• TABLE OF CONTENTS
HIDE
 Cover
 Report documentation page
 Title Page
 Acknowledgement
 Table of Contents
 List of Figures
 Abstract
 Introduction
 Estimates of eustatic seal level...
 Compaction effects
 Tidal range effects
 Storm surge and wind-wave...
 Interaction with natural features...
 Shoreline responce modeling
 Saltwater intrusion
 Upriver saltwater penetration
 Coastal ecosystems
 Summary of research needs
 Bibliography






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 87/012
Title: Some considerations on coastal processes relevant to sea level rise
CITATION DOWNLOADS PAGE IMAGE ZOOMABLE
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Permanent Link: http://ufdc.ufl.edu/UF00076154/00001
 Material Information
Title: Some considerations on coastal processes relevant to sea level rise
Series Title: UFLCOEL
Physical Description: x, 177 p. : ill. ; 28 cm.
Language: English
Creator: Mehta, A. J ( Ashish Jayant ), 1944-
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal and Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1987
 Subjects
Subject: Coast changes -- Mathematical models   ( lcsh )
Saltwater encroachment   ( lcsh )
Beach erosion   ( lcsh )
Coast changes   ( lcsh )
Coastal and Oceanographic Engineering thesis M.S
Coastal and Oceanographic Engineering -- Dissertations, Academic -- UF
Genre: bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by Ashish J. Mehta ... et al.
General Note: "September 1987."
General Note: Sponsoring organization: Oak Ridge National Laboratory.
Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
 Record Information
Bibliographic ID: UF00076154
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: oclc - 24562103

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Table of Contents
    Cover
        Cover
    Report documentation page
        Unnumbered ( 2 )
    Title Page
        Title Page
    Acknowledgement
        Acknowledgement
    Table of Contents
        Table of Contents 1
        Table of Contents 2
        Table of Contents 3
    List of Figures
        List of Figures 1
        List of Figures 2
        List of Figures 3
        List of Figures 4
    Abstract
        Abstract
    Introduction
        Page 1
        Page 2
        Page 3
    Estimates of eustatic seal level rise
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
    Compaction effects
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
    Tidal range effects
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
    Storm surge and wind-wave response
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
    Interaction with natural features and constructed works
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
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        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
    Shoreline responce modeling
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
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        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
    Saltwater intrusion
        Page 98
        Page 99
        Page 100
        Page 101
        Page 102
        Page 103
        Page 104
        Page 105
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        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
    Upriver saltwater penetration
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
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        Page 136
        Page 137
        Page 138
        Page 139
        Page 140
        Page 141
        Page 142
        Page 143
    Coastal ecosystems
        Page 144
        Page 145
        Page 146
        Page 147
        Page 148
    Summary of research needs
        Page 149
        Page 150
        Page 151
        Page 152
        Page 153
        Page 154
        Page 155
        Page 156
        Page 157
        Page 158
        Page 159
        Page 160
        Page 161
    Bibliography
        Page 162
        Page 163
        Page 164
        Page 165
        Page 166
        Page 167
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Full Text


UFL/COEL-87/012


SOME CONSIDERATIONS ON
COASTAL PROCESSES RELEVANT TO
SEA LEVEL RISE







BY

ASHISH J. MEHTA


ROBERT G. DEAN

WILLIAM R. DALLY

CLAY L. MONTAGUE




SEPTEMBER, 1987


Sponsor
Oak Ridge National Laboratory
P.O. Box X
Oak Ridge, TN 37831







REPORT DOCUMENTATION PAGE
1. Report No. 2. 3. ecipient's Acceosion No.


4, Title and Subtitle 3. Report Date
SOME CONSIDERATIONS ON COASTAL PROCESSES September 1987
RELEVANT TO SEA LEVEL RISE 6.

7. Author(s) 8. Performing Organization Report No.
Ashish J. Mehta Robert G. Dean
'UFL/COEL-87/012
William R. Dally Clay L. Montague
9. Performing Organization Name and Address 10. Project/Task/Work Unit No.
Coastal & Oceanographic Engineering Department
University of Florida 11. contract or Grant No.
336 Weil Hall 19X-SA690C
Gainesville, FL 32611 13. T ye of Report
12. Sponsoring Organization Nee and Address
Oak Ridge National Laboratory Final
P.O. Box X
Oak Ridge, TN 37831
14.
15. Supplementary Notes



