Htikm f CRE US Av Gack Gag Ree. a TP TP 78-4 Geometry of Profiles Across Inner Continental Shelves of the Atlantic + and Gulf Coasts of the United States by Craig H. Everts TECHNICAL PAPER NO. 78-4 APRIL 1978 | WHO, DOCUMENT : COLLECTION _ Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING (/¢8 RESEARCH CENTER B/S O Kingman Building | TY Fort Belvoir, Va. 22060 W754 Reprint or republication of any of this material shall give appropriate credit to the U.S. Army Coastal Engineering Research Center. Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copies are available from: National Technical Information Service ATTN: Operations Division 5285 Port Royal Road Springfield, Virginia 22151 The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. 5 TU l/ ai o 0301 0089984 Mt UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO, 3. RECIPIENT'S CATALOG NUMBER TP 78-4 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED GEOMETRY OF PROFILES ACROSS INNER CONTINENTAL Teehnateail Paper SHELVES OF THE ATLANTIC AND GULF COASTS OF 7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s) Craig H. Everts 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS Department of the Army Coastal Engineering Research Center (CERRE-CP) D31194 Kingman Building, Fort Belvoir, Virginia 22060 - CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Department of the Army April 1978 Coastal Engineering Research Center 13. NUMBER OF PAGES Kingman Building, Fort Belvoir, Virginia 22060 92 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of this report) UNCLASSIFIED 15a. DECLASSIFICATION/ DOWNGRADING SCHEDULE - DISTRIBUTION STATEMENT (of this Report) Approved for public release; distribution unlimited. - DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) - SUPPLEMENTARY NOTES - KEY WORDS (Continue on reverse side if necessary and identify by bluck number) Atlantic coast Gulf coast Bathymetric profiles Inner Continental Shelf Beach Evaluation Program | ABSTRACT (Continue oan reverse side if necessary and identify by block number) Along most of the U.S. east and gulf coasts, bottom profiles extending over the Inner Continental Shelves normal from the coast display a character- istic two-sector shape. Near the coast, the shoreface profile sector is steep and concave-up; the seaward ramp sector is planar with a gradual slope away from the coast. As part of the Beach Evaluation Program (BEP) at the Coastal Engineering Research Center, 9 profiles extending from the coast 30.5 kilo- meters (19 miles) seaward at each of 49 localities were averaged to (Continued) DD , aaa W473 —s Er TION OF 1 NOV 65 1S OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) mathematically characterize the profiles and to develop and test criteria for discriminating among groups of profiles. Localities were selected along straight coastal reaches away from inlets and estuaries in areas where the bottom consisted of unconsolidated sediments. Results of the study indicate Inner Continental Shelf profiles can be mathematically defined by four parameters: a = ramp slope (0 to 0.00107); b = depth of the ramp at the shoreline, when the ramp is extended as a straight line below the shoreface sector (0 to 24.7 meters, 0 to 81 feet); 3c = distance from the shoreline to the shoreface-ramp boundary (0.2 to 20.6 kilometers, 0.12 to 12.9 miles); and f = index of concavity of the shoreface sector (0.21 to 1.72). Values in parentheses are the range of values obtained for the 49 averaged profiles. All depths are referenced to mean low water. An equation was developed to define bottom depth as a function of distance from shore incorporating the four relatively easy to obtain parameters. Computed depths using the equation were found to be generally within 5 percent of the actual profile depths at the 49 localities. In most cases, no relationship was found between the geometric characteristics of the shoreface and the ramp. 2 UNCLASS IF IED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) PREFACE This report is published to provide coastal engineers with representative bathymetric profiles of the Inner Continental Shelf along the Atlantic and gulf coasts of the United States. The work was carried out under the Beach Evaluation Program (BEP) of the U.S. Army Coastal Engineering Research Center (CERC). The report was prepared by Dr. Craig H. Everts, under the super- vision of Dr. C.J. Galvin, Jr., Chief, Coastal Processes Branch, Research Division. The author acknowledges the assistance of W.N. Seelig and E. Adams who obtained most of the depth-distance values from charts. Mr. Seelig also assisted in computer programing. R.J. Hallermeier, C.J. Galvin, Jr., and M.P. O'Brien reviewed the manuscript and provided many valuable suggestions for improvement. Comments on this publication are invited. Approved for publication in accordance with Public Law 166, 79th Congress, approved 31 July 1945, as supplemented by Public Law 172, 88th Congress, approved 7 November 1963. Nee A Li , Y Mans / VCE ie LE P27 301N H. COUSINS Colonel, Corps of Engineers Commander and Director IV Witt APPENDIX CONTENTS CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI). SYMBOLS AND DEFINITIONS. INTRODUCTION . BACKGROUND . MEASUREMENT PROCEDURE. 5 1. Inner Continental Shelf Paoeniles 2. Shore-Parallel Contours. RESULTS. 