“…Figure 4 shows the scheme of the retrieval process developed in this study. The core of the inversion scheme is based on the Bayesian algorithm (Rodgers,
2000), which is widely used in non‐linear inversion problems in remote‐sensing observations of atmosphere (e.g., Grassi et al.,
2005; Jiménez‐Monferrer et al.,
2021). This method iteratively calculates new solutions based on the measurements and a priori information:
where x is a vector of retrieved parameters (CO 2 density profile, temperature profile, and a factor for flux correction, in this study), x i is the solution in the previous iteration , x i+1 is the new solution), y is a vector of measured limb profile of oxygen dayglow brightness, S e is a covariance matrix of measurement errors, x a is an a priori vector, S a is a covariance matrix of a priori information, F ( x i ) is a vector calculated by the forward model with x i (calculated vertical profile of oxygen dayglow brightness), and K i is a Jacobian matrix, that is, the partial derivative of the forward model with respect to x i , K i = ∂F/∂x i .…”