Context :

Aims : We present the atmospheric structure and the fundamental properties of the red supergiants ( RSGs ) AH Sco , UY Sct , and KW Sgr based on VLTI/AMBER observations .

Methods : We carried out spectro-interferometric observations of AH Sco , UY Sct , and KW Sgr in the near-infrared K band ( 1.92-2.47 \mu m ) with the VLTI/AMBER instrument with spatial and spectral resolutions of 3 milliarcseconds and 1500 , respectively , and compared the data to a new grid of hydrostatic PHOENIX model atmospheres .

Results : In our visibility data , we observe molecular layers of water and CO in extended atmospheres .
For a uniform disk modeling , we observe size increases at the water band centered at 1.9 \mu m of 10 % to 25 % and at the CO bandheads at 2.3-2.5 \mu m of 20 % -35 % with respect to the near-continuum bandpass at around 2.20 \mu m. Our near-infrared spectra of AH Sco , UY Sct , and KW Sgr are well reproduced by the PHOENIX model atmospheres .
The continuum visibility values are consistent with a limb-darkened disk as predicted by the PHOENIX models .
However , the model visibilities do not predict the large observed extensions of the molecular layers .
Comparing the continuum visibility values to PHOENIX models , we estimate the Rosseland-mean photospheric angular diameters of AH Sco , UY Sct , and KW Sgr to be 5.81 \pm 0.15 mas , 5.48 \pm 0.10 mas , and 3.91 \pm 0.25 mas , respectively .
Together with the distance and the spectro-photometry , we calculate radii of 1411 \pm 124 R _ { \odot } for AH Sco , 1708 \pm 192 R _ { \odot } for UY Sct , and 1009 \pm 142 R _ { \odot } for KW Sgr and effective temperatures of 3682 \pm 190 K for AH Sco , 3365 \pm 134 K for UY Sct , and 3720 \pm 183 K for KW Sgr .

Conclusions : AH Sco , UY Sct , and KW Sgr exhibit extended atmospheric layers of H _ { 2 } O and CO .
The PHOENIX atmosphere models predict the spectra and the continuum visibility values , but can not reproduce the large extensions of the molecular layers .
This indicates that the opacities of the molecular bands are included , but that the model atmospheres are too compact compared to the observations .
The observed extended layers may be levitated by processes such as pulsation or convection , which are not included in the hydrostatic atmospheric models .
The location of the targets in the HR-diagram is confirmed to be close to , and possibly slightly to the right of , the Hayashi limit of recent evolutionary tracks corresponding to masses between about 20 M _ { \odot } and 40 M _ { \odot } .