Results show that contributions have the following four features. (i) Contributions to vertical vorticity (horizontal winds) and perturbations of pressure, potential temperature and density are large; on the contrary, vertical motion and horizontal divergence are little affected. (ii) Equivalent barotropic structure is shown up in contributions to vertical vorticity and pressure perturbation. (iii) Contributions to vorticity and pressure perturbation become large when the meridional gradient of the forcing is large. (iv) All variables are largely affected at the west-side of the forcing.

The above features are physically and comprehensively understood by considering the tilting of meridional component of the planetary vorticity vector due to the meridional gradient of vertical motion, i.e., diabatic heating. If the meridional gradient is large, this tilting also becomes strong. Because the tilting is directly connected to vertical vorticity, and the tilted vorticity adjusts pressure, then contributions to them are large. The equivalent barotropic structure comes from that of vertical motion, which has vertically standing one. Then, potential temperature and density perturbations are quasi-hydrostatically balanced with the others so that contributions to them are also large. In contrast, because of the strong relation between vertical motion and diabatic heating, the NCTs little affect vertical motion and horizontal divergence, which closely related to vertical motion. In addition, large contributions at the west-side of the forcing are explained as a Rossby response. The above results indicate that in order to reduce dynamical error caused by the exclusion of the NCTs, we should use the nonhydrostatic deep (i.e., not assuming the shallow atmosphere approximation) or quasi-hydrostatic equations as a dynamical core in global numerical models.