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1
Grise, Kevin M., and David W. J. Thompson. "Equatorial Planetary Waves and Their Signature in Atmospheric Variability." Journal of the Atmospheric Sciences 69, no. 3 (March 1, 2012): 857–74. http://dx.doi.org/10.1175/jas-d-11-0123.1.
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Abstract Equatorial planetary waves are a fundamental component of the tropical climate system. Previous studies have examined their structure in the climatological-mean circulation, their role in the climatological-mean momentum balance of the tropics, and their contribution to the climatological-mean upwelling across the tropical tropopause. In this study, the authors focus on the contribution of the equatorial planetary waves to variability in the tropical circulation about its climatological-mean state. The equatorial planetary waves that dominate the climatological mean exhibit considerable variability on intraseasonal and interannual time scales. Variability in the amplitude of the equatorial planetary waves is associated with a distinct pattern of equatorially symmetric climate variability that also emerges from empirical orthogonal function analysis of various tropical dynamical fields. Variability in the equatorial planetary waves is characterized by variations in 1) convection in the deep tropics, 2) eddy momentum flux convergence and zonal-mean zonal wind in the tropical upper troposphere, 3) the mean meridional circulation of the tropical and subtropical troposphere, 4) temperatures in the tropical lower stratosphere and subtropical troposphere of both hemispheres, and 5) the amplitude of the upper tropospheric anticyclones over the western tropical Pacific Ocean. It is argued that pulsation of the equatorial planetary waves provides an alternative framework for interpreting the response of the tropical circulation to a range of climate phenomena. Pulsation of the equatorial planetary waves is apparent in association with opposing phases of El Niño–Southern Oscillation and select phases of the Madden–Julian oscillation. Pulsation of the equatorial planetary waves also contributes to variability in measures of the width of the tropical belt.
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Zhang, K. "On equatorially trapped boundary inertial waves." Journal of Fluid Mechanics 248 (March 1993): 203–17. http://dx.doi.org/10.1017/s0022112093000746.
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Solutions of the Poincaré equation describing equatorially trapped three-dimensional boundary travelling waves in rotating spherical systems are discussed. It is shown that the combined effects of Coriolis forces and spherical curvature enable the equatorial region to form an equatorial waveguide tube with characteristic latitudinal radius (2/m)1/2 and radial radius (1/m), where m is azimuthal wavenumber. Inertial waves with sufficiently simple structure along the axis of rotation and sufficiently small azimuthal wavelength must be trapped in the equatorial waveguide tube. The structure and frequency of the inertial waves are thus hardly affected by the presence of an inner sphere or by the condition of higher latitudes. Further calculations on rotating spherical fluid shells of finite internal viscosity and stressfree boundaries are also discussed.
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Durland, Theodore S., Roger M. Samelson, Dudley B. Chelton, and Roland A. de Szoeke. "Modification of Long Equatorial Rossby Wave Phase Speeds by Zonal Currents." Journal of Physical Oceanography 41, no. 6 (June 1, 2011): 1077–101. http://dx.doi.org/10.1175/2011jpo4503.1.
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Abstract Previously unaddressed aspects of how equatorial currents affect long Rossby wave phase speeds are investigated using solutions of the shallow-water equations linearized about quasi-realistic currents. Modification of the background potential vorticity (PV) gradient by curvature in the narrow equatorial currents is shown to play a role comparable to the Doppler shift emphasized by previous authors. The important variables are the meridional projections of mean-current features onto relevant aspects of the wave field. As previously shown, Doppler shifting of long Rossby waves is determined by the projection of the mean currents onto the wave’s squared zonal-velocity and pressure fields. PV-gradient modification matters only to the extent that it projects onto the wave field’s squared meridional velocity. Because the zeros of an equatorial wave’s meridional velocity are staggered relative to those of the zonal velocity and pressure, and because the meridional scales of the equatorial currents are similar to those of the low-mode Rossby waves, different parts of the current system dominate the advective and PV-gradient modification effects on a single mode. Since the equatorial symmetry of classical equatorial waves alternates between symmetric and antisymmetric with increasing meridional mode number, the currents produce opposite effects on adjacent modes. Meridional mode 1 is slowed primarily by a combination of eastward advection by the Equatorial Undercurrent (EUC) and the PV-gradient decrease at the peaks of the South Equatorial Current (SEC). The mode-2 phase speed, in contrast, is increased primarily by a combination of westward advection by the SEC and the PV-gradient increase at the core of the EUC. Perturbation solutions are carried to second order in ε, the Rossby number of the mean current, and it is shown that this is necessary to capture the full effect of quasi-realistic current systems, which are asymmetric about the equator. Equatorially symmetric components of the current system affect the phase speed at O(ε), but antisymmetric components of the currents and distortions of the wave structures by the currents do not influence the phase speed until O(ε2).
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McGregor, Shayne, Neil J. Holbrook, and Scott B. Power. "Interdecadal Sea Surface Temperature Variability in the Equatorial Pacific Ocean. Part II: The Role of Equatorial/Off-Equatorial Wind Stresses in a Hybrid Coupled Model." Journal of Climate 21, no. 17 (September 1, 2008): 4242–56. http://dx.doi.org/10.1175/2008jcli2057.1.
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Abstract Many modeling studies have been carried out to investigate the role of oceanic Rossby waves linking the off-equatorial and equatorial Pacific Ocean. Although the equatorial ocean response to off-equatorial wind stress forcing alone tends to be relatively small, it is clear that off-equatorial oceanic Rossby waves affect equatorial Pacific Ocean variability on interannual through to interdecadal time scales. In the present study, a hybrid coupled model (HCM) of the equatorial Pacific (between 12.5°S and 12.5°N) was developed and is used to estimate the magnitude of equatorial region variability arising from off-equatorial (poleward of 12.5° latitude) wind stress forcing. The HCM utilizes a reduced-gravity ocean shallow-water model and a statistical atmosphere derived from monthly output from a 100-yr Australian Bureau of Meteorology Research Centre (now the Centre for Australian Weather and Climate Research) coupled general circulation model integration. The equatorial region wind stress forcing is found to dominate both the interannual and interdecadal SST variability. The equatorial response to off-equatorial wind stress forcing alone is insufficient to initiate an atmospheric feedback that significantly amplifies the original equatorial region variability. Consequently, the predictability of equatorial region SST anomalies (SSTAs) could be limited to ∼1 yr (the maximum time it takes an oceanic Rossby wave to cross the Pacific Ocean basin in the equatorial region). However, the results also suggest that the addition of off-equatorial wind stress forcing to the HCM leads to variations in equatorial Pacific background SSTA of up to almost one standard deviation. This off-equatorially forced portion of the equatorial SSTA could prove critical for thresholds of El Niño–Southern Oscillation (ENSO) because they can constructively interfere with equatorially forced SSTA of the same sign to produce significant equatorial region ENSO anomalies.
