Natural Hazards

, Volume 94, Issue 3, pp 1225–1253 | Cite as

Advances in surrogate modeling for storm surge prediction: storm selection and addressing characteristics related to climate change

  • Jize Zhang
  • Alexandros A. TaflanidisEmail author
  • Norberto C. Nadal-Caraballo
  • Jeffrey A. Melby
  • Fatimata Diop
Original Paper


This paper establishes various advancements for the application of surrogate modeling techniques for storm surge prediction utilizing an existing database of high-fidelity, synthetic storms (tropical cyclones). Kriging, also known as Gaussian process regression, is specifically chosen as the surrogate model in this study. Emphasis is first placed on the storm selection for developing the database of synthetic storms. An adaptive, sequential selection is examined here that iteratively identifies the storm (or multiple storms) that is expected to provide the greatest enhancement of the prediction accuracy when that storm is added into the already available database. Appropriate error statistics are discussed for assessing convergence of this iterative selection, and its performance is compared to the joint probability method with optimal sampling, utilizing the required number of synthetic storms to achieve the same level of accuracy as comparison metric. The impact on risk estimation is also examined. The discussion then moves to adjustments of the surrogate modeling framework to support two implementation issues that might become more relevant due to climate change considerations: future storm intensification and sea level rise (SLR). For storm intensification, the use of the surrogate model for prediction extrapolation is examined. Tuning of the surrogate model characteristics using cross-validation techniques and modification of the tuning to prioritize storms with specific characteristics are proposed, whereas an augmentation of the database with new/additional storms is also considered. With respect to SLR, the recently developed database for the US Army Corps of Engineers’ North Atlantic Comprehensive Coastal Study is exploited to demonstrate how surrogate modeling can support predictions that include SLR considerations.


Kriging Storm surge Storm selection Surrogate model extrapolation Gaussian process regression Sea level rise 



This work has been done under contract with the US Army Corps of Engineers (USACE), Engineer Research and Development Center, Coastal and Hydraulics Laboratory (ERDC-CHL). The support of the USACE’s Flood and Coastal R&D Program is also gratefully acknowledged.


The funding was provided by Engineer Research and Development (Grant No. W912HZ-16-P-0083-P00001).


