Uncertainty in Manning’s roughness coefficient in multilevel simulations of future tsunamis in Sumatra

Kaiyu Li; Dimitra M. Salmanidou; Devaraj Gopinathan; Mohammad Heidarzadeh; Serge Guillas

doi:10.1098/rspa.2024.0637

Uncertainty in Manning’s roughness coefficient in multilevel simulations of future tsunamis in Sumatra

Kaiyu Li, Dimitra M. Salmanidou, Devaraj Gopinathan, Mohammad Heidarzadeh, Serge Guillas

University College London

Research output: Contribution to journal › Article › peer-review

Abstract

We employ multilevel Bayesian quadrature (MLBQ) to quantify uncertainties in the land cover roughness, a critical but unknown parameter for simulation of structural forces from future tsunamis that inform coastal engineering and urban planning. To account for this uncertainty, we regard roughness as a nuisance parameter and integrate out its effects on the maximum momentum flux. A comprehensive integration over a range of roughness requires large numbers of computationally expensive simulations. We circumvent this hurdle using multilevels of resolution for the simulations, a mix of two levels of mesh sizing for underlying non-uniform unstructured mesh—a low (50 m) and high (25 m) resolution. The computational burden of the overall integration is further reduced by blending the outputs of the multilevel simulations using Bayesian quadrature. Using end-to-end physical and numerical modelling to simulate the entire tsunami life-cycle—earthquake source to coastal inundation—we illustrate our approach by computing probability distributions of local effects from future large tsunamis for Sumatra. Our MLBQ framework, accounting for uncertainties in roughness while reducing computational burden, can improve probabilistic hazard and risk assessments in combination with other uncertainties.

Original language	English
Article number	20240637
Journal	Proceedings of the Royal Society A
Volume	481
Issue number	2316
Early online date	25 Jun 2025
DOIs	https://doi.org/10.1098/rspa.2024.0637
Publication status	Published - 30 Jun 2025

Data Availability Statement

The code and data for this implementation are available at [43] and [44].

Acknowledgements

This work was performed using resources provided by the Cambridge Service for Data Driven Discovery (CSD3) operated by the University of Cambridge Research Computing Service (www.csd3.cam.ac.uk), provided by Dell EMC and Intel using Tier-2 funding from the EPSRC (capital grant EP/T022159/1), and DiRAC funding from the Science and Technology Facilities Council (www.dirac.ac.uk). The authors would like to thank Jack Dignan for his help with the visualization of figure 12, and Daniel Giles for helpful discussions. Geospatial figures were created using The Generic Mapping Tools version 6 [45].

Funding

We acknowledge funding from the Lloyds Tercentenary Research Foundation, the Lighthill Risk Network and the Lloyds Register Foundation-Data Centric Engineering Programme of the Alan Turing Institute. S.G. was funded by EPSRC project EP/W007711/1 Software Environment for Actionable and VVUQevaluated Exascale Applications (SEAVEA). M.H. was partly funded by the Royal Society, the United Kingdom, grant number CHL/R1/180173. D.G. was supported by the EPSRC Impact Acceleration Account (IAA) award to UCL 2017-2022 (grant no. EP/R511638/1), and 2022-25 (grant no. EP/X525649/1). This work was performed using resources provided by the Cambridge Service for Data Driven Discovery (CSD3) operated by the University of Cambridge Research Computing Service (www.csd3.cam.ac.uk), provided by Dell EMC and Intel using Tier-2 funding from the EPSRC (capital grant EP/T022159/1), and DiRAC funding from the Science and Technology Facilities Council (www.dirac.ac.uk). The authors would like to thank Jack Dignan for his help with the visualization of figure 12, and Daniel Giles for helpful discussions. Geospatial figures were created using The Generic Mapping Tools version 6 [45]. This work was performed using resources provided by the Cambridge Service for Data Driven Discovery (CSD3) operated by the University of Cambridge Research Computing Service ( www.csd3.cam.ac.uk ), provided by Dell EMC and Intel using Tier-2 funding from the EPSRC (capital grant EP/T022159/1), and DiRAC funding from the Science and Technology Facilities Council ( www.dirac.ac.uk ). The authors would like to thank Jack Dignan for his help with the visualization of , and Daniel Giles for helpful discussions. Geospatial figures were created using The Generic Mapping Tools version 6 []. We acknowledge funding from the Lloyd\u2019s Tercentenary Research Foundation, the Lighthill Risk Network and the Lloyd\u2019s Register Foundation-Data Centric Engineering Programme of the Alan Turing Institute. S.G. was funded by EPSRC project EP/W007711/1 \u2018Software Environment for Actionable & VVUQ-evaluated Exascale Applications\u2019 (SEAVEA). M.H. was partly funded by the Royal Society, the United Kingdom, grant number CHL/R1/180173. D.G. was supported by the EPSRC Impact Acceleration Account (IAA) award to UCL 2017-2022 (grant no. EP/R511638/1), and 2022-25 (grant no. EP/X525649/1). Acknowledgements

Funders	Funder number
Science and Technology Facilities Council
Science and Technology Facilities Council
SEAVEA
Lloyd's Tercentenary Research Foundation
Alan Turing Institute
Lighthill Risk Network
Royal Society	EP/R511638/1, CHL/R1/180173, EP/X525649/1, 2022-25
Engineering and Physical Sciences Research Council	EP/T022159/1, EP/W007711/1

Keywords

coastal engineering
friction
hazard assessment
multifidelity
probabilistic numerics
uncertainty quantification

ASJC Scopus subject areas

General Mathematics
General Engineering
General Physics and Astronomy

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10.1098/rspa.2024.0637Licence: CC BY

Cite this

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abstract = "We employ multilevel Bayesian quadrature (MLBQ) to quantify uncertainties in the land cover roughness, a critical but unknown parameter for simulation of structural forces from future tsunamis that inform coastal engineering and urban planning. To account for this uncertainty, we regard roughness as a nuisance parameter and integrate out its effects on the maximum momentum flux. A comprehensive integration over a range of roughness requires large numbers of computationally expensive simulations. We circumvent this hurdle using multilevels of resolution for the simulations, a mix of two levels of mesh sizing for underlying non-uniform unstructured mesh—a low (50 m) and high (25 m) resolution. The computational burden of the overall integration is further reduced by blending the outputs of the multilevel simulations using Bayesian quadrature. Using end-to-end physical and numerical modelling to simulate the entire tsunami life-cycle—earthquake source to coastal inundation—we illustrate our approach by computing probability distributions of local effects from future large tsunamis for Sumatra. Our MLBQ framework, accounting for uncertainties in roughness while reducing computational burden, can improve probabilistic hazard and risk assessments in combination with other uncertainties.",

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Uncertainty in Manning’s roughness coefficient in multilevel simulations of future tsunamis in Sumatra

Abstract

Data Availability Statement

Acknowledgements

Funding

Keywords

ASJC Scopus subject areas

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