Simulated observations of sub-millimetre galaxies: the impact of
  single-dish resolution and field variance
  Recent observational evidence suggests that the coarse angular resolution
($\sim20"$ FWHM) of single-dish telescopes at sub-mm wavelengths has biased the
observed galaxy number counts by blending together the sub-mm emission from
multiple sub-mm galaxies (SMGs). We use lightcones computed from an updated
implementation of the \galform semi-analytic model to generate $50$ mock sub-mm
surveys of $0.5$ deg$^2$ at $850$ $\mu$m, taking into account the effects of
the finite single-dish beam in a more accurate way than has been done
previously. We find that blending of SMGs does lead to an enhancement of source
extracted number counts at bright fluxes
($S_{\mathrm{850}\mu\mathrm{m}}\gtrsim1$ mJy). Typically, $\sim3{-}6$ galaxies
contribute $90\%$ of the flux of an $S_{850\mu\mathrm{m}}=5$ mJy source and
these blended galaxies are physically unassociated. We find that field-to-field
variations are comparable to Poisson fluctuations for our
$S_{850\mu\mathrm{m}}>5$ mJy SMG population, which has a median redshift
$z_{50}=2.0$, but are greater than Poisson for the $S_{850\mu\mathrm{m}}>1$ mJy
population ($z_{50}=2.8$). In a detailed comparison to a recent interferometric
survey targeted at single-dish detected sources, we reproduce the difference
between single-dish and interferometer number counts and find a median redshift
($z_{50}=2.5$) in excellent agreement with the observed value ($z_{50}=2.5\pm
0.2$). We also present predictions for single-dish survey number counts at
$450$ and $1100$ $\mu$m, which show good agreement with observational data.
