Wave Activity Diagnostics Applied to Baroclinic Wave Life Cycles

Gudrun Magnusdottir Centre for Atmospheric Science, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom

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Peter H. Haynes Centre for Atmospheric Science, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom

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Abstract

Wave activity diagnostics are calculated for four different baroclinic wave life cycles, including the LC1 and LC2 cases studied by Thorncroft, Hoskins, and McIntyre. The wave activity is a measure of the disturbance relative to some zonally symmetric, time-independent basic state, which need not be the initial zonally averaged state and which satisfies a finite-amplitude conservation relation. The wave activity density and fluxes may be calculated in terms of Eulerian variables provided that the potential vorticity is a monotonic function of latitude on isentropic surfaces in the basic state. The LC1 and LC2 experiments used initial states in which the potential vorticity (PV) did not satisfy this monotonicity condition. Therefore two approaches are taken. The first is to define a basic state that is not the initial state and use this to calculate the wave activity diagnostics. The second is to carry out new LC1- and LC2-type experiments on initial states in which the monotonicity condition is satisfied. New basic states are generated by PV rearrangement and inversion.

The results allow quantification of the difference between LC1- and LC2-type life cycles. They also show that LC1- and LC2-type behavior occurs for different initial states other than those used by Thorncroft, Hoskins, and McIntyre and that the classification is therefore robust in terms of the potential vorticity field and wave activity diagnostics. If one were to consider only eddy kinetic energy, the distinction is no longer clear. In fact, in the evolution of eddy kinetic energy the modified LC1-type life cycle resembles LC2 and the modified LC2 more than it resembles LC1.

The results also shed new light on the role of wave propagation in baroclinic life cycles. In particular, it is found that during the later stages of the life cycle the pattern of equatorward wave activity flux that has often been interpreted as associated with equatorward wave propagation in the subtropical upper troposphere is in fact associated primarily with advective transport of wave activity.

New finite-amplitude expressions are presented for the wave activity associated with potential temperature gradients on the lower boundary. Problems with using PV rearrangement techniques are discussed.

Abstract

Wave activity diagnostics are calculated for four different baroclinic wave life cycles, including the LC1 and LC2 cases studied by Thorncroft, Hoskins, and McIntyre. The wave activity is a measure of the disturbance relative to some zonally symmetric, time-independent basic state, which need not be the initial zonally averaged state and which satisfies a finite-amplitude conservation relation. The wave activity density and fluxes may be calculated in terms of Eulerian variables provided that the potential vorticity is a monotonic function of latitude on isentropic surfaces in the basic state. The LC1 and LC2 experiments used initial states in which the potential vorticity (PV) did not satisfy this monotonicity condition. Therefore two approaches are taken. The first is to define a basic state that is not the initial state and use this to calculate the wave activity diagnostics. The second is to carry out new LC1- and LC2-type experiments on initial states in which the monotonicity condition is satisfied. New basic states are generated by PV rearrangement and inversion.

The results allow quantification of the difference between LC1- and LC2-type life cycles. They also show that LC1- and LC2-type behavior occurs for different initial states other than those used by Thorncroft, Hoskins, and McIntyre and that the classification is therefore robust in terms of the potential vorticity field and wave activity diagnostics. If one were to consider only eddy kinetic energy, the distinction is no longer clear. In fact, in the evolution of eddy kinetic energy the modified LC1-type life cycle resembles LC2 and the modified LC2 more than it resembles LC1.

The results also shed new light on the role of wave propagation in baroclinic life cycles. In particular, it is found that during the later stages of the life cycle the pattern of equatorward wave activity flux that has often been interpreted as associated with equatorward wave propagation in the subtropical upper troposphere is in fact associated primarily with advective transport of wave activity.

New finite-amplitude expressions are presented for the wave activity associated with potential temperature gradients on the lower boundary. Problems with using PV rearrangement techniques are discussed.

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