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Hidenori Aiki
,
Yoshiki Fukutomi
,
Yuki Kanno
,
Tomomichi Ogata
,
Takahiro Toyoda
, and
Hideyuki Nakano

Abstract

A model diagnosis for the energy flux of off-equatorial Rossby waves in the atmosphere has previously been done using quasigeostrophic equations and is singular at the equator. The energy flux of equatorial waves has been separately investigated in previous studies using a space–time spectral analysis or a ray theory. A recent analytical study has derived an exact universal expression for the energy flux, which can indicate the direction of the group velocity for linear shallow water waves at all latitudes. This analytical result is extended in the present study to a height-dependent framework for three-dimensional waves in the atmosphere. This is achieved by investigating the classical analytical solution of both equatorial and off-equatorial waves in a Boussinesq fluid. For the horizontal component of the energy flux, the same expression has been obtained between equatorial waves and off-equatorial waves in the height-dependent framework, which is linked to a scalar quantity inverted from the isentropic perturbation of Ertel’s potential vorticity. The expression of the vertical component of the energy flux requires computation of another scalar quantity that may be obtained from the meridional integral of geopotential anomaly in a wavenumber–frequency space. The exact version of the universal expression is explored and illustrated for three-dimensional waves induced by an idealized Madden–Julian oscillation forcing in a basic model experiment. The zonal and vertical fluxes manifest the energy transfer of both equatorial Kelvin waves and off-equatorial Rossby waves with a smooth transition at around 10°S and around 10°N. The meridional flux of wave energy represents connection between off-equatorial divergence regions and equatorial convergence regions.

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Takahiro Toyoda
,
Hideyuki Nakano
,
Hidenori Aiki
,
Tomomichi Ogata
,
Yoshiki Fukutomi
,
Yuki Kanno
,
L. Shogo Urakawa
,
Kei Sakamoto
,
Goro Yamanaka
, and
Motoki Nagura

Abstract

A method is introduced for diagnosing the time evolution of wave energy associated with ENSO from an ocean reanalysis. In the diagnosis, time changes of kinetic and available potential energy are mainly represented by energy inputs caused by surface wind stress and horizontal energy fluxes for each vertically decomposed normal mode. The resulting time evolutions of the wave energy and vertical thermocline displacements in the 1997/98 and 2014–16 El Niño events are consistent with our previous knowledge of these events. Further, our result indicated that representation of several vertical modes is necessary to reproduce the broadly distributed downward thermocline displacements in the central to eastern equatorial Pacific, generated by a westerly wind event in the western equatorial Pacific (e.g., in March 1997), that are preconditioning for El Niño development. In addition, we investigated the wave energy budget, including the influence of data assimilation, on the complicated time evolution of equatorial thermocline displacements caused by repeated westerly and easterly wind events during the 2014–16 El Niño event. Our result suggests that noise from a momentum imbalance near the equator associated with data assimilation, which possibly affected the El Niño prediction failure in 2014, was much reduced by our developed ocean data assimilation system and reanalysis. This study, which provides a new connection between the theoretical works and reanalysis products that use sophisticated systems for synthesizing OGCMs and observations, should be useful for climate research and operational communities interested in ENSO.

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