Comparison between Eulerian diagnostics and finite-size Lyapunov exponents computed from altimetry in the Algerian basin

TL;DR

This study compares Eulerian and Lagrangian diagnostics, specifically finite-size Lyapunov exponents, in analyzing surface current transport and mixing in the Algerian basin using altimetric data, revealing their complementary strengths.

Contribution

It demonstrates that Lagrangian tools like Lyapunov exponents can detect mesoscale filaments and submesoscale stirring, providing insights beyond traditional Eulerian diagnostics.

Findings

Lyapunov exponents predict filamentary processes along the Algerian current.

Both diagnostics yield similar results for slowly evolving eddies.

Lyapunov exponents reveal submesoscale structures not captured by Eulerian diagnostics.

Abstract

Transport and mixing properties of surface currents can be detected from altimetric data by both Eulerian and Lagrangian diagnostics. In contrast with Eulerian diagnostics, Lagrangian tools like the local Lyapunov exponents have the advantage of exploiting both spatial and temporal variability of the velocity field and are in principle able to unveil subgrid filaments generated by chaotic stirring. However, one may wonder whether this theoretical advantage is of practical interest in real-data, mesoscale and submesoscale analysis, because of the uncertainties and resolution of altimetric products, and the non-passive nature of biogeochemical tracers. Here we compare the ability of standard Eulerian diagnostics and the finite-size Lyapunov exponent in detecting instantaneaous and climatological transport and mixing properties. By comparing with sea-surface temperature patterns, we find that the two diagnostics provide similar results for slowly evolving eddies like the first Alboran gyre. However, the Lyapunov exponent is also able to predict the (sub-)mesoscale filamentary process occuring along the Algerian current and above the Balearic Abyssal Plain. Such filaments are also observed, with some mismatch, in sea-surface temperature patterns. Climatologies of Lyapunov exponents do not show any compact relation with other Eulerian diagnostics, unveiling a different structure even at the basin scale. We conclude that filamentation dynamics can be detected by reprocessing available altimetric data with Lagrangian tools, giving insight into (sub-)mesoscale stirring processes relevant to tracer observations and complementing traditional Eulerian diagnostics.