The Shadow of Truth

Kevin Judd

University of Western Australia

Shadowing is technique that has been developed by taking a dynamical systems view of the problem of data assimilation. Shadowing tries to find solutions of a forecasting model that are consist with past observations, because clearly one cannot forecast the future unless one can shadow the past. One of the advantages of shadowing is that it exploits the nonlinear dynamics to extract information from data. The shadowing approach emphasises the dynamical and geometric aspects of data assimilation, rather than statistical aspects, which may be less important than are generally assumed.

I intend to outline the theory behind shadowing and illustrate its application in both low dimensional chaotic dynamical systems and operational weather forecasting models using real observations. I will argue, using these examples, that geometrical analysis of shadowing results can reveal important connections between a model's attractor and model error.

Last Update: May 24, 2005