1. Shoreface ‘Rypes, 2. Description of Shelf Broiler : 3. Limit Depth of Shore-Parallel Gontouns DISCUSSION . 5 Profile Gharacteniccics GEOMETRIC LIMIT DEPTH OF THE SHOREFACE . SUMMARY. LITERATURE CITED . PROFILE LOCATIONS. DATA COLLECTION SCHEME INNER CONTINENTAL SHELF PROFILES . PROFILE FITTING PROCEDURE. A PROGRAMING LANGUAGE (APL) PROGRAM TO FIT A CURVE TO A PROFILE. TABLES 1 Geometric characteristics of Inner Continental Shelf profiles for the U.S. Atlantic and Gulf of Mexico coasts. N) Shoreface-ramp depths on Inner Continental Shelf profiles. Page 9 19 20 10 CONTENTS FJGURES Map showing the location of the 49 averaged bathymetric profiles obtained between Long Island and the Texas- NeRGHCO Woes 69656 ol o wld Po Profile Jine spacing and bathymetry at profile line 1 Profile line 48 illustrating smooth, shore-paralle] contours which exist beyond the seaward end of the profile. Examples of the three types of shoreface profiles Definition sketch of an idealized Inner Continental Shelf profile showing the planar, seaward-dipping, ramp sector and the concave-up shoreface sector. Ase tothe Rms depth variations along profiles Gulf of Mexico (Texas coast) profiles illustrating an increase in ramp slope, a, from northeast to southwest. Atlantic coast (North and South Carolina) profiles illustrating a decreasing zero-intercept depth, b, from north to south. j Daas Profiles illustrating the concavity parameter, f . Comparison of the geometric criteria in determining the seaward-limit depth. Page 13 14 15 16 21 23 23 26 CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (Si) U.S. customary units of measurement used in this report can be converted UNLTS OF MEASUREMENT to metric (SI) units as follows: Multiply by To obtain inches 25.4 millimeters 2.54 centimeters square inches 6.452 square centimeters cubic inches 16. 39 cubic centimeters feet 30.48 centimeters 0.3048 meters square feet 0.0929 square meters cube) feet 0.0283 cubic meters yards 0.9144 meters square yards 0.836 square meters cubic yards 0.7646 cubic meters miles 1.6093 kilometers square miles Z59rA0 hectares knots 1.8532 kilometers per hour acres 0.4047 hectares foot-pounds 1.3558 newton meters millibars LOS se TOF? kilograms per square centimeter ounces Bie 35 grains pounds 453.6 grams 0.4536 kilograms ton, long 1.0160 metric tons ton, short 0.9072 metric tons degrees (angle) 0.1745 radians Fahrenheit degrees 5/9 Celsius degrees or Kelvins! tie somes C= (5/9) (CF =82)). To obtain Kelvin (K) readings, use formula: K = (5/9)! (F =32)) + 273215. SYMBOLS AND DELINITIONS ramp slope ramp depth at x = 0 when the ramp is extended to tlic mean low water (MLW) shoreline distance from the MLW shoreline to the upper ana Jowa shoreface boundary; 3c 15 the distance to the shoreface- ramp boundary prefile depth at seaward boundary of inner shoreface (c) exponent defining concsvity of shorcface combining term that approximates the influence of shoreface and ramp in the region 2c < x < depth at shoreface-ramp boundary (5c) concavity index (eq. I-10) constants number of distance stations in the interval: 300 meters (L000 she) < bs S © distance from shore distance from shore bottom depth below MLW datum actual depth value at x7 calculated depth valuc at X; ramp depth shoreface depth Av Wanton ir ¥s eats iy ¢ ieee ey A i ae 0 aiid i LARA OA tod f an Da deny ye ROT anh Bota NT ies Pies ee ie (id Pee ares Caan eee if BR oe a hay tpnita oi Data be arnt fe Saad } j ‘Sou ale a 4 ene Wine Mp his eee e a CS) a aets ioale 7 ' 4 ei: yh thaw a rSREHY Tiey’ ee iat pee ue * E ha 4 7 By ib ¥ ae ae tt HIS @ ae At, Fs , x Se ; vs Ae Re ee wie ae et i) lle ' a ne Way Uy i a eK} fo SEAT a ai eine. ' ¥ i te ah 4 me i rt Yee Maes ren iy ai is Regina enlseon api sayin a reich bea tay : eaeene > ws Yoong wh DAE sail ah itd 4 Pearly o@ vdebvaty Vila oan Phartnenete j Ta PRs. Tie VS ent gieieet oa . nee of ed Heya ai Bik wth “athe ties eal uit: ii LP LAY se a) ite sn 2 ee GEOMETRY OF PROFILES ACROSS INNER CONTINENTAL SHELVES OF THE ATLANTIC AND GULF COASTS OF THE UNITED STATES by Cratg H. Everts I. INTRODUCTION A bathymetric profile, when projected over the Inner Continental Shelf along most coastlines, displays a characteristic shape. The profile, which is the intersection of the shelf bottom with a vertical plane, is typically steep and concave-up near the coast. Farther sea- ward it is generally planar with a gradual slope away from the coast. Price (1954) separated this distinctive shelf geometry in the Gulf of Mexico into the near-coast shoreface sector and the more seaward ramp sector. The geometric nature of the Inner Continental Shelves along open and straight parts of the middle and southern Atlantic coast, and the Gulf of Mexico coast, is described and quantified in this report. Forty-nine shore-normal bathymetric profiles, at about a 100-kilometer (62.5 miles) spacing. are presented. Each profile represents an average of nine profiles taken along 12 kilometers (7.6 miles) of adjacent coast. The shoreface and ramp sectors are discussed separately because geometric evidence suggests the possibility of a different origin for the two sectors. A means to approximate the two-part Inner Continental Shelf profile as a function of easily obtained profile