The Annals of Applied Statistics

Functional emulation of high resolution tsunami modelling over Cascadia

Serge Guillas, Andria Sarri, Simon J. Day, Xiaoyu Liu, and Frederic Dias

Full-text: Open access

Abstract

The rarity of tsunamis impels the scientific community to rely on numerical simulation for planning and risk assessment purposes because of the low availability of actual data from historic events. Numerical models, also called simulators, typically produce time series of outputs. Due to the large computational cost of such simulators, statistical emulation is required to carry out uncertainty quantification tasks, as emulators efficiently approximate simulators. There is thus a need to create emulators that respect the nature of time series outputs. We introduce here a novel statistical emulation of the input-output dependence of these computer models. We employ the Outer Product Emulator with two enhancements. Functional registration and Functional Principal Components techniques improve the predictions of the emulator. Our phase registration method captures fine variations in amplitude. Smoothness in the time series of outputs is modelled, and we are thus able to select more representative, and more parsimonious, regression functions than a fixed basis method such as a Fourier basis. We apply this approach to the high resolution tsunami wave propagation and coastal inundation for the Cascadia region in the Pacific Northwest. The coseismic representation in this analysis is novel, and more realistic than in previous studies. With the help of the emulator, we can carry out sensitivity analysis of the maximum wave elevation with respect to the source characteristics, and we are able to propagate uncertainties from the source characteristics to wave heights in order to issue probabilistic statements about tsunami hazard for Cascadia.

Article information

Source
Ann. Appl. Stat., Volume 12, Number 4 (2018), 2023-2053.

Dates
Received: March 2017
Revised: January 2018
First available in Project Euclid: 13 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1542078035

Digital Object Identifier
doi:10.1214/18-AOAS1142

Mathematical Reviews number (MathSciNet)
MR3875691

Keywords
Uncertainty quantification emulation tsunami modelling sensitivity analysis functional data analysis

Citation

Guillas, Serge; Sarri, Andria; Day, Simon J.; Liu, Xiaoyu; Dias, Frederic. Functional emulation of high resolution tsunami modelling over Cascadia. Ann. Appl. Stat. 12 (2018), no. 4, 2023--2053. doi:10.1214/18-AOAS1142. https://projecteuclid.org/euclid.aoas/1542078035


