The climate is a forced and dissipative nonlinear system featuring nontrivial dynamics on a vast range of spatial and temporal scales. The understanding of the climate's structural and multiscale properties is crucial for the provision of a unifying picture of its dynamics and for the implementation of accurate and efficient numerical models. We present some recent developments at the intersection between climate science, mathematics, and physics, which may prove fruitful in the direction of constructing a more comprehensive account of climate dynamics. We describe the Nambu formulation of fluid dynamics and the potential of such a theory for constructing sophisticated numerical models of geophysical fluids. Then, we focus on the statistical mechanics of quasi-equilibrium flows in a rotating environment, which seems crucial for constructing a robust theory of geophysical turbulence. We then discuss ideas and methods suited for approaching directly the nonequilibrium nature of the climate system. First, we describe some recent findings on the thermodynamics of climate, characterize its energy and entropy budgets, and discuss related methods for intercomparing climate models and for studying tipping points. These ideas can also create a common ground between geophysics and astrophysics by suggesting general tools for studying exoplanetary atmospheres. We conclude by focusing on nonequilibrium statistical mechanics, which allows for a unified framing of problems as different as the climate response to forcings, the effect of altering the boundary conditions or the coupling between geophysical flows, and the derivation of parametrizations for numerical models.

We document the development and simulation characteristics of the next generation modeling system for seasonal to decadal prediction and projection at the Geophysical Fluid Dynamics Laboratory (GFDL). SPEAR (Seamless System for Prediction and EArth System Research) is built from component models recently developed at GFDL—the AM4 atmosphere model, MOM6 ocean code, LM4 land model, and SIS2 sea ice model. The SPEAR models are specifically designed with attributes needed for a prediction model for seasonal to decadal time scales, including the ability to run large ensembles of simulations with available computational resources. For computational speed SPEAR uses a coarse ocean resolution of approximately 1.0° (with tropical refinement). SPEAR can use differing atmospheric horizontal resolutions ranging from 1° to 0.25°. The higher atmospheric resolution facilitates improved simulation of regional climate and extremes. SPEAR is built from the same components as the GFDL CM4 and ESM4 models but with design choices geared toward seasonal to multidecadal physical climate prediction and projection. We document simulation characteristics for the time mean climate, aspects of internal variability, and the response to both idealized and realistic radiative forcing change. We describe in greater detail one focus of the model development process that was motivated by the importance of the Southern Ocean to the global climate system. We present sensitivity tests that document the influence of the Antarctic surface heat budget on Southern Ocean ventilation and deep global ocean circulation. These findings were also useful in the development processes for the GFDL CM4 and ESM4 models.

The goal of this paper is to explore the potential multistability of the climate of a planet around the habitable zone. We apply our methodology to the Earth system, but our investigation has more general relevance. A thorough investigation of the thermodynamics of the climate system is performed for very diverse conditions of energy input and infrared atmosphere opacity. Using PlaSim, an Earth-like general circulation model, the solar constant S * is modulated between 1160 and 1510 Wm −2 and the CO 2 concentration, [CO 2 ], from 90 to 2880 ppm. It is observed that in such a parameter range the climate is bistable, i.e. there are two coexisting attractors, one characterised by warm, moist climates (W) and one by completely frozen sea surface (Snowball Earth, SB). Linear relationships are found for the two transition lines (W→SB and SB →W) in (S * ,[CO 2 ]) between S * and the logarithm of [CO 2 ]. The dynamical and thermodynamical properties -energy fluxes, Lorenz energy cycle, Carnot efficiency, material entropy production -of the W and SB states are very different: W states are dominated by the hydrological cycle and latent heat is prominent in the material entropy production; the SB states are eminently dry climates where heat transport is realized through sensible heat fluxes and entropy mostly generated by dissipation of kinetic energy. We also show that the Carnot efficiency regularly increases towards each transition between W and SB, with a large decrease in each transition. Finally, we propose well-defined empirical functions allowing for expressing the global non-equilibrium thermodynamical properties of the system in terms of either the mean surface temperature or the mean planetary emission temperature. This paves the way for the possibility of proposing efficient parametrisations of complex non-equilibrium properties and of practically deducing fundamental properties of a planetary system