r.D(H, T, t) = 0.0622t\y-^^ (24) 



2 

 where t can be taken as the average duration of exceedance of H^L in 



Equation 3. This duration is difficult to assess in practice. Investigations 



of the long-term joint probability distribution F (H , T , t) are needed for 



a more precise definition of this parameter. If the pdf f(H , T , t) could 



in turn be estimated, a particular rubble-mound breakwater design could be 



evaluated for its expected annual damages by 



E ^ = \ ffCfcDiH, T, t) f(H, T, t)dHdTdt (25) 



68. The practical problem in applying Equation 25 is estimating the 

 joint pdf f(H , T , t) . An interim approach to account for duration would 

 be to assume an average t for all storms exceeding the design condition, 

 based on evaluation of hindcast statistics or other long data records. Like- 

 wise, characteristic peak periods and water depths d can be associated with 

 extreme storms in most cases without rigorous definition of the joint pdf or 

 cpd. This is already common practice, since a design wave period and water 

 surface elevation have always been necessary for accompltshment of wave trans- 

 formation analyses and estimates of runup, overtopping, and wave transmission. 

 Methods for estimating the joint long-term probability distribution of H and 

 T are discussed by Sigbjornsson, Haver, and Morch (1976) and Ochi (1980). A 

 practical approach to estimating expected damage by use of the DHI-Iribarren 

 formula, given appropriate wave data, is proposed in Jensen (1984). Assump- 

 tions concerning the mean direction of wave propagation 4) and the associated 

 directional spreading o are also inherent in current practice for defining 

 the wave climate at a site. The effect of wave direction on rubble-mound sta- 

 bility and damage rate is discussed by Losada and Gimenez-Curto (1982) and 

 Christensen et al. (1984). Estimation of expected damages in terms of D(H, 

 T, t, d, 4i, a) and f(H , T , t , d , <)), o) will be possible only after much 

 additional theoretical, laboratory, and field investigation. 



44 



