Effects of Stochastic Parametrization on Extreme Value Statistics

Abstract

Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations are computational tools used in Earth system models, which are aimed at reproducing the impact of unresolved scales on resolved scales. The performance of parametrizations has usually been examined on typical events rather than on extreme events. In this paper we consider a modified version of the two-level Lorenz'96 model and investigate how two parametrizations of the fast degrees of freedom perform in terms of the representation of extreme events. One parametrization is constructed following Wilks (2005) and is constructed through an empirical fitting procedure; the other parametrization is constructed through the statistical mechanical approach proposed by Wouters and Lucarini (2012, 2013). The two strategies show different advantages and disadvantages. We discover that the agreement between parametrized models and true model is in general worse when looking at extremes rather than at the bulk of the statistics. The results suggest that stochastic parametrizations should be accurately and specifically tested against their performance on extreme events, as usual optimization procedures might neglect them.

arXiv comment21 pages and 17 figures

References in corpus (9)

• Stochastic Parameterization: Towards a new view of Weather and Climate Models
• A review of linear response theory for general differentiable dynamical systems
• Stochastic Climate Theory and Modelling
• Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach
• Disentangling multi-level systems: averaging, correlations and memory
• A proof of concept for scale-adaptive parameterizations: the case of the Lorenz '96 model
• Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems
• Extreme value laws in dynamical systems under physical observables
• Convergence of extreme value statistics in a two-layer quasi-geostrophic atmospheric model

Cited by in corpus (4)

• The Physics of Climate Variability and Climate Change
• Mechanics and Thermodynamics of a New Minimal Model of the Atmosphere
• Heterogeneity of the Attractor of the Lorenz '96 Model: Lyapunov Analysis, Unstable Periodic Orbits, and Shadowing Properties
• Analysis of a bistable climate toy model with physics-based machine learning methods