Influence of Wave Energy Dissipation on the Geomorphic Behavior of Rocky and Sandy Coasts

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Title:
Influence of Wave Energy Dissipation on the Geomorphic Behavior of Rocky and Sandy Coasts
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1 online resource (150 p.)
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english
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Kline, Shaun William
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University of Florida
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Gainesville, Fla.
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Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Geology, Geological Sciences
Committee Chair:
Adams, Peter N
Committee Members:
Martin, Ellen Eckels
Jaeger, John M
Masters, Forrest J
Ruggiero, Peter
Plant, Nathaniel Granger

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Subjects / Keywords:
canaveral -- cape -- cliffs -- coastal -- energy -- flux -- geomorphology -- waves
Geological Sciences -- Dissertations, Academic -- UF
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Geology thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
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Abstract:
Coastal geomorphic behavior and the landforms present at the thin border between land and sea depend on numerous processes and inputs acting over a wide range of spatial and temporal scales.  Waves are one of the more notable shaping forces that influence nearshore response over shorter geologic time scales(i.e. hours to potentially millennia). This dissertation explores, both qualitatively and quantitatively, how the patterns of wave energy dissipation near the coast influence other geomorphic processes.  That investigation includes research along both rocky and sandy coasts, through both numerical modeling and more traditional field observations.  After a brief introduction, a numerical model of sea cliff and platform evolution due to wave forcing, mechanical abrasion, and associated feedbacks is presented.  After validating the model parameters, we discuss the influence of platform geometry(shape/slope) and wave forcing on the evolution of the system.  We find that the unsteady nature of sea cliff retreat can be explained by complex interactions that enhance or hinder the erosive efficacy of breaking waves. Our study of wave energy dissipation along sandy coasts takes two fronts.  First, we discuss an observation-driven analysis of beach and sandbar morphodynamics along the Kennedy Space Center shoreline, at Cape Canaveral, Florida.  We find that the surfzone sandbars appear to be in a dynamic equilibrium with wave forcing, at least over the length of our morphologic collections (~2 years).  A large, shore-oblique sand ridge is also shown to control beach and bar behavior by preferentially dissipating wave energy around it and determining the response time of bar and beach migration. Next, we perform regional wave modeling to describe the effect of wave transformation over complex bathymetric features (i.e. shoals and sand ridges) on nearshore geomorphic behavior (i.e. shoreline movement).  We find that large shoal complexes are likely responsible for stabilizing and growing two adjacent capes.  This result offers a new mechanism of large-scale cuspate evolution – one that should be tested at other cape environments.
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Shaun William Kline.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Adams, Peter N.
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RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2014-08-31

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1 INFLUENCE OF WAVE ENERGY DISSIPATION ON THE GEOMORPHIC BEHAVIOR OF ROCKY AND SANDY COASTS By SHAUN WILLIAM KLINE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013

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2 2013 Shaun William Kline

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3 Dedicated to my friends and family that have helped me every step of the way, especially Nicole, Mom, Dad, and Shylah.

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4 ACKNOWLEDGMENTS I would like to thank my parents for their unwavering support of all my pursuits, especially my academic endeavors. This dissertation would not possible without the work of my advisor, Dr. Peter Adams, and all of my committee members (listed alphabetically): Dr. John Jaeger, Dr. Ellen Martin, Dr. Forrest Masters, Dr. Nathaniel Plant, and Dr. Peter Ruggiero. They have all contributed so much of their time to provide thoughtful comments and guidance on my research. A large portion of this work was completed as part of an interdisciplinary team that included researchers at the National Aeronatics and Space Administration, Innovative Health Applications, United States Geological Survey, and the University of Florida. There are too many collaborators to name individually, but I appreciate everyone involved with the dune vulnerability team. The California Energy Commission, United States Geological Survey, and the University of Florida were instrumental in funding con tributions throughout my doctoral career. Lastly, the gratitude and love I have for my fiance, Nicole Sebranek, extends beyond words. Her unwavering support, love, and friendship have strengthened me at every turn, and I would not be at this point of my academic pursuits without her.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 LIST OF ABBREVIATIONS ................................ ................................ ........................... 12 ABSTRACT ................................ ................................ ................................ ................... 13 CHAPTER 1 INTRODUCTION TO COASTAL GEOMORPHOLOGY AND WAVE ENERGY DISSIPATION ................................ ................................ ................................ ......... 15 General Introduction ................................ ................................ ............................... 15 Wave Energy Dissipation ................................ ................................ ........................ 16 2 THE UNSTEADY NATURE OF SEA CLIFF RETREAT DUE TO MECHANICAL ABRASION, FAILURE, AND COMMINUTION FEEDBACKS ................................ 18 Background ................................ ................................ ................................ ............. 21 Wave Action ................................ ................................ ................................ ..... 21 Mechanical Wave Abrasion ................................ ................................ .............. 22 Cliff Resistance ................................ ................................ ................................ 23 Cliff Failur e ................................ ................................ ................................ ....... 23 Model Description ................................ ................................ ................................ ... 24 Shore Platform and Cliff Bathymetry ................................ ................................ 24 Maximum Notch Erosion ................................ ................................ .................. 24 Erosive Efficiency ................................ ................................ ............................. 26 Beach Conf iguration ................................ ................................ ......................... 27 Wave Energy Dissipation ................................ ................................ ................. 28 Weathering ................................ ................................ ................................ ....... 29 Failure Criteria ................................ ................................ ................................ .. 3 0 Comminution and Debris Inclusion ................................ ................................ ... 31 Sediment Budget ................................ ................................ .............................. 32 Description of Numerical Experiments ................................ ................................ .... 33 Discussion ................................ ................................ ................................ .............. 35 Numerical Experime nt 1 Model Validation and Variable Wave Forcing ......... 35 Numerical Experiment 2a Platform Slope Geometry and Deep water Wave Height on Type A platforms ................................ ................................ 37 Numerical Experiment 2b Platform Slope Geometry and Deep water Wave Height on Type B platforms ................................ ................................ 39 Conclusions ................................ ................................ ................................ ............ 43

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6 Future Work ................................ ................................ ................................ ............ 44 3 WAVE TRANSFORMATION AND BEACH AND BAR BEHAVIOR ALONG A MICROTIDAL COAST WITH COMPLEX INNER SHELF BATHYMETRY AND SHOREFACE ATTACHED OBLIQUE SAND RIDGES, KENNEDY SPACE CENTER, CAPE CANAVERAL, FLORIDA ................................ ............................. 58 Background ................................ ................................ ................................ ............. 60 Cape Canaveral ................................ ................................ ............................... 60 Deep water Wave Climate ................................ ................................ ................ 61 Inner shelf Sand Ridges ................................ ................................ ................... 62 Microtidal Surfzone Sandbar and Beach Morphology ................................ ...... 64 Video based Morphologic Observations ................................ ........................... 65 Methods ................................ ................................ ................................ .................. 66 Nearshore Wave Climate ................................ ................................ ................. 66 Video based Morphologic Observations ................................ ........................... 66 Kinematic differential GPS Beach Morphology Surveys ................................ ... 68 Results and Disscussion ................................ ................................ ......................... 68 Inner Shelf Wave Transformation ................................ ................................ ..... 68 General beach and bar morphology ................................ ................................ 69 Equilibrium model for bar positions and beach widths ................................ ...... 73 Conclusions ................................ ................................ ................................ ............ 78 4 INFLUENCE OF COMPLEX INNER SHELF BATHYMETRY ON THE GEOMORPHIC EVOLUTION OF A PROMINENT C USPATE FORELAND AND ADJACENT SHORELINE ................................ ................................ ..................... 102 Background ................................ ................................ ................................ ........... 103 Large scale Cuspate Formation and Evolution ................................ ............... 103 Cape Canaveral ................................ ................................ ............................. 105 Deep water Wave Climate ................................ ................................ .............. 106 Wave Energy Flux and Sediment Transport ................................ ................... 107 Nearshore wave climate ................................ ................................ ................. 108 Meth odology ................................ ................................ ................................ ......... 109 Validation ................................ ................................ ................................ ........ 110 Deep water Wave Forcing and Bathymetric Controls ................................ ..... 110 Interpolated shoreline and 5 m isobath ................................ .......................... 111 Results ................................ ................................ ................................ .................. 112 Validation ................................ ................................ ................................ ........ 112 Deep water Wave Forcing and Bathymetric Controls ................................ ..... 113 Seasonal Wave Climate ................................ ................................ ................. 115 Wave Events ................................ ................................ ................................ .. 117 Discussion ................................ ................................ ................................ ............ 118 Regional shoreline behavior ................................ ................................ ........... 118 Cape Stabilization ................................ ................................ .......................... 120 Long ter m shoal cape interactions ................................ ................................ 122 Conclusions ................................ ................................ ................................ .......... 123

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7 LIST OF REFERENCES ................................ ................................ ............................. 140 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 149

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8 LIST OF TABLES Table page 2 1 Input variables and initial conditions for each simulation scenario. ..................... 45 3 1 Equilibrium model coefficient and best fit power results for mean bar and beach positions ................................ ................................ ................................ ... 80 3 2 Equili brium model coefficient and best fit power results for shadowed zone bar and beach positions ................................ ................................ ..................... 81 3 3 Equilibrium model coefficient and best fit power results for ridge intersection zone bar and beach positions ................................ ................................ ............. 82 3 4 Equilibrium model coefficient and best fit power results for exposed zone bar and beach positions ................................ ................................ ............................ 83 4 2 Major onshore directed wave climate types ................................ ..................... 126

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9 LIST OF FIGURES Figure page 2 1 Schematic diagram showing relati onships among model components. ............. 46 2 2 Plot of wave height at the cliff face (H CLIFF ) versus average retreat rate R LT AVG for a consolidated cliff with a compressive strength (S C ) of 50 MPa ............ 47 2 3 Plot of relative beach elevation (h/d, dimensionless) against E ........................ 48 2 4 Plot of average cliff height (h CLIFF m) versus average notch depth at failure 8 kN/m3, maximum tensile MAX MAX ) of 90 kPa. ....... 49 2 5 Results from first numerical experiment for the type A, gentle gentle (GG A) platform configuration. ................................ ................................ ........................ 50 2 6 Results from first n umerical experiment for the type A, steep steep (SS A) platform configuration ................................ ................................ ......................... 51 2 7 Comparison of the four platform slope com binations for type A profil e (central Californian coast). ................................ ................................ .............................. 52 2 8 Comparison of the gentle gentle (blue) and steep steep (red) s imulations from t=0 to t=1000 years for type A (central Californian coast). ......................... 53 2 9 Comparison of the steep steep (red) and gentle gentle (blue) platform shape simulations for a type A platfor m (central Californian coast). ............................. 54 2 10 Comparison of the four platform slope combinations for the type B profile (North Sea English co ast). ................................ ................................ .................. 55 2 11 Comparison of the steep gentle (blue) and steep steep (red) simulations from t=0 to t=1000 years for type B (North Sea English coast). ................................ .. 56 2 12 Comparison of the steep steep (red) and gentle gentle (blue) platform shape simulations for typ e B (North Sea English coast). ................................ .............. 57 3 1 Base map of the Kennedy Space Center, Cape Canaveral, Florida study site, highlight wave instrument deployment and video based observation field of view. ................................ ................................ ................................ ................... 84 3 2 Nearshore and inner shelf (inset) bathymetry at the Kennedy Space Center, Cap e Canaveral, Florida study site ................................ ................................ .... 85 3 3 Cartoon of potential influence of shoreface attached, shore oblique sand ridge on nearshore bar and beach morphology. ................................ ................ 86

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10 3 4 Wave roses compiled from observations at NDBC buoy 41012 near St Augustine between 2006 and 2012: A) H S and B) T. ................................ ......... 87 3 5 Examples of surfzone bar configuration observed at KSC.. ............................... 88 3 6 Energy transmission across complex inner shelf bathymetry at KSC, Cape Canaveral, Florida. ................................ ................................ ............................. 89 3 7 Energy transmission across complex inner shelf bathymetry at KSC, Cape Canaveral, Florida. ................................ ................................ ............................ 90 3 8 Bar positions and beach c ontours shown with wave forcing .............................. 91 3 9 Bar variability observed at KSC.. ................................ ................................ ........ 92 3 10 Cross correlations of wave fo rcing and beach/bar positions. ............................ 93 3 11 Same as Figure 3 10, except only for mean bar positions and beach widths in the shadow zone. ................................ ................................ ............................ 94 3 12 Same as Figure 3 10, except only for mean bar positions and beach widths in the intersection zone. ................................ ................................ ...................... 95 3 13 Same as Figure 3 11, except only for mean bar positions and beach widths in the exposed zone. ................................ ................................ .......................... 96 3 14 Results of the equilibrium model applied to the entire study area (1.0 4.0 km). Observations are shown as circl es connected by a dashed line. ........................ 97 3 15 Behavior of equilibrium m odel presented in Figure 3 14. ................................ .. 98 3 16 Behavior of equilibrium model presented in Figure 3 14, but only for the shadowed zone ................................ ................................ ................................ .. 99 3 17 Behavior of equilibrium model presented in Figure 3 14, but only for the ridge intersection zone ................................ ................................ ............................ 100 3 18 Behavior of equilibrium model presented in Figure 3 14, but only for the exposed zone ................................ ................................ ................................ 101 4 1 Bathymetry (50 m contours) of continental shelf off the Flo rida Atlantic coast. 127 4 2 Bathymetry (5 m contours) of the n ested SWAN computational grid. .............. 128 4 3 NDBC buoy 410 12 hourly wave history. ................................ .......................... 129 4 4 Nearshore wave energy flux (P) transmission for two ADCP deployments ..... 130

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11 4 5 Comparison of observed (AWAC) and modeled (SWAN) wave characteristics during the fall 2010 deployment. ................................ ................................ ....... 131 4 6 Colormaps of SWAN modeled significant wave heights for conditions representative of typical quie scent summer waves ................................ ......... 132 4 7 Colormaps of SWAN modeled significant wave heights for conditions representative of typical ........................... 133 4 8 Seasonal wave composite results interpolated from SWAN outputs along the 5 m iso bath. ................................ ................................ ................................ ...... 134 4 9 Event wave composite results interpolated from SWAN outputs along the 5 m isobath.. ................................ ................................ ................................ ........ 135 4 10 Longshore wave energy fluxes normalized by a proxy for the surf zone width, the cross shore distance to the 5 m isobath. ................................ .................... 136 4 11 Expected normalized longshore wave energy flux over the total composite wave climate ................................ ................................ ................................ ... 137 4 12 5m SL ) at the 5 m isobath ........................ 138 4 13 Residual tidal currents around the Cape Canaveral shoals from Delft3D flo w simulation of 28 tidal cycles ................................ ................................ .............. 139

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12 LIST OF ABBREVIATIONS GPS Global Positioning System KSC Kennedy Space Center MHW Mean High Water NDBC National Data Buoy Center NOAA National Oceanic and Atmospheric Administration

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13 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy INFLUENCE OF WAVE ENERGY DISSIPATION ON THE GEOMORPHIC BEHAVIOR OF ROCKY AND SANDY COASTS By Shaun William Kline August 2013 Chair: Peter N. Adams Major: Geology Coastal geomorphic behavior and the landforms present at the thin border between land and sea depend on numerous processes and inputs acting over a wide range of spatial and temporal scales. Waves are one of the more notable shaping forces that influence nearshore response over shorter geologic time scales (i.e. hours to potentially millennia). This dissertation explores, both qualitatively and quantitatively, how the patterns of wave energy dissipation near the coast influence other geomorphic processes. That investigation includes research along both rocky and sandy coasts, through both numerical modeling and more traditional field observations. After a brief introduction, a numerical model of sea cliff and platform evolution due to wave forcing, mech anical abrasion, and associated feedbacks is presented. After validating the model parameters, we discuss the influence of platform geometry (shape/slope) and wave forcing on the evolution of the system. We find that the unsteady nature of sea cliff retr eat can be explained by complex interactions that enhance or hinder the erosive efficacy of breaking waves. Our study of wave energy dissipation along sandy coasts takes two fronts First, we discuss an observation driven analysis of beach and sandbar mor phodynamics

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14 along the Kennedy Space Center shoreline, at Cape Canaveral, Florida We find that the surfzone sandbars appear to be in a dynamic equilibrium with wave forcing, at least over the length of our morphologic collections (~2 years). A large, sho re oblique sand ridge is also shown to control beach and bar behavior by preferentially di ssipating wave energy around it and determining the response time of bar and beach migration. Next, we perform regional wave modeling to describe the effect of wave t ransformation over complex bathymetric features (i.e. shoals and sand ridges) on nearshore geomorphic behavior (i.e. shoreline movement). We find that large shoal complexes are likely responsible for stabilizing and growing two adjacent capes. This resul t offers a new mechanism of large scale cuspate evolution one that should be tested at other cape environments.

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15 CHAPTER 1 INTRODUCTION TO COASTAL GEOMORPHOLOGY AND WAVE ENERGY DISSIPATION General Introduction the thin borders that separate the marine and terrestrial realms fluctuate on a scale unmatched by other geological processes. The high density of human populations located near the coastline (more than half of the US population live within 50 miles of the coast), as well as the infrastructure and natural resources there, make ascertaining the behavior of the coast a vital economic and societal exercise. Sandy coasts have the added onus of being a major economic resource furthe r expanding their financial and communal significance. Although lacking the direct economic implications of their sandy brethren, understanding rocky coast morphology is also scientifically important rocky coasts comprise four fifths of the tline (Emery and Kuhn, 1982; Trenhaile, 1987; Sunamura, 1992; Naylor et al 2009). Many variables control coastline evolution, such as eustatic sea levels, tectonic motion, and sediment characteristics and availability (Bray and Hooke, 1997; Sunamura, 1 992; Trenhaile, 2000; Trenhaile, 2004; Walkden and Hall, 2005; Trenhaile, 2009). Still, waves are the dominate factor of shoter term (i.e. years to decades) coastal evolution. They are obviously erosive breaking neashore and delivering their remaining energy to the sand or rock beneath with every impact. Yet, waves (along with nearshore currents) also transport sediment that builds beaches and dunes, and they can reorganize sediment to adjust beach profiles. This feedback becomes more complicated on r ocky coasts: either shore platform beaches can aide erosion by providing abrasive tools or they can buffer the cliff base from wave assault (Sunamura,

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16 1992). Establishing the threshold between this erosive and constructive behavior is not trivial. Rathe r, understanding the transformation of waves from deep to shallow water, and how this transformation relates to the dissipation of energy the driving force of erosion and accretion is paramount in understanding coastal evolution. Wave Energy Dissipatio n Early attempts at modeling wave shoaling and breaking focused on the Goda, 1975). Later works concentrated on integrating the energy flux balance equation from deep to s hallow water (Battjes and Janssen, 1978; Thornton and Guza, 1983; Baldock et al., 1998; Ruessink et al., 2003; Hong et al., 2006; Alsina and Baldock, 2007). Battjes and Janssen (1978) and Thornton and Guza (1983) presented energy dissipation for a random wave spectrum based on the conservation of energy flux, P = EC G outside the breaker zone, where E is the wave energy density (Jm 2 ) and C G is the wave group velocity (ms 1 ). For straight and parallel contours, the divergence of energy flux is equivalen t to energy dissipation: (1 1) (1 1 ) (1 2) B F are energy dissipation (Wm 1 ) due to wave breaking and frictional losses, respectfully, H is The wave height (m), C is the wave celerity (ms 1 ), k is the wave number (m 1 ) corresponding to the average frequency, h is the water depth (m),

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17 and is the mean incident wave angle (). In most cases, frictional losses are several orders of magnitude smaller than wave breaking losses.

