  Absorbing ball in $H^{1}(\mho)$ is obtained for the strong solution to the
three dimensional viscous moist primitive equations under the natural
assumption $Q_{1},Q_{2}\in L^{2}(\mho)$ which is weaker than the assumption
$Q_{1},Q_{2}\in H^{1}(\mho)$ in $\cite{GH2}$. In view of the structure of the
manifold and the special geometry involved with vertical velocity, the
continuity of the strong solution in $H^{1}(\mho)$ is established with respect
to time and initial data. To obtain the existence of the global attractor for
the moist primitive equations, the common method is to obtain the absorbing
ball in $H^{2}(\mho)$ for the strong solution to the equations. But it is
difficult due to the complex structure of the moist primitive equations. To
overcome the difficulty, we try to use Aubin-Lions lemma and the continuous
property of the strong solutions to the moist primitive equations to prove the
the existence of the global attractor which improves the result, the existence
of weak attractor, in $\cite{GH2}$.

Analysis of PDEs