Paper:

# Precise Prediction of Coastal and Overland Flow Dynamics: A Grand Challenge or a Fool’s Errand

## Patrick J. Lynett^{†}

Tsunami Research Center, University of Southern California

Los Angeles, CA, USA

^{†}Corresponding author,

In this paper, the challenges in simulation of tsunami-induced currents are reviewed. Examples of tsunami dynamics in harbors, overland flow, and through urban environments are presented, with a focus on the numerical and natural variability in speed predictions. The discussion is largely aimed to show that high-confidence prediction of location-specific currents with a deterministic approach should not be possible in many cases. It is recommended that the tsunami community should look to some type of stochastic approach for current hazard modeling, whether that be a community-wide ensemble approach or a stochastic re-formation of our hydrodynamic theories. Until such tools are available, existing deterministic simulations of tsunami-induced currents require a high level of expert judgement in the analysis, presentation, and usage of model output.

*J. Disaster Res.*, Vol.11, No.4, pp. 615-623, 2016.

- [1] A. Ayca and P. Lynett, “Effect of Tides and Source Location on Nearshore Tsunami-Induced Currents,” 2016 (in review).
- [2] T. Baba, N. Takahashi, Y. Kaneda, Y. Inazawa, and M. Kikkojin, “Tsunami inundation modeling of the 2011 Tohoku earthquake using three-dimensional building data for Sendai,” Miyagi Prefecture, Japan. In “Tsunami events and lessons learned,” pp. 89-98, Springer Netherlands, 2014.
- [3] T. E. Baldock, D. Cox, T. Maddux, J. Killian, and L. Fayler, “Kinematics of breaking tsunami wavefronts: A data set from large scale laboratory experiments,” Coastal Engineering, Vol.56, No.5, pp. 506-516, 2009.
- [4] J. C. Borrero, D. G. Goring, S. D. Greer, and W. L. Power, “Far-field tsunami hazard in New Zealand ports,” Pure Appl. Geophys., Vol.172, pp. 731-756, doi:10.1007/s00024-014-0987-4, 2015.
- [5] K. F. Cheung, Y. Bai, and Y. Yamazaki, “Surges around the Hawaiian Islands from the 2011 Tohoku tsunami,” J Geophys Res, Vol.118, pp. 5703-5719, DOI 10.1002/jgrc.20413, 2013.
- [6] G. Y. Chock, “Design for tsunami loads and effects in the ASCE 7-16 standard,” J. of Structural Engineering, 04016093, 2016.
- [7] G. Chock, G. Yu, H. Thio, and P. Lynett, “Target Structural Reliability Analysis for Tsunami Hydrodynamic Loads of the ASCE 7 Standard,” J. of Structural Engineering, doi: 10.1061/(ASCE)ST.1943-541X.0001499, 2016.
- [8] D. R. Durran, “Numerical Methods for Wave Equations in Geophysical Fluid Dynamics,” Springer-Verlag, New York, Berlin. 1999.
- [9] D. L. George and R. J. LeVeque, “Finite volume methods and adaptive refinement for global tsunami propagation and local inundation,” Science of Tsunami Hazards, Vol.24, pp. 319-328, 2006.
- [10] D. L. George, “Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation,” J. Comput. Phys., Vol.227, pp. 3089-3113, 2008.
- [11] E. Gica, M. Spillane, V. V. Titov, C. Chamberlin, and J. C. Newman, “Development of the forecast propagation database for NOAA’s Short-term Inundation Forecast for Tsunamis (SIFT),” NOAA Tech. Memo. OAR PMEL-139, 89pp., 2008.
- [12] S. Hayashi and S. Koshimura, “The 2011 Tohoku tsunami flow velocity estimation by the aerial video analysis and numerical modeling,” J. Disaster Res, Vol.8, No.4, pp. 561-572, 2013.
- [13] N. Kalligeris, V. Skanavis, S. Tavakkol, A. Ayca, H. E. Safty, P. Lynett, and C. Synolakis, “Lagrangian flow measurements and observations of the 2015 Chilean tsunami in Ventura, CA,” Geophysical Research Letters, Vol.43, doi: 10.1002/2016GL068796, 2016.
- [14] M. Kazolea, A. I. Delis, and C. E. Synolakis, “Numerical treatment of wave breaking on unstructured finite volume approximations for extended Boussinesq-type equations,” J. of Computational Physics, Vol.271, pp. 281-305, 2014.
- [15] A. B. Kennedy, Q. Chen, J. T. Kirby, and R. A. Dalrymple, “Boussinesq modeling of wave transformation, breaking, and runup. I: 1D,” J. of waterway, port, coastal, and ocean engineering, Vol.126, No.1, pp. 39-47, 2000.
- [16] D.-H. Kim, P. Lynett, and S. Socolofsky, “A Depth-Integrated Model for Weakly Dispersive, Turbulent, and Rotational Fluid Flows,” Ocean Modelling, Vol.27, No.3-4, pp. 198-214, 2009.
- [17] R. J. LeVeque, “Finite Volume Methods for Hyperbolic Problems,” Cambridge University Press, 2002.
