-1
10
Data Points
Best Fit Line
-2
10
-3
10
-4
10
-5
10
1
2
3
4
5
10
10
10
10
10
a, m
Fig. 10. Plot of a versus b values for hyperbolic-tangent shape and best-fit line.
EXAMPLES OF FITTING WITH HYPERBOLIC TANGENT
Two examples of fittings of the hyperbolic tangent shape to beaches in the database
are shown here. Values of obtained fitting coefficients are listed in Appendix A.
Drakes Bay, California, USA
Drakes Bay is a 16.4-km-long crenulate-shaped beach located north of San
Francisco. Its shape is determined by diffraction of Pacific-Ocean waves at a headland
called Point Reyes. The area is tectonically active and lies on the San Andreas Fault.
Beach sediments consist of discontinuous accumulations of well-to-moderately sorted,
fine- to coarse-grained sand interspersed with pebbles and gravel.
Fig. 11 shows the nautical chart with 56 digitized data points and the best-fit curve.
The visual fit is very good in the beach section close to the main headland. The curve
deviates from the shoreline in the middle section because of irregularities in beach plan
form and because of the presence of Drakes Estero (a river mouth).
Rosas Bay, Girona, Spain
Rosas Bay is located on the Northeast coast of Spain. It is a 2.2-km-long crenulate-
shaped beach with 1 to 1.5 headlands. Shoreline shape is controlled in great part by
jetties. Beach material is fine- to medium-size sand with median grain size in the range
of 0.24 to 0.29 mm. Fig. 12 shows an aerial view of the Bay with 29 digitized data
points and best-fit hyperbolic tangent. Excellent visual agreement is seen.
Moreno & Kraus
12
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