Finite Size Lyapunov Exponents on the Patagonian shelf and their role in retaining phytoplankton blooms

Abstract: Finite Size Lyapunov Exponents (FSLEs) were calculated from daily satellite-derived velocity fields (spatial resolution ~0.25°) to identify Lagrangian coherent structures, which indicate regions of strong frontal activity and water mass convergence. The FSLE images were obtained from AVISO satellite altimetry data (https://www.aviso.altimetry.fr). FSLE ridges correspond to transport fronts that can retain phytoplankton blooms by attracting and advecting passive particles along them. This video shows daily FSLE ridge dynamics from November 10 to 25, 2021, in the Patagonian Shelf region of the southwestern Atlantic (44°S–47.5°S and 60.5°W–64°W), where a phytoplankton bloom occurred. The sampling locations were: a pink dot, sampled on November 16 onboard the R/V Bernardo Houssay (Argentina) during the Gayoso expedition; and a blue dot, sampled on November 25 onboard the R/V Víctor Angelescu (Argentina) during the Agujero Azul expedition. Both stations remained within the same water mass, separated by two FSLE maxima. This video corresponds to the supplementary material for the publication Guinder et al. (2025), Extraordinary bloom of toxin-producing phytoplankton enhanced by strong retention on the offshore Patagonian shelf, published in Biogeosciences.  Guinder VA, Tillmann U, Rivarossa M, Ferronato C, Ramírez FJ, Krock B, Gu H, Saraceno M (2025) Extraordinary bloom of toxin-producing phytoplankton enhanced by strong retention on the offshore Patagonian shelf. Biogeosciences. EGUsphere [preprint], https://doi.org/10.5194/egusphere-2024-3157.   
Methodology:
Finite Size Lyapunov Exponents (FSLEs) were calculated to analyze surface flow dynamics in the study area. The FSLE images used have a spatial resolution of approximately 0.25°, and were obtained from AVISO satellite altimetry data (https://www.aviso.altimetry.fr, last accessed TS11). FSLEs approximate Lagrangian Coherent Structures (LCS), which generalize stable hyperbolic trajectories in time-independent flows. Mathematically, FSLEs correspond to the largest eigenvalues of the Cauchy–Green strain tensor derived from the flow map. FSLE values represent the exponential rate, λ (d⁻¹), at which two neighboring fluid particles separate during advection time t, defined as:
λ=1/t x log(δf/​δ0​​)
where δ0 and δf are the fixed initial and final separation distances between particles.
High FSLE values are indicators of frontal activity and stirring intensity in the ocean. Positive maxima (ridges) of FSLEs correspond to convergent transport fronts, where passive particles are attracted and advected along the front. Conversely, negative FSLE values indicate divergent dynamics, promoting particle dispersion away from the front. To study meso- and submesoscale frontal structures during the phytoplankton bloom, daily FSLE images from November 10 to 25, 2021, were analyzed. These daily data were used to create a video illustrating the temporal evolution of FSLE ridges in the bloom region.