Statistical Theory of Inference for Coherent Structures (STICS): Perceptual Organization of Coherent Fluids

Coherence is a ubiquitous feature of natural phenomena in general and of geophysical fluids in particular. Reflecting many elements of the underlying flow, the appearance and geometry of coherent structures and their apparent dynamics are often used as descriptors of the fluid's evolution. They are even used in simulation (e.g., smooth particle hydrodynamics or vortex methods). However, we don't quite understand how to use them for inference.

A Statistical Theory of Inference for Coherent Structures (STICS) is proposed, wherein fluids are organized as a spatial distribution of position-amplitude-scale features of the variables, including any embedded dynamical relationships. Features at preferred locations, amplitudes and scales are analysed from physical fields, which we call Generalized Coherent Structures (GCS), because they don't just contain position information but amplitude and scale as well. The sparse GCS are updated in response to observations, for example, using non-Gaussian data assimilation, and the fluid is synthesized as smooth, dynamically-sound reconstructions from the sparse features.

Preceding this approach was the observation that, for coherent phenomena, position (deformation) is important. This led to a new formulation for Data Assimilation, for calculating the ensemble mean, quantifying uncertainty, EOF/POD analysis and downscaling, among others documented on this site. The applications are truly broad. Here you will find methodology for synthesis, analysis and inference and their applications, along with codes.