  The gas-phase CO abundance (relative to hydrogen) in protoplanetary disks
decreases by up to 2 orders of magnitude from its ISM value ${\sim}10^{-4}$,
even after accounting for freeze-out and photo-dissociation. Previous studies
have shown that while local chemical processing of CO and the sequestration of
CO ice on solids in the midplane can both contribute, neither of these
processes appears capable of consistently reaching the observed depletion
factors on the relevant timescale of $1{-}3\mathrm{~Myr}$. In this study, we
model these processes simultaneously by including a compact chemical network
(centered on carbon and oxygen) to 2D ($r+z$) simulations of the outer
($r>20\mathrm{~au}$) disk regions that include turbulent diffusion, pebble
formation, and pebble dynamics. In general, we find that the CO/H$_2$ abundance
is a complex function of time and location. Focusing on CO in the warm
molecular layer, we find that only the most complete model (with chemistry and
pebble evolution included) can reach depletion factors consistent with
observations. In the absence of pressure traps, highly-efficient planetesimal
formation, or high cosmic ray ionization rates, this model also predicts a
resurgence of CO vapor interior to the CO snowline. We show the impact of
physical and chemical processes on the elemental (C/O) and (C/H) ratios (in the
gas and ice phases), discuss the use of CO as a disk mass tracer, and, finally,
connect our predicted pebble ice compositions to those of pristine
planetesimals as found in the Cold Classical Kuiper Belt and debris disks.
