  The primitive equations of large-scale oceanic dynamics form a fundamental
model in geophysical flows. It is well-known that the primitive equations can
be formally derived by the hydrostatic approximation. On the other hand, the
mathematically rigorous derivation of the primitive equations without coupling
with the temperature is also known. In this paper, we generalize the above
result from the mathematical point of view. More precisely, we prove that the
scaled Boussinesq equations with rotation converge to the full primitive
equations in a strong sense, globally in time, with the convergence rate
$O(\varepsilon)$, as the aspect ratio $\varepsilon$ goes to zero.