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Kinoshita, Takenari, and Kaoru Sato. "A Formulation of Three-Dimensional Residual Mean Flow and Wave Activity Flux Applicable to Equatorial Waves." Journal of the Atmospheric Sciences 71, no. 9 (August 28, 2014): 3427–38. http://dx.doi.org/10.1175/jas-d-13-0161.1.
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Abstract The large-scale waves that are known to be trapped around the equator are called equatorial waves. The equatorial waves cause mean zonal wind acceleration related to quasi-biennial and semiannual oscillations. The interaction between equatorial waves and the mean wind has been studied by using the transformed Eulerian mean (TEM) equations in the meridional cross section. However, to examine the three-dimensional (3D) structure of the interaction, the 3D residual mean flow and wave activity flux for the equatorial waves are needed. The 3D residual mean flow is expressed as the sum of the Eulerian mean flow and Stokes drift. The present study derives a formula that is approximately equal to the 3D Stokes drift for equatorial waves on the equatorial beta plane (EQSD). The 3D wave activity flux for equatorial waves whose divergence corresponds to the wave forcing is also derived using the EQSD. It is shown that the meridionally integrated 3D wave activity flux for equatorial waves is proportional to the group velocity of equatorial waves.
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Jouanno, Julien, Frédéric Marin, Yves du Penhoat, and Jean-Marc Molines. "Intraseasonal Modulation of the Surface Cooling in the Gulf of Guinea." Journal of Physical Oceanography 43, no. 2 (February 1, 2013): 382–401. http://dx.doi.org/10.1175/jpo-d-12-053.1.
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Abstract A regional numerical model of the tropical Atlantic Ocean and observations are analyzed to investigate the intraseasonal fluctuations of the sea surface temperature at the equator in the Gulf of Guinea. Results indicate that the seasonal cooling in this region is significantly shaped by short-duration cooling events caused by wind-forced equatorial waves: mixed Rossby–gravity waves within the 12–20-day period band, inertia–gravity waves with periods below 11 days, and equatorially trapped Kelvin waves with periods between 25 and 40 days. In these different ranges of frequencies, it is shown that the wave-induced horizontal oscillations of the northern front of the mean cold tongue dominate the variations of mixed layer temperature near the equator. But the model mixed layer heat budget also shows that the equatorial waves make a significant contribution to the mixed layer heat budget through modulation of the turbulent cooling, especially above the core of the Equatorial Undercurrent (EUC). The turbulent cooling variability is found to be mainly controlled by the intraseasonal modulation of the vertical shear in the upper ocean. This mechanism is maximum during periods of seasonal cooling, especially in boreal summer, when the surface South Equatorial Current is strongest and between 2°S and the equator, where the presence of the EUC provides a background vertical shear in the upper ocean. It applies for the three types of intraseasonal waves. Inertia–gravity waves also modulate the turbulent heat flux at the equator through vertical displacement of the core of the EUC in response to equatorial divergence and convergence.
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Back, Amanda, and Joseph A. Biello. "Effect of Overturning Circulation on Long Equatorial Waves: A Low-Frequency Cutoff." Journal of the Atmospheric Sciences 75, no. 5 (May 2018): 1721–39. http://dx.doi.org/10.1175/jas-d-17-0173.1.
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Zonally long tropical waves in the presence of a large-scale meridional and vertical overturning circulation are studied in an idealized model based on the intraseasonal multiscale moist dynamics (IMMD) theory. The model consists of a system of shallow-water equations describing barotropic and first baroclinic vertical modes coupled to one another by the zonally symmetric, time-independent background circulation. To isolate the effects of the meridional circulation alone, an idealized background flow is chosen to mimic the meridional and vertical components of the flow of the Hadley cell; the background flow meridionally converges and rises at the equator. The resulting linear eigenvalue problem is a generalization of the long-wave-scaled version of Matsuno’s equatorial wave problem with the addition of meridional and vertical advection. The results demonstrate that the meridional circulation couples equatorially trapped baroclinic Rossby waves to planetary, barotropic free Rossby waves. The meridional circulation also causes the Kelvin wave to develop an equatorially trapped barotropic component, imparting a westward-tilted vertical structure to the wave. The total energy of the linear system is positive definite, so all waves are shown to be neutrally stable. A critical layer exists at latitudes where the meridional background flow vanishes, resulting in a minimum frequency cutoff for physically feasible waves. Therefore, linear Matsuno waves with periods longer than the vertical transport time of the meridional circulation do not exist in the equatorial waveguide. This implies a low-frequency cutoff for long equatorial waves.
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CHAO, Winston C. "Chimeric Equatorial Waves as a Better Descriptor for “Convectively-Coupled Equatorial Waves”." Journal of the Meteorological Society of Japan 85, no. 4 (2007): 521–24. http://dx.doi.org/10.2151/jmsj.85.521.
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Zhou, Cheng, and John P. Boyd. "Cross-equatorial structures of equatorially trapped nonlinear Rossby waves." Dynamics of Atmospheres and Oceans 64 (November 2013): 53–61. http://dx.doi.org/10.1016/j.dynatmoce.2013.08.001.
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Grise, Kevin M., and David W. J. Thompson. "On the Signatures of Equatorial and Extratropical Wave Forcing in Tropical Tropopause Layer Temperatures." Journal of the Atmospheric Sciences 70, no. 4 (April 1, 2013): 1084–102. http://dx.doi.org/10.1175/jas-d-12-0163.1.
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Abstract Temperatures in the tropical tropopause layer (TTL) play an important role in stratosphere–troposphere exchange and in the formation and maintenance of thin cirrus clouds. Many previous studies have examined the contributions of extratropical and equatorial waves to the TTL using coarse-vertical-resolution satellite and reanalysis data. In this study, the authors provide new insight into the role of extratropical and equatorial waves in the TTL using high-vertical-resolution GPS radio occultation data. The results examine the influence of four different wave forcings on the TTL: extratropical waves that propagate vertically into the stratosphere, extratropical waves that propagate meridionally into the subtropical stratosphere, extratropical waves that propagate meridionally into the subtropical troposphere, and the equatorial planetary waves. The vertically and meridionally propagating extratropical stratospheric waves are associated with deep, zonally symmetric temperature anomalies that extend and amplify with height throughout the lower-to-middle tropical stratosphere. In contrast, the extratropical tropospheric waves and the equatorial planetary waves are associated with tropical temperature anomalies that are confined below 20-km altitude. The equatorial planetary waves dominate the zonally asymmetric component of the TTL temperature field, and both the equatorial planetary waves and the extratropical tropospheric waves are linked to large temperature variability in a 1–2-km-deep layer near the tropical tropopause. The fine vertical scale of the TTL temperature features associated with the equatorial planetary waves and the extratropical tropospheric waves is only readily apparent in high-vertical-resolution data.
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Okello, Ochieng, Guirong Tan, Victor Ongoma, and Isaiah Nyandega. "Influence of convectively coupled equatorial Kelvin waves on March-May precipitation over East Africa." Geographica Pannonica 25, no. 1 (2021): 24–34. http://dx.doi.org/10.5937/gp25-31132.
