Classification of Simple Low-order Models in Geophysical Fluid Dynamics and Climate Dynamics

Lorenz derived the famous three-variable dynamical system [l] that contains chaotic solutions in some parameter anges from a numerical model on 2-dimensional Rayleigh-B&mud convection. He called this kind of highly simplified system low-or&r model. In the fields of Geophysical Fluid Dynamics (GFD) and Climate Dynamics (CD), many descendants of the low-order model have been developed to study the essential dynamics of the original much complex systems. In this review article, these low-order models are classified into several groups with the knowledge of nonlinear dynamical systems. Zero-dimensional energy balance climate model and Lore&s “general circulation model” are used as examples of each group. The grouping is as follows: (I) multiple equilibria in nonlinear systems, (II) periodic and chaotic solutions in autonomous ystems, and (III) periodic and chaotic solutions in nonautonomous systems.