Nonlinear/Non-Gaussian Data Assimilation

Data and models, with their inherent uncertainties and errors, are blended within a Bayesian framework with the aim of improving estimates of dynamic processes. This process, called {\it data assimilation}, is said to be responsible for significantly better weather/climate forecasts. Nonlinear/non-Gaussian processes, however, pose special conceptual and computational challenges. In the context of generic transport problems of importance in climate and weather a strategy which I have been investigated involves adding physically based constraints, leading to smaller but higher quality ensembles with which to produce estimates. I will describe some of the tradeoffs and their implications on filtering and forecasting.