  Context. Current and future blind surveys for HI generate large catalogs of
spectral lines for which automated characterization would be convenient.
  Aims. A 6-parameter mathematical model for HI galactic spectral lines is
described. The aim of the paper is to show that this model is indeed a useful
way to characterize such lines.
  Methods. The model is fitted to spectral lines extracted for the 34 spiral
galaxies of the recent high-definition THINGS survey. Three scenarios with
different instrumental characteristics are compared. Quantities obtained from
the model fits, most importantly line width and total flux, are compared with
analog quantities measured in more standard, non-parametric ways.
  Results. The model is shown to be a good fit to nearly all the THINGS
profiles. When extra noise is added to the test spectra, the fits remain
consistent; the model-fitting approach is also shown to return superior
estimates of linewidth and flux under such conditions.
