ABSTRACT

Data assimilation is the process of combining observed data with a physical model. At the heart of this methodology is Bayes Theorem, a massive linear algebra problem and a Monte Carlo approximation known as a particle filter. Besides providing forecasts, data assimilation is also a valuable tool for understanding the limitations of a particular numerical model and identifying components for improvement. Although one important use of data assimilation is in numerical weather prediction, its implementation is difficult due to the nonlinear dynamics of the atmosphere, the sheer size of the problem and resulting non-Gaussian distributions. Our work implements an approximate Bayesian method given the practical constraints of operational weather forecasting. We describe a new approach that is both local in state space and local in observation space. This Local-Local Ensemble filter has the potential to handle non-Gaussian distributions and also high dimensional state vectors.

See:

A nonlinear filter that extends to high dimensional systems, Thomas Bengtsson, Chris Snyder, Doug Nychka, (2003) http://www.gcd.ucar.edu/stats/pub/nychka/manuscripts/JGRrevision.pdf