  We utilise ground-based, balloon-borne and satellite climatology data to
reconstruct site and season-dependent vertical profiles of precipitable water
vapour (PWV). We use these profiles to solve radiative transfer through the
atmosphere, and derive atmospheric brightness temperature ($T_{\rm atm}$) and
optical depth ($\tau$) at centimetre wavelengths.
  We validate the reconstruction by comparing the model column PWV with
photometric measurements of PWV, performed in clear sky conditions pointed
towards the Sun. Based on the measurements, we devise a selection criteria to
filter the climatology data to match the PWV levels to the expectations of the
clear sky conditions.
  We apply the reconstruction to the location of a Polish 32-metre radio
telescope, and characterise $T_{\rm atm}$ and $\tau$ year-round, at selected
frequencies. We also derive the zenith distance dependence for these
parameters, and discuss the shortcomings of using planar, single-layer, and
optically thin atmospheric models in continuum radio-source flux-density
measurement calibrations.
  We obtain PWV-$T_{\rm atm}$ and PWV-$\tau$ scaling relations in clear sky
conditions, and constrain limits to which the actual $T_{\rm atm}$ and $\tau$
can deviate from those derived solely from the climatological data.
  Finally, we suggest a statistical method to detect clear sky that involves
ground-level measurements of relative humidity. Accuracy is tested using local
climatological data. The method may be useful to constrain cloud cover in cases
when no other (and more robust) climatological data are available.
