapour to some degree. The 1658 nm band is affected to a far less extent than the 1670 nm band (~10%). Most likely because the 1658 nm band is narrower than the 1670 nm band. For both bands the scaling of the methane column has a negligible effect, meaning that the high methane scenarios required Table 5. Sensitivity factor for the 1658 nm and 1670 nm wavebands, assuming the low and high water vapour conditions, and a surface albedo of 0.3 specified in Table 2.
Waveband/methane scale Scale = 2% Scale = 4% Scale = 6% Scale = 8% Scale = 10%   to detect 13 Ch 4 will not be subject to water vapour errors, any more than high surface albedo scenarios. The loading of the water vapour column by 100% is not an unreasonable scenario when considering the difference between mid-latitude scenes and tropical scenes.

Comparisons with GOSAT-TANSO-FTS L1B data
The assessments outlined above are predominately based on using synthetic data; it is therefore important to determine if variations in 13 Ch 4 can occur in real measured GOSAT-TANSO-FTS L1B spectra. Based on the method described in the section Applying to GOSAT-TANSO-FTS L1B spectra, direct comparisons can be made between the synthetic data and L1B data. Figure 11 represents an interesting counter perspective to the results shown in the previous sections. Figure 11(a) shows largely good agreement between the ORFM and L1B spectra, aside from two spectral line absorption points in the L1B data, not present in the ORFM simulation [highlighted in Fig. 11(b)], possibly due to residuals not captured in the ORFM simulations. Despite this, there is very little difference between the radiances of the ORFM and L1B spectra in the highlighted portion.
however, considering Fig. 11(c), the closely matching spectra indicate a reasonable fit from the method discussed in the section 'Applying to GOSAT-TANSO-FTS L1B Spectra'. Focusing on the highlighted region in Fig. 11(c) and (d) show a variation in the radiance of the 13 Ch 4 region, suggesting potential for GOSAT measuring changes in 13 Ch 4 over background concentrations. An important point to consider is the water vapour spectral line peak at 1670.68 nm; the ORFM simulations suggest a higher concentration of water vapour in the atmosphere based on the depth of the spectral line than the L1B data. The section ' 13 Ch 4 Detectability under high Water Vapour Conditions' shows that the methane isotopologue spectral lines are heavily influenced by water vapour; therefore the lower concentrations of water vapour in the L1B spectrum, combined with the high reflectance value may allow for variation in the 13 Ch 4 concentration to become more obvious Figure 11 Comparison of simulated spectrum against GOSAT L1B data. in this particular example, the surface reflectance is 0. 33 Methane isotopologues detection with GOSAT-TANSO-FTS than suggested in the simulation studies. Therefore, in some scenarios, a high surface reflectance of at least 0.6 may not be necessary.

Discussion
The range of scenarios where 13 Ch 4 can be detected is very small. We acknowledge that this method is not as sophisticated or as accurate as a full sensitivity analysis using Rodgers' optimal estimation method. however, we argue that the benefits of the method shown in this study is its simplicity, such that a quick analysis can be performed by a lay person interested in the subject area, or it could be used to teach advanced school students, or early year university students. indeed, scientists interested in quickly determining the sensitivity of a trace gas species could use this method as a quick first step, before committing to further analysis. The most complex part of this study is the RTM, and here we use two well-established RTMs to achieve the goals of this study. RTM development is a far more complex task than developing a retrieval algorithm, and independently developing an RTM would no longer make this study simple or quick. There are significantly more open source RTMs available than retrieval algorithms, this variety in RTMs mean that there should be sufficient ranges in solutions and methods that allow for characterisation of any errors in the forward models.
The detection analysis outlined in the section Detecting changes in 13 Ch 4 signal is based on the total column of methane detection of δ 13 C, this method is potentially limiting to a degree since this does not take into account KiEs in the upper troposphere and lower stratosphere due to the destruction of methane. however, as 13 Ch 4 concentration is low, and the KiE factors are less than those at the surface, such factors are unlikely to have a significant impact on the results. in addition, atmospheric air currents interfere with the total column and thus will dampen the signal of δ 13 C in the total column, as opposed to in situ measurements. There are currently no studies that investigate this effect, but we can assume that the δ 13 C differences between source types will be even smaller.
