  Sub-millimetre observations suggest that the filaments of interstellar clouds
have rather uniform widths and can be described with the so-called Plummer
profiles. The shapes of the filament profiles are linked to their physical
state. Before drawing conclusions on the observed column density profiles, we
must evaluate the observational uncertainties. We want to estimate the bias
that could result from radiative transfer effects or from variations of submm
dust emissivity. We use cloud models obtained with magnetohydrodynamic
simulations and carry out radiative transfer calculations to produce maps of
sub-millimetre emission. Column densities are estimated based on the synthetic
observations. For selected filaments, the estimated profiles are compared to
those derived from the original column density. Possible effects from spatial
variations of dust properties are examined. With instrumental noise typical of
the Herschel observations, the parameters derived for nearby clouds are correct
to within a few percent. The radiative transfer effects have only a minor
effect on the results. If the signal-to-noise ratio is degraded by a factor of
four, the errors become significant and for half of the examined filaments the
values cannot be constrained. The errors increase in proportion to the cloud
distance. Assuming the resolution of Herschel instruments, the model filaments
are barely resolved at a distance of ~400 pc and the errors in the parameters
of the Plummer function are several tens of per cent. The Plummer parameters,
in particular the power-law exponent p, are sensitive to noise but can be
determined with good accuracy using Herschel data. One must be cautious about
possible line-of-sight confusion. In our models, a large fraction of the
filaments seen in the column density maps are not continuous structures in
three dimensions.
