Normal modes of the atmosphere as estimated by Prinicipal Oscillation Patterns and derived from quasi-geostrophic theory

The principal oscillation pattern (POP) analysis is a technique to empirically identify time-dependent spatial patterns in a multivariate time series of geophysical or other data. In order to investigate medium-scale and synoptic waves in the atmosphere it has been applied to tropospheric geopotential height fields of ECMWF analyses from 1984 to 1987. The data have been subjected to zonal Fourier decomposition and to time filtering so that variations with periods between 3 and 25 days were retained. Analyses have been performed separately for each zonal wavenumber 5-9 on the Northern Hemisphere in winter and on the Southern Hemisphere in summer (DJF). POPs can be seen as normal modes of a linear approximation to a more complex dynamical system. The system matrix is estimated from observations of nature. This concept is compared with conventional stability analysis where the system matrix of the linear system is derived from theoretical, in this case quasigeostrophic, reasoning. Only the mean basic flow depends on time- and space-averaged fields of observed wind and temperature from the ECMWF data. It turns out that the most significant POPs are very similar in time and spatial structure to the most unstable waves in the stability analysis. They describe the linear growth phase of baroclinic, unstable waves that propagate eastward with periods of 3-7 days. Since the POPs are purely derived from observations, the results indicate the appropriateness of the assumptions usually made in linear stability analysis of zonally symmetric flows to explain high-frequency atmospheric fluctuations. Moreover, the POP analysis reveals patterns that are not found in the linear stability analysis. These can possibly be attributed to the nonlinear decay phase of baroclinic waves. Eliassen-Palm cross sections help clarify the interpretation of the POPs in terms of the life cycle of nonlinear baroclinic waves.