  Correct prediction of particle transport by surface waves is crucial in many
practical applications such as search and rescue or salvage operations and
pollution tracking and clean-up efforts. Recent results have indicated
transport by deep-water breaking waves is enhanced compared to non-breaking
waves. To model particle transport in irregular waves, some of which break, we
develop a stochastic differential equation describing both mean particle
transport and its uncertainty. The equation combines a Brownian motion, which
captures non-breaking drift-diffusion effects, and a compound Poisson process,
which captures jumps in particle positions due to breaking.We corroborate these
predictions with new experiments, in which we track large numbers of particles
in irregular breaking waves. For breaking and non-breaking wave fields, our
experiments confirm that the variance of the particle position grows linearly
with time, in accordance with Taylor's single-particle dispersion theory. For
wave fields that include breaking, the compound Poisson process increases the
linear growth rate of the mean and variance and introduces a finite skewness of
the particle position distribution.
