  The observable quantities that carry the most information regarding the
structures of the images of black holes in the interferometric observations
with the Event Horizon Telescope are the closure phases along different
baseline triangles. We use long time span, high cadence, GRMHD+radiative
transfer models of Sgr A$^*$ to investigate the expected variability of closure
phases in such observations. We find that, in general, closure phases along
small baseline triangles show little variability, except in the cases when one
of the triangle vertices crosses one of a small regions of low visibility
amplitude. The closure phase variability increases with the size of the
baseline triangle, as larger baselines probe the small-scale structures of the
images, which are highly variable. On average, the jet-dominated MAD models
show less closure phase variability than the disk-dominated SANE models, even
in the large baseline triangles, because the images from the latter are more
sensitive to the turbulence in the accretion flow. Our results suggest that
image reconstruction techniques need to explicitly take into account the
closure phase variability, especially if the quality and quantity of data allow
for a detailed characterization of the nature of variability. This also implies
that, if image reconstruction techniques that rely on the assumption of a
static image are utilized, regions of the $u-v$ space that show a high level of
variability will need to be identified and excised.
