IV. COMPUTATION OF SHORELINE CHANGES 



Shoreline changes are generally expressed as feet of horizontal 

 movement, or volumetric change per foot of beach per year. The rate of 

 horizontal advance or retreat is the algebraic of distances measured 

 along the same line perpendicular to the shore between successive 

 surveys converted to an annual basis. Volumetric accretion and erosion 

 rates are usually computed using the average end-area method (Allen, 

 1931; Ruby, Lommel, and Todd, 1950; and Breed, Hosmer, and Bone, 1958) 

 as given by the formula: 



27 2 



where the volume is in cubic yards and the length, L, is the distance 

 in feet between the two proviles, and A and A are the areas at each 



profile between the surveyed surface and an arbitrary datum elevation. 

 The volume at the later survey date is subtracted from the volume at 

 the earlier survey date so that a positive result indicates accretion 

 and a negative result indicates erosion. The result is then divided by 

 the distance, L, and converted to an annual basis in cubic yards per foot 

 of beach per year. 



Assuming that the distance between adjacent profiles is about the 

 same, and that the locations of the profiles are representative of the 

 section of beach being studied, the volumetric computation can be 

 simplified by modifying the average end-area formula. This is accom- 

 plished by replacing the distance between profiles with a unit length, 

 Ly (e.g., 1 foot). The result is that at each profile, a volume is 



computed using the formula: 



L, X A 



V = ^ 



u 27 



where V^ is the unit volume in cubic yards per foot of beach at the 

 profile location; L^ is the unit length (e.g., 1 foot); A is the area 

 between the surveyed ground line and a reference plane, usually the 

 deepest depth of survey (at least -12 feet) in the Great Lakes; and the 

 factor 27 converts from cubic feet to cubic yards. These unit volumes 

 at each profile from one survey can be compared with unit volumes from 

 other surveys at the same profile and reduced to annual volumetric 

 accretion rates at the profile. After tabulating these values for the 

 beach being studied, the means (averages) are easily calculated. An 

 example of this computation is given in Figure 10. 



V. DATA ANALYSIS 



After a system of monitoring programs has been established in an 

 area, the city, county, or State beach erosion district should begin to 

 collate the data collected on the behavior of shore protection struc- 

 tures. Initially, data should be collated from 10 shoreline types 



22 



