coordinates of the MSL contour intercept with the initial survey on each pro- 
file line are defined as the origin of a coordinate system to which all sub- 
sequent surveys are referred (Fig. 7). Negative distances:indicate stations 
landward of the MSL intercept with the initial profile; positive distances 
indicate seaward stations. 
For a profile crossing the MSL elevation, the MSL intercept was linearly 
interpolated. When a profile did not cross the MSL elevation, but reached -the 
0.61-meter MSL elevation, the MSL intercept was determined by extrapolating 
the profile along the slope defined by the two seawardmost surveyed points on 
the profile (DeWall, 1979). Extrapolated shoreline points are indicated by the 
"x" symbol in the plots of Appendix B. Profile lines which could not be sur- 
veyed to the 0.6l-meter MSL elevation were not used for shoreline or volume 
computations. 
The cross-sectional area under each profile was computed. This area is 
bounded by three lines: (a) a vertical line projected from the landwardmost 
distance common to all surveys on a given profile line, (b) a horizontal line 
at the MSL elevation, and (c) the surveyed profile. The calculation was accom- 
plished by summing 30.5-centimeter horizontal slices through the area under the 
profile from the highest elevation to MSL. The area change was then computed 
by subtracting the measured profile area from the previous profile area (Fig. 8). 
Note that the change in area (and volume) is referred to the previous profile 
and not the original profile. Cross-sectional areas were computed in square 
feet and then converted to unit volume in cubic meters per meter of shoreline. 
The plots in Appendix E are profile envelopes; i.e, the plots show two 
lines drawn through the upper and lower extremes of the surveyed sand eleva- 
tions on each of the profile lines. The envelope of extremes contains points 
from many different surveys, rather than trace a particular eroded or accreted 
profile found during one survey. This profile "sweep zone" is useful for 
designing the required depth of footings for coastal structures, burial depth 
for pipelines,and for other beach protection or improvement considerations. 
The temporal and spatial variability of each of the beach profiles was 
also evaluated using empirical eigenfunction analysis. This technique has 
been used in a variety of scientific disciplines for many years (Lorenz, 1959), 
but it is only recently that the technique has been applied to examination of 
variability within the coastal zone. 
When applied to analysis of a profile line resurveyed over a period of 
time, the method is useful in determining ‘the topographic variability in the 
onshore-offshore direction and in time. Comparison of the eigenfunctions of a 
series of profiles taken along a coastline is useful for determining the long- 
shore variability. The technique has been applied to studies on beaches, 
islands, and other coastal and bathymetric features on both coasts (Winant, 
Inman, and Nordstrom, 1975; Vincent, et al., 1976; Resio, et al., 1977; 
Aubrey, 1978). 
The objective of eigenfunction analysis is to separate the temporal and 
spatial dependence of the data set so that it can be represented as a linear 
combination of corresponding functions of time and space (Winant, Inman, and 
Nordstrom, 1975). This helps identify processes responsible for profile 
28 
