Data Assimilation and Uncertainty Quantification in the Geosciences*

Data assimilation is the name commonly given to the estimation process that
generates moments of probability density functions of time dependent processes
modeled by physics, and observations. The inherent uncertainties of model and data
are taken into account using a Bayesian framework. Data assimilation is presently
used in applications as diverse as weather forecasting and spacecraft navigation.
I will appeal to familiar statistical physics to present the general methodoloy. I will
briefly descirbe a couple of computational implementations of the method
summarize some of the key research challenges that arise in their application.
I will also describe some novel applications of the methodology, potentially
useful in tracking targets, hurricanes, and ongoing research in the application
of stochastic parametrization and machine learning for the purpose
of dimension reduction.