Example of data analysis. Panel a: black curve shows the averaged EXES spectrum (over one-third of the entire slit) in the spectral range between 1327.0 and 1327.2 cm⁻¹ . The slit position is “Mars Center ♯1”, and the mean Latitude, Longitude, and Local time of the averaged spectrum are 40^∘ N, 247^∘ W, and 12h, respectively. The strong absorption due the terrestrial CH₄ is visible at 1327.074219 cm⁻¹. The red vertical bar shows the expected spectral position of the Martian CH₄ line shifted due to Doppler velocity between Earth and Mars. The black bars represent the spectral range which was used for retrieval of CH₄ mixing ratio on Mars. Panel b: black points are the same EXES spectrum as shown in panel a but focused around the expected Martian CH₄ lines. The red curve shows the local continuum established by the cubic polynomial fit. The blue points represent the spectral points used to perform the cubic polynomial fit. Panel c: black curve shows the absorption depth spectrum due to Mars atmosphere that is the EXES spectrum divided by the local continuum. The color curves are the synthetic absorption depth with various mixing ratio of the Martian CH₄ (blue: 1 ppb, light blue: 2 ppb, green: 3 ppb, orange: 4 ppb, red: 5 ppb) that is the synthetic spectrum with the Martian CH₄ divided by the one without the Martian CH₄. The one with 1 ppb of CH₄ mixing ratio (the blue one) provides the minimum cost function (i.e., the best-fit synthetic spectrum). Panel d: true CH₄ mixing ratio when the retrieved CH₄ mixing ratio is 1 ppb. The histogram is obtained from the retrieval test using simulated EXES spectra (see Sect. section 3.4). The uncertainty of this retrieval is estimated to be 2 ppb (3σ) from the histogram.