  Estimates of the bulk metal abundance of the Sun derived from the latest
generation of model atmospheres are significantly lower than the earlier
standard values. In Paper I we demonstrated that a low solar metallicity is
inconsistent with helioseismology if the quoted errors in the atmospheres
models (of order 0.05 dex) are correct. In this paper we undertake a critical
analysis of the solar metallicity and its uncertainty from a model atmospheres
perspective, focusing on CNO. We argue that the non-LTE corrections for
abundances derived from atomic features are overestimated in the recent
abundance studies, while systematic errors in the absolute abundances are
underestimated. If we adopt the internal consistency between different
indicators as a measure of goodness of fit, we obtain intermediate abundances
[C/H] = 8.44 +/- 0.06, [N/H] = 7.96 +/- 0.10 and [O/H] = 8.75 +/- 0.08. The
errors are too large to conclude that there is a solar abundance problem, and
permit both the high and low scales. However, the center-to-limb continuum flux
variations predicted in the simulations appear to be inconsistent with solar
data, which would favor the traditional thermal structure and lead to high CNO
abundances of (8.52, 7.96, 8.80) close to the seismic scale. We argue that
further empirical tests of non-LTE corrections and the thermal structure are
required for precise absolute abundances. The implications for beryllium
depletion and possible sources of error in the numerical simulations are
discussed.
