Some Observations of Normal Modes in the Atmosphere (Invited Presentation)

Bernhard Haurwitz was a pioneer in the use of spherical harmonic representations of atmospheric waves. When a spherical harmonic expansion is applied to the linearized shallow water equations on a sphere (the Laplace tidal equations), this approach assumes that such waves have a planetary scale extent, bounded at the surface and the poles. An alternate approach used in the tropics, referred to as the “equatorial beta-plane approximation”, assumes an infinite plane and approximates spherical geometry by setting the meridional gradient of the Coriolis parameter to its value at the equator. In both approaches, linearization of an approximate set of the equations of motion for shallow water yield “normal mode” solutions, or an infinite number of free oscillations with discrete scales in time and space. Despite the gross approximations involved, this approach has been highly successful at representing the dynamics of a wide variety of atmospheric wave disturbances. On a sphere, such modes include the familiar midlatitude “Rossby-Haurwitz” waves, related to extratropical storm track variations, along with a large number of “external” (vertically unbounded) Rossby-Haurwitz waves of global extent. On the equatorial beta plane, solutions derived by Matsuno include the Kelvin, mixed Rossby-gravity, equatorial Rossby and a broad class of inertio-gravity modes that are trapped along the equator. This talk will present examples of such modes in the real atmosphere. It turns out that simple linear statistical techniques such as EOF analysis are quite useful in isolating atmospheric normal modes, once the data have been filtered appropriately. The zonal wavenumber 1 external Rossby-Haurwitz wave, also known as the “5-day” wave, has been studied for several decades, and global reanalysis and satellite data reveal several previously overlooked aspects of this wave, including connections with tropical convection. Stratospheric equatorial waves are also profitably studied by linear techniques applied to reanalysis and satellite data, and their properties conform very nicely to that predicted by Matsuno. In the troposphere, coupling to convection alters the scale and structure of Matsuno waves in more complex ways. The Madden-Julian Oscillation, on the other hand, is in its own class, since it is not a normal mode of any known linearized system, yet it still has many features in common with tropospheric Matsuno modes. As opposed to the free oscillations, but also as in tropical cyclones, the very existence of the MJO appears to be dependent upon the interplay between diabatic processes and the large scale circulation.