Land–Water Boundary Treatment for a Tsunami Model With Dimensional Splitting
- 203 Downloads
The Method of Splitting Tsunamis (MOST) model adapted by National Oceanic and Atmospheric Administration (NOAA) for tsunami forecasting operations is praised for its computational efficiency, associated with the use of splitting technique. It will be shown, however, that splitting the computations between \(x\) and \(y\) directions results in specific sensitivity to the treatment of land–water boundary. Slight modification to the reflective boundary condition in MOST caused an appreciable difference in the results. This is demonstrated with simulations of the Tohoku-2011 tsunami from the source earthquake to Monterey Bay, California, and in southeast Alaska, followed by comparison with tide gage records. In the first case, the better representation of later waves (reflected from the coasts) by the modified model in a Pacific-wide simulation resulted in twice as long match between simulated and observed tsunami time histories at Monterey gage. In the second case, the modified model was able to propagate the tsunami wave and approach gage records at locations within narrow channels (Juneau, Ketchikan), to where MOST had difficulty propagating the wave. The modification was extended to include inundation computation. The resulting inundation algorithm (Cliffs) has been tested with the complete set of NOAA-recommended benchmark problems focused on inundation. The solutions are compared to the MOST solutions obtained with the version of the MOST model benchmarked for the National Tsunami Hazard Mitigation Program in 2011. In two tests, Cliffs and MOST results are very close, and in another two tests, the results are somewhat different. Very different regimes of generation/disposal of water by Cliffs and MOST inundation algorithms, which supposedly affected the benchmarking results, have been discussed.
KeywordsTsunamis numerical modeling dimensional splitting reflective boundary inundation wave runup
Author thanks tsunami modelers—participants of the 2011 NTHMP Model Benchmarking Workshop—for collecting and systemizing data used in this work for testing the inundation algorithm. In particular, bathymetric and land survey data for the Okushiri tsunami have been collected and refined by Dmitry Nicolsky and Frank Gonzalez. The analytical solution to the non-breaking solitary wave runup onto the sloping beach shown in Figs. 13 and 14, and the video frames of the wave-tank experiment with a model of Monai area shown in Figure 20, are courtesy of Dmitry Nicolsky. Author acknowledges NOAA/NOS for providing gauge records, and NOAA/NGDC for providing bathymetry data.
- Briggs, M. J., Synolakis, C. E., Harkins, G. S., and Green, D. R. (1995), Laboratory experiments of tsunami runup on a circular island. Pure Appl. Geophys., 144, 3/4, 569–593.Google Scholar
- Burwell, D., Tolkova, E., and Chawla, A. (2007), Diffusion and Dispersion Characterization of a Numerical Tsunami Model. Ocean Model., 19 (1–2), 10–30. doi:10.1016/j.ocemod.2007.05.003.
- Burwell, D., Tolkova, E, 2008. Curvilinear version of the MOST model with application to the coast-wide tsunami forecast, Part II. NOAA Tech. Memo. OAR PMEL-142, 28 pp.Google Scholar
- Disaster Control Research Center. Tsunami Engineering Technical Report No. 11, Tohoku University, March 1994.Google Scholar
- Gonzalez F.I., LeVeque R.J., Chamberlain P., Hirai B., Varkovitzky J., and George D.L., GeoClaw Model, In: [NTHMP] National Tsunami Hazard Mitigation Program. July 2012. Proceedings and Results of the 2011 NTHMP Model Benchmarking Workshop. Boulder: U.S. Department of Commerce/NOAA/NTHMP; NOAA Special Report. 436 p.Google Scholar
- Hokkaido Tsunami Survey Group (1993), Tsunami devastates Japanese coastal region. Eos Trans. Am. Geophys. Union, 74(37), 417–432.Google Scholar
- Imamura F., Tsunami Modeling: Calculating Inundation and Hazard Maps. In: The Sea, 15. Tsunamis. Ed: Bernard E. and Robinson A. Harvard University Press, Cambridge, MA, London, England 2009.Google Scholar
