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Appendix B Additional Analyses of Shoreline Retreat TREND ANALYSIS FOR SHORELINE WITH NO PROTECTION lighthouse. Numerous studies have been conducted on the rates of shoreline retreat in the immediate vicinity of Cape Hatteras Lighthouse. The long-term rates are not as accurately known as those during the past few decades because of lack of pre- cision of old maps. Nonetheless, rates of retreat before implementation of artificial stabilization measures provide a good base to predict retreat 100 years into the future. The most accurate benchmark for long-term erosion is the lighthouse. The present lighthouse was erected in 1870 at 1,500 feet (460 meters) from the water's edge (MTMA Associates, 1980~. It is now about 160 feet (50 meters) from the shore. This produces an average rate of shoreline retreat of 11.5 feet (3.5 meters) per year. However, strictly natural conditions at this site existed only until 1930, when the first groins were installed along the shore (MTMA Associates, 1980~. The latest measurement of shoreline loca- tion before 1930 was macie in 1919, when the shore was 300 feet (100 meters) from the lighthouse (MTMA Associates, 1980~. Thus, the best estimate of natural rates of retreat is 1,500 feet (360 meters) in 49 years, or 24 feet (7.3 meters) per year. The U.S. Army Corps of Engineers (1984) deter- mined a retreat of 2,000 feet (610 meters) between 1848 and 1917; this is a yearly rate of 29 feet (~.S meters). The aver- age of these two rates is 26.5 feet (~.1 meters) a year. Other determinations of long-term retreat rates include data from the post- 1930 period. A retreat of 2,400 feet (730 111

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112 A ppend ix B meters) between 1852 and 1970, corresponding to 20 feet (6.2 meters) a year. Estimates of future retreat rates for a natural Cape Hat- teras shoreline for different sea-level rise scenarios can be based on the above numbers. In this simple trend analysis, the rate of retreat is assumed to be linearly correlated with sea-level rise (Leatherman, 1984~. Thus, a threefold increase in the rate of sea-level rise would move the shoreline land- ward three times faster. A yearly retreat rate of 26.5 feet (~.1 meters) for a local relative sea-level rise of .08 inches (2.0 mm) a year yields 133 feet (40 meters) of retreat per centimeter of sea-level rise, or a ratio of 1:4,000 between vertical sea-level change and shoreline retreat. This is an exceptionally small ratio, reflecting the highly exposed shore- line at Cape Hatteras. Table B- 1 summarizes predicted shoreline retreat based on this method. It is important to recognize that the island's geomorphology indicates that the materials eroded from the eastern shoreline during the next century will be similar to those cut away in the past. Shoreline retreat at Cape Hatteras in the absence of any form of coastal protection might be rapid. Moreover, the numbers in Table B- 1 might be low. They are based on the assumption that the average eustatic rate of rise of 0.5 inches ( 1.2 mm) per year for the past century (Gornitz et al., 1982) is appropriate for the period before 1930. This num- ber, however, might be too high because of evidence that the global rate of rise has been greater since 1935 than it was before (Braatz and Aubrey, 1987~. Therefore, the calculated annual retreat of 26.5 feet (~.1 meters) might have occurred in response to a rate of sea-level rise of less than the .05inch (1.2 mapper year average. THE BRUUN RULE The Bruun (1962) method to predict shoreline retreat is based on assumed maintenance of an equilibrium shoreface profile during sea-level rise. This requires that sand be removed from the eroding beach and shoreface regions and deposited downdrift or on the offshore continental shelf below the seaward limb of the equilibrium profile (Figure B- 1~.

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Additional Trend Analyses - _ co c~ _ c~ ~ _ _ ~ 1 _ U) ~_ _ ._ c~ J m C: ._ - o s C~ - ._ C: o D - _, - .= oo - ~O - ._ Ct _ ~ o S - cn CO ._ _ ^ ~ _ C~ ~ C) - ._ - - ~ U) S C 113 _ _ _o o o ~ _ ~o o~^ o oo __ _ _ _ o ~o ~_ Lo ~o _ _ _ _ _ o oo oo _ ~_ o ~o ~_ __ _ ~o. o _ t_~ o _ ~o ~_ _~ o - ~ E ._ _ 3 ~ ~_ ~._ - _ ~O 0 Z ZZ o ._ - c c, Z - ~ ~D es - - c u' c~ a~ co ._ - - co . ._ _ I,, 0 co L. _ ._ _ _ c: ._ - 0 ~

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114 A ppend ix B Bruun found reasonable agreement between his model and observed shoreline retreat rates along the coast of Florida. Schwartz ( 1965) verified the theory with small-scale tests in a wave tank, and Hands ( 1976) obtained satisfactory correla- tion between the predictions of this model and observed shoreline retreat on the Great Lakes. Chesapeake Bay, the Bruun rule also results (Rosen, 1978~. The Bruun rule is formulated as follows: L R = . S (B+h) In applications in yielded satisfactory (Equation B-1), where R - shoreline recession due to a sea-level rise of S. B is the height of the berm (the break between the slope of the beach and the flatter shoreline above it) above sea level, h is the water depth at the base of the active profile, and L is the width of the shore zone across which the adjustment occurs. The Bruun model is a strictly geometric relationship that assumes that shoreline retreat is a function only of sea-level rise. However, shorelines also retreat because of differential lon~shore transport rates, ._ =~ , loss of sand into the lagoons by storm overwash, and offshore transport. The "modified Bruun rule" (Dean and Maurmeyer, 1983) is designed to consider a realistic topographic profile explicitly to apply the Bruun rule correctly to beaches that are part of a larger barrier- island system. For the North Carolina coast, the generalized Bruun rule predicts a recession rate about 25% higher than the ori- ginal Bruun rule (Pilkey and Davis, 1987~. ,~n~rtninti~ associated with predictions of sea-level In view of the rise however, there is little justification for using the slightly more precise but more cumbersome generalized Bruun rule. Values used in this calculation of Bruun rule retreat rates are sea-level rise scenarios predicted by NRC ( 1 987b), as well e ~ ~ ~f rise berm height of 3.3 feet (one meter) above mean sea level; and depth of the active shoreface profile of 33 feet ( 10 meters). The most difficult value to estimate is the width of the active zone of profile adjustment. (For a detailed dis- as one scenario based on no acceleration In the rate ot

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Additional Trend Analyses 115 cussion of this slope, see Pilkey and Davis ( 1987~.) L is a measure of the width of the zone of exchange of beach sand. At Diamond Shoals, sand is exchanged at least 12.5 miles (20 km) offshore; the width of the sand-exchange zone at the lighthouse arbitrarily is set here at half of this value, i.e., L=6.25 miles (10 km). Results of the Bruun rule calculations are summarized in Table B-2. These shoreline retreat values are much closer to those in Table 2 than the ones obtained by trend analysis of the natural erosion data, although whether the shoreline is armored is not stipulated in use of the Bruun rule. Retreat rates at Cape Hatteras computed by Pilkey and Davis ( 1987) as part of a statewide study of North Carolina shoreline ero ~ e en slon are similar.

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