long groins, detached breakwaters, and seawalls (Kraus 1983; Kraus and Harikai 
1983; Kraus, Hanson, and Harikai 1985; Hanson and Kraus 1986), both in the 
field and in laboratory physical models. 
85. One-line theory assumptions and equations. Principle assumptions 
in one-line model theory are: 
Nearshore bottom contours move in parallel. 
A depth of closure exists beyond which longshore sediment 
transport does not take place. 
Ion |p 
10 
The volume of beach material in the littoral system, assumed to 
consist mainly of sand, is conserved. 
86. Comparisons of available beach profiles separated by a recent 
32-year interval and by shorter time intervals indicate that the slope of the 
profile along the project site is remarkably stable (cf. Part II, and Appen- 
dix D paragraph 14). In general, beach profile slope adjacent to a groin is 
expected to be milder than average on the updrift side and steeper than aver- 
age on the downdrift side. However, groins along the project shoreline are 
not long and sand bypassing can easily occur during episodes of high longshore 
sediment transport, minimizing the potential offset in slopes. Since the one- 
line model has been successfully used to simulate beach change at groins of 
much greater length at other sites, assumption a is considered to be well sat- 
isfied. A predictive expression for the depth of closure needed to satisfy 
assumption b has recently become available and is described below. Assumption 
ce is necessary for quantitative implementation of the budget analysis 
technique. 
87. The basic equation of the one-line model is: 
wv, tS. (1) 
c 
where 
y = shoreline position 
t = time 
D, = depth of closure 
Q = volume rate of longshore sand transport 
x = distance alongshore 
88. Depth of closure is difficult to determine and becomes, in effect, 
part of the calibration process. In calibration trials, the depth of 
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