Phase Speed Of Rossby Waves Research Articles

Meridional component of oceanic Rossby wave propagation

A three-dimensional spectral analysis of Topex altimeter data reveals a large meridional component k y of the wavevector k for baroclinic Rossby waves of all timescales. Its existence necessitates some refinements in our estimates of certain basic properties of the Rossby wave field. In particular, by taking into account an actual off-zonal direction of k (often exceeding 70°), one finds that the wavelength, phase speed, and group velocity of mid-latitude Rossby waves (with periods less than 2 years) are much smaller than they appear to be on the assumption of a purely zonal wavenumber vector. Because of a shorter wavelength (yielding kL as high as 0.6, where L is the Rossby radius of deformation), these waves are essentially dispersive. Their group velocity vector may depart from zonal by more than 30°. An important intrinsic feature of the wave spectrum confirmed by our analysis is a broad-band distribution with respect to k y . Some of the dynamical implications of the large k y / k x ratio are discussed.

Observed variability of the South Pacific westward sea level anomaly signal in the presence of bottom topography

This study investigates the behavior of westward propagating sea level anomalies across the South Pacific Ocean, with a focus on the long Rossby wave signal determined from filtered TOPEX/Poseidon and ERS satellite altimeter data. An evaluation of the energy variability of the signal using a two‐dimensional Radon Transform analysis suggests that Rossby waves interact with both ridges and seamounts at various locations across the basin. Anomalously slow Rossby wave phase speeds are found over steep, isolated bathymetric features in the tropical South Pacific and over the plateau around New Zealand. Interaction with ridges increases the energetic variability, range of dominant propagation speeds, and meridional deviations in the Rossby wave signal.

Agradient velocity, vortical motion and gravity waves in a rotating shallow‐water model

AbstractA new approach to modelling slow vortical motion and fast inertia‐gravity waves is suggested within the rotating shallow‐water primitive equations with arbitrary topography. The velocity is exactly expressed as a sum of the gradient wind, described by the Bernoulli function, B, and the remaining agradient part, proportional to the velocity tendency. Then the equation for inverse potential vorticity, Q, as well as momentum equations for agradient velocity include the same source of intrinsic flow evolution expressed as a single term J(B, Q), where J is the Jacobian operator (for any steady state J(B,Q)=0). Two components of agradient velocity are responsible for the fast inertia‐gravity wave propagation similar to the traditionally used divergence and ageostrophic vorticity.This approach allows for the construction of balance relations for vortical dynamics and potential vorticity inversion schemes even for moderate Rossby and Froude numbers assuming the characteristic value of |J(B,Q)|=ε to be small. The components of agradient velocity are used as the fast variables slaved to potential vorticity that allows for diagnostic estimates of the velocity tendency, the direct potential vorticity inversion with the accuracy of ε2 and the corresponding potential vorticity‐conserving agradient velocity balance model (AVBM). The ultimate limitations of constructing the balance are revealed in the form of the ellipticity condition for balanced tendency of the Bernoulli function which incorporates both known criteria of the formal stability: the gradient wind modified by the characteristic vortical Rossby wave phase speed should be subcritical. The accuracy of the AVBM is illustrated by considering the linear normal modes and coastal Kelvin waves in the f‐plane channel with topography. Copyright © 2004 Royal Meteorological Society

Seasonality of the Kuroshio Transport Revealed in a Kuroshio Assimilation System

The seasonal variation of the Kuroshio transport south of Japan has been investigated using the results of an assimilation model. Annual and semiannual variations of the transport and dynamic depth anomaly are reconstructed by CEOF (complex orthogonal empirical function) analysis. In the basin west of the Izu-Ogasawara Ridge, the annual component of the variation propagates westward with the phase speed of the long Rossby wave associated with the first baroclinic mode. The variation also shows a similar tendency to that reproduced in a wind-driven, two-layer model with a ridge. This suggests that the annual variation revealed in the assimilation model is associated with the baroclinic first mode of motion excited above the Izu-Ogasawara Ridge. Furthermore, it is found that both the semiannual component and the annual component are important members determining the seasonal variation of the Kuroshio transport south of Japan. The semiannual component is revealed as a double gyre pattern in the basin west of the Izu-Ogasawara Ridge.

