  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.

Chaotic Dynamics;Statistical Mechanics;Atmospheric and Oceanic Physics;Fluid Dynamics