# TOWARD A DYNAMICAL UNDERSTANDING OF PLANETARY-SCALE FLOW REGIMES.

(MARSHALL, J and MOLTENI, F), *JOURNAL OF THE ATMOSPHERIC SCIENCES*, vol. 50, no. 12, pp. pages, 1993.

## Abstract

A strategy for diagnosing and interpreting flow regimes that is firmly rooted in dynamical theory is presented and applied to the study of observed and modeled planetary-scale regimes of the wintertime circulation in the Northern Hemisphere. The method assumes a nonlinear dynamical model of the atmospheric motion, and determines a subspace of the phase space of the model in which multiple quasi-stationary solutions of the equations of motion are likely to be located. The axes that generate this subspace are the vectors that possess the smallest amplitude of the time derivative computed from a linearized version of the model, using the time-mean state of the system as a basic state. These vectors are called here “neutral vectors”, and are shown to be eigenvectors of a self-adjoint operator derived from the linearized model. As a prototype of a dynamical system with quadratic nonlinearity relevant to atmospheric dynamics, the three-variable convection model that generates the well-known Lorenz attractor is first investigated. It is shown that the presence of two unstable stationary solutions, which determine the shape of the attractor, generates a strong bimodality in the projection of the state vector of the system onto the most neutral vector, once a proper time filter is used on the data. To apply this method to the analysis of atmospheric low-frequency variability, a three-level quasigeostrophic model in spherical geometry is adopted as the dynamical model. Neutral vectors are computed using the observed mean atmospheric state in winter as a basic state; alternative basic states, in which the eddies in the time-mean state are partially or fully removed, are also used in sensitivity experiments. The spatial patterns of the leading neutral vectors are relative insensitive to variations in some model parameters, but are strongly controlled by the form of the basic state; such dependence can be understood in terms of linear planetary-wave theory. The neutral vectors of the wintertime climatology are then used to analyze a 32-winter sample of observed atmospheric fields. It is found that the time series of the projection of these fields onto one particular neutral vector has a significantly bimodal probability density function, suggesting the existence of (at least) two separate flow regimes associated with anomalies of opposite sign. The two regimes are hemispheric in extent, and are close to some of the clusters found in previous studies that made use of empirical orthogonal functions. Finally, it is shown that, if an appropriate forcing function is employed, the quasi-geostrophic model is able to generate a very realistic climatology in a long nonlinear integration and, furthermore, two regimes similar to the observed ones. Again, these regimes can be identified by the presence of bimodality in the probability density function of the projections of model fields onto neutral vectors. Modeled and observed regimes have not only similar spatial patterns but also an almost identical distribution of the residence time.