Testing the line-by-line forward model by fitting the CH₄ rotational line. The left hand panel shows the brightness temperatures, with the data given by circles, the smooth spline-fit to the continuum as the dotted line, and the solid grey lines showing the range of mole fractions tested. The central panel converts this to a line-to-continuum ratio relative to the smooth spline. Here, the dotted lines show the error envelope as defined in the main text. The right hand panel shows the Δχ² for the model, with dotted horizontal lines showing the 1σ and 3σ confidence limits on the results. The derived methane abundance depends upon the choice of line data, with a mole fraction of (4.3 ± 0.3) × 10^-3 assuming line intensities from Wishnow et al. (2007) (shown here) and (4.8 ± 0.3) × 10^-3 using intensities from Boudon et al. (2010).