THE SINGULAR-VECTOR STRUCTURE OF THE ATMOSPHERIC GLOBAL CIRCULATION

The local phase-space instability of the atmospheric global circulatio n is characterized by its (nonmodal) singular vectors. The formalism o f singular vector analysis is described. The relations between singula r vectors, normal modes, adjoint modes, Lyapunov vectors, perturbation s produced by the so-called breeding method, and wave pseudomomentum a re outlined. Techniques to estimate the dominant part of the singular spectrum using large-dimensional primitive equation models are discuss ed. These include the use of forward and adjoint tangent propagators w ith a Lanczos iterative algorithm. Results are described, based first on statistics of routine calculations made between December 1992 and A ugust 1993, and second on three specific case studies. Results define three dominant geographical areas of instability in the Northern Hemis phere: the two regions of storm track cyclogenesis, and the North Afri can subtropical jet. Singular vectors can amplify as much as tenfold o ver 36 hours, and in winter there are typically at least 35 independen t singular vectors, which quadruple in amplitude over this timescale. Qualitatively, the distribution of singular vectors can be associated with a simple diagnostic of baroclinic instability from the basic-stat e flow. However, this relationship is not quantitatively reliable, as, for example, the chosen diagnostic takes no account of the horizontal or time-varying structure of the basic-state flow. Three basic types of singular vector are identified. The most important and most frequen t is located in midlatitudes. At initial time, the singular vector is localized in the horizontal, with most amplitude in the lower troposph ere. Energy growth can be interpreted qualitatively in terms of wave p seudomomentum propagation into the jet, resulting in peak amplitudes i n the upper troposphere at optimization time. During evolution the dom inant horizontal wavenumber of the singular vector decreases. Singular vector growth is therefore fundamentally nonmodal. Singular vectors l ocalized first in the tropical upper troposphere, and second with equi valent barotropic structure in the high-latitude troposphere, are also identified.