Spectral models, CCF maps, and S/N maps of ¹²CO, H₂O, and both species together. The left panels show the continuum normalized model spectra. Wavelengths covered by the CRIRES⁺ K2166 setting used in this work are indicated by the gray shaded area. The middle panels illustrate the CCF maps. The spectral signal from WASP-178b’s atmosphere can be identified as a diagonal trail. The expected RV evolution as a function of orbital phase is indicated by the yellow dashed lines. The right panels show the S/N maps. The expected position of the planetary signal is indicated by the yellow dashed lines. We show the CCF maps and S/N maps corresponding to two consecutive runs of SYSREM, which is the number of iterations used in the retrieval in Sec. 5.