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Courtenay Strong
and
Gudrun Magnusdottir

Abstract

Objective analysis of several hundred thousand anticyclonic and cyclonic breaking Rossby waves is performed for the Northern Hemisphere (NH) winters of 1958–2006. A winter climatology of both anticyclonic and cyclonic Rossby wave breaking (RWB) frequency and size (zonal extent) is presented for the 350-K isentropic surface over the NH, and the spatial distribution of RWB is shown to agree with theoretical ideas of RWB in shear flow.

Composites of the two types of RWB reveal their characteristic sea level pressure anomalies, upper- and lower-tropospheric velocity fields, and forcing of the upper-tropospheric zonal flow. It is shown how these signatures project onto the centers of action and force the velocity patterns associated with the North Atlantic Oscillation (NAO) and Northern Hemisphere annular mode (NAM). Previous studies have presented evidence that anticyclonic (cyclonic) breaking leads to the positive (negative) polarity of the NAO, and this relationship is confirmed for RWB over the midlatitudes centered near 50°N. However, an opposite and statistically significant relationship, in which cyclonic RWB forces the positive NAO and anticyclonic RWB forces the negative NAO, is shown over regions 20° to the north and south, centered at 70° and 30°N, respectively.

On a winter mean basis, the frequency of RWB over objectively defined regions covering 12% of the area of the NH accounts for 95% of the NAO index and 92% of the NAM index. A 6-hourly analysis of all the winters indicates that RWB over the objectively defined regions affects the NAO/NAM without a time lag. Details of the objective wave-breaking analysis method are provided in the .

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Christopher C. Walker
and
Gudrun Magnusdottir

Abstract

The nonlinear behavior of quasi-stationary planetary waves excited by midlatitude orographic forcing is considered in a three-dimensional primitive equation model that includes a representation of the Hadley circulation. The Hadley circulation is forced by Newtonian cooling to a zonally symmetric reference temperature and vertical diffusion on the zonally symmetric component of the flow. To quantify the effect of the Hadley circulation on wave propagation, breaking, and nonlinear reflection, an initial state with no meridional flow, but with the same zonal flow as the Hadley state, is also considered. In order to allow the propagation of large-scale waves over extended periods, Rayleigh friction is applied at low levels to delay the onset of baroclinic instability.

As in the absence of a Hadley circulation, the waves in the Hadley state propagate toward low latitudes where the background flow is weak and the waves are therefore likely to break. Potential vorticity fields on isentropic surfaces are used to diagnose wave breaking. Nonlinear pseudomomentum conservation relations are used to quantify the absorption–reflection behavior of the wave breaking region. In the presence of a Hadley circulation representative of winter conditions, the nonlinear reflection requires more forcing to get established, but a reflected wave train is still present in the numerical simulations, both for a longitudinally symmetric forcing and for the more realistic case of an isolated forcing. The effect of the thermal damping on the waves is more severe in the current three-dimensional simulations than in the shallow water case considered in an earlier study. Both the directly forced wave train and the reflected wave train are quite barotropic in character; however, in the shallow water case one is essentially assuming an infinite vertical scale.

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Christopher C. Walker
and
Gudrun Magnusdottir

Abstract

The nonlinear behavior of planetary waves excited by midlatitude topography is considered in an atmospheric GCM. The GCM is run at standard resolution (T42) and includes all of the complexity normally associated with a GCM. Only two simplifications are made to the model. First, it is run in perpetual January mode, so that the solar radiation takes the diurnally varying value associated with 15 January. Second, the lower boundary is simplified so that it is entirely ocean with zonally symmetric SSTs. Planetary waves are excited by Gaussian-shaped topography centered at 45°N, 90°W. As in earlier studies, the excited wave train propagates toward low latitudes where, for sufficiently large forcing amplitude (i.e., height of topography), the wave will break. Several different experiments are run with different mountain heights. Each experiment is run for a total of 4015 days.

The response of the model depends on the height of the mountain. For the small-amplitude mountain (500 m), the wave is dissipated at low latitudes near its critical latitude. For large-amplitude mountains (2000, 3000, and 4000 m), wave breaking and nonlinear reflection out of the wave breaking region is observed. The spatial character of the reflected wave train is similar to that detected in earlier studies with more idealized models.

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Gudrun Magnusdottir
and
Chia-Chi Wang

Abstract

Synoptic-scale variability of vorticity structures in the lower troposphere of the tropics is analyzed in 23 yr of daily averaged high-resolution reanalysis data. The vorticity structures can be divided into zonally elongated vorticity strips, classified as intertropical convergence zones (ITCZs), and more localized maxima, termed westward-propagating disturbances. A composite of such variability is presented for the east to central Pacific and for the east Atlantic/Africa region, both in summer. The composite in the east Pacific is zonally elongated and ITCZ-like, propagating westward over a number of days before dissipating. The spatial structure of the vorticity strip shows the characteristic cyclonic tilt into the latitudinal direction with time that is also seen in modeling experiments. The composite over the Atlantic/Africa region shows two active regions that are correlated on synoptic time scales. The disturbances in the southern region are better developed and longer lasting, even though the time and space scales are smaller than over the east Pacific. Overall, variability over the Atlantic is consistent with variability due to African easterly waves. The double ITCZ in spring in the east Pacific is different from the few earlier studies available. It is stronger south of the equator and located at 10°S, which is farther poleward than earlier studies have indicated. The northern branch that is weak in comparison is located at 5°N. The two branches of the double ITCZ tend to appear in tandem on the 2-week time scale.

