A Computational Study of the Nudging Approach to Data Assimilation

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This work develops and tests new approaches to assimilating data into mathematical models to achieve more accurate prediction, for example in weather forecasts. The novelty is to consider data that is (a) concentrated in a small region (as over a metropolitan area), (b) moving (as from satellites, commercial airplanes, cars, even cell phones), and (c) from easily-measured quantities, such as atmospheric pressure. Numerical experiments will be supported by rigorous mathematical analysis.This work involves computational projects that tie together data assimilation, determining forms, and turbulence. The data assimilation is by nudging, an approach that has proven to be conducive to rigorous mathematical analysis but has undergone much less computational testing than have Kalman filters. Nudging is closely related to determining forms, ordinary differential equations in trajectory spaces that capture the global attractors of systems such as the Navier-Stokes equations of fluid flow. Such systems are expected to display turbulent behavior, which raises a particular set of computational issues addressed by this research.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.