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

TL;DR

This paper introduces a convolution-based covariance model for sea surface temperature analysis in the Mediterranean, accounting for physical barriers and ocean flows to improve future SST projections and hot-spot detection.

Contribution

It presents a novel flow-aware covariance framework using a directed network and penalized estimation, enhancing geostatistical modeling of SST with physical constraints.

Findings

The model accurately captures flow-dependent spatial correlations.

It improves SST hot-spot identification and uncertainty quantification.

The approach prevents unrealistic correlations across land barriers.

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.