Spatiotemporal Modeling of Marine Heatwave Propagation: A Physics-Informed Mathematical Framework.

Source abstract

Marine heatwaves (MHWs) are persistent ocean-temperature extremes whose impacts depend on both intensity and spatial evolution. In this paper, we present a compact mathematical framework for detecting and tracking surface MHW propagation and for constructing physics-informed forecasts. A percentile-based exceedance mask defines local events, connected components represent spatial objects, and a deterministic overlap--displacement rule preserves object identity through translation, splitting, and merging. Propagation is linked to a depth-averaged advection--diffusion heat-budget equation with transport, forcing, entrainment, and an unresolved residual. A physics-informed correction retains the governing balance as a constraint. Verification uses exact advection--diffusion solutions, while validation uses object overlap, centroid, intensity, and calibration metrics.