A NUMERICAL MODEL FOR PREDICTING SHORELINE CHANGES 
by 
Bernard Le Mehaute and Mills Soldate 
I. INTRODUCTION 
This report establishes a mathematical model for shoreline evolution and 
calibrates the model with a test case at Holland Harbor, Michigan. Even though 
the mathematical model is general and could be applied to a number of situa- 
tions, the emphasis is on the Great Lakes, and more specifically, on shoreline 
evolution near navigation structures. 
An interim report by Le Mehaute and Soldate (1977) reported on the feasi- 
bility of applying existing mathematical models to real case situations. This 
report is a continuation of that first investigation. 
The present mathematical model includes many of the characteristics already 
covered in the literature. In addition, the model presents an integrated ap- 
proach on a large number of phenomena previously neglected. Its main purpose 
is to develop a practical numerical scheme which could be used to predict shore- 
line evolution. The model would then be able to point out the shortcomings in 
the present state of knowledge. Therefore, the mathematical model covers some 
aspects of shoreline evolution which cannot be quantified with the data obtained 
from the considered test case of Holland Harbor. The mathematical model then 
has to be regarded as a research guide for the future. 
One important aspect is the effect of sand size and density. It is well 
known that the rate of shoreline erosion and sediment loss is largely affected 
by these parameters. The fine sand is transported offshore, while larger size 
sand tends to proceed alongshore according to a littoral drift formula. This 
effect could not presently be quantified; therefore, it is introduced in the 
mathematical model as a constant. 
The present mathematical model can continuously be upgraded as the state- 
of-the-art progresses, and as the model is tested for a large number of cases. 
It is important to remember that the model deals with long-term shoreline evo- 
lution as defined in Le Mehaute and Soldate (1977). Short-term evolution must 
be considered as local perturbations which are superimposed on the presently 
defined topography. 
Three time scales of shoreline evolution which can be distinguished are 
(a) geological evolution over hundreds and thousands of years, (b) long-term 
evolution from year-to-year or decade, and (c) short-term or seasonal evolu- 
tion during a major storm. 
Associated with these time scales are distances or ranges of influence over 
which changes occur. The geological time scale deals, for instance, with the 
entire area of the Great Lakes. The long-term evolution deals with a more 
limited stretch of shoreline and range of influence; e.g., between two head- 
lands or between two harbor entrances. The short-term evolution deals with 
the intricacies of the surf zone circulation; e.g., summer-winter profiles, 
bar, rhythmic beach patterns, etc. 
