Spatial inference for coherent geophysical fluids by appearance and geometry

In geophysical spatial inference, imperfect model predictions are combined with noisy, sparse measurements to estimate spatial fields better than either source alone. In addition to changing brightness appearance, fields with coherent structures are readily perceived as deforming patterns. Often ignored, the failure to assimilate pattern information leads to poor spatial estimates. Here, a Bayesian inference problem in appearance and geometry is formulated for coherent fluids and a practical application of deformable models is synthesized. The proposed estimation approach uses a Gabor basis and stochastic optimization incorporating fluid dynamical balance to produce parsimonious non-local deformation solutions in deterministic or ensemble settings. Using this approach, the supervised spatial field estimation and the unsupervised mean field estimation problems are solved, with application to meteorological Data Assimilation, Ensemble Analysis and Nowcasting.