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18 CHAPTER 2 THE UNSTEADY NATURE OF SEA CLIFF RETREAT DUE TO MECHANICAL ABRASION, FAILURE, AND COMMINUTION FEEDB ACKS Sea cliff retreat is an episodic process, in which failures are often linked to individual storms or seismic events (Komar and Shih, 1993; Benumof et al., 2000; Hapke and Richmond, 2002). Several marine and subaerial factors contribute to cliff retrea t, such as waves (Wilcock et al., 1998; Ruggiero et al., 2001; Adams et al., 2002; 2005), groundwater flow (Lawrence, 1994; Pierre and Lahousse, 2006), beach geometry (Sallenger et al., 2002; Trenhaile, 2004), cliff lithology (Sunamura, 1992; Collins and S itar, 2008), mechanical and chemical weathering (Sunamura, 1992; Porter and Trenhaile, 2007), and precipitation (Young et al., 2009). On longer time scales, sea level oscillations also are important to rocky coast evolution (>100 k.y., Anderson et al., 19 99; Ashton et al., 2011) as are climate and tectonic activity (Emery and Kuhn, 1982). The aforementioned factors fit into a conceptual model of sea cliff retreat: during elevated sea levels (i.e. storms, high tides) waves impact the base of the cliffs, which may be weakened through weathering, fatigue, or groundwater contact, and exert both hydraulic forces (e.g. wave quarrying, water hammer, air compression) as well as mechanical abrasion if sediment particles are available. These forces drive undercu tting (notch development), which progresses until the upper, cantilevered portion of the cliff fails either in tension or in shear. Uplift (or subsidence) and/or sea level fluctuations are influential in that they change the elevation of the horizontal submergence, wave energy attenuation decreases, which increases the erosion rate at the cliff face. Conversely, uplift of the platform can prevent (temporarily) waves from accessing the cliff face, slowing the retreat rate. These concepts, less the detailed

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19 attention to mechanical abrasion, have been adopted by modelers to explore long term shore platform development (e.g. Trenhaile, 2000) as well as mesoscale (i.e. decades to centuries) cliff erosion (e.g. Walkden and Hall, 2005). Because of the long time scales of these studies, however, failure criteria were not incorporated in the preexisting models. Trenhaile (2000) presented a model of shore platform development ( oper ating o n a timescale of ~10 5 years) that incorporated wave quarrying processes encapsulated i n a surf force. In that model, a threshold minimum surf force was required for erosion, a function of rock resistance, in order to ignore the action of weak inef fective waves. Succe ssive studies provided model update s that include d simplified tectonics and weathering, as well as Hol ocene sea level changes, but neither failure criterion nor specific abrasional effects have yet been applied (Trenhaile, 2004; Trenha ile, 2008; Trenhaile, 2009). Walkden and Hall (2005) developed the Soft Cliff And Platform Erosion (SCAPE) model to investigate mesoscale rocky coast evolution. Erosion was proportional to the ratio of wave height and period to cliff resistance, modified by functions for tidal levels and the vertical erosive profile. A failure criterion was not included as collapse was assumed to occur at proscribed time increments. The model described herein builds on the principles established by preexisting models, by focusing on an explicit treatment of the beach sediment volume dependent abrasion function. Sunamura (1982a, 1992) showed in laboratory experiments that cliffs and their fronting beaches can have internal feedbacks. The amount and configuration of beac h material can enhance wave erosive efficacy by providing abrasive agents (positive feedback) or by preventing waves from breaking near the cliff toe when a voluminous

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20 beach above mean sea level is present (negative feedback). The system is further compli cated by the introduction of debris material after a failure, which waves must first comminute before resuming cliff undercutting. Additionally, a portion of the talus may provide suitable beach material that augments the platform beach. Limber and Murra y (2011) applied these concepts to a numerical model, which explores the long term evolution and equilibrium planform appearance of rocky coasts. Their experiments suggested that there exists a predictable and stable coastline configuration of headlands a nd embayments, even in the absence of lithologic heterogeneities. In this study, a numerical model was developed and used to explore the roles of sediment, cliff failure, and the comminution lag time feedback as controls on temporally (and spatially) episo dic cliff retreat. A sensitivity analysis was performed, and the model was tuned to produce realistic (order of magnitude) retreat rates over a period of time equivalent to a sea level highstand. We then set the initial conditions of shore platforms and w ave climates representative of two natural environments: the central California coast and the North Sea English coast. The experiments described within provide insight on how platform shape/slope and deep water wave height control the abrasional efficacy and dissipation patterns of breaking waves, thereby influencing long term cliff retreat rates. Our exploration of the model had two major objectives: 1) to determine whether the model, when tuned with parameters common to specific coastal environments, co uld yield retreat rates and platform morphologies consistent with field observations (numerical experiment 1) and 2) isolate the relative effects/controls of wave forcing and platform slopes on cliff retreat and mechanical abrasion feedbacks (numerical exp eriment 2).

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21 Background Rocky coasts are cliffed shores composed of consolidated materials ranging from hard rock (e.g. granite, basalt) to soft glacial deposits (Trenhaile, 1987; Sunamura, 1992). Unlike sandy beaches that experience accretion and erosion vacillations, rocky coast evolution is a one way progression of sea cliff retreat (Sunamura, 1992; Davidson Arnott, 2010). Erosion and retreat originate from subaerial weathering and mechanical wave action (Trenhaile, 1987; Sunamura, 1992). The r elative magnitude of these factors to cliff material strength the sole opposing, resisting factor controls the temporal and spatial patterns of rocky coast evolution (Sunamura, 1992). Wave Action Wave action, both hydraulic and mechanical, is the dominant erosional mechanism in most rocky coast environments (Trenhaile, 1987; Sunamura, 1992; Trenhaile and Kanyaya, 2007). Hydraulic erosive action derives from the impact pressures delivered by breaki ng waves, including high shock pressures from encircled air pockets and/or water hammer pressures from vertical wave fronts (Trenhaile, 1987). Breaking waves compress air into cliff joint and fault crevices, then as a wave recedes, the air expands, someti mes explosively. This stress causes the apertures to grow and, eventually the rock fractures (Sunamura, 1992). Wave quarrying then dislodges the fractured pieces (Stephenson and Kirk, 2000; Trenhaile and Kanyaya, 2007). Early attempts to quantify wave qu arrying focused on wave pressures that depended on the breaker form plunging, spilling, or surging (Trenhaile, 1987; Wilcock et al., 1998). Mano and Suzuki (1999), following the methodology introduced by Sunamura (1992), focused on the wave energy flux at the break point since wave

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22 (2000) platform development model used a surf force calculated from wave height, frictional loses, and tidal duration. Mechanical Wave Abrasion Wave orbital motions entrain dislodged rock fragments produced by wave quarrying as well as unconsolidated platform cover (i.e. sand, gravel). Oscillatory wave motion repeatedly grinds these particles against the exposed cliff face and platform transfor ming them into abrading agents. In other geomorphic settings, these abraders are considered tools (Sklar and Dietrich, 2001). Impact stresses increase with the mass and velocity of the abrading particles (Sunamura, 1992). More energetic waves entrain co arser sediments (as determined by the Shields parameter) and transport finer particles more readily Abrasion is usually limited to the intertidal zone, which includes the upper platform and in some instances, the cliff toe (Sunamura, 1992; Trenhaile, 20 00; Walkden and Hall, 2005). Platform abrasional downwearing rates of up to 1.8 mm/yr have been documented (Blanco Chao et al., 2007). L ike wave quarrying, wave abrasive action can remove weak, weathered material (Blanco Chao et al., 2007). Certain rock coasts yield ineffective abrasive tools and/ or prove unaccommodating to sedim ent accumulation and, hence, experience little abrasive erosion (Blanco Chao et al 2007). For other systems, however, the location and volume of sediment accumulation controls its abrasive potential. Sediment accumulation additionally affects weathering rates (Ashton et al. 2001; Valvo et al 2005). Two notable limitations of platform beach construction are the platform gradient and sediment availability (Trenhaile, 2004) Sediment supply comes from three main sources: rivers, gullies, and cliffs. Young and Ashford (2006) determined that sea cliffs

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23 along the Southern California bight, are the predominant source (> 50%); still, river supply is not insignificant especially a djacent to deltas ( Inman and Jenkins, 2005 ). Cliff Resistance As the only factor opposing weathering and wave induced erosion the durability of the cliff and platform material is a critical control on how rocky coasts evolve (Sunamura, 1992). There is little agreement, however, as to which of the v arious lithologic properties should be identified as the most representative of material resistance Most studies and models use the cohesive strength of the cliff material, sometimes modified by a weathering coefficient (Sunamura, 1992; Wilcock et al 1998; fractures relate to strain (Mano and Suzuki, 1999). Adams et al (2005) determined that sea cliff rock parcels experience wave induced, cyclical flexing through as many as 10 9 cycles while the retreating sea cliff face approaches the parcel. This flexural fatigue occurs for years before the rock parcel is ever impacted by a wave directly, and is thought t o reduce bulk rock strength thereby promoting erosion al retreat (Adams et al 2005). Cliff Failure Wave quarrying and abrasive action form a notch at the toe of lithified cliffs, which grow s until the rock strength is exceeded by gravitational forces an d failure occurs Young and Ashford (2008) established tensile and shear failure criteria for a cantilevered block, an analog for cliff material overhanging a wave formed n otch The re criterion is exceeded Failed d ebris must first be removed, by comminution and transport, before additional cliff face erosion occurs. A fraction of the talus material may be incorporated

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24 into the platform beach and the re mainder is c arried away from the site via nearshore currents (Walkd en and Hall, 2005). Model Description The numerical model that we present below is a set of interrelated functions that aims to capture the interrelated processes of notch development, overhanging cliff collapse, and subsequent debris comminution along a cross shore profile of the cliff face and adjoining platform. A schematic of the model is shown in Figure 2 1, which illustrates coupling and feedbacks associated with the various model components, each of which is described below. Shore Platform and Cliff Bathymetry The model calculates erosion across a cross shore profile consisting of an initially vertical cliff face and fronting shore platform. Cliff height, platform width, and platform slope are initialized var iables. The initial shore platform consists of two segments of independent cross shore widths and slopes, a model parameter that has been included to be consistent with observations of rocky coasts of California and Great Britain (Bradley and Griggs, 1976 ; Young and Ashford, 2006; Lim et al., 2010). The landward segment of the platform tends to be narrower and steeper than the seaward segment along the California coast (Bradley and Griggs, 1976). Along the British coast, the landward portion of the platf orm can be very steep (~1/10), and a true seaward segment of the platform may be absent (Lim et al., 2010). Maximum Notch Erosion The controlling equation for notch development (i.e. maximum cliff erosion over the course of one failure event) was originall y proposed by Sunamura (1992) and

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25 relates sea cliff retreat ( x ) to the ratio of assailing wave potential (F W ) to cliff resistance (F R ): ( 2 1) ( 2 2) ( 2 3) CLIFF is the wave height at the cliff toe, S C is the compressive strength of the consolidated cliff material, and E and I are dimensionless coefficients representing efficiency of abrasive beach sediment and weathering induced weakening, respectively (Sunamura, 1992). Cliff retreat occurs only when F W exceeds F R each of which is defined as a force per unit area. Substitution of Equations 2 2 and 2 3 into Equation 2 1 yields: ( 2 4) where the ratio of efficiency to induration. At a set location with a steady wave climate and homogeneous cliff composition, variability Equation 2 4 would be temporal ly constant. Figure 2 2 is a graphical representation of Equation 2 4, showing a plot of H CLIFF versus average retreat rate for an assumed S C time step, is derived fr om Equation (4), by multiplying the rate of retreat by the duration of the time step.

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26 Erosive Efficiency In laboratory studies, Sunamura (1982a, 1992) found that the abrasional efficiency, E is a function of the beach elevation relative to mean sea lev el as shown in Figure 2 3, where h is the beach elevation at the cliff toe and d is instantaneous water level, both measured with respect to mean sea level. There are three distinct operational zones on Figure 2 3 that depend on the relative beach elevat ion: the tools effect zone ( < 1.0), the cover effect zone (1.0 < < 3.0), and the complete coverage zone ( > 3.0). When no beach is present ( = 0.0), waves still exert hydraulic forces that cause erosion, a fact illustrated on the left side of t he diagram in Figure 2 3a (E > 0). In the tools effect zone, as the beach approaches the instantaneous water level on the cliff face, abrasive tools (i.e. mobilized beach sediments) are available to the orbital motions of the breaking waves, enhancing the ir erosive capacity. This effect is optimized when the platform beach is at same elevation as the instantaneous water level (Sunamura, 1982a) resulting in the maximum value of E. As the beach continues to grow reaching beyond the instantaneous water le vel on the cliff face the system enters the cover effect zone of the E curve. Within the cover effect zone, the beach becomes a growing buffer to wave attack, absorbing the energy of breaking waves and preventing waves from accessing the cliff toe excep t during extreme storms, of elevated water levels, and/or during spring high tides. Once the beach has grown to its maximum height on the cliff face, defined as the limit of wave setup plus runup during spring tides, complete coverage is achieved. Since the waves cannot access the sea cliff, no abrasion driven erosion occurs there. This shut down of abrasion occurs when the relative beach elevation is greater than approximately 3,

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27 since the total swash elevation can be approximated as twice the wave indu ced set up (Komar, 1998). Beach Configuration We use a simple representation of beach configuration based on the slope of a planar beach, which is calculated at each time step from an empirical expression offered by Sunamura (1989): ( 2 5) H B is the breaking wave height, D is the sediment grain size, and T is the wave period Trenhaile (2004) used this equation in a numerical model of rocky platform development and, as in that study, we impose a constraint that the beach occupies the portion of the platform from the base of the cliff A restriction to beach shape dictates that the sediment volume cannot exceed th at of the maximum beach configuration, which is controlled by the beach slope and maximum beach height (h MAX ). This height is a function of tidal range and wave climate (Trenhaile, 2004), and is defined as ( 2 6) where TR is the spring tidal range, S is the mean beach or platform slope, H S is the typical significant wave height, and T D is the dominant wave period associated with H S The second term on the right hand side of Equation 2 6 was presented by Holman and Sallenger ( 1985) as the total elevation reached by the swash above the tidal level.

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28 Hence, h MAX represents the highest elevation the swash reaches during spring tides and, therefore, the maximum possible beach height. The beach configuration determined from Equatio ns 2 5 and 2 6 and the sediment budget is defined as the term (i.e. months, years) average position and volume. Yet, more energetic storm (winter) season waves may strike when the beach occupies a more landward position. Accordin from Hansen and Barnard (2010). Hence, we model storm (winter) waves breaking over a representative beach configuration Offshore bathymetric irregularities, including shoals and sand bars, are neglected in our simple formulation. Wave Energy Dissipation Incoming wave energy dissipation depends on: (1) the deep water wave conditions, which set the diameters and depths of oscillatory orbital motion, and (2) nearshore and platform geometry, which describe the nearshore water depth (Komar, 1998). Given that Equation 2 4 requires knowledge of the wave height at the cliff face, the exact pattern of wave energy dissipation is n ot of prime importance. Rather, we focus primarily on whether the incoming wave breaks, and if so, whether the associated run up reaches the cliff face. The model uses the breaking criteria derived by Komar and Gaughan (1972): ( 2 7) w here H B is the breaking wave height, H 0 is the deep water wave height. The breaking wave height is related to the breaking depth, h B by a dimensionless constant, B = H B /h B This constant has been the subject of numerous studies that have generally

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29 offered values between 0.42 and 1.30 (Thornton and Guza, 1983; Dally et al., 1985; Komar, 1998). We have chosen to set B = 1.0, both for simplicity and central location in the range of published values. After a wave breaks, water continues to move landwa rd as swash beyond the instantaneous water line. The model uses the following relationship for calculating the vertical extent of run up (R V ) developed by Holman (1986): ( 2 8) At depth h B the wave has a height H B = h B B whereas at an elevation R V the wave bore has a height of zero. H CLIFF can be determined through linear interpolation. If the cliff toe is submerged so that the incoming wave does not break, then H CLIFF = H B Wave set up, which is equal in magnitude to the vertica l run up, increases the instantaneous water level, and thus the vertical position on the sea cliff whereupon abrasion acts (Komar, 1998; Sunamura, 1992). The water level is adjusted at each time step to account for wave set up. Weathering Weakening of the cliff face material through weathering and fatigue is quantified in the induration constant, I, in Equations 2 3 and 2 4. However, these relationships are insufficient to accurately model spatially variable weathering rates across the shore platform. In stead, we assume mechanical weathering to be related to instantaneous sea level and wave orbital velocities, such that there is an exponential decay in platform weathering, and consequently lowering, from the water surface:

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30 ( 2 9) where is the downwearing at the platform point is the elevation of the platform point in the same reference frame of z MAX PLAT (m), and h EFF erosion (m) that controls the depth of effective downwearing. Platform lowering rates of ~1 mm/yr are typical, but differ by orders of magnitude depending on location (Blanco Chao et al., 2007; Trenhaile, 2001, 2005). Weathering is generally considered a secondary process to platform and cliff evolution (Trenhaile, 2005). D ownwearing is included to regulate the vertical elevation of the cliff toe. If not considered, the toe would move up the cliff face after each successive failure, until wave access of the cliff face is prevented entirely. Failure Criteria Equation 2 4 is a pplied at each iteration to determine the maximum notching depth (x MAX ) at the vertical location on the cliff face ( z MAX ) that corresponds to instantaneous water level, which itself is a function of mean sea level, tidal range, and wave setup (Trenhaile, 2 000; Walkden and Hall, 2005; Co llins and Sitar, 2008). The vertical profile of erosion diminishes smoothly above and below z MAX on the cliff face, resulting in a basal notch. Like platform weathering, this erosion profile uses an exponential decay for er osion depth on the cliff face, for all vertical points above and below the vertical location of maximum notch depth : ( 2 10 )

