A Linear Stochastic Dynamical Model of ENSO. Part I: Model Development

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Abstract
Singular vector analysis and Floquet analysis are carried out on a linearized variant of the Zebiak–Cane atmosphere–ocean model of El Niño–Southern Oscillation (ENSO), hereinafter called the nominal model. The Floquet analysis shows that the system has a single unstable mode. This mode has a shape and frequency similar to ENSO and is well described by delayed oscillator physics. Singular vector analysis shows two interesting features. (i) For any starting month and time period of optimization the singular vector is shaped like one of two nearly orthogonal patterns. These two patterns correspond approximately to the real and imaginary parts of the adjoint of the ENSO mode for the time-invariant basic-state version of the system that was calculated in previous work. (ii) Contour plots of the singular values as a function of starting month and period of optimization show a ridge along end times around December. This result along with a study of the time evolution of the associated singular vectors s... Abstract Singular vector analysis and Floquet analysis are carried out on a linearized variant of the Zebiak–Cane atmosphere–ocean model of El Niño–Southern Oscillation (ENSO), hereinafter called the nominal model. The Floquet analysis shows that the system has a single unstable mode. This mode has a shape and frequency similar to ENSO and is well described by delayed oscillator physics. Singular vector analysis shows two interesting features. (i) For any starting month and time period of optimization the singular vector is shaped like one of two nearly orthogonal patterns. These two patterns correspond approximately to the real and imaginary parts of the adjoint of the ENSO mode for the time-invariant basic-state version of the system that was calculated in previous work. (ii) Contour plots of the singular values as a function of starting month and period of optimization show a ridge along end times around December. This result along with a study of the time evolution of the associated singular vectors s...

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