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K. K. Tung

Abstract

The present paper deals with the fundamental issue of whether one can treat waves as normal modes when critical surfaces, where the phase speed of the wave matches the zonal wind speed, are present. In particular the question of whether a Rossby critical level (such as the zero-wind line for stationary waves) is absorbing or reflecting is raised and subsequently addressed. It is found that the critical level is never totally absorbing; Rossby waves are partially reflected even if the critical layer is dominated by dissipative processes. The relevance of nonlinearity in planetary-scale Rossby wave critical layers is also discussed and it is found to be the dominant mechanism. With the relative magnitudes of nonlinearity versus viscosity relevant to the earth's atmosphere it is found that the steady-state critical level should be almost perfectly reflecting to incident Rossby waves. Consequently, normal-mode solutions can be found; the quantization condition for these waves is also derived.

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K. K. Tung and H. Yang

Abstract

Observational evidence for a global quasi-biennial oscillation (QBO) pattern is reviewed. In particular, the presence of an extratropical, as well as an equatorial, component of the QBO signal in column ozone is established. It is found that the ozone interannual variability is such that as one moves away from the Tropics, the frequency spectrum of the anomaly changes from one that is dominated by the equatorial QBO frequency of 1/30 mo to a two-peak spectrum around the two frequencies: 1/30 mo and 1/20 mo. Instead of treating the 1/20 mo frequency as a separate phenomenon to be filtered away in extracting the QBO in the extratropics, as was previously done, the authors argue that both peaks are integral parts of the extratropical QBO phenomenon. The 1/20 mo frequency happens to be the difference combination of the QBO frequency 1/30 mo and the annual frequency 1/12 mo. Therefore, it can represent the result of the QBO modulating an annual cycle. The authors suggest that previous methods of extracting the extratropical QBO signal severely underestimated the contribution of the QBO to the interannual variability of ozone when data are filtered to pass only the component with the period of equatorial QBO.

Further, it is argued that the transport of equatorial QBO ozone anomaly by a non-QBO circulation can at most account for 6–8 Dobson units (DU) of the observed interannual variability of column ozone in the extratropics. The remaining variability (up to 20 DU) probably cannot be produced without an anomaly in the transporting circulation in the extratropics.

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K. K. Tung and H. Yang

Abstract

Although the phenomenon of equatorial quasi-biennial oscillation is relatively well understood, the problem of how the equatorially confined QBO wave forcing can induce a signal in the extratroics of comparable or larger magnitude remains unsolved. A simple mechanistic model is constructed to provide a quantitative test of the hypothesis that the phenomenon of extratropical QBO is mainly caused by an anomalous seasonal circulation induced by an anomalous Eliassen-Palm flux divergence. The anomaly in E–P flux divergence may be caused in turn by the relative poleward and downward shift of the region of irreversible mixing (breaking) of the extratropical planetary waves during the easterly phase of the equatorial QBO as compared to its westerly phase. The hemispheric nature of the anomaly wave forcing in solstice seasons (viz., no wave breaking in the summer hemisphere) induces a global circulation anomaly that projects predominantly into the first few zonal Hough modes of Plumb. Such a global QBO circulation pattern, although difficult to measure directly, is reflected in the distribution of stratospheric tracers transported by it. Our model produces a global pattern of QBO anomaly in column ozone that appears to account for much of the unfiltered interannual variability in the column ozone observed by the TOMS instrument aboard the Nimbus satellite. Furthermore, the model produces the characteristic spectrum of the observation with peaks at periods of 20 and 30 months.

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H. Yang, K. K. Tung, and E. Olaguer

Abstract

We perform a diagnostic study of Eliassen-Palm flux divergence (□ · F), and isentropic mixing coefficient (Kyy) in the stratosphere for different seasons and for both hemispheres, taking into account nongeostrophic effects. An easily implementable procedure is given which yields a Kyy field that is consistent with advective transport. Evidence shows that the resultant time and space varying structure of Kyy, which is of the order of 105 m2 s−1 in tropics and high latitudes but larger (∼106 m2 s−1) in the midlatitudes in the jet region, leads to improved simulation of stratospheric species whose distributions are affected by dynamical transport.

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H. Yang, E. Olaguer, and K. K. Tung

Abstract

This paper documents our two-dimensional model which incorporates comprehensive radiative transfer and chemistry modules coupled with self-consistent dynamical transports.

A simultaneous simulation of a range of chemical trace gas species with different photochemical time scales, latitudinal and vertical gradients, and with tropospheric or stratospheric sources is attempted and the result compared with available satellite and in situ observations.

The 2-D model utilizes all zonally averaged physical equations of momentum, energy and mass, and self-consistently determines both its advective and diffusive transport parameters from the observed temperature specific to the period of observation. A major assumption in the formulation is that diffusive mixing is caused by large-scale planetary waves which act predominantly along isentropic surfaces. It is also assumed that it is planetary waves that drive the stratophere away from radiative equilibrium, resulting in diabatic vertical and meridional advective transport. It is in this way that energy, momentum and tracer budgets are interconnected.

