Non-stationary wave height climate modeling and simulation

[1] The most popular methods of simulating time series for wave heights and other meteorological and oceanic variables are based on the use of autoregressive models and the transformation of variables to make them normal and stationary. Generally, when these models are used, attention is centered on their capacity to represent the autocorrelation of the series. In this article, a simulation model is proposed that is based on the following: (i) a non-stationary parametric mixture model for the marginal distribution of the variable, that combines a log-normal distribution for main-mass regime and generalized Pareto distributions for upper and lower tail regimes, and (ii) the use of copulas to model the time dependency of the variable. The model has been evaluated by comparing the original series and the simulated series in terms of the autocorrelation function, the mean, the annual maxima and peaks-over-threshold regimes, and the persistences regime. It has also been compared to an ARMA model and found to yield more satisfactory results.

[1]  Francesco Serinaldi,et al.  Fully Nested 3-Copula: Procedure and Application on Hydrological Data , 2007 .

[2]  Christos Stefanakos,et al.  A nonstationary stochastic model for long-term time series of significant wave height , 1995 .

[3]  P. van Gelder,et al.  Estimating joint tail probabilities of river discharges through the logistic copula , 2007 .

[4]  Christos Stefanakos,et al.  A unified methodology for the analysis, completion and simulation of nonstationary time series with missing values, with application to wave data , 2001 .

[5]  Giuseppe Passoni,et al.  A multivariate model of sea storms using copulas , 2007 .

[6]  B. Gouldby,et al.  Statistical simulation of flood variables: incorporating short‐term sequencing , 2008 .

[7]  Melisa Menéndez,et al.  Seasonality and duration in extreme value distributions of significant wave height , 2008 .

[8]  C. Guedes Soares,et al.  Representation of non-stationary time series of significant wave height with autoregressive models , 1996 .

[9]  P. Ruggiero,et al.  Increasing wave heights and extreme value projections: The wave climate of the U.S. Pacific Northwest , 2010 .

[10]  C. Guedes Soares,et al.  Linear models of the time series of significant wave height on the Southwest Coast of Portugal , 1996 .

[11]  C. Guedes Soares,et al.  Modelling the long-term time series of significant wave height with non-linear threshold models , 2000 .

[12]  David P. Callaghan,et al.  Statistical simulation of wave climate and extreme beach erosion , 2008 .

[13]  The effect of temporal dependence on the estimation of the frequency of extreme ocean climate events , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[14]  Inigo J. Losada,et al.  Estimation of the long‐term variability of extreme significant wave height using a time‐dependent Peak Over Threshold (POT) model , 2006 .

[15]  Fentaw Abegaz,et al.  Modeling statistical dependence of Markov chains via copula models , 2008 .

[16]  Konstandinos A. Belibassakis,et al.  Nonstationary Stochastic Modelling of Multivariate Long-Term Wind and Wave Data , 2005 .

[17]  C. Guedes Soares,et al.  Bivariate autoregressive models for the time series of significant wave height and mean period , 2000 .

[18]  Uncertainty assessment: Application to the shoreline , 2008 .

[19]  Marc Prevosto,et al.  Survey of stochastic models for wind and sea state time series , 2007 .

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

[21]  Inigo J. Losada,et al.  Extreme wave climate variability in southern Europe using satellite data , 2010 .

[22]  Fabrizio Durante,et al.  Copula Theory and Its Applications , 2010 .

[23]  Richard L. Smith,et al.  Markov chain models for threshold exceedances , 1997 .

[24]  Gerassimos A. Athanassoulis,et al.  Time series modeling of significant wave height in multiple scales, combining various sources of data , 2006 .

[25]  Gerassimos A. Athanassoulis,et al.  Bivariate Stochastic Simulation Based On Nonstationary Time Series Modelling , 2003 .

[26]  Fentaw Abegaz,et al.  Dynamic Copula-Based Markov Time Series , 2008 .

[27]  Mathieu Ribatet,et al.  Modeling all exceedances above a threshold using an extremal dependence structure: Inferences on several flood characteristics , 2008, 0802.0436.

[28]  Lee Fawcett,et al.  Markov chain models for extreme wind speeds , 2006 .

[29]  Jianqing Fan,et al.  Nonlinear Time Series : Nonparametric and Parametric Methods , 2005 .

[30]  Todd L. Walton,et al.  Simulation of Nonstationary, Non‐Gaussian Water Levels on Great Lakes , 1990 .

[31]  Norman W. Scheffner,et al.  STOCHASTIC TIME-SERIES REPRESENTATION OF WAVE DATA , 1992 .

[32]  R. Nelsen.  An Introduction to Copulas (Springer Series in Statistics) , 2006 .

[33]  B. Gouldby,et al.  A simulation method for flood risk variables , 2007 .

[34]  C. Genest,et al.  Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask , 2007 .