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

Variability in GRMHD simulations of Sgr A$^*$: Implications for EHT closure phase observations