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Adam H. Sobel and R. Alan Plumb

Abstract

Two different approaches are applied to quantify mixing in a shallow water model of the stratosphere. These are modified Lagrangian mean (MLM) theory and a technique referred to as “reverse domain filling with local gradient reversal” (RDF-LGR). The latter is similar to a previously existing technique using contour advection and contour surgery.

It is first proved that in an inviscid shallow water atmosphere subject to mass sources and sinks, if the mass enclosed by a potential vorticity (PV) contour is steady in time, then the integral of the mass source over the area enclosed by the contour must be zero. Next, the MLM and RDF-LGR approaches are used to diagnose the time-averaged transport across PV contours in the model simulations.

The model includes a sixth-order hyperdiffusion on the vorticity field. Except in a thin outer “entrainment zone,” the hyperdiffusion term has only a very weak effect on the MLM mass budget of the polar vortex. In the entrainment zone, the hyperdiffusion term has a significant effect. The RDF-LGR results capture this behavior, providing good quantitative estimates of the hyperdiffusion term, which is equivalent to the degree of radiative disequilibrium at a PV contour. This agreement shows that the main role of the hyperdiffusion is to “mop up” the filaments that are produced by the essentially inviscid large-scale dynamics. All calculations are repeated for two values of the hyperdiffusion coefficient that differ by a factor of 50, with little difference in the results. This suggests that the amount of material entrained from the vortex edge into the surf zone does not depend on the details of the small-scale dissipation, as long as it is sufficiently weak and has some degree of scale selectivity.

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Michael J. Ring and R. Alan Plumb

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Following on their previous work, in which they found the annular modes to be a preferred response of a simplified general circulation model atmosphere to a number of mechanical forcings, the authors now explore the quantitative relationship between forcing and response. In particular, the applicability of the fluctuation–dissipation theorem to this problem is investigated. First, the set of model trials is expanded by including runs in which the applied forcings are thermal rather than mechanical. For thermal forcings confined to the extratropics, “annular mode–like” responses, reminiscent of those found in earlier work, are found, but, as found in previous studies, the response is less like an annular mode when the forcing has significant amplitude in the tropics. Assuming small departures from the control climatology, and making a few further assumptions, the authors derive a theoretical relationship between forcing and response. This relationship is a statement of the fluctuation–dissipation theorem for this problem. The response of the model is found to be qualitatively consistent with the theoretical predictions. However, several aspects of the response diverge quantitatively from the theoretical expectation.

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Ivana Cerovečki, R. Alan Plumb, and William Heres

Abstract

The baroclinically unstable wind- and buoyancy-driven flow in a zonally reentrant pie-shaped sector on a sphere is numerically modeled and then analyzed using the transformed Eulerian-mean (TEM) formalism. Mean fields are obtained by zonal and time averaging performed at fixed height. The very large latitudinal extent of the basin (50.7°S latitude to the equator) allows the latitude variation of the Coriolis parameter to strongly influence the flow. Persistent zonal jets are observed in the statistically steady state. Reynolds stress terms play an important role in redistributing zonal angular momentum: convergence of the lateral momentum flux gives rise to a strong eastward jet, with an adjacent westward jet equatorward and weaker multiple jets poleward. An equally prominent feature of the flow is a strong and persistent eddy that has the structure of a Kelvin cat’s eye and generally occupies the zonal width of the basin at latitudes 15°–10°S.

A strongly mixed surface diabatic zone overlies the near-adiabatic interior, within which Ertel potential vorticity (but not thickness) is homogenized along the mean isopycnals everywhere in the basin where eddies have developed (and thus is not homogenized equatorward of the most energetic eastward jet). A region of low potential vorticity (PV) is formed adjacent to the strong baroclinic front associated with that jet and subsequently maintained by strong convective events.

The eddy buoyancy flux is dominated by its skew component over large parts of the near-adiabatic interior, with cross-isopycnal components present only in the vicinity of the main jet and in the surface diabatic layer. Close to the main jet, the cross-isopycnal components are dominantly balanced by the triple correlation terms in the buoyancy variance budget, while the advection of buoyancy variance by the mean flow is not a dominant term in the eddy buoyancy variance budget.

Along-isopycnal mixing in the near-adiabatic interior is estimated by applying the effective diffusivity diagnostic of Nakamura. The effective diffusivity is large at the flanks of the mean jet and beneath it and small in the jet core. The apparent horizontal diffusivity for buoyancy obtained from the flux–gradient relationship is the same magnitude as the effective diffusivity, but the structures are rather different. The diapycnal diffusivity is strongest in the surface layer and also in a convectively unstable region that extends to depths of hundreds of meters beneath the equatorward flank of the main jet.

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Michael J. Ring and R. Alan Plumb

Abstract

Previous studies using simplified general circulation models have shown that “annular modes” arise as the dominant mode of variability. A simple GCM is used here to explore to what extent these modes are also the preferred response of the system to generic forcing.

A number of trials are conducted under which the model is subjected to an artificial, zonally symmetric angular momentum forcing, and the climatologies of these trials are compared to that of the control. The forcing location is varied among the several trials. It is found that the changes in the model’s climatology are generally annular mode–like, as long as the imposed forcing projects strongly upon the annular modes of the unforced model.

The role of changes to the eddy–zonal flow feedback versus the action of direct forcing is also considered through the use of a zonally symmetric version of the model. It is found that the direct responses to forcing are insufficient to capture either the strength or the structure of the annular mode responses. Instead, the changes in eddy fluxes are needed to produce the correct responses.