elements is developed, and procedures to select the seaward-limiting depth of the shoreface are suggested and evaluated. II. BACKGROUND One means of describing the Inner Continental Shelf profile is to consider the profile as a continuous element. Bruun (1954), for example, used a single-power function in a study of shelf profiles along the Danish and California coasts. Hayden, et al. (1975) applied an eigenvector method of analysis to identify the characteristic forms of profiles to a distance of 365 meters (1,200 feet) offshore. Resio, et al. (1974) also used an eigenvector analysis to characterize bathymetric variability in profile shape, but to a greater distance offshore along the Atlantic and gulf coasts. Resio, et al. discussed the two-segment form of the profiles, but chose to analyze them as continuous features. They noted that the break in profile shape from curvilinear to linear occurred in water depths of 9 to 25 meters (30 to 80 feet) and always within 14 kilometers (8.7 miles) of the shoreline. They also reported that the profile break may represent a transition from a wave-dominated bottom region near the coast to an offshore region where the wave influence is less. fhe Inner Continental Shelf proftle was viewed us a two-element shape by Johnson (1919) and Fisher (1975). In discussing the origin of barrier islands, both made extensive use of the planar ramp sector as it extended through or under the shoreface sector. Shepard (1963) presented evidence from borings obtained along the Gulf of Mexico coast that indicated the shoreface of some barrier islands grew upward on the extended ramp as sea level rose. Sheridan, Dill, and Kraft (1974) re- ported that the Delaware barrier island shoreface migrated westward across and above large lagoonal complexes. This westward transgression of the shoreface was on an undulating crosion surface, or ramp, with a gentle slope toward the offshore. Field and Duane (1974, 1976) also presented evidence that some barrier islands originated seaward of their present positions, and are presently shifting landward. Using seismic evidence they show that shoreface sectors are structurally different from the ramp sectors and are sometimes superimposed upon a landward extension of the ramp. Ina study of the inner shelf near Cape Canaveral, Florida, they found that shallow subbottom strata on the ramp were truncated by a transgressing sea, creating a flat-lying reflector. The shoreface sector now lies above this reflector. No relationship was found between the slope of the reflector and the present nearshore configuration. Results of field studies such as Sheridan, Dill, and Kraft (1974) and Field and Duane (1974, 1976) suggest the geometrically different ramp and shoreface are also genetically different. For this reason, the following empirical approach to define the Inner Continental Shelf profile includes separate descriptions of the ramp and shoreface, and a means to couple the two. III. MEASUREMENT PROCEDURE 1. Inner Continental Shelf Profiles. A total ot 441 bathymetric profiles from 49 coastal localities was assembled for this study, using National Ocean Survey (NOS) (formerly U.S. Coast and Geodetic Survey) 1200 series hydrographic charts. Nine pro- files from each locality were averaged to obtain a single representative profile (Fig. 1). Localities were chosen according to their location on straight, uninterrupted coasts as distant as possible from inlets, estu- aries, or river entrances, and to nearshore regions (up to 10- to 15- meter (30 to 45 feet) water depths) that displayed relatively smooth bathymetric contours parallel to shore. In all instances, profile loca- tions were selected with a 150° land-free arc for a 500-kilometer (312 miles) radius away from the coast. Additionally, locations were selected where bottom materials were unconsolidated as indicated by sediment symbols on the charts. Most of the profiles were obtained from barrier island coastlines. At the center of each locality a profile line was drawn on the chart along an azimuth normal to and away from the coast. The latitude and 10 ‘(6p OUTT eTt Ford) sLep10q ODTXOp-SexXv], 94} pue (][ SUTT e{TTJZoId) YAO moN ‘pueTS]T SuoT usemjzeq poeuteigo sottzord sTIJOWAYIeEq paseIoAe Gy 9Y FO UOTeDOT SY BSutTmMoYs dew ‘T oan3TY oSd 008 oS8 006 oS6 000! oSC 12 ODIXIW JO SM9 ie ae UE BF BE OF pease 2eeepe st NVIIO VNVISINOT e0€ ALNV TLV 05 YNITONYO HLNOS NOILO3LOUd YOLVONSW VNI104V9 oGE HiYON 000 MYOA M3N in longitude of the shoreline intercept of the line were recorded to one one-hundredths of a minute (see App. A). Four additional profile lines spaced at 1.5 kilometers (5,000 feet) were drawn upcoast and four were drawn downcoast parallel to the centerline (App. B). This resulted in a set of nine profile lines at equal spacing along 12 kilometers of coast. Each profile line was extended seaward 30.5 kilometers (19 miles) From the mean low water (MLW) shoreline. Depths were obtained from the charts using an acetate overlay on which marks were scribed at 30 sta- tions, graduated in increasing distance intervals from the zero-depth position (App. B). Higher resolution was used near the shore because wave action tends to create greater slopes there. Selection of the station intervals was also based on the typical frequency distribution of depth variations on the charts between stations away from the coast. Figure 2 is an example of the profile line spacing and bathymetry on a 1200 series chart. At each locality an arithmetic mean depth was de- rived for each of the 30 distance stations by averaging depth values from all 9 profiles. The resultant mean profile constituted the basic data used in the study. These profiles are in Appendix C. Unless otherwise stated, further references to profiles in this report refer to the average of nine profiles. 