  Many recent models consider the structure of individual interstellar medium
(ISM) clouds as a way to explain observations of large parts of galaxies. To
compare such models to observations, one must understand how to translate
between surface densities observed averaging over large (~kpc) scales and
surface densities on the scale of individual clouds (~pc scale), which are
treated by models. We define a "clumping factor" that captures this translation
as the ratio of the mass-weighted surface density, which is often the quantity
of physical interest, to the area-weighted surface density, which is observed.
We use high spatial resolution (sub-kpc) maps of CO and HI emission from nearby
galaxies to measure the clumping factor of both atomic and molecular gas. The
molecular and atomic ISM exhibit dramatically different degrees of clumping. As
a result, the ratio H2/HI measured at ~kpc resolution cannot be trivially
interpreted as a cloud-scale ratio of surface densities. HI emission appears
very smooth, with a clumping factor of only ~1.3. Based on the scarce and
heterogeneous high resolution data available, CO emission is far more clumped
with a widely variable clumping factor, median ~7 for our heterogeneous data.
Our measurements do not provide evidence for a universal mass-weighted surface
density of molecular gas, but also cannot conclusively rule out such a
scenario. We suggest that a more sophisticated treatment of molecular ISM
structure, one informed by high spatial resolution CO maps, is needed to link
cloud-scale models to kpc-scale observations of galaxies.
