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Lee E. Branscome

Abstract

A parameterization of transient eddy heat flux is developed which incorporates baroclinic wave behavior in a continuously stratified fluid on a β-plane. The meridional and vertical heat transports are more sensitive to forced changes in the mean state than suggested by earlier parameterizations. This strong response is analogous to the rapid flux variation in a two-level model near neutral stability. A scheme for applying the parameterization to observed mean zonal flow is suggested and computed fluxes are similar in magnitude and structure to observed eddy heat flux. The flux modeling is consistent with the stronger dependence on meridional temperature gradient and large seasonal variation of the vertical eddy scale observed in lower latitudes.

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Lee E. Branscome

Abstract

The classic Charney baroclinic stability problem is examined through perturbation techniques in the short-wave limit, near the first neutral curve separating Charney and Green modes, and near the second neutral curve separating long and short Green modes. This method provides simple analytical expressions for the vertical structure of the growing waves and the dependence of phase speeds and growth rates on mean flow parameters. The rapidly growing Charney modes have horizontal and vertical scales which crucially depend on the β-parameter. Structures of heat and potential vorticity fluxes are also represented by approximate solutions and their dependence on wavenumber is examined.

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Lee E. Branscome and Enda O'Brien

Abstract

The response of midlatitude temperature structure to changes in radiative forcing is examined in an analytical energy-balance model that includes parameterized eddy heat fluxes and linear radiative heating. The characteristics of heat-transporting baroclinic waves are determined within the model, while simultaneously allowing the waves to adjust the mean-state static stability and meridional temperature gradient. By changing the radiative equilibrium temperature, the forcing is varied through a very wide range in order to investigate qualitative, limiting behavior of the baroclinic eddy feedbacks.

The flux parameterization is based on Charney's continuously stratified, β-plane model of baroclinic instability and incorporates a parameter which is analogous to the supercriticality (i.e., degree of instability) of the Phillips' two-level model. A baroclinic adjustment hypothesis as proposed by other investigators suggests that interaction between baroclinic fluxes and radiative heating keeps the extratropical atmosphere near neutral baroclinic stability, i.e., zero supercriticality. Although the model considered here allows for this feedback, this behavior does not occur.

The model meridional temperature gradient is primarily dependent on its radiative equilibrium value and is insensitive to changes in the static stability of radiative equilibrium. The negative feedback between meridional temperature gradient and eddy heat flux is enhanced as the meridional forcing increases and the eddy flux becomes more efficient. Static stability is very sensitive to changes in the meridional forcing reflecting the strong dependence of vertical heat flux on meridional temperature gradient. A comparison of observed seasonal variation of the baroclinic stability parameter with model results suggests that a stabilizing process like moist convection is important in determining the midlatitude static and baroclinic stability during Northern Hemisphere summer.

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Enda O'Brien and Lee E. Branscome

Abstract

The effects of topography are examined in a class of low-order quasi-geostrophic models on a midlatitude β-plane. In the absence of topography the models are capable of producing qualitatively realistic zonal-mean circulations. The maintenance of the zonally symmetric and asymmetric circulations are examined with different spectral truncations and topographic configurations. The response to an isolated mountain peak is the most thoroughly investigated.

When the model is run without wave–wave interactions, the time-mean wave pattern forced by the isolated mountain is a superposition of waves which are either in phase or 180° out of phase with the mountain. When they are included, transient wave-wave interactions alter the mean zonal flow, which leads to a substantial modification of the time-mean wave. Specifically, the amplitude of the longest planetary wave in the model is enhanced as that wave is pushed closer to resonance by the change in the midlevel zonal flow. A phase shift relative to the topography is also induced. A reduction in surface zonal wind caused by the nonlinear wave interactions leads to weaker topographic forcing and smaller time-mean amplitudes for shorter waves. Although the heat and vorticity budgets of the time-mean wave are dominated by “linear” wave–mean flow interactions for the planetary wave, the nonlinear advective terms are of significant magnitude and generally act to oppose the corresponding linear terms for short waves. At least five meridional modes are required to produce qualitatively realistic stationary waves, which remain relatively unchanged as the resolution is further increased.

