A harmonic projection and least–squares method for quantifying Kelvin wave activity

Abstract. A new method for isolating the equatorial and coastal Kelvin wave signal from alongtrack satellite altimetry data is presented and applied to sea level anomaly (SLA) observations in the tropical Indian Ocean. The method consists of sequential projections onto the SLA data, starting with meridional or cross-shore Kelvin wave profiles derived from shallow water theory (y-projections). Next, Fourier basis functions in x-t (along-waveguide distance and time respectively) space with the phase speed ranges of Kelvin and Rossby waves are projected onto the y-projections. After projections in all three dimensions have been carried out, least-squares methods are applied to optimize the non-orthogonal basis function coefficients and minimize the misfit of their along-waveguide forcing and dissipation. Lastly, the westward-propagating (Rossby wave-related) signals are removed, generating a Kelvin wave coefficient K that represents Kelvin wave activity. Along the Indian Ocean equatorial-coastal waveguide, Hovmöller diagrams of K show reduced high-wavenumber noise compared to analogous diagrams of pre-processed sea level anomaly. Results from a Monte Carlo simulation demonstrate that Kelvin wave signals generated a priori can be effectively recovered even when superimposed with strong Rossby waves; the signs of all but the weakest waves are diagnosed correctly in over 90 % of cases. When the method is applied to 21 years of satellite observations and the SLA signal associated with K is removed, the large residual in the equatorial SLA signal has a spatial distribution consistent with wind-forced Rossby waves. The equatorial SLA variability in the western part of the basin is poorly correlated with the SLA field associated with K, as the superimposed SLA profile of Rossby waves can distort the true origin locations of Kelvin waves in the raw SLA field. Therefore, this method offers improved tracking of Kelvin waves compared to the raw SLA dataset, and may provide the opportunity to study weakly nonlinear aspects of these waves by comparison with linear models.

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Long-Wave Dynamics of Sea Level Variations during Indian Ocean Dipole Events

Journal of Physical Oceanography ◽

10.1175/2008jpo3900.1 ◽

2009 ◽

Vol 39 (5) ◽

pp. 1115-1132 ◽

Cited By ~ 34

Author(s):

Dongliang Yuan ◽

Hailong Liu

Keyword(s):

Indian Ocean ◽

Sea Level ◽

Indian Ocean Dipole ◽

Rossby Waves ◽

Western Boundary ◽

Kelvin Wave ◽

Wave Pulse ◽

Wave Dynamics ◽

Long Wave ◽

Equatorial Rossby Waves

Abstract Long-wave dynamics of the interannual variations of the equatorial Indian Ocean circulation are studied using an ocean general circulation model forced by the assimilated surface winds and heat flux of the European Centre for Medium-Range Weather Forecasts. The simulation has reproduced the sea level anomalies of the Ocean Topography Experiment (TOPEX)/Poseidon altimeter observations well. The equatorial Kelvin and Rossby waves decomposed from the model simulation show that western boundary reflections provide important negative feedbacks to the evolution of the upwelling currents off the Java coast during Indian Ocean dipole (IOD) events. Two downwelling Kelvin wave pulses are generated at the western boundary during IOD events: the first is reflected from the equatorial Rossby waves and the second from the off-equatorial Rossby waves in the southern Indian Ocean. The upwelling in the eastern basin during the 1997–98 IOD event is weakened by the first Kelvin wave pulse and terminated by the second. In comparison, the upwelling during the 1994 IOD event is terminated by the first Kelvin wave pulse because the southeasterly winds off the Java coast are weak at the end of 1994. The atmospheric intraseasonal forcing, which plays an important role in inducing Java upwelling during the early stage of an IOD event, is found to play a minor role in terminating the upwelling off the Java coast because the intraseasonal winds are either weak or absent during the IOD mature phase. The equatorial wave analyses suggest that the upwelling off the Java coast during IOD events is terminated primarily by western boundary reflections.

