Choice of wave climate is the remaining input parameter to be determined, and 
is the most controversial. The wave climate most desirable for the study of 
shoreline evolution is a time series giving wave height, H, period, T, and 
direction, D. Unfortunately, this is seldom available and hence monthly sta- 
tistical summaries must be used, such as those by the SSMO for southern Lake 
Michigan. One possible use of the summaries is to construct monthly times t 
for each possible (H,T,D) triple, i.e., t(H,T,D), and then calculate the evo- 
lution of the shoreline as the (H,T,D) triples are chosen in some determin- 
istic order or at random. This method would be computationally very expensive 
and is not used. The most simple approach is to assume that these are but two 
(H,D,T) triples representing the gross transport north and south, each occur- 
ring for some length of time per month. The entire shoreline is alternately 
calculated for an incremental time, assuming the direction of the incoming 
wave iS positive, then negative. The period, T, used is taken to be the 
average T; i.e., 
ei Osis) 1b 
2p (H,T) 
where the p(H,T) are the (H,T) probabilities given in Table 19 of the SSMO 
(National Oceanic and Atmospheric Administration, 1963-73). The choice of (H,D) 
for north and south, denoted (Hjy,Djy) and (Ho,Dg), respectively, must now be made. 
This choice is subject to the condition that the actual northerly transport, as 
calculated from the statistics and given a straight shoreline for the reach of 
interest, be preserved; 1.e., 
QT oa : a = D2) . 
tH cos a, sin a, = t, » p(T) "p.(H, D) HE cos a, Sin o% 
Eel Dis gaivemnne: 
north transport 
where 
t; = number of hours in a given month 
p(T|H) = conditional probability T occurs given H 
p(1,D) = probability of (H,D) pair (using Table 18 in SSMO as a data base) 
A, = Dy - shoreline orientation 
Ci a(S) 
ty = number of hours the average wave condition exists 
Hy, = average wave height 
ae =) Dy = shorelanel orientation 
Dy = average direction 
and similarly for the directions giving south transport. 
The average directions of the shoreline at the breakwater are calculated 
from the historical records. The directions are chosen for the incoming wave 
angles since the complex geometry of the harbor breakwater shields the nearby 
shoreline from waves arriving from most directions. At present, the time dura- 
tion of waves arriving from the north is assumed to be the same as from the 
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