Regression analysis of macroscopic tsunami intensity and offshore wave height in the Mediterranean Sea

Abstract. Quantifying the physical dimensions of historical tsunamis is fundamental for validating hazard models and informing coastal risk management. However, pre-instrumental records predominantly consist of qualitative descriptions from which macroscopic intensity are defined to quantify the size of the tsunami. In this study, we present the first empirical, statistically robust, and fully invertible relationship linking local macroscopic tsunami intensity to shoreline wave height. By coupling a simplified 1D onshore hydraulic propagation model with high-resolution coastal transects and local roughness constraints, we homogenized observation metrics (run-up and inundation distance) into a consistent wave height reference for three benchmark Mediterranean events: the 1908 Messina Strait, the 2002 Stromboli, and the 2020 Aegean Sea tsunamis. Applying Orthogonal Distance Regression (ODR) to account for uncertainties in both dependent and independent variables, we defined a linear scaling law applicable to any existing historical observation. The relationship is validated against existing observations and subsequently applied to the Italian Tsunami Effects Database (ITED), which collects all the tsunami effects observed along the Italian coasts since 79 AD, reconstructing the tsunami history of Italian coasts and establishing an empirical bridge between historical qualitative archives and modern tsunami modelling and hazard assessments.