DISCRETE AND CONTINUOUS SPECTRA OF THE BAROTROPIC QUASI-GEOSTROPHIC VORTICITY MODEL .1.

The evolution processes of small disturbances in an arbitrary basic fl ow can be expressed as a combination of spectral functions of the disc rete spectra and continuous spectrum of a model that bear distinctly d ifferent evolutionary characteristics. Using the linearized barotropic quasigeostrophic vorticity model, this study formulates the discrete spectral solution into a form that is consistent with traditional norm al modes in time and space, and the continuous spectral solution into a form with the continuum covering the range between minimum and maxim um zonal angular velocities. An estimation of the bounds of the spectr al points is derived to complement those derived from integral constra ints. A theorem is given to describe the possible number of discrete s pectral points away from the continuum. The theoretical analysis is th en used to aid the numerical identification and interpretation of disc rete and continuous spectra of the model with realistic atmospheric ba sic zonal flows. It is shown that neutral spectral points correspond t o either ultralong waves with global meridional coverage or synoptic-s cale waves in low latitudes. The unstable spectral points correspond t o localized waves with developing or decaying timescales longer than 2 weeks. Structures of spectral function of the continuum are also pres ented and discussed. They are shown to restrict on one side to the cri tical latitude and on the other side to the jet core under certain con ditions.