Regime Transitions and Extreme Events in Geophysical Flows
Abstract
Extreme weather events have become more frequent in the last decade, and this trend is expected to continue and intensify in the future. The societal impact, as documented for example by the U.S. Global Change Research Program (USGCRP), is enormous. The death toll of hurricanes, tornadoes, heavy downpours, heat waves, and droughts is increasing and these events affect insignificant ways all sectors of the economy, costing billions of US dollars every year in the USA alone. This increase in frequency is believed to be in part due to climate change and the intensification of the water cycle that comes in its wake. Whatever the long term cause of this trend, there is a high demand for methods permitting higher accuracy in the description and prediction of extreme weather events on the timescale of their occurrence. The complexity and interconnectedness of the underlying atmosphere-ocean system, combined with the uncertainty and stochasticity of its evolution, make a rigorous mathematical treatment extremely challenging, while the relative rarity of extreme events renders naive numerical approaches inefficient. This calls for a shift in the mathematical treatment of extreme weather events, put forward in the present proposal.As plainly apparent from our daily experience, extreme weather events have a random component about them. From a modeling standpoint, this is reflected by the fact that these events are stochastically driven either by imperfect knowledge of the system s initial conditions or by small perturbations not captured by the deterministic models. As a result, a probabilistic description of extreme weather events is necessary, using the framework of statistical mechanics. However, this requires the generalization of this framework to non-equilibrium situations inwhich the systems are driven and subject to small but non-negligible random fluctuations. Large deviation theory (LDT) offers the mathematical foundation to build such a statistical mechanics theory of non-equilibrium systems in general, and extreme weather events in particular. When applicable, LDT predicts the maximum likelihood pathways of regime transitions and extreme events without resorting to brute-force sampling, by instead solving a deterministic optimization problem. LDT-based calculations can be used to generate several outputs of interest:- They permit the estimation of the probability and rate of occurrence of regime transitions and extreme events, as well as their most likely mechanism of creation and evolution.- They enable us to identify event precursors which in principle offers the possibility of predicting their likelihood occurrence in advance.- For incomplete models in which either the parameters in the equations or their initial and boundary conditions are not known perfectly but rather specified statistically, they allows for uncertainty quantification of the model predictions.- They can be used to develop importance sampling strategies that significantly accelerate vanilla Monte-Carlo methods, and can be incorporated in data-assimilation tools such as particle filters to improve their performance as well.This proposal outlines theoretical and numerical steps to further develop LDP techniques with the aims of (i) analyzing some realistic models of atmosphere and ocean dynamics that display regime transitions and extreme events and (ii) creating analytical and numerical tools transportable to other models of similar type. These outcomes will significantly improve the DoD capabilities to predict extreme weather events.The PI certifies this summary as ~Approved for Public Release.~
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 13, 2019
- Source ID
- N000141912438
Entities
People
- Eric Vanden-Eijnden
Organizations
- New York University
- Office of Naval Research
- United States Navy