Stationary Planetary Waves Research Articles

Simulation of the influence of stationary planetary waves on the zonally averaged circulation of the mesosphere/lower thermosphere region

A linearised numerical model has been used to simulate the stationary planetary waves (SPW) structure and investigate its influence on a zonally averaged circulation in the mesosphere and lower thermosphere. The wave-activity density. Eliassen-Palm flux, and its divergence cross-sections are used as a diagnostic of wave propagation and wave-mean flow interaction. The results of numerical simulations show that SPW can provide the substantial accelerations of the mean flow which are comparable with the accelerations due to the breakdown of internal gravity waves and atmospheric tides, and it is necessary to develop three-dimensional models of the general circulation of the lower thermosphere, taking account of the effects of gravity wave and tidal drag. The influence of the eddy thermal conduction and viscosity on the formation of SPW structure in the mesosphere and lower thermosphere and on the distribution of the mean flow accelerations due to SPW dissipation is discussed.

Forced Stationary Planetary Waves in Mars's Winter Atmosphere

Abstract Mariner 9 and Viking spacecraft observations provided evidence for planetary-scale, wavelike disturbances in the Mars winter atmosphere. Possible sources of the wave activity are dynamical instabilities, for example, barotropic and / or baroclinic instabilities. Other candidate sources are forced. quasi-stationary planetary waves—waves that arise predominantly via zonally asymmetric surface properties. The authors attempt to model aspects of the wave activity, focusing on forced planetary waves in representative wintertime atmospheres for Mars, by applying a spherical linear primitive equations model. Basic states representing relatively “nondusty” and “highly dusty” conditions near winter solstice allow wavenumber 1 and 2 disturbances to propagate meridionally and vertically about the jet. Higher wavenumbers are strongly vertically trapped. Stationary waves during winter in the northern and southern extratropics differ strongly in amplitude, phase, and dominant horizontal wave pattern. Northern ...

北半球冬季成層圏-対流圏の年々変動

Interannual variations of the winter stratosphere and troposphere in the Northern Hemisphere are investigated by focusing attention on the long-term variability for the period from 1958 to 1994. Two modes of variability are first extracted by applying an empirical orthogonal function (EOF) analysis to the winter mean 50 hPa height data. The connection of these modes of variability with the troposphere and oceans is then investigated by calculating correlation coefficients between the time coefficients of the EOF and (i) the 500 hPa geopotential height, and (ii) sea surface temperatures (SSTs). The first stratospheric EOF mode alternates between the polar regions and mid-latitudes, and can be traced into the troposphere. The tropospheric circulation pattern associated with this mode is identified as changes in the meridional propagation of stationary planetary waves. Comparison with general circulation model (GCM) results suggests that this mode is essentially produced by atmospheric dynamical processes. Time coefficients of the EOF 1 mode exhibit an increasing trend. This mode appears to be related to the recent tropospheric circulation changes that have occurred over the Euro-Atlantic region and the eastern Asian sectors. The second EOF, on the other hand, exhibits a quite high correlation with SSTs in the equatorial eastern Pacific, and its variability is identified as linked to the El Nino/Southern Oscillation (ENSO) cycle.

Lower stratospheric stationary waves and the longitude dependence of ozone trends in winter

At northern midlatitudes, total ozone trends are largest in winter when the longitudinal distribution of ozone is highly asymmetric owing to dynamical forcing by stationary, planetary‐scale waves. A distinct longitude dependence of these midlatitude trends for the 1979 to 1991 time period has previously been derived statistically from Nimbus 7 total ozone mapping spectrometer data. Here we apply a mechanistic ozone transport model to investigate the extent to which the geographic dependence of total ozone trends in January can be explained as being due to decadal changes in the amplitudes and phases of stationary planetary waves. Results indicate that most or all of the statistically derived geographic dependence can be explained in this manner. In support of the mechanistic model calculations, lower stratospheric geopotential height differences or “anomalies” between groups of Januaries near the end of the 1980s and near the beginning of the 1980s are inversely correlated with the geographic distribution of ozone trends. The observed decadal changes in upper tropospheric and lower stratospheric stationary wave properties are most probably a consequence of decadal climate variability in the troposphere.

