Differential atmospheric dispersion is a wavelength-dependent effect introduced by Earths atmosphere that affects astronomical observations performed using ground-based telescopes. It is important, when observing at a zenithal angle different from zero, to use an Atmospheric Dispersion Corrector (ADC) to compensate this atmospheric dispersion. The design of an ADC is based on atmospheric models that, to the best of our knowledge, were never tested against on-sky measurements. We present an extensive models analysis in the wavelength range of 315-665 nm. The method we used was previously described in the paper I of this series. It is based on the use of cross-dispersion spectrographs to determine the position of the centroid of the spatial profile at each wavelength of each spectral order. The accuracy of the method is 18 mas. At this level, we are able to compare and characterize the different atmospheric dispersion models of interest. For better future ADC designs, we recommend to avoid the Zemax model, and in particular in the blue range of the spectra, when expecting residuals at the level of few tens of milli-arcseconds.
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