Family approximation is used and the transported species include Ox, NOy, N2O, Cly, CH4, CO, CFCs and HF. Partition within a family is calculated assuming photochemical equilibrium. Diurnal variation of nitrogen species is obtained by solving an ordinary differential equation analytically.

The comparison of the model result with observations is very favorable. Some previously known common model deficiencies have largely been overcome. Simulation of climatological ozone, including the details of seasonal, latitudinal and vertical distributions, is especially successful using the present coupled model. The problem of NOy deficit in the equatorial lower stratosphere also appears to have been resolved, and a correct latitudinal profile for nitric acid column is obtained.

We give physical reasons for the improvements in the model results and discuss possible explanations for the remaining systematic deficiencies, now occurring mostly in the model upper stratosphere and mesosphere, where breaking gravity waves may become an important transport process.

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K. K. Tung and A. J. Rosenthal

Abstract

Previous results claiming the existence of multiple equilibria based on simple barotropic or two-layer models of the atmosphere are reexamined. While not ruling out the existence of multiple equilibria we find that the application of these results to the atmosphere, especially with regard to high/low zonal index and zonal/blocked situations, is probably problematic. Results based on truncated low-order models are found to change drastically when full nonlinearity is retained. Although multiple equilibria may still exist in some nonlinear models in some restricted parameter regimes, it is argued that the parameter values adopted in previous studies are probably not physically based.

Mathematically interesting properties of the nonlinear system, such as resonance bending, hysteresis, bifurcation and multiplicity of solutions are also discussed.

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R. S. Lindzen and K. K. Tung

Abstract

It is shown that the necessary conditions for the instability of unstratified plane-parallel shear flow, rotating barotropic flows and rotating baroclinic flows are also sufficient conditions for the existence of propagating waves (essentially Rossby waves) and their overreflection (reflection coefficient exceeds 1 in magnitude) from critical levels (where flow speed and phase speed are equal). The identification of the unstable modes with overreflected waves is strongly suggested and allows greater insight into the meaning of various theorems such as Rayleigh’s inflection point theorem.

The present results also suggest an important distinction between instabilities associated with, redistribution such as Bénard convective instability and instabilities, such as those we are concerned with, associated with the self-excitation of waves.

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K. K. Tung and A. J. Rosenthal

Abstract

Using a nonlinear model of stationary long waves which incorporates wave-wave and wave-mean flow interactions, we assess the variability of the stationary long waves in the stratosphere and troposphere. This note supplements the paper by Tung and Rosenthal, where the formulation was given in more detail, but the climatology and variability of stationary waves (No. 1 and No. 2) were not discussed.

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R. S. Lindzen and K-K. Tung

Abstract

Convective activity is frequently organized into band-like structures with space and time scales appropriate to internal gravity waves. When the convective activity involves cumulonimbus, then latent heat release can form a significant energy source for the waves which in turn may organize the convection [as described, for example, by wave-CISK (Lindzen, 1974; Raymond, 1975)]. However, in other cases strong forcing is absent and the existence of the waves requires the existence of a duct from which very little wave energy leaks. We show that the energy cannot be contained by an inversion. Instead, we find that a stable duct adjacent to the surface must be capped by an unstable layer wherein the mean flow at some level either equals or comes close to the phase speed of the ducted waves. We also find that the wind amplitudes associated with the observed pressure amplitudes in these waves are consistent with observed squall winds. Finally, we find that the horizontal scales of mesoscale waves are closely related to the time scales of convective elements.

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K. K. Tung and R. S. Lindzen

Abstract

A theory is presented that attempts to explain the tropospheric blocking phenomenon caused by the resonant amplification of large-scale planetary waves forced by topography and surface heating. It is shown that a wave becomes resonant with the stationary forcings when the wind condition in the lower atmosphere is such that the phase speed of the wave is reduced to zero. The resonant behavior of the wave in the presence of Ekman pumping and other damping mechanisms is used to account for the time amplification of the pressure ridges that is an essential part of the blocking phenomenon. This same time behavior also allows the waves to interact with the mean flow in the stratosphere, possibly initiating major sudden warmings. Such a situation was, in fact, assumed by Matsuno (1971) in the lower boundary of his stratospheric model of sudden warming.

The basis for reviving the classical normal-mode theory (when faced with the difficulties associated with the zero-wind line) is presented in Part II. The present Part I serves as an introduction to the three-part series and discusses, with the aid of a simple mathematical model, the relevant physical mechanisms involved. Though the theory of resonant Rossby waves is a classical one, the contribution of the present papers is in pointing out that the theory offers, despite the difficulties and controversies associated with it, a viable mechanism that may be the cause of some prominent physical phenomena in the atmosphere.

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