2. Shore: Parallel Contours. For comparison with the location of the shoreface-ramp boundary obtained using the profiles, the seaward limit of shore-parallel contours was measured at the center of each of the 49 localities where depth-distance data were averaged. The seaward limit was defined as the transition depth where bathymetric contours changed from smooth and shore-parallel to irregular or no longer shore-parallel. All seaward- limit values were obtained using the same 1200 series charts used in selecting depth-distance pairs. Figure 2 illustrates a shelf location with an abrupt transition from shore-parallel to irregular contour; a smooth, shore-parallel contour is shown in Figure 3. At 31 of the 49 localities the root mean square (rms) (standard deviation) of the nine depth values for each of the 30 distance stations was also computed. This was done to determine if there was a less sub- jective way than that previously described to determine where contour irregularity replaces shore-parallelism. The thesis was that the devia- tion about the mean of depths obtained at constant distances from shore would reflect the change from the shore profile to the region of offshore (ramp) irregularity. IV. RESULTS 1. Shoreface Types. Three types of shoreface profile predominated (Fig. 4), but the ramp shape (planar, seaward-dipping) was similar on all profiles. The shore- face varied about a profile which smoothly coupled with the ramp as shown for profile line 15. Two extreme cases of shoreface-ramp coupling are also 12 ” 80 gw MS oo: Figure 2. Profile line spacing and bathymetry at profile line 1. Note the abrupt change in contour orientation, from smooth and shore-parallel to irregular, at a distance of 12 kilometers (7.6 miles) from shore (NOS Chart 1214). iS sand dunes Js. 5 >) $ | Figure 3. Profile line 48 illustrating smooth, shore-parallel contours which exist beyond the seaward end of the profile (NOS Chart 1287). 14 SMOOTH SHOREFACE PROFILE LINE |5 DEPRESSED SHOREFACE PRORIEEMEIN Ew. Depth (m) ELEVATED SHOREFACE PROFILE LINE 33 O 5 10 15 20 25 30 35 Distance from Coast (km) Figure 4. Examples of the three types of shoreface profiles. Profiles as obtained from NOS charts are shown as solid lines. Dashlines represent the smoothed ramp profile extended to the coastline. Circles represent points on a profile mathematically fitted to the actual profile. The vertical exaggeration is X 500. shown. Profile line 7 illustrates a depressed lower shoreface region which lies below the landward ramp extension. Profile line 33 represents an elevated lower shoreface which lies above the ramp extension. 2. Description of Shelf Profiles. A procedure developed to mathematically describe the profile shape is given in Appendix D..-The procedure utilizes data obtained from the profile locations listed in Appendix A. As shown in Figure 5, three boundary points are defined on the profile, as follows: (a) The intersection of MLW and the profile which is assigned distance-elevation coordinates (0,0), i.e., the origin; (b) the boundary between the upper and lower shoreface which is assigned distance-elevation coordinates (c,d); and (c) the boundary between the lower shoreface and the ramp which is assigned distance-elevation coordinates (3c,g). x=0 at 9 bd SHOREFACE Shoreface Lower Shoreface RAMP Figure 5. Definition sketch of an idealized Inner Continental Shelf profile showing the planar, seaward-dipping, ramp sector and the concave-up shoreface sector. The horizontal origin, x = 0, and vertical origin, z = 0, indicate the MLW shoreline as obtained from NOS 1200 series charts. Two additional parameters are considered: a = ramp slope and b = ramp intercept depth at the shoreline (when the straight-line ramp is extended landward to the shoreline). The shoreface-ramp boundary, 3c, is the characteristic horizontal distance that is first selected from a profile. However, because irregularities in the shape of the lower part of the shoreface are not uncommon, the region between c and 3c is not useful in evaluating the goodness of fit of a mathematically generated curve to the actual profile (App. D). Consequently, only the upper part of the shoreface was used for that purpose. The ramp sector is approximated by the equation of a straight line. The shoreface sector is approximated by an exponential curve with the slope steepest near the shore and, usually, the maximum concavity near the ramp. An empirical term combines the shoreface and ramp sectors. The result is the equation NCE z= (1-G) (ax + b) +G tales °) (1) where z = bottom depth below MLW datum G = term to combine the shoreface and ramp sectors x = distance seaward of the shoreline g = depth at shoreface-ramp boundary f = exponent