Abstract
In order to accommodate the computational burden of high-fidelity storm surge numerical models, surrogate modeling (metamodeling) techniques have gained significant popularity over the past decade. Utilizing an existing database of synthetic storm simulations, these models provide a fast-to-compute mathematical approximation to the input/output relationship of the numerical model that was used to establish this database. Thus, they offer fast predictions and, when properly calibrated, can maintain the accuracy of the high-fidelity numerical model that generated the original database. This study extends the previous work of the authors and investigates different computational aspects for incorporating Sea Level Rise (SLR) explicitly as an input within such a surrogate modeling framework. Kriging, also referenced as Gaussian process regression, is specifically chosen as the surrogate modeling technique for this study. The storms utilized correspond to a database of 300 synthetic tropical cyclones recently developed by the US Army Corps of Engineers Coastal Hazards System for the Puerto Rico and US Virgin Islands region, which considers three different SLR scenarios. The development of separate surrogate models for each of the three SLR scenarios and of a single surrogate model that predicts across all SLR scenarios are compared, addressing several relevant issues like (1) the proper definition of validation metrics (2) the correct implementation of cross-validation techniques, and (3) the need for adjustment of the surrogate model hyper-parameter calibration. It is shown that proper attention is needed when the same storms have been considered across all the different SLR scenarios in the database; otherwise, the calibration of the surrogate model may be ineffective, and the validation of its accuracy will provide erroneous confidence. The proper normalization of the storm surge output to improve the surrogate model accuracy is also discussed. Finally, the proper selection of storm simulations for establishing the database for the surrogate model development is examined, emphasizing how this selection should be performed efficiently across the different SLR scenarios. It is demonstrated that high surrogate model accuracy can be accommodated with a small number of strategically chosen storm simulations. Leveraging this investigation, recommendations are offered on how to efficiently create future high-fidelity databases to support the development of surrogate models that predict across different SLR scenarios.
Similar content being viewed by others
Availability of data and materials
Database of synthetic storms used in this study is part of the US Army Corps of Engineers (USACE) Coastal Hazards System (CHS) program (https://chs.erdc.dren.mil).
References
AlKajbaf A, Bensi M (2020) Application of surrogate models in estimation of storm surge: comparative assessment. Appl Soft Comput 91:106184
Anarde KA, Kameshwar S, Irza JN, Nittrouer JA, Lorenzo-Trueba J, Padgett JE, Sebastian A, Bedient PB (2018) Impacts of hurricane storm surge on infrastructure vulnerability for an evolving coastal landscape. Nat Hazards Rev 19(1):04017020
Bachoc F (2013) Cross validation and maximum likelihood estimations of hyper-parameters of Gaussian processes with model misspecification. Comput Stat Data Anal 66:55–69
Contento A, Xu H, Gardoni P (2020) Probabilistic formulation for storm surge predictions. Struct Infrastruct Eng 16:1–20
Dangendorf S, Marcos M, Wöppelmann G, Conrad CP, Frederikse T, Riva R (2017) Reassessment of 20th century global mean sea level rise. Proc Natl Acad Sci 114(23):5946–5951
Dubrule O (1983) Cross validation of kriging in a unique neighborhood. J Int Assoc Math Geol 15(6):687–699
Frazier TG, Wood N, Yarnal B, Bauer DH (2010) Influence of potential sea level rise on societal vulnerability to hurricane storm-surge hazards, Sarasota County, Florida. Appl Geogr 30(4):490–505
Hallegatte S, Patmore N, Mestre O, Dumas P, Corfee-Morlot J, Herweijer C, Muir-Wood R (2008) Assessing climate change impacts, sea level rise and storm surge risk in port cities: a case study on Copenhagen. OECD environment working papers (3):0_1
Hartigan JA, Wong MA (1979) Algorithm AS 136: a k-means clustering algorithm. J R Stat Soc Ser C Appl Stat 28(1):100–108
Hsu C-H, Olivera F, Irish JL (2018) A hurricane surge risk assessment framework using the joint probability method and surge response functions. Nat Hazards 91(1):7–28
Irish JL, Resio DT, Cialone MA (2009) A surge response function approach to coastal hazard assessment. Part 2: quantification of spatial attributes of response functions. Nat Hazards 51(1):183–205
Javeline D, Kijewski-Correa T (2019) Coastal homeowners in a changing climate. Clim Change 152(2):259–274
