It is important to point out that wave refraction effect on shoreline evo- 
lution has been found particularly important. It is particularly necessary in 
order to determine a planform stability criteria which can be established from 
the present formulation. 
The problem of shoreline stability needs to be investigated, both physi- 
cally and numerically, as for some deepwater wave angle, shoreline perturbance 
may increase by instability instead of being flattened out. 
Perhaps one of the most significant results of this mathematical approach 
to shoreline evolution is to point out the need for more research to quantify 
the phenomenology relevant to shoreline evolution. The insertion of empirical 
parameters has allowed the investigator to fit (to a large extent) a form of 
shoreline evolution; however, the processes involved in each of these param- 
eters are not well known, and, what fits at Holland, may not necessarily apply 
elsewhere. For example, the research topics which will improve the model are 
(a) onshore-offshore movement; (b) quantity of sand (silt) lost by rip currents 
or density currents; (c) percentage of sand in suspension; (d) distribution of 
sand discharge as a function of the distance from shore; and (e) more impor- 
tantly, how to treat the wave climatology in finite time intervals to obtain 
an equivalent result. The last topic may be the most difficult since the noise, 
(i.e., daily variation and effect of storm) may exceed the signal (i.e., the 
long-term trend). Shoreline evolution is due to a succession of extreme events 
separated by long-period time effects of equal importance. Therefore, the 
treatment of long-term evolution from an average wave climatology is question- 
able, since the complete time history may have to be considered on a daily basis. 
This topic can be investigated by a sensitivity analysis to wave definition; 
€.g., the present model could be used, as well as a research guideline for fill- 
ing many knowledge gaps in shoreline processes. 
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