A delayed action oscillator shared by biennial, interannual, and decadal signals in the Pacific Basin

Biennial, interannual, and decadal signals in the Pacific basin are observed to share patterns and evolution in covarying sea surface temperature (SST), 18°C isotherm depth (Z18), zonal surface wind (ZSW), and wind stress curl (WSC) anomalies from 1955 to 1999. Each signal has warm SST anomalies propagating slowly eastward along the equator, generating westerly ZSW anomalies in their wake. These westerly ZSW anomalies produce cyclonic WSC anomalies off the equator which pump baroclinic Rossby waves in the western/central tropical North Pacific Ocean. These Rossby waves propagate westward, taking ∼6, ∼12, and ∼36 months to reach the western boundary near ∼7°N, ∼12°N, and ∼18°N on biennial, interannual, and decadal period scales, respectively. There, they reflect as equatorial coupled waves, propagating slowly eastward in covarying SST, Z18, and ZSW anomalies, taking ∼6, ∼12, and ∼24 months to reach the central/eastern equatorial ocean. These equatorial coupled waves produce a delayed‐negative feedback to the warm SST anomalies there. The decrease in Rossby wave phase speed with latitude, the increase in meridional scale of equatorial SST anomalies with period scale, and the associated increase in latitude of Rossby wave forcing are consistent with the delayed action oscillator (DAO) model used to explain El Niño. However, this is not true of the western‐boundary reflection of Rossby waves into slow equatorial coupled waves. This requires modification of the extant DAO model. We construct a modified DAO model, demonstrating how the various mechanisms and the size and sources of their delays yield the resulting frequency of each signal.

Global characterization of Rossby waves at several spectral bands

Global sea surface height anomaly signals from the TOPEX/Poseidon satellite altimeter from 1992 to 2000 are filtered into several spectral bands. These bands include propagating (Rossby, Kelvin, and tropical instability waves) and nonpropagating (annual and interannual basin‐scale variability and eddies) signals. These signals are decomposed through a series of finite impulse response band‐pass filters. Phase speed, period, wavelength, and amplitude are estimated. Signal‐to‐noise ratio, methodological errors, and natural variability are also estimated. Results are shown for the Pacific, Atlantic, and Indian basins for four Rossby wave components with periods between 3 and 24 months. Equatorial Kelvin waves and tropical instability waves are shown as peripheral results. The clearest and most energetic wave signals are generally observed for annual Rossby waves. Semiannual Rossby waves often have the largest amplitudes near the tropics. The Rossby wave phase speeds are in agreement with the linear theory, except for a ∼25% bias toward high speeds found in mid to high latitudes. This revitalizes the idea that on the average the Rossby wave signal in the ocean is in the form of free waves.

Propagation of the sea-surface temperature anomalies in the Tropical Atlantic

The evolving modes of the sea-surface temperature (SST) in the Tropical Atlantic on the short interannual (IA) timescale were obtained by performing the extended empirical orthogonal function (EEOF) analyses on this variable separately for the 106-year (1871–1976) and 20-year (1881–1900; 1901–1920; 1921–1940; 1941–1960) periods. The equatorial and inter-hemispheric patterns manifest in the first EEOF mode of each analysis as part of the short IA evolution of the SST anomalies in the Tropical Atlantic. Another outstanding feature of the first EEOF mode of each analysis concerns the propagations of the SST anomalies in the meridional direction within the 20° N–20° S band and in the zonal direction in the sector 40° W–20° W. For all analyses, the SST anomalies propagate northward from the equator to 15° N and southward from 20° N to 15° N, with the same sign anomalies merging approximately at 15° N. On the other hand, the SST anomalies propagate westward in the sector 40° W–20° W with a propagation rate close to that of the phase speed of the fastest baroclinic Rossby wave in the ocean. So, the observed propagations of the SST anomalies in the 20° N–20° S band might result from the combined effect of the surface oceanic currents in this band and the baroclinic Rossby waves in the ocean.

