five observations (only two in shallow water) , they estimated the constants 

 related to a series of hypotheses on the directional structure of natural 

 wind-driven seas. Their intent was to provide guidance for using sea state 

 models in engineering design. As a result, their work is among the most 

 frequently referenced in this regard. However, they did not make enough 

 measurements to estimate a wave climate in shallow water; and their conclu- 

 sions were based on measurements with an intermediate -resolution directional 

 gage. It remains to be seen whether their results are universally applicable, 

 i.e., true at other shallow-water sites, valid in all wave climates, and 

 verified by measurements with a higher resolution directional gage. 



Gage Arrays 



28. High-resolution directional gages almost all rely on synoptic 

 observations of sea surface displacement at many points in space. This 

 sampling requirement is analogous to the resolution of frequency spectra by 

 the measurement of sea surface displacement at many points in time (e.g., a 

 time series from a wave staff) . Simultaneous observations from a spatial 

 array of sea surface sensors enables the spatial properties (i.e., direc- 

 tionality) of a wave field to be determined from the measured sea surface 

 topography. Note that this method does not require any particular knowledge 

 of a relation between wavelength and wave period. If the time series analog 

 is followed exactly, then one must measure as many points in the wavelength of 

 a wave train as one measures in time divisions of the period of a wave train. 

 For example, if a time series collects 20 samples per period of a given wave, 

 then a spatial array must sample a grid of 20 points on a side (since there 

 are 2 horizontal coordinates) which covers the wavelength of the wave. 

 Requiring a total of 400 gages, this condition is normally beyond practical 

 application. 



29. This principle was applied once in an experiment called the Stereo 

 Wave Observation Project (Cote et al . 1960). Stereo photographs of the sea 

 surface were made from low-flying aircraft, and the resulting images were 

 analyzed using topographic techniques. Sea surface elevations were then 

 discretized in a 60- x 90-element grid for an effective 5,400 gage positions. 

 At great expense and effort, one high- resolution directional spectrum was 



13 



