fully arisen sea. The assumption of a universal form for the fully arisen 

 sea permits the computation of other wave characteristics such as total 

 wave energy, significant wave height, and period of maximum energy. The 

 equilibrium state between wind and waves rarely occurs in the ocean, and 

 may never occur for higher wind speeds. 



A more general model may be constructed by assuming that the sea is 

 calm when the wind begins to blow. Integration of the equations governing 

 wave growth then permits the consideration of changes in the shape of the 

 spectrum with increasing fetch and duration. If enough wave and wind 

 records are available, empirical data may be analyzed to provide similar 

 information. Pierson, Neumann, and James (1955) introduced this type of 

 wave prediction scheme based almost entirely on empirical data. Inoue 

 (1966, 1967) repeated this exercise in a manner more consistent with the 

 Miles-Phillips theory using a differential equation for wave growth. Inoue 

 was a member of Pierson 's group when this work was carried out, and his 

 prediction scheme may be regarded as a replacement for the earlier 

 Pierson-Neuman-James (PNJ) wave prediction model. The topic has been 

 extended by Silvester and Vongvisessomjai (1971) and others. 



These simplified wave prediction schemes are based on the implicit 

 assumption that the waves being considered are due entirely to a wind 

 blowing at constant speed and direction for an overwater distance called 

 the fetch and for a time period called the duration. 



In principle it would be possible to consider some effects of variable 

 wind velocity hy tracing each wave train. Once waves leave a generating 

 area and become swell, the wave energy is then propagated according to the 

 group velocity. The total energy at a point, and the square of the signif- 

 icant wave height could be obtained by adding contributions from individual 

 wave trains. Without a computer, this procedure is too laborious, and 

 theoretically inaccurate. 



A more practical procedure is to relax the restrictions implied by 

 derivation of these schemes. Thus wind direction may be considered con- 

 stant if it varies from the mean by less than some finite value, say 30°. 

 Wind speed may be considered constant if it varies from the mean by less 

 than ± 5 knots (2.5 meters/second) or h barb on the weather map. This 

 assumption is not much greater than the uncertainty inherent in wind 

 reports from ships. In this procedure, average values are used and are 

 assumed constant over the fetch area, and for a particular duration. 



The theoretical spectra for the partially arisen sea can be used 

 to develop formulas for such wave parameters as total energy, significant 

 wave height and period of maximum energy density. 



Similar formulas can also be developed empirically from wind and wave 

 observations. A quasi-empirical - quasi-theoretical procedure was used by 

 Sverdrup and Munk (1947) to construct the first widely used wave predic- 

 tion system. The Sverdrup-Munk prediction curves were revised by 

 Bretschneider (1952a, 1958) with additional empirical data. Thus, this 

 prediction system is often called the Sverdrup-Munk-Bretschneider (SMB) 

 method. It is the most convenient wave prediction system to use when a 

 limited amount of data and time are available. 



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