(b) Calibrating, determining empirical constants, and separating 
various effects, such as due to change of lake level, navigation 
Structures, etc. 
(c) Predicting long-term future evolution. 
(d) Assessing the effect of future construction. 
The mathematical model presented in this report is just a first step in this 
direction. Much of the model may be modified after the application of the mathe- 
Matical model to other cases which could be used for further calibration. 
Theoretical developments for the model are presented in Section II. Section 
III describes the shoreline evolution recorded at Holland Harbor, Michigan, and 
compares the mathematical model with the test case investigated. Section IV 
provides recommendations and conclusions. An Appendix describes a computer 
program to investigate shoreline behavior. 
Ii. THEORETICAL DEVELOPMENTS 
Consideration is given to a coastal zone limited by boundaries at a small 
distance from the surf zone (Fig. 1). The bottom topography is defined in a 
three-coordinate system, oxyz, by a function zp = f(x,y,t) where the ox-axis 
is parallel to the average shoreline direction, the oy-axis is perpendicular 
seaward, and oz is positive upward from a fixed horizontal datum. The angle 
of the shoreline with the ox-axis is small. The shoreline is defined by y = y,, 
Z = Zg = Zph(x,yg,t) which also defines the sea level as a function of time. 
Waterline 
Yb Ys Ye Yq y 
Figure 1. Coastal zone. 
