The role of subaerial geomorphology in coastal morphodynamics of barrier islands, Outer Banks, NC

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The role of subaerial geomorphology in coastal morphodynamics of barrier islands, Outer Banks, NC

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Title:
The role of subaerial geomorphology in coastal morphodynamics of barrier islands, Outer Banks, NC
Creator:
Nelson, Eric Eduard
Place of Publication:
Tampa, Florida
Publisher:
University of South Florida
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English
Physical Description:
xi, 111 leaves : ill. (some col.), maps (some col.) ; 29 cm.

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Subjects / Keywords:
Beaches -- North Carolina -- Outer Banks ( lcsh )
Coast changes -- North Carolina -- Outer Banks ( lcsh )
Dissertations, Academic -- Marine Science -- Masters -- USF ( FTS )

Notes

General Note:
Thesis (M.S.)--University of South Florida, 2001. Includes bibliographical references (leaves 88-91).

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University of South Florida
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Universtity of South Florida
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All applicable rights reserved by the source institution and holding location.
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028273344 ( ALEPH )
48762540 ( OCLC )
F51-00161 ( USFLDC DOI )
f51.161 ( USFLDC Handle )

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THE ROLE OF SUBAERIAL GEOMORPHOLOGY IN COASTAL MORPHODYNAMICS OF BARRIER ISLANDS, OUTER BANKS NC by ERIC EDUARD NELSON A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science College of Marine Science University of South Florida May 2001 Major Professor : Sarah F Tebbens, Ph.D.

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Examining Committee : Office of Graduate Studies Univers i ty of South Florida Tampa, Florida CERTIFICATE OF APPROVAL This is to certify that the thesis of ERIC EDUARD NELSON in the graduate degree program of Marine Science was approved on January 5, 2001 for the Master of Science degree. Major Professor: Sarah F Tebbens, Ph.D. Mempec : Peter A. H
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TABLE OF CONTENTS CHAPTER 1 : INTRODUCTION ........... ......... .......... ...... ...... ........ . .......... . ........ 1 Spatial a n d Temporal Variability . .... ... . . ......... . ....... ............. ... ...... ... ...... ... 2 Importance of Beach Width in Protecting Dunes During Storms ....................... 4 CHAPTER 2 : STUDY AREA ... .............. .... ...... ............. ... ... ...... ... ... .... ............. ... 9 History and Geography ......... ... ......... ....... ........... .... ......... ......... . ....... ... ..... 9 Wave Climate ....... .............. ..... ..... ............... ... ........ ...... ... ..... ........ ........ .... ..... 12 CHAPTER 3 : DATA ..... ......... ....... .............................. ............. ............... ............. 22 LIDAR ....... . ...... .... . ........ ....... ........... .... ...... ..... .. ........... ... ........ ... . ........ .... 22 Instrumental Errors ... ... . ... ... . ...... .......... ........ . ... .............. ...... ........ ... .... .... 24 CHAPTER 4 : METHODS ......... ......... ............................... .... ............................ 28 Data Process i ng ..... ....... ....... . . ...... ....... ................................ ... .. ........... ... ... 28 Datum Conversion ...... . ........ . .... ........ ....... ... ..... ...... . ...... .... ... ... ....... . .... 28 Data Preparation ..... .......... ............. ......... ..... . .......... .... . ....... ..................... 29 Filter i ng and Gri dding ....... ... ........................ ... ..... ....... . ............ ........ ........ 33 Profiling ... ... ....... .... ... . . ..... .................................. .... . ....... ..... ...... ...... ........ 35 Parameterization ....... ......... . ... ........... .... ..... .. ......... .... ..... ......... ..... . . ..... 35 Processing Errors ... ........ ...... ......... .... ..... ... ..................... ............................... 38 Statistical Analys i s ................... .... ........ .... ..... ................. ............. ................... 39 Variance and Mean Analysis ............ .... ........ ....... .............. ...... .................... 39 Beach Width versus Dune Ret r eat Cor r elation ............ ............ .................... 40 Non l i near Curve Fitting for Extreme Dune Retreat versus Beach Width .. .. 40 CHAPTER 5 : RESULTS .................... ........................ ............ ....... .................... 42 Frequency D i stribution ....... ....... .... .............. ......... ... .......... ..... ...... ................ 42 Inter Area Comparison of Geomorphologic Parameter Variances and Means43 Dune Height ....... .... ....... .... ................................................ .... ...... ...... ...... . 4 4 Dune Base ... ....... ...... ... ............ ..... ........... ......... .......... ... ........................... 45 Beach W i dth .... .................. ........................... ......... ......... ... ... . ... .... ......... ... 46

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Horizontal Dune Base Change .... .... ........................ ... ..... ...... ......... ........ 47 Shoreline Change ..... ......... ....... ..... .................... ...... ................ ............... 48 Inter-Comparison of Geomorphologic Parameter Variances and Means from 1997 to 1998 within Areas ...... ..... ..... ......... .... ...... ........... .......... . .... .... ......... 49 Area 1 ..... ... .... ..................... ................... ........ ...... ... ........ ... ..... ........... .... 49 Area 2 ............ ..... ......... ............ ..... .................. .... ....... ...... .... . .... ............... 50 Area 3 .................. ............. ............. .... ........... ... ....... .... .... ...... . .............. . ... 51 Beach W i dth versus Dune Retreat Analysis .................. .................... ........ ..... 53 Regression Statistics ...... ............... ............................................. . .......... .. .. 53 Extreme Dune Retreat versus Beach Width ................................................ 55 CHAPTER 6 : DISCUSSION ............................................................................... 58 Inter-Comparison of Areas 1, 2 and 3 ............................................................. 58 Comparison of Area 1 versus Area 2 .................................... .... .................. 59 Comparison of Area 2 versus Area 3 .................................. .... ...... ...... ........ 63 Comparison of Area 1 versus Area 3 ...................... ...... .............. ...... .......... 65 Intra-Comparison of Areas from 1997 to 1998 .................................. .... .......... 67 Area 1 ............ ..... ... ... ......... ........... ............... .......... .... ............. ... ......... ....... 67 Area 3 .................. ........ .................. ............. .......................... . ............... .... 75 Beach Width as a Controlling Factor of Dune Retreat .............. ...................... 79 Maximum Dune Retreat ..... ...... ...................... ............................. .... .......... 81 CHAPTER 7 : CONCLUSIONS ............................................ .... ........................... 85 REFERENCES . ................ ...... ....... ..... ........... .................................................. 88 APPENDICES ...... ......................... ................................................................... 92 Appendix I. Dates when Wave Height at the Seaward End of the Duck Pier Exceeded 2 Meters .... ...... ....... ... .... ... .... ..... ... ........ ............... ... .................... 93 Appendix II. Frequency Distribution Plots of all Parameters .................... ....... 95 Append i x IV T-Test Results of Different Parameter Means between Areas 106 Append ix V. F-and T-Test Results of Parameters between 1997 and 1998 109 ii

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LIST OF TABLES Table 1 Summary of maximum wind speed maximum significant wave height and dominant wind direction for storms #1-#6 .......... .... ........ ...... ................. 20 Table 2 Statistical comparison of dune height (dh97, dh98; suffix 1, 2 and 3 refer to areas 1 2 and 3) variances and means from one area to another within the same year .............. .... .......... ..... ... .......................... ........ ..................... 44 Table 3. Statistical comparison of dune base elevation (db97, db98; suffix 1, 2 and 3 refer to areas 1 2 and 3) variances and means between areas 1, 2 and 3 within the same year .. .................... ...... ................ ...... ........ ................ 45 Table 4 Statistical comparison of variances and means of beach width (bw97 bw98; suffix 1 2 and 3 refer to areas 1 2 and 3) from one area to another within the same year ..................................................................... . ... . ... ... 46 Table 5 Statistical comparison of variances and means of horizontal dune change from one area to another ...................................................... 47 Table 6. Statistical comparison of variances and means of shoreline change sl) from one area to anot her ..... .............................................. .. ............... 48 Table 7 Statistical comparison of variances and means of dune height (dh) dune base elevation (db) and beach width (bw) between 1997 and 1998 of area 1. (Asterisks mark no significant difference.) ................................................... 50 Table 8. Statistical comparison of variances and means of dune height (dh), dune base elevation (db) and beach width (bw) between 1997 and 1998 of area 2. (Asterisks mark no significant difference ) .... .... ........................................... 51 iii

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Table 9. Statistical comparison of variances and means of dune height (dh), dune base elevation (db) and beach width (bw) between 1997 and 1998 of area 3. (Asterisks mark no significant difference.) ................................................... 52 Table 10. Coefficients of exponential and power law curve fitted for the extreme dune retreat values versus 1997 beach width ............................. .. ........ ...... 55 Table 11. Summary of means and standard deviations of all parameters for all three areas and for all areas combined ..................................................... .. 59 iv

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LIST OF FIGURES Figure 1 Terminology of the beach/dune system ............ ... ... ................. ........ ... 2 Figure 2 Swash zone on a beach Rhigh: maximum wave run-up R10w: minimum wave run-up, D high : dune crest elevation, D10w : dune base elevation (from Sallenger 2000). Tis wave period at times t and t2 ............ .......... ............... 5 Figure 3. Four regimes are delineated to categorize storm impacts on barrier islands The threshold between collision and swash is dependent on specific beach characteristics shown as a dashed line (Sallenger, 2000) .......... ....... 6 Figure 4 Wave run-up with and without berm with wavelength (L) and wave height (H) being equal. ... ........ ... .... ... . . . ................. . ..... ...... ... ......... ........ .. 7 Figure 5 Map of the Outer Banks and the three sub-divisions of the study area ... ..... ..... ....... . ...... ................... .......... ......... .... ............... ... .... ........... .. ... .. 10 Figure 6. Natural dunes of Portsmouth (Core Banks) in area 1 (courtesy of USGS) ... ....... ...................... .... ... . .................... ...... ...... ......... ............ ...... 11 Figure 7. Enhanced dunes of Avon in area 3 (courtesy of USGS) ........ ... .... .... 11 Figure 8 Locat i on map of meteorological stations from NOAA, http : //www ndbc noaa.gov/Maps/Southeast.shtml. ... ...... .. . ..... .. .. .. .. .. ..... ... 14 Figure 9 Signif i cant wave heights (H5 ) between 9/1/97 and 9/1/98 at Duck (DUCN7) Diamond Shoals Lt (DSLN7) and Frying Pan Shoals (FPSN7) 15 F i gure 10 Wind speed between 9/1/ 97 and 9/1/98 at Duck (DUCN7) Diamond Shoals Lt (DSLN7), Cape Lookout (CLKN7) and Frying Pan Shoals (FPSN7) .......... ... . .... . .... . .. ...... ...... ........ .......... ..... .... ....... ............... .... 16 v

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Figure 11. Storm #1 (1 0/18/97 to 1 0/21/97) Wind speed (pink) wind direction (blue) and wave height (gr een) for Duck, Diamond Shoals Lt. and Cape Lookout. Left axis shows hourly average wind direction i n degrees clockwise from N Right axi s units are m / s for wind speed and m for s i gn i ficant wave height. . . .... ............. ..... .... ........ ....... ......... ... . .... ......... . .......... ... ..... ..... 18 Figure 12 Storm #6 (8/26/98 to 8/29 / 98). Wind speed (pink) wind direction (blue) and wave height (green) for Duck Diamond Shoals Lt. and Cape Lookout. Left axis shows hourly average wind direction in degrees clockwise from N Right axis units are m / s for wind speed and m for significant wave height. 19 Figure 13. Storm tracks of Hur r icane Bertha (1996) Fran (1996) and Bonnie (1998) 21 Figure 14. Diagram showing the elliptical scan pattern of NASA's Airborne Topographic Mapper (from Sallenger et al. 1999) . ........ . . . .... ........ ......... 24 Figure 15. Top : shore-normal profile within section 23 (see index map in Figure 17 for section location) exhibits a vert i cal erro r due to G PS drift ; bottom: shore normal profile within section 35 exhibits no vertical drift between profiles of 1997 and 1998 ... ...... ........... ..... ... ... . ... ............... ... .... ........... . 2 6 Figure 16. ATM flight coverage during the 1997 and 1998 surveys ......... . ...... 27 Figure 17. Index map of areas 1, 2 and 3 and sections 0 38 .. . ......... ..... ... ... 32 Figure 18 Regress i on statistics and plots of areas 1, 2 a nd 3 for 1997 . ... . ..... 5 4 Figure 19 Least squ are exponenti a l (red) and power law (green) curve fit of maximum dune retreat versu s beach width 1997 for areas 1 2 and 3. Blue stars represent the maximum dune retreat recorded in each 1 m bin .... ... 57 F i gure 20 Illu s tration of dune base elevation (db blue) dune crest elevat i on (dh green) of 1997 and 1998 and horizontal dune change db) of are a 1 ... .. 69 Figure 21. Horizontal dune db), beach width change and shorel i ne change sl) of area 1 ........ ................ ... ... ... ...... ...... ..... . . . ...... ..... ... ........ 70 Figure 22 Illustration of dune b as e elevation (db blue) dune crest e l e vation (dh gre en) of 1997 a nd 1998 and horizontal dune change db) of area 2 ..... 73 Figure 23 Horizontal dune db) beach width ch a nge and shoreline change sl) of area 2 ...... ........... .... ........ .. ... ... .............. ... ........ ... ............ 7 4 v i

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Figure 24 Illustration of dune base elevat i on (db blue), dune crest elevation (dh green) of 1997 and 1998 and horizontal dune change {t1 db) of area 3 ...... 77 Figure 25 Hor i zontal dune change {L1 db), beach width change and shoreline change {t1 sl) of area 3 .......... ............. ............ ... ................. ..................... 78 vii

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THE ROLE OF SUBAERIAL GEOMORPHOLOY IN COASTAL MORPHODYNAMICS OF BARRIER ISLANDS, OUTER BANKS, NC by ERIC EDUARD NELSON An Abstract of a thesis submitted in part i al fulf i llment of the requirements for the degree of Master of Science College of Marine Science University of South Florida May 2001 Major Professor: Sarah F. Tebbens Ph.D. viii

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This study analyzed the change in beach/dune morphology of the Outer Banks, North Carolina, between September 1997 and September 1998 based on two airborne LIDAR surveys During the study period the Outer Banks experienced what is shown to have been a typical storm year including Hurricane Bonnie that passed near the survey region days before the second survey was collected. The survey region was subdivided into three areas based on two distinct characteristics, history of dune enhancement and dominant orientation of the barrier island shorelines Area 1 included the Core Banks from Cape Lookout in the south to Ocracoke Inlet where the dunes have been self sustained. Area 2 included Ocracoke Island and the southern part of Hatteras Island, where the dunes have been enhanced and stabilized Coastlines in areas 1 and 2 strike roughly southwest northeast. Area 3, from Cape Hatteras in the south to Oregon Inlet in the north, has undergone dune stabilization just as area 2, but it has a north-south striking coast, significantly different from the other two areas Within each area, shore normal profiles spaced 20 meters apart were sampled from the data and the following five geomorphic parameters were measured : dune crest elevation of the most shoreward dune, dune base elevation, beach width (the horizontal distance from the shoreline to the dune base), horizontal change in dune base location, and horizontal change in shoreline location. In the first part of this study the average and variance of each parameter ix

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were calculated for each area for statistical comparison spatially, between the three areas, as well as a temporally within each area Several differences were found between and within each area. The enhanced dunes in area 2 have indirectly caused greater shoreline retreat than in area 1 by reflecting more energy of the storm waves, hence increasing the washout of the sediments This, in turn created a narrowing of the beaches, increasing the exposure of dunes to future wave run-up. Area 3 exhibited evidence that the local wave energy is on average greater than in the other two areas based on the presence of a generally higher dune base elevation. All three areas have experienced dune retreat. However, the dunes in area 1 that apparently experienced more overwash than the other two areas retreated the least and did not have a significant decrease in dune height. Hence, area 1 dunes exhibit morphodynamic equilibrium unlike areas 2 and 3. Part two of this study assessed the relation between beach width in 1997 and maximum dune retreat observed between 1997 and 1998 in areas 2 and 3, where most storms occurred within the collision regime (Sallenger, 2000). A non-linear relation was found where maximum dune retreat decreased toward zero with increasing beach width A minimal beach width of-20m, necessary to sustain dunes, was determined by calculating the relative elevation difference between the average dune base and shoreline assuming a maximum beach slope of 1 : 10. The minimal width depends on the dominating wave climate and X