defining concavity of shoreface G is defined as and C= Sac ty (3) where g is a computed quantity. The concavity parameter is obtained From the figure in Appendix D or p= 2.8 (1-4). (4) Points on the profiles in Figure 4 and in Appendix C are depth- distance values obtained using equation (1). The values a, b, c, and d are relatively easy to obtain from the profiles, and appear to provide a first-order mathematical approximation of the profile when used in equation (1). Table 1 presents the values of parameters used in equation ())MEorvedchy o£ ther4 oe proimillesm(Euon eli Appee Cc) 3. Limit Depth of Shore-Parallel Contours. The seaward limit of shore-parallel contours, and the depth where the rms values change significantly are shown in Table 2. The rms values on the landward parts of the profiles averaged 0.6 to 1.0 meter (2 to 3 feet) on profiles along the Atlantic coast, and 0.2 to 0.3 meter (0.7 to 1.0 foot) along the Gulf of Mexico coast. The ratio of the rms values of the near-coast profile segment to the rms values farther seaward are given in the table. Figure 6 shows two representative rms depth curves plotted against distance from shore. The curve on profile line 1 shows a well-defined change in the rms depth values; the profile line 48 curve Suggests no obvious difference in rms along the profile (see bathymetry in Figs. 2 and 3). V. DISCUSSION Profile Characteristics. Steep and concave-up shoreface sectors, and gently dipping and planar ramp sectors are ubiquitous off the mid and south Atlantic, and Gulf of Mexico, barrier island coasts. Values of individual geometric slope parameters in many instances tend to vary in a consistent manner in an alongshore direction, or remain constant and exhibit little alongshore variation over a long coastal reach (Table 1). The consistency of trend between different parameters is not so obvious. This is especially true for the properties of the shoreface and ramp which appear to be mostly unrelated. a. Ramp Slope. The ramp slope, a (Table 1), in the direction normal to shore, varies only slightly from the mean slope of 0.00041 along most of the Atlantic coast. However, as the Continental Shelf 18 Table 1. Geometric characteristics of Inner Continental Shelf profiles for the U.S. Atlantic and Gulf of Mexico coasts.! Profile Ramp Ramp Distance to Depth at Concavity Ramp Shoreface slope, a| intercept] shoreface-ramp| shoreface-ramp| parameter, f | correlation residual depth, b boundary, 3c boundary, g coefficient (m) 0.00065 0.00051 0.00044 0.00047 0.00045 0.00039 0.00049 0.00051 0.00028 0.00022 0.00038 0.00053 0.00081 0.00039 0.00036 0.0003? 0.00031. 0.00024 0.00036 0.00039 0.00045 0.00042 0.00000 0.00011 0.00036 0.00098 0.00052 0.00050 0.00026 0.00039 0.00038 0.00072 0.00052 0.00060 0.00011 0.00065 0.00104 0.00051 0.00011 0.00026 0.00018 0.00019 0.00022 0.00049 0.00046 0.00061 0.00067 0.00074 0.00107 - SCWUOOBNANSWNE | N a er we Sade od WOMBNADAUM WN 20 21 22 a eRe RKPeee NNNNKD NANSW N @ q . FOUCNUNFOAN AUMVWNWNIONWOD WI DOWN RrP Or k WHS N © ENWODWAMOANW ABUUNUAUNHAONNO COI NWOWUWWUAMN W~10 0 AWA WwW WNF Oo w > H PEN PYUNOFP ONLY WLOSUNARIEPRO CONUINEDOHK SR UKE Y ~ PND ee WOOF RFPWUAADAN SC CDOLWRHKH REAR NY WNUNWE UNH DH OCOWUDAAW NORPNORRRPY YNONKFSROHLU NNUONUNKFOCOLF ANOOCAN w > SPWNAWAW me OWOMONAKAUN > N e ppp uhbw ew a ND omy ol a \see Figure 1 for locations. 2Not available. Table 2. Profile Depth at Shoreface-ramp depths on Inner Continental Shelf profiles. Shoreface shoreface-ramp Rms depth boundary (m) (m) 1 38.1 Smooth 32.0 2 19.4 Depressed 21.0 3 18.0 Smooth 17.0 4 13.3 Depressed 5 14.5 Elevated 7/50 6 15.6 Smooth 12/15} 7 16.6 Depressed 15/15 8 8.7 Elevated 9 12.8 Elevated 10 22.5 Smooth 11.5 11 19.5 Elevated 10.0 12 21.6 Elevated 8.0 13 18.4 Smooth 8.5 14 14.5 Depressed ---- 15 13.4 Smooth ---- 16 12.7 Smooth 17 8.7 Elevated sonst 18 9.4 Elevated 19 W083 Elevated 20 8.3 Elevated 21 5.4 Elevated 3.0 22 16.1 Depressed 16.0 23 19.8 Depressed 20.0 24 18.1 Depressed 18.0 25 18.7 Smooth 17.0 26 9.5 Depressed 11.5 2 9.0 Smooth 8.5 28 7.0 Depressed 29 Pe}: Aa en Pie Se y 30 0.3. #| --------- My 31 OG |) Bese ogee # 2.0 32 Woo) Depressed 33 AD a2 Elevated 18.0 34 20.9 Depressed 23.0 35 16.7 Smooth 36 5.5 Depressed “7/ 16.2 Smooth 38 SS Smooth 39 S65 Smooth 40 14.6 Smooth 525 41 952 Smooth 42 12.8 Smooth 8.5 43 18.0 Smooth 14.0 44 15.4 Smooth 45 16.2 Elevated ----2 46 5 7/ Smooth 47 16.8 Elevated 14.0 48 19.5 Elevated ---- 49 12.8 Depressed =s-5 lTwo seaward-limit locations. 2No variation in rms along profile. 3Not available. 4No significant shoreface. SIsobaths shore-parallel to edge of chart. 20 Rms landward sector Rms seaward sector 0.69 0.50/0.68 0.47/0.55 0.48 Shore-parallel isobath limiting ra OUNWOWNW S rFPOoOaAnNnonw PAWUNnhMNO OO o-o0 oo °° GOrNnNUMUNONFAW en Pee eR COWNUrFANUF OC oonNunwoonwoond Rms Depth (m) Profile Line 1 Profile Line 40 Figure 6. 5 10 15 20 25 30 Distance from Shore (km) Rms depth variations along profiles. Note distinct change in values at 12.5 kilometers (32-meter depth) on profile line 1, and lack of significant change along profile line 48. 