(Abridged) We use the statistical tool known as the ``Spectral Correlation
Function" [SCF] to intercompare simulations and observations of the atomic
interstellar medium. The simulations considered mimic three distinct sets of
physical conditions. One of them (run "ISM") is intended to represent a mixture
of cool and warm atomic gas, and includes self-gravity and magnetic fields. For
each simulation, H I spectral-line maps are synthesized and intercompared, both
with each other, and with observations, using the SCF. We find that, when
thermal broadening is large in comparison with fine-scale turbulent velocity
structure, it masks sub-thermal velocity sub-structure in the synthesized
spectra. The H I observations we use here for comparison are of the North
Celestial Pole (NCP) Loop. None of the simulations match the NCP Loop data very
well. The most realistic sets of line profiles and SCF statistics comes from
artifically rescaling the velocity axis of run ISM. Without rescaling, almost
all velocity structure is smeared out by thermal broadening. However, if the
velocity axis is expanded by a factor of 6, the SCF distributions of run ISM an
the NCP Loop match up fairly well. This means that the ratio of thermal to
turbulent pressure in run ISM is much too large as it stands, and that the
simulation is deficient in turbulent energy. This is a consequence of run ISM
not including the effects of supernovae. We conclude that the SCF is a useful
tool for understanding and fine-tuning simulations of interstellar gas, and in
particular that realistic simulations of the atomic ISM need to include the
effects of energetic stellar winds (e.g. supernovae) in order for the ratio of
thermal-to-turbulent pressure to give spectra representative of the observed
interstellar medium in our Galaxy.Comment: 25 pages, 24 figures. ApJ Accepted (May 20). Also available at:
ftp://www.astrosmo.unam.mx/pub/j.ballesteros/Papers