Development and Validation of a Tsunami Numerical Model with the Polygonally Nested Grid System and its MPI-Parallelization for Real-Time Tsunami Inundation Forecast on a Regional Scale
Takuya Inoue*1,*2,, Takashi Abe*1, Shunichi Koshimura*1, Akihiro Musa*3,*4, Yoichi Murashima*1,*5, and Hiroaki Kobayashi*6
*1International Research Institute of Disaster Science, Tohoku University
468-1 Aramaki Aza Aoba, Aoba-ku, Sendai, Miyagi 980-0845, Japan
*2Kokusai Kogyo Co., Ltd., Tokyo, Japan
*3Cyberscience Center, Tohoku University, Miyagi, Japan
*4NEC Corporation, Tokyo, Japan
*5RTi-cast Inc., Miyagi, Japan
*6Graduate School of Information Sciences, Tohoku University, Miyagi, Japan
We have developed a new numerical model suitable for rapid and wide-area estimation of tsunami inundation and damage. The model is based on the world-renowned TUNAMI code solving the two-dimensional nonlinear shallow water equations, and enables one-stop simulation of the initial tsunami distribution based on a fault model, tsunami propagation and inundation, and damage estimation. It extends the configuration of the grid system from conventional rectangular regions to polygonal regions so that deployment of high-resolution grids can be confined to the coastal lowland, resulting in remarkably improved efficiency in computation and better precision. For the purpose of real-time implementation of tsunami inundation simulation using a high-performance computing infrastructure, vectorization and MPI parallelization have also been conducted. Moreover, the model was verified and validated through several benchmark problems that the National Tsunami Hazard Mitigation Program, organized by federal agencies and states in the U.S., developed as the quality standards for simulating and assessing tsunami hazard and risk. The newly-developed model is named “Real-time Tsunami inundation (RTi) model,” and its computational performance was examined using the SX-ACE, a vector supercomputer installed at Tohoku University. The results show that it requires only 128 cores of the SX-ACE for implementing six-hour tsunami inundation simulation with a 10-meter grid resolution within 10 minutes for the 700 km long coastline of Kochi Prefecture, Japan. This means that the RTi model is over 10 times more efficient as the conventional tsunami model with the rectangular domains, and it can be inferred that 2,451 cores of the SX-ACE are the overall computational resources needed for real-time tsunami inundation forecast on the whole coastal regions along the Nankai Trough subduction zone, corresponding to the computational performance of 170 Tflop/s. The resources required are equivalent to 24% of all the SX-ACE resources at Tohoku University, indicating the feasibility of real-time tsunami inundation forecast on a regional scale by using the RTi model. Since the Disaster Information System operated by the Cabinet Office of the Japanese Government adopted a function of tsunami damage estimation using the aforementioned numerical model, at the end of this paper, a brief overview of the subsystem for rapidly estimating tsunami damage on a regional scale is described.
-  M. Numada, M. Inoue, and K. Meguro, “Framework of disaster responses based on the analysis of the 2011 Great East Japan Earthquake disaster, the 2015 Kanto-Tohoku heavy rain disaster and the 2016 Kumamoto earthquake disaster,” J. of Japan Society of Civil Engineers, Series A1 (Structural Engineering & Earthquake Engineering), Vol.73, No.4, pp. 258-269, 2017 (in Japanese with English title and abstract).
-  Y. Murashima, F. Imamura, H. Takeuchi, T. Suzuki, K. Yoshida, M. Yamazaki, and K. Matsuda, “Adaptability of the aircraft-mounted laser data in tsunami inundation forecast,” Proc. of Coastal Engineering, Japan Society of Civil Engineers, Vol.53, pp. 1336-1340, 2006 (in Japanese).
-  Water and Disaster Management Bureau, and National Institute for Land and Infrastructure Management, Ministry of Land, Infrastructure, Transport and Tourism, “A guide for assesement of tsunami inundation ver. 2.00,” 2012, www.mlit.go.jp/river/shishin_guideline/bousai/saigai/tsunami/shinsui_settei.pdf [accessed October 11, 2018] (in Japanese)
-  N. Takahashi, K. Imai, M. Ishibashi, K. Sueki, R. Obayashi, T. Tanabe, F. Tamazawa, T. Baba, and Y. Kaneda, “Real-time tsunami prediction system using DONET,” J. Disaster Res., Vol.12, No.4, pp. 766-774, 2017.
-  N. Yamamoto, S. Aoi, K. Hirata, W. Suzuki, T. Kunugi, and H. Nakamura, “Multi-index method using offshore ocean-bottom pressure data for real-time tsunami forecast,” Earth, Planets and Space, Vol.68, No.128, doi: 10.1186/s40623-016-0500-7, 2016.