2 | narrows from north to south along eastern Florida, the slope increases from about zero to 0.00098 (profile lines 23 to 26). From east Texas to west Texas (profile lines 39 to 49), the ramp slope progressively in- creases from 0.00011 to 0.00107 (Fig. 7). Little difference was found when the ramp slope normal to the shelf break was calculated. b. Ramp Intercept Depth. Alongshore trends in the intercept depth of the) rampiat}thelyshorelane?) Vb, jare evident in) Tables! jeExromeCape Hatteras to Georgia (profile lines 13 to 21) the depth of the ramp when extended to the shoreline decreases fourfold from 14.3 to 4.3 meters (47 to 14 feet) (Fig. 8). Along the Florida coast the intercept depth decreases from 19.8 to 5.5 meters (65 to 18 feet) in a southerly direc- tion (profile lines 23 to 26). Along the western and northwestern coast of Florida the intercept depth is almost zero. This region, which has little wave activity, is where the shoreface is absent or very narrow and the ramp extends nearly to the shoreline. Along the Texas coast (profile lines 40 to 49), the intercept depth varies randomly between 7.3 and 13.4 meters (24 to 44 feet), averaging 10.4 meters (34 feet). The ramp slope along the same coast increases sixfold to the southwest, suggesting the shelf surface slope and present shoreline position are probably not genetically related. c. Shoreface-Ramp Boundary. An accurate distance to the shoreface- ramp boundary, 3c, is difficult to determine because the sectors appear to join asymptotically, and on a very gradual slope (App. C). A further complication in determining the distance exists because the lower shore- face is not always smooth (Fig. 4). There was no significant shoreface on 3 profiles (profile lines 29, 30, and 31); 19 profiles exhibited a smooth lower shoreface; 13 were depressed types; and 14 were elevated. The depth at the shoreface-ramp boundary, g (Table 1), displays a greater profile-to-profile similarity, or progressive alongshore change, than does the distance to the.boundary. For example, between profile line 10 and profile line 21, the boundary depth progressively decreased from 19.5 to 4.7 meters (64 to 15 feet) (Fig. 8); the distance to the boundary did not exhibit as significant a trend. Because the shoreface and ramp appear genetically different, at least in some areas, the boundary loca- tion is important. It may designate the cutoff region of significant active modification of the profile by present wave and current processes. It may also delimit the zone seaward, where man-caused or natural profile changes will not produce a sympathetic effect on the coastal beaches. d. Shoreface Concavity. Concavity, f (Table 1), indicates the deviation of the shoreface slope from planar. A highly concave-up (depressed) shoreface is represented by a low concavity value (Fig. 9). An elevated shoreface will exhibit a larger concavity value. A con- Cavity value above f = 1.87 represents a convex shoreface slope, but no such case occurred in the profiles. Along the Texas coast concavity values are near constant (0.8) and twice as large as the Atlantic coast values. Concavity is to some extent dependent on the energy distribution of waves acting upon the profile. Ze Depth (m) 5 10 oil £20 = 25 30 35 40 O Figure 7. 0) 5 10 15 20 25 30 0) 5 Higure 8. - + w © pss (S)) Profile Nos. bd ~ 48 5 10 15 20 25 30 Distance from Coast (km) Gulf of Mexico (Texas coast) profiles illustrating an increase in ramp slope, a From northeast to southwest. ’ 10 15 20 25 Distance from Coast (km) Atlantic coast (North and South Carolina) profiles illustrating a decreasing zero- intercept depth, b, from north to south. The dashlines show the ramp slope extended landward to the coast. 23 N“N + Profile Nos. Depth (m) ine) (oe) On (28) 30 5 Figure 9. f f f eYolo) VIGO WOLD 10 15 20 25 Distance from Coast (km) Profiles illustrating the concavity parameter, f. 24 30 rofile Nos. Ae VI. GEOMETRIC LIMIT DEPTH OF THE SHOREFACE Changes in the volume of sand on a beach are related, in part, to changes in the volume of sand and the profile shape farther seaward. Neglecting longshore transport, sand may move onto the beach from sources farther seaward, or may be supplied to the seaward region from beach sources. Wave action initiates most of the sand movement. Currents, either wave-produced or resulting from other mechanisms, transport the sand. There is presently an increasing interest in the seaward limit beyond which sand will no longer move to or from the beach, or beyond which changes in bathymetry will not affect processes on the beach. This interest is primarily directed toward the use of offshore sand sources for beach fill. For example, if sediment is removed from the Inner Continental Shelf between the seaward limit and the foredune, i.e., the region often defined as the active profile, the excavation may subsequently fill, possibly with sand that originated near or on the beach, thereby contributing to a decrease of sand on the beach. Con- versely, sediment artificially placed on the active profile will likely move in such a manner that the profile will tend toward an equilibrium shape for the waves acting upon sand of that size, shape, and density. Thus, sand may be placed seaward of the beach during certain times of the year with the expectation it will ultimately move landward to nourish the beach. If placed seaward of the seaward limit, or at a time when it moves beyond the seaward limit, the