Go With the Flow, on Jupiter and Snow. Coherence From Model-Free Video Data without Trajectories

TL;DR

This paper introduces a novel image processing approach to identify coherent structures in fluid systems directly from image data, without requiring flow models or trajectories, applicable to planetary clouds and weather phenomena.

Contribution

It develops an anisotropic, directed diffusion operator based on a directed affinity matrix, extending spectral graph theory to analyze coherence from image data without vector fields.

Findings

Successfully applied to Jupiter cloud patterns

Effectively identified coherence in snow events on Earth

Validated with double-gyre benchmark system

Abstract

Viewing a data set such as the clouds of Jupiter, coherence is readily apparent to human observers, especially the Great Red Spot, but also other great storms and persistent structures. There are now many different definitions and perspectives mathematically describing coherent structures, but we will take an image processing perspective here. We describe an image processing perspective inference of coherent sets from a fluidic system directly from image data, without attempting to first model underlying flow fields, related to a concept in image processing called motion tracking. In contrast to standard spectral methods for image processing which are generally related to a symmetric affinity matrix, leading to standard spectral graph theory, we need a not symmetric affinity which arises naturally from the underlying arrow of time. We develop an anisotropic, directed diffusion operator corresponding to flow on a directed graph, from a directed affinity matrix developed with coherence in mind, and corresponding spectral graph theory from the graph Laplacian. Our methodology is not offered as more accurate than other traditional methods of finding coherent sets, but rather our approach works with alternative kinds of data sets, in the absence of vector field. Our examples will include partitioning the weather and cloud structures of Jupiter, and a local to Potsdam, N.Y. lake-effect snow event on Earth, as well as the benchmark test double-gyre system.