Mathematical and Physical Ideas for Climate Science

Abstract

The climate is a forced and dissipative nonlinear system featuring non-trivial dynamics of 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 non-equilibrium nature of the climate system. First, we describe some recent findings on the thermodynamics of climate and 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 non-equilibrium 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.

44 pages, 22 figures. Major revision with respect to previous version. A glossary of terms is included at the end

References in corpus (50)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods
• Exoplanet Atmospheres
• Inflating Hot Jupiters With Ohmic Dissipation
• A review of linear response theory for general differentiable dynamical systems
• Stochastic Climate Theory and Modelling
• Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows
• The Effects of Irradiation on Hot Jovian Atmospheres: Heat Redistribution and Energy Dissipation
• Random changes of flow topology in two dimensional and geophysical turbulence
• Energetics of PCMDI/CMIP3 Climate Models: Energy Budget and Meridional Enthalpy Transport
• Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem
• Energy and enstrophy fluxes in the double cascade of 2d turbulence
• Direct Statistical Simulation of Out-of-Equilibrium Jets
• A Statistical Mechanical Approach for the Computation of the Climatic Response to General Forcings
• Bistability of the climate around the habitable zone: a thermodynamic investigation
• Hydrological Cycle over South and Southeast Asian River Basins as Simulated by PCMDI/CMIP3 Experiments
• Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach
• Thermodynamic Analysis of Snowball Earth Hysteresis Experiment: Efficiency, Entropy Production, and Irreversibility
• Geophysical turbulence and the duality of the energy flow across scales
• Kinetic theory of jet dynamics in the stochastic barotropic and 2D Navier-Stokes equations
• Disentangling multi-level systems: averaging, correlations and memory
• On the Existence of Shocks in Irradiated Exoplanetary Atmospheres
• Solvable phase diagrams and ensemble inequivalence for two-dimensional and geophysical turbulent flows
• Thermodynamics of atmospheric circulation on hot Jupiters
• Response Theory for Equilibrium and Non-Equilibrium Statistical Mechanics: Causality and Generalized Kramers-Kronig relations
• Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system
• Application of the t-model of optimal prediction to the estimation of the rate of decay of solutions of the Euler equations in two and three dimensions
• Stochastic perturbations to dynamical systems: a response theory approach
• Beyond the linear Fluctuation-Dissipation Theorem: the Role of Causality
• Bottom-trapped currents as statistical equilibrium states above topographic anomalies
• Habitability and Multistability in Earth-like Planets
• New Results on the Thermodynamical Properties of the Climate System
• Hydrological Cycle in the Danube basin in present-day and XXII century simulations by IPCCAR4 global climate models
• A comparative study of two stochastic mode reduction methods
• Hyperviscosity and statistical equilibria of Euler turbulence on the torus and the sphere
• Restricted Equilibrium and the Energy Cascade in Rotating and Stratified Flows
• Fluctuation-Response Relation and modeling in systems with fast and slow dynamics
• Symmetry-break, mixing, instability, and low frequency variability in a minimal Lorenz-like system
• The catalytic role of beta effect in barotropization processes
• Energetics, skeletal dynamics and long-term predictions in Kolmogorov-Lorenz systems
• Additional Invariants and Statistical Equilibria for the 2D Euler Equations on a spherical domain
• Elements of a unified framework for response formulae
• Nonequilibrium thermodynamics of circulation regimes in optically-thin, dry atmospheres
• Modelling Complexity: the case of Climate Science
• Statistical mechanics of Fofonoff flows in an oceanic basin
• Entropy Production and Coarse Graining of the Climate Fields in a General Circulation Model
• Statistical mechanics of quasi-geostrophic flows on a rotating sphere
• Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling
• On the recurrence and robust properties of Lorenz'63 model
• Nonlinear energy transfers and phase diagrams for geostrophically balanced rotating--stratified flows