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Convectively coupled equatorial Kelvin waves (CCEKWs) are those types of equatorially trapped disturbances that propagate eastward and are among the most common intra-seasonal oscillations in the tropics. There exists two-way feedback between the inter-tropical convergence zone (ITCZ) and these equatorially trapped disturbances. Outgoing Longwave Radiation (OLR) was utilized as a proxy for deep convection. For CCEKWs, the modes are located over the West Atlantic, equatorial West Africa, and the Indian Ocean. The influence of other circulations and climate dynamics is studied for finding other drivers of climate within East Africa. The results show a positive relationship between Indian and Atlantic Oceans Sea Surface Temperatures and March-May rainfall over equatorial East Africa over the period of 1980 to 2010. This influence is driven by the Walker circulation and anomalous moisture influx enhanced by winds. Composite analysis reveals strong lower-tropospheric westerlies during the active phase of the CCKWs activities over Equatorial East Africa. The winds are in the opposite direction with the upper-tropospheric winds, which are easterlies. Singular Value Decomposition shows a strong coupling interaction between rainfall over equatorial East Africa and CCKWs. This study concludes that Kelvin waves are not the main factors that influence rainfall during the rainy season. Previous studies show that the main influencing factors are ITCZ, El-Nino Southern Oscillation (ENSO), and tropical anticyclones that borders the African continent. However, CCKWs are a significant factor during the dry seasons.
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Lewis, Neil T., Nicholas A. Lombardo, Peter L. Read, and Juan M. Lora. "Equatorial Waves and Superrotation in the Stratosphere of a Titan General Circulation Model." Planetary Science Journal 4, no. 8 (August 1, 2023): 149. http://dx.doi.org/10.3847/psj/ace76f.
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Abstract We investigate the characteristics of equatorial waves associated with the maintenance of superrotation in the stratosphere of a Titan general circulation model. A variety of equatorial waves are present in the model atmosphere, including equatorial Kelvin waves, equatorial Rossby waves, and mixed Rossby–gravity waves. In the upper stratosphere, acceleration of superrotation is strongest around solstice and is due to interaction between equatorial Kelvin waves and Rossby-type waves in winter hemisphere midlatitudes. The existence of this “Rossby–Kelvin”-type wave appears to depend on strong meridional shear of the background zonal wind that occurs in the upper stratosphere at times away from the equinoxes. In the lower stratosphere, acceleration of superrotation occurs throughout the year and is partially induced by equatorial Rossby waves, which we speculate are generated by quasigeostrophic barotropic instability. Acceleration of superrotation is generally due to waves with phase speeds close to the zonal velocity of the mean flow. Consequently, they have short vertical wavelengths that are close to the model’s vertical grid scale and therefore likely to be not properly represented. We suggest that this may be a common issue among Titan general circulation models that should be addressed by future model development.
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Yang, Gui-Ying, Julia Slingo, and Brian Hoskins. "Convectively Coupled Equatorial Waves in High-Resolution Hadley Centre Climate Models." Journal of Climate 22, no. 8 (April 15, 2009): 1897–919. http://dx.doi.org/10.1175/2008jcli2630.1.
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Abstract A methodology for diagnosing convectively coupled equatorial waves is applied to output from two high-resolution versions of atmospheric models, the Hadley Centre Atmospheric Model, version 3 (HadAM3), and the new Hadley Centre Global Atmospheric Model, version 1 (HadGAM1), which have fundamental differences in dynamical formulation. Variability, horizontal and vertical structures, and propagation characteristics of tropical convection and equatorial waves, along with their coupled behavior in the models, are examined and evaluated against a previous comprehensive study of observed convectively coupled equatorial waves using the 15-yr ECMWF Re-Analysis (ERA-15) and satellite observed data. The extent to which the models are able to represent the coupled waves found in real atmospheric observations is investigated. It is shown that, in general, the models perform well for equatorial waves coupled with off-equatorial convection. However, they perform poorly for waves coupled with equatorial convection. Convection in both models contains much-reduced variance in equatorial regions, but reasonable off-equatorial variance. The models fail to simulate coupling of the waves with equatorial convection and the tendency for equatorial convection to appear in the region of wave-enhanced near-surface westerlies. In addition, the simulated Kelvin wave and its associated convection generally tend to have lower frequency and slower phase speed than that observed. The models are also not able to capture the observed vertical tilt structure and signatures of energy conversion in the Kelvin wave, particularly in HadAM3. On the other hand, models perform better in simulating westward-moving waves coupled with off-equatorial convection, in terms of horizontal and vertical structures, zonal propagation, and energy conversion signals. In most cases both models fail to simulate well a key picture emerging from the observations, that some wave modes in the lower troposphere can act as a forcing agent for equatorial convection, and that the upper-tropospheric waves generally appear to be forced by the convection both on and off the equator.
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Aiyyer, Anantha, Ademe Mekonnen, and Carl J. Schreck. "Projection of Tropical Cyclones on Wavenumber–Frequency-Filtered Equatorial Waves." Journal of Climate 25, no. 10 (May 14, 2012): 3653–58. http://dx.doi.org/10.1175/jcli-d-11-00451.1.
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Abstract The impact of localized convection associated with tropical cyclones (TCs) on activity ascribed to equatorial waves is estimated. An algorithm is used to remove outgoing longwave radiation (OLR) signal in the vicinity of observed tropical cyclones, and equatorial wave modes are extracted using the standard wavenumber–frequency decomposition method. The results suggest that climatological activity of convection-coupled equatorial waves is overestimated where TC tracks are densest. The greatest impact is found for equatorial Rossby (ER)- and tropical depression (TD)-type waves followed by the Madden–Julian oscillation (MJO). The basins most affected are the eastern and western North Pacific Ocean where, on average, TCs may contribute up to 10%–15% of the climatological wave amplitude variance in these modes. In contrast, Kelvin waves are least impacted by the projection of TCs. The results are likely relevant for studies on the climatology of equatorial waves in observations and global climate model simulations and for those examining individual cases of TC genesis modulated by equatorial wave activity.
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Delplace, Pierre, J. B. Marston, and Antoine Venaille. "Topological origin of equatorial waves." Science 358, no. 6366 (October 5, 2017): 1075–77. http://dx.doi.org/10.1126/science.aan8819.
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Brossier, Fran�oise. "Mathematical modelization of equatorial waves." Acta Applicandae Mathematicae 5, no. 1 (January 1986): 37–85. http://dx.doi.org/10.1007/bf00049169.
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Dima, Ioana M., and John M. Wallace. "Structure of the Annual-Mean Equatorial Planetary Waves in the ERA-40 Reanalyses." Journal of the Atmospheric Sciences 64, no. 8 (August 2007): 2862–80. http://dx.doi.org/10.1175/jas3985.1.
