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Ing Sea Level Is One of the Nlost Inlponsnt Applied Problems Facing AHS.~KA~-I:llsing tllc Sort11 C;trt~lic;t harrier isl;tntl sliorclinc :IS thc test :~tca.a \.aricty ol' si~i~l)lcgct~nictric rccr*.\ioti 1111d~lsII;I> hccn itpl~licrl prcilict slir~rr'linccrcbsion ratch filr various sea-level rise scrn;tril,\. All sea-lcvcl rise sccn;trir)s ;~s*unieno ;tccclcr;ttion in r;rw ell' risc. &)utl) t11' C;I~W Ltu~Lt)ut.the liruun Kulc. Gc~~craliic(IL.(J%rcttl~t KLI~ and t11c slt)p 01' thc migratiot~surlhcc all 1citd III \itliilitr r~..i.cssiol~pwdictions. Nonh III' Cap! !.th)kt)ul. tlic slolw crl' the ntigr;tlioll surt;lcc predicts ;I much grcatcr wccssit111lliit~t I#~uIIII-I~L~~;I~c~ nnhlcls. l'l~ihsuggests the possibility th;tt thc islands arc in a11 "out-01'-cquilihriu~ti~position" u.ith rerpcct lo prcsctil sc:~Ic\ocl. If this is llw caw. tllc ptnsibility~cxiststhiit ucr) rapid niipration 111' tlic nortl~crtii\lmds will sewn or-cur. Tl~c;tbsut~iptions usrd in tlic prchcnt n~;tthcn~aticalmodcls depicting shorc1il:c rctrcitt arc gcncrally weak. Bcttcr nitdcls arc ~~ccdctl. cspcchlry li>r slicbrclincs where rcccssion is pan of the harricr island migration process. The large number of types of island!, in a ividc \.;tricty t11' gcoltyic and c~c;tnt)gritphic scttiligs niakes ;I ~t~iiv~rsally;~l>pli~.abIc ~IOLIL'I difficult, if not impossible, 11) for11iul:ttc. risc; B = berm height; 0 = active profile slope; h = depth of active profile base; and L = width of active profile. The response of the open-ocean sandy shoreline to a ris- It is nssurncd that there is no net loss of sediment due to ing sea level is one of the nlost inlponsnt applied problems longshore transport, and that the amount of sand eroded facing coastal geologists today. Predictions of preenhouse- from the subaerial portion of the profile will roughly equal related sea-level rise vary considerably. but all agree that the volume deposited on the lower shoreface. From the ;st:ekration is likely. The Environmental Protection Asency equation, it can be seen that R is directly proportional to projects that future sea-le\~elrise on a world-\vide basis will S. and the amount of recession is larger than the amount range iiom 0.52 to 3.45 n1 by 2100 A.D. (Hoffman and of sea-level rise by an anlount proportional to the tan 0 others. 1983). The Committee of tlie National Research term. Therefore, according to the Bruun R~rle,gentle beaches Council 013Carbon Dioxide Assessment suggests a rate of will recede faster than stecp beaches for a given sea-level U.70 rn/century by the year 2100 (Revclle, 1983). Discus- rise. sions of' sea-level rise and related phenomena are presented Rosen (1978) applied the Bruun Rule to eroding shore- by se\lersl authors in this volume (e,.g.. Braatz and Aubrey. lines of Chesapcakc Bay. He concluded tha:. iil the partic- Gornitz and Lchedeff, and Komr and Enfield) and will not ular circunlstances of the bay shorelines, the Bruun Rule he addressed here. accurately characterized and predicted shoreline recession The purpose of this paper is to test several shoreline rates for known rates of sea-level rise. recession models by applying them to the entire open-ocean In 1968 Edelman de\leloped a model for quantifying Nonh Carolina barrier island coast. The models applied in- shoreline response, based on profiles of the Di~tchcoast, clude the ~munRule (Bruun, 1962). the Edelman rule and concluded that the equilibrium profilc approximates a (Edelman, 1968, 197Oj and the Generalized Bruun Rule constant at any one instant and is of tiniform slope. In ad- (Dean and Maurnleyer, 1983). In addition. rates of shore- dition, Edclnlan concluded that for a given stornl surge. line rno\lenlent due to a sea-level rise are predicted on the higher dunes will recede less than lower dunes. basis of slope of the ravinement surface or barrier island Edelman's secorhd model is much more innovative than niigrarion surface (Swift. 1976a.b). Finally. present erosion his first and actually pro\-idcs a numerical answer to the rates (Kochel and others, 1983; Bentoo, 1983) are extrap- dune erosion question (Edelman, 1970). The assumption 01.1teJ. thn! chanps chi prchiile keep pace wiin rising sea kvel makes lhe Bn~un.Uclman and Modified Bruun ruks are briefly this model rllore realiaic than the first. The Edclmnn I1 nlodel outlined bclow. For more detailed discussions of these is as follows: n~odcls.the reader is referred to the original papers and to Dean and Maurmeyer ( 1983). The i3ruun Rule (Bruun, 1962) is the basis for all other erosion models that are presently used. It is still the rllost ividcly used and recognized method of calculntin_rshorelinc