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Data assimilation with stochastic model reduction

Banff International Research Station for Mathematical Innovation and Discovery

In weather and climate prediction, data assimilation combines data with dynamical models to make prediction, using ensemble of solutions to represent the uncertainty. Due to limited computational resources, reduced models are needed and coarse-grid models are often used, and the effects of the subgrid scales are left to be taken into account. A major challenge is to account for the memory effects due to coarse graining while capturing the key statistical-dynamical properties. We propose a stochastic parametrization method which accounts for the memory effects by nonlinear autoregression moving average (NARMA) type models, and demonstrate by examples that the resulting NARMA type stochastic reduced models can capture the key statistical and dynamical properties and therefore can improve the performance of ensemble prediction in data assimilation. The examples include the Lorenz 96 system (which is a simplified model of the atmosphere) and the Kuramoto-Sivashinsky equation of spatiotemporally chaotic dynamics.

Mathematics; Partial differential equations; Dynamical systems and ergodic theory

video/mp4

Author affiliation: Johns Hopkins University

2018-05-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/66016

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/