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The three-dimensional structure of the annual-mean equatorial planetary waves in the 40-yr ECMWF Re-Analysis (ERA-40) is documented. The features in the free atmosphere are predominantly equatorially symmetric, driven by east–west heating gradients. The geopotential height and wind perturbations are strongest at or just below the 150-hPa level. Below the level of maximum amplitude, the circulations in the waves are thermally direct with latent heat release in deep convective clouds and radiative cooling in the intervening cloud-free regions. Within the overlying capping layer, the wave-related circulations are thermally indirect, with rising of the coldest air and sinking of air that is less cold. At the cold point, just above the 100-hPa (17 km) level, the ERA-40 annual-mean vertical velocity in the equatorial belt ranges up to 3 mm s−1 over the equatorial western Pacific during the boreal winter, implying diabatic heating rates of up to 3°C day−1, an order of magnitude larger than typical clear-sky values. Strong heating is consistent with evidence of widespread thin and subvisible cirrus cloud layers over this region. It is hypothesized that the air mass as a whole is rising (as opposed to just the air in the updrafts of convective clouds) and that this plume of ascending air spreads out horizontally at or just above the cold point, ventilating and lifting the entire lower stratosphere. El Niño years are characterized by anomalously weak equatorial planetary waves in the Indo-Pacific sector and slightly enhanced waves over the Atlantic sector and cold years of the El Niño–Southern Oscillation (ENSO) cycle by the opposite conditions. Equatorial Pacific sea surface temperature is as well correlated with the strength of the equatorial planetary waves in the upper troposphere over the Indo-Pacific sector as it is with the conventional Southern Oscillation index based on sea level pressure.
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Ryu, Jung-Hee, M. Joan Alexander, and David A. Ortland. "Equatorial Waves in the Upper Troposphere and Lower Stratosphere Forced by Latent Heating Estimated from TRMM Rain Rates." Journal of the Atmospheric Sciences 68, no. 10 (October 1, 2011): 2321–42. http://dx.doi.org/10.1175/2011jas3647.1.
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Abstract Equatorial atmospheric waves in the upper troposphere and lower stratosphere (UTLS), excited by latent heating, are investigated by using a global spectral model. The latent heating profiles are derived from the 3-hourly Tropical Rainfall Measuring Mission (TRMM) rain rates, which include both convective- and stratiform-type profiles. The type of heating profile is determined based on an intensity of the surface rain rate. Latent heating profiles over stratiform rain regions, estimated from the TRMM Precipitation Radar (PR) product, are applied to derive the stratiform-type latent heating profiles from the gridded rain rate data. Monthly zonal-mean latent heating profiles derived from the rain rates appear to be reasonably comparable with the TRMM convective/stratiform heating product. A broad spectrum of Kelvin, mixed Rossby–gravity (MRG), equatorial Rossby (ER), and inertia–gravity waves are generated in the model. Particularly, equatorial waves (Kelvin, ER, and MRG waves) of zonal wavenumbers 1–5 appear to be dominant in the UTLS. In the wavenumber–frequency domain, the equatorial waves have prominent spectral peaks in the range of 12–200 m of the equivalent depth, while the spectral peaks of the equatorial waves having shallower equivalent depth (<50 m) increase in the case where stratiform-type heating is included. These results imply that the stratiform-type heating might be relevant for the shallower equivalent depth of the observed convectively coupled equatorial waves. The horizontal and vertical structures of the simulated equatorial waves (Kelvin, ER, and MRG waves) are in a good agreement with the equatorial wave theory and observed wave structure. In particular, comparisons of the simulated Kelvin waves and the High Resolution Dynamics Limb Sounder (HIRDLS) satellite observation are discussed.
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Yuan, Dongliang, and Weiqing Han. "Roles of Equatorial Waves and Western Boundary Reflection in the Seasonal Circulation of the Equatorial Indian Ocean." Journal of Physical Oceanography 36, no. 5 (May 1, 2006): 930–44. http://dx.doi.org/10.1175/jpo2905.1.
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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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Yang, Gui-Ying, Brian J. Hoskins, and Julia M. Slingo. "Equatorial Waves in Opposite QBO Phases." Journal of the Atmospheric Sciences 68, no. 4 (April 1, 2011): 839–62. http://dx.doi.org/10.1175/2010jas3514.1.
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Abstract A methodology for identifying equatorial waves is used to analyze the multilevel 40-yr ECMWF Re-Analysis (ERA-40) data for two different years (1992 and 1993) to investigate the behavior of the equatorial waves under opposite phases of the quasi-biennial oscillation (QBO). A comprehensive view of 3D structures and of zonal and vertical propagation of equatorial Kelvin, westward-moving mixed Rossby–gravity (WMRG), and n = 1 Rossby (R1) waves in different QBO phases is presented. Consistent with expectation based on theory, upward-propagating Kelvin waves occur more frequently during the easterly QBO phase than during the westerly QBO phase. However, the westward-moving WMRG and R1 waves show the opposite behavior. The presence of vertically propagating equatorial waves in the stratosphere also depends on the upper tropospheric winds and tropospheric forcing. Typical propagation parameters such as the zonal wavenumber, zonal phase speed, period, vertical wavelength, and vertical group velocity are found. In general, waves in the lower stratosphere have a smaller zonal wavenumber, shorter period, faster phase speed, and shorter vertical wavelength than those in the upper troposphere. All of the waves in the lower stratosphere show an upward group velocity and downward phase speed. When the phase of the QBO is not favorable for waves to propagate, their phase speed in the lower stratosphere is larger and their period is shorter than in the favorable phase, suggesting Doppler shifting by the ambient flow and a filtering of the slow waves. Tropospheric WMRG and R1 waves in the Western Hemisphere also show upward phase speed and downward group velocity, with an indication of their forcing from middle latitudes. Although the waves observed in the lower stratosphere are dominated by “free” waves, there is evidence of some connection with previous tropical convection in the favorable year for the Kelvin waves in the warm water hemisphere and WMRG and R1 waves in the Western Hemisphere, which is suggestive of the importance of convective forcing for the existence of propagating coupled Kelvin waves and midlatitude forcing for the existence of coupled WMRG and R1 waves.
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Dima, Ioana M., John M. Wallace, and Ian Kraucunas. "Tropical Zonal Momentum Balance in the NCEP Reanalyses." Journal of the Atmospheric Sciences 62, no. 7 (July 1, 2005): 2499–513. http://dx.doi.org/10.1175/jas3486.1.
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Abstract The seasonal cycle of the zonal-mean zonal momentum balance in the Tropics is investigated using NCEP reanalysis data. It is found that the climatological stationary waves in the tropical upper troposphere, which are dominated by the equatorial Rossby wave response to tropical heating, produce an equatorward eddy flux of westerly momentum in the equatorial belt. The resulting westerly acceleration in the tropical upper troposphere is balanced by the advection of easterly momentum associated with the cross-equatorial mean meridional circulation. The eddy momentum fluxes and the cross-equatorial flow both tend to be strongest during the monsoon seasons, when the maximum diabatic heating is off the equator, and weakest during April–May, the season of strongest equatorial symmetry of the heating. The upper-level Rossby wave pattern exhibits a surprising degree of equatorial symmetry and follows a similar seasonal progression. Solutions of the nonlinear shallow water wave equation also show a predominantly equatorially symmetric response to a heat source centered off the equator.
