Return Value Estimation of Significant Wave Heights With Maximum Entropy Distribution

The maximum entropy distribution is proposed to fit the long term and extreme distribution of significant wave heights from which return value estimates are derived. The maximum entropy distribution is applied to data from two sites of different characteristics, namely from Japan characterized by the occurrence of typhoons and from the North Sea with continuous variation of sea state intensity. The compound distribution, Poisson-maximum entropy distribution, is described and adopted to model the data from these two locations. It is shown that in the case of continuous data from the North Sea, this model does not bring any advantage over the direct application of the maximum entropy distribution to adjust the significant wave heights larger than different thresholds. For this case the maximum entropy distribution provides good fits.

[1]  C. Soares,et al.  Statistical Uncertainty in Long-Term Distributions of Significant Wave Height , 1996 .

[2]  A. H. El-Shaarawi,et al.  ON THE CALCULATION OF EXTREME WAVE HEIGHTS: A REVIEW , 1986 .

[3]  C. Guedes Soares,et al.  Application of the r largest-order statistics for long-term predictions of significant wave height , 2004 .

[4]  Edward F. Thompson,et al.  Case Studies of Extreme Wave Analysis: A Comparative Analysis , 1994 .

[5]  C. Guedes Soares,et al.  Modelling distributions of significant wave height , 2000 .

[6]  Dingyong Yu,et al.  Application of Maximum Entropy Distribution to the Statistical Properties of Wave Groups , 2007 .

[7]  Ralph. Deutsch,et al.  Estimation Theory , 1966 .

[8]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[9]  J. B. Berrill,et al.  Maximum entropy and the magnitude distribution , 1980 .

[10]  C. Guedes Soares,et al.  An Application of the Peaks Over Threshold Method to Predict Extremes of Significant Wave Height , 1998 .

[11]  Teb-fu Liu,et al.  Prediction of Extreme Wave Heights and Wind Velocities , 1980 .

[12]  I. Good Maximum Entropy for Hypothesis Formulation, Especially for Multidimensional Contingency Tables , 1963 .

[13]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .

[14]  Wei Liu,et al.  Combination Criteria of Joint Extreme Significant Wave Height and Wind Speed in Weizhoudao Offshore Area , 2008 .

[15]  C. Petrauskas,et al.  Extrapolation of Historical Storm Data for Estimating Design-Wave Heights , 1971 .

[16]  Harald E. Krogstad,et al.  Maximum Entropy Estimation of the Directional Distribution in Ocean Wave Spectra , 1986 .

[17]  C. Guedes Soares,et al.  Modelling the long-term distribution of significant wave height with the Beta and Gamma models , 1999 .

[18]  W. Liu,et al.  Long-Term Statistical Analysis of Typhoon Wave Heights With Poisson-Maximum Entropy Distribution , 2009 .

[19]  W. Cieślikiewicz Determination of the Surface Elevation Probability Distribution of Wind Waves Using Maximum Entropy Principle , 1990 .

[20]  Teh-fu Liu Long-Term Distribution of Hurricane Characteristics , 1982 .

[21]  张立振,et al.  A New Maximum Entropy Probability Function for the Surface Elevation of Nonlinear Sea Waves , 2005 .

[22]  Karel Nacházel Estimation theory in hydrology and water systems , 1993 .

[23]  E. Jaynes Information Theory and Statistical Mechanics , 1957 .

[24]  Michael Isaacson,et al.  Long-Term Distributions of Ocean Waves: A Review , 1981 .

[25]  C. Guedes Soares,et al.  Modelling uncertainty in long-term predictions of significant wave height , 2001 .