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therefore is different for area 2 versus area 3. Maximum dune retreat versus beach width differs between areas of different geomorphology and wave climate. Abstract Approved : ---=---------------Major Professor: Sarah F Tebbens, Ph.D. Assistant Professor, Marine Science Date xi

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CHAPTER 1: INTRODUCTION The U S East Coast consists of a nearly continuous chain of barrier islands (leatherman, 1988). Coastal change in this area has drawn the attention of many researchers because of increasing population pressures. Coastlines especially the sandy shorelines of barrier islands undergo constant change in order to adapt to the ever changing physical nearshore environment. The coastal morphodynamics are governed by changing wave climate, sediment flux and extreme episodic storm events (Fenster and Dolan, 1993). Longand short-term erosion are the primary agents for destruction of coastal properties. Hence, understanding the parameters that control coastal erosion may save both money and lives However, these parameters vary from one region to another and require a spatial understanding The first part of this study will quantify five subaerial geomorphologic parameters for three different areas along the Outer Banks North Carolina, to assess whether the geomorphology of the different areas influences the coastal morphodynamics differently. These five parameters are dune crest elevation, dune base elevation, horizontal beach w i dth horizontal dune change and 1

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horizontal shoreline change The second part will address the question of whether beach width influences dune retreat. Figure 1 depicts the coastal terminology that will be used in this paper Dune Crest *.... Dune ', Height \ Decrease \ DUNE Beach Width BACKSHORE (BERM) BEACH FORE SHORE Figure 1. Term i nology of the beach/dune system. Spatial and Temporal Variability INSHORE zone of nearshore processes It is well accepted by the scientific community that most of the world's beaches are presently retreating due to several reasons such as sea level rise climatic changes, anthropogenic impact and more (DeKimpe et al. 1991; Dolan et al., 1979; Fenster and Dolan 1993 ; Komar 1998 ; Leatherman 1988). 2

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However, on a daily basis the effects of seasonal accretion and erosion are greater than the changes due to long-term trends on an annual to decadal scale (Wright and Short, 1983). Thus, there is an immediate concern for what those effects will be including, among others, the impact of sporadic events such as a northeaster or a tropical storm. The annual variability due to increased wave action during winter months and episodic storms can be very important to coastal communities. Coastal processes have been studied in detail for at least a century. However, those studies have been primarily point studies, meaning that they were based on a spatially narrow data set, i.e., a single beach profile or a group of profiles spanning only several hundred meters The spatial extent of the observed coastal dynamics could not be addressed. Technical advances in the 1990s have revolutionized surveying techniques, allowing collection of large amounts of high-resolution data in short time periods This is particularly beneficial in assessing spatial issues Spatial variability of coastal change is governed by the complex synergistic nature of geomorphologic predisposition such as sediment characteristics and underlying geologic framework (Riggs et al., 1995; Riggs et al., 1992), and dynamic nearshore processes such as changing water levels, waves and currents (Inman and Dolan 1989; Kriebel and Dean 1985; Riggs et al. 1992) In order to gain a better understanding of coastal change it is important to evaluate the spatial variability One approach is to identify areas with dissimilar spatial patterns of variability. Once areas have been 3

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found to show different spatial change patterns, one can infer reasons for those differences This study was designed to take an empirical approach to quantifying a few basic morphological parameters (dune height, beach width, horizontal shoreline change and dune base retreat) for three different areas in the Outer Banks, and assessing their spatial variability Importance of Beach Width in Protecting Dunes During Storms Being able to predict potential storm damage on barrier islands is very important, especially erosion of dunes that on barrier islands are a primary protection for human structures There are two fundamentally different approaches to scaling damage: (1) scale the force of the destructive process (i.e., Saffir-Simpson for hurricanes) and (2) scale the vulnerability of a system to a given process Differences in the predisposition of the environment can cause a different resulting impact. Sallenger (2000) proposed a method for scaling the impact of storms on barrier beaches by categorizing storm impact. He defined the upper and lower elevation limits of the swash zone, Rhigh and R1aw and related these limits to the dune crest and base elevations, Dhigh and D1aw of the first line of defense', either a foredune or beach berm (Figure 2). Rhigh is the maximum elevation of wave run-up that includes the effects of astronomical tides, storm surge, and wave setup R1aw is the minimum wave run-up, below which the beach is at all times submerged Sallenger (2000) defined four regimes by considering 4

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how both Rhlgh and vary relative to Dhlgh and (Figure 3} Storm impact patterns change with each regime Three of the four regimes are important to this study : (1) the 'swash' regime (Rhlgh < where wave run-up is confined to the foreshore of the beach below the dune base, (2) the collision reg ime (Rhlgh > where swash impacts the dune, and (3) the overwash' regime (Rhlgh > Dhlgh and R10w < Dh,gh), where wave run-up overtops the dune (or berm). Figure 2. Swash zone on a beach. Rh,9h: maximum wave run-up, R10w: minimum wave run-up, Dhigh: dune crest elevation, D1ow: dune base elevation (from Sallenger, 2000). Tis wave period at times t1 and t2 This study will adapt the terminology proposed by Sallenger (2000). The s wash reg i me does not impact the dunes directly because it is confined to the 5

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foreshore. Nevertheless, in the swash regime the foreshore typically erodes and recovers following a storm s impact (Komar 1998 ; Larson and Kraus 1994 ; Lee et al. 1998; Morton et al., 1995 ; Plant et al. 1999) Storms within the collision regime may cause more irreversible damage to dunes because dune building processes are very slow and mainly depend on eolian transport. Dunes in the Outer Banks have been found to be eroding at a rapid rate (Birkemeier et al., 1984 ; DeKimpe et al., 1991; Sallenger et al., 2000b) BEACH RESPONSE TO STORMS 2 0 INUNDATION OVERWASH REGIME 1 5 REGIME I CJ I 0 -1 0 I CJ REFLECTION I REGIME a: 0.5 0.0 0 0 0.5 1.5 2.0 Figure 3. Four regimes are delineated to categorize storm impacts on barrier islands. The threshold between collision and swash is dependent on specific beach characteristics shown as a dashed line (Sallenger, 2000). 6

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Wave climate data (Chapter 2) and preliminary analysis of the survey data used in this study suggest that the Outer Banks were subjected to storms within the collision regime several times within the one-year study. Hence, this study focuses on dune impact within the collision regime and introduces beach width as a refining scaling parameter Although nearly horizontal, the backshore of the beach acts as an energy buffer once the maximum wave run-up exceeds the foreshore It is intuitive that the wider the backshore, the more that wave run-up is dissipated before potentially arriving at the dune base (Figure 4). In some cases, the backshore may dissipate so much wave energy that the wave never impacts the dune base, even though the run-up elevation (Rhigh) at the foreshore exceeds the dune base elevation (D10w) Hence, beach width is an important control on the susceptibility of dunes to erosion. No Dune Erosion Dune Base Dune Erosion Wave run-up Berm Wave run-up Figure 4. Wave run-up with and without berm with wavelength (L) and wave height (H) being equal. 7

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The second part of this study will try to establish the importance of beach width in protecting dunes from erosion during the study period The results may provide important information regarding how beaches and dunes respond in general to storms within the collision regime In addition the results may provide a quantitative prediction of dune vulnerability along the Outer Banks. 8

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CHAPTER 2: STUDY AREA History and Geography The study region is located between Cape Lookout and Oregon Inlet on the Outer Banks of North Carolina and is subdivided into three areas (F i gure 5) The Core Banks (area 1) provide an opportunity to observe the morphodynamics of low-lying dunes (2-4m elevation) on a barrier island that has been left in a natural state. The general morphology of the foredune is composed of an array of indiv i dual vegetated sand mounds (Figure 6). Dunes to the east and north along the rest of the Outer Banks (areas 2 and 3) were stab i lized and maintained from the 1930s to 1970s and have higher dune heights (5-10 m elevation). These dunes exhibit a different morphology The morphology of the foredunes is composed of a continuous vegetated ridge as a first line of defense (Figure 7). Since the 1970s some of these dunes have undergone little or no erosion, whereas some have undergone extensive or complete e r osion creating weaknesses in the "lin e of defense" 9

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35.00' ATLANTIC 34.30' 76. 30' 76.00' 75.30' Figure 5. Map of the Outer Banks and the three sub-divisions of the study area. Areas 2 and 3 are separated by the distinct change in orientat i on of the i slands at Cape Hatteras where the barr ier islands shift from a northeasterly to a northerly direction. That change in strike influences the dominant incident angle 10

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of incoming waves as well as the longshore currents. Hence, the strike as well as dune construction could be a factor in altering shoreline change variability Figure 6. Natural dunes of Portsmouth (Core Banks) in area 1 (courtesy of USGS). Figure 7. Enhanced dunes of Avon in area 3 (courtesy of USGS). 11

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Wave Climate The Outer Banks are subjected to frequent storm events During winter months, northeasters can cause severe erosion of the coastline. Through cross shore transport, the eroded sediments are stored in offshore sandbars, which, during summer months, are welded back onto the beach (Lee et al. 1998; Plant et al., 1999) During the summer and early fall, on the other hand, less frequent tropical storms and sometimes hurricanes impact the coastline. The U.S. Army Corps of Engineers at the Field Research Facilities (FRF) in Duck NC, have compiled a record of local storm dates since 1981 Storm days are defined as the days when the measured significant wave height exceeds 2 m. Between the two survey dates of this study, September 1997 and September 1998, there were 35 storm days recorded at Duck (Appendix 1 ). The average number of storm days per year s i nce 1981 is 31. Hence, the number of stormy days during the survey period is comparable to the past 18 years. To understand the local wave climatology in more detail, standard meteorological data from NOAA's National Data Buoy Center (NDBC) were analyzed from four c-man stations around the Outer Banks. The stations are located at Duck (DUCN7), Diamonds Shoals Light. (DSLN7), Cape Lookout ( CLKN7) and Frying Pan Shoals (FPSN7) as illustrated in Figure 8. Cape Lookout (CLKN7) is a land-based station The average water depths at the marine c-man stations are 8.4 m (DUCN7) 15 8 m (DSLN7) and 14 m (FPSN7) 12

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Hourly wind speed and significant wave height are illustrated in Figures 9 and 1 0 for the time period between 9/1 /97 and 9/1/98, with s i gn i ficant wave height defined as the average of the highest one-third of all the wave heights during a 20-minute period The time series includes approximately one extra month of data before the first survey, which shows that there were no storms immediately preceding the date of the initial data set. We assume that the coastline, at the t i me of the 1997 survey, was not recently eroded by a storm and hence was in an accreted non-storm state Figure 9 shows the wave he i ghts of the marine c-man stations and Figure 10 shows the wind speeds for all four c-man stations Because they represented the most complete record (Figure 9 ), Duck (DUCN7) wave data were chosen to identify five major storms (#1 5) during the study period when waves were approximately 3 m or higher. Storm #6 marks the occurrence of Hurricane Bonnie where there is a large data gap possibly caused by an instrument failure due to the severity of the storm. Those storms (#1 6) are assumed to be a representat i ve sample of extreme events that occurred within the study period throughout the Outer Banks and are identified for all stations, where possible The events are labeled 1 through 6 in chronolog i cal order with peak wave heights recorded on Oct. 19th 1997 and Jan 29 th, Feb 5 t h Apr. 51h, May 13t h and Aug. 27th 1998. 13

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Figure 8 Location map of meteorological stations from NOAA, http : //www.ndbc.noaa.gov/Maps/Southeast.shtml. 14

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4 5 4 3. 5 l 3 .&: 2 5 til a; 2 .&: Q) > Ill 1 5 3: 0 5 6 5 l 4 .&: til 'Qj 3 .&: Q) > 2 Ill 3: 10 9 8 l 7 6 til 'Qj 5 .&: Q) 4 > Ill 3 3: 2 Signif i ca n t W ave Height at Duck 4 I 6 A I I J lL a 1 .I l 1 L I lA 'l1. t \f ''\fl Significant W a v e Height at D iamon d Shoals I I 0 l f t I I l \ 5 ,\ l' I t1 \1 I I \ il I . 1 I I ,. \ \1' ' 11 IIi l' T i It I I I 'I ..... . Significant Wave Height at Frying Pan Shoals i N date 4 6 f I .. I .ll. 6 Figure 9. Significant wave heigh t s (H8 ) between 9/1/97 and 9/1/98 at Duck (DUCN7) Diamond Shoals Lt. (DS L N7) and Frying Pan Shoals (FPSN7). 1 5

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I 'tl (/) 'tl c i I l (/) 'tl c i I l c.. (/) 'tl c i Wind Speed at Duck Wind Speed at Diamond Shoals 10 5 i>' # .cfP .cfP .cfP .cfP 0}" 0}".;. .... .... .... ,,,-...<:J .... "' Wind Speed at Cape Lookout 1 0 5 ,,P:. ,P:. ,P:. _,P:. .cfP .cfP .cfP 0}" 0}""'-.... ,,,.._<:J ........ "-'l>' ,p""". ,;.-1 ' _.,::. .cfP .cfP .cfP 0}" 0}""'-.... ....
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Duck is approximately 11 0 km north and Cape Lookout is approximately 120 km southwest of Cape Hatteras (Diamond Shoals). F i gures 11 and 12 i llustrate a typical northeaster (storm #1) and Hurricane Bonnie (storm #6) in greater detail for those three stations The parameters included are wind speed, wind direction and wave height for which the maxima for storms #1 through #6 are shown in Table 1 Storms #1 #5 are typical northeasters with the w i nd blowing dominantly out of the north-northwest. The maximum w i nd speeds are generally in close harmony between Duck and Diamond Shoals However at Cape Lookout the winds are generally weaker This is due to the fact that most northeasters cross open water when they approach Duck or Cape Hatteras However many northeasters are more likely to pass over land when they a pproach Cape Lookout, resulting in a decrease in magnitude of the surface winds 17

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Wind Speed D i rection and Wave Height at Duck from 10/18/97 to 10/21/97 315 ....... ... ... r-4'-=--------t 1 8 16 14 I Wtnd Di.-.clion 135 9 W ave Height 6 12 24 36 48 hours 00 84 W ind Speed, Direction and Wave Height at Diamond Shoals from 10/18/97 t o 10/2 1 /97 uo 3 1 5 270 m n5 .. 100 1 35 00 45 0 0 12 uo 3 1 5 270 J! n5 0,100 Q) 135 00 45 0 0 12 2 4 36 48 hours 5 00 84 Wind Speed and Direction at Cape Lookout from 10/18/97 to 10/21/97 24 36 48 hours 60 10 8 6 84 Wtnd Direction W ave Height Wind Direction Figure 11. Storm #1 (1 0/18/97 to 1 0/21/97). Wind speed (pink), wind direction (blue) and wave height (green) for Duck, Diamond Shoals Lt. and Cape Lookout. Left axis shows hourly average wind direction in degrees clockwise from N. Right axis units are rn/s for wind speed and m for significant wave height. 18

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Wind Speed, Direction and Wave Height at Duck from 8126198 to 8129/98 1 2 24 48 hours 60 72 25 20 15 10 5 0 84 96 Wind Direc tion -Wind Speed W ave Hei g h t Wind Speed, Direction and Wave Height at Diamond Shoals from 8126/98 to 8129/98 315 t---------------------N-=-T-----------------------------i 30 210 r 1 35 tt15 00 1 0 $0 315 270 n5 1 2 24 $ 48 hours 60 72 Wind Speed and Direction at Cape Lookout from 8126/98 to 8129198 Wind Direc tion -Win d Speed Wave Height Win d Direction .. 1 80 C) Gl 15 -WindSpeed t 35 00 1 2 2 4 48 hours 60 72 84 Figure 12. Storm #6 (8/26/98 to 8/29/98). Wind speed (pink), wind direction (blue) and wave height (green) for Duck, Diamond Shoals Lt. and Cape Lookout. Left axis shows hourly average wind direction in degrees clockwise from N. Right axis units are mls for wind speed and m for significant wave height. 19

