Normal Mode Rossby Waves Research Articles

Four Types of Baroclinic Instability Waves in the Global Oceans and the Implications for the Vertical Structure of Mesoscale Eddies

AbstractLinear stability analysis is re‐conducted to fully understand the geostrophic distribution of the different types of baroclinic instability (BCI) in the global oceans, their correspondence to the different vertical structures of the observed mesoscale eddies, and the properties and formation mechanisms of the instability waves. Four principal vertical types of BCI are identified, which are found to exhibit large‐scale patterns in the global ocean. The surface‐ and bottom‐intensified type (called the Eady type hereafter) is mainly located in the Antarctic Circumpolar Current (ACC) region, locations of the bottom‐intensified type (Charney_b type) are scattered around the Eady type, the surface‐intensified type (Charney_s type) primarily occurs in the subtropics (10°–35°), and the interior‐intensified type (Phillips type) occurs primarily between 5° and 20° in both hemispheres. More specifically, both geostrophic locations and the depths of the maximum perturbation velocities of the Phillips type BCIs match those of observed subsurface eddies. Moreover, the BCI waves show regions of uniform propagation properties: eastward in the ACC and the mid‐latitudes (25°–45°), and westward in the low latitudes (30°S–30°N) of both hemispheres and in the high latitudes of the Northern Hemisphere (>50°N). These waves resemble normal mode Rossby waves in structure (i.e., first baroclinic, second baroclinic, and topographic Rossby waves), but their propagation speeds are found to be Doppler shifted by the mean flows relevant for the corresponding BCI type. Propagating signals with the same dispersion relationships as the BCI waves are captured with numerical ocean general circulation models.

Large‐Amplitude Quasi‐10‐Day Waves in the Middle Atmosphere During Final Warmings

AbstractGeopotential height measurements from the Aura Microwave Limb Sounder between 9‐ and 97‐km altitudes during 2004–2018 are used to examine long‐period (3–20 days) wave activity during the Northern Hemisphere winter and spring, with the primary focus on the response of normal mode Rossby waves in the middle atmosphere to sudden stratospheric warmings (SSWs). Unusually large westward propagating waves with Zonal Wave Number 1 and period ∼10 days are observed at 55° latitude at the stratopause height (∼48 km) and above following final warmings of 2016, 2015, and 2005. In each case, large‐amplitude waves are observed for the duration of two to three wave cycles. Characteristics of the waves are in conformity with the second antisymmetric Rossby normal mode of Zonal Wave Number 1, or the quasi‐10‐day wave. The growth rate of the waves is significantly greater than the classical normal mode in the upper stratosphere (approximately 30–50 km) where instability conditions are met, indicating the amplification or excitation of the waves in that region. The response of the quasi‐10‐day wave during midwinter SSWs, and also during the spring transition without an SSW, is not as obvious as the wave response during final warmings. The results suggest that not only the occurrence of SSW but also the seasonal timing of SSW is an important factor for the transient variability of the quasi‐10‐day wave in the middle atmosphere.

Normal mode Rossby waves and their effects on chemical composition in the late summer stratosphere

Abstract. During past MANTRA campaigns, ground-based measurements of several long-lived chemical species have revealed quasi-periodic fluctuations on time scales of several days. These fluctuations could confound efforts to detect long-term trends from MANTRA, and need to be understood and accounted for. Using the Canadian Middle Atmosphere Model, we investigate the role of dynamical variability in the late summer stratosphere due to normal mode Rossby waves and the impact of this variability on fluctuations in chemical species. Zonal wavenumber 1, westward travelling waves are considered with average periods of 5, 10 and 16 days. Time-lagged correlations between the temperature and nitrous oxide, methane and ozone fields are calculated in order to assess the possible impact of these waves on the chemical species. Using Fourier-wavelet decomposition and correlating the fluctuations between the temperature and chemical fields, we determine that variations in the chemical species are well-correlated with the 5- and 10-day waves between 30 and 60 km, although the nature of the correlations depend strongly on altitude. Interannual variability of the waves is also examined.

Equatorial planetary waves in the mesosphere observed by airglow periodic oscillations

Planetary scale waves in the equatorial upper mesosphere were studied by measuring the airglow OI557.7 nm, O2b(0,1) and OH(6,2) emission intensities and OH rotational temperature at São João do Cariri (7.4°S; 36.5°W). From four years of data, 1998–2001, periodic oscillations of the airglow emissions were analyzed using the Lomb–Scargle spectral analysis. An oscillation of 3–4 days was frequently observed, which might be ultra-fast Kelvin waves. No seasonal dependency of the wave activity was found. On some occasions we found a quasi-5-day oscillation with a phase difference between the emissions, suggesting an upward energy flow. This is interpreted as a normal mode Rossby wave.