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Roles of Equatorial Waves and Western Boundary Reflection in the Seasonal Circulation of the Equatorial Indian Ocean

Journal of Physical Oceanography ◽

10.1175/jpo2905.1 ◽

2006 ◽

Vol 36 (5) ◽

pp. 930-944 ◽

Cited By ~ 50

Author(s):

Dongliang Yuan ◽

Weiqing Han

Keyword(s):

Indian Ocean ◽

Sea Level ◽

Rossby Waves ◽

Equatorial Indian Ocean ◽

Kelvin Waves ◽

Wind Forcing ◽

Western Boundary ◽

Central Basin ◽

Sea Levels ◽

Equatorial Rossby Waves

Abstract An ocean general circulation model (OGCM) is used to study the roles of equatorial waves and western boundary reflection in the seasonal circulation of the equatorial Indian Ocean. The western boundary reflection is defined as the total Kelvin waves leaving the western boundary, which include the reflection of the equatorial Rossby waves as well as the effects of alongshore winds, off-equatorial Rossby waves, and nonlinear processes near the western boundary. The evaluation of the reflection is based on a wave decomposition of the OGCM results and experiments with linear models. It is found that the alongshore winds along the east coast of Africa and the Rossby waves in the off-equatorial areas contribute significantly to the annual harmonics of the equatorial Kelvin waves at the western boundary. The semiannual harmonics of the Kelvin waves, on the other hand, originate primarily from a linear reflection of the equatorial Rossby waves. The dynamics of a dominant annual oscillation of sea level coexisting with the dominant semiannual oscillations of surface zonal currents in the central equatorial Indian Ocean are investigated. These sea level and zonal current patterns are found to be closely related to the linear reflections of the semiannual harmonics at the meridional boundaries. Because of the reflections, the second baroclinic mode resonates with the semiannual wind forcing; that is, the semiannual zonal currents carried by the reflected waves enhance the wind-forced currents at the central basin. Because of the different behavior of the zonal current and sea level during the reflections, the semiannual sea levels of the directly forced and reflected waves cancel each other significantly at the central basin. In the meantime, the annual harmonic of the sea level remains large, producing a dominant annual oscillation of sea level in the central equatorial Indian Ocean. The linear reflection causes the semiannual harmonics of the incoming and reflected sea levels to enhance each other at the meridional boundaries. In addition, the weak annual harmonics of sea level in the western basin, resulting from a combined effect of the western boundary reflection and the equatorial zonal wind forcing, facilitate the dominance by the semiannual harmonics near the western boundary despite the strong local wind forcing at the annual period. The Rossby waves are found to have a much larger contribution to the observed equatorial semiannual oscillations of surface zonal currents than the Kelvin waves. The westward progressive reversal of seasonal surface zonal currents along the equator in the observations is primarily due to the Rossby wave propagation.

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Convectively Coupled Kelvin Waves over Tropical Africa during the Boreal Summer: Structure and Variability

Journal of Climate ◽

10.1175/2008jcli2008.1 ◽

2008 ◽

Vol 21 (24) ◽

pp. 6649-6667 ◽

Cited By ~ 44

Author(s):

Ademe Mekonnen ◽

Chris D. Thorncroft ◽

Anantha R. Aiyyer ◽

George N. Kiladis

Keyword(s):

Indian Ocean ◽

Wave Activity ◽

Kelvin Waves ◽

Sub Saharan Africa ◽

Eastern Pacific ◽

Boreal Summer ◽

Kelvin Wave ◽

Tropical Africa ◽

Western Atlantic ◽

Sst Anomalies

Abstract The structure and variability of convectively coupled Kelvin waves during the boreal summer are explored using satellite-observed brightness temperature data and ECMWF reanalyses. Kelvin wave activity is most prominent between the central and eastern Pacific, across Africa, and the Indian Ocean. Composite analysis shows that over sub-Saharan Africa Kelvin wave convection is peaked north of the equator, while the dynamical fields tend to be symmetric with respect to the equator. Convectively coupled Kelvin waves propagate faster over the Pacific and western Atlantic (∼24 m s−1), and slow down over tropical Africa (∼14 m s−1), consistent with stronger coupling between the dynamics and convection over tropical Africa. The Kelvin waves observed over Africa generally propagate into the region from anywhere between the eastern Pacific and the Atlantic, and decay over the eastern Indian Ocean basin. Results show marked interannual variability of Kelvin wave activity over Africa. Anomalously high Kelvin wave variance tends to occur during dry years, while low variance occurs during wet years. African Kelvin wave activity is positively correlated with SST anomalies in the equatorial east Pacific. The same warm SST anomalies that are favorable for enhanced Kelvin wave activity suppress the mean rainfall over tropical Africa via a more slowly varying teleconnection and associated subsidence. A brief analysis of an intense Kelvin wave in August 1987 (a dry year) shows a clear impact of the wave on convective development and daily rainfall over tropical Africa. This Kelvin wave was also associated with a series of easterly wave initiations over tropical Africa.

