Uncertainties in Atomic Data and Their Propagation Through Spectral
  Models. I
  We present a method for computing uncertainties in spectral models, i.e.
level populations, line emissivities, and emission line ratios, based upon the
propagation of uncertainties originating from atomic data. We provide analytic
expressions, in the form of linear sets of algebraic equations, for the coupled
uncertainties among all levels. These equations can be solved efficiently for
any set of physical conditions and uncertainties in the atomic data. We
illustrate our method applied to spectral models of O III and Fe II and discuss
the impact of the uncertainties on atomic systems under different physical
conditions. As to intrinsic uncertainties in theoretical atomic data, we
propose that these uncertainties can be estimated from the dispersion in the
results from various independent calculations. This technique provides
excellent results for the uncertainties in A-values of forbidden transitions in
[Fe II].