Characteristics of quasi‐2‐day oscillations in the ƒoF2 at northern middle latitudes

The temporal variations of the characteristics of ƒoF2 quasi‐2‐day oscillations at middle latitudes in the northern hemisphere are investigated. The hourly data for the period 1976–1986 for four European ionospheric stations, Kiev (50.5°N, 30.5°E), Kaliningrad (54.7°N, 20.62°E), Lannion (48.75°N, 3.45°W) and Slough (51.48°N, 0.57°W), are used for analysis. Periodogram and complex demodulation analysis are used to evaluate the period and amplitude time variations of this oscillation. It is found that quasi‐2‐day oscillations in ƒoF2 are present almost continuously during the year. The amplitude is larger in the equinoxes and lower in the solstices. The amplitude variations are modulated by the long‐term geomagnetic variations during the solar cycle. There is a clear expressed seasonal variation of the oscillation period with minimum in the winter, November–February (42–47 hours), and maximum near summer solstice (48–55 hours). The observations suggest that there are three types of ƒoF2 quasi‐2‐day oscillations with behavior of (1) westward traveling planetary wave with zonal wave number one, predominantly during summer half year, with greatest occurrence in August, (2) stationary planetary wave with a maximum occurrence in the summer solstice with unknown wave number, and (3) independent oscillations in separate locations on relatively long distances. The vertical plasma drift variations can explain the annual and long‐term modulation effects of ƒoF2 quasi‐2‐day amplitude variations but encounter significant difficulties in explaining the discrepancy between zonal wave numbers in the mesosphere (three) and upper ionosphere (one). Another possibility is that the arising of quasi‐2‐day oscillation in the upper ionosphere may be induced by the forcing of such oscillation in the mesosphere with further independent development in the F region.

The Second Haurwitz Memorial Lecture: Stationary Planetary Waves

The linear theory for stationary Rossby waves excited by flow over long ridges is reviewed. The traditional “textbook” model, in which there is no disturbance of the potential temperature surfaces or streamlines upstream of the ridge, is shown to be inadequate. For both the β-plane and the f-plane cases, pressure forces cause lifting of the isentropes and a cyclonic turning of the streamlines upstream of the ridge. The β-plane and f-plane solutions are, however, totally different for long ridges owing to the resonant excitation of stationary Rossby waves and the vertical propagation of the long-wave components in the β-plane case. Curiously, the vertical displacement of the isentropic surfaces is nearly identical in the β-plane and f-plane solutions in the lower troposphere where the response is dominated by the short-wave vertically decaying components.

Interactions between Orographic Gravity Wave Drag and Forced Stationary Planetary Waves in the Winter Northern Hemisphere Middle Atmosphere

A quasigeostrophic model is used to study the combined interaction among orographically generated gravity wave drag, forced planetary waves, and zonal mean flows in the Northern Hemisphere winter stratosphere and mesosphere. The localized gravity wave drag is shown to generate planetary waves in the mesosphere that, in turn, exert a substantial drag on the zonal mean flow via the Eliassen-Palm flux divergence. The amount of planetary wave drag is found to depend not only on the presence of the localized source of orographic gravity wave drag but also on the presence of upward-propagating planetary waves in the lower stratosphere. The zonal mean wind field exhibits a split jet structure with the larger jet maximum situated in the upper stratosphere at 30°N. This feature is shown to arise from the presence of weak winds above the subtropical tropospheric jet maximum, which results in a region of low-level gravity wave breaking and reduced drag and larger winds above.

Simulation of the global structure of stationary planetary waves in the mesosphere and lower thermosphere

When simulating the global structure of stationary planetary waves (SPW) the problem of obtaining the numerical solution in the equatorial region appears. It results from the presence of apparent singularities in the operator of the SPW latitudinal structure when the Coriolis parameter is small. The new method based on SPW latitudinal operator inversion is proposed. This method permits the difficulties arising from the simulation of stationary large scale disturbances at low latitudes to be avoided. The global structure of SPW with zonal wave number m = 1 at the mesosphere and lower thermosphere heights has been calculated for the background zonal wind distribution representing a climatic picture of the solstice conditions. In the region of the mean zonal westerlies the SPW penetration across the equator is obtained. The SPW at low latitudes are shown to appear most significantly in the zonal component of the wind velocity. The influence of planetary wave motions on the distribution of longlived species in the ionospheric D-region and at the heights of lower thermosphere are discussed.