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Tropical temperature variability and Kelvin-wave activity in the UTLS from GPS RO measurements

Atmospheric Chemistry and Physics ◽

10.5194/acp-17-793-2017 ◽

2017 ◽

Vol 17 (2) ◽

pp. 793-806 ◽

Cited By ~ 9

Author(s):

Barbara Scherllin-Pirscher ◽

William J. Randel ◽

Joowan Kim

Keyword(s):

Large Scale ◽

Deep Convection ◽

Wave Activity ◽

Kelvin Waves ◽

Temperature Variability ◽

Stationary Waves ◽

Kelvin Wave ◽

Quasi Biennial Oscillation ◽

Tropical Tropopause ◽

Tropopause Region

Abstract. Tropical temperature variability over 10–30 km and associated Kelvin-wave activity are investigated using GPS radio occultation (RO) data from January 2002 to December 2014. RO data are a powerful tool for quantifying tropical temperature oscillations with short vertical wavelengths due to their high vertical resolution and high accuracy and precision. Gridded temperatures from GPS RO show the strongest variability in the tropical tropopause region (on average 3 K2). Large-scale zonal variability is dominated by transient sub-seasonal waves (2 K2), and about half of sub-seasonal variance is explained by eastward-traveling Kelvin waves with periods of 4 to 30 days (1 K2). Quasi-stationary waves associated with the annual cycle and interannual variability contribute about a third (1 K2) to total resolved zonal variance. Sub-seasonal waves, including Kelvin waves, are highly transient in time. Above 20 km, Kelvin waves are strongly modulated by the quasi-biennial oscillation (QBO) in stratospheric zonal winds, with enhanced wave activity during the westerly shear phase of the QBO. In the tropical tropopause region, however, peaks of Kelvin-wave activity are irregularly distributed in time. Several peaks coincide with maxima of zonal variance in tropospheric deep convection, but other episodes are not evidently related. Further investigations of convective forcing and atmospheric background conditions are needed to better understand variability near the tropopause.

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Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Journal of Fluid Mechanics ◽

10.1017/s0022112007009160 ◽

2007 ◽

Vol 594 ◽

pp. 493-506 ◽

Cited By ~ 10

Author(s):

TIFFANY A. SHAW ◽

THEODORE G. SHEPHERD

Keyword(s):

Conservation Laws ◽

Large Scale ◽

Three Dimensional ◽

Phase Speed ◽

Wave Activity ◽

Two Dimensions ◽

Three Dimensions ◽

Dimensional Problem ◽

Background Flow ◽

Homogeneous Background

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship $A^{\cal E}\,{=}\,cA^{\cal P}$ between pseudoenergy $A^{\cal E}$ and pseudomomentum $A^{\cal P}$, where c is the horizontal phase speed in the direction of symmetry associated with $A^{\cal P}$, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

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Linking Equatorial African precipitation to Kelvin wave processes in the CP4-Africa convection-permitting regional climate simulation

10.5194/egusphere-egu21-8419 ◽

2021 ◽

Author(s):

Godwin Ayesiga ◽

Christopher Holloway ◽

Charles Williams ◽

Gui-Ying Yang ◽

Rachel Stratton ◽

...

