Long Wave Resonance in Tropical Oceans and Implications on Climate: the Atlantic Ocean
Based on the well established importance of long, non-dispersive baroclinic Kelvin and Rossby waves, a resonance of tropical planetary waves is demonstrated. Three main basin modes are highlighted through joint wavelet analyses of sea surface height (SSH) and surface current velocity (SCV), scale-averaged over relevant bands to address the co-variability of variables: (1) a 1-year period quasi-stationary wave (QSW) formed from gravest mode baroclinic planetary waves which consists of a northern, an equatorial and a southern antinode, and a major node off the South American coast that straddles the north equatorial current (NEC) and the north equatorial counter current (NECC), (2) a half-a-year period harmonic, (3) an 8-year sub-harmonic. Contrary to what is commonly accepted, the 1-year period QSW is not composed of wind-generated Kelvin and Rossby beams but results from the excitation of a tuned basin mode. Trade winds sustain a free tropical basin mode, the natural frequency of which is tuned to synchronize the excitation and the ridge of the QSWs. The functioning of the 1-year period basin mode is confirmed by solving the momentum equations, expanding in terms of Fourier series both the coefficients and the forcing terms. The terms of Fourier series have singularities, highlighting resonances and the relation between the resonance frequency and the wavenumbers. This ill-posed problem is regularized by considering Rayleigh friction. The waves are supposed to be semi-infinite, i.e. they do not reflect at the western and eastern boundaries of the basin, which would assume the waves vanish at these boundaries. At the western boundary the equatorial Rossby wave is deflected towards the northern antinode while forming the NECC that induces a positive Doppler-shifted wavenumber. At the eastern boundary, the Kelvin wave splits into coastal Kelvin waves that flow mainly southward to leave the Gulf of Guinea. In turn, off-tropical waves extend as an equatorially trapped Kelvin wave, being deflected off the western boundary. The succession of warm and cold waters transferred by baroclinic waves during a cycle leaves the tropical ocean by radiation and contributes to western boundary currents. The main manifestation of the basin modes concerns the variability of the NECC, of the branch of the South Equatorial Current (SEC) along the equator, of the western boundary currents as well as the formation of remote resonances, as will be presented in a future work. Remote resonances occur at midlatitudes, the role of which is suspected of being crucial in the functioning of subtropical gyres and in climate variability.
KeywordsLong oceanic wave resonance quasi-stationary waves wavelet analysis tuned basin mode
- Arnault S, Ménard Y and Merle J (1990) Observing the tropical Atlantic Ocean in 1986–1987 from altimetry, J. Geophys. Res., 95(C10), 17,921–17,945.Google Scholar
- Arnault S, Morliére A, Merle J, and Ménard Y (1992) Low-frequency variability of the tropical atlantic surface topography: altimetry and model comparison, J. Geophys. Res., 97(C9), 14,259–14,288.Google Scholar
- Arnault S, Cheney RE (1994) Tropical Atlantic sea level variability from Geosat (1985–1989). J. Geophys. Res., 99(C9), 18207–18223.Google Scholar
- Arnault S, Bourlès B, Gouriou Y, Chuchla R (1999) Intercomparison of the upper layer circulation of the western equatorial Atlantic Ocean: in situ and satellite data. J. Geophys. Res., 104(C9), 21171–21194.Google Scholar
- Bonjean F, Lagerloef GSE (2002) Diagnostic model and analysis of the surface currents in the tropical Pacific Ocean, Jour. Phys Oceanog., 32(10), 2938–2954.Google Scholar
- Brandt P and Eden C (2005) Annual cycle and interannual variability of the mid-depth tropical Atlantic Ocean, Deep-Sea Research I, 52, 199–219, doi:10.1016/j.dsr.2004.03.011.
- Cane M and Sarachik E (1981) The response of a linear baroclinic equatorial ocean to periodic forcing, J. Mar. Res., 39, 651–693.Google Scholar
- Carton JA (1989) Estimates of sea level in the tropical Atlantic ocean using Geosat altimetry, J. Geophys. Res., 94(C6), 8029–8039.Google Scholar
- Carton JA, Katz EJ (1990) Estimates of the zonal slope and seasonal transport of the Atlantic North Equatorial Countercurrent, J. Geophys. Res., 95(C3), 3091–3100.Google Scholar
- Carton JA, Huang B (1994) Warm events in the Tropical Atlantic, Jour. Phys Oceanog., 24(5), 888–903.Google Scholar
- Didden N, Schott F (1993) Eddies in the North Brazil Current retroflection region observed by Geosat altimetry, J. Geophys. Res., 98(C11), 20121–20131.Google Scholar
- Ding H, Keenlyside NS and Latif M (2009) Seasonal cycle in the upper equatorial Atlantic Ocean, J. Geophys. Res., 114, C09016, doi:10.1029/2009JC005418.
