Regression Models for Outlier Identification (Hurricanes and Typhoons) in Wave Hindcast Databases

AbstractThe development of numerical wave prediction models for hindcast applications allows a detailed description of wave climate in locations where long-term instrumental records are not available. Wave hindcast databases (WHDBs) have become a powerful tool for the design of offshore and coastal structures, offering important advantages for the statistical characterization of wave climate all over the globe (continuous time series, wide spatial coverage, constant time span, homogeneous forcing, and more than 60-yr-long time series). However, WHDBs present several deficiencies reported in the literature. One of these deficiencies is related to typhoons and hurricanes, which are inappropriately reproduced by numerical models. The main reasons are (i) the difficulty of specifying accurate wind fields during these events and (ii) the insufficient spatiotemporal resolution used. These difficulties make the data related to these events appear as “outliers” when compared with instrumental records. These bad d...

[1]  C. Landsea,et al.  A Reanalysis of the 1911–20 Atlantic Hurricane Database , 2008 .

[2]  Alberto Luceñ,et al.  Detecting possibly non‐consecutive outliers in industrial time series , 1998 .

[3]  A. Sterl,et al.  Intercomparison of Different Wind–Wave Reanalyses , 2004 .

[4]  T. Coleman,et al.  On the Convergence of Reflective Newton Methods for Large-scale Nonlinear Minimization Subject to Bounds , 1992 .

[5]  Vic Barnett,et al.  Outliers in Statistical Data , 1980 .

[6]  K. Bellmann Daniel, C., F. S. WOOD, J. W. GORMAN: Fitting Equations to Data. Computer Analysis of Multifactor Data for Scientists and Engineers. John Wiley & Sons, New York-London-Sydney-Toronto 1974. XIV, 342 S., 132 Abb., 33 Tab., £6.50 , 1975 .

[7]  V. Yohai,et al.  The Detection of Influential Subsets in Linear Regression by Using an Influence Matrix , 1995 .

[8]  Luigi Cavaleri,et al.  Accuracy of the modelled wind and wave fields in enclosed seas , 2004 .

[9]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[10]  J. Simonoff,et al.  Procedures for the Identification of Multiple Outliers in Linear Models , 1993 .

[11]  Inigo J. Losada,et al.  Directional Calibration of Wave Reanalysis Databases Using Instrumental Data , 2011 .

[12]  S. Coles,et al.  An Introduction to Statistical Modeling of Extreme Values , 2001 .

[13]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[14]  L. Weissfeld,et al.  INFLUENCE DIAGNOSTICS FOR THE NORMAL LINEAR MODEL WITH CENSORED DATA , 1990 .

[15]  Brian J Gray A simple graphic for assessing influence in regression G , 1986 .

[16]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[17]  Alberto Luceño,et al.  Multiple outliers detection through reweighted least deviances , 1998 .

[18]  Charles,et al.  A tropical cyclone data tape for the North Atlantic basin, 1886-1977 : contents, limitations, and uses , 1978 .

[19]  A. Atkinson Fast Very Robust Methods for the Detection of Multiple Outliers , 1994 .

[20]  Matthew S. Mayo,et al.  Elemental Subsets: The Building Blocks of Regression , 1997 .

[21]  A. Conejo,et al.  Perturbation Approach to Sensitivity Analysis in Mathematical Programming , 2006 .

[22]  Robert F. Ling,et al.  K-Clustering as a Detection Tool for Influential Subsets in Regression , 1984 .

[23]  Ali S. Hadi,et al.  Extreme Value and Related Models with Applications in Engineering and Science , 2004 .

[24]  Helmut Schneider,et al.  Influence diagnostics for the Weibull model fit to censored data , 1990 .

[25]  Anthony C. Atkinson,et al.  Plots, transformations, and regression : an introduction to graphical methods of diagnostic regression analysis , 1987 .

