  As a first step towards the numerical analysis of the stochastic primitive
equations of the atmosphere and oceans, we study their time discretization by
an implicit Euler scheme. From deterministic viewpoint the 3D Primitive
Equations are studied with physically realistic boundary conditions. From
probabilistic viewpoint we consider a wide class of nonlinear, state dependent,
white noise forcings. The proof of convergence of the Euler scheme covers the
equations for the oceans, atmosphere, coupled oceanic-atmospheric system and
other geophysical equations. We obtain the existence of solutions weak in PDE
and probabilistic sense, a result which is new by itself to the best of our
knowledge.