The structure and propagation of stationary planetary wave packet in the barotropic atmosphere

Monthly or seasonally mean anomalies of large-scale atmospheric circulation are better represented by wave packets or their combination. Both qualitative and quantitative analyses of equations of wave packet dynamics, which are obtained by the use of WKB approximation, are very helpful for the understanding of structure, formation and propagation of stationary and quasi-stationary planetary wave packet patterns in the atmosphere. Indeed, these equations of wave packet dynamics can be directly solved by the method of characteristic lines, and the results can be simply and clearly interpreted by physical laws. In this paper, a quasi-geostrophic barotropic model is taken for simplicity, and the wave packets superimposed on several ideal profiles of the basic current and excited by some ideal forcings are investigated in order to make comparison of the accuracy of calculation with the analytical solution. It is revealed that (a) the rays of stationary planetary wave packet do not coincide with but go away from the great circle with significant difference if the shear of the basic zonal flow is not too small; (b) being superimposed on a westerly jet flow with positive shear (∂U λ/∂y>0), the stationary wave packets excited by low-latitudinal forcing are first intensified during their northeastward propagation in the Northern Hemisphere, then reach their maximum of amplitude at some critical latitude, and after that weaken again; (c) the connected line of extremes (the positive and negative centres) of wave packet does not coincide with but crosses the ray by an angle, the larger the scale of external forcing, the larger the angle; and (d) the whole pattern of a trapped stationary wave packet is complicated by the interference between the incident and reflected waves.

What Causes the Seasonal Cycle of Stationary Waves in the Southern Stratosphere?

Stationary planetary waves in the southern stratosphere display a characteristic seasonal cycle. Previous research based on a one-dimensional model suggests that this behavior is mainly determined by seasonally varying transmission properties of the atmosphere with respect to wave propagation. The issue is investigated with the help of a hemispheric, linear, quasi-geostrophic model. It reproduces well some of the observed qualitative features and is internally consistent in the sense that its seasonal wave cycle can be explained in terms of varying wave transmission properties of the mean circulation. On the other hand, the model does not yield the observed seasonal cycle. Despite considerable sensitivity to modifications in the basic-state wind and dissipation parameterization, the model could not be reasonably fit to reproduce the observed seasonal cycle. Possible reasons for the model deficiency are put forward. In summary, even though suggestive, the present study is not entirely conclusive about the degree to which the observed cycle is determined by wave transmission properties alone.

The role of quasi‐stationary planetary waves in the retrieval of concentrations from satellite measurements

Two recently proposed Reference Atmospheres for the vertical and latitudinal distribution of temperature in the middle atmosphere yield concentration values of nitric oxide (NO) which differ by as much as 25% at high latitudes during winter. The role of the quasi ‐ stationary planetary waves in the temperature distribution at high latitudes during winter is investigated with respect to the above mentioned NO difference. Considering this role, the initial difference is reduced to about 15% maximum.

低次成層圏モデルにおける定常波動のWave-Wave Interactionの研究

Interactions among stationary planetary waves in a low-order spherical stratospheric model are studied both analytically and numerically. A triad of interacting waves is examined using a steadystate hemispheric quasi-geostrophic model with a mean zonal wind in solid body rotation. Due to the structure of the model basic state, dissipation is required for the waves to interact. It is found that the nonlinear structure of the two gravest forced modes is independent of their relative position only if the third mode is unforced at the lower boundary. In this case the degree to which the nonlinearities act to amplify or phase shift the linear waves is shown to be dependent upon the vertical propagation characteristics of the waves. Large horizontal scale waves and weak zonal westerlies are found to be conditions which can result in significant amplitude changes due to the wave-wave interaction. As the scale of the wave is reduced and/or the speed of the mean zonal westerlies is increased, the predominant changes occur in the wave phases. Numerical solutions using realistic boundary forcing amplitudes and realistic dissipation are found to be only weakly nonlinear, despite the fact that the planetary waves distort considerably the polar vortex.

Nonlinear Instability of a Forced Baroclinic Rossby Wave

Two-layer, quasi-geostrophic weakly nonlinear and low-order spectral models are developed and used to investigate the instability of forced baroclinic Rossby waves to finite-amplitude perturbations. The results are then applied to the interaction of planetary-scale stationary eddies with synoptic scale transient eddies. In the weakly nonlinear model, asymptotic series expansions are used in conjunction with the method of multiple time scales. The stability of a forced planetary-scale stationary baroclinic Rossby wave to synoptic-scale perturbations is first examined. The synoptic-scale perturbation modes initially grow exponentially after which they eventually settle into an amplitude vacillation cycle. This vacillation is driven by the linear interference between propagating and stationary synoptic-scale modes with the same zonal and meridional wavenumbers. During this vacillation, the time mean energy of the stationary planetary wave equals its initial value. This indicates that the transient synoptic-scale perturbation has neither an amplifying nor a dissipative influence on the stationary wave. A study of the energetics shows that eddy available potential energy is transferred from the planetary-scale stationary wave to the synoptic-scale perturbation, while eddy kinetic energy is simultaneously transferred in the reverse direction. The asymptotic series expansions are also used to determine the truncation for a fully nonlinear spectral model. The weakly nonlinear and spectral solutions are compared and are found to agree very well. In addition, by comparing spectral model solutions with and without the higher-order modes of the weakly nonlinear model present, it is found that the evolution of the basic wave and the perturbation are extremely sensitive to the presence of these modes. This suggests that the interaction between planetary-scale stationary eddies with synoptic-scale transient eddies is a nonlinear phenomenon that is very sensitive to the detailed structure of the eddies present.

