Schematic illustration of the random overlap method. The original k-distributions of H₂O and CO are shown in panel a), with the combined k-coefficients shown in panel b) calculated using Eqs. (11) and (12) assuming ζ_H2O = 0.9 and ζ_CO = 0.1. Without resorting and rebinning (RO) the k_xy,lm-coefficients with corresponding weights w_xy,lm are used directly. With resorting and rebinning (RORR) the combined k-coefficients in panel b) are resorted, as shown in panel c), and then rebinned down to a smaller number of k-coefficients, as shown in panel d).