Other error sources include the spectroscopy and the forward model. The hiTRAN2016 database in combination with the SCiATRAN forward model assumes a Voigt profile for all methane lines in the GOSAT spectral sensitivity ranges. The Voigt profile has been generally assumed for methane spectral regions in the past, however this shape is now acknowledged to be no longer sufficient [41]. The current hiTRAN2016 database does not include the parameters necessary to estimate non-Voigt line shapes for methane; however, it is anticipated that future updates will include these. We therefore accept that there will be spectroscopic errors present in this study. Following on from the hiTRAN database, the next largest error sources are likely to arise from SCiATRAN, generated from inaccuracies in recreating the absorption or radiance spectra from a given set of atmospheric inputs.
The metrics F d and S f give a useful indication of the feasibility of detecting 13 Ch 4 , and can be used to further inform a user about the feasibility of detection over a wider variety of atmospheric and surface conditions than shown in this study. however, caution must be applied since, as highlighted in Table 5, the influence of water vapour on the 13 Ch 4 peaks might well lead to false positive values of F d , and therefore create an incorrect inference of isotopologues detection.
Although we briefly looked at methane isotopologues absorption in the GOSAT TiR band, we did not investigate this in depth. This is despite the fact that the isotopologues indicated much larger optical depth than their equivalent in the SWiR. however, there is significant evidence to suggest that the spectroscopy of methane in the TiR is not nearly as advanced as that in the SWiR [62], which is important given the short wavebands used in this study. in addition to the high levels of background interference on the 13 Ch 4 spectral lines observed in Fig. 6.
An obvious next or alternative step would be to perform retrievals of the methane isotopologues using the Total Column Carbon Observing Network (TCCON, [63]). TCCON relies on solar occultation measurements as opposed to solar backscatter, and operates at a much higher SNR and spectral resolution than GOSAT. The key disadvantage to TCCON is that it is limited to a small number of sites all over the globe, and cannot be as beneficial to global studies as satellites such as GOSAT. This work has been shown in a separate study, indicating that even with the improved SNR of the TCCON instruments, there are still significant challenges with retrievals of methane isotopologues [64]. UCL  Methane isotopologues detection with GOSAT-TANSO-FTS Conclusions in this paper we investigated the potential to detect the second most common methane isotopologue ( 13 Ch 4 ) using the GOSAT-TANSO-FTS instrument. The ratio of the main methane isotopologues has been shown to be able to differentiate between different methane source types, and could be a useful tool in linking global bottom-up emissions with top-down emissions.
We use a simple and quick residual radiance method in order to investigate the benefit of such techniques, in the wider context of the more sophisticated methods based on Rodgers' optimal estimation techniques. We argue that the residual radiance technique is useful as a simple and quick method for analysing spectral regions for sensitivity to specific trace gases.
The results of this study generally suggest that detecting the second most important methane isotopologue is difficult in most circumstances, apart from unique circumstances such as large biomass burning events. Using these techniques we find that detections of 13 Ch 4 with GOSAT can only occur with surface albedos of >0.3, assuming at least an 8% enhancement in the methane total column. This total column requirement is reduced with increasing surface albedo. in the context of a world where El Nino events are likely to become more frequent, it is possible that the required conditions for 13 Ch 4 detection using this technique, may become more common.
We perform the assessment using the general assumption of δ 13 C = 0 globally as this is built into the hiTRAN databases. however, we also investigate the effects of detecting the 13 Ch 4 isotopologue using different values of δ 13 C, ranging up to −70‰. We find that the spectral lines in the 1670 nm waveband are unaffected by the change in δ 13 C, while other spectral regions are significantly affected by this change.
We also assess the suitability of the TiR region for methane isotopologues, and find that although the optical depth of 13 Ch 4 is greater than that in the SWiR region, the dominance of background trace gases, and the unknowns in the spectroscopy of the region make this region less attractive than the SWiR. Table 6 provides a table of key terms and acronyms.