High-fidelity hurricane surge forecasting using emulation and sequential experiments

Probabilistic hurricane storm surge forecasting using a high-fidelity model has been considered impractical due to the overwhelming computational expense to run thousands of simulations. This article demonstrates that modern statistical tools enable good forecasting performance using a small number of carefully chosen simulations. This article offers algorithms that quickly handle the massive output of a surge model while addressing the missing data at unsubmerged locations. Also included is a new optimal design criterion for selecting simulations that accounts for the log transform required to statistically model surge data. Hurricane Michael (2018) is used as a testbed for this investigation and provides evidence for the approach’s efficacy in comparison to the existing probabilistic surge forecast method.

[1]  S. Peng,et al.  Effect of determining initial conditions by four-dimensional variational data assimilation on storm surge forecasting , 2006 .

[2]  M. Mann,et al.  A Fiscally Based Scale for Tropical Cyclone Storm Surge , 2018, Weather and Forecasting.

[3]  Henry P. Wynn,et al.  Screening, predicting, and computer experiments , 1992 .

[4]  Alexandros A. Taflanidis,et al.  Kriging metamodeling for approximation of high-dimensional wave and surge responses in real-time storm/hurricane risk assessment , 2013 .

[5]  D. Shepard.  A two-dimensional interpolation function for irregularly-spaced data , 1968, ACM National Conference.

[6]  J. O'Brien,et al.  Remote forcing contribution to storm‐induced sea level rise during Hurricane Dennis , 2006 .

[7]  A. Raftery,et al.  Strictly Proper Scoring Rules, Prediction, and Estimation , 2007 .

[8]  Clint Dawson,et al.  Scalability of an Unstructured Grid Continuous Galerkin Based Hurricane Storm Surge Model , 2011, J. Sci. Comput..

[9]  Robert B. Gramacy,et al.  Cases for the nugget in modeling computer experiments , 2010, Statistics and Computing.

[10]  Robert B. Gramacy,et al.  Adaptive Design and Analysis of Supercomputer Experiments , 2008, Technometrics.

[11]  Michael Goldstein,et al.  Galaxy Formation: Bayesian History Matching for the Observable Universe , 2014, 1405.4976.

[12]  M. Plumlee.  Bayesian Calibration of Inexact Computer Models , 2017 .

[13]  Jérémy Rohmer,et al.  A meta-modelling strategy to identify the critical offshore conditions for coastal flooding , 2012 .

[14]  Jeffrey A. Melby,et al.  Surrogate modeling for peak or time-dependent storm surge prediction over an extended coastal region using an existing database of synthetic storms , 2016, Natural Hazards.

[15]  James O. Berger,et al.  Parallel partial Gaussian process emulation for computer models with massive output , 2016 .

[16]  T. J. Mitchell,et al.  Bayesian Prediction of Deterministic Functions, with Applications to the Design and Analysis of Computer Experiments , 1991 .

[17]  Shreyes N. Melkote,et al.  Analysis of Computer Experiments With Functional Response , 2012, Technometrics.

[18]  H. Rue,et al.  An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach , 2011 .

[19]  Ibrahim Hoteit,et al.  A Comparison of Ensemble Kalman Filters for Storm Surge Assimilation , 2014 .

[20]  Ling Li,et al.  Sequential design of computer experiments for the estimation of a probability of failure , 2010, Statistics and Computing.

[21]  C. Jelesnianski,et al.  NUMERICAL COMPUTATIONS OF STORM SURGES WITHOUT BOTTOM STRESS , 1966 .

[22]  Michael A. West,et al.  A dynamic modelling strategy for Bayesian computer model emulation , 2009 .

[23]  Jason L. Loeppky,et al.  Batch sequential designs for computer experiments , 2010 .

[24]  N. Cressie.  The origins of kriging , 1990 .

[25]  Serge Guillas,et al.  Sequential Design with Mutual Information for Computer Experiments (MICE): Emulation of a Tsunami Model , 2014, SIAM/ASA J. Uncertain. Quantification.

[26]  Bledar A. Konomi,et al.  Ice model calibration using semicontinuous spatial data , 2019, The Annals of Applied Statistics.

