  The low-$J$ rotational transitions of $^{12}$CO are commonly used to trace
the distribution of molecular gas in galaxies. Their ratios are sensitive to
excitation and physical conditions in the molecular gas. Spatially resolved
studies of CO ratios are still sparse and affected by flux calibration
uncertainties, especially since most do not have high angular resolution or do
not have short-spacing information and hence miss any diffuse emission. We
compare the low-$J$ CO ratios across the disk of two massive, star-forming
spiral galaxies NGC2903 and NGC3627 to investigate whether and how local
environments drive excitation variations at GMC scales. We use Atacama Large
Millimeter Array (ALMA) observations of the three lowest-$J$ CO transitions at
a common angular resolution of 4$''$ (190pc). We measure median line ratios of
$R_{21}=0.67^{+0.13}_{-0.11}$, $R_{32}=0.33^{+0.09}_{-0.08}$, and
$R_{31}=0.24^{+0.10}_{-0.09}$ across the full disk of NGC3627. We see clear CO
line ratio variation across the galaxy consistent with changes in temperature
and density of the molecular gas. In particular, toward the center, $R_{21}$,
$R_{32}$, and $R_{31}$ increase by 35\%, 50\%, and 66\%, respectively compared
to their average disk values. The overall line ratio trends suggest that
CO(3-2) is more sensitive to changes in the excitation conditions than the two
lower-$J$ transitions. Furthermore, we find a similar radial $R_{32}$ trend in
NGC2903, albite a larger disk-wide average of $\langle
R_{32}\rangle=0.47^{+0.14}_{-0.08}$. We conclude that the CO low-$J$ line
ratios vary across environments in such a way that they can trace changes in
the molecular gas conditions, with the main driver being changes in
temperature.
