Mechanics and Thermodynamics of a New Minimal Model of the Atmosphere

TL;DR

This paper introduces a new minimal atmospheric model combining Lorenz '96 dynamics with temperature variables, exploring its energy cycle, stability, and chaotic behavior to better understand climate system properties.

Contribution

The paper presents a novel atmospheric model that incorporates temperature-like variables and an energy cycle, extending Lorenz '96 to include multiscale dynamics and complex energy interactions.

Findings

Identified parameter regions with stationary, quasi-periodic, and chaotic states.

Demonstrated the model's capacity for extensive chaos.

Developed a multiscale version mimicking Earth's atmospheric energy cycle.

Abstract

The understanding of the fundamental properties of the climate system has long benefitted from the use of simple numerical models able to parsimoniously represent the essential ingredients of its processes. Here we introduce a new model for the atmosphere that is constructed by supplementing the now-classic Lorenz '96 one-dimensional lattice model with temperature-like variables. The model features an energy cycle that allows for conversion between the kinetic and potential forms and for introducing a notion of efficiency. The model's evolution is controlled by two contributions - a quasi-symplectic and a gradient one, which resemble (yet not conforming to) a metriplectic structure. After investigating the linear stability of the symmetric fixed point, we perform a systematic parametric investigation that allows us to define regions in the parameters space where at steady state stationary, quasi-periodic, and chaotic motions are realised, and study how the terms responsible for defining the energy budget of the system depend on the external forcing injecting energy in the kinetic and in the potential energy reservoirs. Finally, we find preliminary evidence that the model features extensive chaos. We also introduce a more complex version of the model that is able to accommodate for multiscale dynamics and that features an energy cycle that more closely mimics the one of the Earth's atmosphere.