top-of-atmosphere low resolution irradiance.

|  | CH [ppt] 4 | H O [ppm] 2 | fraction of CH [%] 4 | noise level |
| --- | --- | --- | --- | --- |
| Value | 0; 100; 500; 1000 | 0; 10; 100 | 1; 5; 10; 50; 100 | 0.001; 0.0001 |

[Table: Table 2: Simulation parameters. Fraction of CH4 is fraction of spectra containing methane hidden in the simulation dataset.]

The AOTF/echelle instrument was modeled using the latest available calibration (Liuzzi et al., 2019; Aoki et al., 2019), considering order addition from +/ −2 nearby orders (5 total). The spectral calibration of NOMAD-SO varies because it is affected by the instrument temperature, and is provided for each individual NOMAD spectra. The 320 spectels cover the range 3056.1 cm−1 to 3080.4 cm−1 with a wavenumber step of 0.0763 cm−1. No simulation of dust has been performed. Due to the limited spectral range on a single order, about 25 cm−1, the major effect of dust and other aerosols is relatively flat baseline, which we remove at the pre-treatment of the spectra. When dust is optically thick, then non-linearity may appear that are out of the scope of this simulation. The simulation dataset consist of 12486 spectra, simulating observations of order 136 in the same configuration as the 106 solar occultations actually observed from May to December 2018. We add to the dataset a random noise with standard deviation of 0.001 and 0.0001 in order to simulate the instrumental noise (corresponding to SNR of 100 and 1000 approximately). We hide spectra containing CH4 in a fraction of the total number of spectra from 1% to 100% in a random manner. In real observation, CH4 may be spatially / temporally coherent but the number of scenarios is infinite. We feel that the random case is interesting enough to be tested. One has to note that contrarily to the previous toy model of section 4, here abundance are quantitative abundance in the atmosphere. The simulation parameters are summed up in table 2.
5.2. Detection limits We applied the psNMF method with NS = 5, which is the most promising one from the previous analysis. We compute the analysis 10 times for 10 different random noise realizations and average the results in order to present robust conclusion. We select a pure CH4 and a pure H2O spectra (noted PCH4 and PH2O) from the simulation as reference spectra.
5.2.1. Methods to analyze the results The main difference with the toy model section in 4 is that H2O and CH4 may be highly mixed in the sources. Simple correlation coefficient to pick the best source is thus not efficient enough. We propose here another approach to estimate the best source. For each estimated source ˙S:i, we analyze it as a linear mixture of PH2O and PCH4:

˙S:i = PH2O.αH2O,i + PCH4.αCH4,i
(13) This problem is called supervised detection algorithm since PH2O and PCH4 are known, contrary to the general one, presented in Eq. 5, where source spectra
are not known.

The source i∗with the maximum αCH4,i∗is selected as the best
target CH4 source, called best source hereafter.

We then propose to use three indicators of good detection :
• Fraction of the 4 main CH4 peaks detected (at 3057.7, 3063.4, 3067.2 and 3076.6 cm−1).

This is computed using the peak detection algorithm from ©Matlab on both simulation and best source with a tolerance of 2 spectels, i.e. detected peaks can be 2 spectels off the expected one.

The peak must be with a maximum amplitude larger than 1/1000 the maximum of ˙S:i∗to be considered significant.

Please note that even there are only 5 possible fraction (0, 0.25, 0.5, 0.75 and 1), since we average on 10 realizations, any number can appear.
• Mean distance to the expected center.

Mean distance in spectel between the CH4 peaks detected in the best source and the reference one.
• Abundance of CH4 in the source. αCH4 (from Eq. 13), which describes the amplitude of the CH4 peaks in the best source.
5.2.2.