Large-Scale Circulations Forced by Localized Mixing over a Sloping Bottom*

Abstract A simple, nonlinear, two-layer, planetary geostrophic model of the large-scale circulation forced by localized mixing over a sloping bottom is discussed. The model is forced by parameterized diapycnal mixing at the density interface and/or by a mass flux downward into (unresolved) deep topographic canyons. Two nondimensional parameters are identified: the ratio of the change in Coriolis parameter over the horizontal mixing length scale to the nominal Coriolis parameter and the ratio of the advective speed to the Rossby wave phase speed. The former controls the strength of horizontal recirculation gyres that are forced by spatially variable diapycnal mixing, while the latter is a measure of the importance of nonlinearity in the density equation. When bottom topography is introduced, bottom pressure torque becomes important and the traditional strong horizontal recirculation gyre found for mixing over a flat bottom (beta plume) is gradually replaced by a zonal flow into or out of the mixing region ...

Indian Ocean Rossby waves observed in TOPEX/POSEIDON altimeter data and in model simulations

Analysis of 3 years of TOPEX/POSEIDON (T/P) altimeter data in the Indian Ocean revealed discrepancies between observed and theoretical Rossby wave phase speeds. Rossby waves were observed at all latitudes using Hovmoller diagrams or longitude/time plots; their phase speeds were computed using twodimensional Fast Fourier Transforms (FFTs). Complex Principal Component Analysis (CPCA) was applied to detect travelling waves. A simple wind-driven layer model was implemented for this region and forced with the ERS-1 scatterometer winds, sampled over the same period as the T/P data, to demonstrate that these winds account for much of the observed Rossby wave activity.

Observations of El Niño‐Southern Oscillation induced Rossby waves in the northeast Pacific using in situ data

Bathythermometric observations from standard National Oceanographic Data Center data sets are used to show evidence of Rossby waves in the northeast Pacific Ocean following several El Niño‐Southern Oscillation events between 1968 and 1991. Observations of a westward propagating warm anomaly following the 1982–1983 El Niño are consistent with evidence from ocean models and satellite observations that coastally trapped Kelvin waves of tropical origin excite Rossby waves in the northeast Pacific. Observed Rossby wave phase speeds are about 1.6 cm s−1 higher than those predicted by linear shallow‐water theory. At midlatitudes, observed waves are more than 1.5 times faster than theory. Phase speeds of Rossby waves in a resolution nonlinear primitive equation model exceed standard linear theory, but only by about 0.1 cm s−1, despite the fact that the model should replicate mechanisms that have recently been proposed to explain the observed anomalously fast phase speeds.

The decay of cyclonic eddies by Rossby wave radiation

It is argued that because shallow water cyclones on a β-plane drift westward at a speed equal to an available Rossby wave phase speed, they must radiate energy and cannot, therefore, be steady. The form of the Rossby wave wake accompanying a quasi-steady cyclone is calculated and the energy flux in the radiated waves determined. Further, an explicit expression for the radiation-induced northward drift of the cyclone is obtained. A general method for determining the effects of the radiation on the radius and amplitude of the vortex based on conservation of energy and potential vorticity is given. An example calculation for a cyclone with a ‘top-hat’ profile is presented, demonstrating that the primary effect of the radiation is to decrease the radius of the vortex. The dimensional timescale associated with the decay of oceanic vortices is of the order of several months to a year.

