EVENT: Applied Mathematics Seminar

Shadowing is used here in the broad sense of finding solutions of a forecast model that are consistent with observations. Clearly one cannot expect to make 4 day forecasts unless one can reliably shadow 4 days of past observations. The original notion of shadowing entered dynamical systems theory in 1960s as a method to obtain theoretical results. In the 1990s it was recognised that a gradient descent method could obtain shadowing trajectories and hence be used in filtering signals of nonlinear systems. In the last 5 years or so I have been collaborating with others to develop shadowing ideas into a more extensive theory. Shadowing methods can, for example, provide fully nonlinear state estimation methods that surpass the extended Kalman filter, and are more efficient than Bayesian particle filters. More importantly, shadowing methods generalise to the imperfect model scenario, the only realisable scenario. In this talk I will attempt to outline the methods and illustrate how they are providing new insights into the nature of model error in an operational weather forecasting model.