A note on the general concept of wave breaking for Rossby and gravity waves

A recently proposed general definition of wave breaking is further discussed, in order to deal with some points on which misunderstanding appears to have arisen. As with surface and internal gravity waves, the classification of Rossby waves into breaking and not breaking is a generic classification based on dynamical considerations, and not a statement about any unique signature or automatically recognizable shape. Nor is it a statement about passive tracers uncorrelated with potential vorticity on isentropic surfaces. A strong motivation for the definition is that proofs of the nonacceleration theorem of wave, mean-flow interaction theory rely, explicitly or implicitly, on a hypothesis that the waves do not break in the sense envisaged.The general definition refers to the qualitative behaviour of a certain set of material contours, namely those, and only those, which would undulate reversibly, with small slopes, under the influence of the waves' restoring mechanism, in those circumstances for which linearized, nondissipative wave theory is a self-consistent approximation to nonlinear reality. The waves' restoring mechanism depends upon the basic-state vertical potential density gradient in the case of gravity waves, and upon the basic-state isentropic gradient of potential vorticity in the case of Rossby waves. In the usual linearized theory of planetary scale Rossby waves on a zonal shear flow, the relevant material contours lie along latitude circles when undisturbed.     

A critical analysis of the concept of planetary wave breaking

The concept of planetary wave breaking (McIntyre andPalmer, 1983; 1984) is critically reviewed. It is concluded that the wave breaking signature is not unique to any particular dynamic event in the stratosphere. Therefore, the classification of stratospheric transport events, such as wave breaking, groups fundamentally different events together. Better qualification of the wave breaking signature and a more solid theoretical basis of planetary wave breaking must be presented if the concept is to be of significant utility in describing stratospheric tracer transport.     

Instability of planetary waves in a high vertical resolution model

Abstract

A high vertical resolution model is used to examine the instability of a baroclinic zonal flow and a finite amplitude topographically forced wave. Two families of unstable modes are found, consisting of zonally propagating most unstable modes, and stationary unstable modes. The former have time scale and spatial structure similar to baroclinic synoptic disturbances, but are localized in space due to interaction with the zonally asymmetric forcing. These modes transport heat efficiently in both the zonal and meridional directions. The second family of stationary unstable modes has characteristics of modes of low frequency variability of the atmosphere. They have time scales of 10 days and longer, and are of planetary scale with an equivalent barotropic vertical structure. The horizontal structure resembles blocking flows. They are maintained by available potential energy of the basic wave, and have large zonal heat fluxes. The results for both families of modes are interpreted in terms of an interaction between forcing and baroclinic instability to create favoured regions for eddy development. Applications to baroclinic planetary waves are also considered.     

Spectral analysis of planetary waves seen in ionospheric total electron content (TEC): First results using GPS differential TEC and stratospheric reanalyses

The coupling of the neutral atmosphere and the ionosphere through planetary waves (PW) (zonal wavenumber 0–5) is investigated by spherical harmonic analyses of the ionospheric total electron content (TEC). These analyses detect mean variations, standing and travelling waves which are assumed to be signatures of PW. Database used for TEC analyses are 3 years of hourly TEC maps covering the higher middle and polar latitudes. They are regularly produced by DLR Neustrelitz. The obtained results are compared with PW analyses using NCEP/NCAR and Met Office stratospheric reanalyses. Case studies show that signatures of PW occur simultaneously in the middle atmosphere and ionosphere.     

On the interaction between a radiatively damped planetary wave and the zonally averaged circulation in the middle atmosphere

The interaction between a planetary wave damped by cooling to space and the zonally averaged circulation in the middle atmosphere is examined for a steady-state situation in middle latitudes. Quasi-geostrophic scaling of Type 2 is assumed (i.e. the space scales are planetary and the superrotation is small).A set of mean equations is derived for this scaling which is complementary to the set of perturbation equations previously studied. The mean equations show that a planetary wave induces a mean meridional circulation which is balanced by an eddy momentum forcing function and a mean diabatic heating which is balanced by an eddy heat flux forcing function. The vertical eddy fluxes enter the forcing at the same order as the horizontal eddy fluxes.An analytical wave solution is found for the case of an atmosphere in constant superrotation. The eddy fluxes and forcing functions are evaluated for this special case. It is found that they are very sensitive to the values of the radiative damping coefficient and the superrotation. Since the damping coefficient depends on the ozone concentration and the intensity of the solar ultraviolet flux, the results suggest that changes in these quantities can strongly modify the wave-mean flow interaction in the middle atmosphere. Possible implications for climate change are discussed.     

