Amplitude Of Rossby Waves Research Articles

The Effects of Wind Forcing and Background Mean Currents on the Latitudinal Structure of Equatorial Rossby Waves

Abstract The latitudinal structure of annual equatorial Rossby waves in the tropical Pacific Ocean based on sea surface height (SSH) and thermocline depth observations is equatorially asymmetric, which differs from the structure of the linear waves of classical theory that are often presumed to dominate the variability. The nature of this asymmetry is such that the northern SSH maximum (along 5.5°N) is roughly 2 times that of the southern maximum (along 6.5°S). In addition, the observed westward phase speeds are roughly 0.5 times the predicted speed of 90 cm s−1 and are also asymmetric with the northern phase speeds, about 25% faster than the southern phase speeds. One hypothesized mechanism for the observed annual equatorial Rossby wave amplitude asymmetry is modification of the meridional structure by the asymmetric meridional shears associated with the equatorial current system. Another hypothesis is the asymmetry of the annually varying wind forcing, which is stronger north of the equator. A reduced-gravity, nonlinear, β-plane model with rectangular basin geometry forced by idealized Quick Scatterometer (QuikSCAT) wind stress is used to test these two mechanisms. The model with an asymmetric background mean current system perturbed with symmetric annually varying winds consistently produces asymmetric Rossby waves with a northern maximum (4.7°N) that is 1.6 times the southern maximum (5.2°S) and westward phase speeds of approximately 53 ± 13 cm s−1 along both latitudes. Simulations with a symmetric background mean current system perturbed by asymmetric annually varying winds fail to produce the observed Rossby wave structure unless the perturbation winds become strong enough for nonlinear interactions to produce asymmetry in the background mean current system. The observed latitudinal asymmetry of the phase speed is found to be critically dependent on the inclusion of realistic coastline boundaries.

Properties of Rossby Waves in the North Atlantic Estimated from Satellite Data

This study uses satellite observations of sea surface height (SSH) to detect westward-propagating anomalies, presumably baroclinic Rossby waves, in the North Atlantic and to estimate their period, wavelength, amplitude, and phase speed. Detection involved a nonlinear fit of the theoretical dispersion relation for Rossby waves to the time–longitude spectrum at a given latitude. Estimates of period, wavelength, and phase speed resulted directly from the detection process. Based on these, a filter was designed and applied to extract the Rossby wave signal from the data. This allowed a mapping of the spatial variability of the Rossby wave amplitude for the North Atlantic. Results showed the familiar larger speed of observed Rossby waves relative to that expected from theory, with the largest differences occurring at shorter periods. The data also show that the dominant Rossby waves, those with periods that are less than annual, propagated with almost uniform speed in the western part of the North Atlantic between 30° and 40°N. In agreement with previous studies, the amplitude of the Rossby wave field was higher in the western part of the North Atlantic than in the eastern part. This is often attributed to the influence of the Mid-Atlantic Ridge. By contrast, this study, through an analysis of the wave spatial structure, suggests that the source of the baroclinic Rossby waves at midlatitudes in the western North Atlantic is located southeast of the Grand Banks where the Gulf Stream and the deep western boundary current interact with the Newfoundland Ridge. The spatial structure of the waves in the eastern North Atlantic is consistent with the formation of these waves along the basin's eastern boundary.

Forcing of Differential Rotation and Rossby Waves at the Interface between the Convectively Stable and Unstable Layers

A model for the high-latitude region near the interface between the solar convection and radiative zones is suggested. The essential feature of the model is an allowance for the deformation of the interface between the convectively stable and unstable parts of the layer, which appears to be due to the influence of large-scale flows on this region's conditions. Two-dimensional numerical simulations for an axisymmetric flow show that one of the consequences of the interface deformation is the appearance of a latitudinal gradient in the temperature distribution, which gives rise to a strong radial gradient of the angular velocity in the vicinity of the interface. Such a differential rotation is, in fact, the thermal wind like that in the Earth's atmosphere. It is found that the penetration of the differential rotation and meridional flow into a convectively stable part of the layer depends strongly on values of the effective turbulent viscosity and thermal conductivity in this region. Two-dimensional numerical simulations of axisymmetric and nonaxisymmetric flows show that another consequence of the deformation of the interface is the forcing of differential rotation and the Rossby wave. It is found that the pumping mechanism is similar to the deformational long-wave instability mechanism that operates in a rotating fluid layer heated from below with the deformable upper stress-free surface. Nonlinear effects lead to the limitation of the differential rotation and Rossby wave amplitude and to the establishment of stationary patterns. Stationary differential rotation is in qualitative agreement with recent results obtained by helioseismology.

