The Vertical Structure of Global Rotational Normal Modes

In a recent study, Lindzen et al. (1984) examined the amplitude and phase evolution of Hough mode projections at 500 mb. The Hough modes represent the simplest normal mode approximation available, and correspond to the neutral eigenfunctions of a shallow water fluid with no mean zonal flow. It was found that when the observed amplitude of a rotational Hough mode was large, it tended to propagate at the phase speed of a normal mode in the presence of mean 500 mb winds, giving a strong indication that normal modes are of relevance to the atmosphere. The vertical structure of the approximately defined rotational normal modes were explored by projecting observed data onto Hough functions at levels other than 500 mb. The stationary and eastward propagating components were filtered out at each level. The evolution of the amplitude in time throughout the troposphere is given for several modes during summer and winter.