Random renormalization groups and Bayesian scaling of dispersion/diffusion in Lake Michigan and the Gulf of Mexico

Abstract

A random renormalization group technique is reviewed, and a related set of Bayesian scaling techniques are presented. The techniques are employed to study the motion of drifters in Lake Michigan on a time scale ranging from 30 min to 5 days and in the Gulf of Mexico on a time scale ranging from 8 h to 85 days. The scaling laws generalize the standard power law scalings. One of the advantages of the Bayesian approach is that scaling laws can be determined even with a paucity of data with the caveat that less data produce greater uncertainty in the scaling laws. Key Points Lagrangian data can be assimilated to determine scaling laws Subsurface drifters in the Gulf o Mexico are superdiffusive for at least 85 days Dispersion is superdiffusive in Lake Michigan for at least 4 hours to 5 days ©2013. American Geophysical Union. All Rights Reserved.