  In this paper we study a three dimensional thermocline planetary geostrophic
``horizontal" hyper--diffusion model of the gyre-scale midlatitude ocean. We
show the global existence and uniqueness of the weak and strong solutions to
this model. Moreover, we establish the existence of a finite dimensional global
attractor to this dissipative evolution system. Preliminary computational tests
indicate that our hyper--diffusion model does not exhibit any of the
nonphysical instabilities near the literal boundary which are observed
numerically in other models.
