Modes of Interannual Tropical Ocean–Atmosphere Interaction—a Unified View. Part II: Analytical Results in the Weak-Coupling Limit

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Abstract
The properties of the eigenmodes of the coupled tropical ocean-atmosphere system, linearized about a climatological basic state—and hence of the first bifurcation, which strongly determines the nature of the interannual variability, such as El Niño—show considerable dependence on the parameters of the coupled system. These eigenmodes are examined in a modified shallow-water model with simplified mixed-layer dynamics and a sea surface temperature (SST) equation, coupled to a simple atmospheric model. The model is designed so as to make analytical approximations feasible in various limits, as in a previous study by Neelin where the x-periodic case was analyzed. The realistic case of a finite ocean basin is treated here. An integral formulation of the eigenvalue problem is derived that provides a basis for making consistent approximations that include the effects of atmospheric and oceanic boundary conditions. We provide a scaling analysis to select parameters that give the most succinct insights in... Abstract The properties of the eigenmodes of the coupled tropical ocean-atmosphere system, linearized about a climatological basic state—and hence of the first bifurcation, which strongly determines the nature of the interannual variability, such as El Niño—show considerable dependence on the parameters of the coupled system. These eigenmodes are examined in a modified shallow-water model with simplified mixed-layer dynamics and a sea surface temperature (SST) equation, coupled to a simple atmospheric model. The model is designed so as to make analytical approximations feasible in various limits, as in a previous study by Neelin where the x-periodic case was analyzed. The realistic case of a finite ocean basin is treated here. An integral formulation of the eigenvalue problem is derived that provides a basis for making consistent approximations that include the effects of atmospheric and oceanic boundary conditions. We provide a scaling analysis to select parameters that give the most succinct insights in...

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