Midlatitude mesopause region winds and waves and comparison with stratospheric variability

We present time series of January–May mean mesosphere/lower thermosphere (MLT) mean winds and planetary wave (PW) proxies over Europe together with stratospheric stationary planetary waves (SPW) at 50°N and time series of European ozone laminae occurrence. The MLT winds are connected with stratospheric PW and laminae at time scales of several years to decades. There is a tendency for increased wave activity after 1990, together with more ozone laminae and stronger MLT zonal winds. However, possible coupling processes are not straightforward. While mean MLT winds before the 1990s show similar interannual variations than stratospheric PW at 100 hPa, later a tendency towards a connection of the MLT with the middle stratosphere SPW is registered. There is also a tendency for a change in the correlation between lower and middle stratosphere SPW, indicating that coupling processes involving the European middle atmosphere from the lower stratosphere to the mesopause region have changed.     

The 11-year solar cycle, the Sun's rotation, and the middle stratosphere in winter. Part II: Response of planetary waves

The effect of the 11-year solar cycle on the response of planetary wavenumbers 1 and 2 at 10 and 30 hPa in winter to solar activity oscillations on the time scale of the Sun's rotation (27.2 day) is discussed in terms of statistical spectral analysis. The three oscillations studied are the 27.2 d (period of the Sun's rotation), 25.3 d (periodicity caused by modulation of the 27.2 d stratospheric response by annual atmospheric variation), and 54.4 d (doubled period of the solar rotation). A significant effect of the 11-year solar cycle is found for the 54.4 d periodicity in planetary wavenumber 1, and for the 27.2 and 25.3 d periodicities in planetary wavenumber 2. The effect of the 11-year solar cycle is expressed in the evident differences between the amplitudes of responses of planetary waves at maximum and minimum of the solar cycle: the amplitudes are much larger at high than at low solar activity. The 11-year modulation of planetary wave activity is most pronounced at mid-latitudes, mainly at 40–60°N, where the observed variability of planetary waves is large. The results obtained are in good agreement with results of the recent modeling study by Shindell et al. (Science 284 (1999) 305).     

水平非均匀基流中行星波的传播

行星波传播理论虽然已有很多研究,但是大多以纬向对称基流为主,无法解释东西风带之间相互作用的事实.鉴于此,本文从理论上系统讨论了纬向对称和水平非均匀基流中定常和非定常波动的传播特征.首先,对纬向对称基流中波动传播的周期特征进行分析后发现,西风中位相东传超长波周期大于30 d,而东风中位相西传超长波的周期则小于30 d.之后,从传播的空间以及周期特征等方面系统研究了水平非均匀基流中球面波动传播理论,得到以下结论:经向基流使得定常波可以穿越东风带,在南北两半球间传播,为东西风带之间的相互作用提供了理论解释;强的经向流使得波动传播具有单向性;亚澳季风区低层纬向1波呈低频特征.     