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Storm# 1 2 3 4 5 Date s 10/18 1 /2 7 2/44 / 45 / 1210 /2 1 / 97 1 /3 1 / 98 2/10/98 4/7/98 5/15 / 98 Duc k max. Wind Speed (m /s) 18.7 22.8 18 7 21.2 16.1 dominant Wind Direction N-NW NW E-NNW NNW N max. Wave He i ght (m) 2 .97 3 93 3.37 2 .86 3 .07 Diamond max Wind Speed (m/s) 19.8 21.4 23.3 22.4 18 Shoals dom inant Wind D i rection N-NW NW E-NNW NNW N max Wave He i ght (m) 4.34 5.56 *5.49 4.35 n / a Ca pe max. Wind Speed (m/s) 11.6 15 3 16.5 15 3 12.5 Lookout dominant W i nd D i rect ion N NW NW E-NW NNW N 6 hours or larger data gaps in wave height from maximum wind speed Table 1. Summary of maximum wind speed, maximum significant wave height and dominant wind direction for storms #1-#6. 6 8 /26-8/29 / 98 23. 1 ESE-WNW 2 .9 1 32.4 SE-W 3 .51 30 .2 E-W Storm #6, unlike the other 5 storms, is not a northeaster but Hurricane Bonnie (Figure 12). The wind speeds during Bonn i e were higher in the southern parts of the Outer Banks and diminished somewhat prior to reaching Duck as a tropical storm. As the storm passed the Outer Banks (F i gure 13), the winds initially blew onshore out of the east, then slowly turned south (clockwise) reaching maximum speeds. The winds continued to shift to the west and the wind speed rapidly decreased as the storm left the region. At Duck the winds shifted counterclockwise because Bonnie, by that time a tropical storm, had left the mainland near Duck 20

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78" W 77 W 76 W 36" N 36" N 35 N 34 N I North Carolina 1 I Bertha I -7/ti-7i14198 I . I Ran .. .. 78" W I 'It I I Hurricane Category -- Tropical Storm ---Category 1 -----Catego ry 2 Catego ry 3 7TW 76"W Figure 13. Storm tracks of Hurricane Bertha (1996), Fran (1996) and Bonnie (1998). There were data gaps in the recorded wave heights during Hurricane Bonnie (marked with an asterisk in Table 1 ) Therefore, the maximum wave heights that occurred are almost certainly greater than those recorded because the observed wind speeds were greater than during any of the northeasters (#1 #5) and the winds blew onshore during or shortly before reaching maximum wind speed. Thus, there is a great difference in wave height recorded between the northeasters and Hurricane Bonnie at Frying Pan Shoals (Figure 9). 21

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CHAPTER 3: DATA The data used for this study consist of two high-resolution LIDAR surveys of the Outer Banks, NC, collected on September 261h, 271h and 291h 1997 and September 15 1 and 7'h, 1998. The first data set was collected to provide a base map representing the topography at an accreted non-storm state, meaning beach morphology had not been altered by a recent storm event. The second data set was collected 4 to 1 0 days after Hurricane Bonnie made landfall on the Outer Banks on August 271h and 281h. LID AA LIDAR is an acronym for Light Detection And Ranging, a technology developed several decades ago to calculate distance by measuring the two-way travel time of a laser pulse. The advent of differential GPS and inertial navigation has enabled detailed topographic and bathymetric measurements from an aircraft with precise positioning of the airborne platform Several LIDAR systems 22

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are currently available internationally (Whitman, 1997) NASA s A i rborne Topographic Mapper (ATM) was used to collect the data used in th i s study as a part of a cooperative effort between USGS NASA and NOAA ATM is a scanning airborne laser altimeter designed by NASA to measure the melting of the Greenland ice sheet (Krabill et al. 1995). ATM has found wide applications among coastal scientists Information about U S.-wide LIDAR data can be found on the NOAA Web site : http:// www.csc.noaa.gov / crs / b e achmap. For each pass along the coast, the ATM scans a 350-m swath approximately half the altitude of the aircraft, along the aircraft s flight line. For most of the study area four overlapping passes were flown y i elding a typical surveyed swath of -700 m wide with laser spot elevations every few square meters (Figure 14). The aircraft pitch roll and heading were obtained with an i nertial navigation system, and the positioning of the aircraft was determined using kinematic Global Positioning System (GPS) techniques A twin engine t urboprop aircraft, a De Havilland Twin Otter, was provided and operated by NOAA's Operations Center, McDill Air Force Base Tampa FL (Brocket al. 1999 ; Sallenger et al. 2000b). .. 23

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NOAA DHC6 Twi n Otter Aircr aft Elevation ( -700 meters) Combined Swath W idth ( 700 meters) Figure 14. Diagram showing the elliptical scan pattern of NASA's Airborne Topographic Mapper (from Sallenger et al., 1999). Instrumental Errors The ATM can survey beach topography along hundreds of k i lometers of coast in a single day w i th data dens i ties of a data po i n t for every 1 to 2 m2 Th i s dens i ty and sampling speed cannot be achieved with traditional survey 24

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technologies. A detailed study was conducted by Sallenger et al. (2000a) at the U .S. Army Corps of Engineers Field Research Facility in Duck, NC, to evaluate the vertical accuracy of the ATM and bias between the ATM and other surveying methods. The study established a RMS of -15 em. However, in an inter comparison study from one ATM survey to another, Sallenger et al. (2000a) found a mean error of up to 13 em that they attributed to an unexplained drift in the differential GPS. This drift has been found to fluctuate over periods of tens of minutes to an hour or more. To estimate the vertical drift between the 1997 and 1998 data sets, I examined the region shoreward of the dune, where it is expected that the elevation is essentially unchanged. Figure 15 shows an extreme case of vertical drift on the order of 0.5 m. However this extreme offset was found to be exceptional within the data set. Most profiles show a minimal vertical offset, as shown in the second set of profiles in Figure 15 Therefore, for this study I will consider the RMS of -15 em as a potential mean error and include this level of instrumental error as a bias in the discussion Figure 16 shows the flight patterns for the 1997 and the 1998 survey where multiple passes were flown over the same area within the same day or on a different day. This multiple collection, probably in different drift phases of the GPS adds to the unlikelihood that the entire data set is biased by as much as 0.5 m 25

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Shore -Normal Profiles of Section23 of 1997/98 from the Outer Bonks, NC I I I I : ; 6 ----------+--------------+-------------j--;t-------------+-------------i--4 ----------!-----------+--------i ----------! ----------+ -.g : / -J : l I I -' I I I 2 ---_:_:_:-=-=4_-.._----T----------:-;_-------r--I c 2 0 > Q> Qi I I I I I -I o -----------i---------t ------------r ----------------_-,..,.... ; 1 : I : I I I I 8 6 4 2 0 2 280 300 320 meters 340 360 380 Shore-Normal P rofi l es of Section35 of 1997/98 f rom the Oute r B onks, NC i ' ' I j j : : l l I I , : I -----1-------------t--: : i i i I : i i '-; i 1 I I I I I : I : ; : ; I I I I I I I I I I I l I I I I I I I : I : : I I I I I I : I l : : ; 100 120 1 4 0 160 1 8 0 200 meters dashed l ine: 1997 lidar data solid line: 1998 lidar data Figure 15. Top: shore-normal profile within section 23 (see index map in Figure 17 for section location) exhibits a vertical error due to GPS drift ; bottom : shore normal pro f ile within section 35 exh i bits no vertical drift between profiles of 1997 and 1998. 26

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76 w 35N 7TW 76 w 7TW 76w 36 N 35N Cape Lookout 7TW 76w 75w 35N 9/26/97 9/27/97 9/29/97 75w 75 w 36. N 35 N --9/1/98 --9/7/98 75 w Approx. Survey Times: 9/26/97: 2 hrs 36 min 9/27/97 : 1 hr 12 min 9/29/97: 1 hr 16 min Approx. Survey Times: 9/1/98: 20 m i n 9/7/98: 58 min *Total approximate survey t i mes are calculated by subtracting the beg i nning time stamp of the last and first pass of the day. Therefore the actual survey time is underest ima ted by the duration (up to 20 30 minutes) of the final pass. Figure 16. ATM flight coverage during the 1997 and 1998 surveys. 27

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CHAPTER4:METHODS Data Processing The data files for this study were several gigabytes in size and required several steps of processing to organize and convert them into a workable format. It was decided to grid the data which would enable volume measurements in the f uture Most of the data processing was done on a Sun workstation using IDL. Datum Conversion Airborne Topographic Mapper (ATM) data are referenced spatially to the World Geodetic System 1984 (WGS84) ellipsoid model. However, the most commonly used ellipsoid (but not the most exact) is the Geodetic Reference System of 1980 (GRS80). The North American Datum of 1983 (NAD83) is refe r enced to that ellipsoid and is the most commonly used datum in the U S today Hence, the irregularly spaced ATM data were first converted horizontally in a 3-step process from WGS84 to NAD83 using the algorithms geod2cart", 28

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" wgs2nad83" and "cart2geod provided by NASA Wallops and the National Geodet i c Survey. WGS84 is a geo-centric ellipsoid model with the smooth surface defined as having an elevation of zero. However the elevat i ons of most po i nts on the Earth's surface do not coincide with the ellipsoid surface, which is defined by local variations in the Earth s gravitational field. For instance, the Outer Banks is in the neighborhood of -37 m WGS84 elevation. Hence, the data are converted to the geo i d (defined by grav i ty) that approximates mean sea level. NOAA and NGS have developed a conversion program called "geoid96". Horizontal and vertical conversion programs are a c cessible on the Web at ftp ://ftp.ngs noaa.gov/pub/pcsoft. Data Preparation In order to grid and analyze such a large data set cover i ng about 200 km of c oastline, it was necessary to subdivide the data set into smaller 5-km sections of coastl i ne reducing the file sizes to tens of megabytes Start and end points of linear reference lines were selected at the land-water interface using the cursor on a computer image of the 1997 LIDAR elevation map (a visualization program written by NASA) that returned the geographic coordinates (lat/lon) This approach was reasonable because the coastline i s fairly straight within the 5-km intervals and the resolution of the LIDAR image is excellent. Start and end points were chosen manually for 39 shore parallel reference lines, ensur i ng an overlap 29

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of a few tens to a 100 meters in order to maintain complete coverage of the shoreline. The reference lines of the sections in 1997 were applied to the sections of 1998 as well assuming a shoreline change of m at the start and /or end point in 1998, that would cause the reference line to rotate by approximately 0.5 which cannot be subjectively distinguished The reference line was used to establish approximate 5-km long rectangular sections of data. The widt h (shore-normal) of the data in each sect ion was the width of the combined LIDAR swaths, which were dete r mined later. In the first ma i n programming step the data were converted from geographic coordinates (NAD83) to cartesian (x y) coord i nates assuming a spherical Earth The radius of the Earth was assumed to be 6,380 km The absolute distance of 1 o longitude changes at different latitudes. Hence, an average latitude of 35 2 N was used for the conversion, marking the mean latitude of the study area which extends between 34 5 Nand 35 9 N. The conversion introduced a maximum error of + 1 -0 86 % distance in t he longitudinal direction at the most northern and southern lat i tude However a maximum absolute error of 1 7 m on a 1 00 m (long i tude) has no impact on the study when comparing vertical elevations or relative horizontal d i stances The only absolute horizontal d i stance measured (in a later step) is beach width However t he scale of importance is several meters and the r efore the potential error can be neglected The x-y coordinate system is assumed to be planar disregarding an i nsignificant curvature of t he Earth over the extent of the study area Th i s 30

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conversion was done to facilitate distance measurements and to allow coordinate rotations of the sections. If the individual sections were to be gridded in the most memory-efficient manner, it was necessary to rotate each section individually to align the elongated coastal sections parallel to either the x-or y-axis in order to avoid unused white space in the corners of a rectangular grid containing the data. To rotate a section, the angles between they-axis and the individual reference lines of the 5-km sections were calculated The same angles were used to rotate the 1997 and 1998 section s coastlines to an orientation as parallel as possible to the y-axis. The aligned sections of each year were stored in separate files. The 39 section locations are illustrated in Figure 17 The data at this processing point are still irregularly spaced. 31

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35.8 NORTH CAROLINA 35. 6 35.4 35. 2 35.0 34.8 ATLANTIC 34.6 Cape Lookout Rodanthe Salvo Little Kinnakeet Avon Cape Hatt eras D Area 1 Area 2 0 Area 3 -76.6 -76.4 -76.2 -76.0 -75.8 -75.6 -75.4 -75.2 Figure 17. Index map of areas 1 2 and 3 and sections 0 38. 32

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Filtering and Gridding Before gridding the data it is important to eliminate as many "bad" data points as possible so that gridded surfaces are not distorted "Bad" data points are considered any points showing >20 m elevations that were higher than any natural coastal feature. Viewing the elevation images of the irregularly spaced LIDAR data gave an initial idea of the morphology of the study area, in particular the maximum elevations This allowed a simple removal of all data points that were higher than 20 m by applying a high-pass filter This caused an approximate data reduction of 1%. These points probably represented return signals off birds clouds and the Cape Hatteras Lighthouse. Some of the high measurements may also have been off wave whitecaps, which tend to cause erratic readings of the LIDAR instrument (Manizade, pers comm., 1999) Each section from 1997 was compared to its matching counterpart from 1998 to determine the maximum x-range (cross-shore range) of common spatial coverage. That cross-shore range marked the width of the individual section for both years in the following gridding process. In the next step, the individual sections were triangulated using the Delaunay triangulation method, an IDL internal function. Delaunay triangulation has the property that the circumcircle of any triangle in the triangulation contains no other vertices in its interior. Hence interpolated values are only computed from the nearest points Thereafter the data were gridded by section to a regularly spaced data set using a 1-m2 grid size The grid size was chosen to obtain the 33

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highest possible resolution without loosing any information. With data elevation points every 1-2 m2 a smaller grid size does not seem justified Gridding may introduce a random horizontal error of one-half the grid size or 0.5 m and vertically 1/2 of the elevation difference of the actual morphology within the grid cell. These random errors cancel each other out within the entire data set. The next filtering step was designed to selectively filter out bad" points Once the data were gridded, it became possible to apply a 3x3-point median box filter A median filter was chosen because it is effective in remov i ng salt and pepper noise ( i solated high and low values) The filtered data were stored in separate files. The non-filtered data set of each section was then compared grid cell by grid cell with the filtered data set. Cell values of the non-filtered data that differed more than 1 m from the filtered data were substituted with the filtered cell value This eliminated single negative or positive grid cell peaks that were greater than 1 m different from median. This was done under the assumption that an extreme peak in a single grid-cell did not represent a natural geomorphologic feature Any geomorphologic feature relevant to this study is assumed to be of greater spatial area than 1 m2 The criterion of 1 m was chosen cautiously in order to eliminate the most obvious outliers without eliminating data points representing real geomorphologic features. Out of 5,000,000 points in one section, about 1 000 (0.02 % ) were substituted through this filtering process After obtaining a preliminary gridded data set, profiles of the data were viewed and a more accurate characterization of the coastal morphology was 34

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obtained With an improved knowledge of maximum geomorphic elevations new upper data limits were defined for each section ranging between 7 and 15 meters The filtering and gridding process was redone applying the more restrictive parameters, removing another -0.5% of "bad" data points Profiling Shore-perpendicular prof i les were constructed every 20m in the alongshore direction for each section. Because the coastline of a section was aligned to be approximately parallel to the y-axis shore-normal cross sections were generated by selecting individual rows of the gridded data at 20 m. The y values that determined the profile locations in the sections were stored in one file Double coverage of profiles within the overlap of sections was eliminated and a continuous progression of 20-m intervals was ensured from one section to another Parameter i zation Various parameters (shoreline retreat beach width, dune height, etc ) were estimated using algorithms. The results were visually spot checked to verify the success of the algorithm The parameters were defined as follows: (1) Shoreline was taken as the 0 8-m contour line of the beach, because during data collection the highest tide never exceeded 0 76 m above mean sea level. Mean sea level was determined by using NOAA s verified tide data although for the 35

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most part data were collected at low tide The possible presence of swash was not accounted for and may have biased the shoreline to be more seaward However most data were collected at low tide and there were no storm waves during the time of the surveys. Therefore, the impact of wave run-up is assumed to be below the large scale of this study. To determine the shoreline and to avoid high waves or other random points detected and classified as land points an algorithm was written to approach the beach from the water (Atlantic Ocean) The algorithm detected the first point at 0.8 m or higher that was followed by at least 30 points (equal to 30m) of equal or higher values Shoreline retreat (.1 sl) is defined as the difference between the horizontal position of the 0 8-m contour (=shoreline) in 1997 and 1998. After plotting and reviewing the results approximately 20 points had to be edited by hand because the algorithm failed to select the shoreline correctly. (2) Dune height (dh) was measured at the crest of the most seaward local maximum within 100 m of the shoreline mark i ng the crest of the 'f i rst line of defense In order to avoid berm crests the point of maximum elevation was determined first. Then the next local maximum was determined within 10 m seaward of the prior local maximum, assuming that the rough topography of a dune would create several local maxima within a short distance. A berm, on the other hand would create a local maximum more than 10 m away from the dune After a visual i nspection some dune crests were edited either manually or by adjusting the window size to less or more than 10 m Change in dune height is the vertical difference between the crest in 1997 and 36

