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Red supergiants (RSGs) are evolved massive stars in a stage precedingcore-collapse supernova. The physical processes that trigger mass loss in theiratmospheres are still not fully understood. Based on observations of $\alpha$Ori, a new semi-empirical method to add a wind to hydrostatic model atmospheresof RSGs was recently developed. We use this method of adding a wind to a MARCSmodel atmosphere to compute synthetic observables, comparing the model tospatially resolved interferometric observations. We present a case study tomodel published data of HD 95687 and V602 Car obtained with VLTI/AMBER. Wecompute model intensities, spectra and visibilities for different mass-lossrates using the radiative transfer code Turbospectrum. The models are convolvedto match the different spectral resolutions of the VLTI instruments, studying awavelength range of $1.8-5\,\mathrm{\mu m}$ corresponding to the $K$, $L$ and$M$-bands for GRAVITY and MATISSE data. We compare the model spectra andvisibilities with the published VLTI/AMBER data. The synthetic visibilitiesreproduce observed drops in the CO, SiO, and water layers that are not shown invisibilities based on MARCS models alone. For the case studies, we find thatadding a wind to MARCS with simple radiative equilibrium dramatically improvesthe agreement with the visibilities and the spectra. Our results reproduceobserved extended atmospheres up to several stellar radii. This paper shows thepotential of our model to describe extended atmospheres in RSGs: it canreproduce the shapes of the spectra and visibilities with better accuracy inthe CO and water lines than previous models. The method can be extended toother wavelength bands for both spectroscopic and interferometric data. Weprovide temperature and density stratifications that succeed for the first timein reproducing observed interferometric properties of RSG atmospheres.

The effect of winds on atmospheric layers of red supergiants I. Modelling for interferometric observations