-  A. R. Gusman, Y. Tanioka, B. T. MacInnes, and H. Tsushima, “A methodology for near-field tsunami inundation forecasting: application to the 2011 Tohoku tsunami,” J. Geophys. Res. Solid Earth, Vol.119, pp. 8186-8206, doi: 10.1002/2014JB010958, 2014.
-  T. Baba, N. Takahashi, and Y. Kaneda, “Near-field tsunami amplification factors in the Kii Peninsula, Japan for Dence Ocean Network for Earthquake and Tsunamis (DONET),” Mar. Geophys. Res., Vol.35, pp. 319-325, 2014.
-  S. Kawamoto, K. Miyagawa, T. Yahagi, M. Todoriki, T. Nishimura, Y. Ohta, R. Hino, and S. Miura, “Development and assessment of real-time fault model estimation routines in the GEONET real-time processing system,” M. Hashimoto (Eds.), Int. Symp. on Geodesy for Earthquake and Natural Hazards (GENAH), International Association of Geodesy Symposia, Vol.145, Springer, Cham, doi: 10.1007/1345_2015_49, 2015.
-  H. Tsushima, R. Hino, H. Fujimoto, Y. Tanioka, and F. Imamura, “Near-field tsunami forecasting from cabled ocean bottom pressure data,” J. Geophys. Res., Vol.114, B06309, 2009.
-  H. Tsushima, R. Hino, Y. Ohta, T. Iinuma, and S. Miura, “tFISH/RAPiD: rapid improvement of near-field tsunami forecasting based on offshore tsunami data by incorporating onshore GNSS data,” Geophys. Res. Lett., Vol.41, doi: 10.1002/2014GL059863, 2014.
-  Y. Oishi, F. Imamura, and D. Sugawara, “Near-field tsunami inundation forecast using the parallel TUNAMI-N2 model: application to the 2011 Tohoku-Oki earthquake combined with source inversions, Geophys. Res. Lett., Vol.42, doi: 10.1002/2014GL062577, 2015.
-  A. Musa, H. Matsuoka, O. Watanabe, Y. Murashima, S. Koshimura, R. Hino, Y. Ohta, and H. Kobayashi, “A real-time tsunami inundation forecast system for tsunami disaster prevention and mitigation,” The Int. Conf. for High Performance Computing, Networking, Storage and Analysis (SC15), Austin, Texas, 2015, sc15.supercomputing.org/sites/all/themes/SC15images/tech_poster/poster_files/post142s2-file3.pdf [accessed October 11, 2018]
-  A. Musa, O. Watanabe, H. Matsuoka, H. Hokari, T. Inoue, Y. Murashima, Y. Ohta, R. Hino, S. Koshimura, and H. Kobayashi, “Real-time tsunami inundation forecast system for tsunami disaster prevention and mitigation,” The J. of Supercomputing, Vol.74, No.7, p. 3093, 2018.
-  S. Koshimura, “Fusion of real-time disaster simulation and big data assimilation – recent progress,” J. Disaster Res., Vol.12, No.2, pp. 226-232, 2017.
-  T. Inoue, T. Abe, S. Koshimura, A. Musa, Y. Murashima, and H. Kobayashi, “Improvement of efficiency of wide-area tsunami simulation through polygonal regions and MPI-parallelization,” J. of Japan Society of Civil Engineers, Series B2 (Coastal Engineering), Vol.72, No.2, pp. 373-378, 2016 (in Japanese with English title and abstract).
-  The Investigative Commmission on Massive Earthquake Models in Nankai Trough, 2012, www.bousai.go.jp/jishin/nankai/model/data_teikyou.html [accessed October 11, 2018] (in Japanese)
-  I. Babuska and J. T. Oden, “Verification and validation in computational engineering and science: basic concepts,” Computer Methods in Applied Mechanics and Engineering, Vol.193, Issues 36-38, pp. 4057-4066, 2004.
-  C. E. Synolakis, E. N. Bernard, V. V. Titov, U. Kanoglu, and F. O. Gonzalez, “Standards, criteria, and procedures for NOAA evaluation of tsunami numerical models,” NOAA Technical Memorandum OAR PMEL-135, 2007.
-  National Tsunami Hazard Mitigation Program, “Proceedings and results of the 2011 NTHMP model benchmarking workshop,” NOAA Special Report, 2012, nws.weather.gov/nthmp/documents/nthmpWorkshopProcMerged.pdf [accessed October 11, 2018]
-  P. J. Lynett, K. Gately, D. Nicolsky, and R. Wilson, “Proceedings and results of the National Tsunami Hazard Mitigation Program 2015 tsunami current modeling workshop,” 2017, nws.weather.gov/nthmp/documents/NTHMP_Currents_Workshop_Report.pdf [accessed October 11, 2018]
-  J. Horrillo, S.T. Grilli, D. Nicolsky, V. Roeber, and J. Zhang, “Performance benchmarking tsunami models for NTHMP’s inundation mapping activities,” Pure Appl. Geophys., doi: 10.1007/s00024-014-0891-y, 2014.
