  We have used a combination of stellar population synthesis and
photoionization models to develop a set of ionization parameter and abundance
diagnostics based only on the use of the strong optical emission lines. These
models are applicable to both extragalactic HII regions and star-forming
galaxies. We show that, because our techniques solve explicitly for both the
ionization parameter and the chemical abundance, the diagnostics presented here
are an improvement on earlier techniques based on strong emission-line ratios.
Our techniques are applicable at all metallicities. In particular, for
metallicities above half solar, the ratio [NII]/[OII] provides a very reliable
diagnostic since it is ionization parameter independant and does not have a
local maximum. This ratio has not been used historically because of worries
about reddening corrections. However, we show that the use of classical
reddening curves is quite sufficient to allow this [NII]/[OII] diagnostic to be
used with confidence as a reliable abundance indicator. The cause of systematic
and random errors inherent in previous techniques are discussed, and we present
a new `optimal' abundance diagnostic method based on the use of line ratios
involving [NII], [OII], [OIII], [SII] and the Balmer lines. This combined
diagnostic appears to suffer no apparent systematic errors, can be used over
the entire abundance range and significantly reduces the random error inherent
in previous techniques. Finally, we give a recommended procedure for the
derivation of abundances in the case that only spectra of limited wavelength
coverage are available so that the optimal method can no longer be used.

Astrophysics