A (5,5) model (which has 5 zonal waves, a zonal flow, and 5 meridional modes) and higher order models exhibit a significant amount of low-frequency variability and produce persistent anomalies whose time scales are not unlike those of observed anomalies. The planetary wave is not confined to a small region of phase, but undergoes considerable fluctuations in position and amplitude as evidenced by large variability in mountain-induced kinetic energy conversions. The most frequently occurring anomaly pattern can be described as an amplification and slight upstream shifting of the time-mean wave pattern. Low-frequency variability is much less pronounced in more severe truncations.

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Enda O'Brien, Douglas A. Stewart, and Lee E. Branscome

Abstract

Observational studies have revealed some coherent extratropical patterns associated with the tropical Madden–Julian (MJ) wave. This study is an attempt to clarify and constrain the interpretation of these patterns by investigating tropical–extratropical interactions on intraseasonal time scales in a global spectral model (GSM). Forcing representative of northern winter is used. A simple heating-only cumulus parameterization scheme is included to generate the MJ wave. The wave period in the model falls within the 30–60 day range observed and has a structure consistent with observations.

Various statistical techniques including compositing, empirical orthogonal function (EOF) analysis, and singular value decomposition (SVD) have been used to identify those extratropical patterns associated with the tropical MJ wave.

Under zonally symmetric external conditions (no topography) the MJ wave maintains a highly regular amplitude and phase speed. Nevertheless, there is no statistically significant coherent variability between the tropics and extratropics—no matter how much one field lags the other, and despite the frequent appearance of upper-level equatorial waveguides. Significance is determined by a Monte Carlo data scrambling method.

When topography is included, the MJ wave has a more variable amplitude in both space and time. All the statistical analyses reveal consistent planetary-scale extratropical patterns associated with different phases of the tropical wave. EOF and SVD analyses indicate that the MJ wave can explain about 10% of the variance in the extratropical 250-mb height field on intraseasonal time scales. Monte Carlo significance testing indicates that about 5% can be attributed to physical processes and 5% to chance.

The signal of tropical–extratropical interaction in the mountain case can be exposed more clearly by reducing the radiative driving by half and by using a specified propagating heat source as a proxy MJ wave. In this case up to 40% of the extratropical variance can be explained by the tropical wave, while the principal patterns of interaction remain similar to those obtained with strong driving.

The authors conclude that topography is essential to the propagation of a coherent MJ signal into the extratropics, while topography tends to disrupt the MJ wave in the tropics. The MJ wave (and its associated extratropical patterns) must be maintained in the presence of topography by wave activity penetrating the tropics from higher latitudes. A sufficiently high level of eddy activity in the extratropics is necessary for this to occur.

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William J. Gutowski Jr., Lee E. Branscome, and Douglas A. Stewart

Abstract

We use a global, primitive equation model to study the evolution of waves growing in a zonal mean state that is initially baroclinically unstable. The waves produce changes in the zonal mean state that we compare with changes predicted by baroclinic adjustment theories We examine mean state adjustment by representative zonal wavenumbers 3, 7 or 12.

In the absence of surface processes, as the wave grows to its maximum amplitude, it reduces the zonal mean state's potential vorticity gradient through the lower troposphere, in accord with adjustment theories. Over the latitudes with largest wave amplitude, changes in the static stability and the zonal wind's vertical shear contribute about equally to the potential vorticity gradient adjustment. However, during the last day of a wave's growth, momentum fluxes strengthen the barotropic component of the zonal wind and the potential vorticity gradient in the middle troposphere, changes that are not anticipated by adjustment theory. The static stability adjustment occurs across the latitudinal band occupied by the growing wave. Further experiments show that the static stability adjustment alone is very effective in reducing the instability of the flow and restricting the maximum amplitude attained by growing waves. Adjustment of the zonal wind's vertical shear is confined to a narrower range of latitude and is partially reversed as the wave decays. Additional experiments indicate that the barotropic governor mechanism of James does not contribute strongly to the mean flow's stabilization in the cases we examine, though it way inhibit secondary growth at latitudes adjacent to the initial disturbance.