Evolution of baroclinic planetary eddies over localized bottom topography in terms of JEBAR

Numerical experiments have been conducted to investigate the evolution of pure baroclinic eddies using two-layer planetary geostrophic equations in the presence of localized bottom topography. In particular, we interpret the eddy motion in terms of JEBAR (joint effect of baroclinicity and relief). It is shown that the emission of barotropic flows (or waves), westward acceleration and energy conversion occur when an eddy interacts with bottom topography. A meridional ridge acts as a repellor for a cold eddy and an attractor for warm eddy due to JEBAR-induced barotropic flows (or waves), which is consistent with the vorticity argument. This mechanism may provide a possible explanation not only for the global distribution of the phase speed of baroclinic Rossby waves observed in the Pacific by the TOPEX/POSEIDON satellite altimeter but also for the abrupt change in the trajectories of the westward propagating baroclinic eddies observed in the North Atlantic.

Global Observations of Oceanic Rossby Waves

Rossby waves play a critical role in the transient adjustment of ocean circulation to changes in large-scale atmospheric forcing. The TOPEX/POSEIDON satellite altimeter has detected Rossby waves throughout much of the world ocean from sea level signals with ≲10-centimeter amplitude and ≳500-kilometer wavelength. Outside of the tropics, Rossby waves are abruptly amplified by major topographic features. Analysis of 3 years of data reveals discrepancies between observed and theoretical Rossby wave phase speeds that indicate that the standard theory for free, linear Rossby waves is an incomplete description of the observed waves.

Rossby Wave Phase Speeds and Mixing Barriers in the Stratosphere. Part I: Observations

Abstract Lagrangian trajectories are used to calculate isentropic mixing properties for unfiltered and filtered Southern Hemisphere stratospheric winds. In wintertime significant mixing is confined to the surf zone between the Tropics and the edge of the polar vortex. The mixing barrier at the edge of the vortex is located near the core of the polar jet stream (where the maximum wind speeds occur), which is also approximately where the meridional potential vorticity gradient is largest. In summer there is significant mixing throughout the hemisphere, and no high-latitude mixing barrier exists. When the winds are filtered by zonal wavenumber to retain either the planetary-scale waves (1–3) or the smaller-scale waves (4–12), mixing in the surf zone is generally reduced but not eliminated. When the winds are filtered by phase speed, however, mixing is significantly reduced in restricted latitude zones where the phase speeds of the filtered waves are close to the speed of the local zonal-mean zonal wind. Thes...

Influence of Linear Depth Variation on Poincaré, Kelvin, and Rossby Waves

Exact solutions to the linearized shallow-water equations in a channel with linear depth variation and a mean flow are obtained in terms of confluent hypergeometric functions. These solutions are the generalization to finite s (depth variation parameter) of the approximate solutions for infinitesimal s. The equations also respect an energy conservation principle (and the normal modes are thus neutrally stable) in contradistinction to those of previous studies. They are evaluated numerically for a range in s from s = 0.1 to s = 1.95, and the range of validity of previously derived approximate solutions is established. For small s the Kelvin and Poincare' solutions agree well with those of Hyde, which were obtained by expanding in s. For finite s the solutions differ significantly from the Hyde expansions, and the magnitude of the phase speed decreases as s increases. The Rossby wave phase speeds are close to those obtained when the depth is linearized although the difference increases with s. The eigenfunctions become more distorted as s increases so that the largest amplitude and the smallest scale occur near the shallowest boundary. The negative Kelvin wave has a very unusual behavior as s increases.

On isallobaric effect in a quasi-geostrophic topographic-drag problem

Abstract Isallobaric effect of a slowly varying quasi-geostrophic flow represented by propagating waves may give rise to a mean steady topographic drag component which turns out to be the principal one when viscous effects are negligibly small. This drag component decreases, in contrast to the quasi-geostrophic component, when statistical properties of the topography become isotropic. When the phase velocity of the incident wave is much larger (smaller) than the phase speed of Rossby waves, the isallobaric drag becomes independent (dependent) on the sign of that velocity.

