  It is still unclear whether the evolution of protoplanetary disks, a key
ingredient in the theory of planet formation, is driven by viscous turbulence
or magnetic disk winds. As viscously evolving disks expand outward over time,
the evolution of disk sizes is a discriminant test for studying disk evolution.
However, it is unclear how the observed disk size changes over time if disk
evolution is driven by magnetic disk winds. Combining the thermochemical code
DALI with the analytical wind-driven disk evolution model presented in Tabone
et al. (2021a), we study the time evolution of the observed gas outer radius as
measured from CO rotational emission ($R_{\rm CO, 90\%}$). The evolution of
$R_{\rm CO, 90\%}$ is driven by the evolution of the disk mass, as the physical
radius stays constant over time. For a constant $\alpha_{\rm DW}$, an extension
of the $\alpha-$Shakura-Sunyaev parameter to wind-driven accretion, $R_{\rm CO,
90\%}$ decreases linearly with time. Its initial size is set by the disk mass
and the characteristic radius $R_c$, but only $R_c$ affects the evolution of
$R_{\rm CO, 90\%}$, with a larger $R_c$ resulting in a steeper decrease of
$R_{\rm CO, 90\%}$. For a time-dependent $\alpha_{\rm DW}$ $R_{\rm CO, 90\%}$
stays approximately constant during most of the disk lifetime until $R_{\rm CO,
90\%}$ rapidly shrinks as the disk dissipates. The constant $\alpha_{\rm
DW}$-models are able to reproduce the observed gas disk sizes in the $\sim1-3$
Lupus and $\sim5-11$ Myr old Upper Sco star-forming regions. However, they
likely overpredict the gas disk size of younger $(\lessapprox0.7\
\mathrm{Myr})$ disks.