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1998. (3) The location of the dune base (db) was determined by using two different approaches. (a) The first of five consecutive data elevation points landward of the shoreline with a sufficient low frequency in an elevation distribution plot that indicates an increase in slope was determined first. The sensitivity of this approach was set to detect the dune base or points seaward of the dune base. The first approach helps insure that the base of beach scarps or other local peaks are not being detected (b) The maximum curvature between the previously determined point and the dune crest was then located Most often these two points do not co i ncide because the maximum curvature point may represent a "bump" in the dune or the low distribution point is not followed by a continuous increase in elevation. Therefore, an iterative process was applied to approach the two points resulting in a single location point selected as the location of the dune base This made more sense than simply choosing the mid point between those points, because the maximum curvature data point often was horizontally closer, but vertically farther away from, the dune base than the low frequency distribution point. (4) Dune db) was defined as the horizontal change in the location of the dune base between the 1997 and 1998 surveys. (5) Beach width (bw) was defined as the horizontal distance between the location of the dune base (db) and the shoreline (sl). If the base of the dune was not located within 1 00 m of the shoreline, that profile was no longer considered in quantifying the beach width and dune parameters. 37

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After visually inspecting each profile several points mainly dune base locations were manually edited where the points were found to be horizontally miss-located by 1 0 m or more Anything less than 1 0 m off would significantly increase the chance of introducing subjectivity to the points selected Approximately 150 points out of 8 000 were revised Processing Errors A possible error was i ntroduced when the irregularly spaced data points were interpolated into a regular grid. The grid size was chosen at 1 m2 with data points collected every 1-2 m2 A maximum horizontal error was introduced of one-half the grid size The vertical error associated with gridding is minor Another added source of error was i ntroduced when the points were converted from a spher i cal coordinate system (long i tude/latitude) to a planar Cartesian coordinate system. However, because the parameters are being compared in a relative sense that error has no net effect. A third source of error is created through dune vegetation. LIDAR has only a limited penetration through vegetation to detect the ground. Soft vegetation can change orientation and inclination daily through changes in the wind pattern and can also exhib i t considerable growth over a period of one year Nevertheless chances are that if in one year the dunes were vegetated heavily enough to bounce a signal off the top, they will likely bounce a signal the following year All in all, the processing 38

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added several sources of error that are assumed not to influence the results of this study. Statistical Analysis Variance and Mean Analysis The mean (J..L) and variance (cr) for the following parameters were determined for each area: dh 97: elevation of dune crest in 1997 dh 98: elevation of dune crest in 1998 db 97 : elevation of dune base in 1997 db 98: elevation of dune base in 1998 bw 97: beach width in 1997 bw 98: beach width in 1998 il db: horizontal change in dune base il sl: horizontal change in shoreline position All statistical analyses were conducted using Excel internal routines at a 95% confidence limit. First, frequency distribution plots were created in order to demonstrate whether the parameters are normally distributed. Standard statistics were applied to assess the statistical significance of the means and variances. Second, applying the f-test, the variances of the parameters were statistically 39

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compared from one area to another. Where the variance was significantly different a t-test with unequal variances was applied to assess statistical difference between means For areas that exhibited equal var i ances a t-test for equal variances was applied Statistical differences of variance and mean between the 1997 and 1998 data sets were established using the f-test and the t-test for paired data points. The t-test for paired variables was chosen because it assesses the same variable at two different times (a year apart) The results are presented in the next two chapters Beach Width versus Dune Retreat Correlation Linear regression statistics were applied to assess the correlation coefficient r between beach width of 1997 and dune retreat for each area. A table provided the significant r value, which was 0 088 for degrees of freedom (dt) greater than 500 Non-linear Curve Fitting for Extreme Dune Retreat versus Beach Width Non-linear curve fitting for extreme dune retreat versus beach width was completed using IDL. A scatter plot of dune retreat versus beach width 1997 was made for each area The data point with maximum dune retreat was identified for each 1-m bin of beach width in order to apply a non-linear least square fit curve with a given function It is intuitive that dunes on a narrow beach are more likely 40

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to be impacted by storm waves than dunes on a wide beach However a minimum beach width (the foreshore) has to be maintained by definition, the separation between dunes and the shoreline. The minimum width of the foreshore depends on the relative elevation difference of the dune base and the shoreline and the maximum slope of the foreshore. The maximum slope is assumed to be about 1:10 for all areas (Inman and Dolan 1989) The relative difference in elevation is calculated from the average dune base elevation and shoreline elevation. Average dune base elevation for areas 1 and 2 is 2.7 m and 3.5 m for area 3 and the shoreline is measured at 0.8 m elevation Hence, the relative difference in dune base elevation to the shoreline elevation is assumed to be 1.9 m in areas 1 and 2 and 2 7 m in area 3 This results in a minimum beach width of 19 m in areas 1 and 2 and 27 m in area 3, respectively. Hence estimates for beach widths below 19 m in areas 1 and 2 and below 27 m in area 3 are not considered in the curve fitting process. Two functions were applied to the scatterplots exponential and power law using the IDL curve fitting routine "curvefit". These functional forms were chosen in order to fit a curve that approaches zero dune retreat with increasing beach width assuming that an infinitely wide beach would provide a sufficiently wide buffer to prevent any dune erosion during collis ion regime storms. 41

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CHAPTERS: RESULTS This chapter presents the results of statistical analyses that assess whether the morphological parameters are distinct from one area to another within one year and within each area between the two survey dates The relation between beach width and dune retreat will also be analyzed. In Chapter 6 the implications of the results will be discussed. Frequency Distribution Frequency distribution plots were made for each parameter to visually assess whether the data are normally distr i buted. The complete set of distribution plots is presented in Appendix II. The frequency distribution plots for dune crest elevations ( dh97, dh98) and horizontal shoreline change sl) are well described by a normal distribution (pp. 95-96). The dune base elevation (db97 db98) distributions are a l so reasonably well described by a normal distribution (pp. 97 98). However, because it is difficult to detect low dune bases, only dune base 42

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elevations of 2m (with some exceptions) or higher were determined. Exceptions occurred when the closest data elevation point to the 2-m threshold was below 2 m The beach width (bw97, bw98) distribution plots show skewness toward the narrow end of the beach (pp 99-1 00). This implies that beach width does not follow a normal distribution because minimum beach width must be positive as discussed earlier There must always be a foreshore. Hence, there is a physical limit, unlike dune base elevations, to a minimally sustained beach width. The horizontal dune change (L\ db) distribution plot (p. 101) is slightly skewed to the right. There is a maximum at modest erosion values of 01 m. There are relatively few accretion values that probably represent slumping of eroded dune faces and a wide range of larger erosion values, resulting in the skewed distribution We proceed to employ standard statistics methods. Inter-Area Comparison of Geomorphologic Parameter Variances and Means The variances and means of all parameters were tested to determine if they differ from one another. All the statistical tests were conducted at a 95% confidence level equivalent to two standard deviations (2 cr). The numeric results of these statistics are subject to several sources of potential error that require careful consideration in interpretation. The interpretation including analysis of potential error, is in the next chapter In the following paragraphs, tables summarizing the mean and variance of each parameter and whether they are 43

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significantly different from between areas are presented. Numbers in regular font represent the means numbers in italic represent the variances, and numbers in bold and marked with an asterisk are statistically equal. More detailed statistical summaries including calculated fand t values are shown in Appendices Ill V. Dune Height Table 2 shows that in all cases the means and variances of dune crest elevation are sign i ficantly different between the three areas. Mean dune heights are lowest in area 1 higher in area 2 and highest in area 3 Mean dune heights range from 4.21 min area 1 to 6 49 min area 3. Variances also increase from area 1 through area 3. Dune Height Comparison Area 1 vs. 2 dh971 dh972 dh981 dh982 Mean !l 4.21 5.64 4.27 5.45 Variance
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Dune Base In table 3 mean and variance of dune base elevation are presented For area 1 and 2 in 1997 and 1998 they are statistically the same at about 2 7 m elevation. However, the variances between areas 1 and 2 are different. The means and variances of areas 1 and 2 compared to area 3 are different, where the mean dune base elevation of area 3 is higher at about 3 5 m. The variance of dune base elevation of both years increases from area 1 to area 3, sim ilar to the variances of dune crest elevation. Dune Base Elevation Comparison Area 1 vs. 2 db971 db972 db981 db982 Meanf..L *2.71 *2.69 *2.71 *2.69 Variance if 0.09 0.13 0 .09 0.13 Area 1 vs. 3 db971 db973 db981 db983 Mean f..l 2.71 3.52 2 .71 3.52 Variance if 0.09 0.40 0.09 0.40 Area 2 vs. 3 db972 db973 db982 db983 Meanf..L 2 69 3 52 2 69 3.52 Variance if 0 .13 0.40 0 13 0.40 Table 3. Statistical comparison of dune base elevation (db97, db98; suffix 1, 2 and 3 refer to areas 1, 2 and 3) variances and means between areas 1, 2 and 3 within the same year. 45

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Beach Width The mean beach widths of the three areas are different from one another with the h i ghest mean beach width for 1997 and 1998 in area 3 at 44.56 and 37.48 m respectively (Table 4) The second widest mean beach width in 1997 and 1998 is in area 1 at 41. 69 and 34 53 m respectively and the narrowest mean beach width is in area 2 at 37 56 and 25 39 m respectively. The variances are also significantly different from one another except between areas 1 and 2 i n 1998 (in bold print with asterisk). In 1997 area 2 had the greatest variance, followed by area 3 then area 1. In 1998, on the other hand area 3 had the greatest variance, followed by areas 1 and 2 with equal variances. Beach Width Comparison Area 1 vs. 2 bw971 bw972 bw981 bw982 MeanJ..L 41.7 37.6 34 5 25.4 Variance <:J2 236. 9 327.8 *230.8 *229.9 Area 1 vs. 3 bw971 bw973 bw981 bw983 MeanJ..L 41. 7 44.6 34 5 37 5 Variance <:J2 236. 9 278.3 230. 8 256.7 Area 2 vs 3 bw972 bw973 bw982 bw983 MeanJ..L 37.6 44. 6 25.4 37.5 Variance <:J2 327. 8 278. 3 229.9 256. 7 Table 4. Statistical comparison of variances and means of beach width (bw97, bw98; suffix 1, 2 and 3 refer to areas 1, 2 and 3) from one area to another within the same year. 46

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Horizontal Dune Base Change There is a significant increase of mean dune retreat from areas 1 to 3 (Table 5). Area 1 only experienced an average dune retreat at the dune base of 0.37 m and the smallest variance of the three areas. In comparison to area 1 area 2 had a larger average retreat of 1.30 m and a significantly higher vari ance Area 3 exhibits the greatest retreat 2.17 m and the greatest variance Horizontal Dune Change Comparison Area 1 vs. 2 L1 db 1 L1 db2 Mean Jl -0.4 -1. 3 Variance if 2 3 8 6 Area 1 vs. 3 L1 db 1 L1 db3 Mean Jl -0.4 -2 2 Variance if 2.3 14.6 Area 2 vs. 3 L1 db2 L1 db3 Mean Jl -1. 3 -2.2 Variance if 8.6 14.6 Table 5. Statistical comparison of variances and means of horizontal dune db) from one area to another. 47

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Shoreline Change The shoreline change pattern is different from the dune change pattern All means and variances are significantly different from each other from one area to another, where area 2 experienced the greatest mean shoreline retreat at 13.44 m (Table 5). The variance on the other hand, is the smallest of the three areas The smallest average retreat occurred in area 1, which was 7.54 m with a higher variance than area 2. Area 3 experienced an average retreat of 9.26 m significantly less than in area 2 however, more than in area 1 Area 1 had the least beach and dune erosion. Horizontal Shoreline Change Comparison Area 1 vs. 2 L1 s/1 L1 s/2 Mean f..l -7.5 -13.4 Variance if 59.1 46.6 Area 1 vs. 3 L1 s/1 L1 s/3 MeanJ..L -7 5 -9.3 Variance if 59.1 144 8 Area 2 vs. 3 L1 s/2 L1 s/3 MeanJ..L -13.4 -9.3 Variance if 46. 6 144.8 Table 6. Statistical comparison of variances and means of shoreline sl) from one area to another. 48

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Inter-Comparison of Geomorphologic Parameter Variances and Means from 1997 to 1998 within Areas For most parameters, the means and variances from one area to another are significantly different. The following sections present the statistical results from comparison of the means and variances from 1997 to 1998 within each area Area 1 The means of dune height, dune base elevation and beach width in area 1 all changed from 1997 to 1998 at a confidence level of 95% (Table 7). Mean dune crest elevation increased by 5 em, whereas mean dune base elevation statistically decreased by 1 mm. The mean beach width decreased by 7.16 m. The variances of dune height decreased while the others remained the same in 1998. The magnitudes of these change measurements relative to the magnitude of sample errors will be discussed in Chapter 6 49

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Comparison of Area 1 from 1997 to 1998 Dune Height dh971 dh981 MeanJ..L 4 .21 4 27 Variance if 0.43 0 .37 Dune Base Elevation db971 db981 Mean J..L 2 .71 2 .71 Variance if *0.09 0.09 Beach Width bw971 bw981 MeanJ..L 41. 7 34.5 Variance if *236.9 *230.8 Table 7. Statistical comparison of variances and means of dune height (dh), dune base elevation (db) and beach width (bw) between 1997 and 1998 of area 1. (Asterisks mark no significant difference.) Area2 In area 2 all the means are statistically different and decrease from 1997 to 1998 (Table 8) Mean dune height decreased by about 20 em while mean dune base elevation decreased by a few millimeters The mean beach width decreased by about 12.2 m. The vari ances of dune base elevation are the same, whereas the other variances decreased from 1997 to 1998. 50

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Comparison of Area 2 from 1997 to 1998 Dune Height dh972 dh982 Meanl..l 5.64 5.45 Variance if 1.31 1 19 Dune Base Elevation db972 db982 Meanl..l 2.69 2 69 Variance if *0.13 *0 13 Beach Width bw972 bw982 Meanl..l 37. 6 25.4 Variance if 327. 8 229.9 Table 8. Statistical comparison of variances and means of dune height (dh}, dune base elevation (db} and beach width (bw} between 1997 and 1998 of area 2. (Asterisks mark no significant difference.} Area 3 Area 3 also exhibits statistically significant changes between the means of both years (Table 9), like areas 1 and 2. Mean dune crest el e vation decreased about 24 em and the mean dune base elevation decreased by a few millimeters similar to area 2. The mean beach width is narrower by about 7 1 m The 51

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variances of the dune crest and dune base parameters did not change from one year to the other However, the variance of beach width decreased slightly Comparison of Area 3 from 1997 to 1998 Dune Height dh973 dh983 Mean 11 6 .50 6.25 *1.70 *1.61 Dune Base Elevation db973 db983 Mean 11 3 52 3 52 *0.40 *0.40 Beach Width bw973 bw983 Mean 11 44. 6 37.5 278.3 256. 7 Table 9. Statistical comparison of variances and means of dune height (dh), dune base elevation (db) and beach width (bw) between 1997 and 1998 of area 3. (Asterisks mark no significant difference.) 52

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Beach Width versus Dune Retreat Analysis Regression Statistics Figure 18 shows the regression statistics for plots of beach width in 1997 versus dune retreat for each area. The calculated correlation coefficients for each area are significantly greater than 0.088, the r value of 95% confidence Hence, beach width in 1997 and dune retreat are to some degree correlated in each area. Figure 18 shows that the correlation is greatest in area 3, less in area 2 and least in area 1. R2 estimates the proportion of dune retreat that can be attributed to its linear regression on beach width, in other words, how much of the variation in dune retreat can be associated to the beach width in a linear regression (Snedecor and Cochran, 1980). R2 shows that in area 3, about 25% of the variation of dune retreat could be attributed to the beach width in 1997. In area 2 only about 10 % could be attributed to beach width in 1997 and in area 1 about 5 %. 53

