Disk structures as proposed by Banzatti et al. (2018) (left) and CO vibrational ratio v2∕v1 and emitting radius from near-infrared CO spectra of Herbig stars used for comparison with models in this work (right, see details in Sect. 2). The three groups from Banzatti et al. (2018), are shown in different colors: group II in magenta, high-NIR group I in green, low-NIR group I in blue. Disks where F_NIR is not available are marked in black. We mark two regions that are used for comparison with models: disks that have CO inside 5 AU, which show a low vibrational ratio (group II and high-NIR group I, bottom left corner), and disks that have CO only outside of 5 AU, which show high vibrational ratios (low-NIR group I, top right corner).