Lagrangian motion of air parcels in the stratosphere in the presence of planetary waves

Development of thoughts on tracer transport mechanisms in the stratosphere which lead to new approaches to two-dimensional modeling of the tracer problem is reviewed.Three-dimensional motions of individual air parcels affected by a planetary wave are investigated theoretically, treating a steady, upward propagating wave in a uniform flow. It is shown that trajectories of air parcels are of elliptical form when projected onto the meridional plane and that they have no mean meridional or vertical motion, even though the usual zonal Eulerian-mean vertical motion exists. The origin of the difference between the mean air parcel motion and the Eulerian-mean motion is discussed.On the basis of the knowledge of air parcel motion, two approaches to two-dimensional modeling are considered. The generalized Lagrangian mean motion (quasi-zonal weighted mean taken over a meandering material tube), recently introduced by Andrews and McIntyre, is identical with the mean motion of an air parcel in a steady state. Such a mean meridional circulation may be used for advecting a tracer in the meridional plane in a two-dimensional model. The transport effect is represented solely by the advection and an eddy transport does not appear in this scheme, to a first approximation.The finding that trajectories of air parcels are elliptical necessitates a reexamination of the Reed-German eddy diffusivity currently used in two-dimensional chemical-dynamical models. By applying a mixing length type hypothesis, we derive an eddy diffusivity formula for use in Eulerian-mean calculations, which, in the case of a conservative tracer is dominated by an anti-symmetric tensor. The eddy transport due to this anti-symmetric tensor diffusivity is of advective type (not diffusive) and has the effect of taking the Stoke drift effect into account, when used in the usual Eulerian-mean formulation.     

The boreal spring stratospheric final warming and its interannual and interdecadal variability

Based on the daily NCEP/DOE reanalysis II data,dates of the boreal spring Stratospheric Final Warming(SFW) events during 1979–2010 are defined as the time when the zonal-mean zonal wind at the central latitudes(65°–75°N) of the westerly polar jet drops below zero and never recovers until the subsequent autumn.It is found that the SFW events occur successively from the mid to the lower stratosphere and averagely from the mid to late April with a temporal lag of about 13 days from 10 to 50 hPa.Over the past 32 years,the earliest SFW occurs in mid March whereas the latest SFW happens in late May,showing a clear interannual variability of the time of SFW.Accompanying the SFW onset,the stratospheric circulation transits from a winter dynamical regime to a summertime state,and the maximum negative tendency of zonal wind and the strongest convergence of planetary-wave are observed.Composite results show that the early/late SFW events in boreal spring correspond to a quicker/slower transition of the stratospheric circulation,with the zonal-mean zonal wind reducing about 20/5 m s-1 at 30 hPa within 10 days around the onset date.Meanwhile,the planetary wave activities are relatively strong/weak associating with an out-of-/in-phase circumpolar circulation anomaly before and after the SFW events in the stratosphere.All these results indicate that,the earlier breakdown of the stratospheric polar vortex(SPV),as for the winter stratospheric sudden warming(SSW) events is driven mainly by wave forcing;and in contrast,the later breakdown of the SPV exhibits more characteristics of its seasonal evolution.Nevertheless,after the breakdown of SPV,the polar temperature anomalies always exhibit an out-of-phase relationship between the stratosphere and the troposphere for both the early and late SFW events,which implies an intimate stratosphere–troposphere dynamical coupling in spring.In addition,there exists a remarkable interdecadal change of the onset time of SFW in the mid 1990s.On average,the SFW onset time before the mid 1990s is 11 days earlier than that afterwards,corresponding to the increased/decreased planetary wave activities in late winter-early spring before/after the 1990s.     

Traveling planetary waves in the stratosphere

This paper reviews the theory and observations of some traveling planetary waves in the stratosphere. Two categories of waves which appear prominently in the literature are discussed: westward propagating waves of periods in the range 3–7 days (the 5-day wave) and in the range 10–20 days (the 16-day wave). Although the observations seem to indicate that these waves are waves of the Rossby type (planetary waves), the evidence is less clear regarding (1) the question of whether these waves are forced internal waves or free (resonant) external waves, and (2) the identification of the observed waves with specific theoretical waves of the Rossby type. When recent observations are compared with theory, the evidence seems to favor the notion that the 5-day and 16-day waves of longitudinal wave number 1 may be identified, respectively, with the gravest and next gravest symmetric free Rossby modes. However, the observational evidence seems to be less clear regarding the nature of the 16-day wave than the 5-day wave.     

