Maybe you have seen the singularity exponents maps we are offering in this CP34-BEC data server. Singularity analysis is a technique for estimating, at any point, the singularity exponent of a signal. Singularity exponents, usually denoted by h, are dimensionless variables providing information about the local regularity (if positive) or irregularity (if negative) of the signal at any given point. When h is integer it means that the function has h continuous derivatives, while non-integer values indicate a more complex topological situation.
Why should we be interested in such a mathematical, abstract concept? Because if a flow exhibits horizontal turbulence – and the ocean is a quasi-2D turbulent flow at scales greater that a few kilometers – singularity exponents derived from any ocean scalar are the same and, in fact, they represent the streamlines of the flow! (Turiel et al., Physical Review Letters, 2005; Isern-Fontanet et al, Journal of Geophysical Research, 2007; Nieves et al, Geophysical Research Letters, 2007; Turiel et al., Remote Sensing of Environment, 2008; Turiel et al., Ocean Science, 2009).