Normal Mode Rossby Waves as Revealed byUARS/ISAMS Observations

Global behavior of the 5- and 10-day waves, which are typical modes of normal mode Rossby waves, has been investigated for the region up to the mesopause with the aid of Upper Atmosphere Research Satellite Improved Stratosphere and Mesospheric Sounder observations. It is found that wave structures are easily influenced in the mesosphere by nonuniform and strong background zonal winds and an increasing damping effect with height. The vertical growth of wave amplitudes is prohibited in the mesosphere even without critical regions, and amplitudes become constant or slightly decay near the mesopause. Nevertheless, estimated variations of the wind field in the mesosphere related to the waves are consistent with results of radar observations, and Rossby normal modes may fairly contribute to total wave variance there.

A Numerical Experiment of Excitation of the 5-Day Wave by a GCM

Though normal mode Rossby waves frequently appear in the troposphere and the stratosphere, excitation mechanisms of normal mode Rossby waves are not clear. In this study, excitation mechanisms of the 5-day wave, which is one of the normal mode Rossby waves, are investigated by a series of general circulation model (GCM) experiments. The results of the numerical simulation show that the amplitude of the 5-day wave simulated by the GCM with uniform lower boundaries is similar to that with the realistic topography. On the other hand, the amplitude of the 5-day wave without moist convection is much smaller than that with realistic topography. The amplitude of the 5-day wave grows when the rainfall amplitude in the 5-day range is large. These results indicate that heating due to moist convection is most important for excitation of the 5-day wave.

Modes in a continuous spectrum of atmospheric oscillations

Atmospheric observational studies reveal synoptic‐scale eastward‐traveling modes, but barotropic models of the atmosphere do not have free Rossby modes in the discrete spectrum that travel eastward. Nevertheless, we show that eastward‐traveling barotropic modes can be excited in the same way as discrete westward‐traveling normal‐mode Rossby waves. Within a linearized shallow water model, we have examined the response to forcing in individual hemispheres. This response includes eastward‐traveling modes that agree well with observations. The study also shows resonant low‐frequency responses in the continuous spectrum confined to a single hemisphere (“hemispheric Rossby modes”).

Excitation and Evolution of the Quasi-2-Day Wave Observed inUARS/MLS Temperature Measurements

The quasi-2-day wave is known as a strong and transient perturbation in the middle and upper atmosphere that often occurs shortly after solstice. The excitation mechanisms of this transient wave have been discussed for years, but no clear answer has yet been attained. In this paper, propagating characteristics of the 2-day wave are studied based on 8-mon temperature measurements from the Microwave Limb Sounder onboard the Upper Atmosphere Research Satellite. The studies are focused on the wave events that happened in January 1993 and in July-August 1993. The observations suggest that winter planetary waves could be responsible for triggering the summer 2-day wave through long penetration into the summer stratosphere. A connection is evident in the evolution of the wave amplitude between the summer 2-day wave generation and winter wave penetration. The data also suggest that the enhancement of the wave amplitude is a manifestation of both a local unstable wave and a global normal-mode Rossby wave.

Evolution of the Southern Hemisphere Subpolar Middle Atmosphere during Summer and Autumn

The evolution of zonal wind and zonal wavenumber one (wave 1) in the Southern Hemisphere subpolar middle atmosphere is described for the period December 1978 - May 1979 using temperature and ozone measurements from the Limb Infrared Monitor of the Stratosphere (LIMS) experiment. In late December maximum zonal easterlies of approx. -70 m/s are observed at 0.1 mb, 60 deg S. A zonal flow reversal occurs during late February and westerlies subsequently increase to 60-70 m/s in the upper stratosphere by April - May. LIMS zonal winds are compared with rocketsonde measurements and nadir sounder (derived) winds for summer and autumn. Although quantitative agreement is found at stratospheric levels, substantial discrepancies are evident in the mesosphere, most likely a reflection of sampling and resolution differences in the respective datasets. Stationary and traveling wave 1 temperature disturbances (amplitudes approx. 1 - 2 K at 60 deg S) are observed by LIMS during summer. The stationary wave is confined to the lower stratosphere near the level of zero zonal- mean wind flow, whereas the traveling wave is prominent in the middle stratosphere moves west at a rate similar to the zonal-mean wind, and exhibits a vertical - meridional structure similar to a P(sub 4)(sup 1) normal mode Rossby wave. A substantial intensification of wave 1 activity occurs during autumn (amplitudes approx. 5 - 10 K), which is found to be associated with an upward-directed Eliasse - Palm flux near the subpolar tropopause level. Evidence relating wave 1 activity in the lower - middle stratosphere to the occurrence of zonal ozone perturbations of 10% - 20% amplitude is presented for summer and autumn.

