  The HI 21cm absorption line is masked by bright foregrounds and systematic
distortions that arise due to the chromaticity of the antenna used to make the
observation coupling to the spectral inhomogeneity of these foregrounds. We
demonstrate that these distortions are sufficient to conceal the 21cm signal
when the antenna is not perfectly achromatic and that simple corrections
assuming a constant spatial distribution of foreground power are insufficient
to overcome them. We then propose a new physics-motivated method of modelling
the foregrounds of 21cm experiments in order to fit the chromatic distortions
as part of the foregrounds. This is done by generating a simulated sky model
across the observing band by dividing the sky into $N$ regions and scaling a
base map assuming a distinct uniform spectral index in each region. The
resulting sky map can then be convolved with a model of the antenna beam to
give a model of foregrounds and chromaticity parameterised by the spectral
indices of the $N$ regions. We demonstrate that fitting this model for varying
$N$ using a Bayesian nested sampling algorithm and comparing the results using
the evidence allows the 21cm signal to be reliably detected in data of a
relatively smooth conical log spiral antenna. We also test a much more
chromatic conical sinuous antenna and find this model will not produce a
reliable signal detection, but in a manner that is easily distinguishable from
a true detection.
