On the equivalence between Singularity Exponents and Finite Size Lyapunov Exponents

GHRSST talk of 20th April 2023.

On the equivalence between Singularity Exponents and Finite Size Lyapunov Exponents

Exponents in remote sensed images of the ocean. Horizontal transport and mixing processes are key to properly understand changes in the global ocean. Finite Size Lyapunov Exponents characterise the rate of separation of infinitesimally close trajectories and therefore provide information of the dispersion processes and the Lagrangian Coherent Structures (i.e. transport barriers and fronts). In order to estimate the Finite Size Lyapunov Exponents (and also Finite Time Lyapunov Exponents), a sequence long enough of the velocity field is required. The Singularity Exponents are a dimensionless measure of the degree of regularity or irregularity of a function at each point of its domain. The estimation of the Singularity Exponents is related to the multifractal properties of any ocean scalar satellite image and then no velocity field is required. Numerical estimations of Singularity Exponents show evidence that different ocean scalars present the same Singularity Exponents and that they coincide with the streamlines of the fow. This in particular means that we can estimate the streamlines from the Singularity Exponents derived from Sea Surface Temperature maps. Here we explore the possibility of computing the Finite Size Lyapunov Exponents without the need of any velocity field. For this we numerically analyse one year of satellite ocean images of Absolute Dynamic Topography and Sea Surface Temperature. Numerical estimations show a linear relationship between the Singularity Exponents and the Finite Size Lyapunov Exponents which is more robust in the case of the Singularity Exponent from Sea Surface Temperature than in the case of the Absolute Dynamic Topography. In the talk, we plan to discuss the causes of these differences and the steps forward to address this equivalence from a theoretical point of view.

Recordings:  https://www.ghrsst.org/meetings/20-april-2023-lluisa-puig-moner-on-the-equivalence-between-singularity-exponents-and-finite-size-lyapunov-exponents/