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Prashant D. Sardeshmukh and Isaac M. Held

Abstract

The time mean vorticity balance in the summertime tropical upper troposphere of an atmospheric general circulation model constructed at the Geophysical Fluid Dynamics Laboratory is examined, with particular emphasis on the detailed balance in the Tibetan anticyclone. The model produces a reasonable simulation of the large-scale features of the northern summer 200 mb flow in the tropics, without the inclusion of subgrid scale processes that strongly damp the upper tropospheric vorticity. The vorticity balance is essentially nonlinear and nearly inviscid. There is considerable cancellation between the stretching and horizontal advection of vorticity by the time mean flow in the vicinity of the Tibetan anticyclone, with much of the remainder balanced by vertical advection and twisting. Mixing by the resolved transients is not negligible in some regions, but considerably smaller than the horizontal advection overall and less well correlated with the stretching. Subgrid scale mixing (consisting only of a biharmonic horizontal diffusion) plays a negligible role in this vorticity budget.

To relate this study to linear models of the stationary flow in the tropics, the steady state barotropic voracity equation on the sphere is linearized about the GCM's July mean zonal flow at 200 mb and forced with the GCM's July mean vortex stretching. It is found that the strength of the Tibetan anticyclone can be reproduced only by including a very strong damping of vorticity in this linear model. The strong damping needed by other authors (e.g., Holton and Colton) in their linear diagnoses of the tropical upper tropospheric vorticity balance is therefore interpreted as possibly accounting for neglected nonlinearities, and not necessarily cumulus friction. Our conclusions are, however, potentially suspect, since the terms in our vorticity budget have considerable structure on the smallest scales that can be resolved by the GCM.

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R. Lee Panetta and Isaac M. Held

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Statistically steady states of a two-layer quasi-geostrophic model truncated to retain only the zonal mean flow and one nonzero zonal wavenumber, but with high meridional resolution, are described. The model is forced by imposing a time-mean unstable meridional temperature gradient, assuming that deviations from the time-mean are doubly periodic. A comparison is made with a more conventional channel model with the same zonal truncation, in which the flow is forced by radiative relaxation to an unstable temperature gradient. It is shown that the statistics of the channel model approach those of the doubly periodic model as the width of the unstable region in the former is increased. Implications for parameterization theories are discussed.

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Pablo Zurita-Gotor and Isaac M. Held

Abstract

An instability involving the resonant interaction of a Rossby wave and a Kelvin wave has been proposed to drive equatorial superrotation in planetary atmospheres with a substantially smaller radius or a smaller rotation rate than Earth, that is, with a large thermal Rossby number. To pursue this idea, this paper investigates the equilibration mechanism of Kelvin–Rossby instability by simulating the unforced initial-value problem in a shallow-water model and in a multilevel primitive equation model. Although the instability produces equatorward momentum fluxes in both models, only the multilevel model is found to superrotate. It is argued that the shortcoming of the shallow-water model is due to its difficulty in representing Kelvin wave breaking and dissipation, which is crucial for accelerating the flow in the tropics. In the absence of dissipation, the zonal momentum fluxed into the tropics is contained in the eddy contribution to the mass-weighted zonal wind rather than the zonal-mean zonal flow itself. In the shallow-water model, the zonal-mean zonal flow is only changed by the eddy potential vorticity flux, which is very small in our flow in the tropics and can only decelerate the flow in the absence of external vorticity stirring.

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J. David Neelin and Isaac M. Held

Abstract

The vertically integrated moist static energy equation provides a convenient starting point for the construction of simple models of the time-mean low level convergence in the tropics. A vertically integrated measure of the moist static stability, the “gross moist stability,” proves to be of central importance. Minima in this quantity mark the positions of the tropical convergence zones. We argue that the positions of these minima are determined by the time-mean moisture field, which is, in turn, closely tied to the time-mean surface temperature.

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Isaac M. Held and Peter J. Phillips

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A barotropic model is described that is designed to study the interaction of the Hadley cell with a Rossby wave forced in midlatitudes by a stationary “topographic” source. The Hadley cell is driven by a mass source/sink that is partly fixed, representing solar heating, and partly dependent on the layer thickness, representing infrared cooling. The response of the mean zonal and meridional winds to infinitesimal wave forcing is analyzed in detail; then the forcing is gradually increased to examine the departures from linearity.

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Chiung-Yin Chang and Isaac M. Held

Abstract

In idealized models of the extratropical troposphere, both β and surface friction can control the equilibrated scales of baroclinic eddies by stopping the inverse cascade. A scaling theory on how surface friction alone sets these scales was proposed by Held in 1999 in the case of a quadratic drag law. However, the theory breaks down when friction is modeled by linear damping, and there are other reasons to suspect that it is oversimplified. An ideal system to test the theory is the homogeneous two-layer quasigeostrophic model in the β = 0 limit with quadratic damping. This study investigates some numerical simulations of the model to analyze two causes of the theory’s breakdown. They are 1) the asymmetry between two layers due to confinement of friction to the lower layer and 2) deviation from a spectrally local inverse energy cascade due to the spread of wavenumbers over which energy is input into the barotropic mode. The former is studied by comparing the simulations with drag appearing asymmetrically or symmetrically between the two layers. The latter is addressed with a heuristic modification of the theory. A regime where eddies equilibrate without an inverse cascade is also examined. A comparison is then made between quadratic and linear drag simulations. The connection to a competing theory based on the dynamics of equivalent barotropic vortices with thermal signatures is further discussed. Finally, we present an example of an inhomogeneous statistically steady state to argue that the diffusivity obtained from the homogeneous model has relevance to more realistic configurations.

