Mechanics and Thermodynamics of a New Minimal Model of the Atmosphere

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.

arXiv comment16 pages, 5 Figures; accepted version

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Cited by in corpus (5)

• Heterogeneity of the Attractor of the Lorenz '96 Model: Lyapunov Analysis, Unstable Periodic Orbits, and Shadowing Properties
• Analysis of a bistable climate toy model with physics-based machine learning methods
• Inferring the instability of a dynamical system from the skill of data assimilation exercises
• Learning to Assimilate in Chaotic Dynamical Systems
• Predictors and Predictands of Linear Response in Spatially Extended Systems