  The primitive equations are fundamental models in geophysical fluid dynamics
and derived from the scaled Navier-Stokes equations. In the primitive
equations, the evolution equation to the vertical velocity is replaced by the
so-called hydrostatic approximation. In this paper, we give a justification of
the hydrostatic approximation by the scaled Navier-Stoke equations in
anisotropic spaces $L^\infty_H L^q_{x_3} (\Torus^3)$ for $q \geq 1$.
