155. This definition is introduced in analogy with the spectrally 

 weighted peak direction parameter proposed by The lAHR Working Group on Wave 

 Generation and Analysis (1989). Here, the bulk spread obtains most of its 

 value from regions of high energy in the frequency spectrum. Furthermore, the 

 effect of refraction from frequency to frequency is less pronounced. In 

 particular, if the general spread for all frequencies is about the same (see 

 Figure 7b), the result of Equation 23 will be close to this spread estimate. 

 It will generally be less than the estimate of Equation 22 because the 

 smearing effect (see Figure 7a, direction spectrum panel) is reduced. 



156. Other parameters of the bulk frequency-direction spectrum can be 

 computed from the characteristic directions given by Equations 21(a-c) . For 

 instance, asymmetry and positioning parameters can be assigned like the 

 individual frequency parameters given in Equations 18 and 19, respectively. 

 These have not been used in this report and are not explicitly defined. 



Parameters for Modal Analysis 



157. An important property of directional distributions is the number 

 of distinct peaks or modes that occur. These can suggest the existence of 

 various sources or sinks of wave energy (e.g., island sheltering, see 



Pawka 1983 and Pawka, Inman, and Guza 1984) or may be a signature of nonlinear 

 interactions among wave trains (Elgar and Guza 1985a, 1985b). All of these 

 mechanisms act to distribute wave energy in direction and need to be consider- 

 ed. In this report, a simple modal analysis is conducted wherein the number 

 and relative strengths of modes are computed from the directional distribu- 

 tions at each frequency. This is intended to determine the frequency of 

 occurrence of multimodal distributions, to compute their relative importance, 

 and to indicate if further research is required. 



158. The first requirement is a definition of a mode. As mentioned in 

 Part III, IMLE results can have maxima and minima that are simply deviate 

 approximations to a true unimodal directional distribution and not truly 

 distinct modes. To ensure that a minimum of D(f„,d^) between two maxima is 

 more likely a true modal separation and not just an artifact of analysis, the 

 following is used as a definition: a distinct mode occurs when a minimum in a 

 directional distribution is less than half of the smaller of the two surround- 

 ing maxima. 



62 



