Well-posedness and long time dynamics for a quasi-geostrophic ocean-atmosphere model with radiation balance

TL;DR

This paper establishes the well-posedness and analyzes the long-term behavior of a coupled quasi-geostrophic ocean-atmosphere model with radiative forcing, demonstrating finite-dimensional attractors and reconstructibility of temperature from velocity data.

Contribution

It introduces a coupled ocean-atmosphere model with radiative forcing and proves existence, uniqueness, and long-term dynamics, including finite-dimensional attractors and mode determination.

Findings

Existence and uniqueness of solutions established.

Long-term dynamics are governed by a finite-dimensional attractor.

Ocean temperature evolution can be reconstructed from velocity observations.

Abstract

We investigate a coupled atmosphere-ocean model including the mechanical and thermodynamical interaction between the two fluids for the mid-latitudes. The formulation combines a multilayer quasi-geostrophic dynamical framework with temperature equations incorporating long- and short-wave radiative forcing, as in energy balance models. Within a suitable functional framework, we establish the existence and uniqueness of solutions, and their continuous dependence on the radiation parameters. We also prove that the long-time dynamics are described by a finite-dimensional global attractor and, moreover, that the system possesses a finite set of determining modes that governs its asymptotic behaviour. In particular, we show that the long-term evolution of the ocean's temperature can be reconstructed solely from observations of the velocity fields across the model's layers.