Continental Shelf for numerous locations along the Atlantic and gulf 

 shorelines, and finds that an exponential curve fits averaged profiles 

 quite well across the nearshore segment of the profile. A preliminary 

 view indicates that a semilogarithmic profile also fits data from the 

 Pacific coast. In general, an equation of the form, 



y - y Q = de" ax , (3) 



can be fitted to the profile data, where y is the vertical coordinate 

 of the profile, x is the horizontal coordinate, y Q is a datum adjust- 

 ment factor that must be established by trial and error, d is the depth 

 at the seaward limit of effective sediment transport, and a is an em- 

 pirical coefficient that describes the rate of increase in water depth 

 with distance offshore. Other investigators have applied other equations 

 to approximate the nearshore beach profile (e.g., Bruun, 1954; Resio, et 

 al., 1974; Dean, 1977). 



The method of fitting equation 3 to actual profile data is best illus- 

 trated by an example (Table). The table gives profile data at Ocean Beach, 

 San Francisco, California, taken in November and December 1972. The data 

 are averaged from three profile lines located about 1,500 feet (457 meters) 

 apart. Columns 1 and 2 in the Table are the original average profile data. 

 Column 3 represents a first approximation to determine the datum correc- 

 tion term, y . The first approximation is obtained by taking the datum 

 at the elevation of the seawardmost point on the profile (i.e., assume 

 y = -37.5 feet or 11.4 meters). Hence, column 3 is obtained by adding 

 37.5 to the values in column 2. The resulting profile is shown plotted 

 (solid circles) on semilogarithmic graph paper in Figure 2. A line is 

 fitted to the points of the profile in the nearshore region to obtain a 

 correction to the first approximation. The correction, which is to be 

 added to the first approximation values, is read from the fitted line at 

 the seawardmost point of the profile (e.g., at 3,400 feet or 1,036 meters 

 in Fig. 2). The 6.0-foot (1.83 meters) adjustment is added to column 3 of 

 the table to obtain the second approximation given in column 4. A cor- 

 rection to the second approximation is subsequently obtained from a line 

 fitted to the plotted second approximation values (see Fig. 2). The cor- 

 rection in the example is 1.5 feet (0.46 meter) which is added to the 

 values in column 4 of the table to obtain a third approximation. Plotting 

 the third approximation in Figure 2 indicates only a small change in the 

 location of the fitted line. The value of y is thus found to be -37.5 

 - 8.1 = -45.6 feet (-13.9 meters); the depth beyond which significant 

 sediment movement does not occur can be read from the y intercept of 

 Figure 2 as d = 55.0 feet (16.8 meters). The value of a in equation 3 

 is obtained from the slope of the line in Figure 2. Hence, for the 

 example, 



o = A£njr = In 55 - In 10 = Q ^^ (4) 



Ax 3025 - 



where the y intercept and the point where the line crosses y = 10 have 

 been used to evaluate the slope. The logarithm to the base e, tn, is 