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 261–262:24–38
Jia G, Taflanidis AA, Nadal-Caraballo NC, Melby JA, Kennedy AB, Smith JM (2016) Surrogate modeling for peak or time-dependent storm surge prediction over an extended coastal region using an existing database of synthetic storms. Nat Hazards 81(2):909–938
Karim MF, Mimura N (2008) Impacts of climate change and sea-level rise on cyclonic storm surge floods in Bangladesh. Glob Environ Change 18(3):490–500
Kijewski-Correa T, Taflanidis A, Vardeman C II, Sweet J, Zhang J, Snaiki R, Wu T, Silver Z, Kennedy A (2020) Geospatial environments for hurricane risk assessment: applications to situational awareness and resilience planning in New Jersey. Front Built Environ. https://doi.org/10.3389/fbuil.2020.549106
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):565–585
Kleijnen JP (2009) Kriging metamodeling in simulation: a review. Eur J Oper Res 192(3):707–716
Kleijnen JP, van Beers W (2019) Statistical tests for cross-validation of Kriging models
Kohavi R (1995) A study of cross-validation and bootstrap for accuracy estimation and model selection. In: IJCAI, Montreal, Canada, pp 1137–1145
Link H, Barrett C (2018) Adaptation to future risks in coastal megacities—New York City case study: local assessment and survey findings in water front neighborhoods. J Extreme Events 5(01):1850002
Luettich Jr RA, 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. Coastal engineering research center Vicksburg MS
Nadal-Caraballo N, Melby J, Gonzalez V, Cox A (2015) North Atlantic Coast Comprehensive Study (NACCS): coastal storm hazards from Virginia to Maine. US Army Engineer Research and Development Center (ERDC), Technical Report ERDC-CHL-TR-15-5
Nadal-Caraballo NC, Gonzalez V, Campbell MO, Torres MJ, Melby JA, Taflanidis AA (2020) Coastal hazards system: a probabilistic coastal hazard analysis framework. In: Malvárez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp.1211–1216. Coconut Creek (Florida), ISSN 0749-0208. https://doi.org/10.2112/SI95-235.1
Nicholls RJ, Cazenave A (2010) Sea-level rise and its impact on coastal zones. Science 328(5985):1517–1520
Oulahen G, McBean G, Shrubsole D, Chang SE (2019) Production of risk: multiple interacting exposures and unequal vulnerability in coastal communities. Reg Environ Change 19(3):867–877
Owensby M, Bryant M, Hesser T, Provost L, Ding Y (2019) Calibration and validation of the Puerto Rico/U.S. Virgin Island domain model setup for the South Atlantic Coast Study (SACS). Letter report. U.S. Army Engineer Research and Development Center, Vicksburg, MS
Pant R, Thacker S, Hall JW, Alderson D, Barr S (2018) Critical infrastructure impact assessment due to flood exposure. J Flood Risk Manag 11(1):22–33
Resio DT, Westerink JJ (2008) Modeling the physics of storm surges. Phys Today 61(9):33
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):1765–1792
Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Statistical Science 4(4):409–435
Schobi R, Sudret B, Wiart J (2015) Polynomial-chaos-based Kriging. Int J Uncertain Quant 5(2):171–193
Shepard CC, Agostini VN, Gilmer B, Allen T, Stone J, Brooks W, Beck MW (2012) Assessing future risk: quantifying the effects of sea level rise on storm surge risk for the southern shores of Long Island, New York. Nat Hazards 60(2):727–745
Simm J, Guise A, Robbins D, Engle J (2015) US North Atlantic coast comprehensive study: resilient adaptation to increasing risk
Smith JM, Sherlock AR, Resio DT (2001) STWAVE: steady-state spectral wave model user’s manual for STWAVE, version 3.0. Engineer Research And Development Center Vicksburg Ms Coastal And Hydraulicslab
Sundararajan S, Keerthi SS (2001) Predictive approaches for choosing hyperparameters in Gaussian processes. Neural Comput 13(5):1103–1118
Tanaka S, Bunya S, Westerink JJ, Dawson C, Luettich RA (2011) Scalability of an unstructured grid continuous Galerkin based hurricane storm surge model. J Sci Comput 46(3):329–358
Zhang J, Taflanidis AA, Nadal-Caraballo NC, Melby JA, Diop F (2018) Advances in surrogate modeling for storm surge prediction: storm selection and addressing characteristics related to climate change. Nat Hazards 94(3):1225–1253
Acknowledgements
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 Systems R&D Program, USACE's South Atlantic Division (SAD) and Jacksonville District (SAJ) is also gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kyprioti, A.P., Taflanidis, A.A., Nadal-Caraballo, N.C. et al. Incorporation of sea level rise in storm surge surrogate modeling. Nat Hazards 105, 531–563 (2021). https://doi.org/10.1007/s11069-020-04322-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11069-020-04322-z