sand will not fulfill the purpose of the dumping. Additionally, in calculating the sediment budget of a coastal area where sediment volume changes are occurring, the seaward limit of sediment movement is a required parameter. One of its practical uses comes in predicting the volume of sand needed to artificially extend the shoreline while keeping the active profile in equilibrium. The data in this report may be used when two general geometric pro- cedures are considered in establishing a seaward limit. Each procedure is based wholly on geometric characteristics of the Inner Continental Shelf, and not on direct evidence of sediment transport. No evidence is available that indicates the results actually designate a seaward limit of sediment movement. The geometric criteria that might be useful to establish a limit depth of the shoreface, and possibly a seaward-limiting depth of signifi- cant sediment transport, are (a) depth at the shoreface-ramp intersection, coordinates (g, 3c) in Figure 5, and (b) depth at the transition from shore-parallel, smooth bathymetric contours near the coast to irregular contours farther offshore (U.S. Army, Corps of Engineers, Coastal Engineer- ing Research Center, 1977). Examples are shown in Figures 2 and 3, and both depths are given in Table 2. As illustrated in Figure 10, the depth of the seawardmost shore-parallel bathymetric contour does not agree well with the seaward-limit depth obtained using the shoreface-ramp criterion. For the Atlantic coast and the gulf coast east of the Mississippi River Delta, the shoreface-ramp criterion depth on 89 percent of the profiles was greater than the depth obtained using the shore-parallel contour criterion. West of the Mississippi River Delta, 85 percent of the shore- Zo Atlantic Coast, and Gulf Coast East of Mississippi River Delta o Gulf Coast, West of Mississippi River Delta Greater than Limit Shown, and Farther than 7 — 30.5 km from-the Shoreline Je we oO ate 2 @ ei ag 7 e165) 7 Oo 7 2 a i=) 2 30 Whe a v4 = 25 e / 3 7 a @ vi o bd e 7 ms @ @ 3) Bt i 15 € /o og Oe oF (2p) bn Oe Coe < cre Ee y ss dl@ 7 a) @ 8 f @ (Od 2 cA > Raye) @® (Tp) O 5 10 15 20 25 30 35 40 45 Seaward Limit, Shore-Parallel Criterion (m) Figure 10. Comparison of the geometric criteria in detcrmining the seaward-limit depth (data from Table 2). 26 parallel criterion depths were larger. Along-coast trends obvious in the seaward-limit depth using the shoreface-ramp criterion were not as obvious when using the shore-parallel contour criterion (Table 2). In the western part of the gulf, many contours were shore-parallel past the end of the profiles (30.5 kilometers). A problem in using the shore-parallel contour criterion was created because some of the depths beyond which the contours are shore-parallel, exceeded 55 meters (180 feet). This is probably well below the depth of significant sediment transport. In other areas, contour shore-parallelism was lost because of shore-connected shoals. The shoals angle away from the coast, and often begin in quite shallow depths. In most cases, they are probably SulimparcOLmtne active profrale.e On profile lanes 29750) and) Ssiswhere a shoreface is absent, shore-parallel contours do not exist. No signifi- cant offshore sediment transport is suggested in this region of the Florida coast. The rms depth criterion is a quantitative measure to describe the shore-parallelism of contours. It proved least consistent of any method. It is less subjective than the shore-parallel contour method, but directed at the same boundary; i.e., the transition between shore-parallel and irregular contours. The rms criterion also becomes less useful when the contours are parallel, but oriented at a slight angle relative to the coast. Results of this study indicate the shoreface-ramp criterion is more consistent in an alongshore direction than the shore-parallel contour criterion. The shoreface-ramp method is also more objective when calcu- lated as discussed in this report. The limiting depth obtained by either method is the depth of the change in shape or smoothness of the Inner Continental Shelf. It may or may not be indicative of the seaward limit of sediment transport to or from the beach. VII. SUMMARY 1. The Inner Continental Shelf profile along the U.S. Atlantic and Gulf of Mexico coasts exhibits a two-sector shape. Near the coast the shoreface sector is steep and concave-up. Farther seaward, the ramp sector is planar with a gradual slope away from the coast. The steepest slope is near the shore. The largest concavity is near the shoreface- ramp boundary. 2. In most cases, no relationship was found between the geometric characteristics of the shoreface and those of the ramp (Table 1). Likewise, no relationship was evident in the along-coast trend of the geometric characteristics on the shoreface and those on the ramp. This lack of correlation suggests different origins for these sectors. The shoreface today may be in, or approaching, some form of equilibrium with the existing wave climate, shelf currents, available sediment supply, sea level changes, and other factors; the large-scale ramp bathymetry is Zl probabl]l;) iargely a function of past events. These are julcrerees however, and are not directly substantiated by the result? of thy study. 