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An Asymptotic Expansion for the Recharge–Discharge Model of ENSO

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  • 1 Laboratoire d'Etudes en Géophysique et Océanographie Spatiales, Toulouse, France
  • | 2 Université de Toulouse, INPT, CNRS, IMFT, Toulouse, France
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Abstract

The dynamics of El Niño–Southern Oscillation (ENSO) in the equatorial Pacific Ocean are largely associated with the slow thermocline adjustment at interannual and basin scales. This adjustment involves, among other things, the fast propagation and reflection of equatorial waves by wind stress forcing. A simple and straightforward asymptotic expansion of the long-wave equations is proposed using the low-frequency approximation. The asymptotic expansion is performed in Fourier space, retaining only the gravest equatorial long waves and baroclinic modes with the largest scale, and considering small dissipation by friction and boundary reflections. This leads to an asymptotic model for the thermocline response to wind stress forcing, which is in essence the ocean component of the recharge–discharge model of ENSO. The asymptotic model is nonheuristic and in broad agreement with some essential results scattered in previous studies. Thermocline variability is divided into a sloping “Tilt mode” that adjusts instantly to wind stress forcing and a zonal-mean “Warm Water Volume mode” that adjusts as a time integrator to wind stress curl. The model has a plausible energy budget and its solutions are in good agreement with observations. Results suggest that the net adjustment rather than the explicit delays of equatorial waves is essential for the slow thermocline adjustment, and this is best described by the recharge–discharge model.

Corresponding author address: Sulian Thual, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012. E-mail: sulian.thual@gmail.com

Abstract

The dynamics of El Niño–Southern Oscillation (ENSO) in the equatorial Pacific Ocean are largely associated with the slow thermocline adjustment at interannual and basin scales. This adjustment involves, among other things, the fast propagation and reflection of equatorial waves by wind stress forcing. A simple and straightforward asymptotic expansion of the long-wave equations is proposed using the low-frequency approximation. The asymptotic expansion is performed in Fourier space, retaining only the gravest equatorial long waves and baroclinic modes with the largest scale, and considering small dissipation by friction and boundary reflections. This leads to an asymptotic model for the thermocline response to wind stress forcing, which is in essence the ocean component of the recharge–discharge model of ENSO. The asymptotic model is nonheuristic and in broad agreement with some essential results scattered in previous studies. Thermocline variability is divided into a sloping “Tilt mode” that adjusts instantly to wind stress forcing and a zonal-mean “Warm Water Volume mode” that adjusts as a time integrator to wind stress curl. The model has a plausible energy budget and its solutions are in good agreement with observations. Results suggest that the net adjustment rather than the explicit delays of equatorial waves is essential for the slow thermocline adjustment, and this is best described by the recharge–discharge model.

Corresponding author address: Sulian Thual, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012. E-mail: sulian.thual@gmail.com
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