Ocean Wave Dynamics and El Niño

The response of an ocean general circulation model to specified wind stress is used to understand the role of ocean wave propagation in the evolution of El Niño events in sea surface temperature (SST) in the equatorial Pacific Ocean. In a control experiment the ocean model reproduces observed equatorial Pacific interannual variability in response to forcing by the observed wind stress. The ocean model is then forced with the same wind stress but with the time evolution of the wind stress forcing reversed. An analysis of the anomalies from the annual cycle in these two experiments delineates the parts of the response that are in equilibrium with and out of equilibrium with the wind stress forcing. In the western equatorial Pacific the SST anomalies are in equilibrium with the wind stress anomalies. In the eastern equatorial Pacific the SST anomalies are not in equilibrium with the wind stress anomalies but rather tend toward equilibrium with the upper-ocean beat content anomalies. The experiment demonstrates that the heat content is not in equilibrium with the wind stress forcing either on or near the equator. Very close to the equator the slope of the thermocline is in equilibrium with the wind stress, but the mean heat content is far from equilibrium. Slightly off of the equator in the western Pacific westward propagating heat content anomalies appear to originate in regions of strong wind stress forcing and then propagate to the western boundary. These westward propagating anomalies also depart significantly from equilibrium with the wind stress forcing. Additional experiments allow these westward propagating anomalies to be identified as freely propagating Rossby waves. The Rossby waves are shown to determine the equatorial heat content response to the wind stress forcing when they arrive at the western boundary and to be responsible for the nonequilibrium behavior of the equatorial mean heat content. A simplified coupled model is derived by fitting the results and estimating parameter values from the numerical experiments. In this model the time delay introduced by the Rossby waves is responsible for coupled instability, and dependence of the Rossby wave amplitude on the frequency of the forcing is responsible for the long period of the coupled oscillations.

Rossby Wave Generation by Poleward Propagating Kelvin Waves: The Midlatitude Quasigeostrophic Approximation

Abstract The phenomenon of Rossby wave generation by poleward propagating baroclinic coastal Kelvin waves is discussed in the low-frequency quasigeostrophic (QG) limit. The response of the system is divided into three frequency regimes: a low-frequency regime (longer than annual periods) for which the previously studied long-wave models are quite accurate, a high-frequency regime (semiannual or shorter) for which the Kelvin waves are coastally trapped (and thus of negligible importance to the interior), and an intermediate regime for which dispersive effects are important to the scattering process. It is shown that the retention of the y dependence of the radius of deformation in a locally 1D, QG model is necessary and sufficient to describe the dominant energy flux out of the coastal waveguide for all three of these frequency regimes. This Rossby wave energy flux directly determines the interior Rossby wave amplitudes and modifies the evolution of the Kelvin wave amplitude along the coast. The result of ...

Seasonal Development of the Extratropical QBO in a Numerical Model of the Middle Atmosphere

Abstract The seasonal (wintertime) development of middle atmosphere circulation in opposite phases of the equatorial quasi-biennial oscillation (QBO) was simulated with a three-dimensional nonlinear numerical model. In the stratosphere, the effect of equatorial QBO was generally consistent with the extratropical QBO observed by Holton and Tan, namely, a stronger midwinter polar vortex in the westerly phase, and vice versa. However, the extratropical response to the QBO was sensitive to other factors such as mesospheric gravity wave drag and the amplitude of Rossby waves specified at the model's lower boundary. The extratropical QBO was realistic only when a drag parameterization was included and Rossby wave amplitudes lay in an intermediate range close to the observed. At somewhat stronger forcing, the model's response was largest in the mesosphere where (in this case) westerlies were stronger in the easterly phase of equatorial QBO. This was apparently due to a shielding effect. The theory of planetary w...

