Development and Propagation of Equatorial Waves

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Intraseasonal modulation of Wyrtki jet in the eastern Indian Ocean by equatorial waves during spring 2013

A strong spring Wyrtki jet(WJ)presents in May 2013 in the eastern equatorial Indian Ocean.The entire buildup and retreat processes of the spring WJ were well captured by two adjacent Acoustic Doppler Current Profilers mounted on the mooring systems.The observed zonal jet behaved as one intraseasonal event with the significant features of abrupt emergence as well as slow disappearance.Further research illustrate that the pronounced surface westerly wind burst during late-April to mid-May,associated with the active phase of a robust eastwardpropagating Madden–Julian oscillation in the tropical Indian Ocean,was the dominant reason for the rapid acceleration of surface WJ.In contrasting,the governing mechanism for the jet termination was equatorial wave dynamics rather than wind forcing.The decomposition analysis of equatorial waves and the corresponding changes in the ocean thermocline demonstrated that strong WJ was produced rapidly by the wind-generated oceanic downwelling equatorial Kelvin wave and was terminated subsequently by the westward-propagating equatorial Rossby wave reflecting from eastern boundaries of the Indian Ocean.

Equatorial Wave Expansion of Instantaneous Flows for Diagnosis of Equatorial Waves from Data:Formulation and Illustration

This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows（EWEIF） uses dynamic constraints in conjunction with projections of data onto parabolic cylinder functions to determine the amplitude of all equatorial waves.EWEIF allows us to decompose an instantaneous wave flow into individual equatorial waves with a presumed equivalent depth without using temporal or spatial filtering a priori.Three sets of EWEIF analyses are presented. The first set is to confirm that EWEIF is capable of recovering the individual waves constructed from theoretical equatorial wave solutions under various scenarios. The other two sets demonstrate the ability of the EWEIF method to derive time series of individual equatorial waves from instantaneous wave fields without knowing a priori exactly which waves exist in the data as well as their spatial and temporal scales using outputs of an equatorial β-channel shallow-water model and ERA-Interim data. The third set of demonstrations shows, for the first time, the continuous evolutions of individual equatorial waves in the stratosphere whose amplitude is synchronized with the background zonal wind as predicted by quasi-biennial oscillation theory.

A Survey of Statistical Relationships between Tropical Cyclone Genesis and Convectively Coupled Equatorial Rossby Waves

Convectively coupled equatorial Rossby waves(ERW)modulate tropical cyclone activities over tropical oceans.This study presents a survey of the statistical relationship between intraseasonal ERWs and tropical cyclone genesis(TCG)over major global TC basins using four-decade-long outgoing longwave radiation(OLR)and TC best-track datasets.Intraseasonal ERWs are identified from the OLR anomalies using an empirical orthogonal function(EOF)analysis method without imposing equatorial symmetry.We find that westward-propagating ERWs are most significant in four tropical ocean basins over the summer hemisphere and that ERWs exhibit similar northeast-southwest(southeast-northwest)tilted phase lines in the northern(southern)hemisphere,with an appreciable poleward advance of wave energy in most TC basins.The EOF-based ERW indices quantitatively show that ERWs significantly modulate TC genesis.The convectively active(suppressed)phases of ERWs coincide with increased(reduced)TCG occurrences.The TCG modulation by ERWs achieves the maximum where the ERWs propagate through the climatological TCG hotspots.As a result,the total number of TCG occurrences in the TC basins varies significantly according to the ERW phase.The ERW-TCG relationship is significant over the northwestern Pacific Ocean,northeastern Pacific Ocean,and the northern Indian Ocean during the northern summer seasons.In the southern summer season,the ERW-TCG relationship is significant over the southern Indian Ocean,Indonesian-Australia basin,and the southwestern Pacific Ocean.However,ERW activities are weak in the main TC development region of the Atlantic Ocean;and the impact on Atlantic TCG appears to be insignificant.

Theoretical analysis of equatorial near-inertial solitary waves under complete Coriolis parameters

An investigation of equatorial near-inertial wave dynamics under complete Coriolis parameters is performed in this paper.Starting from the basic model equations of oceanic motions,a Korteweg de Vries equation is derived to simulate the evolution of equatorial nonlinear near-inertial waves by using methods of scaling analysis and perturbation expansions under the equatorial beta plane approximation.Theoretical dynamic analysis is finished based on the obtained Korteweg de Vries equation,and the results show that the horizontal component of Coriolis parameters is of great importance to the propagation of equatorial nonlinear near-inertial solitary waves by modifying its dispersion relation and by interacting with the basic background flow.

