  We study Giant Molecular Cloud (GMC) environments surrounding 10 Infrared
Dark Clouds (IRDCs), using $^{13}$CO(1-0) emission from the Galactic Ring
Survey. We measure physical properties of these IRDCs/GMCs on a range of scales
extending to radii, R, of 30 pc. By comparing different methods for defining
cloud boundaries and for deriving mass surface densities and velocity
dispersions, we settle on a preferred "CE,$\tau$,G" method of "Connected
Extraction" in position-velocity space plus Gaussian fitting to
opacity-corrected line profiles for velocity dispersion and mass estimation. We
examine how cloud definition affects measurements of the magnitude and
direction of line-of-sight velocity gradients and velocity dispersions,
including associated dependencies on size scale. CE,$\tau$,G-defined GMCs show
velocity dispersion versus size relations $\sigma\propto{s}^{1/2}$, which are
consistent with the large-scale gradients being caused by turbulence. However,
IRDCs have velocity dispersions that are moderately enhanced above those
predicted by this scaling relation. We examine the dynamical state of the
clouds finding mean virial parameters $\bar{\alpha}_{\rm{vir}}\simeq 1.0$ for
GMCs and 1.6 for IRDCs, broadly consistent with models of magnetized virialized
pressure-confined polytropic clouds, but potentially indicating that IRDCs have
more disturbed kinematics. CE,$\tau$,G-defined clouds exhibit a tight
correlation of $\sigma/R^{1/2}\propto\Sigma^n$, with $n\simeq0.7$ for GMCs and
1.3 for IRDCs (c.f., a value of 0.5 expected for a population of virialized
clouds). We conclude that while GMCs show evidence for virialization over a
range of scales, IRDCs may be moderately super virial. Alternatively, IRDCs
could be virialized but have systematically different $^{13}$CO gas phase
abundances, i.e., due to freeze-out, affecting mass estimations.