Upper Boundary Effects in a General Circulation Model

The effects of an artificial upper boundary on the climate of a general circulation model are examined using two versions of the model. The complete model has 26 levels extending from the surface to 0.1 mb (∼65 km) and the second version approximates the usual tropospheric general circulation model, having 15 levels extending to 10 mb (∼30 km). The two model versions are identical over the common part of the domain. Vertically propagating Kelvin waves are found in the tropics of both versions of the model. In the version extending only to 10 mb, the Kelvin waves are reflected by the top boundary, and resemble standing oscillations in the vertical. while retaining (approximately) their original zonal phase speed. Some of these reflected waves develop much larger lower stratospheric amplitudes than when they are able to propagate freely into the mesosphere. Placing the topmost model level at 10 mb is found to radically alter the winter stratospheric circulation and to produce significant changes in the tropospheric circulation. Stationary planetary waves are reflected off the model's top boundary and become approximately equivalent barotropic in the stratosphere, with no vertical phase tilt and reduced meridional phase tilt. The altered planetary waves have larger geopotential amplitude but produce very small poleward fluxes of heat. The stationary planetary wave amplitudes in the troposphere are not strongly affected by the changed upper boundary, but the phase structures are quite different. A third experiment was performed in which the zonal mean wind was controlled directly through an additional Rayleigh friction term. The results of this experiment indicate that the tropospheric stationary planetary wave structure responds to the mean flow structure of the lower stratosphere, rather than directly to the presence of a top boundary.

The Effect of the Hadley Circulation On the Meridional Propagation of Stationary Waves

AbstractThe effect on the meridional propagation of stationary planetary waves of the inclusion of the zonal mean Hadley circulation in linearized models of the atmosphere is examined. In a forced barotropic vorticity equation model a meridional wind in the basic state enables wave propagation through tropical easterlies in the direction of the wind. This is shown to be consistent with the WKB solution.In a multi‐level linearized steady primitive equation model with an idealized meridional circulation tropical forcing can still produce response through easterlies although propagation from one mid‐latitude to the other is much less than in the barotropic result. This is explained through WKB and wave‐tracing methods for a simplified three‐dimensional vorticity equation. the near non‐divergence of the unforced tropical motion permits a wave to travel largely within a layer of favourable winds.In a twelve‐level model using observed January and July zonal mean conditions the Hadley circulation changes the response to earth topographic forcing mainly in the subtropics. However, tropical heat forcing can now produce a large mid‐latitude response, in the winter hemisphere especially. the resulting subtropical jets suggest a mechanism for the maintenance of those observed over Australia during the northern monsoon season and adjacent to the anomalous forcing of the 1983 El Niño.

The effect of the Hadley circulation on the meridional propagation of stationary waves

The effect on the meridional propagation of stationary planetary waves of the inclusion of the zonal mean Hadley circulation in linearized models of the atmosphere is examined. In a forced barotropic vorticity equation model a meridional wind in the basic state enables wave propagation through tropical easterlies in the direction of the wind. This is shown to be consistent with the WKB solution. In a multi-level linearized steady primitive equation model with an idealized meridional circulation tropical forcing can still produce response through easterlies although propagation from one mid-latitude to the other is much less than in the barotropic result. This is explained through WKB and wave-tracing methods for a simplified three-dimensional vorticity equation. the near non-divergence of the unforced tropical motion permits a wave to travel largely within a layer of favourable winds. In a twelve-level model using observed January and July zonal mean conditions the Hadley circulation changes the response to earth topographic forcing mainly in the subtropics. However, tropical heat forcing can now produce a large mid-latitude response, in the winter hemisphere especially. the resulting subtropical jets suggest a mechanism for the maintenance of those observed over Australia during the northern monsoon season and adjacent to the anomalous forcing of the 1983 El Niño.

