  We study astrometric residuals from a simultaneous fit of Hyper Suprime-Cam
images. We aim to characterize these residuals and study the extent to which
they are dominated by atmospheric contributions for bright sources. We use
Gaussian process interpolation, with a correlation function (kernel), measured
from the data, to smooth and correct the observed astrometric residual field.
We find that Gaussian process interpolation with a von K\'arm\'an kernel allows
us to reduce the covariances of astrometric residuals for nearby sources by
about one order of magnitude, from 30 mas$^2$ to 3 mas$^2$ at angular scales of
~1 arcmin, and to halve the r.m.s. residuals. Those reductions using Gaussian
process interpolation are similar to recent result published with the Dark
Energy Survey dataset. We are then able to detect the small static astrometric
residuals due to the Hyper Suprime-Cam sensors effects. We discuss how the
Gaussian process interpolation of astrometric residuals impacts galaxy shape
measurements, in particular in the context of cosmic shear analyses at the
Rubin Observatory Legacy Survey of Space and Time.
