  We develop a stochastic parametrization, based on a `simple' deterministic
model for the dynamics of steady longshore currents, that produces ensembles
that are statistically consistent with field observations of these currents.
Unlike deterministic models, stochastic parameterization incorporates
randomness and hence can only match the observations in a statistical sense.
Unlike statistical emulators, in which the model is tuned to the statistical
structure of the observation, stochastic parametrization are not directly tuned
to match the statistics of the observations. Rather, stochastic
parameterization combines deterministic, i.e physics based models with
stochastic models for the "missing physics" to create hybrid models, that are
stochastic, but yet can be used for making predictions, especially in the
context of data assimilation. We introduce a novel measure of the utility of
stochastic models of complex processes, that we call {\em consistency of
sensitivity}. We show, in the context of data assimilation, the stochastic
parametrization of longshore currents achieves good results in capturing the
statistics of observation {\em that were not used} in tuning the model.