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SUMMARY OLJrPUT Area3 Reg_ression Statistics 20 Multiple R 0.50131055 15 10 R Square 0 .25131227 e 5 Adjusted R Square 0 .25097441 Q) 0 Ill Standard Error 3.30464268 "' -5 .c Observations 2218 Q) 10 c ::::J "C -15
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Extreme Dune Retreat versus Beach Width An exponential funct i on of the general form y = a e b x and a power law function of the form y =a* x b were fitted through the points plotting maximum dune retreat versus binned dune width (1 m bins) A lower beach width limit of maximum dune retreat was applied at 19 m for areas 1 and 2 and 27 m for area 3 based on a minimum stable beach w i dth as discussed in Chapter 4 Figure 19 i llustrates the best-fit exponential and power law curves. The curves are extrapolated by an extra 5 m beyond the minimum estimated beach width to indicate a possible dune retreat trend for except i onally narrow beaches. The curves coefficients a, band x2 are summarized in Table 10 Function: y = a e b'x Function : y = a x b 1997 1997 a b x 2 a b x 2 Area3 -48 369 -0.0367 0 14131 -3620 9 -1.5908 0 17196 Area2 4 3 0812 0 0540 0 074045 -2252 7 -1.6645 0 06741 Area 1 15 .921 0 0408 0 080 2 8 356 2 1 3000 0 088.5 2 X2 : chi square Table 1 0. Coefficients of exponential and power law curve fitted for the extreme dune retreat values versus 1997 beach width. Greater absolute v a lues of coefficient b relate to greater maximum curvature of the exponential and power law function (Figure 19) Coefficient b of both functions is greatest in area 2. However between areas 1 and 3, b is 55

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greater for area 1 if the exponential funct ion is used and b is greater for area 3 if the power law function is used The x2-values indicate a reasonable fit of the curves in areas 1 and 2 and a less good fit in area 3. Maximum dune retreat in relation to beach width exhibits a decreasing closeness of fit from area 1 to area 3. 56

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-E -Cl C7l c 0 s;. 0 II c ::I 0 0 c -20 0 N ;: 0 J: 5 I 0 Cl 5 C7l c 0 s;. 0 -10 Cl c ::I 0 1 5 Ci c 2 0 0 .!:! ... 0 X 2 5 -30 0 E -Cl C7l c 0 s;. 0 Gl c ::I 0 :s c 0 N 0 J: 0 Area 3 . I I I 1 : . : : : 20 + + + ++ ++++++ 40 60 Beach Width 97 (m) Area 2 . 80 . . 100 . . 0 I I 0 I 0 I I / I I I 1 : : : : I I I I I I I J I I I I . I : I 20 4 0 60 8 0 100 Beo c h Widt h 97 (m) I I I I I I I . . ' . . . 20 40 60 80 100 Bea c h Widt h 97 (m) Figure 19. Least square exponent i al (red) and power law (green) curve f i t of maximum dune re t reat versus beach w i dth 1997 for areas 1 2 and 3. Blue stars represent the maximum dune retreat reco r ded i n each 1-m bin. 5 7

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CHAPTER 6: DISCUSSION Inter -Comparison of Areas 1 2 and 3 A detailed study of means and variances has provided insight to the different spatial patterns of variability across the Outer Banks Statistical analyses were reported at the 95 % confidence level with significant differ e nces on the scale of millimeters. There is a mismatch between the accuracy of the statistics (millimeters) and resolution of the data(> centimeters) The statistics should not be interpreted at a resolution more accurate than the data The vertical resolution of the ATM was estimated to have a RMS of -15 em (Chapter 3), thus, differences at smaller scales are not significant. This will be taken into account in interpreting the statistical results. Tabl e 11 summarizes means and standard deviations instead of variances, to convey the amount of variability recorded in each area and all three areas combined. 58

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Means Std. Dev. Means Std. Dev. !!. Means Dune Height dh97 dh98 L1 dh Area 1 4.21 0 65 4 27 0.61 0 06 Area2 5 64 1 14 5.45 1 09 -0 19 Area3 6.50 1 30 6.25 1.27 -0.24 Total 5.76 1.44 5.59 1.34 -0 17 Dune Base db97 db98 L1 db Area 1 2.71 0 30 2 .71 0 30 0.00 Area 2 2 69 0 36 2 69 0 36 0 .00 Area 3 3 52 0.63 3 52 0.63 0 00 Total 3.10 0 65 3.09 0 65 0.00 Beach Width bw97 bw98 L1 bw Area 1 41.7 15.4 34 5 15 2 -7.2 Area 2 37 6 18 1 25.4 15 2 -12 2 Area 3 44.6 16 7 37 5 16.0 -7 1 Total 41.8 17.2 33.1 16 5 -8 7 !!. db and !!. sl Ll db L1 sl Area 1 -0.4 1.5 -7 5 7.7 Area2 -1.3 2 9 -13.4 6.8 Area3 -2.2 3.8 9 3 12 0 Total 1 5 3 3 -10 2 10.1 Table 11. Summary of means and standard deviations of all parameters for all three areas and for all areas combined. Comparison of Area 1 versus Area 2 The data in Table 11 show that between 1997 and 1998 areas 1 and 2 have distinctly different geomorphology and response to coastal processes The boundary between areas 1 and 2 was initially chosen because of the difference in dune history primarily natural in area 1 versus artificially enhanced in area 2. Statistical analyses support this object i ve split. 59

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In area 2 the dunes are significantly higher (1-2 m) than in area 1 The standard deviation for area 2 is almost twice as large as for area 1 which shows that there is a greater variability in dune heights in area 2 Given that at one time there was a continuos line of stabilized dunes, the high standard deviation indicates that some dunes have undergone much more erosion than others in the past. This would confirm what has been suggested previously (Birkemeier et al., 1984; DeKimpe et al., 1991; Fenster and Dolan, 1993), that the stabilized" dunes are not as in equilibrium with the environment as the naturally evolved dunes of the Core Banks (area 1 ) Note that area 1 has large data gaps in the dune and beach width data because of the low topography of the dunes, particularly in the lower Core Banks, causing the dune detection algorithm to fail in detecting a dune base Therefore it is likely that the average dune height in area 1 is somewhat lower that 4.2 m. This would result in even greater differences in dune height between areas 1 and 2 than reported in Table 11. Beaches wider than 100 m were not accounted for either, thus the average beach width in area 1 is likely larger. The dune base elevations, on the other hand are statistically the same in both areas 1 and 2 at about 2 7 m, indicating that the basic energy environment between areas 1 and 2 is the same. Dunes develop at a certain elevation above mean sea level where wave interference is sufficiently infrequent to allow vegetation that supports dune growth. Hence, the elevation above which the dunes grow depends in part on the local wave energy environment that 60

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dominates that part of the coastline. A similar energy environment in areas 1 and 2 is reasonable because both areas comprise a single continuous coastline with a constant relative orientation Areas 1 and 2 are part of the same littoral cell (Inman and Dolan, 1989). The relatively small difference in standard deviations may be attributed to the wider range of dune heights, assuming that a higher dune has to have a higher base elevation to allow even less wave interference in order to reach that height, or in this case, maintain that height. The widths of the beaches in areas 1 and 2 are quite different, even though one might assume that a given energy environment would produce similar beach width The reason for the narrower beaches in area 2 relative to area 1 is the enhanced dunes. The dunes of area 1 are in natural equilibrium They are naturally lim i ted i n height by episodic overwash At the same time, overwash causes the dunes to migrate l andward as part of dune evolution during rising sea level (Dolan and Godfrey 1973 ; Leatherman 1988) The beaches are wide because the dunes do not act as a barrier to island migr a tion. In area 2 the dunes have been built higher in order to prevent overwash and protect properties from damage Preventing overwash prevents dune migration Hence, as sea level rises the beaches become narrower The standard deviations of beach width for 1997 are a few meters different between area 1 and 2 primarily due to the fact that some dunes in area 2 have eroded and reverted to a more natural morphology increasing the dune height variability as well as beach width var i ability 61

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The significantly smaller average dune retreat in area 1 relative to area 2 may be due to the fundamentally different physical processes of overwash in combination with the sparse presence of dunes creating a different pattern of resistance to wave run-up This causes transport of sediments across and around the dunes instead of complete wave reflection which caused severe dune erosion exhibited in area 2. The dune retreat variability i s greater in area 2 because of an increased variability in the geomorphology such as beach width and dune height consequently influencing dune impact in a greater variety The higher dune morphology in area 2 provides a wider window for storms to be within the collision regime, whereas that window in area 1 is relatively narrow Hence storms act more often in the overwash regime The shoreline change is dramatically different between areas 1 and 2 Area 2 exhibits twice the shoreline retreat of area 1, even though standard deviations are practically the same. Sediment transport processes may contribute to the difference During non-storm periods sediment transport may be different between both areas where Diamond Shoals Cape Lookout Shoals and the inlets, in conjunction with varying wave patterns, may impact the shoreline differently However during storms the different dune morphology may cause a s i gnificantly different shoreline impact. As mentioned in the previous paragraph large storm events will occur in different regimes in areas 1 and 2. Storms in the collision regime in area 2 cause the waves to reflect off the duneface, creating a strong backflow of water back into the ocean. However the same storm maybe 62

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in the overwash regime in area 1 where waves overtop dunes and the volume of backflow is a fraction of the initial wave The withdrawal of water creates an undertow and ripcurrents, commensurate with the amount of backflow, that force sediments offshore. The greater the undertow and ripcurrents, the greater the sediment transport offshore Comparison of Area 2 versus Area 3 Areas 2 and 3 have both experienced extensive dune stabilization (Table 11 ) Hence dunes of those two areas are somewhat higher (2-3 m) on average than the dunes in area 1 In an absolute sense, the dunes of area 3 are higher than in area 2 However, in a relative sense from dune base to crest both areas have the same mean dune height. The standard deviations are almost the same between areas 2 and 3 suggesting that the dunes of area 3 are not in equilibrium with their surrounding environment. Some dunes have undergone significant erosion reverting to lower dune heights and thereby increasing the variability of dune heights The dune bases in area 3 are on average 0.8 m higher than in area 2 because wave energy is higher in area 3 Higher potential wave run-up will prevent dune growth at lower elevations The standard deviation in dune base elevation is almost twice as large in area 3 This may be due to a greater variability in nearshore bathymetries i.e Wimble Shoals and Kinnakeet Shoals may locally focus or disperse wave energy along the coastline creating 63

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gradations in the energy environment (Fenster and Dolan, 1993; Pilkey et al., 1993). Mean beach width is significantly greater in area 3 than in area 2 and may be related to differences in nearshore environment and sand supply. Increased wave energy may not simply result in dunes forming at higher elevations, but may also cause dunes to evolve, on average, farther away from the shoreline. The dunes have retreated significantly more in area 3 than in area 2, implying that the storms within the study period have caused an overall greater dune impact on area 3 than area 2. Nummedal (1977) has calculated the deep water wave energy flux for the southeastern U.S. He broke down the flux for North Carolina into directional components where the northern components were greater than the eastern and southern components. Therefore area 3, being more exposed to the northern components, would experience an overall greater wave energy flux than area 2. He also measured a decrease in annual wave height from Cape Hatteras to Cape Lookout. The shoreline showed the greatest average retreat in area 2. However, area 3 has the greatest standard deviation. Tropical Storm Bonnie was the last major event to take place within the study period. We have established that effects of Tropical Storm Bonnie were stronger in the southern parts of the Outer Banks than in the northern parts The change in orientation of the shoreline may have significantly impacted the local wave climate. Hence area 2 was more impacted than area 3 during Tropical Storm Bonnie, causing an overall greater 64

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shoreline retreat. The greater shoreline variability and variability in dune retreat in area 3 indicates that the regional wave climate is affected by differences in the bathymetry Comparison of Area 1 versus Area 3 The comparison between areas 1 and 3 revealed a combination of differences, such as dune morphology observed between areas 1 and 2, and wave climate, observed between areas 2 and 3 The same processes produced differences in mean dune heights between areas 1 and 3 (Table 11) and between areas 1 and 2. Dunes in area 3 are on average about 2-3 m higher than in area 1, and the standard deviation is significantly larger implying that some area 3 dunes eroded more than others. Area 3 dunes were stabilized and maintained at one point in time, accounting for a greater variability in dune height. The average dune base elevations between the two areas are significantly different due to the difference in wave climate As discussed above, wave climate may regionally be influenced by differences in bathymetry. The mean beach widths appear to be greater in area 3 than in area 1 However, as mentioned in the comparison of areas 1 and 2, the values of beach width in area 1 are underestimated. Hence a comparison of beach width in an absolute sense cannot be made The beach widths of area 3 may or may not be greater than in area 1. As in area 2, the dunes in area 3 are rarely overwashed, 65

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but those in area 1 experience frequent overwash. This causes the dunes of area 1 to migrate landward, whereas the dunes of area 3 are more stationary. Therefore, the beach in area 1 readjusts itself regularly with increasing sea level whereas effects on beaches in area 3 are more limited due to a more confining dune line While storms in area 1 often occur within the overwash regime, storms in area 3 are still within the collision regime The dune bases in area 3 have retreated significantly more than in area 1. The difference is primarily due to the fact that dunes in area 3 are too high to allow any overwash during storms of the magnitude that occurred during the study period. In addition, as mentioned earlier, the dunes in area 1 are very discontinuous; hence, wave energy is deflected. A low foredune will partly deflect and dissipate the impacting wave energy and will allow it to continue to the backdune area whereas a high dune will focus the energy at the dune base and will force a reversal of the water flow that can cause a severe washout of sediments. With an increased storm surge the dune base becomes temporally part of the foreshore where the steeper sloped dune is particularly heavily impacted and achieves a storm (bar) profile (Komar, 1998). The greater variability in dune retreat is directly related to the higher variability in dune morphology and beach width The shoreline changes on a daily basis in direct response to the wave climate, although Tropical Storm Bonnie most certainly caused a major change Many other processes impact the coastline on a daily, weekly, and monthly basis 66

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over the course of the year, e g. the migration of giant cusps (Dolan, 1971 ). In addition the different pred i sposition of geomorphology and orientation offer no parallels to make any assumptions of the relative influence of geomorphology over nearshore processes on the shoreline change. The variability of shoreline change on the other hand, is partly an indicator for different wave climates, where a higher range of wave energy creates a greater range of equilibr i um profiles hence shoreline positions Intra-Comparison of Areas from 1997 to 1998 The figures presented in this section outline the data that were used to assess the statistics of the parameters Dashed lines mark data intervals that were excluded because of influence of inlets and capes Area 1 The dunes in area 1 appear to have grown 5 em between 1997 and 1998. However this change is within the known mean vertical error of 15 em Therefore, it cannot be concluded that the average dune height has changed No change would imply that the dunes were stable in their environment over the study period. Where some dunes may have eroded others have accreted to maintain equilibrium. The standard deviation has not significantly changed either within the 15-cm margin of error, indicating a morphodynamic balance 6 7

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The average dune bases from one year to the other in area 1 have essentially remained the same Dune morphology in 1997 and 1998 and the associated dune retreat are illustrated in Figure 20. Regional differences in dune height can be observed at Cape Lookout and north of Drum Inlet. The two data sets indicate that beach erosion occurred in area 1 between 1997 and 1998 (Figure 21 ). Tropical Storm Bonnie caused severe shoreline retreat. However the dunes have only been minimally affected, proving the effects of overwash Overwash has caused a slight retreat of the dunes without significantly impacting overall dune height. 68

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'(!) .D E ::l c 0 0.. 3 000 2500 2000 500 j --j i }. 1 i 1 1 t -t-i 1 ] -1 1 j I j t ! i i i i i i i i i i i i i i r 1 1 -40-20 0 20 4 0 dune chang e ( m ) 3000 2500 2000 . : """'?5iiF"""7 j !:i : l: I C : .... : ; ::r,: : -+ 1 T j_ i fW' -r-L-:: i-e:--: -i ----= : : : 1 500 r_, -p---r-1 1000 r-500 1 : -i -7; i ! --r-: a ,,Jrttt"i' 0 20 40 5 0 8 0 1 00 beach w idth 97/98 (m) 500 -40-20 0 20 4 0 s horel ine change ( m ) Ocracoke I n let Figure 20. Illustration of dune base elevation (db, blue), dune crest elevation (dh, green) of 1997 and 1998 and horizontal dune change (L\ db) of area 1. 69

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_j Ocracoke Inlet ..... Q) .D E ::J c 0 ..... a. ------.: ?" :!:::-: --= : 3000 ;_;h: ,"7-.i;r--::-.:.-t :: 2500 +-... .: ..:-.,.,_ 5-!""",..,.; 'i. --; -..;-. 2000 : i 1000 500 I -... .. .... '":'" :."' -Ou.u..L.!.J..UJ..:..u..ul.!...Lll..l.!..I..LU.J 2 4 6 8 1 0 1 2 db97 ond dh97 (m) 2000 1500 1000 500 _,_ l -i:: ""' 3000 t l -1 1 t 2500 ---J-J J '""' t .. i j: 2000 I j I ..:h i Drum -l -i 1500 i f f i l c i 1000 l + i l i i i 500 I "t 1 + 0 Cope -30 -20 -10 0 10 dune change (m) Figure 21. Horizontal dune change (L\ db), beach width change and shoreline change (L\ sl) of area 1. 70 Inlet Lookout