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• The Physics of Climate Variability and Climate Change
• Stochastic Parameterization: Towards a new view of Weather and Climate Models
• Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations
• Seasonal cycle of Precipitation over Major River Basins in South and Southeast Asia: A Review of the CMIP5 climate models data for present climate and future climate projections
• A new framework for climate sensitivity and prediction: a modelling perspective
• Edge States in the Climate System: Exploring Global Instabilities and Critical Transitions
• Predicting Climate Change using Response Theory: Global Averages and Spatial Patterns
• Statistical and Dynamical Properties of Covariant Lyapunov Vectors in a Coupled Atmosphere-Ocean Model - Multiscale Effects, Geometric Degeneracy, and Error Dynamics
• Fluctuations, Response, and Resonances in a Simple Atmospheric Model
• Fingerprinting Heatwaves and Cold Spells and Assessing Their Response to Climate Change using Large Deviation Theory
• Equivalence of Non-Equilibrium Ensembles and Representation of Friction in Turbulent Flows: The Lorenz 96 Model
• A New Mathematical Framework for Atmospheric Blocking Events
• A proof of concept for scale-adaptive parameterizations: the case of the Lorenz '96 model
• Beyond Forcing Scenarios: Predicting Climate Change through Response Operators in a Coupled General Circulation Model
• Theoretical tools for understanding the climate crisis from Hasselmann's program and beyond
• Global Stability Properties of the Climate: Melancholia States, Invariant Measures, and Phase Transitions
• Dynamical Landscape and Multistability of a Climate Model
• Response Operators for Markov Processes in a Finite State Space: Radius of Convergence and Link to the Response Theory for Axiom A Systems
• Applications of large deviation theory in geophysical fluid dynamics and climate science
• Co-existing climate attractors in a coupled aquaplanet
• Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models
• Robustness of competing climatic states
• Dynamical Analysis of Blocking Events: Spatial and Temporal Fluctuations of Covariant Lyapunov Vectors
• Stability analysis of chaotic systems from data
• Restricted Equilibrium and the Energy Cascade in Rotating and Stratified Flows
• Covariant Lyapunov Vectors of a Quasi-geostrophic Baroclinic Model: Analysis of Instabilities and Feedbacks
• A Large Deviation Theory-based Analysis of Heat Waves and Cold Spells in a Simplified Model of the General Circulation of the Atmosphere
• Lévy-noise versus Gaussian-noise-induced Transitions in the Ghil-Sellers Energy Balance Model
• The impact of oceanic heat transport on the atmospheric circulation
• Quadratic response of random and deterministic dynamical systems
• Parametrization of stochastic multiscale triads
• Dissipation properties of transport noise in the two-layer quasi-geostrophic model
• Nonequilibrium oscillations, probability angular momentum, and the climate system
• Detecting and Attributing Change in Climate and Complex Systems: Foundations, Green's Functions, and Nonlinear Fingerprints
• Entropy Production and Coarse Graining of the Climate Fields in a General Circulation Model
• On the computation of the extremal index for time series
• Lyapunov analysis of multiscale dynamics: The slow bundle of the two-scale Lorenz 96 model
• Response Formulae for $n$-point Correlations in Statistical Mechanical Systems and Application to a Problem of Coarse Graining
• Linear Response for a Family of Self-Consistent Transfer Operators
• Spectral decomposition and extremes of atmospheric meridional energy transport in Northern Hemisphere midlatitudes
• Mechanics and Thermodynamics of a New Minimal Model of the Atmosphere
• Point vortex dynamics in three-dimensional ageostrophic balanced flows
• Analysis of a two-layer energy balance model: long time behaviour and greenhouse effect
• Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks
• Rigorous justification for the space-split sensitivity algorithm to compute linear response in Anosov systems
• A Stochastic Model for Induced Seismicity at the Geothermal Systems: A Case of the Geysers
• Eddy saturation in a reduced two-level model of the atmosphere
• An Introduction to Large Deviations and Equilibrium Statistical Mechanics for Turbulent Flows
• Thermodynamic efficiency of atmospheric motion governed by Lorenz system
• Introduction to the Special Issue on the Statistical Mechanics of Climate