Export citation

References

  • Adams, J. (1990). Paleoseismicity of the Cascadia subduction zone: Evidence from turbidites off the Oregon–Washington margin. Tectonics 9 569–583.
  • Atwater, F. B., Nelson, R. A., Clague, J. J., Carver, A. G., Yamaguchi, K. D., Bobrowsky, T. P., Bourgeois, J., Darienzo, E. M., Grant, C. W., Hemphill-Haley, E., Kelsey, M. H., Jacoby, C. G., Nishenko, P. S., Palmer, P. S., Peterson, D. C. and Reinhart, M. A. (1995). Summary of coastal geologic evidence for past great earthquakes at the Cascadia subduction zone. Earthq. Spectra 11 1–18.
  • Bayarri, M. J., Berger, J. O., Cafeo, J., Garcia-Donato, G., Liu, F., Palomo, J., Parthasarathy, R. J., Paulo, R., Sacks, J. and Walsh, D. (2007). Computer model validation with functional output. Ann. Statist. 35 1874–1906.
  • Beck, J. and Guillas, S. (2016). Sequential design with mutual information for computer experiments (MICE): Emulation of a tsunami model. SIAM/ASA J. Uncertain. Quantificat. 4 739–766.
  • Behrens, J. and Dias, F. (2015). New computational methods in tsunami science. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 373 20140382.
  • Bernard, E. and Titov, V. (2015). Evolution of tsunami warning systems and products. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 373 20140371.
  • Bilionis, I., Zabaras, N., Konomi, B. A. and Lin, G. (2013). Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification. J. Comput. Phys. 241 212–239.
  • Bricker, J. D. and Nakayama, A. (2014). Contribution of trapped air, deck superelevation, and nearby structures to bridge deck failure during a tsunami. J. Hydraul. Eng. 140 05014002.
  • Castro, P. E., Lawton, W. H. and Sylvestre, E. A. (1986). Principal modes of variation for processes with continuous sample curves. Technometrics 28 329–337.
  • Chang, W., Applegate, P. J., Haran, M. and Keller, K. (2014). Probabilistic calibration of a Greenland Ice Sheet model using spatially resolved synthetic observations: Toward projections of ice mass loss with uncertainties. Geosci. Model Dev. 7 1933–1943.
  • Day, S. and Fearnley, C. (2015). A classification of mitigation strategies for natural hazards: Implications for the understanding of interactions between mitigation strategies. Nat. Hazards 79 1219–1238.
  • Dutykh, D., Poncet, R. and Dias, F. (2011). The VOLNA code for the numerical modeling of tsunami waves: Generation, propagation and inundation. Eur. J. Mech. B Fluids 30 598–615.
  • Giles, M. B., Mudalige, G. R., Sharif, Z., Markall, G. and Kelly, P. H. (2011). Performance analysis of the OP2 framework on many-core architectures. ACM SIGMETRICS Perform. Eval. Rev. 38 9–15.
  • Goldfinger, C., Nelson, C. H., Johnson, J. E., Morey, A. E., Gutierrez-Pastor, J., Karabanov, E., Eriksson, A. T., Gracia, E., Dunhill, G., Patton, J., Enkin, R., Dallimore, A. and Vallier, T. (2012). Turbidite event history: Methods and implications for Holocene paleoseismicity of the Cascadia Subduction Zone. U.S. Geol. Surv. Professional Paper 1661.
  • González, F. I., Geist, E. L., Jaffe, B., Kânoğlu, U., Mofjeld, H., Synolakis, C. E., Titov, V. V., Arcas, D., Bellomo, D., Carlton, D. et al. (2009). Probabilistic tsunami hazard assessment at seaside, Oregon, for near- and far-field seismic sources. J. Geophys. Res., Oceans 114 C11023.
  • Guillas, S., Sarri, A., Day, S. J., Liu, X. and Dias, F. (2018). Supplement to “Functional emulation of high resolution tsunami modelling over Cascadia.” DOI:10.1214/18-AOAS1142SUPP.
  • Gusman, A. R., Tanioka, Y., MacInnes, B. T. and Tsushima, H. (2014). A methodology for near-field tsunami inundation forecasting: Application to the 2011 Tohoku tsunami. J. Geophys. Res., Solid Earth 119 8186–8206.
  • Hawkes, A. D., Horton, B. P., Nelson, A. R., Vane, C. H. and Sawai, Y. (2011). Coastal subsidence in Oregon, USA, during the giant Cascadia earthquake of AD 1700. Quat. Sci. Rev. 30 364–376.