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Chia-chi Wang
and
Gudrun Magnusdottir

Abstract

The intertropical convergence zone (ITCZ) is observed to undulate and at times break down into a series of tropical disturbances in several days. Some of these disturbances may develop into tropical cyclones and move to higher latitudes, while others dissipate, and the ITCZ may reform in the original region. It has been proposed that the ITCZ may break down because of its heating-induced potential vorticity (PV) anomalies. Here this process is examined in three-dimensional simulations using a primitive equation model. A simulation of the ITCZ in a background state of rest is compared to simulations in different background flows. The effect of different vertical structures of the prescribed heating is also examined.

Deep heating induces a positive PV anomaly in the lower troposphere, leading to a reversal of the PV gradient on the poleward side of the heating, while the induced PV anomaly at upper levels is negative, leading to a reversal of the PV gradient on the equatorward side of the heating. The response at upper levels leads to a weaker PV gradient change, but the response is greater in areal extent than the lower-tropospheric response. For shallow heating, the lower-tropospheric PV response is greater than that for deep heating, and there is no upper-tropospheric PV response. The ITCZ lasts longer before breaking in this case than in the deep heating case.

Effects of the background flow are mainly felt in the deep heating cases. When the background flow enforces the PV-induced wind field, ITCZ breakdown occurs more rapidly, whereas when the background flow is opposite to the PV-induced flow, ITCZ breakdown takes longer and the ITCZ may dissipate before breakdown.

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John T. Abatzoglou
and
Gudrun Magnusdottir

Abstract

Planetary wave breaking (PWB) over the subtropical North Atlantic is observed over 45 winters (December 1958–March 2003) using NCEP–NCAR reanalysis data. PWB is manifested in the rapid, large-scale and irreversible overturning of potential vorticity (PV) contours on isentropic surfaces in the subtropical upper troposphere. As breaking occurs over the subtropical North Atlantic, an upper-tropospheric PV tripole anomaly forms with nodes over the subtropical, midlatitude, and subpolar North Atlantic. The northern two nodes of this tripole are quite similar to the spatial structure of the North Atlantic Oscillation (NAO), with positive polarity.

Nonlinear reflection is identified in approximately a quarter of all PWB events. Following breaking, two distinct circulation regimes arise, one in response to reflective events and the other in response to nonreflective events. For reflective events, anomalies over the North Atlantic rapidly propagate away from the breaking region along a poleward arching wave train over the Eurasian continent. The quasi-stationary wave activity flux indicates that wave activity is exported out of the Atlantic basin. At the same time, the regional poleward eddy momentum flux goes through a sign reversal, as does the polarity of the NAO. For nonreflective events, the dipole anomaly over the North Atlantic amplifies. Diagnostics for nonreflective events suggest that wave activity over the Azores gets absorbed, allowing continued enhancement of both the regional poleward eddy momentum flux and the positive NAO.

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Gudrun Magnusdottir
and
Wayne H. Schubert

Abstract

We develop here the isentropic–geostrophic coordinate version of semigeostrophic theory on a midlatitude β-plane. This approach results in a simple mathematical form in which the horizontal ageostrophic velocities are implicit and the entire dynamics reduces to a predictive equation for the potential pseudodensity and an invertibility relation. Linearized versions of the theory lead to a generalized Charney–Stern theorem for combined barotropic–baroclinic instability and to Rossby wave solutions with a meridional structure different from that in quasi-geostrophic theory.

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Gudrun Magnusdottir
and
Wayne H. Schubert

Abstract

This paper presents the combined isentropic and spherical geostrophic coordinate version of semigeostrophic theory. This is accomplished by first proposing a spherical coordinate generalization of the geostrophic momentum approximation and discussing its associated conservation principles for absolute angular momentum, total energy, potential vorticity and potential pseudodensity. We then show how the use of the spherical geostrophic coordinates allows the equations of the geostrophic momentum approximation to be written in a canonical form that makes ageostrophic advection implicit. This leads to a simple equation for the prediction of the potential pseudodensity. The potential pseudodensity can then be inverted to obtain the associated wind and mass fields. In this way the more general semigeostrophic theory retains the same simple mathematical structure as quasi-geostrophic theory—a single predictive equation which does not explicitly contain ageostrophic advection and an invertibility principle. The combined use of isentropic and spherical geostrophic coordinates is crucial to retaining this simplicity.

In order to demonstrate how the theory applies to problems of barotropic–baroclinic instability and Rossby–Haurwitz wave dispersion, we derive the semigeostrophic generalization of the Charney–Stern theorem and compare the semigeostrophic Rossby–Haurwitz wave frequencies with those of Laplace's tidal equations. The agreement between these frequencies is generally better than 0.5%. Thus, the theory appears to encompass a wide range of meteorological phenomena including both planetary-scale and synoptic-scale waves, along with their finer scale aspects such as fronts and jets.

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Gudrun Magnusdottir
and
Peter H. Haynes

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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Wayne H. Schubert
and
Gudrun Magnusdottir

Abstract

A potential pseudodensity principle is derived for the quasi-static primitive equations on the sphere. An important step in the derivation of this principle is the introduction of “vorticity coordinates”—that is, new coordinates whose Jacobian with respect to the original spherical coordinates is the dimensionless absolute isentropic vorticity. The vorticity coordinates are closely related to Clebsch variables and are the primitive equation generalizations of the geostrophic coordinates used in semigeostrophic theory. The vorticity coordinates can be used to transform the primitive equations into a canonical form. This form is mathematically similar to the geostrophic relation. There is flexibility in the choice of the potential function appearing in the canonical momentum equations. This flexibility can be used to force the vorticity coordinates to move with some desired velocity, which results in an associated simplification of the material derivative operator. The end result is analogous to the way ageostrophic motions become implicit when geostrophic coordinates are used in semigeostrophic theory.

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