  Gravitational memory effects are predictions of general relativity that are
characterized by an observable effect that persists after the passage of
gravitational waves. In recent years, they have garnered particular interest,
both due to their connection to asymptotic symmetries and soft theorems and
because their observation would serve as a unique test of the nonlinear nature
of general relativity. Apart from the more commonly known displacement and spin
memories, however, there are other memory effects predicted by Einstein's
equations that are associated with more subleading terms in the asymptotic
expansion of the Bondi-Sachs metric. In this paper, we write explicit
expressions for these higher memory effects in terms of their charge and flux
contributions. Further, by using a numerical relativity simulation of a binary
black hole merger, we compute the magnitude and morphology of these terms and
compare them to those of the displacement and spin memory. We find that,
although these terms are interesting from a theoretical perspective, due to
their small magnitude they will be particularly challenging to observe with
current and future detectors.