- du Penhoat Y, Cane MA, Patton RJ (1983) Reflections of low frequency equatorial waves on partial boundaries. In: Nihoul JCJ (eds) Hydrodynamics of the Equatorial Ocean, pp 237–258.Google Scholar
- Farge M (1992) Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech., 24, 395–457.Google Scholar
- Gill AE (1982) Atmosphere–Ocean Dynamics, International Geophysics Series, 30, Academic Press, London, pp 662.Google Scholar
- Illig S, Dewitte B, Ayoub N, du Penhoat Y, Reverdin G, De Mey P, Bonjean F and Lagerloef GSE (2004) Interannual long equatorial waves in the tropical atlantic from a high resolution OGCM experiment in 1981–2000. J. Geophys. Res., 109, 405–437.Google Scholar
- Illig S, Gushchina D, Dewitte B, Ayoub N, and du Penhoat Y (2006) The 1996 equatorial Atlantic warm event: origin and mechanisms, Geophys. Res. Lett., 33(9): L09701.Google Scholar
- Johnson ES, Bonjean F, Lagerloef GSE, Gunn JT, and Mitchum GT (2007) Validation and error analysis of OSCAR sea surface currents. J. At-mos. Oceanic Technol., 24, 688–701.Google Scholar
- Kalnay E et al., (1996) The NCEP/NCAR Reanalysis 40-year Project. Bull. Amer. Meteor. Soc., 77, 437–471.Google Scholar
- Katz EJ, Carton JA, Chakraborty A (1995) Dynamics of the equatorial Atlantic from altimetry: TOPEX/POSEIDON: scientific results, J. Geophys. Res., 100(C12), 25061–25067.Google Scholar
- Lagerloef GSE, Mitchum G, Lukas R and Niiler P (1999) Tropical Pacific near-surface currents estimated from altimeter, wind and drifter data, J. Geophys. Res., 104, 23,313–323,326.Google Scholar
- Maraun D, Kurths J (2004) Cross wavelet analysis: significance testing and pitfalls. Nonlinear Proces. Geophys., 11, 505–514, doi:10.5194/npg-11-505-2004.
- Merle J (1980) Variabilité thermique annuelle et interannuelle de l’océan Atlantique équatorial Est. L’hypothèse d’un El Niño Atlantique, Oceanol. Acta., 3(2), 209–220.Google Scholar
- Moore DW, Hisard P, McCreary JP, Merle JP, O’Brien J, Picaut JJ, Verstraete JM, and Wunsch C (1978) Equatorial adjustment in the eastern Atlantic, Geophys. Res. Lett., 5, 637–640.Google Scholar
- Nystuen JA, Andrade CA (1993) Tracking Mesoscale Ocean features in the Caribbean Sea using geosat altimetry, J. Geophys. Res., 98(C5), 8389–8394.Google Scholar
- Pegion PJ, Bourassa MA, Legler DM, and O’Brien JJ (2000) Objectively-derived daily “winds” from satellite scatterometer data. Mon. Wea. Rev., 128, 3150–3168.Google Scholar
- Philander S and Pacanowski R (1986), A model of the seasonal cycle in the tropical Atlantic Ocean, J. Geophys. Res., 91:14192–14206.Google Scholar
- Picaut J, Servain J, Busalacchi AJ, and Seva M (1984) Interannual variability versus seasonal variability in the Tropical Atlantic, Geophys. Res. Lett., 11(8), 787–790.Google Scholar
- Pinault JL (2012) Global warming and rainfall oscillation in the 5–10 yearr band in Western Europe and Eastern North America, Climatic Change, doi:10.1007/s10584-012-0432-6.
- Scharffenberg MG, Stammer D (2010) Seasonal variations of the large-scale geostrophic flow field and eddy kinetic energy inferred from the TOPEX/Poseidon and Jason-1 tandem mission data, J. Geophys. Res., 115, C02008, doi:10.1029/2008JC005242.
- Schouten MW, Matano RP, Strub TP (2005) A description of the seasonal cycle of the equatorial Atlantic from altimeter data, Deep-sea research. Part 1. Oceanographic research papers, 52(3), 477–493.Google Scholar
- Smith RL (1978) Poleward propagating disturbances in currents and sea-levels along the Peru coast, J. Geophys. Res., 83, 6083–6092.Google Scholar
- Stammer D (1997) Steric and wind-induced changes in TOPEX/POSEIDON large-scale sea surface topography observations. J. Geophys. Res., 102, 20987–21009.Google Scholar
- Torrence C, Compo GP (1998) A practical guide for wavelet analysis. Bull. Amer. Meteor. Soc., 79, 1, 61–78.Google Scholar