Quasigeostrophic planetary waves in a two-layer ocean with one-dimensional periodic bottom topography

Although the study of topographic effects on the Rossby waves in a stratified ocean has a long history, the wave property over a periodic bottom topography whose lateral scale is comparable to the wavelength is still not clear. The present paper treats this problem in a two-layer ocean with one-dimensional periodic bottom topography by a simple numerical method, in which no restriction on the wavelength and/or the horizontal scale of the topography is required. The dispersion diagram is obtained for a wavenumber range of [?π/L _b , π/L _b ], where L _b is the periodic length of the topography. When the topographic?β?is not negligible compared to the planetary β, the Rossby wave solutions around the wavenumbers which satisfy the resonant condition among the waves and topography disappear and separate into an infinite number of discrete modes. For convenience, each mode is numbered in order of frequency. As topographic height is increased, the high frequency barotropic Rossby wave (mode 1) becomes a topographic mode which can exist even on the f plane, and the highfrequency baroclinic mode (mode 2) becomes a surface intensified mode. Behaviors of low frequency modes are somewhat complicated. When the topographic amplitude is small, the low frequency baroclinic modes tend to be bottom trapped and the low frequency barotropic modes tend to be surface intensified. As topographic amplitude further increases, the relation between the mode number and vertical structure changes. This change can be attributed to the increase of the frequency of the topographic mode with the topographic amplitude.     

Variability of planetary waves as a signature of possible climatic changes

The long-term variability of stationary and traveling planetary waves in the lower stratosphere has been investigated using the data of NCEP/NCAR reanalysis. The results obtained show that during the last decades winter-mean amplitude of the stationary planetary wave with zonal wave number 1 (SPW1) increases at the higher middle latitudes of the Northern Hemisphere. It has been suggested that the observed increase in the SPW1 amplitude should be accompanied by the growth in the magnitude of the stratospheric vacillations. The analysis of the SPW1 behavior in the NCEP/NCAR data set supports this suggestion and shows a noticeable increase with time in the SPW1 intra-seasonal variability. The amplitudes of the long-period normal atmospheric modes, the so-called 5-, 10- and 16-day waves, diminish. It is supposed that one of the possible reasons for this decrease can be a growth of radiative damping rate caused, for instance, by the increase of CO₂. To investigate a possible climatic change of the middle atmosphere dynamics caused by observed changes in the tropospheric temperature, two sets of runs (using zonally averaged temperature distributions in the troposphere typical for January 1960 and 2000) with the middle and upper atmosphere model (MUAM) have been performed. The results obtained show that on average the calculated amplitude of the SPW1 in the stratosphere increased in 2000 and there is also an increase of its intra-seasonal variability conditioned by nonlinear interaction with the mean flow. This increase in the amplitudes of stratospheric vacillations during the last four decades allows us to suggest that stratospheric dynamics becomes more stochastic.     

Large-scale thermodynamics of the stratosphere and mesosphere during the major stratospheric warming in 2003/2004

The stratosphere–mesosphere response to the major sudden stratospheric warming (SSW) in the winter of 2003/2004 has been studied. The UKMO (UK Meteorological Office) data set was used to examine the features of the large-scale thermodynamic anomalies present in the stratosphere of the Northern Hemisphere. The vertical and latitudinal structure of the genuine anomalies, emphasized by removing the UKMO climatology, has been investigated as well. The features of the stratospheric anomalies have been related to the mesospheric ones in measured neutral winds from radars and temperatures from meteor radars (90 km). It was found that the stratospheric warming spread to the lower mesosphere, while cooling occurred in the upper mesosphere, a feature that may be related to the large vertical scales of the stationary planetary waves (SPWs). It was shown also that the beginning of the eastward wind deceleration in the stratosphere–mesosphere system coincided with the maximum amplification of the SPW1 accompanied by short-lived bursts of waves 2 and 3.     

