EXTENDED KALMAN FILTERING FOR VORTEX SYSTEMS - PART-I - METHODOLOGY AND POINT VORTICES

Planetary flows-atmospheric and oceanic-are approximately two-dimensio nal and dominated by coherent concentrations of vorticity. Data assimi lation attempts to determine optimally the current state of a fluid sy stem from a limited number of current and past observations. In this t wo-part paper, an advanced method of data assimilation, the extended K alman filter, is applied to the Lagrangian representation of a two-dim ensional flow in terms of vortex systems. Smaller scales of motion are approximated here by stochastic forcing of the vortices. In Part I, t he systems studied have either two point vortices, leading to regular motion or four point vortices and chaotic motion, in the absence of st ochastic forcing, Numerical experiments are performed in the presence or absence of stochastic forcing. Point-vortex systems with both regul ar and chaotic motion can be tracked by a combination of Lagrangian ob servations of vortex positions and of Eulerian observations of fluid v elocity at a few fixed points, Dynamically, the usual extended Kalman filter tends to yield insufficient gain if stochastic forcing is absen t, whether the underlying system is regular or chaotic. Statistically, the type and accuracy of observations are the key factors in achievin g a sufficiently accurate flow description. A simple analysis of the u pdate mechanism supports the numerical results and also provides geome trical insight into them. In Part II, tracking of Rankine vortices wit h a finite core area is investigated and the results are used for obse rving-system design. (C) 1997 Elsevier Science B.V.