The critical depth averaged a little more than 7 meters on the north side 

 of Little Sable Point, and a little more than 8 meters on the south side 

 (stations 16 to 29, see Fig. 9). North of the point, the average pinch-out 

 depth was 10 meters. South of the point, there was no clear pinch-out on 

 several of the stations because the 1969 profiles were too short; where the 

 pinch-out was identified it averaged 11.5 meters. Thus, both definitions 

 suggest deeper profile closure south of the point. 



The individual profiles in Appendix A may be useful to the engineer in 

 determining depths of measured changes. 



6. Volume Changes. 



a. Stations. To test the assumption that the volume of sand eroded from 

 the upper beach during recession was matched by an equal volume deposited off- 

 shore, the cross-sectional area between profiles at each station was cal- 

 culated. The earlier profiles were usually too short to include all of the 

 active zone, so most area determinations are based on changes between 1971 and 

 1975. Because only 16 stations were reprofiled in 1971, 4 of the longest 1969 

 profiles were used to supplement the area change measurements. 



b. Calculations. The profiles selected for volume calculations were 

 digitized at 5-meter intervals in the horizontal from the landwardmost to the 

 lakewardmost points common to both the earlier and later surveys (e.g.. Fig. 

 12). The results of all the volume calculations are given in Appendix B. The 

 difference between the sequences resulting from digitization provides a se- 

 quence of changes, with positive values indicating a fill and negative values 

 indicating a cut. Multiplying the digitizing interval (5 meters) times the 

 summation of all elements in the change sequence gives a measure of the net 

 volume change per unit width alongshore. If the elements in the difference 

 sequence are summed from their landwardmost point to some arbitrary point 

 offshore, the product of that sum and the digitizing interval gives the net 

 change in volume per unit width over that arbitrary span. Below each set of 

 digitized elevations there is a continuous curve showing the change in volume 

 per unit width from the innermost point to each succeeding point across the 

 entire active profile. This cumulative volumetric curve is drawn to the same 

 horizontal scale as the profile. 



A dashed curve plotted on the same axis shows the average thickness of the 

 net volume change if it were distributed uniformly from the innermost point to 

 the end point for which the change was summed (Fig. 12). 



c. Results. Inevitably, on a receding shore the cumulative volume curve 

 is negative from the inner point out beyond the shoreline, indicating net 

 degradation or cutting over the upper beach. Small zones of aggradation or 

 fill offshore cause the cumulative volume curve to increase toward zero (Fig. 

 12). At a point farther offshore the cumulative volume curve returns to 

 zero. Between this balance point and the backshore the cut and fill exactly 

 balance each other; i.e., neglecting compaction and expansion, the sediment 

 could have been redistributed within that zone without requiring any gain or 

 loss to the outside. Offshore from this balance point the cumulative volume 

 curve would ideally not depart significantly from zero. With the real pro- 

 files, however, the cumulative volume curve offshore often increases about as 

 far above zero as it was below zero inside the first balance point (App. B). 



22 



