  The gas and dust are spatially segregated in protoplanetary disks due to the
vertical settling and radial drift of large grains. A fuller accounting of the
mass content and distribution in disks therefore requires spectral line
observations. We extend the modeling approach presented in Williams & Best
(2014) to show that gas surface density profiles can be measured from high
fidelity 13CO integrated intensity images. We demonstrate the methodology by
fitting ALMA observations of the HD 163296 disk to determine a gas mass, Mgas =
0.048 solar masse, and accretion disk characteristic size Rc = 213au and
gradient gamma = 0.39. The same parameters match the C18O 2--1 image and
indicates an abundance ratio [13CO]/[C18O] of 700 independent of radius. To
test how well this methodology can be applied to future line surveys of
smaller, lower mass T Tauri disks, we create a large 13CO 2--1 image library
and fit simulated data. For disks with gas masses 3-10 Jupiter masses at 150pc,
ALMA observations with a resolution of 0.2-0.3 arcseconds and integration times
of about 20 minutes allow reliable estimates of Rc to within about 10au and
gamma to within about 0.2. Economic gas imaging surveys are therefore feasible
and offer the opportunity to open up a new dimension for studying disk
structure and its evolution toward planet formation.
