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An empirical solution for tsunami run-up on compound slopes

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Abstract

Deterministic numerical models for tsunami inundation provide the most accurate means for estimating tsunami run-up when the bathymetry/topography and water-level time history at the seaward boundary are well known. However, it is often the case that there is uncertainty in both the bathymetry/topography and water level at the seaward boundary. For these reasons, empirical solutions for tsunami run-up may be preferred because the run-up can be computed quickly allowing a probabilistic estimate the tsunami run-up risk. In this paper, an empirical solution for tsunami run-up is developed based on an analytic solution and calibrated using a Boussinesq wave model for plane-sloped and compound-sloped cases, including the effects of bottom friction, wave breaking, and the slope of the inundated land area. The new relation is a function of the tsunami wave amplitude at a specific water depth (100 m) to provide clear guidance for practical application, and of two values of the surf-similarity parameter to account for a compound slope. The model comprises three equations for three regions: breaking, transition, and non-breaking. The model predictions are compared with survey data from the 2011 Tohoku tsunami in Japan without recalibration. The new equation provides reasonable estimates of run-up height and is generally conservative.

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Abbreviations

A 0 :

Tsunami wave amplitude (L)

d 1 :

Distance from the slope to the end of the land (L)

d 2 :

Distance from the slope to the center of the tsunami wave (L)

d 3 :

Distance from the slope to the end of the model (L)

Dist1 :

Averaging distance from 100-m contour to shoreline (L)

Dist2 :

Averaging distance from shoreline to the end of run-up point (L)

F :

Friction factor

g :

Acceleration of gravity (L/T2)

H 0 :

Wave height (L)

h 0 :

Water depth at the flat bottom (L)

MIN:

Minimum value

R :

Tsunami run-up height (L)

STD:

Standard deviation

T :

Representative wave period (T)

SWL:

Still water level

β 1 :

Offshore slope

β 2 :

Onshore slope

γ :

Empirical coefficient dependent on ξ 2

η :

Surface elevation (L)

ξ 1 :

Surf-similarity (Iribarren number) for offshore slope

ξ 2 :

Surf-similarity for onshore slope

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Acknowledgments

This research is based upon the work partially supported by the National Science Foundation under Grant No. 0830378 and Oregon Sea Grant under Award No. NB223X. Any opinion, findings, and conclusions or recommendations expressed in this document are those of the authors and do not necessarily reflect the views of the National Science Foundation or Oregon Sea Grant. The authors thank two anonymous reviewers for their constructive comments.

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Authors and Affiliations

  1. School of Civil and Construction Engineering, Oregon State University, Corvallis, OR, 97331-2302, USA

    Hyoungsu Park & Daniel T. Cox

  2. LP4 Associates LLC Affiliate Faculty, University of Washington, Seattle, WA, USA

    Catherine M. Petroff

  3. Department of Civil and Environmental Engineering, University of Washington, Seattle, WA, USA

    Catherine M. Petroff

Authors
  1. Hyoungsu Park
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  2. Daniel T. Cox
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  3. Catherine M. Petroff
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Correspondence to Hyoungsu Park.

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Park, H., Cox, D.T. & Petroff, C.M. An empirical solution for tsunami run-up on compound slopes. Nat Hazards 76, 1727–1743 (2015). https://doi.org/10.1007/s11069-014-1568-7

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  • DOI: https://doi.org/10.1007/s11069-014-1568-7

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