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Tang, T. Y., Y. J. Yang, and Miug-Chin Wu. "Effect of Equatorial Long Waves on the North Equatorial Countercurrent." Terrestrial, Atmospheric and Oceanic Sciences 3, no. 2 (1992): 199. http://dx.doi.org/10.3319/tao.1992.3.2.199(o).
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Boyd, John P. "Barotropic Equatorial Waves: The Nonuniformity of the Equatorial Beta-Plane." Journal of the Atmospheric Sciences 42, no. 18 (September 1985): 1965–67. http://dx.doi.org/10.1175/1520-0469(1985)042<1965:bewtno>2.0.co;2.
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Chen, Guanghua, and Chi-Yung Tam. "A New Perspective on the Excitation of Low-Tropospheric Mixed Rossby–Gravity Waves in Association with Energy Dispersion." Journal of the Atmospheric Sciences 69, no. 4 (March 30, 2012): 1397–403. http://dx.doi.org/10.1175/jas-d-11-0331.1.
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Abstract This study investigates the synoptic-scale equatorial response to Rossby wave energy dispersion associated with off-equatorial wave activity sources and proposes a new mechanism for triggering low-level mixed Rossby–gravity (MRG) waves. A case study based on observations in boreal summer 2002 reveals that a vortex related to tropical cyclogenesis generated a coherent wave train through southeastward energy dispersion. The southeastward-propagating energy packet gave rise to the equatorial atmospheric response with a temporal scale similar to the wave train and with a structure consistent with the equatorially trapped MRG wave. A baroclinic multilevel anomaly model is employed to verify the excitation of MRG associated with the energy dispersion originating outside of the equatorial region and to explore the discrepancy in the equatorial responses under the different background flows corresponding to El Niño and La Niña. The results show that the prevalence of the low-level westerly flow, the associated zonal wind convergence, and the easterly vertical wind shear can be more favorable for the enhancement of southeastward-propagating energy dispersion and equatorial MRG response in the low troposphere during El Niño than those during La Niña. In addition, the strength of the mean flow can strongly affect the extent of equatorial wave response and modulate its phase and group velocity due to the Doppler shift effect.
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Maury, P., and F. Lott. "On the presence of equatorial waves in the lower stratosphere of a general circulation model." Atmospheric Chemistry and Physics Discussions 13, no. 8 (August 30, 2013): 22607–37. http://dx.doi.org/10.5194/acpd-13-22607-2013.
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Abstract. To challenge the hypothesis that equatorial waves in the lower stratosphere are essentially forced by convection, we use the LMDz atmospheric model extended to the stratosphere and compare two versions having very different convection schemes but no quasi biennial oscillation (QBO). The two versions have realistic time mean precipitation climatologies but very different precipitation variabilities. Despite these differences, the equatorial stratospheric Kelvin waves at 50 hPa are almost identical in the two versions and quite realistic. The Rossby-gravity waves are also very close but significantly weaker than in observations. We demonstrate that this bias on the Rossby-gravity waves is essentially due to a dynamical filtering occurring because the model zonal wind is systematically westward: during a westward phase of the QBO, the Rossby-gravity waves in ERA-Interim compare well with those in the model. These results suggest that in the model the effect of the convection scheme on the waves is in part hidden by the dynamical filtering and the waves are produced by other sources than equatorial convection. For the Kelvin waves, this last point is illustrated by an Eliassen and Palm flux analysis, showing that in the model they come more from the subtropics and mid-latitude regions whereas in the ERA-Interim reanalysis the sources are more equatorial. We also show that non-equatorial sources are significant in reanalysis data, and we consider the case of the Rossby-gravity waves. We identify situations in the reanalysis where here are large Rossby-gravity waves in the middle stratosphere, and for dates when the stratosphere is dynamically separated from the equatorial troposphere. We refer to this process as a "stratospheric reloading".
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Rydbeck, Adam V., Tommy G. Jensen, and Matthew R. Igel. "Idealized Modeling of the Atmospheric Boundary Layer Response to SST Forcing in the Western Indian Ocean." Journal of the Atmospheric Sciences 76, no. 7 (June 26, 2019): 2023–42. http://dx.doi.org/10.1175/jas-d-18-0303.1.
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Abstract The atmospheric response to sea surface temperature (SST) variations forced by oceanic downwelling equatorial Rossby waves is investigated using an idealized convection-resolving model. Downwelling equatorial Rossby waves sharpen SST gradients in the western Indian Ocean. Changes in SST cause the atmosphere to hydrostatically adjust, subsequently modulating the low-level wind field. In an idealized cloud model, surface wind speeds, surface moisture fluxes, and low-level precipitable water maximize near regions of strongest SST gradients, not necessarily in regions of warmest SST. Simulations utilizing the steepened SST gradient representative of periods with oceanic downwelling equatorial Rossby waves show enhanced patterns of surface convergence and precipitation that are linked to a strengthened zonally overturning circulation. During these conditions, convection is highly organized, clustering near the maximum SST gradient and ascending branch of the SST-induced overturning circulation. When the SST gradient is reduced, as occurs during periods of weak or absent oceanic equatorial Rossby waves, convection is much less organized and total rainfall is decreased. This demonstrates the previously observed upscale organization of convection and rainfall associated with oceanic downwelling equatorial Rossby waves in the western Indian Ocean. These results suggest that the enhancement of surface fluxes that results from a steepening of the SST gradient is the leading mechanism by which oceanic equatorial Rossby waves prime the atmospheric boundary layer for rapid convective development.
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Holmes, R. M., and L. N. Thomas. "Modulation of Tropical Instability Wave Intensity by Equatorial Kelvin Waves." Journal of Physical Oceanography 46, no. 9 (September 2016): 2623–43. http://dx.doi.org/10.1175/jpo-d-16-0064.1.
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AbstractTropical instability waves (TIWs) and equatorial Kelvin waves are dominant sources of intraseasonal variability in the equatorial Pacific Ocean, and both play important roles in the heat and momentum budgets of the large-scale flow. While individually they have been well studied, little is known about how these two features interact, although satellite observations suggest that TIW propagation speed and amplitude are modulated by Kelvin waves. Here, the influence of Kelvin waves on TIW kinetic energy (TIWKE) is examined using an ensemble set of 1/4° ocean model simulations of the equatorial Pacific Ocean. The results suggest that TIWKE can be significantly modified by 60-day Kelvin waves. To leading order, TIWs derive kinetic energy from the meridional shear and available potential energy of the background zonal currents, while losing TIWKE to friction and the radiation of waves. The passage of Kelvin waves disrupts this balance. Downwelling (upwelling) Kelvin waves induce decay (growth) in TIWKE through modifications to the background currents and the TIWs’ Reynolds stresses. These modulations in TIWKE affect eddy heat fluxes and the downward radiation of waves, with implications for the variability of SST and the energetics of abyssal flows in the eastern equatorial Pacific.
