  We present a model for the full-sky diffuse Galactic synchrotron spectral
index with an appropriate level of spatial structure for a resolution of 56
arcmin (to match the resolution of the Haslam 408 MHz data). Observational data
at 408 MHz and 23 GHz have been used to provide spectral indices at a
resolution of 5 degrees. In this work we make use of convolutional neural
networks to provide a realistic proxy for the higher resolution information, in
place of the genuine structure. Our deep learning algorithm has been trained
using 14.4 arcmin observational data from the 1.4 GHz Parkes radio continuum
survey. We compare synchrotron emission maps constructed by extrapolating the
Haslam data using various spectral index maps, of different angular resolution,
with the Global Sky Model. We add these foreground maps to a total emission
model for a 21 cm intensity mapping experiment, then attempt to remove the
foregrounds. The different models all display different spectral or spatial
behaviour and so each provide a useful and different tool to the community for
testing component separation techniques. We find that for an experiment
operating using a cosine aperture taper beam with a primary Full Width at Half
Maximum between 1.1 and 1.6 degrees, and the principal component analysis
technique of foreground removal, there is a discernible difference between
synchrotron spectral index models with a resolution larger than 5 degrees but
that no greater resolution than 5 degrees is required.
