Survey of planetary‐scale traveling waves: The state of theory and observations

Abstract

There exists a considerable body of evidence relating the gravest‐scale transient components of planetary wave activity (periods shorter than a couple of weeks) to the eigenmodes of an unbounded isothermal atmosphere in uniform rotation. The latter, termed “Lamb modes,” have horizontal structures of Hough functions, with a 10‐km equivalent depth, and the external vertical structure of a Lamb wave. They asymptote, for large total wave number, to normal modes of the nondivergent barotropic vorticity equation. Phase speeds of the gravest modes, however, are significantly retarded by divergence. A historical account of the development of large‐scale traveling waves is presented, culminating with the emergence of global observations and the identification of several modes in atmospheric data. Theoretical ingredients of the simple normal mode problem are reviewed. The relationship between these features and extratropical transients is developed via the notion of a “planetary wave spectrum.” Influences of realistic distributions of dissipation and refractive properties are discussed for a prototypical mode. Calculations for several of the gravest modes are then presented for typical climatological configurations. For all of these the simple eigenstructures are largely preserved at tropospheric levels. Recent observational evidence is collected from global satellite and conventional meteorological analyses and compared with theoretical concepts. An overview of realistic considerations, requisite for an understanding of “particular realizations” of these features, is developed. Response to localized, transient forcing is shown to consist not of any single mode, but rather of a spectrum of normal modes. For sufficiently large amplitudes, Lamb modes can give rise to vacillations in eddy flux fields via modulation of the stationary waves. These, in turn, may be accompanied by vacillations in the basic stream.

Intensive radiosonde observations of the diurnal tide and planetary waves in the lower atmosphere over Yichang (111°18' E, 30°42' N), China

“…Figures 9 and 10 are the frequency spectra for observations in August 2006 and January 2007, respectively, and the spectral magnitudes are wave amplitudes. Since oscillations with periods greater than 20 days are conventionally not classified as PWs because their periods do not conform to those expected for common Rossby modes (Salby, 1984;Beard et al, 2001), only the oscillations with periods between 2-20 days are presented in Figs. 9 and 10.…”

Sq and EEJ—A Review on the Daily Variation of the Geomagnetic Field Caused by Ionospheric Dynamo Currents

“…The oscillations with periods close to 2 days, 5 days, 10 days, and 16 days are often considered to be due to planetary waves or Rossby waves that have been observed in the lower and middle atmosphere. Those planetary waves represent "normal mode" or "resonant" oscillations of the atmosphere (e.g., Salby 1984). Global climatology of 2-, 5-, 10-and 16-day waves has been established by satellite measurements, e.g., Gu et al (2013), Moudden and Forbes (2014) for 2-day waves; Wu et al (1994) If the amplitude of the planetary waves is sufficiently large in the dynamo region, they will drive ionospheric currents and affect geomagnetic perturbations on the ground.…”

Observational evidence of quasi-27-day oscillation propagating from the lower atmosphere to the mesosphere over 20° N

“…Gravity waves are middle-and small-scale perturbations, and planetary waves are global-scale perturbations. Theoretical work indicates that planetary waves correspond to a series of eastward-or westward-propagating normal modes with periods of about 2, 5, 10 and 16 days derived from Laplace's tidal equation under an isothermal atmosphere (Andrews et al, 1987;Salby, 1984). In the realistic atmosphere, quasi-6.5-day wave can also follow the atmospheric waveguide and propagates to the mesosphere from the stratosphere (Liu et al, 2004).…”