Demonstration of the algorithm in a case study profile from IUVS observations is shown as the light blue line and the data uncertainty is the grey shading, in panel (a) together with the forward model simulation using the a priori CO₂ vertical density together with the total model uncertainty in shaded red. (b) The CO₂ number densities: the black dashed line represents the a priori, the dashed red the final vertical distribution of CO₂ number density where the fit satisfies the algorithm and Φ(λ) can be retrieved. The shaded red region is the total uncertainty, (c) The difference in percentage of the final vertical profile with the a priori and the total uncertainty, same as (b).