UVic Dynamics Seminar: Elizabeth Carlson

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. Unfortunately, the development of data assimilation methods has not actively take this finite dimensionality into account, as it has been developed independent of a considered system. This will be an informal presentation of what I currently understand with regards to data assimilation, both statistical and continuous methods. In particular, I will highlight the difficulties in equating the existing methods, and where these difficulties are presenting themselves in current research directions.