The dynamics of molecular clouds is characterized by supersonic random motions in the presence of a magnetic field. We study this situation using numerical solutions of the three-dimensional compressible magneto-hydrodynamic (MHD) equations in a regime of highly supersonic random motions. The non-LTE radiative transfer calculations are performed through the complex density and velocity fields obtained as solutions of the MHD equations, and more than 5x10^5 synthetic molecular spectra are obtained. We use a numerical flow without gravity or external forcing. The flow is super-Alfvenic and corresponds to model A of Padoan and Nordlund (1997). Synthetic data consist of sets of 90x90 synthetic spectra with 60 velocity channels, in five molecular transitions: J=1-0 and J=2-1 for 12CO and 13CO, and J=1-0 for CS. Though we do not consider the effects of stellar radiation, gravity, or mechanical energy input from discrete sources, our models do contain the basic physics of magneto-fluid dynamics and non-LTE radiation transfer and are therefore more realistic than previous calculations. As a result, these synthetic maps and spectra bear a remarkable resemblance to the corresponding observations of real clouds.
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