Stochastic Parameterization: Towards a new view of Weather and Climate Models

Abstract

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy and improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing longstanding climate biases and relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups which show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface and cryosphere of comprehensive weather and climate models (a) gives rise to more reliable probabilistic forecasts of weather and climate and (b) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics and turbulence is reviewed, its relevance for the climate problem demonstrated, and future research directions outlined.

26 pages, 15 figures. Final published version

References in corpus (8)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• A review of linear response theory for general differentiable dynamical systems
• Stochastic Climate Theory and Modelling
• Mathematical and Physical Ideas for Climate Science
• A new framework for climate sensitivity and prediction: a modelling perspective
• A data-driven method for the stochastic parametrisation of subgrid-scale tropical convective area fraction
• Non-equilibrium statistical mechanics of turbulence
• Focus on some Nonequilibrium Issues

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