Stochastic Parameterization: Toward 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 represent model inadequacy better and to 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 long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) 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 is demonstrated; and future research directions are outlined.

Exchange Processes in the Atmospheric Boundary Layer Over Mountainous Terrain

“…Modern EPSs rely not only on perturbed initial conditions but also on a model error representation that aims at quantifying the forecast uncertainty arising from an imperfect model design or from unknown physical processes [238]. One way of accounting for model errors is to introduce stochastic perturbations in some aspects of the parameterization schemes adopted by the ensemble members (multi-physics ensembles [239] offer another approach to the problem).…”

Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance

“…Traditionally, the development of parametrizations boiled down to deriving deterministic empirical laws able to describe the effect of the small-scale dynamical processes. More recently, it has become apparent that it is important to include stochastic terms in the parametrization that are able to provide a theoretically more coherent representation of such effects and that lead, on a practical level, to an improved skill (Palmer and Williams, 2008;Franzke et al, 2015;Berner et al, 2017). A first way to derive or at least justify the need for stochastic parametrizations comes from homogenization theory (Pavliotis and Stuart, 2008), which leads to constructing an approximate representation of the impact of the fast scales on the slow variables as the sum of two terms, a mean field term and a white noise term.…”

Parameterization of stochastic multiscale triads

“…(1); therefore, direct comparison is possible and will be performed on a number of metrics, namely initial ensemble spread, correlation functions and exit times from an interval. We intend our results to be of relevance for providing sound foundations for stochastic parameterizations in weather and climate models (Palmer and Williams, 2009;Franzke et al, 2015;Berner et al, 2016).…”