where R = recession due to sea-level rise; L = width of change. Bruun maintained that the shoreface profile reacts active profile: S = sea-level risc; Irl>,, = dep~hof ac:ive to a sea-level rise by siniply retreating landward and up- profile base: atid All,, = height of' dunes. ward such that the profile remains constant relative to sea The two n~ainassun~ptions hchind cquaiion 2 arc the con- level down to the depth of effective wave motion. This depth stancy of wave conditions throughout the time jxriod ana- is as~unledto be 10 m for the purposes of this study. The lyzed, urld the direct relationship between sea-level rise and active profilc in Bruun's equation essentially co~~esponds the speed of profilc migrition. resulting in propfrionul rates to the shorclhce. Thr Bruun Rule is stated as: of nlo\fenlenu for the two pnxesscs. The sole difference bctwecn the Edelrilan i111~1 Bruun moclcls is the allowance L I li)r it retluction in tlurrc. I~eighttlrroirgh tinre whcn using tlrc h' = -s=- S (U + I?) tan 6 Edclmnn li model. '['his itIlo\v:rncc causes the Edclnian I1 model to picld s1ight:y grcatcr recession \lalucs than those where R = rccessiorl tluc to sea-lcvcl rise: .$ = sca-lcvcl Sound by using tlic I3rt1un Kulc. Ilcan and Maurnleycr (1983) li;lvc niotlil'ictl tlx 1Jruun Rule, adopting it for usage in predicting thc reccssion/nli- gmtion of a retreating beach which is part ol'a larger barricr island system. Their model, which they call the Gcncral- ized Bruun Rule, is as follows: where R = recession due to sea-level rise; S = sea-level rise; L, = width of oceanside active profile: L, = width of lagoon-side active profile; hb,, = depth of base of active zone; hb, = depth of base of active zone of lagoon side: 11,. = open-ocean berm height; B, = lagoon berm height: and \V = width of the barrier island. The main assumptions associated with the use of this model are the constancy of island width M' through time by the overwash of sand. and the vertical growth of the entire is- land at the sanie rate as sea level rises. This di\:crsion of island sand from the shoreface causes the Generalized Bruun Rule to predict a hiiher recession value than the Bruun Rulc does for the same setting. As will be discussed more fully subsequently, this is a logical outgro\vth of the different rates of shoreline nlovement lor migrating barrier islands conlpared to islands which are merely experiencing shore- line recession without significant overwash. Recently, Evens (1984 and this volun~e)de\:elopcd a model for shoreline recession differing from Bruun's work in several imponant ways. As Evens states (p. 998), his model "is not constrained to the singular movement of sed- iment in an offshore direction; il accounts for changes in sand volunle within a shoreline reach, including that caused by alongshore and cross-shore transport, transport into in- WI111".1.. lets, o\*erwash. beach nourishment, sand mining, and 0111- Manonboro ers; it allows for barrier island preservation during a rising Island sea level; and it treats sediment movement in a more ana- lytical way." These developments are very important be- Cap. cause they address many, if not all, of the weaker aspects Fwr of the Bruun Rule. Conversely, Everts' model is similar to Bmun's in other ways, namely. that the shoreface is as- sumed to be in equilibrium with sea level and will thus translate vertically an amount equal to the rise in sea level. FIG. I .-ltldrs niap of the Nonh Carolinn stutly ma. This means that, as in any model. sand redistribution is needed to maintain the equilibrium profile. Unfortunately. the Evens' model could not be applied to Sea level, unless stated otherwise, is assumed to be rising the coast in this study because of the lack of thc requisite at the rate of 23 cm/century. No acceleration of sea-le\lel accurate nearshore and shoreface profiles. (See Evens, this rise is assunled. The depth of the base of the active profile. volume, for application of his model to other coastal areas.) ~qui\~itlentto the shoreface. is assumed to be 10 nl for all of the North Carcilina coast. For Bruun Rulc calculations. bcnn height, B. is assunled to be I n~above mcan sea level. For the Generalized Bruun Rule the open-ocean bcml height The Bruun Rule, Generalized Bruun Rulc and Edclmiln is assunled to be I n1, the lagoclnal berm height 0.5 m, the I1 models were applied as shoreline recession predictors for depth of significant sediment nlo\.cment on the lagoon side the entire Nonh Carolina coast (Fig. 1 ). Most of the data 1 nl, and the \vidth of the zone of active sediment move- used in this study are measurements obtained from the U.S.
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