  We demonstrate the large deviation principle in the small noise limit for the
three dimensional stochastic planetary geostrophic equations of large-scale
ocean circulation. In this paper, we first prove the well-posedness of weak
solutions to this system by the method of monotonicity. As we know, a recently
developed method, weak convergent method, has been employed in studying the
large deviations and this method is essentially based on the main result of
\cite{ba2} which discloses the variational representation of exponential
integrals with respect to the Brownian noise. The It\^{o} inequality and
Burkholder-Davis-Gundy inequality are the main tools in our proofs, and the
weak convergence method introduced by Budhiraja, Dupuis and Ganguly in
\cite{ba3} is also used to establish the large deviation principle.