  1. Bachoc F (2013) Cross validation and maximum likelihood estimations of hyper-parameters of Gaussian processes with model misspecification. Comput Stat Data Anal 66:55–69CrossRefGoogle Scholar
  2. Bass B, Bedient P (2018) Surrogate modeling of joint flood risk across coastal watersheds. J Hydrol 558:159–173CrossRefGoogle Scholar
  3. Bengio Y, Grandvalet Y (2004) No unbiased estimator of the variance of k-fold cross-validation. J Mach Learn Res 5:1089–1105Google Scholar
  4. Das HS, Jung H, Ebersole B, Wamsley T, Whalin RW (2010) An efficient storm surge forecasting tool for coastal Mississippi. Paper presented at the 32nd international coastal engineering conference, Shanghai, ChinaGoogle Scholar
  5. Fischbach JR, Johnson DR, Kuhn K (2016) Bias and efficiency tradeoffs in the selection of storm suites used to estimate flood risk. J Mar Sci Eng 4(1):10CrossRefGoogle Scholar
  6. Ginsbourger D, Dupuy D, Badea A, Carraro L, Roustant O (2009) A note on the choice and the estimation of Kriging models for the analysis of deterministic computer experiments. Appl Stoch Models Bus Ind 25(2):115–131CrossRefGoogle Scholar
  7. Hartigan JA, Wong MA (1979) Algorithm AS 136: a K-means clustering algorithm. J Roy Stat Soc Ser C (Appl Stat) 28(1):100–108Google Scholar
  8. Irish J, Resio D, Cialone M (2009) A surge response function approach to coastal hazard assessment. Part 2: quantification of spatial attributes of response functions. Nat Hazards 51(1):183–205CrossRefGoogle Scholar
  9. Jia G, Taflanidis AA (2013) Kriging metamodeling for approximation of high-dimensional wave and surge responses in real-time storm/hurricane risk assessment. Comput Methods Appl Mech Eng 261–262:24–38CrossRefGoogle Scholar
  10. Jia G, Taflanidis AA, Nadal-Caraballo NC, Melby J, Kennedy A, Smith J (2015) Surrogate modeling for peak and time dependent storm surge prediction over an extended coastal region using an existing database of synthetic storms. Nat Hazards 81(2):909–938CrossRefGoogle Scholar
  11. Kennedy AB, Westerink JJ, Smith J, Taflanidis AA, Hope M, Hartman M, Tanaka S, Westerink H, Cheung KF, Smith T, Hamman M, Minamide M, Ota A (2012) Tropical cyclone inundation potential on the Hawaiian islands of Oahu and Kauai. Ocean Model 52–53:54–68CrossRefGoogle Scholar
  12. Kijewski-Correa T, Smith N, Taflanidis A, Kennedy A, Liu C, Krusche M, Vardeman C (2014) CyberEye: development of integrated cyber-infrastructure to support rapid hurricane risk assessment. J Wind Eng Ind Aerodyn 133:211–224CrossRefGoogle Scholar
  13. Kim S-W, Melby JA, Nadal-Caraballo NC, Ratcliff J (2015) A time-dependent surrogate model for storm surge prediction based on an artificial neural network using high-fidelity synthetic hurricane modeling. Nat Hazards 76(1):565–585CrossRefGoogle Scholar
  14. Kleijnen JP, Beers WV (2004) Application-driven sequential designs for simulation experiments: Kriging metamodelling. J Oper Res Soc 55(8):876–883CrossRefGoogle Scholar
  15. Kohavi R (1995) A study of cross-validation and bootstrap for accuracy estimation and model selection. In: International joint conference on artificial intelligence, pp 1137–1145Google Scholar
  16. Lin N, Emanuel K, Oppenheimer M, Vanmarcke E (2012) Physically based assessment of hurricane surge threat under climate change. Nat Clim Change 2(6):462–467CrossRefGoogle Scholar
  17. Liu H, Ong Y-S, Cai J (2017) A survey of adaptive sampling for global metamodeling in support of simulation-based complex engineering design. Struct Multidiscipl Optim 57(1):393–416CrossRefGoogle Scholar
  18. Lophaven SN, Nielsen HB, Sondergaard J (2002) DACE-A MATLAB Kriging toolbox. Technical University of DenmarkGoogle Scholar
  19. Luettich RA, Jr., Westerink JJ, Scheffner NW (1992) ADCIRC: an advanced three-dimensional circulation model for shelves, coasts, and estuaries. Report 1. Theory and methodology of ADCIRC-2DDI and ADCIRC-3DL. Dredging Research Program Technical Report DRP-92-6, U.S Army Engineers Waterways Experiment Station, Vicksburg, MSGoogle Scholar
  20. Meckesheimer M, Booker AJ, Barton RR, Simpson TW (2002) Computationally inexpensive metamodel assessment strategies. AIAA J 40(10):2053–2060CrossRefGoogle Scholar