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31 where is the calculated retreat, during a time step, for each cliff face elevation in the same reference frame of z MAX (m), and z EFF controls the height of not ch formation, which the model approximates as equivalent to H CLIFF (Sunamura, 1992). We aim to model naturally observable, realistic notc hes, although their actual shape is inconsequential to the long er term (i.e. centuries, millennia) evolution of the platform cl iff system, which is controlled by x MAX (Sunamura, 1992). The model uses simplified cantilevered e criteria ( Young a nd Ashford, 2008) The former is a function of average overhang height ( h CLIFF ) and both are a function of average notch depth (N): ( 2 11 ) ( 2 12 ) where CLIFF is the unit weight of the cliff material. A n example plot of N at failure as a function of h CLIFF CLIFF = 18 kN/m3, MAX MAX = 90 kPa, is shown in Figure 2 4 The graph illustrates that taller cliffs collapse due to shear failure, whereas shorter cliffs fail in tension. In the model, e ach failure regardless of mode results in a vertical failure plane that connects the back of the notch to the top of the cl iff. Comminution and Debris Inclusion Irrespective of the mode (tensile or shear) undercutting failures result in a cliff ap at the base of the sea cliff Collapsed material is then treated as weakened cliff material, repre senting the fact that debris provides an obstacle

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32 that waves must remove before resuming abrasive action on the cliff face. The model calculates the wave/run up height at the previous cliff face position, and uses this value to determine the vertically in tegrated erosion had the debris not been present. This strength (Walkden and Hall, 2005). This process continues at each time step until the debris volume is reduced to zer o however, we are mindful that some fraction of t he talus cone will provide suitable beach sediment. The percentage of talus sediment larger than the littoral cutoff diameter can range from 0% up to 80% (Trenhaile, 2000; Walkden and Hall, 2005; Young and Ashford, 2006, and references therein). Our model assumes 60% of debris material is suitable beach material, a typical value for the central and southern California coast (Young and Ashford, 2006). Sediment Budget C liff failure s serve as a major sedime nt so urce to many platform beaches, and have been estimated to contribute at least half of the total sediment input ( Runyan and Griggs, 2003; Young and Ashford, 2006). Our model assumes cliff failures provide 50% of beach sediment budget, whereas the rema inder is provided to the system from terrestrial sources (Young and Ashford, 2006). Hence, beach sediment volumes are strongly influenced by long term cliff retreat rates. A steady input from gullies and rivers (with some random variation to account for small scale climatic fluctuations) is assumed, while the input from cliff failures will temporally vary with failures and subsequent comminution. In the model, the nearshore system begins in quasi equilibrium, a valid assumption if the initial beach heigh t is above the instantaneous water level (Limber et al., 2011), the cover effect region depicted in Figure 2 2. Therefore, sediment losses should equal the inputs derived from long term cliff retreat.

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33 Beach reconfiguration accommodates changes to 1) plat form morphology or 2) sediment inputs driven by enhanced or diminished cliff erosion. This reconfiguration alters the erosive efficiency (E), either positively or negatively, of the incoming waves, as well as the pattern of wave energy dissipation (H CLIFF ). Description of Numerical Experiments For each of the two experiments, we prescribed an initial beach width that was used to compute the initial beach volume. Long term retreat rates were used to determine the rates of sediment input from non cliff fail ure sources (i.e. rivers, gullies) with an assumed homogeneous sediment size (D 50 ). Equation 2 4 was used with annual time steps, assuming most erosion occurs during intense wave activity and elevated surge levels associated with seasonal (winter) storms. Maximum tensile (60 MPa) and shear (90 MPa) strengths obtained from the southern California coa st were used as the failure criteria for both scenarios (Young and Ashford, 2008). Processes affecting induration (I) were ignored in these simulations to isolate the changes in erosive efficiency (E) associated with sediment, failure, and comminution fee dbacks. Likewise, sea level rise and tectonic uplift were not incorporated in these model runs. Preliminary simulations suggested relatively steady long term retreat rates up to ~3.5 k.y., comparable with the duration of Holocene sea level highstands. T he following simulations were truncated at 1 k.y. to save processing time while capturing general process feedbacks. The first numerical experiment employed wave forcing chosen to replicate normal and extreme conditions on a characteristic shore platform and cliff face configuration. NOAA NDBC Buoy 46042, located west of Monterey Bay in ~2000 m water depth, has

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34 height distribution ( = 2.16 m, var. = 1.3 m 2 ) for this da ta set was derived for the normal Rayleigh distribution with twice the variance ( = 3.00 m, var. = 2.6 m 2 ) of the California coast are shown in Table 2 1, platform type A. The main objectives of this reproducing realistic retreat rates from known wave forcing and nearshore morphology and 2) study the effect of an extreme wave climate on retreat rates. The second numerical experiment explored the effect of shore platform geometry, specifically shape and slope on the temporal pattern of retreat for a range o f deep water wave forcing Two starting platform profile shapes typical of the modern central California (type A) and English (type B) coasts were used, as described in Table 1, both with the same platform width, 1500 m. Type A is a concave upward platform, as the landward platform segment is steeper than the seaward segment. Type B is a convex upward platform with a narrower landward segment. We prescribed two slopes segment). To determine how the expected abrasional and comminution feedbacks differ with varying deep water wave climates, a range of deep water significant wave heights (using steady period T =15s) that encompasses normal to winter storm

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35 conditions on both coasts were used. On the California coast, winter significant wave heights up to ~10 m can occur (Benumof et al., 2000), whereas on the English North Sea coast, seasonal waves range from ~1 to 5 m (Woolf et al., 2002). This simulation suite (60 total model runs) isolated the effects of wave forcing and platform slope on retreat rates, erosive efficiency, and beach configuration. Discussion Numerical Experiment 1 Model Validation and Variable Wave Forcing In the first experiment, we test the model for its ability to produce realistic retreat rates for a natural wave climate, and examine the effect of wave intensification on cliff and platform evolution. Two synthetic wave climate s de rived from the NDBC buoy 46042 wave record offshore central California, were applied to a platform morphology representative of central California to validate the model (Bradley and Griggs, 1976). The evolution histories of cross shore profiles subjected wave climates for an initially prescribed gentle gentle type A platform (GG A) are shown in Figure 2 5a and 2 5b, respectively. Figure 2 5c and 2 5d illustrate the c umulative c liff retreat (i.e. the location of the cliff toe) and deep water wave heights (H DW ) fo r both simulations Wave intensification causes a ~10% increase in cumulative wave retreat, yet initially (t=0 300 years), more energetic waves yield slightly less cliff retreat than the To explore the influence of initial profile configuration, the same (two) identical wave forcing scenarios were applied to an initial steep steep type A platform (SS A). The slopes for both platform segments were double the GG A configuration. The results are depicted in Figures 2 6a (normal waves) and 2 6b (extreme waves), along with the cumulative cliff retreat (Figure 2 6c). Both wave forcing scenarios produced

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36 identical amounts of total retreat at the end of the SS A simulations, but their temporal patterns differ ed (Figure 2 6c). The extreme wave simulation lagged behind the normal wave experiment, akin to the GG A tests (Figure 2 5c). Yet, the extreme wave case never exceeds the retreat from normal wave activity, suggesting the higher platform slopes control th e potential wave energy delivered to the cliff face. In this instance, cliff retreat is a slope limited process. Both sets of simulations produced long term retreat rates comparable to slower rates observed on t he central Californian coast, 0.16 m/yr for normal wave forcing and ranging between 0.21 and 0.23 m/yr for an extreme wave climate (Bradley and Griggs, 1976; Young and Ashford, 2008). The simulated rates are a product of abrasive action alone and the inclusion of platform/ cliff weakening and fa tigue processes through the induration constant, I, likely would produce higher retreat rates more consistent with measured field values for the central Californian coast. The resulting platform slopes are also characteristic of the central California coa st (Bradley and Griggs, 1976). The results suggest that mechanical abrasion is a feasible mechanism of sea cliff and platform evolution T he associated failure and comminution feedbacks appear to be a plausible explanation for observed episodic (unsteady) nature of sea cliff retreat even in the absence of major climat ic or tectonic variations. For concave up profiles, such as those found on the central California coast, platform slope has a larger control on retreat rates than wave forcing. A doubling of both platform segment slopes led to a ~33% increase in retreat rates on average. Conversely, a doubling of wave climate variance (extreme wave activity) caused only 10% or less increase and increased temporal variability to cliff retreat rates

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37 Numerical Experiment 2 a Platform Slope Geometry and Deep water Wave Height on Type A platforms The second simulation set nears hore bathymetry (platform slope and shape) influence sea cliff retreat rate under steady wave forcing (H DW ) Figure 2 7 shows the cross shore profiles at 100 year intervals for each of the type A platform geo metries (all concave upward e.g. central California coast) for H DW = 5 m simulation s The geometries are designated by the relative slop e (steep or gentle) of the landward and seaward segments of the shore platform (see Table 1). Short retreat distances (slow long term rates), ~90 m, appear to accompany gently sloped inner platforms (Figures 2 7a and 2 7c), whereas long retreat distances (high long term rates) accompany profiles with a steep inner platform (Figure 2 7b and 2 7d ) : 120 m (GS A) and 144 m (SS A ). A comparison of temporal behavior of sea cliff retreat for the gentle gentle (GG A) and steep steep (SS A) profiles is shown in F igure 2 8, separated into panels displaying cumulative c liff retreat distance ( Figure 2 8 a), wave height at the cliff base, H CLIFF ( Figure 2 8 b), relative beach elevation, ( Figure 2 8c ), and the ratio of efficiency Figure 2 8d ) The GG A profile experiences relatively high wave energy, on average ( = 0.55 m ), but only 12.5% of the time steps recorded wave strikes. An intensification of H CLIFF towards the end of the simulation was offset by long intervals (decades) of no wave st rikes, which resulted in steady cliff retreat. Conversely, the SS A profile experienced persistent wave activity on the cliff face (100% strike percentage), albeit with smaller waves ( =0.38 m). This is due largely to the fact that wave run up is dir ectly proportional to nearshore (platform) slope.

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38 Erosive efficiency ( was quite variable for GG A, following the saw toothed behavior of beach volume (Figure 2 8c). Cliff failures provide an instantaneous addition of beach sediment, w hich lowers efficiency. Over time, comminution works to deplete the beach sediment, which raises efficiency and leads to the next failure. For SS A, erosive efficiency reached a quasi equilibrium, allowing the beach sediment ccommodation space is created through cliff face retreat. These trends persist throughout the entire type A simulation suite: the slope of the seaward platform segment has little effect on the cliff retreat rate for the entire range of deep water wave heig hts. However, steepening of the landward segment led to considerably higher retreat rates for large deep water waves (H DW > 4 m). Profiles exposed to l ess energetic wave forcing (H DW < 4 m) showed response s similar to one another, regardless of platform geometry. Figure 2 9 shows a comparison of the effects of platform geometries for each of the 10 deep water wave height simulation s with mean values shown as circles, ranges shown as vertical lines with hashed ends, and percent differences shown as bars. More energetic waves correspond to higher retreat rates for steeper sloped profiles (Figure 2 9a), although this trend is dependent upon platform configuration and inconsistent, and juxtaposed against the GG A simulations that show a slightly negative rel ationship between H DW and cliff retreat. Doubling the inner platform ( SS A ) slope led to a maximum 83% increase in cliff retreat rates for deep water wave heights of 7 m Every simulation with deep water waves larger than 4 m which can be considered mod erate for winter storms along the central California coast experienced a > 50% increase (as compared to the gently sloped case) equivalent to ~50 m additional cliff retreat over the 1 k .y. simulation. The retreat rates

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39 correlate weakly (r 2 =0.75 for GG A and 0.24 for SS A ) with the wave strike percentage the fra ction of time during the simulation that waves accessed the cliff base (H CLIFF > 0), but correlate more strongly (r 2 =0.89 for GG A and 0.79 for SS A) with (Figure 2 9 b) T he variance of H CLIFF (Figure 2 9 b) was smaller for SS A implying that wave energy delivery was more temporally c onsistent than in the GG A case. Steeper platform slopes a ltered platform accommodation space, leading to modest changes in beac h configuration and the accom panying values. T he largest discrepancy was a 13% decrease when H DW = 10 m (Figure 2 9 c values were practically zero (< 2%) for all deep water wave heights (Figure 2 9 d ), suggesting alterations to wave abrasional effic acy were not the cause of enhanced erosion produced by the SS A simulations. Instead, the modeling generally shows that larger and less variable H CLIFF values, enhance cliff retreat. Still, H CLIFF is intrinsically linked to beach configuration through th e wave run up calculation, so sediment feedbacks do contribute to cliff evolution. Numerical Experiment 2b Platform Slope Geometry and Deep water Wave Height on Type B platforms The cross shore profile results (100 year intervals) for the four type B pla tform geometries (North Sea English coast, convex upward profile) are shown in Figure 2 10 for H DW = 3 m Unlike type A platforms which are approximately half as steep as type B platforms the slope of the seaward segment of the type B platform shows a greater control on cliff retreat (>100% increase), with the slope of the landward segment having a more modest effect (~50% increase). As with the concave up profiles, the steep outer and inner platform slopes (SS B) yielded the greatest retreat, more than three times greater than the gentle gentle (GG B) configuration 158 m vs. 48 m A comparison of

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40 these two cases (Figure 2 1 1 ) reveals that SS B experienced higher wave access ( Figure 2 1 1 b). In s i milarity to the type A simula tions, subsequent retreat of the cliff face provided accommodation space for a platform beach and, thus, a more stable (Figure 2 1 1c 2 1 1d ) values Yet, for both SS B scenarios, never approached the same magnitude as the complimen tary type A simulations (Figure 8b). This reduced energy delivery was insufficient to drive additional cliff retreat, yielding high (h/d > 1.0) platform beaches that provided additional buffering from wave attack. Only when the beaches were depleted coul d wave assault resume (Figures 2 11b and 2 11 c). In contrast, the SS A and SS G cases show more frequent wave attack that created (through cliff face retreat) additional accommodation space for the platform beach, which could assume a lower relative eleva tion (h/d), and, thus, higher erosive efficiency. In summary, the negative feedbacks appear to dominate for type B platforms, whereas the positive feedbacks control type A profile evolution. Comparison of the SS B and GG B cases by wave height reveals the accommodation space mechanism is more influential for larger values of H DW with up to a 240% higher retreat rates (Figure 2 1 2 a) for H DW =5 m A dditional retreat is produced by larger and less variable (Figure s 2 1 2 b and 2 1 2 c). An increase to erosive efficacy is more pronounced during periods of lower wave height (Figure 2 1 2 e). The simulations presented here provide evidence that t he relationship between platform slope and cliff retreat rate depend s up on the shape of the pl atform. For concave type A platforms such as the central California coast the slope of the landward platform segment has a dominant control on retreat rates for all deep water wave forcing scenarios that we examined Conversely, for convex type B platf orms,

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41 such as the North Sea English coast, the slope of the seaward segment had a ~50% greater effect than the landward segment slope. In both ca ses, steeper platform slopes le d to greater average retreat rates. Higher platform slopes tend to elevate wav e run up (increased and strike percentage). In turn, erosion rates increase, creating more platform beach accommodation space and regulating the relative beach elevation ( ), and, hence, the erosive efficacy (E). This stabilization is a positive feedback that continues to drive cliff retreat. The role of deep water wave energy (H DW ) on cliff erosion appears connected to slope on both concave and convex platforms. On the gentlest configurations, higher H DW did not produce significantly higher retr ea t rates However, for the steepest configurations, more energetic wave forcing generally led to increased cliff retreat. This effect was dampened for very large H DW Even in our simplified experiments, the feedback behavior remains notably complex. Fo r instance, in the type B simulations, steeper platform slopes resulted in higher wave run up (H CLIFF ), which in turn drove cliff face retreat. This retreat provided additional accommodation space and a lower relative beach elevation, closer to maximum ef ficiency (h/d = 1.0). This is an example of a positive feedback loop, since cliff retreat begets more cliff retreat. Yet, if platform slope was the controlling factor, one would expect cliff retreat to be larger for type B platforms. In these instances negative feedbacks, arising from the platform beach (with a higher relative elevation) buffering the cliff face from wave attack, decelerates long term cliff retreat. No linear relationships between wave forcing, platform slope or beach elevation were a ble to be determined.

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42 This initial work also supports the concept of long term equilibrium behavior of rocky coast geomorphology posited by Limber et al. (2011). Each simulation began with the relative beach elevation, in the cover effect zone (1.0 < < 3.0) For the central California coast simulations, the beach maintained this equilibrium: diminished erosion rates starved the beach of sediment and fell towards 1.0, the optimal level of beach where erosive efficacy is at its maximum (Figure 2 3) Consequently, the increased volume flux from cliff failures, associated with higher erosion rates, increased beach sediment level r a ising values ( Figure 2 7, fourth panel ). For the North Sea coast simulations, the beach did not reach a long term equilibrium, with oscillating between 0.0 and 2.0. This behavior suggests that a persistent beach is unlikely given the decreas ed sediment supply and steeper platform s lopes. Rather, the platform serves as a transient home to comminuted debris before i t is removed from the abrasional zone of the nearshore system. The cliffed Holderness Coast, UK, which faces the North Sea, is a possible example of this model inference. Holderness is a sediment poor system where beach sediment is sourced largely from the rapid retreat of glacial till sea cliffs (1.55 m yr 1 on average, Quinn et al., 2009) that consist of approximately 30% sand ( Mason, 1985; Robertson, 1990) Frequent cliff failures due to notch development and subsequent overhang collapse leave debris pil es at the cliff toe that temporarily protect the cliff from wave attack (Castedo et al., 2012). The debris pile is comminuted by waves (Castedo et al., 2012), but only a small fraction of the clay dominated debris is retained as beach sediment. As a result the beach is unstable, and a wide, persistent beach that could protect the cliffs from wave attack

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43 does not develop, allowing cliff retreat to continue (Quinn et al., 2009; Barkwith et al., 2013). Beach sediment, where present, only locally affects cliff retreat rates as small developed shore platform ( Mason, 1985; Pringle, 1985). Conclusions We have developed a numerical model of sea cliff evolution that incorporates feedbacks associated with mechanical abrasion, as well as subsequent failure and debris comminution. The model yields realistic retreat rates for two different platform/cliff configurations representing the central California and North Sea English coasts. The results suggest abrasion driven processes may be responsible for the unsteadiness observed in the temporal pattern of sea cliff retreat. The effect of wave intensification, as is hypothesized to be associated with climate change, appears to be linked to the slope of the seaward platform segment: increased retreat (between 15% and 75%) for gently sloped platforms. Retreat rates for steeply sloped platform segments remained unchanged. More observations are needed to verify the universality of this trend. For concave platf orms, retreat rates are higher for systems with a steeper sloped landward platform segment, whereas the steeper sloped seaward platform segments control retreat rates on convex platforms. In both cases, however, the evolution appears tied to the magnitude and regularity of wave strikes on the cliff face, which is influenced by 1) the cross shore position of wave breaking, 2) slope of the platform or overlying beach material.

