corresponding to a given level of losses can be predicted. The form of this 

 function is illustrated in Figure 16 in the main text. The program will also 

 apply an Extremal Type I cumulative probability distribution of significant 

 wave heights as follows: 



F(H ) = e" 

 s 



[e-H^/*] 



(A2) 



where 



F(Hg) = cumulative probability distribution of events 



where ~H < H 

 s s 



e and 4) = site-specific coefficients derived by regression of 



historical wave data 



to estimate the expected annual economic losses by 



Lo 



dF(H ) 

 s 



dH 

 s J 



dHg (A3) 



where 



the average number of extreme events per year above the 

 threshold H value original 

 (must be input by the user) 



threshold H value originally used to derive e and 4) 



H ^ = a practical upper limit taken as the H value whose 

 probability of exceedance is 0.0000001 



4. This formulation assumes that the number of extreme events per year 

 is random and can be represented by a mean value and is independent of the 

 significant wave heights representing the intensity of the individual storms. 

 The lower limit of integration is Hj^^ , below which the expected losses are 

 taken as zero. Extrapolation of F(H ) to H values below the threshold 

 value applied to data used to originally derive e and ^ is probably con- 

 servative, but this question will be the subject of further study. A thresh- 

 old Hg value set equal co U^^ would presumably resolve any problems if 

 adequate statistical confidence can be maintained. The integration is accom- 

 plished by a numerical application of Simpson's Rule with 100 intervals. 



5. The majority of the expected losses statistically occur during 

 storms whose H is just above U^^ where the probability density is sub- 

 stantial. The higher H values occur on the tail of the probability density 

 function and may even be precluded by depth limitations. The program does not 

 deal with depth limitations and assumes the Extremal Type I function fully 



A2 