Long-period planetary waves in the mesosphere and lower thermosphere above Davis, Antarctica

The accumulation of MF radar wind and hydroxyl temperature measurements at Davis from 1997 to 2005 has enabled the compilation of a climatology of long-period (period >1 day) wave activity. A time domain filtering technique that makes allowance for the differing sampling characteristics of the measurements is described and wave amplitudes are presented for 1.7–4, 4–8 and 8–16 day period bands. Product averages of the time series yield horizontal heat and momentum fluxes for the height of the hydroxyl layer (approximately 86 km). The climatology is then discussed in terms of current knowledge of planetary wave characteristics and forcing. Heat and momentum fluxes during the year of the southern hemisphere stratospheric warming (2002) are also presented.     

冬季太阳11年周期活动对大气环流的影响

利用气象场的再分析资料和太阳辐射活动资料,对太阳11年周期活动影响北半球冬季(11月~3月)大气环流的过程进行了统计分析和动力学诊断.根据赤道平流层纬向风准两年振荡(QBO)的东、西风状态对太阳活动效应进行了分类讨论,结果表明：东风态QBO时,太阳活动效应主要集中在赤道平流层中、高层和南半球平流层,强太阳活动时增强的紫外辐射加热了赤道地区的臭氧层,造成平流层低纬明显增温,同时加强了南半球的Brewer-Dobson(B-D)环流,引起南极高纬平流层温度增加;而北半球中高纬的环流主要受行星波的影响,太阳活动影响很小.西风态QBO时,太阳活动效应在北半球更为重要,初冬时强太阳活动除了加热赤道地区臭氧层外,还抑制了北半球的B-D环流,造成赤道平流层温度增加和纬向风梯度在垂直方向的变化,从而改变了对流层两支行星波波导的强度;冬末时在太阳活动调制下,行星波向极波导增强,B-D环流逐渐恢复,造成北半球极地平流层明显增温,同时伴随着赤道区域温度的下降.     

On resonant over-reflection of waves by jets

It is well known that internal or Rossby waves propagating across a jet can be amplified, a phenomenon usually referred to as over-reflection. In some cases, over-reflection can be infinitely strong – physically, this means that the reflected and transmitted waves can exist without an incident one, i.e. they are spontaneously emitted by the mean flow. In this article, it is shown that infinitely strong over-reflection (resonant over-reflection) occurs for gravity-wave scattering by ageostrophic jets in a rotating barotropic ocean and Rossby-wave scattering by a two-jet configuration on the quasigeostrophic beta-plane. It is further demonstrated that, generally, a resonantly over-reflected wave is always marginal to instability, i.e. either an increase or a decrease of its wavenumber transforms it into an unstable eigenmode localised near the jet.     

The influence of tropical Indian Ocean warming on the Southern Hemispheric stratospheric polar vortex

During the past decades, concurrent with global warming, most of global oceans, particularly the tropical Indian Ocean, have become warmer. Meanwhile, the Southern Hemispheric stratospheric polar vortex (SPV) exhibits a deepening trend. Although previous modeling studies reveal that radiative cooling effect of ozone depletion plays a dominant role in causing the deepening of SPV, the simulated ozone-depletion-induced SPV deepening is stronger than the observed. This suggests that there must be other factors canceling a fraction of the influence of the ozone depletion. Whether the tropical Indian Ocean warming (IOW) is such a factor is unclear. This issue is addressed by conducting ensemble atmospheric general circulation model (AGCM) experiments. And one idealized IOW with the amplitude as the observed is prescribed to force four AGCMs. The results show that the IOW tends to warm the southern polar stratosphere, and thus weakens SPV in austral spring to summer. Hence, it offsets a fraction of the effect of the ozone depletion. This implies that global warming will favor ozone recovery, since a warmer southern polar stratosphere is un-beneficial for the formation of polar stratospheric clouds (PSCs), which is a key factor to ozone depletion chemical reactions. Supported by National Natural Science Foundation of China (Grant Nos. 40775053 and 90711004), National Basic Research Program of China (Grant No. 2009CB421401), and Innovation Key Program of Chinese Academy of Sciences (Grant Nos. KZCXZ-YW-Q11-03, KZCZ2-YW-Q03-08)