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44 Future Work Incorporation of eustatic sea level oscillations and tectonic uplift w ould allow simulations to extend further than the current ~3 k.y. time scale and yield meaningful results Integrating platform and cliff weakening (induration constant, I) through weathering and fatigue should produce higher retreat rates. Inclusion of retreat rates and platform beach data from other rocky coast settings would further modify the

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45 Table 2 1 Input variables and initial conditions for each simulation scenario. Type A has cliff characteristics and platform configuration typical of the modern central California coast (Bradley and Griggs, 1976; Young and Ashford, 2008), whereas type B has characteristics of the English North Sea coast (Lim et al., 2010). Modern pla tform beach configurations (estimated via Google Earth), long term retreat rates (Bradley and Griggs, 1976; Young and Ashford, 2008; Lim et al., 2010; Sunamura, 2002), spring tidal ranges (Bradley and Griggs, 1976; Lim et al., 2010), and wave climates (Ben umof et al., 2000; Woolf et al., 2002) found at these locations were also used. Platform Type Cliff Characteristics Seaward Platform Segment Landward Platform Segment Platform Beach Long term Retreat Rate (m/yr) Spring Tidal Range (m) Wave Climate Height (m) S C (MPa) (kN/m 3 ) Width (m) Slope (m/m) Width (m) Slope (m/m) Width (m) D 50 (mm) H S Range (m) T (s) A 20 50 18 1,000 1/100 1/200 500 1/25 1/50 50 0.05 0.1 0.5 2.5 1.0 10.0 15 B 50 40 25 1,375 1/10 1/20 125 2/25 1/25 40 0.10 0.05 5.0 1.0 5.0 15

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46 Figure 2 1. Schematic diagram showing relationships among model components. Maximum notch erosion is determined by two competing processes: 1) resistance potential, or induration, of the cliff material and 2) assailing potential, or efficiency, of waves and sediment particles acting as abrasive agents. At each time step, notch erosion is distributed vertically on the cliff face and the failure criteria are evaluated to determine if a failure occurs during the time step. If a failure does occur, comminution alters the beach sediment volume, and configuration of the platform and cliff are updated.

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47 Figure 2 2 A) Plot of wave height at the cliff face (H CLIFF ) versus average retreat rate R LT AVG for a consolidated cliff with a compressive strength (S C ) of 50 MPa. nding average retreat rate by Equation 2 4. B) Plot of wave height at the cliff face (H CLIFF ) LT AVG contours are also shown. Note the logarithmic relationship between gamma and average retreat rate; i.e., doubling gamma results in more than a doubling in average retreat rate. This effect is more pronounced for larger H CLIFF

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48 Figure 2 3 Plot of relative beach elevation (h/d, dimensionless) against E, the dimensionless coefficient representing sediment action both as an abrasive agent (tools effect) and a protective buffer (cover effect and complete coverage). The lower three insets show the definition for the relative beach elevation for different pot ential configurations : h is the height of the platform beach above mean sea level, whereas d is the height of the instantaneous water level about mean sea level. A relative beach elevation of <1.0 corresponds to a beach present below the current water lev el (or no beach at all) in the tools effect zone. A relative beach elevation of >1.0 corresponds to a beach present above the current water level up to a relative beach elevation >3.0 that indicates complete coverage. The maximum value of the relative be ach elevation is also controlled by the grain size of beach material (which dictates the slope), tidal range, and wave climate. This figure has been modified from Sunamura, 1982a.

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49 Figure 2 4 Plot of average cliff height (h CLIFF m) versus average notch depth at failure MAX MAX ) of 90 kPa. These characteristics are typical of southern California sea c liffs. Note that the failure mode is the determined by which critical notch depth is reached first. In this scenario, shorter cliffs (<10 m) will fail in tension, with an average notch depth less than 3.3 m. Taller cliffs (>10 m) will fail in shear with an average notch depth of 3.3 m. This result occurs because Equation 2 11 is dependent only on the average notch depth, not the average cli ff height, whereas Equation 2 12 is a function of both characteristics.

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50 Figure 2 5 Results from first n umerical experiment for the type A, gentle gentle (GG A) platform configuration. The top two panels show cross shore profiles of the simulations, respectively, at 100 year interval s. The third panel shows the total amount of cliff retreat (relative to the initial cliff face position). The bottom panel shows the offshore significant wave height series provided to the model. These series were generated by random selection (with rep lacement) of a Rayleigh distribution created from NOAA NDBC Buoy 46042 dat a collected from 1988 to 201

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51 Figure 2 6 Results from first numerical experiment for the type A, steep steep (SS A) platform configuration. The top two panels show cross s hore profiles of the simulations, respectively, at 100 year intervals. The third panel shows the total amount of cliff retreat (relative to the initial cliff face position). The b ottom panel shows the offshore significant wave height series provided to the model.

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52 Figure 2 7 Comparison of the four platform slope combinations for type A profile (central Californian coast). Each panel shows the cross shore profiles thro ughout the 1 k.y. simulations for H DW = 5 m. The slope of the landward segment of the shore platform has a greater control on retreat rates than the slope of the seaward segment.

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53 Figure 2 8 Comparison of the gentle gentle (blue) and steep steep (red) simulations from t=0 to t=1000 years for type A (central Californian coast). The steep steep platform (SS A) experienced more cliff retreat because 1) higher wave activity at the cliff toe and stable erosive efficiency of the beach configuration.

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54 Figure 2 9 Comparison of the steep steep (red) and gentle gentle (blue) platform shape simulations for a type A platform (central Californian coast). The purple bars correspond to percent differences between the two platform shapes. Error bars, signifying one standard deviation, are present where appropriate.

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55 Figure 2 10 Comparison of the four platform slope combinations for the type B profile (North Sea English coast). Each panel shows the cross shore profiles throughout the 1 k.y simulations for H DW = 3 m. The slope of the seaward segment of the shore platform has a greater control on retreat rates than the slope of the landward segment.

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56 Figure 2 11 Comparison of the steep gentle (blue) and steep steep (red) simulatio ns from t=0 to t=1000 years for type B (North Sea English coast).

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57 Figure 2 12. Comparison of the steep steep (red) and gentle gentle (blue) platform shape simulations for type B (North Sea English coast). The purple bars correspond to percent differences between the two platform shapes. Error bars, signifying one standard deviation are present where appropria te.

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58 CHAPTER 3 WAVE TRANSFORMATION AND BEACH AND BAR BEHAVIOR ALONG A MICROTIDAL COAST WITH COMPLEX INNER SHELF BATHYMETRY AND SHOREFACE ATTACHED OBLIQUE SAND RIDGES, KENNEDY SPACE CENTER, CAPE CANAVERAL, FLORIDA Changes in surf zone sandbar and beach morphology associated with variable (i.e. seasonal oscillations, storm events) wave forcing have been extensively studied, resulting in simplified predictive models that yield a desired characteristic (i.e. beach state, bar position) based on a few easily parameterized forcing and system characteristics (Wright and Short, 1984; Lippman and Holman, 1990; Plant et al., 1999). Yet, these models are difficult to extend to geomorphically complex environments, such as shores adjacent to ca pe related shoals or large shore oblique ridges, where one line wave transformation estimations breakdown. Further, model parameters must be tuned to the specific system dynamics. This is problematic, given that such nearshore bathymetric complexities ha ve been linked to shoreline retreat (Schupp et al., 2006). Kennedy Space Center (KSC) lies on the Florida Atlantic coast, ~20 km north of Cape Canaveral, Florida (Figure 3 1). Numerous cuspate related bathymetric features occupy the inner continental shel f, drastically transforming deep water wave fields before they reach the surfzone (Figure 3 2). A large, shore oblique sand ridge also intersects the shoreface here (Figure 3 2), approximately coinciding with the location of a persistent erosional hotspot and dune overwash (Figure 3 1, Adams et al., in preparation). Wave breaking has been observed along the ridge during energetic wave events. We hypothesize the oblique sand ridge may control nearshore morphology through two mechanisms shown in Figure 3 3 : 1) by focusing, dissipating, and shadowing wave energy, thus altering alongshore patterns of sediment transport, and 2) providing a potential sediment source to the nearshore zone. As a whole, this study site

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59 provides a natural laboratory to test how su ch inner shelf features dissipate wave energy and, subsequently, influence beach bar morphology. We have collected over four years of morphologic observations at KSC and coupled this data with nearshore wave instrument deployments to better understand geo morphic response over seasonal to annual wave forcing. This chapter investigates the patterns of wave transformation over complex inner shelf bathymetry, and how these dissipation patterns link to bar and beach morphologic characteristics (i.e. cross sho re bar position, planview crescentic amplitude, beach width/slope) at the KSC shoreline, Cape Canaveral, Florida. We first examine the controls of wave energy dissipation over inner shelf shoals and ridges and develop a proxy of wave transformation as a f unction of deep water wave direction, height, and period. We then present the observed monthly to seasonal morphologic behavior of a shore parallel, stable surfzone bar system, noting response to wave forcing as well as internal feedbacks. The observed b ar and beach dynamics are tested with a simple equilibrium model. We apply the same model to data subsets corresponding to three distinct zones related to the oblique, shoreface attached ridge (highlighted in Figure 3 3) to better understand how wave forc ing, feedbacks, and response times differ: 1) the shadowed region, buffered from wave attack landward of the ridge, 2) the ridge intersection with the shoreface, and 3) the exposed coast. The quantitative and qualitative skills of the model are assessed, as well as the implied morphodynamics mechanisms in each subset. Implications of our findings to other complex bathymetric and barred environments are also discussed.

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60 Background Cape Canaveral The Florida Atlantic coast, along a ~500 km span from Jacksonv ille to Palm Beach, is generally straight, with the exception of the Cape Canaveral Merritt Island complex (Figure 3 1, inset). For the last several decades, many formation mechanisms have been offered for the promontory. Brooks (1972) and Pirkle et al. (1972) believed Cape Canaveral to be either a transgressive or regressive features, formed due to sea level fluctuations since the Pleistocene. Kofoed(1962) favored the convergence of two (or more) littoral cells and mapped out the potential evolution of Merritt Island using topographic contours. Antecedent geologic structure(s), namely the Anastasia Formation (lower Pleistocene), have also been proposed as an alongshore control on nd, near present day Orlando (White, 1958; Brown et al., 1962; Winker and Howard, 1977; Randazzo and Jones, 1997). Most beach ridge sets on Cape Canaveral are likely Holocene in age, although some have been dated to the late Pleistocene (Osmond et al., 19 70; Rink and Forrest, 2005). These findings support the current Cape Canaveral as a geologically recent, prograding cuspate feature (Osmond et al., 1970; Rink and Forrest, 2005). A southeastern migration of Cape Canaveral has been documented in the last century, possibly originating from the present location of a smaller cuspate feature, False Cape, to the north (Figures 3 1 and 3 2; Shepard and Wanless, 1971; Pirkle et al., 1972; Winker and Howard, 1977). The inner shelf bathymetry is composed of cape related shoals and banner banks, as well as linear sand ridges adjacent to False Cape (Figure 3 2). One of these linear sand ridges connects to the shoreface along the Kennedy Space Center

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61 shoreline, whereas the other two terminate at the shoals adjacent to False Cape (Figure 3 2). These bathymetric complexities are primarily concentrated in depths shallower than 15 m. Most of the extensive shoals/banks complexes are relatively small (length ~5 km, width ~100 m, height ~2 m), but three oblique sand ridges are an order of magnitude more extensive in planview and slightly taller (length ~50 km, width ~1 km, height ~5 m). A 19 th century bathymetric chart shows three linear ridges of similar size at approximately the same present locations (Patterson, 1878), suggesting these ridges are likely either controlled by an underlying geologic feature (potentially an outcrop of the aforementioned Anastasia Formation) or in a stable, dynamic equilibrium between tidal, wave induced storm currents, and/or prevailing alon gshore flows. If they are ephemeral, it appears they regularly reform to the same dimensions at the same geographic location. The original sediment source of the linear ridges is likely either reworked sediment from the adjacent shoals fronting False Cape or perhaps a paleo ebb delta (Snedden et al., 1992). Deep water Wave Climate and 41009, located ~220 km (~870 m depth) and ~37 km (44 m depth) east of Cape Canaveral, Florida, respec tively have measured hourly non directional offshore wave conditions since 1988 (Figure 1, inset). Mean wave directions have been recorded by NDBC buoy 41012, ~75 km east of St. Augustine, Florida, and ~150 km north of Cape Canaveral (Figure 3 1 inset) s ince 2006. Figures 3 4a and 3 4b are wave histograms, in 10 bins, showing significant wave height (H S ), dominant wave period (T D ) observed by NBDC buoy 41012 between 2002 and 2013, respectively. Figures 3 4c and 3 4d, are wave histograms from the

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62 same data, but only for large waves (>3 m), as are common during tropical wave events generally quiescent seas (H S ~ 1 m, T D ~ 8s) originating from the east (60 120 with respect to north, 0 ). Major tropical wave events, punctuate the late summer and early autumn wave record. Winter and spring (October to April) are characterized by S ~ 2.0+ m, T D ~ 12+ s) emanating from the north north east (330 60 ). Inner shelf Sand Ridges Inner shelf sand ridges are ubiquitous bathymetric features of many passive continental shelves (Duane et al., 1972; Swift et al., 1978; Antia, 1996; Dyer and Huntley, 1999; Snedden et al., 1999), including the U.S. east coast, North Sea, and west African margin. Much debate has centered on whether these features are relict, or if they formed and evolved during the Holocene (Field, 1974; Swift et al., 1985; Dyer and Huntley, 1999; Calvete et al., 2001). Accordingly, many processes have been postulated for their creation, such as barrier island subsidence (Penland et al., 1988), infragravity waves (Boczr Karakieqicz and Bona, 1986), and secondary storm currents (Swift et al., 1973). The most prominently cited potential mechanism of large scale sand ridge g enesis is the Huthnance (1982) theory, which requires a sufficient quantity of sediment, currents capable of transporting that sediment, and an irregular bathymetric precursor (Snedden et al., 2011; Hayes and Nairn, 2004). Various inner shelf flow regimes have been invoked to build and maintain these features, including asymmetrical tidal currents (Huthnance, 1982), deflected alongshore currents (Throwbridge, 1995) and storm wave induced currents (Calvete et al., 2001). Abandoned ebb tidal deltas, due to a combination of downdrift migration of tidal inlets

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63 and landward migration of the coastline, are a likely initial source of uncohesive sediment (McBride and Maslow, 1991; Dyer and Huntley, 1999; Snedden et al., 1999). Nearshore morphology and inner she lf bathymetric features have been linked to et al., 1995; Bender and Dean; 2003; McNinch, 2004; Barnard and Hanes, 2005; Schupp et al., 2006; Stockdon et al., 2007; Ho user et al., 2008). Shore oblique bars have been linked to erosional hotspots and high shoreline variability, inferably through wave refraction and the resulting gradients of alongshore wave energy flux (McNinch, za, 1993). Figure 3 3 illustrates this mechanism. For near normal wave approach, the oblique ridge would dissipate wave energy before reaching the nearshore bars, yielding lower (relative) sediment transport rates than the adjacent exposed coast. Conseq uently, the beach immediately downdrift would be expected to retreat, assuming the alongshore migration of the oblique ridge is much smaller than the shoreline retreat rate. Further, since wave energy is relatively less dissipated along the exposed portio n of the beach, dune overwash events would be expected to be more frequent in this zone. The ridge may also provide a sediment source to the nearshore system, especially when breaking is activated over it during large storm events. The long term influen ce of such sediment communication is difficult to estimate without two dimensional sediment transport models and quantifiable annual yield rates, but, on shorter time scales, the zone near the ridge shoreface intersection should receive sediment inputs fro m the ridge.

