The limit depth of interest is the offshore edge of the region par- 

 ticipating in the yearly onshore-offshore cycle of sand transport. With 

 the rationale that extreme storm waves will carry sand beyond the limit 

 depth, removing it from the cycling system, this yearly limit depth can 

 be estimated using the previoios development with a yearly extreme wave 

 condition typical of a specific site. A representative extreme might be 

 the high waves expected to give extreme bottom velocity for 12 hours per 

 year. 



Considering nearshore wave measurements in Thompson (1977), the 10 

 design wave conditions in Table 2 were selected as a representative range 

 for exposed U.S. coasts. The table shows that the limit depths calculated, 

 using equation (6), are all roughly twice the input wave height. This 

 direct dependence on wave height and the fine trends of the calculated 

 results are in agreement with an approximate form of equation (6) . Re- 

 taining only the dominant first term on the left-hand side of equation 

 (7) leads to the expression: 



dg - 2.28 H (1 - 4.78 H/Lq) , (8) 



For the 10 conditions in Table 2, at a given wave height, the calculated 

 limit depth increases above twice the wave height as wave period or L^ 

 increases; at a given wave period, the calculated depth drops below twice 

 the decreasing wave height. Equation (8) gives a depth within 3 percent 

 of that obtained using equation (6) for these conditions. 



The calculated results (Table 2) show general agreement with other 

 published conclusions concerning the limit depth to the active beach 

 (Bruun, 1954; Dietz and Fairbridge, 1968; Winant, Inman, and 

 Nordstrom, 1975). Some unpublished bathymetry studies at the Coastal 

 Engineering Research Center (CERC) resulted in conclusions summarized by 

 Duane (1976). Repetitive profiles superposed, revealing little bed change 

 beyond these approximate depths: 15 feet for the Great Lakes, 20 feet 

 for the U.S. Atlantic coast, and 25 feet for the southern California 

 Pacific coast. Design wave conditions 2, 5, and 8 in Table 2 would be 

 reasonable first choices for these three locations, and the calculated 

 depths agree with the stated limit depths, so it appears the proposed 

 calculation procedure may give an accurate estimate of the yearly sea- 

 ward limit to the active profile. 



Further evaluation of the proposed calculation procedure can be made 

 using bottom changes offshore of La Jolla, California, which have been 

 intensively investigated by the Scripps Institution of Oceanography. 

 Shepard and Inman (1951) reported bathymetric survey data establishing 

 significant bed cut and fill to water depths of at least 100 feet; how- 

 ever, "On the outer shelf the movement takes place more parallel to the 

 shore than normal to it." Inman and Rusnak (1956) measured ranges in 

 sand level over a 3-year period. In mean water depths of 18, 30, 52, and 

 70 feet, ranges were (>2) , 0.29, 0.16, and 0.15 foot, respectively, and a 

 seasonal trend in sand level was detected at the 30- foot depth, but not 

 at the two deeper stations. 