  • Heidarzadeh, M., Pirooz, M. D. and Zaker, N. H. (2009). Modeling the near-field effects of the worst-case tsunami in the Makran subduction zone. Ocean Eng. 36 368–376.
  • Higdon, D., Gattiker, J., Williams, B. and Rightley, M. (2008). Computer model calibration using high-dimensional output. J. Amer. Statist. Assoc. 103 570–583.
  • Hung, Y., Joseph, V. R. and Melkote, S. N. (2015). Analysis of computer experiments with functional response. Technometrics 57 35–44.
  • Hyndman, R. D. (2013). Downdip landward limit of Cascadia great earthquake rupture. J. Geophys. Res., Solid Earth 118 5530–5549.
  • Jolliffe, I. T. (2002). Principal Component Analysis, 2nd ed. Springer, New York.
  • Joseph, V. R., Hung, Y. and Sudjianto, A. (2008). Blind kriging: A new method for developing metamodels. J. Mech. Des. 130 031102.
  • Kaufman, C. G., Bingham, D., Habib, S., Heitmann, K. and Frieman, J. A. (2011). Efficient emulators of computer experiments using compactly supported correlation functions, with an application to cosmology. Ann. Appl. Stat. 5 2470–2492.
  • Kleiber, W., Katz, R. W. and Rajagopalan, B. (2013). Daily minimum and maximum temperature simulation over complex terrain. Ann. Appl. Stat. 7 588–612.
  • Kneip, A. and Ramsay, J. O. (2008). Combining registration and fitting for functional models. J. Amer. Statist. Assoc. 103 1155–1165.
  • Lay, T., Kanamori, H., Ammon, C. J., Nettles, M., Ward, S. N., Aster, R. C., Beck, S. L., Bilek, S. L., Brudzinski, M. R., Butler, R. et al. (2005). The great Sumatra-Andaman earthquake of 26 December 2004. Science 308 1127–1133.
  • Lay, T., Ammon, C. J., Kanamori, H., Koper, K. D., Sufri, O. and Hutko, A. R. (2010). Teleseismic inversion for rupture process of the 27 February 2010 Chile (Mw 8.8) earthquake. Geophys. Res. Lett. 37 L13301.
  • Leonard, L. J., Rogers, G. C. and Mazzotti, S. (2014). Tsunami hazard assessment of Canada. Nat. Hazards 70 237–274.
  • Leonard, L. J., Currie, C. A., Mazzotti, S. and Hyndman, R. D. (2010). Rupture area and displacement of past Cascadia great earthquakes from coastal coseismic subsidence. Geol. Soc. Am. Bull. 122 2079–2096.
  • Liu, X. and Guillas, S. (2017). Dimension reduction for Gaussian process emulation: An application to the influence of bathymetry on tsunami heights. SIAM/ASA J. Uncertain. Quantificat. 5 787–812.
  • López-Pintado, S. and Romo, J. (2009). On the concept of depth for functional data. J. Amer. Statist. Assoc. 104 718–734.
  • Ludwin, R. S., Dennis, R., Carver, D., McMillan, A. D., Losey, R., Clague, J., Jonientz-Trisler, C., Bowechop, J., Wray, J. and James, K. (2005). Dating the 1700 Cascadia earthquake: Great coastal earthquakes in native stories. Seismol. Res. Lett. 76 140–148.
  • Masterlark, T. and Hughes, K. L. (2008). Next generation of deformation models for the 2004 M9 Sumatra-Andaman earthquake. Geophys. Res. Lett. 35 L19310.
  • Mazzotti, S., Dragert, H., Henton, J., Schmidt, M., Hyndman, R., James, T., Lu, Y. and Craymer, M. (2003). Current tectonics of northern Cascadia from a decade of GPS measurements. J. Geophys. Res., Solid Earth 108 2554.
  • Moore, G. F., Bangs, N. L., Taira, A., Kuramoto, S., Pangborn, E. and Tobin, H. J. (2007). Three-dimensional splay fault geometry and implications for tsunami generation. Science 318 1128–1131.
  • Morris, M. D. (2012). Gaussian surrogates for computer models with time-varying inputs and outputs. Technometrics 54 42–50.
  • Mudalige, G. R., Giles, M. B., Reguly, I., Bertolli, C. and Kelly, P. H. J. (2012). OP2: An active library framework for solving unstructured mesh-based applications on multi-core and many-core architectures. In 2012 Innovative Parallel Computing (InPar) 1–12. IEEE, Los Alamitos, CA.
