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Ka Kit Tung

Abstract

A zonally averaged model of stratospheric tracer transport is formulated in isentropic coordinated There are some conceptual and computational advantages, as well as some disadvantages in adopting the potential temperature, instead of pressure, as the vertical coordinate. The main disadvantage is that the “density” (mass per unit coordinate volume) in isentropic coordinates is no longer a constant as in the pressure coordinate system under the hydrostatic approximation. However, it can be shown that this density effect is almost negligible in the calculation of the mean diabatic circulation and the eddy advective transports. What is gained by adopting the new formulation is a conceptually simpler picture of the interplay of diabatic and adiabatic process in the transport of tracers. Mean diabatic heating (cooling) forces a direct rising (descending) mean mass flow. Along the streamlines of this mean mass circulation, tracers are advected in the mean. These surfaces slope downward and poleward in the lower stratosphere. In addition to advection, tracers are also dispersed from their mean path by transient adiabatic processes in a direction parallel to the local isentropic surface. As a result, the lines of mean constant tracer mass mixing ratio slope less steeply than the mean streamlines, but more steeply than the isentropic surfaces. The effect of eddy transport on chemically reacting minor constituent gases is also discussed.

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Ka Kit Tung

Abstract

For quasi-geostrophic stationary long waves forced by topography, the nonlinear lower boundary condition is derived in terms of the geopotential height and compared with the linearized version. The common practice of replacing terms describing the flow over and around a mountain by upstream zonal flow over the mountain and evaluating the resulting condition at sea level is found to be a good approximation for the cases considered and does not need to be modified as sometimes suggested. Specifically, it is found that this approximation does not affect, for most cases, the lower boundary condition expressed in terms of the geopotential height provided that the stationary wave is not near resonance. At resonance, the eddy advection terms may become important for large-amplitude waves when dissipation and surface diabatic heating are taken into account

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Ka Kit Tung
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Ka Kit Tung

Abstract

A nongeostrophic theory of zonally averaged circulation is formulated using the nonlinear primitive equations on a sphere, taking advantage of the more direct relationship between the mean meridional circulation and diabatic heating rate which is available in isentropic coordinates. Possible differences between results of nongeostrophic theory and the commonly used geostrophic formulation are discussed concerning (i) the role of eddy forcing of the diabatic circulation, and (ii) the “nonlinear nearly inviscid” limit versus the geostrophic limit.

A set of general diagnostic tools comparable in scope to their geostrophic counterparts is given in Part I, including (i) a generalized definition of Eliassen–Palm flux divergence (without restriction to small amplitudes, to steady state or to adiabatic flows), the vanishing of which is a necessary condition for nonacceleration, (ii) a generalized nonlinear Taylor formula that relates the flux of Ertel's potential vorticity to the Eliassen–Palm flux divergence and (iii) a relationship between the Eliassen–Palm flux divergence and isentropic mixing coefficient, Kyy, used in chemical tracer transport equations in isentropic coordinates. From the mean momentum budget, we give in Part II in estimate of the Eliassen–Palm flux divergence using fitted “observed” field of net radiative heating rate. From this an estimate of the magnitude and latitudinal/seasonal variation of Kyy is also provided.

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Ka Kit Tung

Abstract

The problem of barotropic instability of zonal flows to infinitesimal normal-mode perturbations is considered. The zonal flow is assumed to be continuous. but is allowed to be monotonic or nonmonotonic, and can have one or more inflection-points (which are the zeroes of the mean vorticity gradient., the zeroes are allowed to be of any order). A sufficient condition for instability is derived for this general flow profile. The present result complements the condition for stability found by Arnol'd (1965).

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Ka Kit Tung

Abstract

Through a critical analysis of the convergence properties of spectral series, it is shown that Clark's method of solution leads to a divergent series; hence all his recent results on quasi-geostrophic wave propagation in distorted background flows are erroneous. A general condition for convergence is derived. The convergent solution (if it exists) to a general second-order recurrence formula is given, which is then applied to Clark's problem, yielding an exact closed form solution. The solution consists of an interacting trio of waves whose wavenumbers add up to zero. With results thus obtained, it is found that the propagation of wavenumber 2 disturbances is not affected by wavenumber 1 finite-amplitude distortions in the background flow, in disagreement with the result of Clark.

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Priscilla Cehelsky and Ka Kit Tung

Abstract

Previous results based on low- and intermediate-order truncations of the two-layer model suggest the existence of multiple equilibria and/or multiple weather regimes for the extratropical large-scale flow. The importance of the transient waves in the synoptic scales in organizing the large-scale flow and in the maintenance of weather regimes was emphasized. Our result shows that multiple equilibria/weather regimes that are present in lower order models examined disappear when a sufficient number of modes are kept in the spectral expansion of the solution to the governing partial differential equations. Much of the chaotic behavior of the large-scale flow that is present in intermediate order models is now found to be spurious. Physical reasons for the drastic modification are offered.

We further note a peculiarity in the formulation of most existing two-layer models that also tends to exaggerate the importance of baroclinic processes and increase the degree of unpredictability of the large-scale flow.

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Ming Fang and Ka Kit Tung

Abstract

The classical problem of viscosity-driven, axially symmetric meridional circulation, partly solved only for the midlatitudes by Charney, is solved here analytically in the whole globe and for any value of viscosity coefficient ν. The solution satisfies Hide's theorem for any Ekman number when Ro < 80E 2, where Ro is the Rossby number and E is the Ekman number. For Ro > 80E 2, the linear solution ceases to be asymptotically valid. The nonlinear, nearly inviscid regime of Held and Hou presumably is a subset of the second regime (for E → 0+ and Ro fixed).

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Priscilla Cehelsky and Ka Kit Tung

Abstract

The concept of baroclinic adjustment is reexamined in the context of a fully nonlinear two-layer model on a β-plane. Based on our results we propose a single, conceptually very simple mechanism of the nonlinear equilibration of waves and the mean flow, which we term “nonlinear baroclinic adjustment.” The new concept appears applicable to cases that currently require different explanations, varying from case to case, to account for the equilibration of the mean temperature gradient in the presence of external driving.

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Ming Cai and Ka-Kit Tung

Abstract

Despite the differences in the spatial patterns of the external forcing associated with a doubling CO2 and with a 2% solar variability, the final responses in the troposphere and at the surface in a three-dimensional general circulation model appear remarkably similar. Various feedback processes are diagnosed and compared using the climate feedback–response analysis method (CFRAM) to understand the mechanisms responsible.

At the surface, solar radiative forcing is stronger in the tropics than at the high latitudes, whereas greenhouse radiative forcing is stronger at high latitudes compared with the tropics. Also solar forcing is positive everywhere in the troposphere and greenhouse radiative forcing is positive mainly in the lower troposphere. The water vapor feedback strengthens the upward-decreasing radiative heating profile in the tropics and the poleward-decreasing radiative heating profile in the lower troposphere. The “evaporative” and convective feedbacks play an important role only in the tropics where they act to reduce the warming at the surface and lower troposphere in favor of upper-troposphere warming. Both water vapor feedback and enhancement of convection in the tropics further strengthen the initial poleward-decreasing profile of energy flux convergence perturbations throughout the troposphere. As a result, the large-scale dynamical poleward energy transport, which acts on the negative temperature gradient, is enhanced in both cases, contributing to a polar amplification of warming aloft and a warming reduction in the tropics. The dynamical amplification of polar atmospheric warming also contributes additional warming to the surface below via downward thermal radiation.

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