  Bright debris discs can contain large amounts of CO gas. This gas was thought
to be a protoplanetary remnant until it was recently shown that it could be
released in collisions of volatile-rich solids. As CO is released, interstellar
UV radiation photodissociates CO producing CI, which can shield CO allowing a
large CO mass to accumulate. However, this picture was challenged because CI is
inefficient at shielding if CO and CI are vertically mixed. Here, we study for
the first time the vertical evolution of gas to determine how vertical mixing
affects the efficiency of shielding by CI. We present a 1D model that accounts
for gas release, photodissociation, ionisation, viscous evolution, and vertical
mixing due to turbulent diffusion. We find that if the gas surface density is
high and the vertical diffusion weak ($\alpha_{\rm v}/\alpha<[H/r]^2$) CO
photodissociates high above the midplane, forming an optically thick CI layer
that shields the CO underneath. Conversely, if diffusion is strong
($\alpha_{\rm v}/\alpha>[H/r]^2$) CI and CO become well mixed, shortening the
CO lifetime. Moreover, diffusion could also limit the amount of dust settling.
High-resolution ALMA observations could resolve the vertical distribution of CO
and CI, and thus constrain vertical mixing and the efficiency of CI shielding.
We also find that the CO and CI scale heights may not be good probes of the
mean molecular weight, and thus composition, of the gas. Finally, we show that
if mixing is strong the CO lifetime might not be long enough for CO to spread
interior to the planetesimal belt where gas is produced.