Keyword(s):

Observational Studies ◽

Model Simulation ◽

Wave Activity ◽

Kelvin Waves ◽

Specific Humidity ◽

Climate Simulation ◽

Kelvin Wave ◽

Low Level ◽

Equatorial Africa ◽

Precipitation Anomalies

Synoptic timescale forecasts over Equatorial Africa are important for averting weather-and climate-related disasters and the resulting agricultural losses. Observational studies have shown that rainfall anomalies often propagate eastward across Equatorial Africa, and that there is a linkage between synoptic-scale eastward-propagating precipitation and Convectively Coupled Kelvin Waves (CCKWs) over this region. We explore the mechanisms in which CCKWs modulate the propagation of precipitation from West to East over Equatorial Africa. We examine the first Africa-wide climate simulation from a convection permitting model (CP4A) along with its global driving-model simulation (G25) and evaluate both against observations (TRMM) and ERA-Interim (ERA-I), with a focus on precipitation and Kelvin wave activity.Lagged composites show that both simulations capture the eastward propagating precipitation signal seen in observational studies, though G25 has a weaker signal. Composite analysis on high-amplitude Kelvin waves further shows that both simulations capture the connection between the eastward propagating precipitation anomalies and Kelvin waves. In comparison to TRMM, however, the precipitation signal is weaker in G25, while CP4A is more realistic. As the Kelvin wave activity is also well represented in both simulations when compared to ERA-I, the weak precipitation signal in G25 may be partly associated with the weak coupling between the precipitation and Kelvin waves. We show that CCKWs modulate the eastward propagation of convection and precipitation across Equatorial Africa through at least two related physical processes. Firstly, an enhancement of the low-level westerlies leads to increased low-level convergence; secondly, westerly moisture flux anomalies amplify lower-to-mid-tropospheric specific humidity. Results show that both CP4A and G25 generally simulate the key horizontal features of CCKWs, with anomalous low-level westerlies in phase with positive precipitation anomalies. However, both models show a weakness in capturing the vertical profile of anomalous specific humidity, and the zonal-vertical circulation is too weak in G25 and incoherent in CP4A compared to ERA-I.In both ERA-I and the simulations, Kelvin wave-induced convergence and the westward tilt with height of anomalous zonal winds and specific humidity tends to weaken to the east of the East African highlands. It appears that these highlands impede the coherent eastward propagation of the wave-precipitation coupled structure.

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Baroclinic Characteristics and Energetics of Annual Rossby Waves in the Southern Tropical Indian Ocean

Journal of Physical Oceanography ◽

10.1175/jpo-d-19-0294.1 ◽

2020 ◽

Vol 50 (9) ◽

pp. 2591-2607

Author(s):

Ke Huang ◽

Dongxiao Wang ◽

Ming Feng ◽

Weiqing Han ◽

Gengxin Chen ◽

...

Keyword(s):

Indian Ocean ◽

Sea Level ◽

Large Scale ◽

Rossby Waves ◽

Tropical Indian Ocean ◽

High Energy ◽

High Order ◽

Baroclinic Mode ◽

Sea Level Variability ◽

Low Order

AbstractThe first baroclinic mode Rossby wave is known to be of critical importance to the annual sea level variability in the southern tropical Indian Ocean (STIO; 0°–20°S, 50°–115°E). In this study, an analysis of continuously stratified linear ocean model reveals that the second baroclinic mode also has significant contribution to the annual sea level variability (as high as 81% of the first baroclinic mode). The contributions of residual high-order modes (3 ≤ n ≤ 25) are much less. The superposition of low-order (first and second) baroclinic Rossby waves (BRWs) primarily contribute to the high energy center of sea level variability at ~10°S in the STIO and the vertical energy penetration below the seasonal thermocline. We have found that 1) the low-order BRWs, having longer zonal wavelengths and weaker damping, can couple more efficiently to the local large-scale wind forcing than the high-order modes and 2) the zonal coherency of the Ekman pumping results in the latitudinal energy maximum of low-order BRWs. Overall, this study extends the traditional analysis to suggest the characteristics of the second baroclinic mode need to be taken into account in interpreting the annual variability in the STIO.

