Decoding the spatial spread of cyanobacterial blooms in an epilimnion

Cyanobacterial blooms (CBs) pose significant global challenges due to their harmful toxins and socio-economic impacts, with nutrient availability playing a key role in their growth, as described by ecological stoichiometry (ES). However, real-world ecosystems exhibit spatial heterogeneity, limiting the applicability of simpler, spatially uniform models. To address this, we develop a spatially explicit partial differential equation model based on ES to study cyanobacteria in the epilimnion of freshwater systems. We establish the well-posedness of the model and perform a stability analysis, showing that it admits two linearly stable steady states, leading to either extinction or a spatially uniform positive equilibrium where cyanobacterial biomass stabilizes at its carrying capacity. Further, we discuss the possibility of long-term spatially nonuniform solution with small diffusion and space-dependent parameters. We use the finite elements method (FEM) to numerically solve our system on a real lake domain derived from Geographic Information System (GIS) data and realistic wind conditions extrapolated from ERA5-Land. Additionally, we use a cyanobacteria estimation (CE) obtained from Sentinel-2 to set initial conditions, and we achieve strong model validation metrics. Our numerical results highlight the importance of lake shape and size in bloom monitoring, while global sensitivity analysis using Sobol Indices identifies light attenuation and intensity as primary drivers of bloom variation, with water movement influencing early bloom stages and nutrient input becoming critical over time. This model supports continuous water-quality monitoring, informing agricultural, recreational, economic, and public health strategies for mitigating CBs.