  Inspired by spatiotemporal observations from satellites of the trajectories
of objects drifting near the surface of the ocean in the National Oceanic and
Atmospheric Administration's `Global Drifter Program', this paper develops
data-driven stochastic models of geophysical fluid dynamics (GFD) with
non-stationary spatial correlations representing the dynamical behaviour of
oceanic currents. Three models are considered. Model 1 from Holm [2015] is
reviewed, in which the spatial correlations are time independent. Two new
models, called Model 2 and Model 3, introduce two different symmetry breaking
mechanisms by which the spatial correlations may be advected by the flow. These
models are derived using reduction by symmetry of stochastic variational
principles, leading to stochastic Hamiltonian systems, whose momentum maps,
conservation laws and Lie-Poisson bracket structures are used in developing the
new stochastic Hamiltonian models of GFD.
