A Gyrostatic Low-Order Model for the El Ñino-Southern Oscillation

Alexander Gluhovsky

doi:10.1155/2017/6176045

Abstract

The paper demonstrates that, similar to other important models of atmospheric phenomena, beginning with the celebrated Lorenz model of the Rayleigh-Bénard convection, the Vallis low-order model (LOM) of the El Ñino-Southern Oscillation admits a gyrostatic form and discusses how gyrostatic LOMs may offer a general framework for deriving effective physically sound models for atmospheric dynamics and time series analysis. Any such model has a quadratic integral of motion (interpreted as some form of energy), which eliminates unphysical behaviors that have often plagued atmospheric LOMs and paves way for developing Hamiltonian LOMs. Restricting LOMs to a gyrostatic form also helps to design LOMs of optimum size and provides a modular construction of LOMs using gyrostats as elementary building blocks.

Highlights

A Gyrostatic Low-Order Model for the El Ñino-Southern OscillationThe paper demonstrates that, similar to other important models of atmospheric phenomena, beginning with the celebrated Lorenz model of the Rayleigh-Benard convection, the Vallis low-order model (LOM) of the El Nino-Southern Oscillation admits a gyrostatic form and discusses how gyrostatic LOMs may offer a general framework for deriving effective physically sound models for atmospheric dynamics and time series analysis
Atmospheric and climate dynamics exhibit complex behavior reflected in a hierarchy of models from “simple” nonlinear 3mode ordinary differential equations (ODEs) to full-fledged climate-system models involving nonlinear partial differential equations (PDEs)
An effective way to deal with formidable mathematical difficulties posed by the PDEs of fluid dynamics via approximating them with finite systems of nonlinear ODEs (the so-called low-order models (LOMs)) has been established in pioneering work by Kolmogorov, Lorenz [4, 5], and Obukhov [6, 7]

Summary

A Gyrostatic Low-Order Model for the El Ñino-Southern Oscillation

The paper demonstrates that, similar to other important models of atmospheric phenomena, beginning with the celebrated Lorenz model of the Rayleigh-Benard convection, the Vallis low-order model (LOM) of the El Nino-Southern Oscillation admits a gyrostatic form and discusses how gyrostatic LOMs may offer a general framework for deriving effective physically sound models for atmospheric dynamics and time series analysis. Restricting LOMs to a gyrostatic form helps to design LOMs of optimum size and provides a modular construction of LOMs using gyrostats as elementary building blocks

Introduction

G-Models

Results and Discussion

Conclusions