Non-Parametric Ensemble Analyses with Examples from Advective Flow Data Assimilation
If observations are sufficiently infrequent relative to the advective time-scale, significantly nonlinear and non-gaussian distributions occur when doing ensemble data assimilation for geophysical systems. With current observing networks, many important mesoscale atmospheric (and oceanic) events are in this regime. While standard ensemble filter methods are surprisingly robust for some mesoscale applications, more general methods that can deal explicitly with nonlinearity and non-gaussianity have been demonstrated to lead to improved analyses and forecasts. However, many of these methods are extremely costly or difficult to apply.
An extension of a scalar non-parametric ensemble data assimilation technique, the rank histogram filter, to a multivariate method is described. With a sufficiently large ensemble, this method can represent arbitrary distributions and produce accurate non-gaussian analyses of the marginal distribution for any state variable. However, the method struggles in representing analysis multivariate distributions. Approaches similar to the use of proposal densities for particle filters show promise in addressing this deficiency. There is potential to combine these extended rank histogram methods with particle filters to create methods with the strengths of both that may avoid many of the scaling challenges of the particle filters. The methods are illustrated with simple advective flows that are directly relevant to mesoscale analysis.
Dr. Jeffrey Anderson National Center for Atmospheric Research