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Yang, Gui-Ying, John Methven, Steve Woolnough, Kevin Hodges, and Brian Hoskins. "Linking African Easterly Wave Activity with Equatorial Waves and the Influence of Rossby Waves from the Southern Hemisphere." Journal of the Atmospheric Sciences 75, no. 6 (May 17, 2018): 1783–809. http://dx.doi.org/10.1175/jas-d-17-0184.1.
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Abstract A connection is found between African easterly waves (AEWs), equatorial westward-moving mixed Rossby–gravity (WMRG) waves, and equivalent barotropic Rossby waves (RWs) from the Southern Hemisphere (SH). The amplitude and phase of equatorial waves is calculated by projection of broadband-filtered ERA-Interim data onto a horizontal structure basis obtained from equatorial wave theory. Mechanisms enabling interaction between the wave types are identified. AEWs are dominated by a vorticity wave that tilts eastward below the African easterly jet and westward above: the tilt necessary for baroclinic wave growth. However, a strong relationship is identified between amplifying vorticity centers within AEWs and equatorial WMRG waves. Although the waves do not phase lock, positive vorticity centers amplify whenever the cross-equatorial motion of the WMRG wave lies at the same longitude in the upper troposphere (southward flow) and east of this in the lower troposphere (northward flow). Two mechanisms could explain the vorticity amplification: vortex stretching below the upper-tropospheric divergence and ascent associated with latent heating in convection in the lower-tropospheric moist northward flow. In years of strong AEW activity, SH and equatorial upper-tropospheric zonal winds are more easterly. Stronger easterlies have two effects: (i) they Doppler shift WMRG waves so that their period varies little with wavenumber (3–4 days) and (ii) they enable westward-moving RWs to propagate into the tropical waveguide from the SH. The RW phase speeds can match those of WMRG waves, enabling sustained excitation of WMRG. The WMRG waves have an eastward group velocity with wave activity accumulating over Africa and invigorating AEWs at similar frequencies through the vorticity amplification mechanism.
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Yang, Gui-Ying, Brian Hoskins, and Julia Slingo. "Convectively Coupled Equatorial Waves. Part I: Horizontal and Vertical Structures." Journal of the Atmospheric Sciences 64, no. 10 (October 1, 2007): 3406–23. http://dx.doi.org/10.1175/jas4017.1.
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Abstract Multilevel 15-yr ECMWF Re-Analysis (ERA-15) and satellite-observed brightness temperature (Tb) data for the period May–October 1992 are used to examine the horizontal and vertical structures of convectively coupled equatorial waves. Dynamical waves are isolated using a methodology developed previously. Composite structures of convectively coupled equatorial waves are obtained using linear regression/correlation between convection (Tb) and dynamical structures. It is found that the relationship depends on the ambient flow and the nature of the convective coupling, and varies between off-equatorial- and equatorial-centered convection, different hemispheres, and seasons. The Kelvin wave structure in the Western Hemisphere is generally consistent with classic equatorial wave theory and has its convection located in the region of low-level convergence. In the Eastern Hemisphere the Kelvin wave tends to have convection in the region of enhanced lower-tropospheric westerlies and a tilted vertical structure. The Kelvin wave also tends to have a third peak in zonal wind amplitude at 500 hPa and exhibits upward propagation into the lower stratosphere. Lower-tropospheric westward-moving mixed Rossby–gravity (WMRG) and n = 1 Rossby (R1) wave structures and their relationship with convection are consistent with classic equatorial wave theory and the implied lower-tropospheric convergences. In the Eastern Hemisphere the WMRG and R1 waves have first baroclinic mode structures in the vertical. However, in the Western Hemisphere, the R1 wave has a barotropic structure. In the Eastern Hemisphere the R1 wave, like the Kelvin wave, tends to have equatorial convection in the region of enhanced lower-level westerlies, suggesting that enhanced surface energy fluxes associated with these waves may play an important organizing role for equatorial convection in this warm-water hemisphere. In the upper troposphere, eastward-moving Rossby–gravity (EMRG) and n = 1 gravity waves are found in the Eastern Hemisphere, and eastward-moving WMRG and R1 waves are found in the Western Hemisphere, suggestive of Doppler shifting of waves by the ambient flow.
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Liu, Junjun, and Tapio Schneider. "Convective Generation of Equatorial Superrotation in Planetary Atmospheres." Journal of the Atmospheric Sciences 68, no. 11 (November 1, 2011): 2742–56. http://dx.doi.org/10.1175/jas-d-10-05013.1.
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Abstract In rapidly rotating planetary atmospheres that are heated from below, equatorial superrotation can occur through convective generation of equatorial Rossby waves. If the heating from below is sufficiently strong that convection penetrates into the upper troposphere, then the convection generates equatorial Rossby waves, which can induce the equatorward angular momentum transport necessary for superrotation. This paper investigates the conditions under which the convective generation of equatorial Rossby waves and their angular momentum transport lead to superrotation. It also addresses how the strength and width of superrotating equatorial jets are controlled. In simulations with an idealized general circulation model (GCM), the relative roles of baroclinicity, heating from below, and bottom drag are explored systematically. Equatorial superrotation generally occurs when the heating from below is sufficiently strong. However, the threshold heating at which the transition to superrotation occurs increases as the baroclinicity or the bottom drag increases. The greater the baroclinicity is, the stronger the angular momentum transport out of low latitudes by baroclinic eddies of extratropical origin. This competes with the angular momentum transport toward the equator by convectively generated Rossby waves and thus can inhibit a transition to superrotation. Equatorial bottom drag damps both the mean zonal flow and convectively generated Rossby waves, weakening the equatorward angular momentum transport as the drag increases; this can also inhibit a transition to superrotation. The strength of superrotating equatorial jets scales approximately with the square of their width. When they are sufficiently strong, their width, in turn, scales with the equatorial Rossby radius and thus depends on the thermal stratification of the equatorial atmosphere. The results have broad implications for planetary atmospheres, particularly for how superrotation can be generated in giant planet atmospheres and in terrestrial atmospheres in warm climates.
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Maury, P., and F. Lott. "On the presence of equatorial waves in the lower stratosphere of a general circulation model." Atmospheric Chemistry and Physics 14, no. 4 (February 18, 2014): 1869–80. http://dx.doi.org/10.5194/acp-14-1869-2014.
