Research: Data assimilation and prediction in geophysical fluid dynamics.
Due to the lack of precise information in many fronts (initial state, physical processes etc), or the impossibility of fully
processing the available (otherwise necessary) information in due time, the prediction of future states of an evolutive
system is a stochastic initial value problem. Particle Filters is a class of Sequential Monte-Carlo numerical methods for
filtering problems with stochastic equations. The major drawbacks of such methods are the demand for tracing large
sets of stochastic paths and the lack of an adequate admissible definition of prediction in nonlinear problems. I work
on partial fixes to this. Some proposals are currently being tested for the assimilation of Lagrangian data into oceanic
models.
Papers:
- "Data assimilation through particle filters for small diffusion kernels within branches of prediction"; submitted.
- "Dimensional reduction for a Bayesian filter"; w/ A. J. Chorin; Proceedings of the National Academy of Science of USA,
101:42 (2004) pp. 15013-15017.
