A Unified Three-Dimensional Instability Theory of the Onset of Blocking and Cyclogenesis

The instability characteristics of three-dimensional flow typical of the Northern Hemisphere average winter troposphere are examined in a two-layer spherical quasigeostrophic model. The properties of the four fastest-growing small-amplitude disturbances that develop on the basic state have been analyzed for three cases (case 1, 2a and 3) having increasingly larger static stability parameters. For case 1, the fastest-growing disturbance mode, which is propagating eastward rather rapidly, has a monopole cyclogenesis structure with maximum amplitudes slightly downstream of the jetstream maxima in the Pacific ocean and off the cast coast of North America. Comparisons of streamfunctions squared and momentum and heat fluxes with bandpass filtered observations for transient eddies, which pick out the developing storms, are quite reasonable considering that a two-layer model is used and the contributions from individual linear modes are considered. For case 2a, the fastest growing mode has large-scale high–low dipole structures with maximum amplitudes in the Pacific Ocean and has a period which is between two and three times that of the fastest growing mode for case 1. Comparison of the disturbance streamfunction squared for case 2 with the low-pass filtered rms height deviation for observed eddies corresponding to blocking in the Pacific is quite reasonable. The observed finite amplitude blocking regions occur slightly downstream of the regions of maximum amplitude of the disturbance streamfunction. For both observation and theory, there are two distinct maxima in the Pacific Ocean. Another flow configuration (case 2b) having the same static stability as case 2a but slightly different planetary wave structure is also considered. For this case, the fastest growing mode has aspects in common with those of both case 1 and 2a. For case 3, the fastest growing mode has large-scale high–low dipole structures with maximum amplitudes slightly upstream of the regions in both the Pacific and Atlantic Oceans where blocking generally occurs. It is argued that the slow-moving dipole structures that occur in the Pacific and Atlantic Oceans when the model atmosphere is less unstable than usual, correspond to the onset of blocking, just as the fast moving monopole structures in the most unstable case correspond to cyclogenesis.