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Area2 The dunes of area 2 decreased -19 em in average height. Considering the nature of erosive processes and the magnitude of change regions of low dunes observed in the 1997 data indicate long-term erosion has been occurring in some parts of area 2 since dune stabilization in the 1970s There appears to be a trend for the dunes of area 2 to revert to a lower mean elevation Mean dune base elevation remained constant across areas 1 and 2 indicating a common wave climate. Figure 22 illustrates the dune morphology of area 2 with the dune change The dune bases on Ocracoke Island exhibit a decrease in elevation around the inlets indicating a difference in the wave pattern due to wave refraction by the inlets. North of Hatteras Inlet, there is a hotspot of dune erosion around profile number 5300 where low dunes have been seve r ely eroded This may be due to a local wave refraction pattern caused by a localized bend in the island and the presence of Diamond Shoals off Cape Hatteras. The beaches of area 2 are the narrowest of the three areas The shoreline has retreated more than in areas 1 or 3 showing a trend of extremely high erosion rates (Figure 23). It is interesting to note that the standard deviation for area 2 beach width decreased dramatically from 1997 to 1998, whereas that was not the case for the other two areas. There is a threshold to how narrow a stable beach ultimately can become within a beach/dune system There has to be at least a foreshore that supports the regular swash zone seaward of the dune base The width of the foreshore is dependent on the current wave conditions as well as grain size, which in turn influences the slope. The minimum area 2 beach 71

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width was estimated to be-20m. Thus the beaches seem to be approaching that threshold where the variability is naturally confined toward the narrower side. The implications are that many parts of the area 2 coastline have become so narrow that the beach widths have reached a lower threshold Thus, dune erosion rates are at least equal to or greater than shoreline erosion rates, or else the beaches would disappear which in the present environment is impossible 72

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-40-20 0 20 40 dune change (m) 5500 5000 4500 4000 Jl brn!II I i I : l Lh-J : : : s ,.=r : : -=..l-:... : -r Cope Hotteros 5000 Hatteras In let 4500 4000 3500 : T T -T Ocracoke Inlet i i i i 3 50 0 u_;_LL.L,;...LL..LJ..J...J....L:....l.J...L:...U 0 20 40 60 80 1 00 beach w idth 97/98 (m) -40-20 0 20 40 shoreline change (m) F i gure 22. Illustration of dune base elevation (db, blue), dune crest elevation (dh, green) of 1997 and 1998 and hor i zontal dune change {tl db) of area 2. 73

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' Q) .D E :J c 0 0.. 2 4 6 8 10 12 db97 and dh97 (m) 2 4 6 8 10 12 db98 and dh98 (m) -30 -20 -10 0 10 dune change (m) Cope Hatteras Hatteras I n let Ocracoke In let Figure 23. Horizontal dune change ( il db) beach width change and shoreline change ( il sl) of area 2. 74

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Area 3 The mean dune height has significantly decreased from 1997 to 1998 in area 3 as in area 2 where similar processes are taking place in reverting the dunes to a lower elevation. Dune erosion is not consistent throughout the area Instead, there is a high variability that may be due to regional variations of geomorphology and processes (Figure 24). The dune bases remained constant in area 3 However, Figure 25 shows that dune base elevations decrease north of Rodanthe Rodanthe is a headland and the coastline to the north shifts a little toward the west. There are also two shoals that surround that area : Platt Shoals off Oregon Inlet and Wimble Shoals off Rodanthe These variations in bathymetry and orientation may be the primary causes of decr e ase in dune base elevation In area 3 the beaches are narrower but maintain the same variance, unlike in area 2 where the variance decreased in 1998 (Figure 25) This could be because Tropical Storm Bonnie was the last event during the study period to impact the beach before the second survey was conducted Since the wave heights decrease north of Cape Hatteras, as discussed above, less shoreline retreat occurred in area 3 than in area 2. The standard deviations in beach width remain the same between years, unlike in area 2. Area 3 may be better adapted to its environment meaning that the beaches are wider and can accommodate the high variability beach widths that the wave climate entails. This, in combination with less impact of Tropical Storm Bonnie than in area 2 may have 7 5

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been enough for the beach width not to be eroded to the lower threshold of stable beach widths as i n area 2. 76

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.... CIJ .D E :::J c: e a. 6000 -4G-20 0 20 40 dune change (m) 8500 8000 7500 7000 6500 6000 0 20 40 60 80 1 00 beoch width 97/98 (m) Rodanthe Salvo Little Kinnokeet Avon LL.:...L.l..L'-..L..J..j::t:l!lil=..t.J...L:.'.J...J Cope Hotteros -40-20 0 20 40 shoreline change (m) Figure 24. Illustration of dune base elevation (db blue), dune crest elevation (dh green) of 1997 and 1998 and horizontal dune change (L1 db) of area 3. 77

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L (lJ .0 E :J c (lJ 0 L 0.. 2 4 6 8 10 12 db97 and dh97 (m) 2 4 6 8 0 1 2 db98 and d h 9 8 (m) 8500 8000 R odanth e 7500 Salvo 7000 Little Kinnakeet 6500 Avon 600 0 3 0 -20 -10 0 10 dune change (m) Figure 25. Horizontal dune db), beach width change and shoreline change sl) of area 3 78

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Beach Width as a Controlling Factor of Dune Retreat Dune retreat was compared to beach width at the start of the study period The regression analysis has illustrated that beach width is in part a key factor in dune erosion. Dune retreat reflects a composite of several erosion events over the course of one year, whereas sand redistribution is a constant process during calmand storm-periods. Even though the second data set was collected in direct response to Tropical Storm Bonnie there are beach profiles within the study area that show considerable accretion of up to 20 m between 1997 and 1998 Such differences in shoreline change are astounding if one were to expect a single event to provoke a similar shoreline response However we only know where the shoreline was one year before not where it was just prior to the storm event. Dolan has described large coastal crescentic landforms along the Outer Banks that can migrate hundreds of meters along the coast. These landforms, called sand waves, resemble huge beach cusps with maximum amplitudes of 40 m between the innermost part of the embayments and maximum point of the projections (Dolan, 1971; Dolan and Hayden, 1981 ). It is possible that a beach profile, initially surveyed when the shoreline was in an embayment of a sand wave, then resurveyed when it was at the tip of a projection, can still show net accretion after a severe storm It can be argued at this point that perhaps the 1998 beach width is a more accurate representation of the shoreline location relative to the dune base, prior to Tropical Storm Bonnie. However, this is true for 79

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the shoreline but not the dune baseline. There is no way that two data sets acquired one year apart can resolve how much the dunes have eroded during any given storm event, particularly when there were several during the study year. Therefore, the 1998 shoreline offers a less appropriate baseline for this study The profiles of the 1997 shoreline, on the other hand, provide a baseline before a series of events. If no net erosion or accretion occurs along the entire profile, then shoreline position changes constantly within a window that is defined by the highest and lowest energy conditions although a lag time may prevent the shoreline from reaching the position appropriate to the current wave condition Because the 1997 shoreline offers a baseline of a non-storm profile this study assesses how much the potential dune impact can be when the shoreline shifts toward a storm equilibrium. Although one cannot attribute dune retreat to any particular event by itself, one can infer the outcome after a combination of events. These events include seasonal weather patterns and non seasonal sediment migration, such as giant cusp movement, that influence the coastal morphodynamics. The events do not include long-term changes in sediment budget and sea level. Hence, chances are that the composite effect of a full annual cycle of shoreline dynamics and episodic dune-impact events will provide a complete spectrum of variability that represent an average storm year. 80

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Maximum Dune Retreat Assessing extreme dune retreat values is important in predicting short term potential damage to human structures. Average rates, on the other hand, have little significance in predicting the worst case scenario that can occur within storm events. Average rates are more important to society over longer time scales of years and decades. In this section, maximum dune retreat values are examined to assess their relation to beach width. It has been established that for dune erosion to occur, wave run-up has to impact the dune. Hence, the storm event must be at least within the collision regime All three areas have experienced storms within the collision regime during the study period. However, most storms that were in the collision regime in areas 2 and 3 often were in the overwash regime in area 1 The Core Banks (area 1) are mostly unpopulated so that the frequent backshore flooding that occurs through overwash has few societal consequences. Also, the processes involved within the overwash regime and collision regime are fundamentally different. Hence, area 1 will not be considered in evaluating dune retreat maxima. This part of the study deals only within a narrow window of Sallenger's (2000) collision regime The concept of shoreline retreat is that the slope of the submarine part of a shore-normal profile adjusts itself to the wave energy (Komar, 1998). In a storm event, the slope of the foreshore becomes shallower, thus moving the shoreline shoreward until the profile has reached equilibrium with the storm conditions. As 81

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the shoreline is being driven shoreward, the excess water of the wave run-up that exceeds the foreshore rushes across the berm. Water percolation and friction cause dissipation of the wave run-up Depending on amount of energy of the wave run-up that gets dissipated flowing toward the dune and the return backwash that is reflected off the dune, sediments are either deposited on top of the berm or are washed seaward Either way the wave run up as long as it does not dissipate before reaching the dune base causes dune scarp i ng resulting in net dune erosion (Komar, 1998) This study has estimated a wide range of dune changes with extreme values of over 25 m for dune base erosion or over 5 m for dune base accretion. Part of the change observed may have been due to anthropogenic impact. Even though dune stabilization efforts ceased in the 1970s individual and community efforts to maintain beaches and dunes may cause a bias in the data. However the data vo l ume is so large that the anthropogenic impact is assumed to be insignificant to the outcome of this study Extreme values appear to be well organized indicating a trend that is assumed to not be noise in the data. Figure 19 illustrates that there i s great variability in dune retreat for any given beach width As d i scussed earlier, sand waves and smaller sinusoidal featu r es are important agents in causing spatial variability These are migrating geomorphologic features that can change the local setting i n short time and can influence storm impact potential which i s believed to be related to beach width The maximum values are assumed to represent the worst case scenario and can 82

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either represent a composite of individual storm impacts over a one -year period or the impact of a single long-lasting storm Figure 19 shows that maximum dune retreat follows a non-linear trend relative to beach width. Exponential and power law curves were fit through the maximum dune retreat values. As the beach becomes wider maximum dune erosion decreases The curve approaches zero as the beach becomes infinitely wide. This is intuitive because the shoreline will no longer retreat once the foreshore i s in equilibrium with storm conditions Hence the berm will eventually be wide enough to dissipate the entire wave energy before wave run-up reaches the dune base Thus there is a maximum beach width at which there should be no erosion; when a storm occurs within the collision regime and the minimum wave run up (R1aw) never exceeds the dune base (D10w ) On narrow beaches however there appears to be two d i fferent scenarios depending on which function is used to describe the non-linear curve fit. For stable beaches with widths above the minimal threshold both curves show a similar trend However, the trend becomes particularly critical if one considers what happens when beach widths decrease below the threshold. The beaches are no longer stable and the difference in potential dune erosion is dramatic, although the data are insufficient to determine which relational function is the more accurate The implication of either non-linear curve is that a several-meter difference of beach width between two narrow beaches can significantly change the dune impact potential. Approaching the threshold of minimum beach width 83

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the slope of the curve decreases to where a change in beach width nearly equals the change in potential dune impact. The relation of beach width and maximum dune retreat is slightly different from one area to another (Figure 19). Therefore it is necessary for any kind of prediction to establish individual maximum dune retreat curves for different areas, where there is a different geomorphology and/or wave climate Area 3 has higher maxima values due to a higher energy wave climate than area 2. These empirical relations of beach width to maximum potential dune erosion have important implications for any nearshore urban development. 84

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CHAPTER 7: CONCLUSIONS This study has compared some geomorphologic parameters of two LIDAR surveys taken one year apart for three areas within the Outer Banks. The measured parameters are dune crest elevation of 'the first line of defense", dune base elevation, beach width, the horizontal distance from the shoreline to the dune base and relative horizontal dune base and shoreline change Area 1 includes the Core Banks from Cape Lookout in the south to Ocracoke Inlet where the dunes have not been stabilized by man. Area 2 includes Ocracoke Island and the southern part of Hatteras Island, where the dunes have been enhanced Area 3 extends from Cape Hatteras i n the south to Oregon Inlet in the north, where the island has a significantly different shoreline orientation than the other two areas Part one of this study compared of those parameters between the three areas, as well as from 1997 to 1998 within each area Part two was to assess the relation between beach width in 1997 and maximum dune retreat observed one year later The following conclusions were made: 85

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Different dune morphology, in particular dune height, influences shoreline change, dune impact and beach width. Dune retreat is related to beach width during storms that are within the collision regime. The wider the beach is, the lesser the chance of dune erosion. Maximum potential dune erosion during storm wave run-up within the collision regime increases as a non-linear (exponential or power law) function with decreasing beach width. The functional relation between maximum dune erosion and beach width varies as a function of geomorphology and/or wave climate. In the first part of this study it has become evident how much beach and dune morphology are influenced by response to nearshore processes If man alters the geomorphology of barrier islands (e g., dune enhancement), it will impact the coastal morphodynamics This is also true if man alters the nearshore processes (Komar, 1998) Either way, whatever mankind does, there are consequences to the geomorphology In the second part of this study we established a strong relationship between beach width to maximum dune erosion for storms within the collision regime. This has great significance to coastal development of barrier islands. With today's technologies, it is possible to collect high-resolution data across large areas to assess the spatial variability of coastal morphodynamics. This 86

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technique allows us to estimate and map potential hazard zones of shoreline and dune erosion that should help prevent future economic and human losses. This study of Core Banks demonstrates that spatial variability is very different from one area to another, even though the areas are only 1 Os of kilometers apart. Many studies have been done at point locations, which have greatly improved the understanding of nearshore processes. However, it has been difficult to validate those results elsewhere Numerous factors play a role in spatial variability of nearshore processes that simply cannot be detected in a point study. Technological advances offer new opportunities to expand our scientific expertise to include a larger, spatial dimension. This study was a first attempt at analyzing such variability over large spatial scales and has enabled insight into the potential storm (and non-storm) damage to three different areas in the Outer Banks. 87

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REFERENCES Birkemeie r W Dolan, R., and Fisher, N., 1984, The Evolution of a Barrier Island: 1930-1980: Shore & Beach, v 52, no 2, p 3-12. Brock, J., Sallenger, A. H., Jr., Krabill, W Swift, R., Manizade, S., Meredith, A., Jansen, m., and Eslinger, D., 1999, Aircraft Laser Altimetry for Coastal Process Studies, in Coastal Sediments '99, p. 2414-2428. DeKimpe, N. M Dolan, R and Hayden, B. P., 1991, Predicted Dune Recession on the Outer Banks of North Carolina, USA: Journal of Coastal Research v. 7, no 2, p. 451-463 Dolan, R., 1971, Coastal Landforms : Crescentic and Rhythmic: Geological Society of America Bulletin, v. 82, p. 177-180. Dolan, R., and Godfrey, P 1973, Effects of Hurricane Ginger on the Barrier Islands of North Carolina: Geological Society of America Bulletin, v. 84, p 1329-1334. Dolan, R., and Hayden, B., 1981, Storms and Shoreline Configuration: Journal of Sedimentary Petrology, v. 51, no. 3, p. 737-744. 88

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Dolan, R., Hayden, B., Rea, C., and Heywood, J 1979, Shoreline Erosion Rates along the middle Atlantic Coast of the United States: Geology, v 7 p 602-606. Fenster, M. S., and Dolan, R., 1993, Historical Shoreline Trends along the Outer Banks, North Carolina : Processes and Responses: Journal of Coastal Research, v 9 no 1, p 172-188 Inman, D. L., and Dolan R., 1989 The Outer Banks of North Carolina: Budget of Sediment and Inlet Dynamics along a Migrating Barrier System : Journal of Coastal Research, v 5, no 2, p. 193-237. Komar, P D., 1998, Beach Processes and Sedimentation: Upper Saddle River, New Jersey, Prentice Hall Inc., 544 p. Krabill W B., Thomas, R. H., Martine C F. Swift R. N., and Frederick, E. B., 1995, Accuracy of Airborne Laser Altimetry over the Greenland Ice Sheet: Int. J Remote Sensing v. 16, no. 7 p. 1211-1222 Kriebel D L., and Dean R. G. 1985 Numer i cal Simulation of Time-Dependent Beach and Dune Erosion: Coastal Engineering, v. 9, p. 221-245. Larson, M and Kraus N.C., 1994, Temporal and Spatial Scales of Beach Profile Change, Duck North Carolina : Marine Geology, v. 117 p 75-94. Leatherman S. P 1988 Barrier Island Handbook, Coastal Publications Series : College Park, Maryland, University of Maryland 92 p 89

