| A Probability Distribution of Surface Elevation for Wind Waves in Terms of the Gram-Charlier Series |
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| 作者姓名： | HUANG Chuan-jiang |
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| 作者单位： | Physical Oceanography Laboratory，Ocean University of China，Qingdao 266003，China，Physical Oceanography Laboratory，Ocean University of China，Qingdao 266003，China，Physical Oceanography Laboratory，Ocean University of China，Qingdao 266003，China，Physical Oceanography Laboratory，Ocean University of China，Qingdao 266003，China |
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| 基金项目： | This project was financially supported by the National Nature Science Foundation of China(Grant No.49876012,49976003) |
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| 摘 要： | Laboratory experiments are conducted to study the probability distribution of surface elevation for wind waves and the convergence is discussed of the Gram-Charlier series in describing the surface elevation distribution. Results show that the agreement between the Gram-Charlier series and the observed distribution becomes better and better as the truncated order of the series increases in a certain range, which is contrary to the phenomenon observed by Huang and Long (1980) . It is also shown that the Gram-Charlier series is sensitive to the anomalies in the data set which will make the agreement worse if they are not preprocessed appropriately. Negative values of the probability distribution expressed by the Gram-Charlier series in some ranges of surface elevations are discussed, but the absolute values of the negative values as well as the ranges of their occurrence become smaller gradually as more and more terms are included. Therefore the negative values will have no evident effect on the form of t
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A Probability Distribution of Surface Elevation for Wind Waves in Terms of the Gram-Charlier Series |
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| HUANG Chuan-jiang,DAI De-jun WANG Wei and QIAN Cheng-chun
Physical Oceanography Laboratory,Ocean University of China,Qingdao ,China.A Probability Distribution of Surface Elevation for Wind Waves in Terms of the Gram-Charlier Series[J].China Ocean Engineering,2003,17(4):605-616. |
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| Authors: | HUANG Chuan-jiang DAI De-jun WANG Wei and QIAN Cheng-chun
Physical Oceanography Laboratory Ocean University of China Qingdao China |
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| Institution: | Physical Oceanography Laboratory, Ocean University of China, Qingdao,266003, China Physical Oceanography Laboratory, Ocean University of China, Qingdao,266003, China Physical Oceanography Laboratory, Ocean University of China, Qingdao,266003, China Physical Oceanography Laboratory, Ocean University of China, Qingdao,266003, China |
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| Abstract: | Laboratory experiments are conducted to study the probability distribution of surface elevation for wind waves and the convergence is discussed of the Gram-Charlier series in describing the surface elevation distribution. Results show that the agreement between the Gram-Charlier series and the observed distribution becomes better and better as the truncated order of the series increases in a certain range, which is contrary to the phenomenon observed by Huang and Long (1980) . It is also shown that the Gram-Charlier series is sensitive to the anomalies in the data set which will make the agreement worse if they are not preprocessed appropriately. Negative values of the probability distribution expressed by the Gram-Charlier series in some ranges of surface elevations are discussed, but the absolute values of the negative values as well as the ranges of their occurrence become smaller gradually as more and more terms are included. Therefore the negative values will have no evident effect on the form of the whole surface elevation distribution when the series is truncated at higher orders. Furthermore, a simple recurrence formula is obtained to calculate the coefficients of the Gram-Charlier series in order to extend the Gram-Charlier series to high orders conveniently. |
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| Keywords: | Gram-Charlier series wave surface elevation probability distribution |
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