  A system of stochastic differential equations is formulated describing the
heat and salt content of a two-box ocean. Variability in the heat and salt
content and in the thermohaline circulation between the boxes is driven by fast
Gaussian atmospheric forcing and by ocean-intrinsic, eddy-driven variability.
The eddy forcing of the slow dynamics takes the form of a colored, non-Gaussian
noise. The qualitative effects of this non-Gaussianity are investigated by
comparing to two approximate models: one that includes only the mean eddy
effects (the `averaged model'), and one that includes an additional Gaussian
white-noise approximation of the eddy effects (the `Gaussian model'). Both of
these approximate models are derived using the methods of fast averaging and
homogenization.
  In the parameter regime where the dynamics has a single stable equilibrium
the averaged model has too little variability. The Gaussian model has accurate
second-order statistics, but incorrect skew and rare-event probabilities. In
the parameter regime where the dynamics has two stable equilibria the eddy
noise is much smaller than the atmospheric noise. The averaged, Gaussian, and
non-Gaussian models all have similar stationary distributions, but the jump
rates between equilibria are too small for the averaged and Gaussian models.
