Normal modes of atmospheric variability in observations, numerical weather prediction, and climate models

MOTIVATION. Normal modes, which we deal with here, are eigensolutions to the linearized primitive equations of the atmosphere. Known as the solutions of the first and second kinds or inertia–gravity (IG) and balanced (Rossby type) oscillations, normal modes have been extensively applied for the initialization of numerical weather prediction (NWP) models in the 1980s to early 1990s. The global horizontal structures of normal modes, known as Hough functions, have been used to study various atmospheric dynamical phenomena in weather and climate. The basic properties of the large-scale circulations in the tropics for both the atmosphere and oceans have been elucidated in terms of normal modes on the equatorial beta plane. In the last decade, global data assimilation and forecasting systems have reached resolutions at which IG waves across many scales have become resolved. Furthermore, a rich spectrum of the equatorially trapped IG and the mixed Rossby–gravity waves, in addition to the equatorial Kelvin and Rossby waves, has been identified in observations.