Research on the Propagation Acting of the Equatorial Planetary Waves on the Western Equatorial Pacific Warm Pool Heat

Based on the long-term buoy data from the Tropical Atmosphere Ocean ( TAO ) —array during the TOGA ( Tropical Ocean and Global Atmosphere ) Program (19801996), the propagation acting of the Equatorial planetary waves on the Western Equatorial Pacific warm pool heat is analyzed. Results show that the zonal heat transmission in the Western Equatorial Pacific takes palace mainly in the subsurface water and spreads eastwards along the thermocline; while the seasonal westward-spreading heat change structure occurs in the mixed layers in the middle and western Pacific. The standing-form transmission in the western Pacific appears in the thermocline layer, while in the eastern pacific, it exists in the mixed layer as well as in the thermocline layer. The standing-form and eastward-spreading sign of zonal heat transmitting in the upper water is predominant and strong, and the westward sign is weak.The component force of Kelvin Equatorial wave pressure runs through the western and eastern Equatorial pacific, and transmits heat energy eastwards. And the heat transmitted by zonal current component occurs mostly in the western Pacific; The heat transmitted by the component force of Rossby wave pressure mainly appears in the eastern and middle areas of the Pacific, while the zonal current component transmitting occurs mainly in the western Pacific; Mixed-Rossby gravity wave’s action on the zonal current is stronger than that of the thermocline layer. In the mean state, the standing wave model of Equatorial Pacific up layer ocean temperature confines the transport of western Pacific warm pool heat to the eastern Pacific. Under abnormal conditions, the standing wave model of Equatorial Pacific up layer ocean temperature weakens, the eastwardly transmitting model enhances, and subsequently n^the El Ni o event occurs.

Role of Equatorial Wave Transitions in Tropical Cyclogenesis over the Western North Pacific

This study associates tropical cyclone (TC) activity over the western North Pacific (WNP) with the equatorial wave transition from an interannual viewpoint, revealing that the tropical cyclogenesis mean location may be modulated by a longitudinal shift in the transition of Mixed Rossby-gravity (MRG) waves to off-equatorial tropical depression (TD) disturbances from year to year. To a large extent, the wave transition is attributable to the monsoon trough in response to the thermal state of the warm pool (WP) over the WNP. During the cold state years in the WP, the basic flow confluence region associated with the monsoon trough penetrates eastward, leading to an eastward shift in the location of the wave transition. Such an environment, in which wave accumulation and energy conversion occur, is favorable for tropical cyclogenesis; as a result, the averaged cyclogenesis location moves eastward. The condition is reserved during the warm years in the WP, resulting in the prominent westward-retreating mean TC formation.

Wind-forced equatorial wave dynamics of the Pacific Ocean during 2014/2015 and 2015/2016 E1 Nino events

The equatorial wave dynamics of interannual sea level variations between 2014/2015 and2015/2016 El Nino events are compared using the Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics Climate Ocean Model(LICOM) forced by the National Centers for Environmental Prediction(NCEP) reanalysis I wind stre s s and heat flux during 2000-2015.In addition,the LICOM can reproduce the interannual variability of sea surface temperature anomalies(SSTA) and sea level anomalies(SLA) along the equator over the Pacific Ocean in comparison with the Hadley center and altimetric data well.We extracted the equatorial wave coefficients of LICOM simulation to get the contribution to SLA by multiplying the meridional wave structure.During 2014/2015 El Nino event,upwelling equatorial Kelvin waves from the western boundary in April2014 reach the eastern Pacific Ocean,which weakened SLA in the eastern Pacific Ocean.However,no upwelling equatorial Kelvin waves from the western boundary of the Pacific Ocean could reach the eastern boundary during the 2015/2016 El Nino event.Linear wave model results also demonstrate that upwelling equatorial Kelvin waves in both 2014/2015 and 2015/2016 from the western boundary can reach the eastern boundary.However,the contribution from stronger westerly anomalies forced downwelling equatorial Kelvin waves overwhelmed that from the upwelling equatorial Kelvin waves from the western boundary in 2015.Therefore,the western boundary reflection and weak westerly wind burst inhibited the growth of the 2014/2015 El Nino event.The disclosed equatorial wave dynamics are important to the simulation and prediction of ENSO events in future studies.

