A Convolution Process for Sea Surface Temperature Hot-Spot Identification in the Mediterranean Sea

40/2026

A Convolution Process for Sea Surface Temperature Hot-Spot Identification in the Mediterranean Sea

Thursday 28th May 2026

Marchesin, L.; Menafoglio, A.; Secchi, P.

Sea surface temperature (SST) is a fundamental determinant of global climate dynamics and economic activity. Reliable projections of future SST patterns depend critically on a rigorous characterization of the underlying spatial random field. In this study, we introduce a novel convolution-based covariance framework tailored to geostatistical domains constrained by physical barriers and influenced by vector-driven flows. By discretizing the continuous marine domain into a directed linear network that preserves the orientation of ocean currents, we construct a moving-average stochastic process whose dynamic is encoded via a Markovian transitionprobability matrix on the network’s vertices. The induced covariance structure emerges as a weighted combination of a spatial kernel and flow-dependent weights, giving rise to a complex estimation problem. To stabilize inference, we propose a penalized estimator that regularizes covariance parameters while enforcing consistency with known hydrodynamic properties. We then embed this covariance model into a Monte Carlo simulation framework to refine RCPbased SST projections and to identify thermal “hot spots” of heightened ecological risk. Our approach delivers a statistically principled framework that prevents physical inconsistencies – such as correlations across land barriers – providing a robust basis for quantifying uncertainty in future SST forecasts and for guiding targeted environmental assessments.