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

2026-05-06

Abstract

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 transition-probability 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 RCP-based 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.

Problem

• sea surface temperature
• hot-spot identification
• spatial covariance
• geostatistics
• ocean currents

Innovation

• convolution-based covariance
• directed linear network
• Markovian transition-probability matrix
• penalized estimator
• SST hot-spot identification