Analysis of remotely forced oceanic Rossby waves off California

Complex empirical orthogonal function (CEOF) analysis is used to investigate the coastal Kelvin wave driven Rossby wave response in the northeast Pacific. Using CEOF analysis, a spatial structure function is obtained from model upper layer thickness data. The model is a nonlinear, reduced gravity model of the northeast Pacific forced by coastal Kelvin waves originating in the equatorial Pacific. The spatial structure function is used to extract the interannual Rossby wave response from observed 300‐m‐depth temperature anomalies. The observed Rossby wave signal is termed the projection mode. Rossby wavelike features observed in the projection mode are order 1000 km long with most periods ranging between 2 and 4 years. The wave numbers and frequencies found are consistent with Rossby dynamics. The mean phase speed of the Rossby wavelike features within the projection mode is 1.3 cm s−1, in agreement with the theoretical Rossby wave phase speed at 40°N. Large amplitude nearshore and decreasing amplitude away from shore suggests nearshore generation of these waves. An important source of sea level variability along the east coast of North America at periods of 2–4 years was identified by Pares‐Sierra and O'Brien (1989) as poleward propagating Kelvin waves. Since the Rossby wavelike features observed in the projection mode have a majority of their periods ranging between 2 and 4 years, their forcing can be attributed to long‐period Kelvin waves. Spectral comparisons between the nearshore values in the projection mode and coastal sea level show greater than 90% coherence in the period band 3–4.4 years. The high coherence between coastal sea level variations and the projection mode shows that there is a strong correlation between the Rossby wavelike features within the projection mode and coastal Kelvin wave propagation. It is concluded that the Rossby waves within the projection mode are forced by coastal Kelvin wave propagation. The projection mode accounts for 47.5% of the variance in the 300‐m‐depth temperature anomalies. The implication of this result is that the physical mechanism of the numerical model, i.e., Rossby waves excited by coastal Kelvin wave propagation, accounts for 47.5% of the variance in the observed 300‐m depth temperature anomalies.

Equatorial Kelvin and Rossby waves evidenced in the Pacific Ocean through Geosat sea level and surface current anomalies

Equatorial Kelvin and Rossby waves are comprehensively demonstrated over most of the equatorial Pacific basin, through their signatures in sea level and zonal surface geostrophic current anomalies. This was made possible with altimeter data pertaining to the first year of the Geosat (Geodetic Satellite) 17‐day exact repeat orbit (November 8, 1986, to November 8, 1987). To this end, along‐track corrected Geosat sea level anomalies (SLAs), relative to the time period of interest, were first smoothed using nonlinear and linear filters. The original 17‐day time step was then reduced by combining all ascending and descending tracks within 10° longitudinal bands. Finally, SLAs were gridded onto a regular grid, and low‐pass filters were applied in latitude and time in order to smooth out remaining high‐frequency noise. Anomalies of zonal surface geostrophic current were calculated using the first and second derivatives of the SLA meridional gradient, off and on the equator, respectively. Sea level and surface current anomalies are validated in the western equatorial Pacific with in situ data gathered during seven hydrographic cruises at 165°E, and through expendable bathythermograph and mooring measurements. Following their chronological appearance along the 165°E meridian, the major low‐frequency SLAs and zonal surface current anomalies are described and explained in terms of the equatorial wave theory. An equatorial downwelling Kelvin wave, known to be the main oceanic signal of the 1986‐1987 El Niño, is generated in December 1986, concomitant with a strong westerly wind anomaly occurring west of the dateline. The associated propagating equatorial SLAs correspond to an elevation of 15 cm. Independent estimates of this Kelvin wave phase speed are obtained through time‐lag correlation matrix analysis (2.82 ± 0.96 m s−1) and the least squares fit of the SLA meridional structures to theoretical Kelvin wave shape (2.26 ± 1.02 m s−1). Both estimates indicate that the Kelvin wave has the characteristic of a first baroclinic mode. An equatorial upwelling Kelvin wave is then detectable in June 1987. It is characterized by a 10‐cm sea level drop, propagating only from the western to the central equatorial Pacific. A first meridional mode (m = 1) equatorial upwelling Rossby wave crossing the entire Pacific basin from March 1987 (eastern part) to September 1987 (western part) shows up in SLAs and zonal surface current anomalies. Such a Rossby wave corresponds to propagating sea level drops which are extreme (−12 cm) at about 4°N and 4°S latitudes. The consequences on zonal surface geostrophic current are very important since, in the case of the upwelling, it dramatically decreases the three major surface currents (the North and South Equatorial Countercurrents, and South Equatorial Current) by an amplitude similar to their mean annual velocity values. The least squares fit of the Rossby wave SLA meridional structures to its theoretical m = 1 form cogently suggests the dominance of the first baroclinic mode (c = 2.59 ± 0.65 m s−1). This dominance is corroborated by an estimate of the Rossby wave phase speed (1.02 ± 0.37 m s−1), which roughly corresponds to the theoretical phase speed (c/2m + 1) of the m = 1 equatorial Rossby wave. It is suggested that the equatorial upwelling Rossby wave is mostly due to a reflection of an equatorial upwelling Kelvin wave generated in January 1987 near the dateline. Whether or not the overall propagating features are part of the 1986–1987 El Niño or belong to the “normal” seasonal cycle cannot be decided in the absence of longer altimeter sea level time series.

