I gave a guest lecture for the graduate tropical meteorology course at SNU on the subject of the vertical normal modes (VNMs) of the atmosphere. The notes are a mostly self-contained guide on what the VNMs are, how their forms can be derived in the case of constant stratification (i.e., $\partial_z N^2=0$), and how the VNMs can be computed numerically from data.

The notes are available as a PDF download. A complementary Python notebook demonstrates the numerical computation, and can also be opened directly in Google Colab.

Plot of the first few vertical normal modes