Chaos and Observability in Variational Data Assimilation

Daniel Rey, University of California, San Diego

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Observation, estimation and prediction are universal challenges that become especially difficult when the system under consideration is dynamical and chaotic. Chaos injects dynamical noise into the estimation process and it must be suppressed to satisfy the necessary conditions for success, namely synchronization of the estimate and the observed data. The ability to control the growth of errors is constrained by the observations' spatiotemporal resolution, and often exhibits critical thresholds below which the probability of success becomes effectively zero. This talk introduces a framework to identify these limits and examine how they vary with certain parameters of the analysis, such as the resolution of the forecast model or the length of the estimation window. Preliminary results given for the chaotic Lorenz 1996 model show how this approach may be used to assess the adequacy of the coupled observation-analysis-forecast system and suggests ways to improve its overall design.

Abstract Author(s): Daniel Rey, Henry D.I. Abarbanel