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Lee, G.-H., Nicholls, R. J and Birkemeier, W. A., 1998, Strom-Driven Variability of the Beach-Nearshore Profile at Duck North Carolina USA, 1981-1991: Marine Geology, v. 148, p 163-177. Morton, R. A., Gibeaut, J. C., and Paine J G., 1995, Meso-Scale Transfer of Sand during and after Storms : Implications for Prediction of Shoreline Movement: Marine Geology, v. 126 p. 161-179. Nummedal, D., Oertel, G F., Hubbard, D K., and Hine, A. H 1977, Tidal Inlet VariabilityCape Hatteras to Cape Canaveral : Proc Coastal Sed 1977 ASCE, p. 543-562. Pilkey, 0. H. Young R. S., Riggs, S. R., Smith, S. A. W., Wu, H., and Pilkey, W D., 1993, The Concept of Shoreface Profile of Equilibr i um: A Crit i cal Review : Journal of Coastal Research, v. 9, no. 1, p. 255-278. Plant N G., Holman R A., and Freilich M H., 1999 A Simple Model for Interannual Sandbar Behavior : Journal of Geophysical Research v 104, no. C7, p. 15,755-15,776. Riggs S R., Cleary W. J., and Snyder S W., 1995, Influence of inherited geologic framework on the barrier shoreface morphology and dynamics: Marine Geology, v. 126, p. 213-234 Riggs S. R., York, L. L., Wehmiller, J F., and Snyder, S W. 1992 Depositional patterns resulting from high-frequency quaternary sea-level fluctuations in northeastern North Carolina: SEPM Special Publ i cation, no. 48, p 141153. 90

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Sallenger, A. H., Jr., 2000, Storm Impact Scale for Barrier Islands: Journal of Coastal Research, v 16, no. 3, p. 890-895. Sallenger A. H Jr. Krabill, W., Brock, J., Swift R., Jansen, M ., Manizade, S Richmond, B., Hampton, M. and Eslinger, D., 1999, Airborne Laser Study Quantifies El Nino-induced Coastal Change : EOS Transportations, American Geophysical Union, v. 80, no. 8, p. 89, 92-93 Sallenger, A. H., Jr. Krabill, W., Swift, R., Brock, J., List, J., Hansen, M ., Holman R. A Manizade S., Sontag, J., Meredith, A., Morgan, K., Yunkel, J K., Frederick, E. B., and Stockdon, H 2000a Evaluation of Airborne Topographic Lidar for Quantifying Beach Changes: draft, p. 20 Sallenger A. H Jr., Stockdon, H., Haines, J., Krabill, W., Swift, R and Brock, J., 2000b, Probablistic Assessment of Beach and Dune Changes, in International Conference Coastal Engineering 2000, Sydney, Australia, p 13 Snedecor, G. W., and Cochran, W. G. 1980, Statistical Methods: Ames, Iowa The Iowa State University Press, 507 p Whitman, E. C., 1997, Laser Airborne Bathymetry-Lifting the Littoral: Sea Technology, August, p. 95-98. Wright, L. D ., and Short, A. D., 1983, Morphodynamics of Beaches and Surf Zones in Australia, in Komar, P D., ed., CRC Handbook of Coastal Processes and Erosion: Boca Raton, FL, CRC Press, p 305. 91

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APPENDICES 92

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Appendix I. Dates when Wave Height at the Seaward End of the Duck Pier Exceeded 2 Meters 1981 Feb 11, 14 Mar8-9 Aug 19-23 Sep4, 23 Oct 11-16, 24, 29-31 Nov 1-2 12-15, 25-26 Dec 5-6,25 32 days 1984 Jan 1,11-15 Feb 14-15, 23, 28 Mar 13 May31 Sep 27, 29-30 Hurricane lsodore Oct 1115 Hurricane Josephine Oct, 17-18 Nov 3, 20 Dec6 25 days 1987 Jan 1-2 17 25-27 Feb 16-18, Mar 10-16, 23-24, 30-31 Apr 16, 25-28 May 4-5 Aug 14-15 Sep 4-5 Oct 12-15 Nov 11-12, 27-29 Dec 29-30 42 days 1982 Jan 1, 26-27 Feb 13, 17-19,27Mar 1 Mar 16 Apr28 May 12 Aug29 Oct 1 0-13, 23-25 Nov 19-25 Dec 9, 12, 17-19 34 days 1985 Jan 3-4 Feb 12 Mar 22-23 Apr14 May3 Aug2 Sep 27 Hurricane Gloria passed offshore at 0230 Oct 2122 Nov 4-5 Dec 1-2 15 days 1988 Jan 3, 7-8 14 Feb 12 28 Mar 11 Apr8, 12-14,19 Jun 3-5 Oct 4, 8 Nov 1 24 Dec 4 15-16 22 day s 93 1983 Jan 4 10-12, 21-22, 27-29 Feb 11-12, 14-15, 18, 20 22, 26-27 Mar 1, 12, 17 19,24-27, 31-Apr 1 Mar24 Jun 9 Sep 15, 28-30, Tropical Storm Dean Oct 1 0-12, 20-22, 25 Dec 12-13, 19-22,31 50 days 1986 Jan 11, 23-25 Feb25 Mar7-8, 21-22 Apr 18-21 May 9-13 Aug 17 Hurricane Charlie's eye made landfall 1530-1700 Oct 10-12, 18-19 Dec 1 3 ,24 28 days 1989 Jan 4 23-24 Feb 17-19, 23-25 Mar 7 -11, 23-24, Apr 11, Sep 4-10 Hurricane Gabrielle well offshore Sep 21-22 Hurricane Hugo Sep 23-24, 27 Oct 25-26 Nov23 Dec 8-1 0, 13, 22, 23-25 40 days

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Appendix I. (continued) 1990 Feb5 Mar6, 29 May 22-23 Oct 12 13 Hurricane Lili remained offshore Oct 25-27 Nov 10, 17-19, 30 Dec 8-9 17 days 1993 Jan 9-11, 16-17, 26-27 Feb 1-4 12, 26-28 Mar 13(Storm of the Century) Mar 18-19 Apr 6-9, 27-30 Aug 31-01 Sep Hurricane Emily 50 km offshore FRF at 0000 31st Oct 1 0-11 26-27 Nov 25-28 Dec 16-18 39 days 1996 Jan 7 19 27 Feb 2-5 16-17 Mar 10-13 27-30 Aug 31-2 Sep Hurricane Edouard, 400km offshore Sep 5-6 Hurricane Fran landfall at Wilmington NC at 2000 EST on 5th Oct 4-8 22-24 Nov 15-18, 22 26 Dec 14-16 39 days 1991 Jan 7-9, 11-12 Feb23 Mar 6-7,29 Ap r 20-21 May 18-19 Jun 23 Aug 18-19 Hurricane Bob 48 km offshore Cape Hatteras Aug25 Sep 1-2 20 Oct 3, 16-17, 28-Nov 1 Nov 8-10 Dec19,31 32 days 1994 Jan 3-4, 26-28, 30-31 Mar2-3 May 4, 20-21 Sep 3-5 22 Oct 3 12-13, 14-17 Nov 7 10, 16-19 Hurricane Gordon never came close Dec 8 14-19, 22-24 39 days 1997 Feb 8-9 14 Apr 1-2 23-24 May 27-28 Jun 3-7 Sep 4 Oct 18-20 Nov 6-7 13-14 Dec 27-28 24 days 94 1992 Jan 3-5 Feb 6-8 Mar 26-27 Apr 13, 2830 May 6-8, 19-20 Sep 23 Tropical Storm Danielle Oct 4-6 Dec 10-11 12-16, 29 29 days 1995 Jan 15-16 28-29 Mar2 Aug 7 9, 15-20 Hurricane Felix remained offshore Aug28 Sep 19, 23, 29-30 19 days 1998 Jan 27-29 Feb 3-10, 16-18, 23 Apr 4-5, 14, 2223 May 12 14 Aug 26-28 Hurricane Bonnie, landfall at FRF Dec 14, 16 28 days

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Appendix II. F requency Distribution Plots of all Parameters Frequency Distributi on of Area 3 200 150 >u c QJ 100 ::J CT QJ '--'+-50 0 3 4 5 6 7 8 9 10 1 1 dune crest elevation 97 (m) Frequency Distribution of Area 2 200 150 >u c QJ 100 ::J CT QJ '--..._ 50 0 3 4 5 6 7 8 9 dune crest elevation 97 (m) Frequency Distribution o f Area 200 150 >u c QJ 100 ::J CT QJ '--50 0 3 4 5 6 du n e crest elevation 97 (m) 95

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Appendix II. (continued) 200 150 >. u c Q) 100 ::l a-Q) \..._ 50 0 3 150 >. 100 u c Q) ::l aQ) \..._ --50 0 200 150 >. u c Q) 100 ::l a-Q) \..._ 50 0 2 4 3 3 Frequency Distribution of Area 3 5 6 7 8 9 10 1 1 dune crest e levation 98 ( m) Frequency Distribution of Area 2 4 5 6 7 8 dune crest e levati on 98 (m) Frequency Distribution of Area 4 5 6 dune crest elevation 98 (m) 96

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Appendix II. (continued) >. 200 (.) c :::> cr 100 0 2.0 400 300 >. (.) c 200 :::> cr 100 0 2.4 2.8 3 2 3 6 4.0 4.4 dune base elevation 97 (m) Frequency Distribution of Area 2 0 2.4 2 8 3.2 300 250 >. 200 (.) c 150 cr \.. 100 dune base elevation 97 (m) Freque ncy Distribution of Area 4 8 5 2 2 3 6 4 .0 50 2 .0 2 4 2 8 3 2 3 6 dun e base elevation 97 (m) 97

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Appendix II. (continued) Frequency Distribution of Area 3 >-200 u c: Q) ::J cr Q) I... 100 Oc_ __ > u c: 2.0 400 300 200 cr Q) I... 100 2.4 2.8 3.2 3.6 4.0 4.4 4.8 5.2 dune bose elevation 98 (m) Frequency Distributi on o f Area 2 QL_ ____ 2.0 300 250 >-200 u c: Q) ::J cr Q) I... 150 100 50 2.4 2.8 3.2 3.6 4.0 dune bose elevation 98 (m) F requency Dis tribution of Area QL_ ____ __ 2.0 2.4 2 8 3.2 3.6 dune bose elevation 98 (m) 98

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Appendix II. (continued) Frequency Distribution of Area 3 250 >. 200 u c 150 CJ Q) '-'+1 00 50 0 250 200 >. u 150 c Q) ::> CJ Q) 100 '-50 0 200 150 >. u c Q) 100 ::> CJ Q) '-50 0 20 20 20 40 60 80 beach width 97 (m) Frequency Distribution of Area 2 40 60 80 beach width 97 (m) Frequency Distribution of Area 40 60 80 100 beach width 9 7 ( m) 99

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Appendix II. (continued) Frequency Distribution of Area 3 >... u c 300 200 CJ Q) 1... ->, u c 100 400 300 200 CJ Q) 1... >, u c 100 200 150 100 CJ Q) 1... 50 20 20 20 40 60 beach w idth 98 (m) Frequency Distribution of Area 2 40 60 beach width 98 (m) Frequency Distributi on of Area 1 40 60 beach width 98 (m) 100 80 80 80

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Appen d i x II. (con t inue d ) 500 400 >... () 300 c Q) ::::> a-Q) 200 '-100 0 -14 300 >... 200 () c Q) ::::> 0"" Q) '-100 0 -10 400 300 >, () c Q) 200 ::::> a-Q) 1.... '-100 0 -6 12 -8 Frequency Distribution o f Area -10 -8 -6 -4 -2 0 2 horizontal dune bose change (m) Frequency Distribution of Area -6 -4 -2 0 2 horizontal dune base change (m) Frequency Distribution of Area -4 2 0 2 horizontal dune base change (m) 101 3 4 6 8 2 4 6 4

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Appendi x II. (continued) >. (.) c 200 150 100 oQ) '->. (.) c 50 200 150 100 oQ) '->. (.) c Q) ::J oQ) '-50 100 80 60 40 20 -30 -40 Frequency Distribution of Area 3 -20 10 0 1 0 horizontal s horeline change (m) Frequency Distribution of Area 2 -30 -20 -10 horizontal s horeline change (m) Frequency Distribution of Area -20 -10 0 horizontal shoreline change (m) 102 20 0 1 0

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Appendix Ill. F-Test Results of Different Parameter Var i ances between Areas F-Test Two-Sample for Variances F-Test Two-Sample for Variances dh971 dh972 dh981 dh982 Mean 4 210494737 5 637833917 Mean 4.2671 04211 5 446413455 Variance 0 426924381 1 30467 4599 Variance 0 368070376 1.194269513 Observations 950 1427 Observations 950 1427 df 949 1426 df 949 1426 F 0 327226713 F 0 308197079 P(F<=f) one-tail 0 P(F<=f) one-tail 0 F Critical one-tail 0 906608122 F Critical one-ta il 0 906608122 > Variances are different >Variances are different db971 db972 db981 db982 Mean 2 711976211 2.693524597 Mean 2. 71 0669263 2 692455221 Va ria nce 0 088010532 0 130897634 Variance 0.087752146 0.13004091 Observations 950 1427 Observations 950 142 7 df 949 1426 df 949 1426 F 0 6723615 22 F 0 674804151 P(F < =f) one-tail 2.24214E-11 P(F<=f) one-tail 3 3317E-11 F Critical one-tail 0 906608122 F Critical one-tail 0 906608122 >Variances are different > Variances are d ifferen t bw971 bw972 bw981 bw982 Mean 41. 6894 7368 37.55921514 Mean 34.52736842 25.39453399 Variance 236 8634296 327 8132863 Variance 230 829071 229.9360991 Observations 950 1427 Observations 950 1427 df 949 1426 df 949 1426 F 0 722555917 F 1 003883566 P(F<=f) one-tail 3.1546 3E-08 P(F<=f) one tail 0 472341588 F Critical one-tail 0 90660812 2 F Critical one-tail 1.101792657 >Variances are different > Variances are not different d_db 1 d_db2 d_s/1 d_s/2 Mean -0.374736842 1 295024527 Mean -7 536842105 -13.43938332 Variance 2 329392713 8 561567093 Variance 59.12983196 46 64762038 Observations 950 1427 Observations 950 1427 df 949 1426 df 949 1426 F 0.272075508 F 1.267585173 P(F<=f) one-tail 0 P(F <=f) one-tai l 2 75659E-05 F Critical one-tail 0.906608122 F Critical one tail 1 10179265 7 >Variances are different >Variances are differen t 103

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Appendix Ill. (continued) FTest Two-Sample for Variances F-Test Two-Samp l e fo r Variances dh971 dh973 dh981 dh983 Mean 4.210494737 6.497271867 Mean 4 267104211 6.252564022 Variance 0.426924381 1 697583235 Variance 0 368070376 1 606535342 Observations 950 2218 Observations 950 2218 df 949 2217 df 949 2217 F 0.251489513 F 0 229108172 P(F<=f) one-tail 0 P(F< =f) one-tail 0 F Critical one ta i l 0 912818043 F Cri tical onetail 0 912818043 >Variances are d i fferent >Variances are d i fferent db971 db973 db981 db983 Mean 2. 711976211 3 517921912 Mean 2 710669263 3.516008656 Variance 0 088010532 0 398670526 Variance 0 087752146 0 398689308 Observation s 950 2218 Observations 950 2218 df 949 2217 df 949 2217 F 0.220760068 F 0 2 2 0101577 P(F<=f) one-tail 0 P(F<=f) one-tail 0 F Critical one-ta i l 0 912818043 F Critical one-tail 0.912818043 >Variances are different >Variances are d i fferent bw971 bw973 bw981 bw983 Mean 41.6894 7368 44.56041479 Mean 34. 52736842 37 4792606 Variance 236 8634296 278 3348689 Variance 230 829071 256.7 467506 Observat i ons 950 2218 Observations 950 2218 df 949 2217 df 949 2217 F 0.851001639 F 0.899053525 P(F<=f) one-tail 0 001862649 P(F<=f) one-tail 0.027554771 F Critical one-tail 0 912818043 F Critical one tail 0 .912818043 >Variances are d i fferent >Variances are d i fferen t d_db1 d_db3 d _s/1 d_s/3 Mean -0 374736842 -2 174481515 Mean -7 536842105 9 255635708 Variance 2.329392713 14.57982664 Variance 59.12983196 144. 7902817 Observations 950 2218 Observations 950 2218 df 949 2217 df 949 2217 F 0 159768204 F 0.408382602 P(F<=f) one-ta i l 0 P(F < =f) one-tail 0 F Critical one-tail 0 912818043 F Critical one-tail 0.912818043 >Variances are different >Variances are different 104