[27]  J. Westerink,et al.  Modeling the physics of storm surges , 2008 .

[28]  Marcel Zijlema,et al.  Modeling hurricane waves and storm surge using integrally-coupled, scalable computations , 2011 .

[29]  V. R. Joseph,et al.  An Efficient Surrogate Model for Emulation and Physics Extraction of Large Eddy Simulations , 2016, Journal of the American Statistical Association.

[30]  Christopher W. Reed,et al.  Quadrature-based approach for the efficient evaluation of surge hazard , 2010 .

[31]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[32]  R. Sakia.  The Box-Cox transformation technique: a review , 1992 .

[33]  D. Hill,et al.  Emulation as an approach for rapid estuarine modeling , 2019, Coastal Engineering.

[34]  Fangzheng Xie,et al.  A Theoretical Framework of the Scaled Gaussian Stochastic Process in Prediction and Calibration , 2018, SIAM/ASA J. Uncertain. Quantification.

[35]  George Michailidis,et al.  Sequential Experiment Design for Contour Estimation From Complex Computer Codes , 2008, Technometrics.

[36]  A. O'Hagan,et al.  Gaussian process emulation of dynamic computer codes , 2009 .

[37]  Long Wang,et al.  Scaled Gaussian Stochastic Process for Computer Model Calibration and Prediction , 2017, SIAM/ASA J. Uncertain. Quantification.

[38]  S. Hagen,et al.  Terrain-driven unstructured mesh development through semi-automatic vertical feature extraction , 2015 .

[39]  Daniel P Weikel,et al.  Phenomenological forecasting of disease incidence using heteroskedastic Gaussian processes: a dengue case study , 2017, 1702.00261.

[40]  C. Willmott,et al.  Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance , 2005 .

[41]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[42]  A. Cox,et al.  Data and numerical analysis of astronomic tides, wind-waves, and hurricane storm surge along the northern Gulf of Mexico , 2016 .

[43]  D. Lindley.  On a Measure of the Information Provided by an Experiment , 1956 .

[44]  Thomas A. Hardy,et al.  Progress and Recent Developments in Storm Surge Modeling , 1997 .

[45]  Chris E. Forest,et al.  Statistical calibration of climate system properties , 2009 .

[46]  Sudipto Banerjee,et al.  Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets , 2014, Journal of the American Statistical Association.

[47]  J. Feyen,et al.  A Basin to Channel-Scale Unstructured Grid Hurricane Storm Surge Model Applied to Southern Louisiana , 2008 .

[48]  C. F. Wu,et al.  Efficient Calibration for Imperfect Computer Models , 2015, 1507.07280.

[49]  Jim W. Hall,et al.  Adaptive importance sampling for risk analysis of complex infrastructure systems , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[50]  J. Westerink,et al.  Rapid Assessment of Wave and Surge Risk during Landfalling Hurricanes: Probabilistic Approach , 2013 .

[51]  D. Higdon,et al.  Computer Model Calibration Using High-Dimensional Output , 2008 .

[52]  C. Jelesnianski,et al.  SLOSH: Sea, Lake, and Overland Surges from Hurricanes , 1992 .

[53]  N. Cressie,et al.  Fixed Rank Filtering for Spatio-Temporal Data , 2010 .

[54]  Taylor G. Asher,et al.  Low frequency water level correction in storm surge models using data assimilation , 2019, Ocean modelling.

[55]  D. Pollard,et al.  Calibrating an Ice Sheet Model Using High-Dimensional Binary Spatial Data , 2015, 1501.01937.

[56]  Robert B. Gramacy,et al.  laGP: Large-Scale Spatial Modeling via Local Approximate Gaussian Processes in R , 2016 .

[57]  Stephen C. Medeiros,et al.  Unstructured finite element mesh decimation for real-time Hurricane storm surge forecasting , 2020 .

[58]  Brian Blanton,et al.  Variability in Coastal Flooding predictions due to forecast errors during Hurricane Arthur , 2018, Coastal Engineering.

[59]  M. Haran,et al.  Fast dimension-reduced climate model calibration and the effect of data aggregation , 2013, 1303.1382.