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64 Microtidal Surfzone Sandbar and Beach M orphology Sandbars are a common nearshore morphologic feature comprised of unconsolidated sediment. Typically, sandbars are shore parallel, although their exact orientation and position are determined by the incident wave climate (Wright and Short, 1984; Lippman and Holman, 1990; Plant et al., 1999). The breakpoint hypothesis, based on beach and sandbar occupying a stable equilibrium, suggests that surfzone bars form and/or migrate to the cross shore l ocation of wave breaking (Dean, 1973; Sallenger and Howd, 1989). Indeed, bar crest positions have been linked to oscillatory wave forcing on the time scales of weeks to months (Wright and Short, 1985; Lippman and Holman, 1990; Plant et al., 1999). Over l onger time scales (years to decades) surfzone sandbars often undergo a net seaward migration, independent of wave climates or tidal range (years to decades; Lippman et al., 1993; Ruessink and Kroon, 1994). Plant et al. (1999) presented an equilibrium model that linked interannual cross shore bar dynamics to wave forcing, following the breakpoint hypothesis. Movement of the bar crest position through time ( ) was a function of its current position (x), characteristic response time ( 1 ), and equilibrium pos ition (x EQ ): ( 3 1 ) The response time parameter ( ) was assumed to be a function of wave height (H) raised to a power, p, (0 3) and a constant parameter, a 1 A similar estimation of the x EQ was made, except with p=0 and a different c onstant, a 2 These parameters were normalized to produce a scaled version of Equation 3 1:

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65 ( 3 2 ) where x* = x C /x SZ t* = t H* = H/H MAX a 1 = a 1 H MAX p / 2 = a 2 H MAX /X SZ x SZ is the Bar response times were found to be much longer than wave forcing time scales and temporally variable. Thus, the introduction of bar transients (major deviations) could results in n et offshore bar migration. Video based Morphologic O bservations Video based monitoring systems have been used to study various coastal environments (Lippman and Holman, 1989; Holman et al., 1991), including the morphologic response of sandy beaches to i ndividual storm events (Aagaard et al., 2005), wave run up (Salmon et al., 2007), inter annual wave forcing (Plant and Holman, 1997) and to explore the morphodynamics of mixed sediment beaches (Adams et al., 2007; Ruggiero et al., 2007). Digital images ar e georectified using known survey points in the field of view, providing quantifiable morphologic evolution (O~1 m) at the frequency of collection, which in our study was hourly during daylight (Holland et al., 1997). Three digital image outputs are typic ally collected: 1) a snapshot, 2) a 10 minute time averaged exposure (timex), (collected at 2 Hz in our study), and 3) a variance composite of the timex exposure. In the latter two outputs, dynamic objects/features (i.e. swash zone, surf zone) are smoothe d through individual wave movements, and show as white bands. Since breaking points correlate to areas of surfzone bars and swash run up, these georectified images can be used to track the geographic coordinates of these features (i.e. the cross shore pos ition of the bar crests) through

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66 time, using statistically significant Gaussian intensities (Plant and Holman, 1997; van Enckevort and Ruessink, 2003; Plant et al., 2006). Methods Nearshore Wave Climate Acoustic Doppler Current Profilers (ADCPs) were de ployed twice to measure nearshore sub hourly wave and current characteristics. A Nortek Acoustic Wave and Current (AWAC) profiler was deployed from September 2010 to January 2011 in ~15 m depth, ~5 km offshore False Cape, just beyond the three oblique sand ridges (Figures 3 1 and 3 2). It measured directional wave characteristics (every half hour) and current profiles (every ten minutes). A Sontek Argonaut XR was deployed at the same time in ~5 m depth and measured current profiles every 10 minutes (Figur e 3 1). In Feburary 2012, a Nortek Aquadopp was deployed and measured wave conditions every 30 minutes until July 2012. That instrument was positioned ~400 m offshore in ~5 m depth, which was landward of the westernmost oblique sand ridge, (Figures 3 1 a nd 3 2). The Sontek Argonaut XR was again deployed, approximately ~1 km to the south of its fall 2010 position. Once the ADCP equipment was retrieved, the data was extracted and processed using the Nortek Storm (AWAC and Aquadopp) and ViewArgonaut (Argon aut XR) software to remove erroneous or ambiguous data. The major focus of the nearshore wave deployments was to understand wave transformations from deep water to the nearshore zone, across a complicated inner shelf bathymetry, as well as which character istics (wave height, period, or direction) controlled energy transmission. Video based Morphologic Observations An autonomous camera has been deployed since April 2010 on the Eagle 4 security tower at the northeastern corner of KSC property (Figure 3 1). The camera is

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67 directed alongshore to the southeast, with a maximum alongshore view extent of ~5 km. Mid day images (between 12:00 p.m. and 4:00 p.m. local time) with low tidal elevations (< 0 m) were identified, totaling 1283 images (both timex and varian ce). This initial filtering reduced errors introduced by lighting associated with sunrise and sunset; additionally, during higher tidal elevations and quiescent waves, little to no breaking would occur over the outer bar, making its location undeterminabl e. Comparisons of inner bar position throughout the tidal cycle revealed typical movement of <1 m during a tidal cycle under constant wave forcing, so this technique introduces no residual errors at the time scales (weeks to months) and spatial scales (O~ 10 m) of interest in this study. From these images, inner and outer bar positions were derived from an established approach using a Hanning filter (Figure 3 5, Plant and Holman, 1997; Plant et al., 1999). The analysis that follows was limited to a ~3 km stretch of KSC shoreline (1.0 4.0 km in camera coordinates (Figures 3 1 and 3 5). The outer bar annually migrated out of the field of view close to the camera (0.0 1.0 km), and many inner bar positions were statistically unreliable in this zone. A lack o f consistent resolution beyond 4.0 km, made bar migration rates and crest positions in this area highly questionable. Still, the 3 km extent (1.0 4.0 km) encapsulates a major area of interest an intersection of a large, shore oblique ridge at ~2.0 km fr om the camera location and persistent erosional hotspot at ~3.0 km. Hence, we have reliable, daily bar crest positions in the three zones of interest discussed previously (Figure 3 3): 1) the shadow zone landward of the oblique ridge (1.0 1.5 km), the rid ge intersection (2.0 2.5 km), and the exposed shoreline (3.0 3.5 km). We separated each zone by 500 m to better isolate differing

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68 responses to wave forcing as well as internal feedbacks, but overall bar system behavior encapsulates all observed bar positi ons between 1.0 and 4.0 km. Kinematic differential GPS Beach Morphology Surveys Kinematic differential GPS beach surveys were performed monthly, coinciding with the spring tide, and around major (tropical) storm events. Rasters of the beach surface, exten ding from the dune line to MHW (0.28 m) or often lower (<0.00 m) were compiled from each survey. From these products, elevation contours were extracted at the same alongshore points as cross shore bar positions were determined. A detailed description of collection and processing techniques for the survey data was provided by Adams et al. (in preparation) and MacKenzie (2012). Results and Disscussion Inner Shelf Wave Transformation Using the significant wave height (H S ) and dominant periods (T D ) measur ed by NDBC buoy 41009 and the ADCP instruments, we determined the energy transmission across the ridges (Figure 3 6). Wave energy flux (P) is defined as ( 3 3 ) where H is the wave height and Cg is the wave group velocity, a function of wave period (T) and water depth (h). If no wave energy is dissipated between deep and shallow water, P deep = P shallow (conservation of energy). In general, however, only 10 100% of th e wave energy is transmitted from 40 m to 15 m depth (Figure 3 6a). About half of the remaining energy remained by 5 m depth (Figure 3 6b). Regressions were fit for both deployments; no relationship (e.g. power, exponential) performed statistically bette r than a linear trend (r 2 =0.71 and 0.64), which is shown in Figure 3 6.

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69 This data was then classified by deep water wave direction ( ), provided by the closest directional data, NDBC buoy 41012 (Figure 1). Linear trends were fit by directional bins (10 intervals) from 330 to 150 (with respect to 0 north), comprising the entire spectrum of onshore directed waves (Figure 3 7). The transmission coefficients (Figure 3 7b) ranged from 0.12 to 0.28. Using these relationships, predicted nearshore wave ene rgy fluxes were calculated and compared to the Aquadopp observations (Figure 3 7a). This direction based transformation model improved slightly our predictions (r 2 =0.75). The model errors were compared to determine biasing against wave characteristic: H S (Figure 3 7c), T (Figure 3 7d), and 7e). None systematic biasing was found among these variables, suggesting the remaining variance is likely attributable to other effects, such as the difference in local wave direction between NDBC 41012 and KSC or nonlinear interactions. The largest errors occur for medium (1 m < H S < 2 m), average period (8 s < T < 12 s) near normal waves, the most common wave type during the deployment. General beach and bar morphology Figure 3 8a shows the wave forcing ( P 41009 ) observed at NDBC buoy 41009 (Figure 3 1) throughout the observation period, April 2010 to July 2012. Since the spring 2012 Aquadopp deployment was just seaward of surfzone, nearshore energy transmission (P O uter Bar Figure 3 8a) was calculated usi ng the coefficients shown in Figure 3 7b and directions measured at NDBC buoy 41012. Mean cross shore bar positions between 1.0 and 4.0 km alongshore distance were derived from camera outputs, as outlined previously (Figure 3 1). Daily mean positions are shown in Figure 3 8b (dashed); 28 day mean positions, equivalent to the frequency of beach surveys, show lower frequency bar oscillations (Figure 3 8b, solid lines). Beach elevation

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70 contours (Figure 3 8b), derived from kd GPS surveys, can serve as beach width proxies. Overall, the outer bar experiences approximately twice the annual cross shore movement as the inner bar (50 m vs. 25 m). In response to increased wave forcing s response to storms is more damped and variable; qualitatively, it can be characterized as net landward movement. Outside of major storm events such as Hurricane Irene in September 2011, when the beach underwent temporary landward retreat, the beach elev ation contours remained relatively static, within annual observed shoreline change envelopes of O~10 m (Adams et al., in preparation). Observed bar variance was relatively static, hovering around ~10 m (Figure 3 9b). Peaks in inner bar variance correspond ed to very low wave energy. Figure 3 9c shows the crescentic scale amplitude (a OB and a IB ), defined as the root mean variance determined from an alongshore spatial Fourier analysis of length scales between 50 m and 1 km, for both surfzone bars (Plant et al., 2006). Thus, a OB and a IB are a measure of variance over a range of lengths rather than a true measure of bar shape. The bars were always quite straight (a OB and a IB < 1.0) with peaks of variance typically occurring in the late spring, after winter wave forcing, this evidence supports bar variance (i.e. a OB ) a function of bar reorganization as the bars transition between winter and summer equilibrium positions. Cross correlations were perfo rmed to determine the response time between wave forcing (P nearshore ) and bar position (X OB and X IB ), as well as the lag between potential feedbacks (Figure 3 10). Mean outer bar position (X OB ) responds positively

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71 (r=0.62) with a 1 month lag to wave forci ng (Figure 3 10a), implying a seaward movement of the bar in response to more energetic storm and seasonal waves. No significant longer term responses are observed. The mean inner bar position (X IB ) correlates negatively (r= 0.53) with wave forcing over a longer response time, 3 months. This result corresponds well to the damped, net mean landward inner bar migration qualitatively observed in Figure 3 8b. A potential interaction feedback between the outer and inner bar positions is seen at a lag of 6 mo nths (Figure 3 10c), although it is likely a product of the varying, lagged response of bar positions to wave forcing and their subsequent return to quiescent equilibrium. Two beach width proxies were considered in the cross correlations: the 0.00 m cont our (W DL to 0.00 m contour measured as the cross shore distance from the dune line) and the 2.00 m contour (W DL to 2 .00 m contour ). The former serves as a representative of lower beach behavior; the latter corresponds to the upper beach. The upper beach responds almost instantaneously (lag of 1 month, r=0.59) as W DL to 2 .00 m contour decreases with high wave forcing (Figure 3 10d). On the contrary, the lower beach (0.00 m contour) does not show a significant response to wave forcing (r=0.91) until much later (9 months; Figure 3 10d). The response of the outer bar position and upper beach width to wave forcing are highlighted again in Figure 3 10e, where X OB and W DL to 2.00m are instantaneously negatively correlated (r= 0.60). Negative responses between the inner bar position and the lower beach (r= 0.90, lag of 5 months) and upper beach (r= 0.57, lag of 7 months) suggests that as the inner bar moves seaward to an equilibrium position following wave forcing (Figure 3 10b), the beach experiences reorganiz ation and, presumably, cross shore transport of sediment onto the beach, widening the

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72 elevation contours (Figure 3 10f). This beach recovery/reorganization likely produce the significant (positive) correlation between wave forcing and the lower beach widt h (Figure 3 10d) and the delayed, negative response of the lower beach to outer bar position (Figure 3 10e). Other indirect relationships, such as feedbacks between the two surfzone bars and the inner bar and the lower beach are also possible. Cross corre lations were also performed on each zone differentiated by the presence of the shoreface attached oblique sand ridge. In the shadowed zone, landward of the oblique ridge (alongshore distance: 1.0 1.5 km, Figure 3 1), mean bar behavior closely mimics that of the overall system (Figures 3 11a, b, and c). The beach width proxies (Figure 3 10d) also respond similarly to wave forcing. Yet, the relationship between outer bar position and upper beach width differs in this zone (Figure 3 11e): when the outer bar moves offshore, the upper beach widens, with at a lag of 4 months. A lagged, negative recovery/reorganization between the bar and beach observed on the overall system (Figure 3 10e) is again present in the shadowed zone, except that the lower and upper beach seem more closely linked. At the ridge intersection (alongshore distance: 2.0 2.5 km, Figure 1), bar responses to wave forcing and bar feedbacks were very similar to the system as a whole (Figures 3 12a, b, and c). The beach responses, however, diff ered substantially. No negative correlations are found between wave forcing and beach widths (Figure 3 12d). In fact, significant positive correlations exist at longer time scales (9 10 months) for both the lower (r=0.80) and upper beach (r=0.61). The o uter bar position did not appear to have any significant control on beach response (Figure 3 12e). Inner bar position still had a negative correlation, but the response time was much shorter than

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73 the system as a whole, for both the lower beach (4 months) and especially the upper beach (0 lag). In both instances, landward migration of the inner bar results in retreat of the beach (erosion). The exposed zone (alongshore distance: 3.0 3.5 km, Figure 1), beyond the assumed influence of the oblique ridge, is shown in Figure 3 13. The outer bar initially moves seaward in response to large wave forcing, but then moves landward over the next few months (Figure 3 13a). Inner bar and beach width response to wave forcing, as well as outer bar inner bar feedbacks closely resemble that of the mean system (Figures 3 13b, c, and d). The outer bar position has significant, albeit opposing effects on the upper and lower beach (Figure 3 13e). The inner bar position shows no correlation to upper beach behavior at any me aningful lags, but does appear linked to lower beach retreat/erosion at lags of 4 and 11 months. Equilibrium model for bar positions and beach width s Although the cross correlations are informative regarding the driving wave forces and corresponding bar beach responses, they fall short of providing longer term morphologic understanding. A simple equilibrium model of bar behavior (Equation 3 2) is appropriate if 1) the cross shore bar crest position can describe overall bar morphology and 2) external (wave) forcing is the primary driver of bar equlibrium (Plant et al., 1999). Since, the surfzone bars at KSC showed no perceptible offshore decay, we tested whether a dynamic equilibrium exists here, so that the bars are persistently maintained. Althoug h the beach is certainly not in equilibrium (Adams et al., in preparation), we applied the same model to infer the typical response time of the lower and upper beach.

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74 Wave energy flux recorded at NDBC buoy 41009 was converted into equivalent nearshore ene rgy flux (P nearshore ) using the directionally dependent energy transmission coefficients (Figure 3 7b) and hourly mean wave directions measured at NDBC buoy 41012. From these estimates, mean nearshore wave heights (H) were determined via Equation 3 4. Mon thly mean cross shore bar positions were found to compare trends and feedbacks on the time scales of the beach morphologic surveys (i.e. complete monthly tidal cycles). The nondimensional forms of wave height (H*) and time (t*) were determined through sca ling by the maximum observed monthly wave height (H MAX ) and forcing frequency ( ), assumed to be 2 /yr (i.e. annual variations), respectively (Plant et al., 1999). The nondimensional form of cross shore bar position (x*) was scaled by the surfzone width, X SZ Following the methodology of Plant et al. (1999), the surfzone was approximated by ( 3 4 ) where =0.78 and tan is the beach slope near the bars, assumed to be 0.01. Testing showed little sensitivity to the range of observed beach slopes. The nondimensional equilibrium model (Equation 3 2) was then evaluated for observed monthly outer and inner bar positions (cal culated from daily bar positions with at least 50% coverage over the desired zone) and mean wave forcing over the entire study area (1.0 4.0 km) as well as the three zones described previously. The optimal power, p, as well as the nondimensional character istic response time (a 1 *) and equilibrium bar position (a 2 *), were found through linear regression by stepping the model through time.

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75 To extend the model to beach behavior, monthly beach widths were normalized by the maximum observed beach width (at the 0.00 m contour) from the dune line, yielding a nondimensional beach width, w*. The MHW (0.28 m) and 1.5 m contour were used to characterize the lower and upper beach, respectively, and to provide more comparisons to model predictions than the 0.00 m and 2.00 m contour elevations (see Figure 3 8); the model did not appear sensitive to the exact contour selected (i.e. the MHW and 0.00 m contours behaved quite similarly). Whereas the other nondimensional parameters have real physical interpretations (Plant et al., 1999), w* is difficult to interpret, since a beach largely experiencing long term retreat (Adams et al., in preparation) would not be in equilibrium. Still, if we assume that w* scales with wave forcing, H*, than model interpretations are not futi le: w*>1 would correspond to a predicted prograding beach and w*<1 implies retreat. Figure 3 14 shows the results of a variable response time equilibrium model evaluation on the mean monthly cross shore bar positions over the entire system. Table 3 1 cont ains the best fit power relationships, p, that relates wave forcing to bar response time (Equation 3 2). The best fit outer bar and upper beach response time was not a function of H (p=0), whereas the inner bar and lower beach showed a response time propo rtional to H 3 (p=3). The model had the most skill with the outer bar position, accounting for 60% of the observed variance, followed by the inner bar monthly position (r 2 =0.45). The characteristic response times (a 1 *) are identical for the bars (0.5); th ese values indicate the bars respond on time scales longer than a year (a 1 *=1). The predicted equilibrium positions (a 2 *) of both bars lie within the maximum monthly surfzone (a 2 *=1), suggesting some mechanism is preventing bar migration to

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76 the full break point. The beach responds to wave forcing on much longer characteristic time scales (a 2 fit by p=3. The behavior predicted by the model parameters shown in Table 3 1 are shown in Figure 3 15. Scaled bar velocities (dx*/dt*) of the outer bar (Figure 3 15a) are greatest when the instantaneous bar position is far from equilibrium and when waves are unusual (i.e. H* ~0 or ~1). Since the best fit p=3 for the scaled inner bar velocities, the bar shows essenti ally no movement under low waves (H*<0.5). For larger waves, bar velocities increase, driving the inner bar position towards its equilibrium. The right hand of Figure 3 15 (e h) shows the evolution of bar positions (x*) and beach widths (w*) initiated a t a variety of positions for a parameterized seasonal wave forcing (H* = 0,5 [1+ sin (2 t*)]), shown as a dashed grey line in each panel. For observed outer bar (0.25
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77 showed no dependence on wave forcing; neither did the upper beach. The model skill was slightly worse than the overall system, except for the lower beach width where 50% of the observed variance was predicted by the equilibrium model (Table 3 2). 2 *) of ~1 (lower beach) and ~0.8 (upper beach) corresponds to presumably stable long term conditions (Figures 3 16g and h ). The characteristic response times of the bars are again nearly identical (0.65 and 0.6) and long compared to seasonal waves, and the equilibrium positions are similar to the overall system. Because the best fit power for the inner bar is 1 rather than 3, the instantaneous response time (a 1 *H* p ) 1 of the inner bar is not as sensitive to wave height (Figure 3 16b), supporting the supposed buffering effect conceptualized in Figure 3 3. At the ridge intersection (Table 3 3, Figure 3 sponse time was again independent of wave forcing, but a 1 was similar for both bars (Figures 3 17a and b). The equilibrium position of the inner bar was nearer to the shoreline (a 2 *=0.1) than the shadowed zone. Beach response time (a 1 *) here approached the same frequency as annual wave forcing (Figures 13 3c and d). That change, along with much faster than in the shadow zone (i.e. it is more dynamic). A nearly deplete d beach would return in ~3 forcing cycles here (Figure 3 17g); conversely a healthy berm would disappear in the same interval (Figure 3 17h). The outer bar and inner bar characteristic response time (a 1 *) differed in the exposed zone (Table 3 4, Figures 3 18a and b) The inner bar approached a characteristic response time on the order of seasonal wave, whereas the outer bar

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78 remained longer (and independent of wave height). The beach here responds very slowly to annual wave forcing (p=0 1,a 1 *=0.1). Any bea ch transients (large deviations from equilibrium) would take many forcing cycles (>10) to approach equilibrium. This finding may explain one reason why the erosional hotspot at ~3 km alongshore distance persists. If the beach in this zone responds very s lowly to wave forcing, a major storm event (and dune overwash) would deplete the beach. As seen in Figures 3 18g and h, that an upper or lower beach beginning at zero width would take many annual cycles to grow seaward. The skill of the equilibrium mode l was best for the outer bar dynamics. This model behavior would be expected since the outer bar is receiving (relatively) pure wave forcing as waves enter the surfzone. Conversely, the inner bar and beach receive a somewhat corrupted forcing signal. Fu rther, feedbacks between the beach and bar systems, specifically the inner bar and lower beach, likely complicate the overall morphologic behavior. Still, nearshore wave forcing alone can explain approximately half of the inner bar behavior. Applications of the model to the upper and lower beach are much more dubious, especially in the exposed zone. The equilibrium model and correlation analysis reveal that the outer and inner bar dynamics remain relatively unchanged by the presence of the outer bar. The complex beach morphology (stable in the shadow zone, vulnerable in the exposed zone) may well be linked to the presence of the shoreface attached ridge, but such a mechanism does not have major impacts on bar morphology. Conclusions The effect of shore oblique ridge on surfzone bar and beach morphology has been studied and a simple equilibrium model has been applied. A simple, linearized

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79 model of wave energy transmission, based on deep water wave height, period, and direction, was de veloped that still captured at least 75% of the observed variance, even as waves passed over very complex inner shelf bathymetry. An equilibrium model with good predictive skill (up to 60% of bar crest variance) leads us to conclude that a breakpoint deri ved equilibrium model, where bar positions migrate to a temporally variable equilibrium position, can be applied to this system. The response time for the surfzone bars was long (greater than annual forcing), which suggests that the introduction of transi ents could result in long term offshore migration (Plant et al., 1999). The fact that such behavior has not been observed, even in the face of fairly severe tropical storms (Figure 3 8), indicates other mechanisms might be stabilizing the bar system.