Sea Level Variations Due to Equatorial Rossby Waves Associated with El Nin˜o

Abstract Interannual variations of sea level in the tropical Pacific are examined in relation to the El Nin˜o phenomenon. The amplitude of equatorial Rossby waves forced by wind and the sea level due to the waves are calculated from the analytical solutions in a two-layer reduced-gravity ocean model using filtered monthly wind data during the period 1961–87. Sea level variations with interannual periods at Truk, Ponape, and Majuro islands, located around 7°N, as well as at Rabaul, Honiara, and Funafuti in the South Pacific, are almost explained by Rossby waves remotely forced by winds. Reflected Rossby waves generated at the eastern coast of the Pacific may not significantly be effective. The interannual Rossby wave components of sea level are produced by odd meridional-mode waves excited from the equatorially symmetric component wind, which is composed of wind data in the same hemisphere as the studied sea level grid. Therefore, the Rossby components in the North Pacific are not affected by wind in the S...

Rossby Waves in the Pacific Ocean Extracted from Geosat Altimeter Data

Abstract Rossby waves have been detected in the northeast Pacific in time series of in situ hydrographic data, but the limited geographic coverage of such data has restricted the search for Rossby waves to small regions. Two years of continuous Geosat altimetry data were used here to extract the signatures of Rossby waves from the entire Pacific Ocean. This relatively long time series of global data presents an excellent opportunity to examine the surface expression of large-scale ocean phenomena such as Rossby waves. For this analysis the Pacific Ocean was divided into 10-degree square regions, and Rossby waves defined by the Rossby wave dispersion relation were fit to the Geosat data in each region. Rossby waves fit to each 10-degree region were separated by Fourier components in wavenumber space, with frequencies determined by the dispersion relation. Barotropic and first mode baroclinic Rossby waves were fit separately to the Geosat data. Rossby wave amplitudes from the least-squares fit were plotted ...

Reflection of interannual Rossby waves at the maritime western boundary of the tropical Pacific

The reflection of interannual Rossby waves over a 2.7‐year period (i.e., November 1986 to August 1989) is examined in the western tropical Pacific utilizing altimetric sea level observations from the Geosat Exact Repeat Mission. In 1987 this reflection process generates upwelling Kelvin waves that tended to limit the growth of the 1986–1987 El Niño in the eastern equatorial Pacific. Two‐dimensional autocorrelation and spectral analyses verify the existence of westward traveling Rossby waves in both the equatorial and off‐equatorial domains, and eastward propagating Kelvin waves in the equatorial domain. Extended empirical orthogonal function (EEOF) analysis characterizes the time‐space evolutionary behavior of the Rossby wave reflection process, extending from the El Niño in 1986–1987 toward the anti‐El Niño in 1988–1989. Both the Philippines Archipelago in the northern hemisphere and the Solomon Archipelago/Bismarck Archipelago/New Guinea complex in the southern hemisphere appear to reflect incident Rossby waves, with maximum amplitude near 8°N and 8°S, generating Kelvin waves in the equatorial wave guide that conduct the anomalous signal eastward along the equator. This apparent reflection process is examined in terms of the linear theory, with sea level phase information in the northern hemisphere at the western boundary (130°W) expanded in terms of the Kelvin and symmetric Rossby meridional wave modes. These modes are formed as weighted sums of parabolic cylinder functions. This procedure, operating under the constraint that the reflection process occurred according to linear theory, determines the percent contribution that each incident Rossby wave mode amplitude has upon the amplitude of the reflected Kelvin wave. This percentage changed little over the evolution of the EEOF pattern. The amplitude of the first‐mode Rossby wave (i.e., mode 2) accounts for most of the Kelvin wave amplitude (i.e., 70–80%), with the higher‐mode Rossby wave amplitudes (i.e., 4, 6, and 8) contributing less (i.e., 20%, −10%, and 10%, respectively), interacting both constructively and destructively with the first.

Wave–Mean Flow Statistics

Abstract A relation between the statistics of large-scale waves and the mean flow is derived from the potential enstrophy equations integrated over an isobaric surface. The difference between time-averaged zonal-mean state and the radiative-dynamical equilibrium state due to the symmetric circulation is determined by three components: the steady wave enstrophy, the variance in the wave enstrophy and the variance mean flow enstrophy. With some simplifications, the relationship between these components can be used to estimate the maximum amplitude for Rossby waves derived from a statistical data set. We obtain an upper limit of ∼1200 gpm for a wave disturbance with a meridional scale of ∼1800 km. If the Rossby wave amplitudes are observed near that upper limit, then the wave energy spectrum should exhibit a −5 power law. The three enstrophy components are estimated for a parameterized model of wave–mean flow interaction at a single level. We find that the steady wave enstrophy, the wave enstrophy variance a...