  The primitive equations for geophysical flows are studied under the influence
of {\em stochastic wind driven boundary conditions} modeled by a cylindrical
Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic
boundary value problems to define a notion of solutions. Then a rigorous
treatment of these stochastic boundary conditions, which combines stochastic
and deterministic methods, yields that these equations admit a unique, local
pathwise solution within the anisotropic $L^q_t$-$H^{-1,p}_zL^p_{xy}$-setting.
This solution is constructed in critical spaces.
