This is due to the complexity of both the PDEs themselves, and the initial and boundary conditions. Put succinctly, SEM combines the accuracy of conventional spectral methods and the geometric flexibility of finite element methods. This presentation has several purposes. Disadvantages are also mentioned. Another goal is to remedy the current lack of a description of SEM which is accessible to an audience other than advanced specialists in the numerical solution of PDEs.
Spurious reflection is prevented by a sponge layer near the model top.
These features converge, and PV gradients steepen, as resolution is increased.