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80 Table 3 1. Equilibrium model coefficient and best fit power results for mean bar and beach positions Component p (best fit) a 1 a 2 r 2 (n) Outer bar 0 0.53 0.73 0.6 (26) Inner bar 3 0.53 0.14 0.45 (26) MHW (0.28 m) contour 3 0.21 1.08 0.25 (29) 1.5 m contour 0 0.15 0.70 0.01 (26)

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81 Table 3 2 Equilibrium model coefficient and best fit power results for shadowed zone bar and beach positions Component p (best fit) a 1 a 2 r 2 (n) Outer bar 0 0.60 0.75 0.55 (26) Inner bar 1 0.65 0.20 0.40 (26) MHW (0.28 m) contour 1 0.11 1.38 0.50 (29) 1.5 m contour 0 0.18 0.82 0.07 (26)

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82 Table 3 3 Equilibrium model coefficient and best fit power results for ridge intersection zone bar and beach positions Component p (best fit) a 1 a 2 r 2 (n) Outer bar 0 0. 62 0.75 0.55 (26) Inner bar 3 0. 37 0.20 0.55 (26) MHW (0.28 m) contour 3 0. 70 1.38 0.50 (29) 1.5 m contour 3 1.15 0. 43 0.10 (26)

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83 Table 3 4 Equilibrium model coefficient and best fit power results for exposed zone bar and beach positions Component p (best fit) a 1 a 2 r 2 (n) Outer bar 0 0.51 0.73 0.55 (26) Inner bar 1 0.85 0.19 0.25 (26) MHW (0.28 m) contour 0 0.12 1.14 0.01 (29) 1.5 m contour 1 0.12 0.59 0.140 (26)

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84 Figure 3 1. Base map of the Kennedy Space Center, Cape Canaveral, Florida study site, highlight wave instrument deployment and video based observation field of view.

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85 Figure 3 2 Nearshore and inner shelf (inset) bathymetry at the Kennedy Space Center, Cap e Canav eral, Florida study site. Instrument deployment locations and video based observation field of view from Figure 3 1 are overlain in grey for reference

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86 Figure 3 3 Cartoon of potential influence of shoreface attached, shore oblique sand ridge on nearshore bar and beach morphology When waves approach near normal to the coast, wave energy is preferentially dissipated over the ridge, resulting in an increase to the gradient of alongshore sediment transport (Q S ). In turn, the shoreline is expected to retreat landward. The ridge presumably affects bar morphology and spacing.

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87 Figure 3 4 Wave roses compiled from observations at NDBC buoy 41012 near St Augustine between 2006 and 2012 : A ) H S and B ) T. Wave roses for the largest waves (H S >3.0 m) are shown in panels C (H S ) and D (T).

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88 Figure 3 5 Examples of surfzone bar configuration observed at KSC A) Crescentic, yet parallel configuration. B) Linear, parallel configuration. C) Linea r and parallel configuration with welding of inner and outer bar.

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89 Figure 3 6 Energy transmission across complex inner shelf bathymetry at KSC, Cape Canaveral, Florida

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90 Figure 3 7 Energy transmission across complex inner shelf bathymetry at KSC, Cape Canaveral, Florida. A) Model predictions compared against observations made during the spring 2012 deployment of a Nortek Aquadopp instrument in ~5 m depth. B) Energy transmission coe fficients shown as function of direction, determined through linear regression. C E) Relative errors (normalized by the maximum observed wave energy flux, graphed against significant wave height, H S

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91 Figure 3 8 Bar positions and beach contours shown with wave forcing. A) Wave forcing in intermediate water observed at NDBC 41009 buoy and predicted nearshore wave energy energy flux, as determined from coefficients from Figure 3 7b. B) Daily bar positions (dashed) shown for inner (light blue) and outer (dark blue) surfzone bars with 28 day running average positions (solid). Beach contours (0 2.0 m) are also displayed and were extracted from monthly kd GPS morphologic su rveys.

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92 Figure 3 9 Bar variability observed at KSC. A) Wave forcing, filtered over running 28 day intervals in intermediate (grey) and shallow (purple) water. B) Mean outer (dark blue) and inner (light blue) bar positions with standard deviation envelopes (light dashed lines). Equivalent standard deviation values are shown as heavier dashed lines along the bottom of the panel. C) Crescentic scale amplitudes of the outer (dark blue) and inner (light blue) bars, determined from the root mean deviations of Fourier decomposition for 50 m < L < 1 km.

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93 Figure 3 10 Cross correlations of wave forcing and beach/bar positions. All lags are in months. Areas in grey correspond to negative lags that have no physical meaning.

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94 Figure 3 11 Same as Figure 3 10, except only for mean bar positions and beach widths in the shadow zone (1.0 1.5 km), landward of the shoreface attached oblique sand ridge.

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95 Figure 3 12 Same as Figure 3 10, except only for mean bar positions and beach widths in the intersection zone (2.0 2.5 km) of the shoreface attached oblique sand ridge.

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96 Figure 3 13 Same as Figure 3 11, except only for mean bar positions and beach widths in the expo sed zone (3.0 3.5 km) beyond the influence of shoreface attached oblique sand ridge.

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97 Figure 3 14 Results of the equilibrium model applied to the entire study area (1.0 4.0 km). Observations are shown as circles connected by a dashed line. Model predictions are shown as solid lines. See Table 3 1 for best fit powers and coefficients. A) Outer bar (dark blue) and inner bar (light blue). B) MHW contour (yellow) and 1.5 m contour (maroon).

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98 Figure 3 15 Behavior of equilibrium model presented in Figure 3 14. The left hand side (A D) show the nondimensional scale rates of bar position and beach width. The right hand side shows the evolution of characteristic no ndimensional bar positions and beach widths under periodic wave forcing

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99 Figure 3 1 6 Behavior of equilibrium model presented in Figure 3 14, but only for the shadowed zone (alongshore distan ce: 1.0 1.5 km), landward of the shoreface attached oblique ridge. See Table 3 2 for the best fit powers and coefficients.

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100 Figure 3 17 Behavior of equilibrium model presented in Figure 3 14, but only for the ridge inter section zone (alongshore distance: 2.0 2.5 km), at the shoreface attached oblique ridge. See Table 3 3 for the best fit powers and coefficients.

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101 Figure 3 18 Behavior of equilibrium model presented in Figure 3 14, but only for the exposed zone (alongshore distance: 3.0 3.5 km), beyond the shoreface attached oblique ridge. See Table 3 4 for the best fit powers and coefficients.

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102 CHAPTER 4 INFLUENCE OF COMPLEX INNER SHELF BATHYMETRY ON THE GEOMORPHIC EVOLUTI ON OF A PROMINENT CUSPATE FORELAND AND ADJACENT SHORELINE Geomorphic response to external wave forcing is poorly understood on coasts with complex inner shelf bathymetry, such as shoals or linear sand ridges associated with capes. The pattern and magnitude of wave energy delivery to the surfzone are difficult to predict. Further, those spatial patterns are likely to vary given that time dependent deep water wave characteristics (height, period, and direction) are unsteady. In some instances, shoals and ridges may dissipate energy, buffering the nearshore zone ( relative to the adjacent shoreline), leading to an accumulation of sediment and progradation as the alongshore current loses transport capacity (Swift et al., 1972; Swift et al., 1978; Pethick, 1984). Conversely, inner shelf ridges have been linked to ero sional hotspots and areas of chronic shoreline retreat because they can alter the 1994; McNinch, 2004; Schup et al., 2006). This dichotomy is exemplified by the different be haviors among capes along the southeastern U.S. Atlantic coast. Cape Canaveral is a cuspate foreland located on the Florida Atlantic coast with a smaller, cuspate feature on its north side, known as False Cape (Figures 4 1 and 4 2). Cape Canaveral has ge nerally experienced accretion during the Holocene (Hoyt and Henry, 1971), and analysis of recent trends in decadal shoreline position reveals a progradation of False Cape and retreat along its northward adjacent shoreline, resulting in a counterclockwise c oastline rotation (Adams et al., in preparation). Other large capes along the southeastern U.S. Atlantic coast, notably Capes Hatteras, Lookout, and Romain, have similar inner shelf shoals and ridges, but

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103 appear to be experiencing uniform retreat (Moslow and Heron, 1981; Komar, 1998). This raises a question about the interaction between nearshore bathymetry and external wave forcing, and how this interaction works to shape capes and sandy shorelines of the decadal (short term) and millennial (long term) t ime scale. This paper investigates how complex inner shelf bathymetry controls the spatial distribution of nearshore wave energy flux along a cuspate foreland on the Florida Atlantic coast for a range of natural wave climates. We first validate a thi rd generation wave model (SWAN) against observed nearshore wave records. We then prescribe stationary deep water wave conditions (height, period, and direction) to explore whether wave transformations around nearshore shoals and ridges, and the resulting gradients of longshore component of wave energy flux interpolated at a prescribed isobath, are able to produce observed shoreline trends found by Adams et al. (in preparation). We comment on how these results apply to the evolution and stability of this cu spate system, as well as the implications to other sandy cape environments. Background Large scale Cuspate Formation and E volution Large cuspate forelands, or capes, protrude from the general coastal planform of a continent some 30 50 km over an alongs hore reach of 75 200 km and are common along the southeastern U.S. Atlantic coast (Dolan and Ferm, 1968). Many mechanisms have been proposed for cape formation and growth. Edge waves operating at the same spatial scales as large cuspates could potentiall y form and maintain these features (Dolan, 1979). Many researchers have stressed the importance of underlying or inherited geology in controlling the alongshore location of large scale capes (White, 1966; Hoyt and Henry, 1971; Valvo et al., 2006). Hoyt a nd Henry (1971) noted how

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104 many large cuspates coincided with major rivers and proposed modern capes are the re working of deltaic sediment of coastal rivers that build across continental shelves during sea level lowstands. Similarly, excess sediment coul d arise from a convergence of littoral cells, which subsequently form a dynamic equilibrium with nearshore waves and currents (Inman and Dolan, 1992). Finally, pre existing shoreline irregularities have been modeled to grow and stabilize due to the patter n of sediment transport arising from highly oblique incident waves (Zenkovitch, 1967; Ashton et al., 2001; Ashton and Murray, 2006). To date, no theory has completely resolved the observed spatial and temporal scales of cape development, suggesting some c ombination of the above processes or another mechanism. Most southeastern U.S. capes have associated seaward shoals ~10 km offshore (Shepard and Wanless, 1971; Komar, 1998). Many traditional theories posited the shoals to be relict features that became ab andoned as they were submerged beneath breaking wave processes (McNinch and Leuttich, 2000). McNinch and Leuttich Jr. (2000) found seaward directed Eulerian residual tidal currents with eddies on both sides of the shoals at Cape Lookout, North Carolina. This tidal flow pattern matched other studies (Pingree and Maddock, 1977; Signell and Geyer, 1991) and provided a way for sediment communication between the cuspate headland and shoals. In this way, the shoals are maintained and could migrate landward as many capes retreat with rising sea level (Moslow and Heron, 1981; McNinch and Leuttich Jr., 2000). White (1966) noted this potential relationship and its role on cape development, but these mechanisms have not been explored numerically in great detail (Th ieler and Ashton, 2010).

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105 Cape Canaveral The Cape Canaveral Merritt Island sedimentary complex is a prominent salient 4 1). It is the only major promontory along ~1,000 km of coastline between the next cuspate foreland, Tybee Island, to the north and the end of the Florida peninsula to the south. There are several competing theories chanism; most are linked to the overall cape formation hypotheses discussed in the last section. Merritt Island has been identified as both a transgressional (Pirkle et al., 1972) and regressional feature (Brooks, 1972). Kofoed (1963) used topographic co ntours to reconstruct a potential convergence (and stabilization) of two or more littoral cells following the last sea level highstand. Antecedent geology, namely the apex of a structural arch of the Anastasia Formation (lower Pleistocene) may provide a l explanation has been invoked to explain reoccurring relict capes, some 50 km inland, dating back to the early Pleistocene at the same alongshore location (White, 1958; Brown et al., 1962; Winker and Howard, 1 977; Randazzo and Jones, 1997). Beach ridge sets on modern Cape Canaveral have been dated to as early as the late Pleistocene (~100 ka), but most are likely Holocene in age, which suggests the current Cape Canaveral is a geologically recent, prograding geo morphic construction (Osmond et al., 1970; Rink and Forrest, 2005; Burdette et al., 2010). In at least the last century, a southeastern migration of Cape Canaveral has been documented, possibly originating from the present location of a smaller cuspate fe ature, False Cape, on Cape 4 2; White, 1966; Shepard and Wanless, 1971; Pirkle et al., 1972; Winker and Howard, 1977).

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106 The offshore bathymetry is composed of cape related shoals and banner banks, as well as linear, shorefac e connected sand ridges adjacent to False Cape (Figure 4 2). These bathymetric complexities are primarily concentrated in depths shallower than 15 m. Most of the shoals/banks are relatively small (length ~5 km, width ~100 m, height ~2 m), but three obliqu e sand ridges are substantially larger (length ~50 km, width ~1 km, height ~5 m). Deep water Wave Climate Hourly offshore wave characteristics, including significant wave height (H S ) and dominant wave period (T D ), have been measured continuously (except d uring short (NDBC, www.ndbc.noaa.gov) buoys 41010 and 41009, located ~220 km (~870 m depth) and ~37 km (44 m depth) east of Cape Canaveral, Florida, respectively (Figure 1). Hou rly mean wave directions ( ) have been recorded by NDBC buoy 41012, positioned ~75 km east of St. Augustine, Florida, ~150 km north of Cape Canaveral (Figure 4 1). Buoy 41012 has been deployed since 2002 and has recorded directional data since 2006. Figures 3a, 3b, and 3c show H S T D and measured by NBDC buoy 41012 between 2002 and 2013, respectively. Figures 4 3d, 3e, and 3f show the same wave characteristics during 2010. The summer months (June to August) are dominated by generally quiescent s eas (H S ~ 1 m, T D ~ 8s) originating from the east (60 120 with respect to north, 0 ). Major tropical wave events, like Hurricane Igor in Figure 3d, punctuate the late summer and early autumn wave record. Winter and spring (October to April) are charact S ~ 2.0+ m, T D ~ 12+ s) emanating from the north northeast (330 60 ). Like most of the U.S. east coast,

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107 this cumulative wave activity produces a net southward alongshore current of sediment transport (De Canaveral has been estimated to be between 200,000 and 300,000 m 3 /yr (Dean and by van Gaalen (2004) sugges ts as much as 50,000 m 3 /yr is sequestered between False Cape and Port Canaveral to the south of Cape Canaveral. This sediment surplus may be responsible for the maintenance or growth of the nearshore shoals and ridges that characterize the inner shelf bat hymetry. Wave Energy Flux and Sediment Transport Wave power or energy flux, P, the rate of wave energy transfer through a vertical plane of unit width, is given by ( 4 1 ) where is the density of seawater (~1020 kg/m 3 ), H is the wave height, and C g is the group velocity, which is a function of the wave period (T), wavelength (L), and water depth (h). As waves move through intermediate and shallow depths, bottom drag dissipates energy and P decreases (Komar, 1998). Convergence or divergence of wave rays additionally impacts the spatial distribution of P. The energy flux that is converted to breaking waves in the surfzone is responsible for geomorphic change. The longshore vector component of wave energy flux, P long is the quantity considere d to be of greatest importance in the calculation of longshore sediment transport, and is defined as ( 4 2 )

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108 where H B is the breaking wave height and B SL is the angle between the breaking wave ( B ) and the shoreline ( SL ). P long is directly proportional to immersed weight (I long ) and volumetric transport (Q long ) rates, converted by dimensionless coefficients often set by field data (Komar, 1998; Dean and Dalrymple, 2002). Areas of accretion and erosion are controlled by divergence of drift, dQ long /dx where x is the alongshore direction. Assuming Q long and x are oriented in the same alongshore direction, then coastal reaches where dQ long /dx < 0 witness accretion, whereas coastal reaches where dQ long /dx > 0 witness erosion. Therefore, it is the gradient of alongshore sediment transport rate, in addition to the necessity of sediment supply to the nearshore system, that controls long term beach morphology along sandy coasts, assuming cross shore sediment tra nsport beyond the closure depth is negligible (Komar, 1998). Nearshore wave climate Acoustic Doppler Current Profilers (ADCPs) were deployed for two multi month intervals to measure nearshore sub hourly wave and current characteristics. A Nortek AWAC instr ument was deployed from September 2010 to January 2011 in ~15 m depth, ~5 km offshore False Cape, just beyond the three oblique sand ridges (Figure 4 2). A Nortek Aquadopp measured wave conditions in ~5 m depth, ~400 m offshore, which was landward of the westernmost oblique sand ridge, from February to July, 2013 (Figure 4 2). Using the significant wave height (H S ) and dominant periods (T D ) measured by NDBC buoy 41009 and the ADCP instruments, we determined the energy transmission across the ridges (Figur e 4 4). In general, 20 100% of the wave energy is transmitted from 40 m to 15 m depth (Figure 4 4a). About half of the remaining energy remains by 5 m depth after waves have passed over the oblique ridge field (Figure 4

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109 4b). Regressions were fit for bot h deployments; the correlations (r 2 = 0.71 and 0.64, respectively) indicate the variance in energy transmissions, especially for more energetic deep water waves. The importance of the ridges and shoals on dissipating incoming wave energy is apparent, but the lack of dependable relationships requires us to turn to more sophisticated numerical modeling techniques, in order to better resolve the spatial distribution of wave transformation. Methodology Simulating WAves Nearshore (SWAN) is a third generation wave model that solves the spectral action balance equation in two horizontal dimensions, where action is equivalent to the energy density divided by the relative frequency (Booij et al., 1999). All of our simulations were computed on two grids: a main, co arse grid and a finer nested grid. The main computational grid was 375 by 430 km, occupying longitudes minute); its limits are shown in Figure 4 1. Output wave conditi ons from simulating wave transformation over the coarse grid are used as boundary conditions for the finer, nested grid. The finer nested computational grid, 50 by 50 km with a resolution of 80 m (3 arc seconds), was used for nearshore wave transformation s around the Cape Canaveral shoreline (Figures 4 1 and 4 2). Coastal Relief Model (CRM) with 3 arc second resolution (~80 m). The most northeast portion of our main grid was outside of the CRM limits. Accordingly, these depths, arc minute (~1600 m) Global Relief model (Amante and Eakins, 2009), and stitched together with the CRM bathymetric grid.

