“…2 of Schneider et al, 2012) as well as four spectral auxiliary microwindows containing CO 2 lines (in order to optimally estimate the temperature from the measured spectra; Schneider and Hase, 2008). We use HITRAN 2008 (High-Resolution Transmission Molecular Absorption Database) spectroscopic parameters (Rothman et al, 2009(Rothman et al, , with 2009, while for the water vapour isotopologues we use parameters that have been adjusted for the speeddependent Voigt line shape (Schneider et al, 2011b O, O 3 , N 2 O, CH 4 , HCl, and C 2 H 6 . For the constraint of the water vapour isotopologue state we construct a priori covariances for humidity and δD (S aH and S aI , respectively; see Eq.…”