  We have studied the incommensurate moir\'e structure of epitaxial graphene
grown on iridium(111) by dynamic low energy electron diffraction [LEED-I(V)]
and non-contact atomic force microscopy (AFM) with a CO terminated tip. Our
LEED-I(V) results yield the average positions of all the atoms in the surface
unit cell and are in qualitative agreement with the structure obtained from
density functional theory (DFT). The AFM experiments reveal local variations of
the moir\'e structure: the corrugation varies smoothly over several moir\'e
unit cells between 42 and 56 pm. We attribute these variations to the varying
registry between the moir\'e symmetry sites and the underlying substrate. We
also observe isolated outliers, where the moir\'e top sites can be offset by an
additional 10 pm. This study demonstrates that AFM imaging can be used to
directly yield the local surface topography with pm accuracy even on
incommensurate 2D structures with varying chemical reactivity.
