  It is well known that metal-poor red giant branch (RGB) stars show variations
in some elemental abundances, including carbon, due to the internal mixing
accompanied by their own in situ CN cycle in the hydrogen burning shell. With
our new photometric carbon abundance measurements of RGB stars in M22 and other
globular clusters (GCs) in our previous studies, M5, M3, and M92, we derive the
carbon depletion rates against the $V$ magnitude, $d\mathrm{[C/Fe]}/M_V$, for
individual populations in each GC. We find the metallicity dependence of the
carbon depletion rates, $d\mathrm{[C/Fe]}/M_V$ $\propto$ $-$0.25[Fe/H]. Our
results also suggest that the carbon depletion rates of the second generation
(SG) of stars are larger than those of the first generation (FG) of stars in
our sample GCs, most likely due to different internal temperature profiles with
different initial helium abundances between the FG and SG. Our results can
provide critical constraints both on understanding the mixing efficiency in the
theoretical models, which is largely unknown, and on interpretation of the
observational carbon abundance evolution of the bright halo RGB stars.
