Stochastic Climate Theory and Modelling

Abstract

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations as well as for model error representation, uncertainty quantification, data assimilation and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochastic components and non-Markovian (memory) terms. Stochastic approaches in numerical weather and climate prediction models also lead to the reduction of model biases. Hence, there is a clear need for systematic stochastic approaches in weather and climate modelling. In this review we present evidence for stochastic effects in laboratory experiments. Then we provide an overview of stochastic climate theory from an applied mathematics perspectives. We also survey the current use of stochastic methods in comprehensive weather and climate prediction models and show that stochastic parameterizations have the potential to remedy many of the current biases in these comprehensive models.

References in corpus (1)

• A review of linear response theory for general differentiable dynamical systems

Cited by in corpus (41)

• The Physics of Climate Variability and Climate Change
• Stochastic Parameterization: Towards a new view of Weather and Climate Models
• Extremes and Recurrence in Dynamical Systems
• Mathematical and Physical Ideas for Climate Science
• Predicting Climate Change using Response Theory: Global Averages and Spatial Patterns
• Geophysical flows under location uncertainty, Part II: Quasi-geostrophy and efficient ensemble spreading
• Geophysical flows under location uncertainty, Part I Random transport and general models
• 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
• Learning physics-constrained subgrid-scale closures in the small-data regime for stable and accurate LES
• Emergence of molecular friction in liquids: bridging between the atomistic and hydrodynamic pictures
• A proof of concept for scale-adaptive parameterizations: the case of the Lorenz '96 model
• Reduced-Order Models for Coupled Dynamical Systems: Data-driven Methods and the Koopman Operator
• Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows
• Rotating shallow water flow under location uncertainty with a structure-preserving discretization
• Applications of large deviation theory in geophysical fluid dynamics and climate science
• The linear response function of an idealized atmosphere. Part 1: Construction using Green's functions and applications
• Detection of Approaching Critical Transitions in Natural Systems Driven by Red Noise
• Parametrization of stochastic multiscale triads
• Stochastic parameterization of subgrid-scale processes in coupled ocean-atmosphere systems: Benefits and limitations of response theory
• Equivalence of nonequilibrium ensembles in turbulence models
• Analytical Properties for a Stochastic Rotating Shallow Water Model under Location Uncertainty
• Lyapunov analysis of multiscale dynamics: The slow bundle of the two-scale Lorenz 96 model
• A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization
• A consistent stochastic large-scale representation of the Navier-Stokes equations
• Comparison of stochastic parameterizations in the framework of a coupled ocean-atmosphere model
• Mechanics and Thermodynamics of a New Minimal Model of the Atmosphere
• Stochastic Parametrization of the Richardson Triple
• Analysis of a bistable climate toy model with physics-based machine learning methods
• A deep learning approach to the measurement of long-lived memory kernels from Generalised Langevin Dynamics
• Stochastic Climate Theory
• Effects of Stochastic Parametrization on Extreme Value Statistics
• Simple Stochastic Modeling of Snowball Probability Throughout Earth History
• What is the correct cost functional for variational data assimilation?
• Stability of Travelling Waves for Reaction-Diffusion Equations with Multiplicative Noise
• Reduction Methods in Climate Dynamics -- A Brief Review
• Random attractor of the 3D viscous primitive equations driven by fractional noises
• Statistical Response of ENSO Complexity to Initial Condition and Model Parameter Perturbations
• A Unifying and Canonical Description of Measure-Preserving Diffusions
• Quantum-inspired memory-enhanced stochastic algorithms
• Stochastic representation of the Reynolds transport theorem: revisiting large-scale modeling