Context : Procyon is one of the brightest stars in the sky and one of our nearest neighbours .
It is therefore an ideal benchmark object for stellar astrophysics studies using interferometric , spectroscopic , and asteroseismic techniques .

Aims : We used a new realistic three-dimensional ( 3D ) radiative-hydrodynamical ( RHD ) model atmosphere of Procyon generated with the Stagger Code and synthetic spectra computed with the radiative transfer code Optim3D to re-analyze interferometric and spectroscopic data from the optical to the infrared .
We provide synthetic interferometric observables that can be validated against observations .

Methods : We compute intensity maps from a RHD simulation in two optical filters centered at 500 and 800 nm ( Mark  III ) and one infrared filter centered at 2.2 \mu m ( Vinci ) .
We constructed stellar disk images accounting for the center-to-limb variations and used them to derive visibility amplitudes and closure phases .
We computed also the spatially and temporally averaged synthetic spectrum from the ultraviolet to the infrared .
We compare these observables to Procyon data .

Results : We study the impact of the granulation pattern on center-to-limb intensity profiles and provide limb-darkening coefficients in the optical as well as in the infrared .
We show how the convective related surface structures impact the visibility curves and closure phases with clear deviations from circular symmetry from the 3rd lobe on .
These deviations are detectable with current interferometers using closure phases .
We derive new angular diameters at different wavelengths with two independent methods based on 3D simulations .
We find \theta _ { { { \sc Vinci } } } = 5.390 \pm 0.03 mas and prove that this is confirmed by an independent asteroseismic estimation ( \theta _ { seismic } = 5.360 \pm 0.07 mas .
The resulting T _ { { eff } } is 6591 K ( or 6556 K , depending on the bolometric flux used ) , which is consistent with T _ { { eff,IR } } = 6621 K found with the infrared flux method .
We find also a value of the surface gravity { log { \it g } } = 4.01 \pm 0.03 [ cm/s ^ { 2 } ] that is larger by 0.05 dex from literature values .
Spectrophotometric comparisons with observations provide very good agreement with the spectral energy distribution and photometric colors , allowing us to conclude that the thermal gradient of the simulation matches fairly well Procyon . Finally , we show that the granulation pattern of a planet hosting Procyon-like star has a non-negligible impact on the detection of hot Jupiters in the infrared using interferometry closure phases .
It is then crucial to have a comprehensive knowledge of the host star to directly detect and characterize hot Jupiters .
In this respect , RHD simulations are very important to reach this aim .

Conclusions :