  • Mudalige, G. R., Giles, M. B., Thiyagalingam, J., Reguly, I. Z., Bertolli, C., Kelly, P. H. and Trefethen, A. E. (2013). Design and initial performance of a high-level unstructured mesh framework on heterogeneous parallel systems. Parallel Comput. 39 669–692.
  • Nelson, A. R., Sawai, Y., Jennings, A. E., Bradley, L.-A., Gerson, L., Sherrod, B. L., Sabean, J. and Horton, B. P. (2008). Great-earthquake paleogeodesy and tsunamis of the past 2000 years at Alsea Bay, central Oregon coast, USA. Quat. Sci. Rev. 27 747–768.
  • Oakley, J. E. and O’Hagan, A. (2004). Probabilistic sensitivity analysis of complex models: A Bayesian approach. J. R. Stat. Soc. Ser. B. Stat. Methodol. 66 751–769.
  • Okada, Y. (1992). Internal deformation due to shear and tensile faults in a half-space. Bull. Seismol. Soc. Am. 82 1018–1040.
  • Okal, E. A. (2015). The quest for wisdom: Lessons from 17 tsunamis, 2004–2014. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 373 20140370.
  • Ramsay, J., Hooker, G. and Graves, S. (2009). Functional Data Analysis with R and MATLAB. Springer, Dordrecht.
  • Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis, 2nd ed. Springer, New York.
  • Rougier, J. (2008). Efficient emulators for multivariate deterministic functions. J. Comput. Graph. Statist. 17 827–843.
  • Rougier, J., Guillas, S., Maute, A. and Richmond, A. D. (2009). Expert knowledge and multivariate emulation: The thermosphere-ionosphere electrodynamics general circulation model (TIE-GCM). Technometrics 51 414–424.
  • Salmanidou, D. M., Guillas, S., Georgiopoulou, A. and Dias, F. (2017). Statistical emulation of landslide-induced tsunamis at the Rockall Bank, NE Atlantic. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 473 20170026.
  • Sarri, A., Guillas, S. and Dias, F. (2012). Statistical emulation of a tsunami model for sensitivity analysis and uncertainty quantification. Nat. Hazards Earth Syst. Sci. 12 2003–2018.
  • Satake, K., Wang, K. and Atwater, B. F. (2003). Fault slip and seismic moment of the 1700 Cascadia earthquake inferred from Japanese tsunami descriptions. J. Geophys. Res., Solid Earth 108 2535.
  • Satake, K., Shimazaki, K., Tsuji, Y. and Ueda, K. (1996). Time and size of a giant earthquake in Cascadia inferred from Japanese tsunami records of January 1700. Nature 379 246–249.
  • Satake, K., Fujii, Y., Harada, T. and Namegaya, Y. (2013). Time and space distribution of coseismic slip of the 2011 tohoku earthquake as inferred from tsunami waveform data. Bull. Seismol. Soc. Am. 103 1473–1492.
  • Silverman, B. W. (1996). Smoothed functional principal components analysis by choice of norm. Ann. Statist. 24 1–24.
  • Simons, M., Minson, S. E., Sladen, A. et al. (2011). The 2011 magnitude 9.0 Tohoku-Oki earthquake: Mosaicking the megathrust from seconds to centuries. Science 332 1421–1425.
  • Spiller, E. T., Bayarri, M. J., Berger, J. O., Calder, E. S., Patra, A. K., Pitman, E. B. and Wolpert, R. L. (2014). Automating emulator construction for geophysical hazard maps. SIAM/ASA J. Uncertain. Quantificat. 2 126–152.
  • Wang, K., Mulder, T., Rogers, G. C. and Hyndman, R. D. (1995). Case for very low coupling stress on the Cascadia Subduction Fault. J. Geophys. Res., Solid Earth 100 12907–12918.
  • Wang, P.-L., Engelhart, S. E., Wang, K., Hawkes, A. D., Horton, B. P., Nelson, A. R. and Witter, R. C. (2013). Heterogeneous rupture in the great Cascadia earthquake of 1700 inferred from coastal subsidence estimates. J. Geophys. Res., Solid Earth 118 2460–2473.
  • Wells, D. L. and Coppersmith, K. J. (1994). New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull. Seismol. Soc. Am. 84 974–1002.
  • Witter, R. C., Zhang, Y. J., Wang, K., Priest, G. R., Goldfinger, C., Stimely, L., English, J. T. and Ferro, P. A. (2013). Simulated tsunami inundation for a range of Cascadia megathrust earthquake scenarios at Bandon, Oregon, USA. Geosphere 9 1783–1803.

Supplemental materials