南半球で解析された惑星規模の循環形態の多様性

An observational study is made of low-frequency variations of the general circulation in the Southern Hemisphere troposphere with the aid of daily data analyzed at the National Meteorological Center (NMC).In the winter of 1983 there exist two typical patterns of the zonal mean geostrophic wind in the meridional plane. We name them the single jet regime and the double jet regime, each of which persisted with a characteristic duration of a month and appeared twice alternatively. In the single jet regime, the subtropical jet at the tropopause level is strong and the stationary wave of zonal wavenumber (WN=)3 has a larger amplitude than WN=2. On the other hand, in the double jet regime the subtropical jet is weak and the polar night jet extends down to the surface at about 55°S. Dominant stationary planetary waves are WN=1 and 2. These two regimes are also observed in the three years 1980-1982.In terms of the quasi-geostrophic Eliassen-Palm (E-P) flux diagnostics, the vertical component of the E-P flux, which is proportional to the horizontal eddy heat flux, is larger around the mid-latitude troposphere in the single jet regime than in the double jet regime. Consequently, the convergence of the E-P flux, which acts as a wave drag on the mean westerly wind, is larger around the mid- and high latitude tropopause level in the single jet regime than in the double jet regime. The larger wave drag tends to keep the weaker westerlies in the single jet regime.An empirical orthogonal function (EOF) analysis is made to define an index of the zonal mean wind of two dimension The first component of EOF, which represents over 40% of the total variance, corresponds to the variations between the two regimes. The amplitude of this component is used as a kind of 'zonal index'. Time variation of the zonal index is not considered an internal oscillation with an intrinsic frequency because the 'period', which is not an appropriate concept for the present phenomenon, is different in each year. The transition between the regimes is rather rapid compared with the duration of each regime. No clear relation is found between the regime transitions and the annual variation. These observational evidences support an interpretation that this low-frequency variation of the zonal index is the transition between multiple planetary flow regimes in the Southern Hemisphere.

Interactions between Gravity Waves and Planetary-Scale Flow Simulated by the GFDL “SKYHI” General Circulation Model

In order to study interactions between gravity waves and planetary flow in the middle atmosphere, a 3° latitude by 3.6° longitude version of the 40-level GFDL “SKYHI” general circulation model is analyzed using bihourly sampled output data. It is shown by a space-time spectral analysis that gravity waves in the mean zonal westerlies (easterlies) mainly consist of westward- (eastward-) moving components, and carry easterly (westerly) momentum upward, and decelerate the mean zonal westerlies (easterlies) in the mesosphere. Zonal momentum flux convergence due to gravity waves accounts for nearly all of the Eliassen–Palm (E–P) flux divergence in the summer mesosphere. This convergence accounts for 30%–50% of that in the winter upper mesosphere. However, this percentage is probably an underestimate since the convergence is significantly enhanced in a high resolution (1° × 1.2°) model currently being integrated. Vertical propagation of gravity waves is affected not only by the, mean zonal wind but also by velocity perturbations associated with planetary waves. The drag force due to gravity waves acts to suppress stationary planetary waves in the winter mesosphere.

Interactions between Stationary Planetary Waves in the Stratosphere

The interactions between stationary planetary waves 1 and 2 are investigated using a truncated quasi-geostrophic model in a midlatitude beta channel. The model includes eight interacting horizontal modes with three zonal wave numbers and two meridional scales in a quasi-geostrophic beta channel 40 deg wide; all wave-wave interactions in the model are a result of dissipation. The procedures for solving the model equations are examined. The theory of dissipation-induced interactions is discussed in terms of interactions between weak waves under severe truncation. The behavior of small amplitude waves 1 and 2 in basic states is discussed; it is observed that wave 1 is amplified in a wave 2 basic state, and a wave 2 disturbance in a wave 1 basic state is affected by the relative phases of the waves. The dynamics of these wave interactions are analyzed using potential enstrophy budgets of the waves. The relevance of the waves to the atmosphere is studied. It is noted that the wave behavior is a combination of the linear results with an amplification of wave 1 and a strong dependence on the relative phases of waves 1 and 2 in the stratosphere.

Effects of mountain barrier on a barotropic jet

In the present paper effect of mountain barrier which is very steep on a airflow has been studied. The intensity of blocking effect depends on the steepness of a mountain as well as on the height. A smooth mountain does not block the flow and hence the stretching and shrinking effect of vortex tube produces stationary planetary waves, while a steep mountain blocks the flow and the waves are not produced. For this purpose westerly jet has been Studied to see the dynamical effect of the mountains on Its structure and movement over the eastern Asia.