  21. Nadal-Caraballo NC, Melby JA, Gonzalez VM, Cox AT (2015) North Atlantic coast comprehensive study—coastal storm hazards from Virginia to Maine, ERDC/CHL TR-15-5. U.S. Army Engineer Research and Development Center, VicksburgGoogle Scholar
  22. Niedoroda AW, Resio DT, Toro GR, Divoky D, Reed C (2010) Analysis of the coastal Mississippi storm surge hazard. Ocean Eng 37(1):82–90CrossRefGoogle Scholar
  23. Pronzato L, Müller WG (2012) Design of computer experiments: space filling and beyond. Stat Comput 22(3):681–701CrossRefGoogle Scholar
  24. Rao RB, Fung G, Rosales R (2008) On the dangers of cross-validation. An experimental evaluation. In: Proceedings of the 2008 SIAM international conference on data mining. SIAM, pp 588–596Google Scholar
  25. Resio DT, Boc SJ, Borgman L, Cardone V, Cox A, Dally WR, Dean RG, Divoky D, Hirsh E, Irish JL, Levinson D, Niedoroda A, Powell MD, Ratcliff JJ, Stutts V, Suhada J, Toro GR, Vickery PJ (2007) White paper on estimating hurricane inundation probabilities. Consulting Report prepared by USACE for FEMAGoogle Scholar
  26. Resio D, Irish J, Cialone M (2009) A surge response function approach to coastal hazard assessment—part 1: basic concepts. Nat Hazards 51(1):163–182CrossRefGoogle Scholar
  27. Resio DT, Irish JL, Westering JJ, Powell NJ (2012) The effect of uncertainty on estimates of hurricane surge hazards. Nat Hazards 66(3):1443–1459CrossRefGoogle Scholar
  28. Resio DT, Asher TG, Irish JL (2017) The effects of natural structure on estimated tropical cyclone surge extremes. Nat Hazards 88(3):1609–1637CrossRefGoogle Scholar
  29. Rohmer J, Lecacheux S, Pedreros R, Quetelard H, Bonnardot F, Idier D (2016) Dynamic parameter sensitivity in numerical modelling of cyclone-induced waves: a multi-look approach using advanced meta-modelling techniques. Nat Hazards 84(3):1765–1792CrossRefGoogle Scholar
  30. Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4(4):409–435CrossRefGoogle Scholar
  31. Santner TJ, Williams BJ, Notz WI (2013) The design and analysis of computer experiments. Springer, BerlinGoogle Scholar
  32. Smith JM, Sherlock AR, Resio DT (2001) STWAVE: Steady-state spectral wave model user’s manual for STWAVE, Version 3.0. DTIC DocumentGoogle Scholar
  33. Smith JM, Westerink JJ, Kennedy AB, Taflanidis AA, Smith TD (2011) SWIMS Hawaii hurricane wave, surge, and runup inundation fast forecasting tool. In: 2011 Solutions to coastal disasters conference, Anchorage, Alaska, 26–29 JuneGoogle Scholar
  34. Sundararajan S, Keerthi SS (2001) Predictive approaches for choosing hyperparameters in Gaussian processes. Neural Comput 13(5):1103–1118CrossRefGoogle Scholar
  35. Taflanidis AA, Kennedy AB, Westerink JJ, Smith J, Cheung KF, Hope M, Tanaka S (2013) Rapid assessment of wave and surge risk during landfalling hurricanes; probabilistic approach. ASCE J Waterw Port Coast Ocean Eng 139(3):171–182CrossRefGoogle Scholar
  36. Tanaka S, Bunya S, Westerink J, Dawson C, Luettich R (2011) Scalability of an unstructured grid continuous Galerkin based hurricane storm surge model. J Sci Comput 46:329–358. CrossRefGoogle Scholar
  37. Toro GR, Resio DT, Divoky D, Niedoroda A, Reed C (2010) Efficient joint-probability methods for hurricane surge frequency analysis. Ocean Eng 37:125–134CrossRefGoogle Scholar
  38. USACE (2015) North Atlantic coast comprehensive study: resilient adaption to increasing risk. US Army Corps of Engineers, WashingtonGoogle Scholar
  39. Wynn H (2004) Maximum entropy sampling and general equivalence theory. In: Di Bucchianico A, Läuter H, Wynn HP (eds) mODa 7—advances in model-oriented design and analysis. Contributions to statistics. Physica, Heidelberg, pp 211–218CrossRefGoogle Scholar
  40. Zijlema M (2010) Computation of wind-wave spectra in coastal waters with SWAN on unstructured grids. Coast Eng 57(3):267–277CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Civil and Environmental Engineering and Earth SciencesUniversity of Notre DameNotre DameUSA
  2. 2.Engineer Research and Development Center, Coastal and Hydraulics LaboratoryUnited States Army Corps of EngineersVicksburg, MIUSA
  3. 3.Noble Consultants-G.E.C., Inc.Baton Rouge, LAUSA

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