Permutation entropy reveals coherent structures and ecological boundaries in North Atlantic phytoplankton blooms

We apply ordinal-pattern analysis and permutation entropy (PE) to satellite-derived chlorophyll-a (Chl-a), sea surface temperature (SST), and mixed-layer depth (MLD) data to investigate the spatiotemporal dynamics of the North Atlantic phytoplankton spring bloom. Using both temporal and spatial versions of PE, together with mutual information-based functional networks, we identify coherent dynamical regimes and ecological boundaries that are difficult to detect with classical linear methods. Temporal PE at the annual time scale reveals two well-separated low-entropy regions corresponding to the North Atlantic Subtropical and Subpolar Gyres, divided by a sharp zonal boundary consistent with a transition between light-limited and nutrient-limited phytoplankton regimes. Area-Weighted Connectivity maps further suggest that the Subpolar bloom region is itself divided into two dynamically distinct subregions in the Labrador and Irminger Seas. Analysis of spatial PE uncovers a characteristic entropy-chlorophyll cycle in which bloom growth occurs during periods of high spatial disorder, while the recession phase is associated with the emergence of large-scale meridional Chl-a gradients. Mutual information between Chl-a and physical drivers reveals seasonal, predominantly non-linear coupling with SST and MLD, with SST exhibiting a significant negative correlation during spring and autumn and MLD showing surprisingly weak local control during the bloom phase. Our results demonstrate the potential of ordinal-pattern methods as a complementary, model-free framework for characterizing the interplay between ocean physics and marine ecosystem dynamics from remote sensing observations.