  Cosmic ray (CR) air showers, detected via the air fluorescence technique, are
reconstructed in part using functions that parameterize the longitudinal
profile of each shower. The profile parameterization yields the position of
shower maximum, X_max, which is sensitive to the incident CR particle type:
e.g. p, C/N/O, Fe or photons. The integral of the profile is directly related
to the shower energy. The Pierre Auger fluorescence reconstruction uses the
Gaisser-Hillas 4-parameter form. The HiRes group has used both the
Gaisser-Hillas form and a 3-parameter Gaussian in Age form. Historically
analytic shower theory suggested yet other forms; the best known is a
3-parameter form popularized by Greisen. Our work now uses the shower full
width half-maximum, "fwhm", and shower asymmetry parameter, "f", to unify the
parameterization of all three profile functions. Furthermore shower profiles
expressed in terms of the new parameters: (fwhm, f) have correlations greatly
reduced over Gaisser-Hillas parameters (X_0, lambda). This allows shower
profile reconstructions to add constraints (if needed) on the mostly
uncorrelated parameters (fwhm, f).
