  Small-scale density fluctuations can significantly affect reionization but
are typically modelled quite crudely. Unresolved fluctuations in numerical
simulations and analytical calculations are included using a gas clumping
factor, typically assumed to be independent of the local environment. In Paper
I, we presented an improved, local density-dependent model for the sub-grid gas
clumping. Here we extend this using an empirical stochastic model based on the
results from high-resolution numerical simulations which fully resolve all
relevant fluctuations. Our model reproduces well both the mean density-clumping
relation and its scatter. We applied our stochastic model, along with the mean
clumping one and the Paper I deterministic model, to create a large-volume
realisation of the clumping field, and used these in radiative transfer
simulations of cosmic reionization. Our results show that the simplistic mean
clumping model delays reionization compared to local density-dependent models,
despite producing fewer recombinations overall. This is due to the very
different spatial distribution of clumping, resulting in much higher
photoionization rates in the latter cases. The mean clumping model produces
smaller HII regions throughout most of the reionization, but those percolate
faster at late times. It also causes a significant delay in the 21-cm
fluctuations peak and yields lower non-Gaussianity and many fewer bright pixels
in the PDF distribution. The stochastic density-dependent model shows
relatively minor differences from the deterministic one, mostly concentrated
around overlap, where it significantly suppresses the 21-cm fluctuations, and
at the bright tail of the 21-cm PDFs, where it produces noticeably more bright
pixels.

Cosmology and Nongalactic Astrophysics