  A framework for the study of surface ocean inertial particle motion is built
from the Maxey--Riley set. A new set is obtained by vertically averaging each
term of the original set, adapted to account for Earth's rotation effects,
across the extent of a sufficiently small spherical particle that floats at an
assumed unperturbed air--sea interface with unsteady nonuniform winds and ocean
currents above and below, respectively. The inertial particle velocity is shown
to exponentially decay in time to a velocity that lies close to an average of
seawater and air velocities, weighted by a function of the seawater-to-particle
density ratio. Such a weighted average velocity turns out to fortuitously be of
the type commonly discussed in the search-and-rescue literature, which alone
cannot explain the observed role of anticyclonic mesoscale eddies as traps for
marine debris or the formation of great garbage patches in the subtropical
gyres, phenomena dominated by finite-size effects. A heuristic extension of the
theory is proposed to describe the motion of nonspherical particles by means of
a simple shape factor correction, and recommendations are made for
incorporating wave-induced Stokes drift, and allowing for inhomogeneities of
the carrying fluid density. The new Maxey--Riley set outperforms an ocean
adaptation that ignored wind drag effects and the first reported adaption that
attempted to incorporate them.