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Pablo Zurita-Gotor and Isaac M. Held

Abstract

This work investigates the characteristics of westward-propagating Rossby modes in idealized global general circulation models. Using a nonlinear smoothing algorithm to estimate the background spectrum and an objective method to extract the spectral peaks, the 4 leading meridional modes can be identified for each of the first 3 zonal wavenumbers, with frequencies close to the predictions from the Hough modes obtained by linearizing about a state of rest. Variations in peak amplitude for different modes, both within a simulation and across simulations, may be understood under the assumption that the forcing of the modes scales with the background spectrum. Surface friction affects the amplitude and width of the peaks but both remain finite as friction goes to zero, which implies that some other mechanism, arguably nonlinear, must also contribute to the damping of the modes. Although spectral peaks are also observed for the precipitation field with idealized moist physics, there is no evidence of mode enhancement by the convective heating. Subject to the same friction, the amplitude of the peaks are very similar in the dry and moist models when both are normalized by the background spectra.

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Isaac M. Held and In-Sik Kang

Abstract

A series of linear and nonlinear barotropic models are used to interpret the extratropical response to El Niflo equatorial surface temperatures as simulated by an atmospheric general circulation model (GCM). The divergence, time-mean vorticity tendency due to transients, and the zonal mean tlow are specified from the GCM, and the deviation of the streamfunction from its zonal mean at an upper-tropospheric level is predicted. Nonlinearsteady-state models suggest that the extratropical wave train is primarily forced from the central rather than the western Pacific and that subtropical divergence anomalies are of more importance than tropical anomalies. These nonlinear solutions can be reproduced with little loss in accuracy by linearizing about the zonally asymmetric climatological flow. If one linearizes about the zonally symmetric flow, the part of the solution forced from thewestern Pacific deteriorates significantly. The solution in the tropics and subtropics also deteriorates if advection of vorticity by the divergent flow is omitted.

Forcing by transients plays a secondary role in generating the extratropical wave train in these barotropic models, but it is pointed out that the subtropical convergence that forces the bulk of this wave train could itself be closely related to anomalies in the transient forcing.

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Kerry H. Cook and Isaac M. Held

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Stationary waves generated over orography in a linear model and a general circulation model (GCM) are compared to examine how the atmosphere's response is established for small mountains and how linear theory breaks down over large orographic features. Both models have nine vertical levels and are low-resolution (R15) spectral models. The linear model solves the stationary linear primitive equations. The GCM's control integration uses zonally uniform and hemispherically symmetric boundary conditions, with a global swamp surface. Five experiments are performed by perturbing the GCM with Gaussian mountains of various heights introduced in midlatitudes. The stationary wave model is linearized about zonal mean fields from the GCM climatology.

The linear model's response to a Gaussian mountain at 45°N latitude is dominated by a single wave train radiating toward the southeast. For mountain heights between 0.7 and 2 km, the GCM's stationary waves are similar to the linear model response to orography, although amplitudes increase less rapidly than linearly with mountain height. For larger mountains, closed isentropes and distinctly nonlinear flow occur along the surface of the mountain and a large poleward-radiating wave train develops. The development of closed isentropes, and the breakdown of linear theory, can be predicted whenever the slope of the surface exceeds the slope of the isentropes in the unperturbed (no mountain) basic state.

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Nicholas J. Lutsko and Isaac M. Held

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A dry atmospheric general circulation model is forced with large-scale, Gaussian orography in an attempt to isolate a regime in which the model responds linearly to orographic forcing and then to study the departures from linearity as the orography is increased in amplitude. In contrast to previous results, which emphasized the meridional propagation of orographically forced stationary waves, using the standard Held–Suarez (H–S) control climate, it is found that the linear regime is characterized by a meridionally trapped, zonally propagating wave. Meridionally trapped waves of this kind have been seen in other contexts, where they have been termed “circumglobal waves.” As the height of the orography is increased, the circumglobal wave coexists with a meridionally propagating wave and for large-enough heights the meridionally propagating wave dominates the response. A barotropic model on a sphere reproduces this trapped wave in the linear regime and also reproduces the transition to meridional propagation with increasing amplitude. However, mean-flow modification by the stationary waves is very different in the two models, making it difficult to argue that the transitions have the same causes. When adding asymmetry across the equator to the H–S control climate and placing the orography in the cooler hemisphere, it becomes harder to generate trapped waves in the GCM and the trapping becomes sensitive to the shape of the orography. The barotropic model overestimates the trapping in this case. These results suggest that an improved understanding of the role of circumglobal waves will be needed to understand the stationary wave field and its sensitivity to the changes in the zonal-mean climate.

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