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Chih-Ping F. Hsu

Abstract

In this study the role of nonlinear wave-wave interactions is investigated by performing two experiments using a numerical model adapted from that of Holton (1976). In the first experiment the model simulates a sudden stratospheric warming involving the interaction between the mean (zonally averaged) flow and a single zonal harmonic of wavenumber 1 which is forced at the lower boundary; presumably the tropopause level. In the second experiment the model includes an additional wave 2 which is not forced at the lower boundary but generated through nonlinear interaction between wave 1 and itself. This wave 2 interacts with both the mean flow and wave 1. However, zonal wavenumbers higher than 2 are all neglected. These two experiments are referred to as the linear and the nonlinear cases, respectively.

The results are first described in an Eulerian framework. It is found that the simulated warming for the nonlinear case is more intense and rapid than that for the linear case. In order to describe how the different wave components change the mean flow, the transformed equations for the zonally averaged fields of Andrews and McIntyre (1976) are studied diagnostically. Evidence based on the model results is presented to show that the transformed equations provide a more direct view of the wave-forcing processes than the conventional equations. The results of this diagnostic study indicate that, in the nonlinear model experiment, the mean zonal deceleration induced by wave 2 is ∼60% of that induced by wave 1 during the rapid warming stage.

The Lagrangian air motions during the two model experiments are described by tracing a large number of marked particles. The format of presentation is the same as that used by Hsu (1980) who discusses the three-dimensional air motions during a simulated warming involving wavenumber 2. It is shown that the particle motions during the model simulation involving a single zonal wave (either wavenumber 1 or 2) are qualitatively similar. In the nonlinear model experiment which includes both waves 1 and 2 and their interactions, the vertical displacements of particles are larger in magnitude and the mixing of polar and tropical air occurs faster, as compared with those in the linear model which involves only wavenumber 1; consistent with the fact that the simulated warming is more intense for the nonlinear model experiment.

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Chih-Ping F. Hsu

Abstract

The three-dimensional mass motions in a mechanistic numerical model of a sudden stratospheric warming are investigated by tracing a large number of marked particles. The model is adapted from that described by Holton (1976). A sudden stratospheric warming is simulated by allowing a large amplitude, single harmonic wave forced at the lower boundary of the model to interact with the zonal mean flow. The results of a model simulation involving zonal wavenumber 2 are reported.

Rings of marked particles are placed along latitude circles at the time when the forcing is turned on at the lower boundary and their motions are traced for a period of 30 days. The particle displacements near the level of maximum warming are described in detail, the trajectories of particles exhibit two different types of characteristics depending upon whether the particles originate from high or low latitudes. The particle motions are therefore described in terms of two regimes, the polar and the tropical regimes.

The polar regime is characterized by organized motions of the particles around the elongated polar cyclonic vortex. When projected onto the meridional plane, the rings of particles appear as ellipses whose centers of mass remain at the same location during the prewarming stage, but descend during the warming stage despite the fact that the zonal mean vertical velocities are directed upward in the same region at all times.

The tropical regime is characterized by the trapping of some particles inside the cutoff anticyclones which first appear in middle latitudes and then migrate poleward. As a result, these particles spiral poleward and downward. Eventually the particles which originate from tropical latitudes are scattered all over the hemisphere. When projected onto the meridional plane, a cloud of particles spreads out poleward and downward until the particles are dispersed between the equator and the pole.

These results of particle motions are interpreted in terms of the two quasi-conservative tracers, namely, potential temperature and potential vorticity. For conservative motions a thin tube bounded by two surfaces of constant potential temperature and two surfaces of constant potential vorticity always coincides with the same material line of air particles. These tubes bulge downward (upward) in the polar (tropical) stratosphere during the event of sudden stratospheric warming. It is shown that due to the Newtonian cooling processes the particles are displaced further downward (upward) away from the tubes from which they originate. The horizontal projections of these tubes are displayed and it is found that their shapes are much simpler than those of the material lines of air particles. The nonconservative processes which are responsible for these differences are discussed.

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Chih-Ping F. Hsu
and
John M. Wallace

Abstract

The annual march of sea-level pressure is documented on a global basis by mapping the amplitudes and phases of the annual and semiannual cycles in a vectorial format.

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Chih-Ping F. Hsu
and
John M. Wallace

Abstract

The annual march of precipitation is documented on a global basis by mapping the amplitudes and phases of the annual and semiannual cycles in a vectorial format. The various climatic regimes proposed by Kendrew (1922) show up quite clearly in the results. In addition, the results give some indication of the seasonal variation of precipitation over the oceanic regions.

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