  Measurement of the global 21-cm signal during Cosmic Dawn (CD) and the Epoch
of Reionization (EoR) is made difficult by bright foreground emission which is
2-5 orders of magnitude larger than the expected signal. Fitting for a
physics-motivated parametric forward model of the data within a Bayesian
framework provides a robust means to separate the signal from the foregrounds,
given sufficient information about the instrument and sky. It has previously
been demonstrated that, within such a modelling framework, a foreground model
of sufficient fidelity can be generated by dividing the sky into $N$ regions
and scaling a base map assuming a distinct uniform spectral index in each
region. Using the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH)
as our fiducial instrument, we show that, if unaccounted-for, amplitude errors
in low-frequency radio maps used for our base map model will prevent recovery
of the 21-cm signal within this framework, and that the level of bias in the
recovered 21-cm signal is proportional to the amplitude and the correlation
length of the base-map errors in the region. We introduce an updated foreground
model that is capable of accounting for these measurement errors by fitting for
a monopole offset and a set of spatially-dependent scale factors describing the
ratio of the true and model sky temperatures, with the size of the set
determined by Bayesian evidence-based model comparison. We show that our model
is flexible enough to account for multiple foreground error scenarios allowing
the 21-cm sky-averaged signal to be detected without bias from simulated
observations with a smooth conical log spiral antenna.
