Seminar: Continuous Data Assimilation: Deepening Understanding of the Connections Between Physics and Data

Speaker

Elizabeth Carlson, University of Victoria

Bio

Elizabeth Carlson is a PIMS Postdoctoral Fellow at the University of Victoria. Her continuing research from her PhD (University of Nebraska-Lincoln + Los Alamos National Laboratory COSIM group MPAS-O) has been on investigating a somewhat novel data assimilation algorithm that resembles nudging both theoretically and computationally.

Abstract

Many systems whose physics is generally well understood are modeled with differential equations. However, many of these differential equations have the property that they are sensitive to the choice of initial conditions. If one instead has snapshots of a system, i.e. data, one can make a more educated guess at the true state by incorporating the data via data assimilation. Many of the most popular data assimilation methods were developed for general physical systems. However, in the context of fluids, data assimilation works better than would be anticipated for a general physical system. In particular, turbulent fluid flows have been proven to have the property that, given enough perfect observations, one can recover the full state irrespective of the choice of initial condition. This property is surprisingly unique to turbulent fluid flows, a consequence of their finite dimensionality. In this presentation, we will discuss the continuous data assimilation algorithm that was used to prove the convergence in the original, perfect data setting, present various robustness results of the continuous data assimilation algorithm, and discuss how continuous data assimilation can be used to identify and correct model error. Finally, we will make connections to modern sophisticated data assimilation algorithms and discuss future theoretical and practical directions of modern data assimilation.

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