- [18] P. M. Lloyd and P. K. Stansby, “Shallow water flow around model conical island of small slope. II: Submerged,” J. of Hydraulic Engineering, ASCE Vol.123, No.12, pp. 1068-1077, 1997a.
- [19] P. M. Lloyd and P. K. Stansby, “Shallow water flow around model conical island of small slope. II: Submerged,” J. of Hydraulic Engineering, ASCE Vol.123, No.12, pp. 1057-1067, 1997b.
- [20] P. Lynett, et al. “Inter-Model Analysis of Tsunami-Induced Coastal Currents,” 2016 (in review).
- [21] P. J. Lynett, J. Borrero, R. Weiss, S. Son, D. Greer, and W. Renteria, “Observations and modeling of tsunami-induced currents in ports and harbors,” Earth Planet. Sci. Lett., Vol.327–328, pp. 68-74, 2012.
- [22] P. J. Lynett, J. Borrero, S. Son, R. Wilson, and K. Miller, “Assessment of the tsunami-induced current hazard,” Geophys. Res. Lett, Vol.41, pp. 2048-2055, doi:10.1002/2013GL058680, 2014.
- [23] L. Montoya, P. Lynett, H. Thio, and W. Li, “Spatial Statistics of Tsunami Overland Flow Properties,” in press, J. of Waterway, Port, Coastal, and Ocean Engineering (ASCE), 2016.
- [24] H. Park, D. Cox, P. Lynett, D. Wiebe, and S. Shin, “Tsunami Inundation Modeling in Constructed Environments: A Physical and Numerical Comparison of Free-Surface Elevation, Velocity, and Momentum Flux,” Coastal Engineering, Vol.79, pp. 9-21, doi: 10.1016/j.coastaleng.2013.04.002, 2013.
- [25] B. Richmond, W. Szczuci’nski, C. Chagué-Goff, K. Goto, D. Sugawara, R. Witter, and J. Goff, “Erosion, deposition and landscape change on the Sendai coastal plain, Japan, resulting from the March 11, 2011 Tohoku-oki tsunami,” Sedimentary Geology, Vol.282, pp. 27-39, 2012.
- [26] F. Shi, J. T. Kirby, J. C. Harris, J. D. Geiman, and S. T. Grilli, “A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation,” Ocean Modelling, Vol.43-44, pp. 36-51, 2012.
- [27] N. Shuto, C. Goto, and F. Imamura, “Numerical simulation as a means of warning for near-field Tsunami,” Coastal Engineering in Japan, Vol.33, No.2, pp. 173-193, 1990.
- [28] S. Son, P. Lynett, and D.-H. Kim, “Nested and Multi-Physics Modeling of Tsunami Evolution from Generation to Inundation,” Ocean Modelling, Vol.38, No.1-2, pp. 96-113, doi: 10.1016/j.ocemod.2011.02.007, 2011.
- [29] A. Suppasri, E. Mas, I. Charvet, R. Gunasekera, K. Imai, Y. Fukutani, and F. Imamura, “Building damage characteristics based on surveyed data and fragility curves of the 2011 Great East Japan tsunami,” Natural Hazards, Vol.66, pp. 319-341, 2013.
- [30] C. E. Synolakis, E. N. Bernard, V. V. Titov, U. Kânouglu, and F. I. González, “Validation and verification of tsunami numerical models,” Pure and Applied Geophysics, Vol.165, No.11-12, pp. 2197-2228, 2008.
- [31] V. V. Titov and C. Synolakis, “Modeling of breaking and nonbreaking long-wave evolution and runup using VTCS-2,” J. Waterw. Port Coast. Ocean Eng., Vol.121, No.6, pp. 308-316, 1995.
- [32] K. Tokimatsu, M. Ishida, and S. Inoue, “Tsunami-Induced Overturning of Buildings in Onagawa during 2011 Tohoku Earthquake,” Earthquake Spectra, 2016.
- [33] X. Wang and P. L. F. Liu, “Numerical simulations of the 2004 Indian Ocean tsunamis–coastal effects,” J. of Earthquake and Tsunami, Vol.1, No.03, pp. 273-297, 2007.
- [34] G. Wei, J. T. Kirby, S. T. Grilli, and R. Subramanya, “A fully nonlinear Boussinesq model for surface waves: Part I. Highly nonlinear unsteady waves,” J. Fluid Mech. 294, pp. 71-92, 1995.
- [35] Y. Wei, E. Bernard, L. Tang, R. Weiss, V. Titov, C. Moore, M. Spillane, M. Hopkins, and U. Kânouglu, “Real-time experimental forecast of the Peruvian tsunami of August 2007 for U.S. coastlines,” Geophys. Res. Lett., Vol.35, L04609, doi: 10.1029/2007GL032250, 2008.
- [36] N. N. Yanenko, “The Method of Fractional Steps,” (Translated from Russian by M. Holt), Springer, New York, Berlin, Heidelberg, 1971.
- [37] H. Yeh, “Design tsunami forces for onshore structures,” J. Disaster Research, Vol.2, pp. 531-536, 2007.
- [38] H. Yeh, I. Robertson, and J. Preuss, “Development of design guidelines for structures that serve as tsunami vertical evacuation sites (Vol. 4),” Washington State Department of Natural Resources, Division of Geology and Earth Resources, 2005.
- [39] Y. J. Zhang, G. Priest, J. Allan, and L. Stimely, “Benchmarking an Unstructured-Grid Model for Tsunami Current Modeling,” Pure and Applied Geophysics, pp. 1-13, 2016.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.