夏半球成層圏における日潮汐とノーマルモードロスビー波の干渉

An investigation was conducted into the interference among the tidal wave, the 5-day, and 10-day normal-mode Rossby waves in the summer upper stratosphere, making use of a general circulation model. It was found that the EP flux due to the interference has a period of slightly longer than one day, and that two kinds of periodic structures of the EP flux also exist, having about 10-day periods. One structure is an amplitude modulation of the quasi-diurnal variation while the other is a long-term variation in the low-pass filtered data. It was also found that the acceleration of the zonal-mean zonal wind is mainly composed of the zonally symmetric diurnal tide. The EP flux due to the diurnal tide for zonal wavenumber 1 and the normal-mode Rossby waves of zonal wavenumber 1 plays a minor role in the acceleration of the zonal-mean zonal wind. When the Rossby waves simultaneously amplify, however, the EP flux brings about a noticeable long-term forcing of the zonal-mean zonal wind.The interference of the tide and normal-mode Rossby waves appearing in the NMC analysis data were also examined. The diurnal tide was analyzed as a quasi-stationary wave due to the once-daily sampling. It was found that the observed 5-day and 10-day variations in the EP flux are superficial and result from aliasing phenomena due to the once-daily sampling.

Observations of the 2-Day Wave in NMC Stratospheric Analyses

Abstract Observational characteristics of the 2-day wave, a westward-propagating zonal wave 3 oscillation in the summer subtropical upper stratosphere and mesosphere, are studied based on five years of National Meteorological Center (NMC) operational stratospheric analyses. These data show episodic occurrence of the 2-day wave in the upper stratosphere in January (centered near 20°S) and July–August (centered near 20°N). These episodes are strongly correlated with observed reversals of the zonal mean potential vorticity gradient near the core of the summer easterly jet, consistent with previous suggestions that the 2-day wave is generated by an in situ instability of this jet. On the other hand, the horizontal and vertical structure of the waves is very similar to that calculated by Salby for a global normal-mode Rossby wave. The combination of normal-mode structure and instability signature suggests that the 2-day wave is a near-resonant mode forced by dynamical instability.

Evidence of Traveling External Rossby Waves in the ECMWF Analyses

Abstract Ten years of global tropospheric data from the European Centre for Medium-Range Weather Forecasts analyses were used to obtain a climatology of quasi-stationary waves and transient normal-mode Rossby waves. The data were split up into a mean annual cycle, reflecting the forced fields, and a transient part, containing the traveling waves. Data were then projected onto Hough normal modes, yielding a mean annual behavior of the quasi-stationary fields and time series of expansion coefficients for the transient waves. The latter were analyzed by a space-time spectral method independently for each of the four seasons. The Hough normal modes with low zonal wavenumber and low meridional index show clear peaks in the power spectra at theoretically predicted frequencies. Some modes have a strong seasonality.

Normal-Mode Rossby Waves Observed in the Wavenumber 1–5 Geopotential Fields of the Stratosphere and Troposphere

Abstract Daily global geopotential height fields have been analyzed for zonally propagating, planetary scale structures with periods in the range of 4 to 30 days. The geopotentials extend from the 850- to 2-mb levels and 85°N to 85°S latitudes, and describe four Northern Hemisphere winters. The analyses indicate that variations in geopotential are dominated by westward moving waves that resemble normal mode Rossby waves. Structures are determined which correspond to the firs symmetric modes of zonal wavenumbers 1–5, the second and antisymmetric modes of wavenumbers 1–3, the second symmetric modes of wavenumbers 1–3, and perhaps the third antisymmetric mode of wavenumber 1. Mode structures are found to agree in general with the predictions of theory and numerical models. Only the first symmetric modes are found to maintain their symmetry throughout the troposphere and lower stratosphere. Other modes are found to resemble their predicted Hough function structures in the troposphere but, to varying degree, n...

Further evidence of normal mode Rossby waves

Further observational evidence of normal mode Rossby waves with higher meridional mode numbers is presented with the aid of global data from the troposphere to the stratosphere over the period November 1979 through April 1986.