- LeVeque, R.J., Finite volume methods for hyperbolic problems. Cambridge University Press, UK 2002.Google Scholar
- Li, Y., and Raichlen, F. (2002), Non-breaking and breaking solitary wave run-up. J. Fluid Mech., 456, 295–318.Google Scholar
- Liu, P.L.-F., Cho, Y.-S., Briggs, M., Kanoglu, U., and Synolakis, C. (1995), Runup of solitary waves on a circular island. Journal of Fluid Mech. 302, 259–285.Google Scholar
- Liu, P.L.-F., Yeh, H., and Synolakis C. (2008), Advanced Numerical Models for Simulating Tsunami Waves and Runup. Advances in Coastal and Ocean Engineering, 10, 223–230.Google Scholar
- Nicolsky, D.J., Suleimani, E.N., and Hansen, R.A. (2011), Validation and verification of a numerical model for tsunami propagation and runup. Pure Appl. Geophys. 168, 1199–1222.Google Scholar
- [NTHMP] National Tsunami Hazard Mitigation Program, July 2012. Proceedings and Results of the 2011 NTHMP Model Benchmarking Workshop. Boulder: U.S. Department of Commerce/NOAA/NTHMP; NOAA Special Report. 436 p.Google Scholar
- Roeber, V., Cheung, K.F., and Kobayashi, M.H. (2010), Shock-capturing Boussinesq-type model for nearshore wave processes. Coastal Engineering 57, 407–423.Google Scholar
- Shi, F., Kirby, J.T., Harris, J.C., Geiman, J.D., Grilli, S.T. (2012), A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation. Ocean Modelling, 43–44, 36–51.Google Scholar
- Strang, G. (1968), On the construction and comparison of difference schemes. SIAM Journal on Numerical Analysis, 5(3), 506–517.Google Scholar
- Synolakis, C.E. (1987), The runup of solitary waves. J. Fluid Mech., 185, 523–545.Google Scholar
- Synolakis, C.E., Bernard, E.N., Titov, V.V., Kanoglu, U., and Gonzalez, F.I. (2007), Standards, criteria, and procedures for NOAA evaluation of tsunami numerical models. NOAA Tech. Memo. OAR PMEL-135, NTIS: PB2007-109601, NOAA/Pacific Marine Environmental Laboratory, Seattle, WA, 55 pp.Google Scholar
- Tang, L., Titov, V. V., and Chamberlin, C. D. (2009), Development, testing, and applications of site-specific tsunami inundation models for real-time forecasting, J. Geophys. Res., 114, C12025, doi:10.1029/2009JC005476.
- Tang L., Titov, V.V., Bernard, E., Wei, Y., Chamberlin, C., Newman, J.C., Mofjeld, H., Arcas, D., Eble, M., Moore, C., Uslu, B., Pells, C., Spillane, M.C., Wright, L.M., and Gica, E. (2012), Direct energy estimation of the 2011 Japan tsunami using deep-ocean pressure measurements, J. Geophys. Res., VOL. 117, C08008, doi:10.1029/2011JC007635.
- Takahashi, T. (1996), Benchmark problem 4: the 1993 Okushiri tsunami - Data, conditions and phenomena. In Long-Wave Runup Models, World Scientific, 384–403.Google Scholar
- Titov, V. V., and Synolakis, C. E. (1995), Modeling of breaking and nonbreaking long-wave evolution and runup using VTCS-2, J. Waterw., Port, Coastal, Ocean Eng., 121(6), 308–316.Google Scholar
- Titov, V., and Gonzalez F.I. (1997), Implementation and testing of the Method of Splitting Tsunami (MOST) model. NOAA Tech. Memo. ERL PMEL-112 (PB98-122773), NOAA/Pacific Marine Environmental Laboratory, Seattle, WA, 11 pp.Google Scholar
- Titov, V. V., and Synolakis, C. E. (1998), Numerical modeling of tidal wave runup, J. Waterw., Port, Coastal, Ocean Eng., 124(4), 157–171.Google Scholar
- Titov V. V., Gonzalez, F. I., Bernard, E. N., Eble, M. C., Mofjeld, H. O., Newman, J. C., and Venturato, A. J. (2005), Real - Time Tsunami Forecasting: Challenges and Solutions, Natural Hazards, 35:41–58.Google Scholar
- Tolkova, E. (2012), MOST (Method of Splitting Tsunamis) Numerical Model. In: [NTHMP] National Tsunami Hazard Mitigation Program. Proceedings and Results of the 2011 NTHMP Model Benchmarking Workshop. Boulder: U.S. Department of Commerce/NOAA/NTHMP; NOAA Special Report. 436 p.Google Scholar
- Van Dorn, W. G. (1984), Some tsunami characteristics deducible from tide records, J. Phys. Oceanogr., 14, 353–363.Google Scholar
- Wei, Y., Mao, X.-Z., and CCheung, K.F. (2006), Well-Balanced Finite-Volume Model for Long-Wave Runup. Journal of Waterway, Port, Coastal, and Ocean Engineering, 132 (2), 114–124.Google Scholar