3. The shore-ramp boundary was penerslly not at the Be Oh ucypt) as the depth at which shore-paiallel contours ceasc 28 LITERATURE CITED BRUUN, P., "Coast Erosion and Development of Beach Profile, TM-44, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., June 1954. FIELD, M.E., and DUANE, D.B., "Geomorphology and Sediments of the Inner Continental Shelf, Cape Canaveral, Florida," TM-42, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., Mar. 1974. FIELD, M.E., and DUANE, D.B., ''Post Pleistocene History of the United States Inner Continental Shelf: Significance to Origin of Barrier Islands," The Geologteal Society of Amertca Bulletin, Vol. 87, No. 5, May 1976, pp. 691-702. FISCHER, J.J., ''Bathymetry Projected Profiles and Origin of Barrier Islands - Johnson's Shoreline of Emergence, Revisited," Coastal Geomorphology, D.R. Coates, ed., Publications in Geomorphology, State University of New York, Binghampton, New York, 1973, pp. 161-179. HAYDEN, B., et al., "Systematic Variations in Inshore Bathymetry,"' Technical Report No. 10, Department of Environmental Science, University of Virginia, Charlottesville, Va., Jan. 1975. JOHNSON, D.W., Shore Processes and Shoreline Development, 1st ed., John Wiley & Sons, Inc., New York, 1919. PRICE, W.A., "Correlation of Shoreline Type With Offshore Conditions in the Gulf of Mexico,"' Second Coastal Geography Conference, National Academy of Sciences, National Research Council, 1954, pp. 11-30. RESIO, D., et al., "Systematic Variations in Offshore Bathymetry,"' Technical Report No. 9, Department of Environmental Sciences, University of Virginia, Charlottesville, Va., 1974. SHEPARD, F.P., Submarine Geology, Harper and Row, New York, 1963. SHERIDAN, R.E., DILL, C.E., and KRAFT, J.C., "Holocene Sedimentary Environment of the Atlantic Inner Shelf off Delaware," The Geologtcal Soetety of Amertca Bulletin, Vol. 85, No. 8, Aug. 1974, pp. 1319-1328. U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protection Manual, 3d ed., Vols. I, II, and III, Stock No. 008-022-00113-1, U.S. Government Printing Office, Washington, D.C., WS77 5 WA joe ZS ET aks een Geis ae ddrs ANOS ULI pant Byers ey "s alt aa nye pf bees i F ei ao itis COM raleng a hey ae a Vek, i vr yi oe ae Tio SSS (D-10) 89 in which d is the profile depth at c, and g is the depth at 3c. Figure D-1 is a semilogarithmic plot of f versus I. 4. Combination Term. A combining function is necessary to define the influence of the ramp and shoreface profiles (eqs. D-1 and D-8) as they asymptotically merge. An analysis of various smooth-type shoreface profiles, such as profile line 15 in Figure 4, indicates that approximately 88 percent of the change from the shoreface to the ramp sector shape occurs between x = 2c and x = 3c; i.e., about 88 percent of the shape of the actual profile in that region can be described using equation (D-8). The term that approximates the influence of both the shoreface and the ramp in that region is AB (se\eY G = exp 3c (D-11) in which the constant 2.8 ensures that less than 6 percent of the profile at x = 3c is influenced by the shoreface sector, and that less than 6 percent of the profile at x = 2c is influenced by the ramp sec- tor. The value 3c is considered to be the seaward limit of the shoreface. 5. Inner Continental Shelf Profile Equation. Four constants: a = ramp slope, b = ramp intercept depth at the shoreline, c = seaward limit of upper shoreface, and d = depth at c, are combined in the equation for the Inner Continental-Shelf profile: =>S ae Gh e O) (xe Sb) e i - exp c,* | (D-12) Points on the profiles in Figure 4 and Appendix C are depth-distance points obtained using equation (D-12). An APL computer program of equation (D-12) is in Appendix E. 90 2.0 0.4 O:2 0 | 2 3 I Figure D-1. Semilogarithmic plot of f versus I, where I = 3d/g (see Fig. 5). An approximation of the plotted values is f = 2.8 (l1-d/g) with a correlation coefficient of -0.94. 9| Eat J [2m non] C4] ESI [6] LVI [3] [9] Lao J palaa pal 2 | aoa] eager] APPENDIX E A PROGRAMING LANGUAGE (APL) PROGRAM TO FIT A CURVE TO A PROFILE V ReSHEL Ms: G SHEL IS A FUNCTION FO DESCRIBE AH INNER-CONTTNENWTAL SHELF PROFILE PROGRAMMER: C EVERTS, 3 JUNE -1976 THE REQUIRED COUSTANT VALUES ARE: A=RAMP SLOPE BSSUORE SHOR CBRIOK NG Kea C=DISTANCE 70 UPPER/LOWER SHOREFACE BOUNDARY (3C=SHOREFACE/RAMP BOUNDARY ) F=CONCAVITY PARAMETER X=DISTAICE PROM SHORELINE ANY UNITS, APPLIED CONSISTANTLY, MAY BE USED GD Bake (G D5 BEC CE SEG) 251.0) ))) F<«(AxCx3)+B R<«((1-G)x((AxX)+3B))4+°0G* (2x ( (1-0 2.781%(-(X2C))))*F))) V DovVDVIDIIDIIIVIVOIVID 22 £29 -8L ou d3pgcn° €029L *peg/ cou Joded TeoTuypey, “*tejUeD YOIeessy SupieseuTsuq Te se0D *S*N :seftes “II “STIFL “I “FTES Teq3UeUTZUOD *G *4SeOD JIN) *y (°S*N) 3sB0D OFIUeTIY “¢ “AaQoMAYIeG *Z “*SeTTJoIg *| *sdnoi3 eTzyord Buome Buty -CUTUFIOSTP AoJ PTIeIFIO 3saq pue doTeaep o7 pue seTTyord ezTrz90j,.eAeYO ATTEOFIEMSYIeM 0 peseTSAS VOM SOTITTBIOT Gy JO yoea ye saTTjoid sutN *ado—Ts Tenpea3 e yzTM JeueTd sft 1t0}300s dmwez paemess 9y} fdn-aAeouod pue daeaqs sft 1030eS aTTjoid soejsezoys oy :aedeys 10}00S-0mM}) DTASTIaqVOeIeYO e Aketdstp jseod ay} WO’ TewIOU sSaATEeUS Te}UsUTJUOD ABeUUT ey} A2eAO BUT -pueqzxe soTtjord moj,0q ‘sqyseod J[NB pue 4see *s*n oy. 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