Influence of Normal Mode Rossby Waves on the Mean Field: Interference with Quasi-Stationary Waves

Abstract The influence of normal mode Rossby waves on the mean field is investigated with the aid of TIROS-N/NOAA satellite observations by applying the Eliassen-Palm (E-P) flux diagnostics. Despite the fact that the normal mode Rossby wave is essentially a free wave without E-P fluxes, it is found that the constructive and destructive interference between the traveling free Rossby wave and the quasi-stationary forced wave induces the periodic change of the EP-flux and its divergence, which in turn gives rise to vacillations in the basic flow. Three typical cases of the interference in the stratosphere are presented for the periods of the equinoctial season when the 5-day, 10-day and 16-day waves globally appear, and it is shown that observed vacillations of the zonal mean wind are well elucidated by the quasi-periodic change of the E-P flux divergence due to the interference.

Climatology of Normal Mode Rossby Waves

Abstract Three years of twice-daily NMC global operational analyses were projected onto normal mode Rossby waves to produce a climatology of these waves. For zonal wavenumbers. 1 through 4, annual average geopotential amplitudes at 50 kPa are about 5 gpm for the gravest symmetric meridional mode, and 10 and 20 gpm for the next two meridional model although the amplitude for a given time and latitude can greatly exceed the average. Seasonal average amplitudes differ by less than ±25% from the annual average. The modes’ frequencies drift during the course of a year, but this variation is not correlated with season. Autocorrelations of Rossby wave time series become negligible for lags greater than approximately ten days, which is of the order of the wave period. For all ten modes examined, geopotential fluctuations exist in both Northern and Southern Hemispheres.

Normal Mode Rossby Waves Observed in the Upper Stratosphere. Part II: Second Antisymmetric and Symmetric Modes of Zonal Wavenumbers 1 and 2

As an extension of our recent previous study, the global structure and behavior of higher-mode Rossby waves am investigated with the aid of TIROS-N and NOAA-A satellite observations for the period November 1979 through April 1982. It is shown that the second antisymmetric and symmetric modes of zonal wavenumbers 1 and 2 exist in the upper stratosphere, although the existence of zonal wavenumber 2 modes somewhat uncertain. These waves are amplified in the winter hemisphere over a period of 1-2 months. The vertical structure of the waves is similar to that of the simple Lamb mode except for a little westward phase tilt. The period band of the higher-degree modes is variable, as predicted by numerical models. The period band of the second antisymmetric mode of zonal wavenumber 1, i.e.,(1, 2) mode, sometimes falls into that of a 16-day wave which is the manifestation of the (1, 3) mode. However, the two modes don't coexist in the same period band. The higher-degree modes are often largely amplified simultaneously. In particular, it is remarkable that they are enhanced before the occurrence of stratospheric sudden warmings. Since the amplitude of these waves is of the same order of magnitude as that of stationary waves, the interference between the traveling and stationary waves may play an important role in the sudden warming event.

Normal Mode Rossby Waves Observed in the Upper Stratosphere. Part I: First Symmetric Modes of Zonal Wavenumbers 1 and 2

A global analysis is made of large-scale traveling planetary waves in the upper stratosphere by the use of stratospheric height and thickness data up to the 1 mb level derived from the Stratospheric Sounding Unit (SSU) on TIROS-N and NOAA-A satellites for the period December 1979 through November 1981. The results of space-time power and cross-spectral analyses show the global existence of a westward traveling wave of zonal wavenumber 1 with a period of about 5 days and a westward traveling wave of zonal wavenumber 2 with a period of about 4 days. The structure and behavior of these waves are investigated by using the components of these period bands separated by a numerical band-pass filter. The 5-day wave is very similar to the (1, 1) mode, which is the first symmetric wavenumber 1 Rossby normal mode in an isothermal atmosphere. Similarly, the 4-day wave appears to correspond to the (2, 1) mode. The vertical structure of both waves agrees well with the theoretical expectation of free external waves. With regard to the seasonal variation, both waves are irregularly predominant throughout the year except for the December–January–February season, and this evidence is significantly related to the temporal variation of the refractive index of the zonal mean field.

Normal-Mode Global Rossby Waves: Theory and Observations

Abstract This study addresses first the question of what normal-mode global Rossby waves might exist in the Earth's atmosphere. Then it identifies fourteen of these theoretically predicted waves in the NMC global tropospheric analyses. Normal modes of linearized global primitive shallow water equations were found given a basic state of latitudinally dependent steady zonal flow. The solutions are free Rossby and gravity waves. Many of the waves' north-south structures are similar to Hough functions, which are the solutions of the simpler problem of free waves in an atmosphere at rest. By projecting 1200 consecutive days of twice-daily NMC global tropospheric analyses of velocity and geopotential onto idealized three-dimensional, normal-mode Rossby wave structures, time series of wave amplitudes and phases were formed. Spectral analyses of these time series for zonal wavenumbers 1–4 revealed statistically significant peaks at eight out of 25 theoretical Rossby wave frequencies. Six additional woes may exist...