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110 Validation The valida tion simulations compared SWAN outputs to wave conditions observed by our nearshore ADCP instruments. We completed two non stationary simulations with hourly deep water boundary conditions prescribed by significant wave heights (H S ) and dominant wave peri ods (T D ) recorded by NDBC buoy 41010, and wave directions measured by NDBC buoy 41012, since NDBC buoy 41010 does not record wave direction. Wave height, period, and direction were defined as boundary conditions, hourly along the north, east, and south bo undaries of the main grid. No wind or water level inputs were prescribed, so the simulations captured only the swell transformation neglecting locally generated seas and tidal conditions. The time dependent boundary conditions for the nested computationa l grid were interpolated from the main computational grid outputs. Modeled wave characteristics at the locations of the three NDBC buoys and two ADCP deployments were extracted from the SWAN output for examination and comparison to ADCP observations. Deep water Wave Forcing and Bathymetric Controls Our second experiment included a suite of 288 stationary simulations with wave encapsulate ~99% of onshore directed wave condition s experienced in the area. Three deep water significant wave heights (H DW = 1, 2, and 4 m) and two wave periods (T=8 and 12s) were chosen to span quiescent to storm conditions (Figure 4 3). Sixteen deep water wave directions ( DW =330 to 120 in 10 degree intervals) were used to simulate any on shore directed wave (note: 0 is north). Since the Bahamian islands shelter Cape Canaveral from waves approaching between 120 and 150 (Figure 4 1) these deep water wave directions were neglected. A mid tide/mean sea level was chosen as

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111 the reference water level, but water level was also altered 1m to determine whether bathymetric shape (the shoals) had a variable effect depending on tidal elevat ion. Boundary conditions for the nested computational grid were again extracted from the main computational grid. Simulations were analyzed individually by wave characteristic (height, period, and direction), but also as compilations that were considered representative of seasonal or event conditions, as shown in Table 4 1. These composites provide insight into how inner shelf bathymetric complexities affect commonly observed wave conditions over seasonal and event time scales. Interpolated shoreline and 5 m isobath A shoreline and 5 m isobath were extracted from the nested grid bathymetry. Shoreline points were then interpolated with equidistant, 50 m alongshore spacing (SL 50m ) to adequately address orientation changes around the two cuspate features (Fa lse Cape and Cape Canaveral proper). The 5 m isobath was then smoothed with a two dimensional, 5 km moving average filter to eliminate abrupt orientation changes around the shoals and ridges (Figure 4 2). Because of this technique, the 5m isobath becomes slightly shallower than 5 m (~4 m) briefly around the Cape Canaveral shoals. A shore normal line was extended from each SL 50m and its intersection with the 5 m isobaths was determined. These points were used to linearly interpolate desired wave character istics (independently) from the SWAN outputs for each simulation. The 5 m isobath was chosen because SWAN, as a spectral wave model, does not predict a single breaking point; rather it provides a percentage of waves that break at every grid location (Booi j, 1999). Therefore, index wave parameters commonly used for analyses in quantitative monochromatic wave coastal geomorphologic calculations, like breaking wave height (H B ) and breaking water depth (h B ), lose their significance (List et al.,

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112 2007). Acco rdingly, it is challenging to apply gradients of alongshore energy flux (dP long /dx) to formulations of annual sediment transport rates (Davidson Arnott, 2010). Although the transport and shoreline change rates that are presented below are approximated, we propose that they represent the general zones of shoreline retreat, accretion, or stasis. Results Validation Two validation runs were conducted to determine the performance of the SWAN model during two nearshore ADCP deployments. NDBC buoy 41010 obser vations, which were used as boundary conditions for the validation simulations, correlated best with the SWAN modeled outputs, with r 2 = 0.64 and 0.52 for the peak period (T P ) and significant wave height (H S ), respectively. An hourly comparison between th e Nortek AWAC (see Figure 4 2 for location) observations and SWAN modeled wave characteristics at the same location is shown in Figure 4 5. T P and wave direction ( have the best correlations (r 2 =0.46 and 0.45, respectively). Modeled H S achieves the same general temporal patterns as the AWAC observations, but the correlation (r 2 = 0.26) is poor. Using intermediate depth wave directions measured at NDBC buoy 41012 as the deep water boundary conditions likely contributed to the model error, since wave refr waves. The cross correlations are best for smaller waves (<2 m) indicating either 1) SWAN over predicts larger waves or 2) larger waves are affected by local winds, water levels, or other processes not incorporated into the model. The second validation simulation for the spring 2012 deployment of a Nortek Aquadopp (see Figure 4 2 for location) yielded stronger correlations for wave heights

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113 (r 2 =0.42). A disagreement between modeled a nd observed peak wave periods (r 2 =0.20) suggests that the boundary conditions did not adequately represent the actual deployment, which was instead dominated by loca l wind generated seas. Booij et al. (1999) found rms errors of less than 10% for significant wave heights using the JONSWAP method in SWAN, the same used during our simulations. We consider our higher errors to be attributable to two potential factors: 1 ) over simplification of the deep water wave field, ignoring local winds and water levels and/or 2) dynamic nearshore bathymetry that has a drastically different configuration from the CRM data. Although we cannot exclude the latter, the former seems more plausible, since the correlations in intermediate to deep water were also poor to acceptable (r 2 =~0.5 0.8). Further, the time series comparisons show a consistent temporal pattern of directional overprediction (Figure 4 5), consistent with not adequatel y prescribing the deep water wave conditions. Still, we are aware that for this bathymetry, nearshore wave heights and energy fluxes may be overpredicted by SWAN, especially for larger (>2 m) deep water waves. Deep water Wave Forcing and Bathymetric Contr ols For small, short period waves originating out of the east (H DW =1 m, T=8 s, and DW =90 ), common of quiescent conditions witnessed at Cape Canaveral during the summer months, the cape related shoals appear to exert two main effects: 1) they promote wave shoaling, which increases wave height over the features, while 2) refracting the incoming wave crests (Figure 4 6a). The latter phenomenon is best displayed by the wave direction vectors in the vicinity of the larger and shallower shoals

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114 seaward of the Cape proper, where incoming wave rays converge directly south of the cuspate tip. For larg er (H DW =4 m) and longer period (T=12 s) waves originating from the same direction ( DW =90 ), analogous to passing tropical systems, the effect of shoal induced refraction increases, especially around False Cape (Figure 4 6b). Yet, the larger waves break o n the outer edges of the shoals, leading to similar Hs (and P) values over the shoals (relative to the quiescent conditions described above), since wave breaking is a depth limited process (Komar, 1998). The spatial pattern and magnitude of nearshore wave energy delivery near Cape Canaveral and False Cape are nearly identical during both seasonal and event instances. Yet, the open coast adjacent to the cape related shoals is exposed to a larger percentage of deep water wave energy, especially during storm events (Figure 4 6b). For larger easterly waves, the oblique ridges north of False Cape buffer the shoreline from wave energy, leading to a ~25% reduction in H S landward of the shoreface connected oblique ridge (Figures 4 6b). The inner shelf bathymetry has similar effects on waves originating from the northeast. Figure 4 7a shows modeled H S for H DW =2 m, T=12 s, and DW =40 a Canaveral shoals considerably refract incomi ng waves after they break. Larger waves (H DW =4 m) are refracted to a greater degree by the False Cape shoals, but experience a similar transformation pattern around Cape Canaveral (Figure 4 7b). When water levels were altered, simulating high and low tides, the shoals and ridges dissipated wave energy in the manner observed for simulations at the reference water level. Modeled wave heights and energy fluxes were reduced during low tide ( 1

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115 m), since more wave breaking was induced over the shoals, and conversely, amplified during high tide (+1 m). Nevertheless, the same refraction patterns were found, indicating the shoals do not show a strong dependence on water level. Seasonal Wave Climate or ~80% of the overall wave climate along the Florida Atlantic coast, were set as deep water wave inputs using the values listed in Table 4 1. SWAN outputs matching the seasonal wave environments were averaged to determine a composite (mean) along the 5 m isobath. coast, which causes a steady rotation of approaching wave angle from north to northeast (Figures 4 3 and 4 5), as well as the minor variations around 90 ( east) during quiescent wave intervals. Significant wave height (H S ) and energy flux (P) were smoothed, using a weighted, linear least squares method in 5 km moving windows, to provide general alongshore trends on the order of observed shoreline behavior (Adams et al., in preparation), as well as to remove the influence of smaller bathymetric features on the order of ~1 km in length. H S and P along the 5 m isobath are shown in Figure 4 8a and 4 8b, respectively, for both the composite summer (red) and no alongshore zones associated with False Cape and Cape Canaveral are shaded for north (0 km) to south (60 km), as incoming waves interac t with the cape related bathymetric features (Figure 4 2). H S for the composite summer simulations are more uniform, except behind the shoals that sit in front of Cape Canaveral, where H S decreases, in a manner consistent with the results provided in Figu res 4 6 and 4 7.

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116 Energy fluxes match the general wave height trends, as expected given the relationship in Equation 4 1. The alongshore component of energy flux, P long is shown in Figure 4 8c. Summer wave P long values are generally smaller and negative (northward) whereas the long values are positive (southward), consistent with net southward 1987). Around False Cape (~26 km) and Cape Canaveral (~43 km), P long values become more positive, indicating an intensifying southward (or declining northward) alongshore flux. The gradient of P long with respect to alongshore distance, x, is shown in Figure 4 8d. Assum ing that the coastal zone is blanketed with mobile sediment to provide an adequate sediment supply, negative values indicate shoreline progradation and positive values correspond to shoreline retreat. These results indicate that the shoreline near the ti p of Cape Canaveral should experience progradation under both composite wave climates (quiescent summer and the other hand, the shoreline above the Cape tip should experien ce retreat, albeit at a reduced rate. Around False Cape, the summer composite shows a mildly positive alongshore flux gradient at the cuspate feature, whereas the adjacent shorelines have aster wave composite, but the magnitudes of the gradients are larger, as expected with more energetic waves. On a regional scale (~50 100 km), P long suggests net seasonal sediment deposition own in alongshore

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117 transport rate studies, and growth of the capes and/or cape related shoals (van Galen, 2003). Wave Events Using the same technique as was applied to the seasonal wave composites, we investigated two wave event conditions that each characterize approximately 1% of the wave record: 1) a passing tropical storm, such as Hurricane Irene in 2011 or Hurricane Although such conditions are infrequent, we consid er it important to investigate their results, given that the geomorphic record is largely dominated by extreme, infrequent events. Wave characteristics for these extreme events can be found in Table 4 1. Figure 4 9a and 4 9b show H S and P along the 5 m i sobath for the tropical (orange) and related shoals reduced H S causing up to ~80% reduction in P; the dissipation of wave energy over the fronting shoals is noticeable near the two c uspate forelands (Figure 4 9a and 4 9b). The alongshore component of wave energy flux (P long ) follows similar trends to the seasonal composites, albeit at higher magnitudes, with two exceptions (Figure 4 9c). First, P long becomes more negative north of False Cape (0 15 km alongshore distance) during the tropical storm composite, as the influence of cape related bathymetry diminishes. In turn, the gradient of alongshore flux (dP long /dx) becomes positive here, indicating a zone of shoreline retreat (Figur e 4 9d). Second, shoal induced refraction of tropical storm waves causes P long to switch directions, turning slightly positive (directed southward) north of False Cape.

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118 Discussion Regional shoreline behavior The seasonal and event composites suggest a general behavior of the compound cuspate foreland system. To better represent the inferred sediment transport patterns, we normalized the alongshore energy flux gradients (P long /dx) by a proxy for the width of the surf zone, the cross shore distance betwe en the interpolated, equidistant shoreline and smoothed 5 m isobath. These normalized gradients are shown in Figures 4 10a and 4 10b. This correction shows the most dynamic portion of ~5 km (see Figure 4 2). Three hotspots zones that are predicted to experience consistent retreat or progradation are evident around False Cape and are shown in Figure 4 10c. The documented erosional hotspot is shown as the grey circ le, near the top of the northern predicted erosional hotspot. We combined the normalized gradients shown in Figure 4 11 by assuming these individual trends persist for the same portion of time as their corresponding wave climates (Table 4 1). For instan ce, the summer composite gradients contribute 60% to the overall behavior. 18% of the wave record is assumed to be mostly offshore directed and/or small waves (<0.5 m) that do not factor into shoreline morphology. An annual composite shoreline behavioral trend (retreat vs. accretion) is shown in Figure 4 11a, and is compared against the regional shoreline orientation smoothed over 100 m intervals with the salient tips highlighted by dashed lines (Figure 4 11b). False Cape experiences a negative gradient i n alongshore energy flux (P long /dx), and, thus, progradation of the shoreline there should be expected. This accretional peak closely coincides with the False Cape tip, suggesting that False Cape would not migrate

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119 significantly alongshore if the current b athymetric configuration and wave climate were to remain steady. Conversely, the adjacent shorelines north and south of False Cape should be retreating due to positive dP long /dx. This retreat progradation retreat regime should grow the False Cape salient (Figure 4 11c). The normalized gradients around Cape Canaveral are much smaller and not uniform. The Cape Canaveral salient should be expected to grow at a reduced rate as the cape migrates to the south, which is in agreement with observed behavior (Dea preparation). The shoreline updrift of Cape Canaveral should be expected to retreat at a moderate rate (Figures 4 11a and c) We can use a simplified one line model approach to convert alongshore energy flux gradie nts into shoreline change rates (Komar, 1998; Dean and Dalrymple, 2002). Employing the relationship Q long = 2.58P long when using significant wave heights to calculate energy flux (Komar, 1998), as well as some general approximations about the nearshore zo ne (i.e. slope, =0.10), we calculate the maximum accretion rates around False Cape to be ~2 m/yr, slightly larger than observed rates (Adams et al., in preparation). Near the erosional hotspot, this method produces retreat rates of ~1.5 m/yr, approximate ly three times greater than the last century retreat rate (Adams et al., in preparation). At Cape Canaveral, accretion of ~1 m/yr is predicted, less than the these disc repancies may be due to our use of the 5 m isobath, which in most cases, for the observed wave fields, is deeper than the breaking depth, h b A fraction of the incoming wave energy is dissipated between 5 m depth and h b and will not contribute significant ly to geomorphic work. Another factor may be a systematic overestimation of

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120 nearshore wave heights and, thus, wave energy fluxes, by SWAN. Our validation results suggest that small wave heights (<2 m) are reproduced accurately by SWAN, but larger waves (> 2 m) are slightly overestimated. Negative feedbacks, such as wave refraction and sediment transport, between False Cape and the adjacent shorelines, may also be operating, but were not considered in this study. Such mechanisms would likely retard Cape pro trusion, but other feedbacks are possible. For instance, some of the sediment accumulating near False Cape might be transported downdrift, mitigating the predicted retreat rates there. Cape Stabilization The seasonal and event wave composites predict the stabilization, and potential growth, of False Cape and Cape Canaveral. Our results suggest shoal induced wave refraction and the resulting alongshore energy flux gradients are the primary mechanisms for stabilization and salient growth. This idea is not novel. White (1966) discussed the importance of shoals in cape maintenance, and indeed these arguments have implications for nearly all cuspate environments. Cape stabilization in this study does not appear to be linked only to uniform wave energy dissip ation. Rather, the spatial patterns of total, and alongshore components of, wave energy flux are inharmonious. Instead, the cape related shoals refract the incoming wave field in a counter clockwise direction while dissipating wave energy. Figures 4 12a and 4 12b show the relative angle of wave ray approach with respect to the shoreline ( 5m SL ). A relative wave angle of 0 corresponds to a shore normal approach, whereas 90 is an oblique, alongshore directed wave. North of False Cape (0 15 km), wave s are nearly normal (within ~10 ) to the coast for both seasonal and event composites. Around