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Abstract. To challenge the hypothesis that equatorial waves in the lower stratosphere are essentially forced by convection, we use the LMDz atmospheric model extended to the stratosphere and compare two versions having very different convection schemes but no quasi-biennial oscillation (QBO). The two versions have realistic time mean precipitation climatologies but very different precipitation variabilities. Despite these differences, the equatorial stratospheric Kelvin waves at 50 hPa are almost identical in the two versions and quite realistic. The Rossby gravity waves are also very similar but significantly weaker than in observations. We demonstrate that this bias on the Rossby gravity waves is essentially due to a dynamical filtering occurring because the model zonal wind is systematically westward. During a westward phase of the QBO, the ERA-Interim Rossby gravity waves compare well with those in the model. These results suggest that (i) in the model the effect of the convection scheme on the waves is in part hidden by the dynamical filtering, and (ii) the waves are produced by other sources than equatorial convection. For the Kelvin waves, this last point is illustrated by an Eliassen and Palm flux analysis, showing that in the model they come more from the subtropics and mid-latitude regions, whereas in the ERA-Interim reanalysis the sources are more equatorial. We show that non-equatorial sources are also significant in reanalysis data sets as they explain the presence of the Rossby gravity waves in the stratosphere. To illustrate this point, we identify situations with large Rossby gravity waves in the reanalysis middle stratosphere for dates selected when the stratosphere is dynamically separated from the equatorial troposphere. We refer to this process as a stratospheric reloading.
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Schreck, Carl J., Lei Shi, James P. Kossin, and John J. Bates. "Identifying the MJO, Equatorial Waves, and Their Impacts Using 32 Years of HIRS Upper-Tropospheric Water Vapor." Journal of Climate 26, no. 4 (February 15, 2013): 1418–31. http://dx.doi.org/10.1175/jcli-d-12-00034.1.
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Abstract The Madden–Julian oscillation (MJO) and convectively coupled equatorial waves are the dominant modes of synoptic-to-subseasonal variability in the tropics. These systems have frequently been examined with proxies for convection such as outgoing longwave radiation (OLR). However, upper-tropospheric water vapor (UTWV) gives a more complete picture of tropical circulations because it is more sensitive to the drying and warming associated with subsidence. Previous studies examined tropical variability using relatively short (3–7 yr) UTWV datasets. Intersatellite calibration of data from the High Resolution Infrared Radiation Sounder (HIRS) has recently produced a homogeneous 32-yr climate data record of UTWV for 200–500 hPa. This study explores the utility of HIRS UTWV for identifying the MJO and equatorial waves. Spectral analysis shows that the MJO and equatorial waves stand out above the low-frequency background in UTWV, similar to previous findings with OLR. The fraction of variance associated with the MJO and equatorial Rossby waves is actually greater in UTWV than in OLR. Kelvin waves, on the other hand, are overshadowed in UTWV by horizontal advection from extratropical Rossby waves. For the MJO, UTWV identifies subsidence drying in the subtropics, poleward of the convection. These dry anomalies are associated with the MJO’s subtropical Rossby gyres. MJO events with dry anomalies over the central North Pacific Ocean also amplify the 200-hPa flow pattern over North America 7 days later. These events cannot be identified using equatorial OLR alone, which demonstrates that UTWV is a useful supplement for identifying the MJO, equatorial waves.
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van der Linden, Roderick, Andreas H. Fink, Joaquim G. Pinto, Tan Phan-Van, and George N. Kiladis. "Modulation of Daily Rainfall in Southern Vietnam by the Madden–Julian Oscillation and Convectively Coupled Equatorial Waves." Journal of Climate 29, no. 16 (July 28, 2016): 5801–20. http://dx.doi.org/10.1175/jcli-d-15-0911.1.
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Abstract Rainfall extremes have a large socioeconomic relevance for southern Vietnam. More than 30 million people live in this low-lying, flood-prone region in Southeast Asia. In this study the influence of the Madden–Julian oscillation (MJO) and convectively coupled equatorial waves on the modulation of daily rainfall during the rainy season (May–October) is evaluated and quantified using an extensive station database and the gridded Asian Precipitation–Highly Resolved Observational Data Integration Toward Evaluation of Water Resources (APHRODITE) product for different phases of the equatorial waves. The MJO, Kelvin, and equatorial Rossby (ER) waves significantly modulate daily rainfall in Vietnam south of 16°N. The MJO shows the most coherent signals across the region, followed by ER waves, whose influence is strongest in central Vietnam; Kelvin waves only affect the southern parts of Vietnam. For all waves, the frequency of occurrence of intense daily rainfall larger than 25 mm is significantly enhanced during wet phases, whereas the magnitude of rainfall anomalies is related to the wave’s amplitude only in the MJO and ER cases. A novel wave interference diagram reveals strong positive interferences of dry and wet anomalies when the MJO occurs concurrently with Kelvin and ER waves. In terms of causes of rainfall anomalies, the waves modulate tropospheric moisture convergence over the region, but a strong influence on the depth of the monsoon flow and the vertical wind shear is discernible from radiosonde data only for the MJO. The results suggest new opportunities for submonthly prediction of dry and wet spells in Indochina.
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Sousasantos, Jonas, José Humberto Andrade Sobral, Esfhan Alam Kherani, Marcelo Magalhães Fares Saba, and Diovane Rodolfo de Campos. "Relationship between ionospheric plasma bubble occurrence and lightning strikes over the Amazon region." Annales Geophysicae 36, no. 2 (March 9, 2018): 349–60. http://dx.doi.org/10.5194/angeo-36-349-2018.
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Abstract. The vertical coupling between the troposphere and the ionosphere presents some remarkable features. Under intense tropospheric convection, gravity waves may be generated, and once they reach the ionosphere, these waves may seed instabilities and spread F and equatorial plasma bubble events may take place. Additionally, there is a close association between severe tropospheric convection and lightning strikes. In this work an investigation covering an equinox period (September–October) during the deep solar minimum (2009) presents the relation between lightning strike activity and spread F (equatorial plasma bubble) detected over a low-latitude Brazilian region. The results show a considerable correlation between these two phenomena. The common element in the center of this conformity seems to be the gravity waves. Once gravity waves and lightning strikes share the same source (intense tropospheric convection) and the effects of such gravity waves in the ionosphere include the seeding of instabilities according to the gravity waves magnitude, the monitoring of the lightning strike activity seems to offer some information about the subsequent development of spread F over the equatorial region. Keywords. Ionosphere (equatorial ionosphere)
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Abrashkin, Anatoly. "Wind generated equatorial Gerstner-type waves." Discrete & Continuous Dynamical Systems - A 39, no. 8 (2019): 4443–53. http://dx.doi.org/10.3934/dcds.2019181.
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Haertel, Patrick T., and George N. Kiladis. "Dynamics of 2-Day Equatorial Waves." Journal of the Atmospheric Sciences 61, no. 22 (November 1, 2004): 2707–21. http://dx.doi.org/10.1175/jas3352.1.
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Abstract The dynamics of the 2-day wave, a type of convectively coupled disturbance that frequents the equatorial western Pacific, is examined using observations and a linear primitive equation model. A statistical composite of the wave's kinematic and thermodynamic structure is presented. It is shown that 1) the wave's wind and temperature perturbations can be modeled as linear responses to convective heating and cooling, and 2) the bulk of the wave's dynamical and convective structure can be represented with two vertical modes. The observations and model results suggest that the 2-day wave is an n = 1 westward-propagating inertio–gravity wave with a shallow equivalent depth (14 m) that results from the partial cancelation of adiabatic temperature changes due to vertical motion by convective heating and cooling.
