The Singular-Vector Structure of the Atmospheric Global Circulation

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  • 1 European Centre for Medium-Range Weather Forecasts, Shinfield Park Reading, Berkshire, United Kingdom
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Abstract

The local phase-space instability Of the atmospheric global circulation is Characterized by its (nonmodal) singular vectors. The formalism of singular vector analysis is described. The relations between singular vectors, normal modes, adjoint modes, Lyapunov vectors, perturbations produced by the so-called breeding method, and wave pseudomomentum are outlined. Techniques to estimate the dominant part of the singular spectrum using large-dimensional primitive equation models are discussed. These include the use of forward and adjoint tangent propagators with a Lanczos iterative algorithm. Results are described, based first on statistics of routine calculations made between December 1992 and August 1993, and second on three specific case studies.

Results define three dominant geographical areas of instability in the Northern Hemisphere: the two regions of storm track cyclogenesis, and the North African subtropical jet Singular vectors can amplify as much as tenfold over 36 hours, and in winter there are typically at least 35 independent 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-state 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 frequent is located in mid latitudes. At initial time, the singular vector is localized in the horizontal, with most amplitude in the lower troposphere. Energy growth can be interpreted qualitatively in terms of wave pseudomomentum propagation into the jet, resulting in peak amplitudes in the upper troposphere at optimization time. During evolution the dominant horizontal wavenumber of the singular vector decreases. Singular vector growth is therefore fundamentally nonmodal. Singular vectors 1ocalized first in the tropical upper troposphere. and second with equivalent barotropic structure in the high-latitude troposhpere, are also identified.

Abstract

The local phase-space instability Of the atmospheric global circulation is Characterized by its (nonmodal) singular vectors. The formalism of singular vector analysis is described. The relations between singular vectors, normal modes, adjoint modes, Lyapunov vectors, perturbations produced by the so-called breeding method, and wave pseudomomentum are outlined. Techniques to estimate the dominant part of the singular spectrum using large-dimensional primitive equation models are discussed. These include the use of forward and adjoint tangent propagators with a Lanczos iterative algorithm. Results are described, based first on statistics of routine calculations made between December 1992 and August 1993, and second on three specific case studies.

Results define three dominant geographical areas of instability in the Northern Hemisphere: the two regions of storm track cyclogenesis, and the North African subtropical jet Singular vectors can amplify as much as tenfold over 36 hours, and in winter there are typically at least 35 independent 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-state 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 frequent is located in mid latitudes. At initial time, the singular vector is localized in the horizontal, with most amplitude in the lower troposphere. Energy growth can be interpreted qualitatively in terms of wave pseudomomentum propagation into the jet, resulting in peak amplitudes in the upper troposphere at optimization time. During evolution the dominant horizontal wavenumber of the singular vector decreases. Singular vector growth is therefore fundamentally nonmodal. Singular vectors 1ocalized first in the tropical upper troposphere. and second with equivalent barotropic structure in the high-latitude troposhpere, are also identified.

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