the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Oct 2026
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.
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Status: open (until 13 Nov 2026)
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AC1: 'Higher quality figures of egusphere-2026-5023', Jacopo Selva, 09 Oct 2026
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RC1: 'Reply on AC1', Gerasimos Papadopoulos, 27 Oct 2026
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-5023/egusphere-2026-5023-RC1-supplement.pdf
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AC2: 'Reply on RC1', Jacopo Selva, 10 Nov 2026
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Dear Gerasimos
Thank you for your thorough revision. We completely agree with all points. Effectively, we missed the reference Papadopoulos and Fokaefs (2005, hereinafter PF05), and we apologize for this. The method we selected is substantially different from the one adopted in PF05. However, PF05 and our model have a similar goal, and we fully agree that it is fundamental to revise our manuscript fully acknowledging the contribution of PF05 and adding a thorough comparison of the results. We already started working in this direction. In attachment, you can find a preliminary report in which we discuss the main methodological differences along with the results of our preliminary comparison.
Thank you again,
Jacopo Selva in behalf of all co-authors
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AC2: 'Reply on RC1', Jacopo Selva, 10 Nov 2026
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RC1: 'Reply on AC1', Gerasimos Papadopoulos, 27 Oct 2026
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RC2: 'Comment on egusphere-2026-5023', Anonymous Referee #2, 06 Nov 2026
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I like the Manuscript by Selva et al. and very much encourage the idea to build a quantitative relationship between the macroscopic tsunami intensity on land and wave height at the shoreline – a dream of many tsunami modellers who face the gap between what they can model – wave height – and what is available for past historical events -- scarce on-land observations often expressed by means of (rather qualitative) intensity scale. To that end, current Manuscript indeed represents an important step providing modeling community with a very useful tool. Accuracy of the tool is not perfect, sigma of log(H) is equal to 0.25 which, for two sigmas, corresponds to factor 3 in wave heights. That’s nevertheless is a good result, taking into account all the inevitable uncertainties of various nature behind the method.
That said, I strongly recommend this manuscript for publication and would recommend publishing with minor revisions.
My only point that shall be treated as recommendation, not as request, is following. As retrospectively estimated wave heights along the Italian coasts (Fig. 8) to some extent represent tsunami history of the region, it may sound tempting to compare inferred «historical» wave heights against the predictions of the NEAMTHM18 PTHA model for the corresponding return periods. Shall such a comparison be considered as a generic validation of the newly proposed method or, instead, rather as validation of the NEAM PTHA model itself – I’d leave this decision to Authors. I believe such an exercise may further increase the added value of this, already highly valued, publication.
Below are couple of specific comments.
L33: «sold»: should be «solid»
L35: «events rare»: should be «rare events»
L36: provide link/reference to the Global Historical Tsunami Database
L90-93, Figure 1 caption: the scheme is not fully described. E.g., what the arrow labeled as «v^2/2g» stays for? Is it energy lost due to the velocity reduction? Since neither Sf, nor V are further mentioned in Eq. 2, consider removing them from the sketch. Or better describe the model of inundation.
L99: should be: «Fig.1b»
L99: accordiing to Fig: «S0», not «S»
L124: «offshore wave height»: maybe «wave height at the coastline»?
L135: check if Glimsdahl 2019 is a right reference for onshore propagation model (reflection wall b.c.)
L145: from wave height where? At the coastline?
L201: «several cross-sections»?
L275-280, Figure 3: would be great if Authors could also show calculation uncertainties for runups or ingressions. Using error bars, for example? I mean the total assessed uncertainty which may arise from all the possible sources like accuracy of the Google topo model (within 2 m), local topo lateral variations(?), uncertainty by a-value assumption(?), etc. Just to have idea on the calculated accuracy.
L265: inside equation 2, not 4?
L273: comma instead of a period
Figure 4b: SOR instead of SQR on plot. Also probably «simple» instead of «standard».
Lines 323 and below: what is «ODR»? Is ODR = SOL? Please check and unify your abbreviations.
Line 344: two times «parameters»
Line 394: suggest to add «… for all the three cases».
Line 404: instead of «are not large» better «are small»?
Line 410: «… generally larger for SOR...» -- I cannot see that. Uncertainties are generally the same with the only exception for Stromboli case.
Figure 6, Titles both (a) and (b): should be: «...excluding flagged»
Figure 5 and 5 captions: When mentioning «wave height», specify -- where this wave height is measured. Even it was said many times in the text, still makes sense to define this metric again and again in captions.
L424: suggest to insert «(Figure 7b)» after the words «function of the intensity»
L428: «Figure 7b» – no. Probably, Authors mentioned Fig. 6b.
L459: add space between «.U».
L460: «to estimate wave height» -- indicate once again: where wave height is going to be estimated: at the shoreline.
L469: provide reference to ITED
Citation: https://doi.org/10.5194/egusphere-2026-5023-RC2
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We attach here a PDF including all figures and captions with a resolution higher than the one reported in the preprint.