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Appendix Ill. (continued) F-Test Two-Sample for Variances F-Test Two-Sample for Variances dh972 dh973 dh982 dh983 Mean 5 637833917 6.497271867 Mean 5.446413455 6.252564022 Variance 1 30467 4599 1 697583235 Variance 1.194269513 1 606535342 Observations 1427 2218 Observations 1427 2218 df 1426 2217 df 1426 2217 F 0 768548235 F 0. 7 43382036 P(F<=f) one-tail 2 97296E-08 P(F<=f) one-tail 5.40576E-10 F Critical one-tail 0 923689569 F Critical one-tail 0 923689569 > Variances are different > Var i ances are d i fferent db972 db973 db982 db983 Mean 2 693524597 3 517921912 Mean 2 692455221 3.516008656 Variance 0 130897634 0.398670526 Variance 0 13004091 0.398689308 Observations 1427 2218 Observations 1427 2218 df 1426 2217 df 1426 2217 F 0.328335368 F 0 326171048 P(F<=f) one-tail 0 P(F<=f) one-tail 0 F Critical one-tail 0 923689569 F Critical one-tail 0 923689569 > Variances are different > Variances are different bw972 bw973 bw982 bw983 Mean 37.55921514 44 56041479 Mean 25 39453399 37.4792606 Variance 327.8132863 278.3348689 Variance 229 9360991 256 7467506 Observations 1427 2218 Observations 1427 2218 df 1426 2217 df 1426 2217 F 1 177765788 F 0 895575499 P(F<=f) one-tail 0 000302123 P(F<=f) one-tail 0 011189078 F Critical one tail 1 0817649 F Critical one tail 0.923689569 >Variances are different > Variances are different d_db2 d _db3 d_s/2 d_s/3 Mean -1. 295024527 -2.174481515 Mean -13.43938332 9 255635708 Variance 8 561567093 14 57982664 Variance 46 64762038 144 7902817 Observations 1427 2218 Observations 1427 2218 df 1426 2217 df 1426 2217 F 0 587220089 F 0 322173697 P(F<=f) one-tail 0 P (F<=f) one-tail 0 F Critical one-tail 0.923689569 F Critical one-tail 0.923689569 > Variances are different > Variances are different 105

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Appendix IV T-Test Results of Different Parameter Means between Areas t-Test : Two-Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances dh971 dh972 dh981 dh982 Mean 4 210494737 5 637833917 Mean 4.267104211 5.446413455 Variance 0.426924381 1 30467 4599 Variance 0 368070376 1 194269513 Observations 950 1427 Observations 950 1427 Hypothesized Mean Diff 0 Hypothesized Mean Diff 0 df 2327 df 2309 t Stat -38 65202254 t Stat -33. 70346854 P(T <=t) two-tail 6 7535E-253 P(T <=t) two-tail 7 2406E-203 t Critical two-tail 1. 960984264 t Critical two-tail 1 960993359 >Means are different >Means are different db971 db982 db981 db982 Mean 2 711976211 2.693524597 Mean 2 710669263 2.692455221 Variance 0 088010532 0.130897634 Variance 0 087752146 0 13004091 Observations 950 1427 Observations 950 1427 Hypothesized Mean Diff 0 Hypothesized Mean Oiff 0 df 2275 df 2273 t Stat 1 358898343 t Stat 1 344586766 P(T <=t) two-tail 0 174313508 P(T <=t) two-tail 0 178892879 t Critical two-tail 1 961007001 t Critical two-ta i l 1 .961 007001 >Means are not different >Means are not different t-Test: Two-Sample Assuming Equal Va riances bw971 bw972 bw981 bw982 Mean 41.6894 7368 37 55921514 Mean 34. 52736842 25.39453399 Variance 236.8634296 327.8132863 Variance 230 829071 229 9360991 Observations 950 1427 Observations 950 1427 H ypothesized Mean Diff 0 Pooled Variance 230 2929119 df 2239 Hypothesized Mean Diff 0 t Stat 5 967 41 0936 df 2375 P(T <=t) two-tail 2 79471 E-09 t Critical one-tail 1.645494194 t Crit i cal two-tail 1 961025191 P(T <=t) two-tail 5 63043E-45 t Critical two-tail 1 960961526 >Means are different >Means are d i fferent d_db 1 d_db2 d_s/1 d_s/2 Mean -0.374 736842 -1. 295024527 Mean -7.5368421 05 -13 43938332 Variance 2 329392713 8.561567093 Variance 59 12983196 46.64762038 Observations 950 1427 Observat i ons 950 1427 Hypothesized Mean Diff 0 Hypothesized Mean Diff 0 df 2262 df 1865 t Stat 10 01040982 t Stat 19 1573086 P(T <=I) two-tail 4.11985E-23 P(T <=I) two-tail 8 08378E-75 t Critical two-tail 1.961011549 t Critical two-tail 1.961234375 >Means are different >Means are different 106

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Appendix IV. (continued) t-Test: Two-Sample Assuming Unequal Variances t-Test: Two-Samp le Assum i ng Unequal Variances dh971 dh973 dh981 dh983 Mean 4.210494737 6.497271867 Mean 4.267104211 6 252564022 Variance 0.426924381 1 697583235 Variance 0.368070376 1 606535342 Observations 950 2218 Observations 950 2218 Hypothesized Mean Diff. 0 Hypothesized Mean Diff 0 df 3093 df 3131 t Stat 65 61127341 t Stat -59 .54641984 P(T <=t) two-tail 0 P(T <=I) two-tail 0 t Critical two-tail 1.960729605 t Critical two-ta i l 1 96072051 >Means are d i fferent >Means are different db971 db973 db981 db983 Mean 2.711976211 3 517921912 Mean 2 710669263 3 516008656 Variance 0.088010532 0 398670526 Variance 0.087752146 0 .3 98689308 Observations 950 2218 Observations 950 2218 Hypothes ized Mean Diff 0 Hypothesized Mean Diff. 0 df 3142 df 3142 t Stat -48.83300613 t Stat -48.81989035 P(T <= t) two-tail 0 P(T <=t) two-tai l 0 t Critical two-tail 1.9607 2051 t Critical two-tail 1.96072051 >Means are different >Means are different bw971 bw973 bw981 bw983 Mean 41.68947368 44. 56041479 Mean 34 52736842 37.4792606 Variance 236.8634296 278.3348689 Variance 230 .82907 1 256.7467506 Observations 950 2218 Observations 950 2218 Hypothesized Mean Diff. 0 Hypothesized Mean D i ff 0 df 1935 df 1885 t Stat 4 689358736 t Stat -4.928494245 P(T <=I) two-tail 2.93219E-06 P(T <=t) two-tail 9.0117E-07 t Critica l two-tail 1 9611889 t Critical two-tail 1.96122528 >Mea n s are different > M eans are different d_db1 d _db3 d _sl 1 d _s/3 Mean -0.37 4736842 -2. 174481515 Mean -7 5368421 05 -9.255635708 Variance 2 329392713 14.57982664 Variance 59.12983196 144 7902817 Observations 950 2218 Observations 950 2218 Hypothesized Mean Diff. 0 Hypothesized Mean Diff. 0 df 3154 df 2708 t Sta t 18.94425697 t Stat 4 813177468 P(T <=t) two-tail 6.91058E-76 P(T <=I) two-tail 1 .56706E-06 t Critical two-tail 1 960715963 t Critical two-tail 1 9608387 45 >Mea ns are d iffe rent >Means are different 107

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Appendix IV. (continued) !-Test : Two-Sample Assuming Unequal Variances t-Test: Two-Sample Assuming Unequal Variances dh972 dh973 dh982 dh983 Mean 5 637833917 6.497271867 Mean 5 446413455 6 252564022 Variance 1 30467 4599 1 697583235 Variance 1 194269513 1 606535342 Observations 1427 2218 Observations 1427 2218 Hypothesized Mean D i ff 0 Hypothesized Mean Diff 0 df 3317 df 3349 I Stat -20 97035731 t Stat -20.40249242 P(T <=I) two tail 8 61784E-92 P(T <=t) two-tail 2 6184E -87 t Critical two-tail 1 960679583 t Critical two-tail 1 960670488 >Means are different >Means are different db972 db973 db982 db983 Mean 2 693524597 3 517921912 Mean 2 692455221 3.516008656 Variance 0.130897634 0 398670526 Variance 0 13004091 0 398689308 Observations 1427 2218 Observations 1427 2218 Hypothesized Mean Diff 0 Hypothesized Mean Diff 0 df 3600 df 3597 I Stat -50 03497086 I Stat -50 0383333 P(T <=I) two-tail 0 P(T <=t) two ta i l 0 t Criti c al two-tail 1 960625013 t Critical two-tail 1 960625013 >Means are different >Means are different bw972 bw973 bw982 bw983 Mean 37 55921514 44 56041479 Mean 25 39453399 37 4792606 Variance 327 8132863 278 3348689 Variance 229 9360991 256.7 467506 Observations 1427 2218 Observations 1427 2218 Hypothesized Mean Diff 0 Hypothesized Mean Diff 0 df 2860 df 3161 I Stat -11. 74706006 I Stat -22 9659481 P(T <=t) two tail 3 75558E-31 P(T <=t) two-tail 4.4893E-1 08 t Crit i cal two-tail 1 96079327 t Critical two-tail 1.960715963 >Means are different >Means are d i fferent d _db2 d _db3 d_s/2 d_s/3 Mean -1. 295024527 -2 174481515 Mean 13.43938332 9.255635708 Variance 8 561567093 14. 57982664 Variance 46 64762038 144 7902817 Observations 1427 2218 Observations 1427 2218 Hypothesized Mean Diff 0 Hypothesized Mean Diff 0 df 3534 df 3593 t Stat 7 843199814 I Stat -13. 36660916 P(T <=I) two-tail 5 7719E -15 P(T <=t) two tail 8 33545E-40 t Critical two-tail 1 960634108 t Critical two-tail 1 960625013 >Means are different >Means are different 108

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Appendix V. Fand T-Test Results of Parameters between 1997 and 1998 F-Test Two-Sample for Var i ances t-Test: Paired Two Sample for Means dh971 dh981 dh971 dh981 Mean 4.210494737 4.267104211 Mean 4.210494737 4 2671 04211 Variance 0.426924381 0 368070376 Variance 0 426924381 0 368070376 Observations 950 950 Observations 950 950 df 949 949 Pea rson Correlation 0.877080422 F 1 159898783 Hypo thesized Mean D i ff 0 P(F<=f) one-tail 0 011211933 df 949 F Critical one-tail 1.11275833 t Stat -5.527740492 P(T <=t) two-tail 4 19206E-08 t Critical two-tail 1 96246674 > Variances are different >Means are different db971 db981 db971 db981 Mean 2 711976211 2 710669263 Mean 2 711976211 2 710669263 Variance 0.088010532 0 087752146 Variance 0 088010532 0 087752146 Observations 950 950 Observations 950 950 df 949 949 Pearson Correlation 0 997788019 F 1 .002944508 Hypothesized Mean Diff 0 P(F<=f) one-ta i l 0.481943863 df 949 F Critical one-ta i l 1 11275833 t Stat 2 042490445 P(T <=t) two-tail 0 041378825 t Critical two-ta il 1.96246674 >Variances are not different >Means are d iff erent bw971 bw981 bw971 bw981 Mean 41. 6894 7368 34. 52736842 Mean 41. 68947368 34.52736842 Variance 236 8634296 230.829071 Varian ce 236 8634296 230 829071 Observations 950 950 Observations 950 950 df 949 949 Pearson Correlation 0 8642865 F 1 026142108 Hypo thesize d Mean Diff 0 P(F<=f) one tail 0 345543105 df 949 F Critical one-tail 1.11275833 t Stat 27.70101566 P(T <=t) two-tail 3 0215E-124 t Critical two-tail 1 96246674 >Variances are not different >Means are differe nt 109

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Appendix V (continued) F-Test Two-Sample for Variances t-Test: Paired Two Sample for Means dh972 dh982 dh972 dh982 Mean 5 637833917 5.446413455 Mean 5 637833917 5 446413455 Variance 1 30467 4599 1 194269513 Variance 1 .30467 4599 1.194269513 Observations 1427 1427 Observations 1427 1427 df 1426 1426 Pearson Correlation 0 901802434 F 1 092445703 Hypothesized Mean Diff 0 P(F<=f) one-tail 0 04756938 df 1426 F Critical one-tail 1 091054802 t Stat 1 4.53226092 P(T <=t) two-tail 1 00625E-44 t Critical two-tail 1 961630005 >Variances are different >Means are different db972 db982 db972 db982 Mean 2.693524597 2.692455221 Mean 2 693524597 2 692455221 Variance 0 130897634 0.13004091 Variance 0 130897634 0 13004091 Observat i ons 1427 1427 Observations 1427 1427 df 1426 1426 Pearson Correlation 0 998662448 F 1 006588115 Hypothesized Mean Diff 0 P(F<=f) one-tail 0.450672745 df 1426 F Critica l one-tail 1 091054802 t Stat 2 157973034 P(T <=t) two-tail 0 031096433 t Critical two tail 1 961630005 >Variances are not different >Means are different bw972 bw982 bw972 bw982 Mean 37. 55921514 25.39453399 Mean 37.55921514 25.39453399 Variance 327. 8132863 229. 9360991 Variance 327. 8132863 229.9360991 Observa t ions 1427 1427 Observations 1427 1427 df 1426 1426 Pear son Correlat i on 0 926360941 F 1.425671252 Hypothesized Mean Diff 0 P(F<=f) one-ta i l 1 21532E-11 df 1426 F Critical one-ta i l 1 091054802 t Stat 65. 5867823 P(T <=t) two-tail 0 t Crit i cal two-tail 1.961630005 >Variances are different >Means are different 110

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Appendix V. (continued) F-Test Two-Sample for Variances t-Test: Pa i red Two Sample for Means dh973 dh983 dh973 dh983 Mean 6.497271867 6.252564022 Mean 6 497271867 6.252564022 Vari ance 1.697583235 1.606535342 Variance 1 697583235 1 606535342 Observations 2218 2218 Observations 2218 2218 df 2217 2217 Pearson Correlation 0 889105652 F 1 056673446 Hypothesized Mean Diff 0 P(F< =f) onetail 0.097217664 df 2217 F Critical one-tail 1 072381961 t Stat 19 .0101713 P(T < =t) two tail 9 04638E-75 t Critical two-tail 1.961034286 >Variances are not different >Means a r e different db973 db983 db973 db983 Mean 3.517921912 3.516008656 Mean 3 517921912 3.516008656 Variance 0.398670526 0 398689308 Variance 0 398670526 0 398689308 Observations 2218 2218 Observations 2218 2218 df 2217 2217 Pearson Correlation 0 998418136 F 0.999952891 Hypothes i zed Mean Diff 0 P(F < =f) one-ta il 0.499557544 df 2217 F Critical one-ta i l 0.932503408 t Stat 2 537125056 P(T < = t) two tail 0 011244715 t Crit i cal two-ta i l 1.961 034286 >Variances are not different >Means are d i fferent bw973 bw983 bw973 bw983 Mean 44. 56041479 37.4792606 Mean 44. 56041479 37. 4792606 Variance 278. 3348689 256. 7467506 Variance 278. 3348689 256.7467506 Observat i ons 2218 2218 Observations 2218 2218 df 2217 2217 Pearson Correlat i on 0. 725329665 F 1.084083317 Hypothes i zed Mean Diff 0 P(F<=f) one-tail 0 028701668 df 2217 F Critical one-tail 1 072381961 t Stat 27.47910216 P(T <=t) two-tail 2 6078E-143 t Critical two-tail 1 961034286 > Variances are different >Means are different 111


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