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O'brien, James J., and Fred Parham. "Equatorial Kelvin Waves Do Not Vanish." Monthly Weather Review 120, no. 8 (August 1992): 1764–66. http://dx.doi.org/10.1175/1520-0493(1992)120<1764:ekwdnv>2.0.co;2.
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Constantin, A. "On the modelling of equatorial waves." Geophysical Research Letters 39, no. 5 (March 2012): n/a. http://dx.doi.org/10.1029/2012gl051169.
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Boardsen, S. A., D. L. Gallagher, D. A. Gurnett, W. K. Peterson, and J. L. Green. "Funnel-shaped, low-frequency equatorial waves." Journal of Geophysical Research 97, A10 (1992): 14967. http://dx.doi.org/10.1029/92ja00827.
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Raupp, Carlos F. M., and Pedro L. Silva Dias. "Dynamics of resonantly interacting equatorial waves." Tellus A: Dynamic Meteorology and Oceanography 58, no. 2 (January 2006): 263–79. http://dx.doi.org/10.1111/j.1600-0870.2006.00151.x.
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Katz, Eli Joel. "Equatorial Kelvin waves in the Atlantic." Journal of Geophysical Research 92, no. C2 (1987): 1894. http://dx.doi.org/10.1029/jc092ic02p01894.
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Medvedev, S. B., and V. Zeitlin. "Weak turbulence of short equatorial waves." Physics Letters A 342, no. 3 (July 2005): 217–27. http://dx.doi.org/10.1016/j.physleta.2005.05.046.
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Henry, David, and Hung-Chu Hsu. "Instability of internal equatorial water waves." Journal of Differential Equations 258, no. 4 (February 2015): 1015–24. http://dx.doi.org/10.1016/j.jde.2014.08.019.
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Li, Xiao fan, and Han-Ru Cho. "Development and propagation of equatorial waves." Advances in Atmospheric Sciences 14, no. 3 (September 1997): 323–38. http://dx.doi.org/10.1007/s00376-997-0053-6.
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Allison, Michael. "Planetary waves in Jupiter's equatorial atmosphere." Icarus 83, no. 2 (February 1990): 282–307. http://dx.doi.org/10.1016/0019-1035(90)90069-l.
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Hsu, Hung-Chu. "An exact solution for equatorial waves." Monatshefte für Mathematik 176, no. 1 (March 22, 2014): 143–52. http://dx.doi.org/10.1007/s00605-014-0618-2.
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Van Tuyl, Andrew H. "Nonlinearities in Low-Frequency Equatorial Waves." Journal of the Atmospheric Sciences 44, no. 17 (September 1987): 2478–92. http://dx.doi.org/10.1175/1520-0469(1987)044<2478:nilfew>2.0.co;2.
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McPhaden, M. J., and A. E. Gill. "Topographic Scattering of Equatorial Kelvin Waves." Journal of Physical Oceanography 17, no. 1 (January 1987): 82–96. http://dx.doi.org/10.1175/1520-0485(1987)017<0082:tsoekw>2.0.co;2.
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Chan, Ian H., and Theodore G. Shepherd. "Balance model for equatorial long waves." Journal of Fluid Mechanics 725 (May 14, 2013): 55–90. http://dx.doi.org/10.1017/jfm.2013.146.
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AbstractGeophysical fluid models often support both fast and slow motions. As the dynamics are often dominated by the slow motions, it is desirable to filter out the fast motions by constructing balance models. An example is the quasi-geostrophic (QG) model, which is used widely in meteorology and oceanography for theoretical studies, in addition to practical applications such as model initialization and data assimilation. Although the QG model works quite well in the mid-latitudes, its usefulness diminishes as one approaches the equator. Thus far, attempts to derive similar balance models for the tropics have not been entirely successful as the models generally filter out Kelvin waves, which contribute significantly to tropical low-frequency variability. There is much theoretical interest in the dynamics of planetary-scale Kelvin waves, especially for atmospheric and oceanic data assimilation where observations are generally only of the mass field and thus do not constrain the wind field without some kind of diagnostic balance relation. As a result, estimates of Kelvin wave amplitudes can be poor. Our goal is to find a balance model that includes Kelvin waves for planetary-scale motions. Using asymptotic methods, we derive a balance model for the weakly nonlinear equatorial shallow-water equations. Specifically we adopt the ‘slaving’ method proposed by Warn et al. (Q. J. R. Meteorol. Soc., vol. 121, 1995, pp. 723–739), which avoids secular terms in the expansion and thus can in principle be carried out to any order. Different from previous approaches, our expansion is based on a long-wave scaling and the slow dynamics is described using the height field instead of potential vorticity. The leading-order model is equivalent to the truncated long-wave model considered previously (e.g. Heckley & Gill, Q. J. R. Meteorol. Soc., vol. 110, 1984, pp. 203–217), which retains Kelvin waves in addition to equatorial Rossby waves. Our method allows for the derivation of higher-order models which significantly improve the representation of Rossby waves in the isotropic limit. In addition, the ‘slaving’ method is applicable even when the weakly nonlinear assumption is relaxed, and the resulting nonlinear model encompasses the weakly nonlinear model. We also demonstrate that the method can be applied to more realistic stratified models, such as the Boussinesq model.
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Schreck, Carl J. "Convectively Coupled Kelvin Waves and Tropical Cyclogenesis in a Semi-Lagrangian Framework." Monthly Weather Review 144, no. 11 (October 5, 2016): 4131–39. http://dx.doi.org/10.1175/mwr-d-16-0237.1.
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Abstract This study examines how convectively coupled Kelvin waves interact with the semi-Lagrangian circulation of easterly waves to modulate tropical cyclogenesis. Recent studies have shown that fewer tropical cyclones form in the three days before passage of the Kelvin wave’s peak convection and more develop in the three days thereafter. Separately, other studies have identified the recirculation of moisture and vorticity within easterly waves using a semi-Lagrangian frame of reference. That framework is achieved by subtracting the easterly wave phase speed from the earth-relative winds. This study combines these recent findings by testing whether the equatorial westerlies from Kelvin waves can help close the semi-Lagrangian circulation. Past studies have shown that Kelvin waves tilt westward with height in the troposphere such that equatorial westerlies build upward from the surface in the days following the convective peak. This study shows that the easterly wave’s semi-Lagrangian closed circulation grows upward as it intersects the Kelvin wave’s westward tilt. The Kelvin wave’s westerly anomalies reach 500 hPa about three days after the convection has passed, which establishes the deep, vertically aligned easterly wave vortex necessary for tropical cyclogenesis. This study focuses on the eastern Pacific, but similar results are found for the North Atlantic. In other basins, the Kelvin wave accentuates the westerlies from the Madden–Julian oscillation and/or the monsoon trough. Given that Kelvin waves often last weeks and circumnavigate the globe, these results may advance long-range tropical cyclogenesis forecasting.