[26]  S. Chatterjee,et al.  Influential Observations, High Leverage Points, and Outliers in Linear Regression , 1986 .

[27]  George L. Edgett Multiple Regression with Missing Observations Among the Independent Variables , 1956 .

[28]  Andrew T. Cox,et al.  Evaluation of Contemporary Ocean Wave Models in Rare Extreme Events: The “Halloween Storm” of October 1991 and the “Storm of the Century” of March 1993 , 1996 .

[29]  Alberto Luceño,et al.  Estimation of missing values in possibly partially nonstationary vector time series , 1997 .

[30]  Tsung-Chi Cheng,et al.  Robust diagnostics for the heteroscedastic regression model , 2011, Comput. Stat. Data Anal..

[31]  D. Montgomery,et al.  A comparative analysis of multiple outlier detection procedures in the linear regression model , 2001 .

[32]  S. Sinha Methods of nonlinear programming , 2006 .

[33]  I. Losada,et al.  A method for spatial calibration of wave hindcast data bases , 2008 .

[34]  Luigi Cavaleri,et al.  The calibration of wind and wave model data in the Mediterranean Sea , 2006 .

[35]  Cuthbert Daniel,et al.  Fitting Equations to Data: Computer Analysis of Multifactor Data , 1980 .

[36]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[37]  Sanford Weisberg,et al.  Directions in Robust Statistics and Diagnostics , 1991 .

[38]  W. W. Muir,et al.  Regression Diagnostics: Identifying Influential Data and Sources of Collinearity , 1980 .

[39]  H. Krogstad,et al.  Satellite wave measurements for coastal engineering applications , 1999 .

[40]  P. Rousseeuw,et al.  A fast algorithm for the minimum covariance determinant estimator , 1999 .

[41]  D. Pregibon Logistic Regression Diagnostics , 1981 .

[42]  Peter J. Rousseeuw,et al.  Robust Regression and Outlier Detection , 2005, Wiley Series in Probability and Statistics.

[43]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[44]  Douglas M. Hawkins Identification of Outliers , 1980, Monographs on Applied Probability and Statistics.

[45]  S. Chatterjee Sensitivity analysis in linear regression , 1988 .

[46]  Enrique F. Castillo,et al.  A General Method for Local Sensitivity Analysis With Application to Regression Models and Other Optimization Problems , 2004, Technometrics.

[47]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[48]  J. Brian Gray,et al.  Leverage, residual, and interaction diagnostics for subsets of cases in least squares regression , 1997 .

[49]  Karen Y. Fung,et al.  A generalized estreme Studentized residual multiple-outlier-detetection procedure in linear regression , 1991 .

[50]  G. Dodet,et al.  Wave climate variability in the North-East Atlantic Ocean over the last six decades , 2010 .

[51]  A. Sterl,et al.  A New Nonparametric Method to Correct Model Data: Application to Significant Wave Height from the ERA-40 Re-Analysis , 2005 .

[52]  Michael A. Saunders,et al.  Large-scale linearly constrained optimization , 1978, Math. Program..

[53]  Martin Mächler,et al.  Robust regression:a weighted least squares approach , 1997 .

[54]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[55]  Mark D. Powell,et al.  The HRD real-time hurricane wind analysis system , 1998 .

[56]  R. Welsch,et al.  The Hat Matrix in Regression and ANOVA , 1978 .

[57]  C. Guedes Soares,et al.  44-year wave hindcast for the North East Atlantic European coast , 2008 .

[58]  Bernd Schwarzmann,et al.  A connection between local-influence analysis and residual diagnostics , 1991 .

[59]  V. J. Cardone,et al.  Hindcasting the Directional Spectra of Hurricane-Generated Waves , 1976 .

[60]  Mia Hubert,et al.  LIBRA: a MATLAB library for robust analysis , 2005 .

[61]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[62]  Thomas F. Coleman,et al.  On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds , 1994, Math. Program..