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Nikki C. Privé and R. Alan Plumb

Abstract

The roles of eddies and forcing asymmetry in the dynamics of the large-scale monsoon circulation are investigated with a general circulation model. The net impact of eddies is found to be a slight weakening of the zonal mean monsoon circulation. The eddies strongly impact the momentum budget of the circulation, but the qualitative behavior of the monsoon flow is not substantially altered. The introduction of asymmetric forcing reveals the limitations of axisymmetric studies in representing the fully three-dimensional monsoon. Advection of low subcloud moist static energy air from the midlatitude oceans is seen to strongly impact the subcloud moist static energy budget in the continental subtropics, limiting the poleward extent of the monsoon. The advection of low moist static energy air must be blocked by orography, or the source of low moist static energy air must be removed, in order to induce strong precipitation over the subtropical landmass. An equatorial SST gradient is needed to induce a cross-equatorial meridional monsoon circulation. The location of the maximum subcloud moist static energy remains a good indicator for the limit of the monsoon.

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Darryn W. Waugh and R. Alan Plumb

Abstract

We present a trajectory technique, contour advection with surgery (CAS), for tracing the evolution of material contours in a specified (including observed) evolving flow. CAS uses the algorithms developed by Dritschel for contour dynamics/surgery to trace the evolution of specified contours. The contours are represented by a series of particles, which are advected by a specified, gridded, wind distribution. The resolution of the contours is preserved by continually adjusting the number of particles, and finescale features are produced that are not present in the input data (and cannot easily be generated using standard trajectory techniques). The reliability, and dependence on the spatial and temporal resolution of the wind field, of the CAS procedure is examined by comparisons with high-resolution numerical data (from contour dynamics calculations and from a general circulation model), and with routine stratospheric analyses. These comparisons show that the large-scale motions dominate the deformation field and that CAS can accurately reproduce small scales from low-resolution wind fields. The CAS technique therefore enables examination of atmospheric tracer transport at previously unattainable resolution.

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C. Juno Hsu and R. Alan Plumb

Abstract

The authors investigate the nonlinear dynamics of almost inviscid, thermally forced, divergent circulations in situations that are not axisymmetric. In shallow-water numerical calculations, asymmetry is imposed on a locally forced anticyclone by imposition of a mean wind, or a planetary vorticity gradient. Behavior is similar in the two cases. With weak asymmetry, the forced anticyclone is distorted but remains intact and is qualitatively unchanged from the symmetric response. For sufficiently large asymmetry, however, the elongated anticyclone becomes unstable and periodically sheds eddies. This behavior shows how the circulation constraint can be satisfied, even when the time-mean absolute vorticity remains finite in the divergent region, and provides a continuous evolution between the nonlinear (symmetric) and linear (highly asymmetric) limits.

Westward shedding of anticyclones from the Tibetan anticyclone is indeed evident in NCEP reanalysis data. These eddies are trapped near the tropopause. Cutoff potential vorticity features are confined to within about 20 K of the tropopause; in geopotential, they extend somewhat further, but not below about 400 hPa.

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Eric M. Leibensperger and R. Alan Plumb

Abstract

Large-scale chaotic stirring stretches tracer contours into filaments containing fine spatial scales until small-scale diffusive processes dissipate tracer variance. Quantification of tracer transport in such circumstances is possible through the use of Nakamura’s “effective diffusivity” diagnostics, which make clear the controlling role of stirring, rather than small-scale dissipation, in large-scale transport. Existing theory of effective diffusivity is based on a layerwise approach, in which tracer variance is presumed to cascade via horizontal (or isentropic) stirring to small-scale horizontal (or isentropic) diffusion. In most geophysical flows of interest, however, baroclinic shear will tilt stirred filamentary structures into almost-horizontal sheets, in which case the thinnest dimension is vertical; accordingly, it will be vertical (or diabatic) diffusion that provides the ultimate dissipation of variance. Here new theoretical developments define effective diffusivity in such flows. In the frequently relevant case of isentropic stirring, it is shown that the theory is, in most respects, unchanged from the case of isentropic diffusion: effective isentropic diffusivity is controlled by the isentropic stirring and, it is argued, largely independent of the nature of the ultimate dissipation. Diabatic diffusion is not amplified by the stirring, although it can be modestly enhanced through eddy modulation of static stability. These characteristics are illustrated in numerical simulations of a stratospheric flow; in regions of strong stirring, the theoretical predictions are well supported, but agreement is less good where stirring is weaker.

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Angela M. Zalucha, R. Alan Plumb, and R. John Wilson

Abstract

Previous work with Mars general circulation models (MGCMs) has shown that the north–south slope in Martian topography causes asymmetries in the Hadley cells at equinox and in the annual average. To quantitatively solve for the latitude of the dividing streamline and poleward boundaries of the cells, the Hadley cell model of Lindzen and Hou was modified to include topography. The model was thermally forced by Newtonian relaxation to an equilibrium temperature profile calculated with daily averaged solar forcing at constant season. Two sets of equilibrium temperatures were considered that either contained the effects of convection or did not. When convective effects were allowed, the presence of the slope component shifted the dividing streamline upslope, qualitatively similar to a change in season in Lindzen and Hou’s original (flat) model. The modified model also confirmed that the geometrical effects of the slope are much smaller than the thermal effects of the slope on the radiative–convective equilibrium temperature aloft. The results are compared to a simple MGCM forced by Newtonian relaxation to the same equilibrium temperature profiles, and the two models agree except at the winter pole near solstice. The simple MGCM results for radiative–convective forcing also show an asymmetry between the strengths of the Hadley cells at the northern summer and northern winter solstices. The Hadley cell weakens with increasing slope steepness at northern summer solstice but has little effect on the strength at northern winter solstice.

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Ted Shepherd, R. Alan Plumb, and Steven C. Wofsy
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