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121 before returning to nearly shore normal. A more exaggerated example of inc reased wave obliquity can be seen around Cape Canaveral, although part of this obliquity is attributable to the wide surf zone. For the summer seasonal and tropical event composites, the shoals have the opposite effect: waves are rotated ~10 15 counter c lockwise and generally become more normal to the shoreline. The effect of this seemingly slight alteration in wave approach angle can be better understood with Figure 4 12c, which shows a plot of relative wave angle ( 5m SL ) versus the directional depen dence term of the longshore component of wave energy flux, sin( 5m SL )cos( 5m SL ), described in Equation 4 2. The peak value (0.5) occurs for waves incoming at 45 ; the potential influence of these highly oblique waves on cape formation has been noted by Zenkovitch (1967) and Ashton et al. (2001). Figure 12d shows the effect of 1 and 10 shifts in relative wave angle. For waves that are nearly completely obliqu e ( 5m SL <10 ) or nearly normal ( 5m SL >80 ), small changes in wave direction can result in dramatic (>100%) changes in longshore energy become ~10 more oblique, a near doubl ing of longshore wave energy flux can be expected. Increases in longshore flux produced steepened longshore gradients. For summer and tropical waves originating out of the east, the clockwise rotation of wave direction has the same influence on longshore flux gradients. Neither the seasonal nor event wave climates are characterized as highly oblique ( 5m SL > 45 and shoals to become non oblique waves by the 5 m isobath in our sim ulations. Hence, we found no evidence in our results to support the high angle wave instability as a

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122 feasible mechanism of cape growth or stability at Cape Canaveral (Ashton et al., 2001; Ashton and Murray, 2006a and 2006b). Since similar refraction patt erns likely occur in other cape environments, our results challenge whether highly oblique waves ever truly are present in most nearshore systems. Interestingly, however, shoal influenced (refracted), shore normal waves can produce similar sediment transpo rt patterns as the high angle wave instability model (Ashton et al., 2001; Ashton and Murray, 2006a and 2006b). Thus, we suggest shoal complexes not the incident wave climate may be the stabilizing mechanism in most cuspate shorelines. Long term shoal cape interactions We have shown how inner shelf bathymetry may control cape maintenance and evolution, but the longevity of these mechanisms on long term shoreline evolution is uncertain. Are the shoals static features that will be drowned and adan doned by rising sea level or do feedbacks exist that could keep the system connected? We used the Delft3D flow model by Delatares (Delft Hydraulics, 2003) with the nested SWAN computational grid to determine whether similar residual tidal currents persiste d at either False Cape or Cape Canaveral. Using the M1 and M2 tidal constituents from Trident Pier in Port Canaveral just south of Cape Canaveral (www.ndbc.noaa.gov), we completed a two week (28 tidal cycle) simulation. The residual tidal currents over t he Cape Canaveral shoals are shown in Figure 4 13. Residual tidal currents up to ~2 cm/s flow from Cape Canaveral seaward across the shoals; smaller counter rotating eddies exist on either side. No such residual pattern was found around False Cape and it s associated shoals. The only non zero residuals near False Cape were located in the troughs between the shore oblique ridges and were directed shoreward (<<1 cm/s). The residual flow pattern around Cape Canaveral closely resembles that modeled by

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123 McNinc h and Leuttich (2000) across the Cape Lookout shoals, both spatially and by magnitude (2 cm/s compared to 5 cm/s). Thus, it appears this residual flow regime may be a characteristic of many cape shoal systems. The Delft3D flow results suggest there is a communication link between Cape Canaveral and its shoals. Since sediment can be passed between the headland and the shoals, it seems likely that the shoals can migrate, both alongshore and cross shore, with the cuspate foreland in response to slow to moderate sea level rise scenarios (Thieler and Ashton, 2011). Hence, the southerly directed migration of Cape Canaveral predicted by our SWAN simulations would seem likely to occur well into the future. False Cape and its shoals do not seem inter connect ed, and its long term stability is unknown. Our numerical experiments suggest the current shoal configuration will cause substantial progradation, which agrees with shoreline advancement of ~1.5 m/yr observed over the last century at False Cape (Adams et al., in preparation) Such a progradation seems at odds with rising sea levels, which will likely minimize the effects of the shoals and lead to shoreline retreat. However, if a residual tidal flow link can develop between a prograding False Cape and its shoals, then a stable cuspate foreland may emerge there, as well. Conclusions Our investigation into how nearshore bathymetric features control beach morphology has provided insight into the mechanisms that may be responsible for large cuspate stabiliza tion and evolution. Our SWAN outputs suggest that the shoals directly seaward of False Cape and Cape Canaveral have two major effects on incoming wave energy. Indeed they dissipate wave energy, resulting in smaller waves landward of these features, as wo uld be expected. Yet, they also refract natural incoming wave

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124 fields counterclockwise, resulting in the relative wave direction between the incoming wave and local shoreline ( 5m SL ) to become ~10 and ~10 more shore no rmal for quiescent wave conditions and tropical events. Since alongshore wave energy flux, a proxy for volumetric sediment transport rate, is directly proportional to sin( 5m SL )cos( 5m SL ), this small change in relative wave angle has a profound effect in the gradients of alongshore sediment transport. Accordingly, the capes rotate, grow, and migrate, a trend observed in the shoreline data documented over the past century (Adams et al., in preparation). This study does not provide results that definiti vely demonstrate how the above interactions persist over geologic time scales for a number of reasons. First, the mobility of the shoals and ridges is unknown. Shoreface attached ridges may migrate downdrift up to 3 m annually (Calvete et al., 2001). Al though oblique ridges quite similar to the current configuration were observed over a century ago (Patterson, 1878), the dearth of reliable 20 th century bathymetric data leads us to only suppose their stability. Tidal residual flows suggest a communicatio n between the Cape Canaveral shoreline and its shoals, but current sea level rise rates may overwhelm this process link, leaving the shoals disconnected and ultimately drowned. No sediment link is obvious between False Cape and its shoals, although a seaw ard migration of the cuspate foreland, predicted by our modeling results, might initiate (or revive) cross shore transport. Finally, as the model was run in stationary mode without sediment transport processes, potential feedbacks that could limit cuspate growth (e.g. increased convergence, decreased alongshore flux gradients) were not explored. This limitation may explain why the observed shoreline retreat downdrift of the cuspate features has not been

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125 observed close to the predicted magnitudes. Neverthe less, we predict that the shoreline trends observed in the last century will continue for the foreseeable future and have found evidence that the shoals are the major mechanism controlling modern shoreline morphology. Shoals in other cape related environme nts may be responsible for cuspate foreland stabilization and/or growth. Other oft cited processes, such as highly oblique waves or underlying geology, may not be required (Ashton et al., 2001; Ashton and Murray, 2006a and 2006b). Our results indicate lar ge cuspate features could be initiated, grown, and stabilized only with the presence of shoals seaward of a straight coastline. This modeling technique should be applied to other cape environments to confirm its plausibility. Additionally, other factors (i.e. tidal range, sediment availability, sea level rise) should be considered to assess whether these modeled wave refraction patterns should persist over time scales of multiple sea level cycles.

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126 Table 4 2 Major onshore directed wave climate types Name Description Portion of wave climate (%)* H DW (m) T (s) DW ( )** Summer Seasonal quiescent waves 60 1 8 60 120 Seasonal storm activity 20 2 12 0 60 Tropical system Passing, intense tropical event 1 4 12 60 120 Strong Intense winter storm event 1 4 12 0 60 Es timated from analysis of NDBC buoy# 41012 directional data from 2006 2012. ** Deep water wave directions are in nautical convention, with 0 corresponding to north.

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127 Figure 4 1 Bathymetry (50 m contours) of continental shelf off the Florida Atlantic coast. Locations of three NDBC buoys (41009, 41010, and 41012) are shown. A wave rose, surrounding buoy 41012, shows the recorded distribution of directional wave data since 2006. Location of the nested SWAN computational grid is shown as the red box around C ape Canaveral. Coordinates of the main figure correspond to the main (coarse) SWAN computational grid. The inset shows the southeast U.S. Atlantic and Gulf coasts with the black box outlining the location of the main SWAN computational grid.

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128 Figure 4 2 Bathymetry (5 m contours) of the nested SWAN computational grid. Deployment locations of two nearshore ADCP instruments, as well as the location of a persistent erosional hotspot, are shown. Note the series of shoals, banner banks, and oblique ridges associated with False Cape and Cape Canaveral. These features extend from the shoreline ~15 km out onto the inner shelf. The interpolated shoreline (blue line) and 5 m isobaths (green line) are also shown in panel (A), al ong with the surfzone width proxy, the cross shore distance from the shoreline to 5 m i sobaths shown in panel (B)

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129 Figure 4 3 NDBC buoy 41012 hourly wave history. A) Significant wave height. B) Dominant wave period. C ) Mean wave direction. D) Significant wave height recorded during 2010. E) Dominant wave period recorded during 2010. F) Mean wave direction recorded during 2010. Note the seasonality of the wave climate punctuated by storm events (i.e. hurricanes, energe

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130 Figure 4 4 Nearshore wave energy flux (P) transmission for two ADCP deployments. A) Comparison of P transmission between 40 m and 15 m depth during the fall 2010 AWAC deployment. B) Comparison of P transmission between 40 m and 5 m depth during the spring 2012 Aquadopp deployment. Note the scatter of wave energy transmission, which may be attributable to the presence of offshore shoals and ridges.

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131 Figure 4 5 Comp arison of observed (AWAC) and modeled (SWAN) wave characteristics during the fall 2010 deployment. A) Significant wave height, H S (m). B) Peak wave period, T P (s). C) Mean wave direction, ( ).

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132 Figure 4 6 Colormaps of SWAN modeled significant wave heights for conditions representative of typical quiescent summer waves, (A) H DW =1 m, T=8 s, DW =90, and a passing tropical storm event (B) H DW DW =90. Note the wave refraction and transformations around the sh oals fronting Cape Canaveral and False Cape.

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133 Figure 4 7 Colormaps of SWAN modeled significant wave heights for conditions DW =2 m, DW =40, H DW DW =40.

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134 Figure 4 8 Seasonal wave composite results interpolated from SWAN outputs along the 5 (H DW =2 m, T=12 s, DW = 0 60) are shown in blue and results from quiescent conditions, typical of summer months (H DW DW =60 120) are shown in red. A) activity, the in ner shelf bathymetry dissipates wave energy around the capes (~15 50 km alongshore distance) C) Alongshore energy flux, P long Just above the salients of False Cape and Cape Canaveral, P long increases for both seasonal composites. D) Alongshore energy flux gradients, dP long /dx. Positive gradients correspond to shorelines expected to retreat and negative gradients correspond to areas of progradation, under the modeled wave conditions.

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135 Figure 4 9 Event wave composite results interpolated from SWAN outputs along the 5 DW =4 m, T=12 s, DW = 0 60) are shown in navy blue and results from the passing tropical event, akin to Hurricane Irene in 2011 or Hurricane Sandy in 2012 (H DW =4 m, DW =60 120) are shown in orange. A) Smoothed significant wave height. B) Smoothed energy flux. For storm events, the inner shelf bathymetry dissipates wave energy around the capes (~15 50 km alongshore distance) C) Alongshore en ergy flux, P long D) Alongshore energy flux gradients, dP long /dx. Positive gradients correspond to shorelines expected to experience retreat and negative gradients correspond to areas expected to experience progradation.

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136 Figure 4 10 Longshore wave energy fluxes normalized by a proxy for the surf zone width, the cross shore distance to the 5 m isobath for A) seasonal composites and B) event composites with the seaward tip of the salients highlighted by a dashed line in each zone. C) Zones of persistant accretion (green) and erosion (red), as indicated by A and B are highlighted. Position of the observed erosional hotspot is shown by a grey dot. All four wave composites predict a stable to slightly north migrating salie nt at False Cape. Cape Canaveral is shown to be stable, but migrating in the south direction.

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137 Figure 4 11 A) Expected normalized longshore wave energy flux over the total composite wave climate, compiled by assuming each individual seasonal and event wave composite makes up a certain percentage of the overall wave climate. B) 100 m moving average orientation of the shoreline. C) Contour plot of gradients depicted in A to spatially show areas of expected progradation (negative values) and retreat (positive values).

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138 Figure 4 12 5m SL ) at the 5 m isobath for A) 5m SL ) versus 5m SL )co 5m SL ). D) Effect of small changes to wave angle approach to the quantity of energy flux conveyed in the alongshore direction. The effect of slight changes to the approaching wave angle are most pronounced for near normal (<10) and highly oblique (>8 0) waves.

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139 Figure 4 13 Residual tidal currents around the Cape Canaveral shoals from Delft3D flow simulation of 28 tidal cycles. The seaward residuals connect the headland to the outer shoals. Counter rotating eddies north and south of the shoals would also be expected to yiel d net transport to the features.

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140 LIST OF REFERENCES Adams, P. N., R. S. Anderson, and J. Revenaugh ( 2002), Microseismic measurement of wave energy delivery to a rocky coast, Geology 30 895 898. Adams, P. N., C. D. Storlazzi, and R. S. Anderson (2005), Neashore wave induced cyclical flexing of sea cliffs, Journal of Geophysical Research 110 F02002, doi:10.1029/2004JF000217. Adams, P. N. (in preparation), Decadal wave climate changes and shoreli ne rotation at Kennedy Space Center, Cape Canaveral, Florida. Amante, C. and B. W. Eakins (2009), ETOPO1 1 Arc Minute Global Relief Model: Procedures, Data Sources and Analysis. NOAA Technical Memorandum N ESDIS NGDC 24, 19 pp Anderson, R., Densmore, A ., & Ellis, M. (1999). The generation and degradation of marine terraces. Basin Research 11 (1), 7 20. Antia, E. E. (1996), Shoreface Connected Ridges in German and U.S. Mid Atlantic Bights: Similarities and Contrasts, Journal of Coastal Research, 12 (1), 141 146. Ashton, A., A. B. Murray, and O. Arnault (2001), Formation of coastline features by large scale instabilities induced by high angle waves, Nature 414 196 300. Ashton, A. D., and A. B. Murray (2006a), High angle wave instability and emergent s horeline shapes: 1. Modeling of sand waves, flying spits, and capes, Journal of Geophysical Research, 11, F04011, doi: 10.1029/2005JF000422. Ashton, A. D., and A. B. Murray (2006b), High angle wave instability and emergent shoreline shapes: 2. Wave climat e analysis and comparisons to nature, Journal of Geophysical Research, 11, F04011, doi: 10.1029/2005JF0004223. Ashton, A. D., M. J. A. Walkden, and M. E. Dickson (2011), Equilibrium responses of cliffed coasts to changes in the rate of sea level rise, Marine Geology 284(1 4) 217 229. Barnard, P. L., and D. M. Hanes (2006), Integrating Field Research, Modeling, and Remote Sensing to Quantify Morphodynamics in a High Energy Coastal Setting, Ocean Beach, San Francisco, California, American Society of Ci vil Engineers, 5 th International Conference on Coastal Dynamics 2005 Conference Proceedings, Barcelona, Spain, 14 pp. Bender, D. D., and R. G. Dean (2003), Wave field modification by bathymetric anomalies and resulting shoreline changes: a review with rec ent results, Coastal Engineering, 49 (1 2), 125 153.

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141 Benumof, B. T., C. D. Storlazzi, R. J. Seymour, and G. B. Griggs (2000), The relationship between incident wave energy and seacliff erosion rates: San Diego County, California, Journal of Coastal Resea rch 16(4) 1162 1178. Blanco Chao, R., A. Prez Alberti, A. S. Trenhaile, M. Costa Casais, and M. Valcrcel Daz (2007), Shore platform abrasion in a para periglacial environment, Galicia, northwestern Spain, Geomorphology 83 136 151. Boczar Karakiewi cz, B., and J. L. Bona (1986), Wave Dominated Shelves: A Model of Sand Ridge Formation by Progressive Infragravity Waves, In: Knight, R.J., McLean, J.R. (Eds.), Shelf Sands and Sandstones. Canadian Society of Petroleum Geologists, Memoir II, pp. 163 179. Booij, N., R. C. Ris, and L. H. Holthuijsen (1999), A third generation wave model for coastal regions 1. Model description and validation, Journal of Geophysical Research, 104 (C4), 7649 7666. Bradley, W. C., and G. B. Griggs (1976), Form, genesis, and de formation of central California wave cut platforms, Geological Society of America Bulletin 87 (3) 433 449. Brooks, H. K. (1972), Geology of Cape Canaveral, Southeastern Geological Society, 16 th Field Conference, Kennedy Space Center, Florida, 35 44. Brown, D. W., W. E. Kenner, J. W. Crooks, and J. B. Foster (1962), Water Resources of Brevard County, Florida, Volume Report of Investigation 28, Florida Geological Survey, Tallahassee, Florida, 59 pp. Burdette, K. E., W. J. Rink, D. J. Mallinson, P. R. P arham, and E. G. Reinhardt (2010), Geologic investigation and optical dating of the Merritt Island sand ridge sequence, eastern Florida, USA, Southeastern Geology, 37, 175 190. Calvete, D., A. Falques, H. E. DeSwart, and M. Walgreen (2001), Journal of Flu id Mechanics, 441, 169 193. Collins, B. D., and N. Sitar (2008), Processes of coastal bluff erosion in weakly lithified sands, Pacifica, California, USA, Geomorphology 97 483 501. Cox III, M. O., P. A. Howd, and J. T. Kirby (1995), Application of a wea kly non linear wave refraction/diffraction model to the Wimble shoals, NC region, Eos Trans., 76(46), 297. Dally, W. R. R. G. Dean, and R. A. Dalrymple (1985), Wave height variation across beaches of arbitrary profile, Journal of Geophysical Research 90 917 927.

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149 BIOGRAPHICAL SKETCH Although born in 1984 in Arlington, Texas, Shaun Kline grew up in Lecanto, Florida, a small rural town about ~60 miles southwest of Gainesville, Florida Living Motivated by his desire to become an architect and his mathematical and scientific skills, Shaun pursued an undergraduate degree in civil engineering at the University of Florida. While completing his degree, Shaun gained an intense interest in water res engineering under the advisement of Dr. Don Slinn. During this work, Shaun learned a major tool of a modern coastal engineer numerical modeling. He studied storm surge contr ibutions from wave and mass flux effects by coupling a wave model to a stand alone storm surge model. Shaun found this work to be very fulfilling because it factored into better coastal design standards and evacuation plans that would help the many people affected when hurricanes ravaged coastal communities across the United States and the world. under the advisement of Dr. Peter Adams. Here, Shaun broadened his numerical modeling skills while incorporating field research into his research. The focus of his research was the influence of wave energy dissipation on the geomorphic behavior of coastlines. Under this large scientific umbrella, many processes operate beach an d bar morphodynamics, wave transformations, mechanical abrasio n on sea cliffs and Shaun thoroughly enjoyed learning the controlling mechanisms of coastal evolution across different environments and timescales.

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150 Shaun truly hope d his work benefit ed earth science research and can be built scientists. Ultimately, Shaun wa s satisfied with any da y spent completing work that directly (or indirectly) help ed people and society as a whole.