Nonlinearly Coupled KdV Equations Describing the Interaction of Equatorial and Midlatitude Rossby Waves

Amplitude equations governing the nonlinear resonant interaction of equatorial baroclinic and barotropic Rossby waves were derived by Majda and Biello and used as a model for long range interactions （teleconnections） between the tropical and midlatitude troposphere. An overview of that derivation is nonlinear wave theory, but not in atmospheric presented and geared to readers versed in sciences. In the course of the derivation, two other sets of asymptotic equations are presented： the long equatorial wave equations and the weakly nonlinear, long equatorial wave equations. A linear transformation recasts the amplitude equations as nonlinear and linearly coupled KdV equations governing the amplitude of two types of modes, each of which consists of a coupled tropical/midlatitude flow. In the limit of Rossby waves with equal dispersion, the transformed amplitude equations become two KdV equations coupled only through nonlinear fluxes. Four numerical integrations are presented which show （i） the interaction of two solitons, one from either mode, （ii） and （iii） the interaction of a soliton in the presence of different mean wind shears, and （iv） the interaction of two solitons mediated by the presence of a mean wind shear.

Two-Way Interactions Between Equatorially-Trapped Waves and the Barotropic Flow

Lateral energy exchange between the tropics and the midlatitudes is a topic of great importance for understanding Earth＇s climate system. In this paper, the authors address this issue in an idealized set up through simple shallow water models for the interactions between equatorially trapped waves and the barotropic mode, which supports Rossby waves that propagate poleward and can excite midlatitude teleconnection patterns. It is found here that the interactions between a Kelvin wave and a fixed meridionai shear （mimicking the jet stream） generates a non-trivial meridional velocity and meridional convergence in phase with the upward motion that can attain a maximum of about 50%, which oscillates on frequencies ranging from one day to 10 days. When, on the other hand, the barotropic flow is forced by slowly propagating Kelvin waves a complex flow pattern emerges; it consists of a phase-locked barotropic response that is equatoriaily trapped and that propagates eastward with the forcing Kelvin wave and a certain number of planetary Rossby waves that propagate westward and toward the poles as seen in nature. It is suggested here that the poleward propagating waves are to some sort of multi-way resonant interaction with the phase locked response. Moreover, it is shown here that a numerical scheme with dispersion properties that depend on the direction perpendicular to the direction of propagation, namely the 2D central scheme of Nessyahu and Tadmor, can artificially alter significantly the topology of the wave fields and thus should be avoided in climate models.

EQUATORIAL TRAPPED WAVES IN THE MEAN STATE WITH SLOW VARIATION:INHOMOGENOUS EQUATORIAL DUCT

The effects of zonally varying mean state of equatorial Pacific on planetaryequatorial trapped waves were analytically investigated. A WKB approximation was used with the slowzonal variation hypothesis, acceptable in the context of equatorial trapped low-frequencyvariability, and a working space transformation was made to turn the meridional trappedlow-frequency variability, and a working space transformation was made to turn the meridional modeequation into the Weber-Hermite equation in the new space. The inhomoge-neous equatorial wave ductwas proposed and the theoretical results were compared with observation. It matches the real stateof the equatorial Pacific to a certain degree.

THEORETICAL ANALYSIS OF ATMOSPHERIC WAVES IN EQUATORIAL ZONE

In the equatorial zone the dynamic equations of the atmospheric motion are written inthe β-plane.These equations are linearized according to the mean atmospheric conditions.Numerical method is used to obtain a characteristic wave solution. Results obtained showthat the easterly wind shear changes the phase speed of low frequency waves more strikinglythan that of high frequency waves. The structure of the characteristic disturbances is sim-ilar to that in middle latitudes only with some exceptions in the relationship of geopo-tential field with vorticity field.

NUMERICAL EXPERIMENTS ON THE TROPICAL AIR-SEA INTERACTION WAVES

By means of the numerical method,the tropical air-sea interaction waves are studied.The results show that when the Kelvin waves are filtered out and only the equatorial Rossby waves are reserved both in the atmosphere and in the ocean,the disturbances can also propagate eastward because of the air-sea interaction.The critical wavelength of the eastward propagating waves is related to the intensity of the air-sea interaction.The stronger the air-sea interaction,the larger the eastward propagating components of the air-sea interaction waves.The results of the numerical experiments are in good agreement with those of the theoretical analysis(Chao and Zhang,1988).

