Performance Benchmarking Tsunami Models for NTHMP’s Inundation Mapping Activities

The coastal states and territories of the United States (US) are vulnerable to devastating tsunamis from near-field or far-field coseismic and underwater/subaerial landslide sources. Following the catastrophic 2004 Indian Ocean tsunami, the National Tsunami Hazard Mitigation Program (NTHMP) accelerated the development of public safety products for the mitigation of these hazards. In response to this initiative, US coastal states and territories speeded up the process of developing/enhancing/adopting tsunami models that can be used for developing inundation maps and evacuation plans. One of NTHMP’s requirements is that all operational and inundation-based numerical (O&I) models used for such purposes be properly validated against established standards to ensure the reliability of tsunami inundation maps as well as to achieve a basic level of consistency between parallel efforts. The validation of several O&I models was considered during a workshop held in 2011 at Texas A&M University (Galveston). This validation was performed based on the existing standard (OAR-PMEL-135), which provides a list of benchmark problems (BPs) covering various tsunami processes that models must meet to be deemed acceptable. Here, we summarize key approaches followed, results, and conclusions of the workshop. Eight distinct tsunami models were validated and cross-compared by using a subset of the BPs listed in the OAR-PMEL-135 standard. Of the several BPs available, only two based on laboratory experiments are detailed here for sake of brevity; since they are considered as sufficiently comprehensive. Average relative errors associated with expected parameters values such as maximum surface amplitude/runup are estimated. The level of agreement with the reference data, reasons for discrepancies between model results, and some of the limitations are discussed. In general, dispersive models were found to perform better than nondispersive models, but differences were relatively small, in part because the BPs mostly featured long waves, such as solitary waves. The largest error found (e.g., the laboratory experiment case of a solitary wave on a simple beach) was 10 % for non-breaking wave conditions and 12 % for breaking conditions; these errors are equal or smaller than the thresholds (10 % and 20 %, respectively) defined by the OAR-PMEL-135 for predicting the surface profile; hence, all models examined here are deemed acceptable for inundation mapping purposes.

[1]  B. V. Leer,et al.  Towards the Ultimate Conservative Difference Scheme , 1997 .

[2]  Michael C. Spillane,et al.  Real‐time experimental forecast of the Peruvian tsunami of August 2007 for U.S. coastlines , 2008 .

[3]  Thomas,et al.  PREDICTING TSUNAMI AMPLITUDES ALONG THE NORTH AMERICAN 147 COAST FROM TSUNAMIS GENERATED IN THE NORTHWEST PACIFIC OCEAN DURING TSUNAMI WARNINGS , 1999 .

[4]  Stephan T. Grilli,et al.  Landslide tsunami case studies using a Boussinesq model and a fully nonlinear tsunami generation model , 2003 .

[5]  Stephan T. Grilli,et al.  PROGRESS IN FULLY NONLINEAR POTENTIAL FLOW MODELING OF 3D EXTREME OCEAN WAVES , 2010 .

[6]  Z. Kowalik,et al.  Numerical Modeling of Ocean Dynamics , 1993 .

[7]  Gangfeng Ma,et al.  Shock-capturing non-hydrostatic model for fully dispersive surface wave processes , 2012 .

[8]  D. Peregrine Long waves on a beach , 1967, Journal of Fluid Mechanics.

[9]  Dmitry J. Nicolsky,et al.  Validation and Verification of a Numerical Model for Tsunami Propagation and Runup , 2011 .

[10]  K. Cheung,et al.  Boussinesq-type model for energetic breaking waves in fringing reef environments , 2012 .

[11]  W. Hansen Theorie zur Errechnung des Wasserstandes und der Strömungen in Randmeeren nebst Anwendungen , 1956 .

[12]  Qin Chen,et al.  Funwave 1.0: Fully Nonlinear Boussinesq Wave Model - Documentation and User's Manual , 1998 .

[13]  C. W. Hirt,et al.  SOLA-VOF: a solution algorithm for transient fluid flow with multiple free boundaries , 1980 .

[14]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[15]  Yong-Sik Cho,et al.  Runup of solitary waves on a circular Island , 1995, Journal of Fluid Mechanics.

[16]  V. Titov,et al.  Direct energy estimation of the 2011 Japan tsunami using deep‐ocean pressure measurements , 2012 .

[17]  C. Goto Numerical method of tsunami simulation with the leap-frog scheme , 1997 .

[18]  NUMERICAL MODELING OF THE GLOBAL TSUNAMI , 2005 .

[19]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow , 1977 .