When the model includes surface friction and heat flux, the waves adjust the zonal mean state less effectively, especially near the surface. Surface heat flux inhibits static stability adjustment, and surface friction inhibits adjustment of the zonal wind's vertical shear. In the absence of surface processes, the adjusted state produced by the wave is quite different from observed mean structures. However, with both surface processes included, the vertical profiles of the adjusted static stability, wind shear and potential vorticity gradient are similar to observed profiles. The model' interaction between the waves and the mean flow corroborates results from previous studies of baroclinic adjustment that used simpler representations of atmospheric dynamics.

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Lee E. Branscome, William J. Gutowski Jr., and Douglas A. Stewart

Abstract

The nonlinear development of baroclinically unstable waves in the presence of surface friction and heat flux is studied, using a global primitive equation model. The experiments use zonal wavenumber 3.7 or 12 and a variety of initial conditions, mostly representative of observed initial states. Other initial states consist of solidbody rotation with vertical shear of the zonal wind. In addition to comparisons of inviscid and dissipative experiments, the effect of linear and nonlinear drag formulations is compared. Starting from a small-amplitude perturbation in the temperature field, a modal structure emerges and grows exponentially for a few days. Unstable waves assume a structure that reduces frictional energy IOU when surface drag is present, but they still retain a normal mode character during a period of rapid growth. As the wave grows in amplitude, the ratio of upper-level to low-level eddy kinetic energy increases substantially in the presence of nonlinear surface drag. In the absence of surface drag or in the presence of linear drag the waves experience less structural change. Surface processes reduce the maximum amplitude achieved by the wave and damp the slowly growing wavenumber-3 and shallow wavenumber-12 disturbances more effectively than the rapidly growing, deep wavenumber 7.In the mature wave, surface momentum drag and heat flux suppress eddy velocity and temperature fields near the surface, causing the meridional heat flux to peak at about 800 mb rather than near the surface as itdoes when surface fluxes are excluded. When surface fluxes are present, the structures of mature waves resemble observations more closely than when the fluxes are absent. When initial conditions are similar to those used by Simmons and Hoskins, the Eliassen-Palm flux produced by the mature wave tends to converge in the upper troposphere, primarily as the result of the vertical gradient in poleward heat flux. However, the convergence is sensitive to initial conditions and is spread more broadly through the troposphere for other configurations of the initial state.

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William J. Gutowski Jr., Lee E. Branscome, and Douglas A. Stewart

Abstract

The interaction between moisture and baroclinic eddies was examined through eddy life-cycle experiments using a global, primitive equation model. How condensation affects the structural evolution of eddies, their fluxes of heat, moisture, and momentum, and their subsequent interaction with the zonal average state was examined. Initial states corresponded to climatological winter and summer zonal average states. For most experiments the perturbation had a fundamental zonal wavenumber 7, representing an appropriate scale for transient eddies that reach substantial amplitudes in the atmosphere. Additional experiments used fundamental wavenumber 4, 10, or 14.

The wave's vertical motion produced midtropospheric supersaturation whose heating further amplified the vertical motion. Consequently, the largest effects of condensation were associated with vertical transports. Compared to corresponding dry experiments, intensified vertical motions increased the maximum kinetic energy attained by the wave, but they also depleted the eddy available potential energy more rapidly, thus inducing a faster evolution of the life cycle. Even greater condensation occurred near the surface as warm, moist air moving poleward became supersaturated by heat loss into a cooler surface. However, the latent heat thus released was balanced by the heat loss into the surface and so produced no dynamical effect. The hydrological cycle induced by the wave was largely confined to the lower troposphere, but the strongest effects of condensation on eddy dynamics occurred in the upper troposphere, so the condensational heating altered only weakly the intensity of the wave-induced moisture cycle.

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