Ocean-Atmosphere Interaction in the Lifecycle of ENSO:The Coupled Wave Oscillator

To explain the oscillatory nature of E1 Nino/Southern Oscillation （ENSO）, many ENSO theories emphasize the free oceanic equatorial waves propagating/reflecting within the Pacific Ocean, or the discharge/recharge of Pacific-basin-averaged ocean heat content. ENSO signals in the Indian and Atlantic oceans are often considered as remote response to the Pacific SST anomaly through atmospheric teleconnections. This study investigates the ENSO life cycle near the equator using long-term observational datasets. Space-time spectral analysis is used to identify and isolate the dominant interannual oceanic and atmospheric wave modes associated with ENSO. Nino3 SST anomaly is utilized as the ENSO index, and lag-correlation/regression are used to construct the composite ENSO life cycle. The propagation, structure and feedback mechanisms of the dominant wave modes are studied in detail. The results show that the dominant oceanic equatorial wave modes associated with ENSO are not free waves, but are two ocean-atmosphere coupled waves including a coupled Kelvin wave and waves are not confined only to the Pacific a coupled equatorial Rossby （ER） wave. These Ocean, but are of planetary scale with zonal wavenumbers 1-2, and propagate all the way around the equator in more than three years, leading to the longer than 3-year period of ENSO. When passing the continents, they become uncoupled atmospheric waves. The coupled Kelvin wave has larger variance than the coupled ER wave, making the total signals dominated by eastward propagation. Surface zonal wind stress （x） acts to slow down the waves. The two coupled waves interact with each other through boundary reflection and superposition, and they also interact with an off-equatorial Rossby wave in north Pacific along 15N through boundary reflection and wind stress forcing. The precipitation anomalies of the two coupled waves meet in the eastern Pacific shortly after the SST maximum of ENSO and excite a dry atmospheric Kelvin wave which quickly circles the whole equator and leads to a zonally symmetric signal of troposphere temperature. ENSO signals in the Indian and Atlantic oceans are associated with the two coupled waves as well as the fast atmospheric Kelvin wave. The discharge/recharge of Pacific-basin-averaged ocean heat content is also contributed by the two coupled waves. The above results suggest the presence of an alternative coupled wave oscillator mechanism for the oscillatory nature of ENSO.

Dynamical effect of the zonal wind anomalies over the tropical western Pacific on ENSO cycles

The circulation and zonal wind anomalies in the lower troposphere over the equatorial western Pacific and their roles in the developing and decaying processes of the 1982–1983, 1986 –1987, 1991–1992 and 1997–1998 El Ni?o events and the occurrence of La Ni?a events are analyzed by using the observed data in this paper. The results show that before the developing stage of these El Ni?o events, there were cyclonic circulation anomalies in the lower troposphere over the tropical western Pacific, and the anomalies brought the westerly anomalies over the Indonesia and the tropical western Pacific. However, when the El Ni?o events developed to their mature phase, there were anticyclonic circulation anomalies in the lower troposphere over the tropical western Pacific, and the anomalies made the easterly anomalies appear over the tropical western Pacific. A simple, dynamical model of tropical ocean is used to calculate the response of the equatorial oceanic waves to the observed anomalies of wind stress near the sea surface of the equatorial Pacific during the 1997/98 ENSO cycle, which was the strongest one in the 20th century. It is shown that the zonal wind stress anomalies have an important dynamical effect on the devel-opment and decay of this El Ni?o event and the occurrence of the following La Ni?a event.

Multi-scale variability of the tropical Indian Ocean circulation system revealed by recent observations

The tropical Indian Ocean circulation system includes the equatorial and near-equatorial circulations, the marginal sea circulation, and eddies. The dynamic processes of these circulation systems show significant multi-scale variability associated with the Indian Monsoon and the Indian Ocean dipole. This paper summarizes the research progress over recent years on the tropical Indian Ocean circulation system based on the large-scale hydrological observations and numerical simulations by the South China Sea Institute of Oceanology(SCSIO), Chinese Academy of Sciences. Results show that:(1) the wind-driven Kelvin and Rossby waves and eastern boundary-reflected Rossby waves regulate the formation and evolution of the Equatorial Undercurrent and the Equatorial Intermediate Current;(2) the equatorial wind-driven dynamics are the main factor controlling the inter-annual variability of the thermocline in the eastern Indian Ocean upwelling;(3) the equatorial waves transport large amounts of energy into the Bay of Bengal in forms of coastal Kelvin and reflected free Rossby waves. Several unresolved issues within the tropical Indian Ocean are discussed:(i) the potential effects of the momentum balance and the basin resonance on the variability of the equatorial circulation system, and(ii) the potential contribution of wind-driven dynamics to the life cycle of the eastern Indian Ocean upwelling. This paper also briefly introduces the international Indian Ocean investigation project of the SCSIO, which will advance the study of the multi-scale variability of the tropical Indian Ocean circulation system, and provide a theoretical and data basis to support marine environmental security for the countries around the Maritime Silk Road.