[20]  Kwok Fai Cheung,et al.  Depth‐integrated, non‐hydrostatic model with grid nesting for tsunami generation, propagation, and run‐up , 2010 .

[21]  Stephan T. Grilli,et al.  A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation , 2012 .

[22]  Marcel Zijlema,et al.  An accurate and efficient finite‐difference algorithm for non‐hydrostatic free‐surface flow with application to wave propagation , 2003 .

[23]  Vasily Titov,et al.  Modeling of Breaking and Nonbreaking Long-Wave Evolution and Runup Using VTCS-2 , 1995 .

[24]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[25]  António M. Baptista,et al.  An Efficient and Robust Tsunami Model on Unstructured Grids. Part I: Inundation Benchmarks , 2008 .

[26]  Stephan T. Grilli,et al.  Numerical modeling of tsunami waves generated by the flank collapse of the Cumbre Vieja Volcano (La Palma, Canary Islands): Tsunami source and near field effects , 2012 .

[27]  Stephan T. Grilli,et al.  Numerical Simulation of the 2011 Tohoku Tsunami Based on a New Transient FEM Co-seismic Source: Comparison to Far- and Near-Field Observations , 2013, Pure and Applied Geophysics.

[28]  G. Fischer Ein numerisches Verfahren zur Errechnung von Windstau und Gezeiten in Randmeeren , 1959 .

[29]  G. Wei,et al.  A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves , 1995, Journal of Fluid Mechanics.

[30]  Costas E. Synolakis,et al.  NOAA Technical Memorandum OAR PMEL-135 STANDARDS, CRITERIA, AND PROCEDURES FOR NOAA EVALUATION OF TSUNAMI NUMERICAL MODELS , 2007 .

[31]  Michael J. Briggs,et al.  Laboratory experiments of tsunami runup on a circular island , 1995 .

[32]  O. Nwogu Alternative form of Boussinesq equations for nearshore wave propagation , 1993 .

[33]  Akio Arakawa,et al.  Computational Design of the Basic Dynamical Processes of the UCLA General Circulation Model , 1977 .

[34]  Jeffrey C. Harris,et al.  1 NUMERICAL MODELING OF COASTAL TSUNAMI DISSIPATION AND IMPACT , 2012 .

[35]  Zygmunt Kowalik,et al.  Oral Session Abstracts: Numerical Modeling of the Global Tsunami: Indonesian Tsunami of 26 December 2004 - Abstract , 2005 .

[36]  C. W. Hirt,et al.  Methods for calculating multi-dimensional, transient free surface flows past bodies , 1975 .

[37]  J. Hammack,et al.  Tsunamis - a model of their generation and propagation , 1972 .

[38]  W. Rider,et al.  Stretching and tearing interface tracking methods , 1995 .

[39]  C. E. Synolakis,et al.  Validation and Verification of Tsunami Numerical Models , 2008 .

[40]  P. Dunbar,et al.  United States and Territories National Tsunami Hazard Assessment: Historical Record and Sources for Waves - Update , 2015 .

[41]  K. Cheung,et al.  Modeling near‐field tsunami observations to improve finite‐fault slip models for the 11 March 2011 Tohoku earthquake , 2011 .

[42]  Kwok Fai Cheung,et al.  Depth‐integrated, non‐hydrostatic model for wave breaking and run‐up , 2009 .

[43]  Arun Chawla,et al.  Diffusion and dispersion characterization of a numerical tsunami model , 2007 .

[44]  Stephan T. Grilli,et al.  Numerical simulation of waves generated by landslides using a multiple-fluid Navier–Stokes model , 2010 .

[45]  Juan Horrillo,et al.  A simplified 3-D Navier-Stokes numerical model for landslide-tsunami: Application to the Gulf of Mexico , 2013 .

[46]  C. Synolakis,et al.  The Runup of Long Waves , 1986 .

[47]  D. Goring,et al.  Tsunamis -- the propagation of long waves onto a shelf , 1978 .

[48]  Stephan T. Grilli,et al.  Modeling the 26 December 2004 Indian ocean tsunami : Case study of impact in Thailand - art. no. C07024 , 2007 .

[49]  S. Grilli,et al.  The Papua New Guinea tsunami of 17 July 1998: anatomy of a catastrophic event , 2008 .

[50]  R. LeVeque,et al.  Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems , 1998 .

[51]  Jeffrey C. Harris,et al.  Near- And Far-field Tsunami Hazard From the Potential Flank Collapse of the Cumbre Vieja Volcano , 2012 .

[52]  Franklin Liu,et al.  Modeling wave runup with depth-integrated equations , 2002 .