-  T. Inoue, T. Abe, S. Koshimura, A. Musa, Y. Murashima, and H. Kobayashi, “A study on applicability of a tsunami inundation model with the polygonally nested grid system and its MPI-parallelization to nation-wide tsunami forecast at multiple grid resolutions,” J. of Japan Society of Civil Engineers, Series B2 (Coastal Engineering), Vol.73, No.2, pp. 319-324, 2017 (in Japanese with English title and abstract).
-  A. Musa, T. Abe, T. Inoue, H. Hokari, Y. Murashima, Y. Kido, S. Date, S. Shimojo, S. Koshimura, and H. Kobayashi, “A real-time tsunami inundation forecast system using vector supercomputer SX-ACE,” J. Disaster Res., Vol.13, No.2, pp. 234-244, 2018.
-  J. J. Dronkers, “Tidal computations: in rivers and coastal waters,” Elsevier Science Publishing, USA, 1964.
-  C. Goto and N. Shuto, “Numerical simulation of tsunami propagations,” K. Iida and T. Iwasaki (eds.), Tsunamis – Their science and engineering, Terra Scientific Publishing Company, Tokyo, pp. 439-451, 1983.
-  C. Goto, Y. Ogawa, N. Shuto, and F. Imamura, “IUGG/IOC Time project: numerical method of tsunami simulation with the leap-frog scheme,” IOC Manuals and Guides, No.35, UNESCO, 1997.
-  F. Imamura and C. Goto, “Truncation error in numerical tsunami simulation by the finite difference method,” Coastal Engineering in Japan, Vol.31, No.2, pp. 245-263, 1988.
-  F. Imamura, “Review of tsunami simulation with a finite difference method,” H. Yeh, P. Liu, and C. Synolakis (Eds.), Long-Wave Runup Models, pp. 25-42, World Scientific Publishing, 1995.
-  Y. Okada, “Internal deformation due to shear and tensile faults in a half-space,” Bulletin of the Seismological Society of America, Vol.82, No.2, pp. 1018-1040, 1992.
-  T. Inoue, Y. Ohta, S. Koshimura, R. Hino, S. Kawamoto, Y. Hiyama, and Y. Doke, “A study on methods for applying fault models rapidly estimated using real-time GNSS to tsunami simulation,” J. of Japan Society of Civil Engineers, Series B2 (Coastal Engineering), Vol.72, No.2, pp. 355-360, 2016 (in Japanese with English title and abstract).
-  Y. Tanioka and K. Satake, “Tsunami generation by horizontal displacement of ocean bottom,” Geophysical Research Letters, Vol.23, pp. 861-864, 1996.
-  K. Kajiura, “The leading wave of a tsunami,” Bulletin of the Earthquake Research Institute, Vol.41, pp. 535-571, 1963.
-  S. Koshimura, T. Oie, H. Yanagisawa, and F. Imamura, “Developing fragility functions for tsunami damage estimation using numerical model and post-tsunami data from Banda Aceh, Indonesia,” Coastal Engineering J., JSCE, Vol.51, No.3, pp. 243-273, 2009.
-  nctr.pmel.noaa.gov/benchmark/index.html [accessed October 11, 2018]
-  github.com/rjleveque/nthmp-benchmark-problems [accessed October 11, 2018]
-  M. J. Briggs, C. E. Synolakis, G. S. Harkins, and D. Green, “Laboratory experiments of tsunami runup on a circular island,” Pure Appl. Geophys., Vol.144, pp. 569-593, 1995.
-  H. Yeh, P. F. Liu, M. Briggs, and C. E. Synolakis, “Tsunami catastrophe in Babi Island,” Nature, Vol.372, pp. 6503-6508, 1994.
-  T. Takahashi, “Benchmark problem 4. The 1993 Okushiri tsunami – data, conditions, and phenomena,” H. Yeh, P. Liu, and C. Synolakis (Eds.), Long-Wave Runup Models, pp. 384-403, World Scientific Publishing, 1995.
-  http://nlftp.mlit.go.jp/ksj-e/index.html [accessed October 11, 2018]
-  T. Takahashi, T. Takahashi, N. Shuto, F. Imamura, and M. Oritz, “Source models for the 1993 Hokkaido Nansei-Oki earthquake tsunami,” Pure Appl. Geophys., Vol.144, pp. 747-767, 1995.
-  Y. Ohta, T. Inoue, S. Koshimura, S. Kawamoto, and R. Hino, “Role of real-time GNSS in near-field tsunami forecasting,” J. Disaster Res., Vol.13, No.3, pp. 453-459, 2018.