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Wind-Driven Oceanic Rossby Waves in the Tropical South Indian Ocean with and without an Active ENSO

Journal of Physical Oceanography ◽

10.1175/jpo2723.1 ◽

2005 ◽

Vol 35 (5) ◽

pp. 729-746 ◽

Cited By ~ 10

Author(s):

Astrid Baquero-Bernal ◽

Mojib Latif

Keyword(s):

Indian Ocean ◽

Wind Stress ◽

Time Scale ◽

Rossby Waves ◽

Heat Content ◽

Kelvin Waves ◽

South Indian Ocean ◽

South Indian ◽

Coastal Kelvin Waves ◽

The Tropical Pacific

Abstract The interannual heat content variability in the tropical south Indian Ocean (SIO) and its relationship with El Niño–Southern Oscillation (ENSO) is studied. The baroclinic ocean response to stochastic wind stress predicted by a simple analytical model is compared with two integrations of the ECHO-G coupled general circulation model. In one integration, ocean–atmosphere interactions are suppressed in the tropical Pacific Ocean, so that this integration does not simulate ENSO. In the other integration, interactions are allowed everywhere and ENSO is simulated. The results show that basinwide variability in the SIO heat content can be produced by two mechanisms: 1) oscillatory forcing by ENSO-related wind stress and 2) temporally stochastic and spatially coherent wind stress forcing. Previous studies have shown that transmission of energy from the tropical Pacific to the southern Indian Ocean occurs through coastal Kelvin waves along the western coast of Australia. The results in this paper confirm the occurrence of such transmission. In the ECHO-G simulations, this transmission occurs both at the annual time scale and at interannual time scales. Generation of offshore Rossby waves by these coastal Kelvin waves at interannual time scales—and, in particular, at the ENSO time scale—was found.

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Intraseasonal Variability of the Equatorial Indian Ocean Observed from Sea Surface Height, Wind, and Temperature Data

Journal of Physical Oceanography ◽

10.1175/jpo3006.1 ◽

2007 ◽

Vol 37 (2) ◽

pp. 188-202 ◽

Cited By ~ 40

Author(s):

Lee-Lueng Fu

Keyword(s):

Indian Ocean ◽

Rossby Waves ◽

Intraseasonal Variability ◽

Equatorial Indian Ocean ◽

Sea Surface Height ◽

Kelvin Waves ◽

Wind Forcing ◽

Sea Surface ◽

Vertical Mode ◽

Basin Mode

Abstract The forcing of the equatorial Indian Ocean by the highly periodic monsoon wind cycle creates many interesting intraseasonal variabilities. The frequency spectrum of the wind stress observations from the European Remote Sensing Satellite scatterometers reveals peaks at the seasonal cycle and its higher harmonics at 180, 120, 90, and 75 days. The observations of sea surface height (SSH) from the Jason and Ocean Topography Experiment (TOPEX)/Poseidon radar altimeters are analyzed to study the ocean’s response. The focus of the study is on the intraseasonal periods shorter than the annual period. The semiannual SSH variability is characterized by a basin mode involving Rossby waves and Kelvin waves traveling back and forth in the equatorial Indian Ocean between 10°S and 10°N. However, the interference of these waves with each other masks the appearance of individual Kelvin and Rossby waves, leading to a nodal point (amphidrome) of phase propagation on the equator at the center of the basin. The characteristics of the mode correspond to a resonance of the basin according to theoretical models. For the semiannual period and the size of the basin, the resonance involves the second baroclinic vertical mode of the ocean. The theory also calls for similar modes at 90 and 60 days. These modes are found only in the eastern part of the basin, where the wind forcing at these periods is primarily located. The western parts of the theoretical modal patterns are not observed, probably because of the lack of wind forcing. There is also similar SSH variability at 120 and 75 days. The 120-day variability, with spatial patterns resembling the semiannual mode, is close to a resonance involving the first baroclinic vertical mode. The 75-day variability, although not a resonant basin mode in theory, exhibits properties similar to the 60- and 90-day variabilities with energy confined to the eastern basin, where the SSH variability seems in resonance with the local wind forcing. The time it takes an oceanic signal to travel eastward as Kelvin waves from the forcing location along the equator and back as Rossby waves off the equator roughly corresponds to the period of the wind forcing. The SSH variability at 60–90 days is coherent with sea surface temperature (SST) with a near-zero phase difference, showing the effects of the time-varying thermocline depth on SST, which may affect the wind in an ocean–atmosphere coupled process governing the intraseasonal variability.

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