  The one-point statistics of column density distributions of turbulent
molecular cloud models are investigated and compared with observations. In
agreement with the observations, the number N of pixels with surface density S
is distributed exponentially N(S)=exp(-S/S0) in models of driven compressible
supersonic turbulence. However, in contrast to the observations, the
exponential slope defined by S0 is not universal but instead depends strongly
on the adopted rms Mach number and on the smoothing of the data cube. We
demonstrate that this problem can be solved if one restricts the analysis of
the surface density distribution to subregions with sizes equal to the
correlation length of the flow which turns out to be given by the driving
scale. In this case, the column density distributions are universal with a
slope that is in excellent agreement with the observations and independent of
the Mach number or smoothing. The observed molecular clouds therefore are
coherent structures with sizes of order their correlation lengths. Turbulence
inside these clouds must be driven on the largest scales, if at all. Numerical
models of turbulent molecular clouds have to be restricted to cubes with sizes
similar to the correlation lengthscale in order to be compared with
observations. Our results imply that turbulence is generated on scales that are
much larger that the Jeans length. In this case, gravitational collapse cannot
be suppressed and star formation should start in molecular clouds within a
dynamical timescale after their formation.