Westward Propagation of Annual Sea Level and Wind Signals in the Western Pacific Ocean

The annual cycle of sea level variability is examined for the period 1976–1985 at seven stations that lie along the mere axis (near 7°N)) of the north equatorial countercurrent (NECC) sea level trough in the western Pacific. The technique of complex demodulation is used to describe the year to year modulation of the phase and amplitude of the annual cycle of sea level along this line. This technique reveals differences in the character of the annual cycle that are related to the occurrence of the El Niño/Southern Oscillation (ENSO) phenomenon. During non-ENSO time periods, the amplitude of the annual cycle averages 4–5 centimeters and increases towards the west at approximately 1 mm per degree of longitude. The annual cycle during thew periods also shows a phase propagation towards the west at about 50 cm/s, which is comparable to the Rossby wave phase speed at this latitude. During the ENSO events, the amplitude of the annual cycle averages 7–8 centimeters and increases towards the west at about 2 mm per degree of longitude. During these times the annual cycle is nearly in phase from the dateline to the coast of the Philippines. Interannual modulations of the amplitude of the annual cycle of wind in this region are similar to those seen in the sea level field, but no westward phase propagation is observed. A global analysis of the FGGE winds reveals a westward propagating zonal wind component that is obscured at the latitude of the NECC trough by a larger zonally uniform signal. The zonally uniform signal varies with latitude, following the solar heating, and accounts for the zonal mean phase of the annual cycle. The propagating component has a phase speed of about 50 cm/s and has maximum amplitude at 7.5°N. The energy source for this wind signal appears to be in the monsoon region of the Indian Ocean. It is hypothesized that the propagating annual sea level signal observed in the western Pacific results from resonant forcing by this westward propagating feature of the wind field.

The northeast Pacific Ocean response to the 1982–1983 El Niño

The ocean's response to atmospheric forcing and to forcing along the coast by Kelvin waves is examined in light of nearshore seasonal variability and the major 1982–1983 El Niño. In addition to driving the northeast Pacific gyre and local currents, the wind modifies the depth to the main thermocline, changing the apparent westward phase speed of Rossby waves excited by passing Kelvin waves. The amplitude of the passing Kelvin wave determines whether the Rossby wave depresses or raises the thermocline while propagating westward. Along the northeast Pacific coast from Oregon to Washington, model results suggest that the wind raises the main thermocline during the 1982–1983 El Niño. Generally, the coastal response off Oregon and Washington appears to be strongly driven by the large‐scale atmosphere, while along the California coast and south to the equator, the dominant El Niño signal has an oceanic origin. That signal, with periods between 2 and 5 years, originates in the western equatorial Pacific Ocean and is tracked eastward through the equatorial waveguide and then poleward along the coast to 50°N using data from two reduced gravity, primitive equation models coupled at 18°N. At shorter, seasonal time scales, the acceleration of the wind appears to be an important mechanism in driving coastal currents.