16. Abstract
The effects of potential sea level rise on the shoreline and shore environment
have been briefly examined by considering the interactions between sea level rise and
relevant coastal processes. These interactions have been reviewed beginning with a
discussion of the need to reanalyze previous estimates of eustatic sea level rise and
compaction effects in water level measurement. This is followed by considerations on
sea level effects on coastal and estuarine tidal ranges, storm surge and water level
response, and interaction with natural and constructed shoreline features. The
desirability to reevaluate the well known Bruun Rule for estimating shoreline recession
has been noted. The mechanics of ground and surface water intrusion with reference to
sea level rise are then reviewed. This is followed by sedimentary processes in the
estuaries including wetland response. Finally comments are included on some probable
effects of sea level rise on coastal ecosystems.
These interactions are complex and lead to shoreline evolution (under a sea level
rise) which is highly site-specific. Models which determine shoreline change on the
basis of inundation of terrestrial topography without considering relevant coastal
processes are likely to lead to erroneous shoreline scenarios, particularly where the
shoreline is composed of erodible sedimentary material.
With some exceptions, present day knowledge of shoreline response to hydrodynamic
forcing is inadequate for long-term quantitative predictions. A series of inter-
related basic and applied research issues must be addressed in the coming decades to
determine shoreline response to sea level change with an acceptable degree of
confidence.
17. Originator's Key Words 18. Availability Statement
Coastal ecosystem Estuarine sedimentation
Coastal processes Salt water intrusion
Coastal structures Sea level rise
Coastal tides Shoreline evolution
Compaction Shore-structure interaction
19. U. S. Security Classif. of the Report 20. U. S. Security Classif. of This Page 21. No. of Pages 22. Price
Unclassified Unclassified 187










UFL/COEL-87/012


SOME CONSIDERATIONS ON
COASTAL PROCESSES RELEVANT TO
SEA LEVEL RISE




By


Ashish J. Mehta
Robert G. Dean
William R. Dally
Clay L. Montague


September, 1987

















Submitted to:
Oak Ridge National Laboratory
P.O. Box X
Oak Ridge, TN 37831










ACKNOWLEDGEMENTS


The authors acknowledge assistance provided throughout the study by
Robert M. Cushman of the Carbon Dioxide Information Analysis and Research
Program, Environmental Sciences Division at the Oak Ridge National Laboratory,
Oak Ridge, TN. Thanks are also due to Drs. Dag Nummedal, Ernest Estevez,
Louis Motz and Ray B. Krone for their helpful suggestions and discussions.
This study was conducted as a subcontract (No. 19X-SA690C) between Martin
Marietta Energy Systems, Inc., Oak Ridge and the University of Florida. The
research was sponsored by the Carbon Dioxide Research Division, Office of
Energy Research, U.S. Department of Energy, under Contract No.
DE-AC05-840R21400 with Martin Marietta Energy Systems, Inc.


L










TABLE OF CONTENTS

ACKNOWLEDGEMENTS ....................................................... ii

LIST OF TABLES ................................ ........... ...... .... v

LIST OF FIGURES.... ........... .............................. ....... .... vi

ABSTRACT...... .... .................................. ............ ...... x

1. INTRODUCTION.... ... ................. ............................... 1

2. ESTIMATES OF EUSTATIC SEA LEVEL RISE .................. .......... .. 4
2.1 INTRODUCTION.... ....................................... ..... .... 4
2.2 LITERATURE REVIEW.. ........................................ 5
2.3 THE NATURE AND ANALYSIS OF SEA LEVEL DATA..................... 13
2.4 RESEARCH NEEDS.. ............. ............................... 14
2.4.1 Use of Existing Data.......................... ........ 14
2.4.2 Need for New Data....................................... 15

3. COMPACTION EFFECTS.................................................. 20
3.1 INTRODUCTION.... ..... .... .............. ....... ................ .. 20
3.2 MEASURING COMPACTION.......................................... 21
3.3 IMPLICATIONS OF COMPACTION...................................... 24
3.4 REMEDIAL MEASURES..... .......................................... 24
3.5 EXAMPLES ................................ ............... ..... 25
3.6 RESEARCH NEEDS... ..... .. ..... ........ ................ .. ........ 26

4. TIDAL RANGE EFFECTS................................................. 30
4.1 INTRODUCTION.................................................. 30
4.2 LITERATURE REVIEW............................................. 30
4.3 PHYSICAL PRINCIPLES ............................................ 32
4.3.1 Tidal Propagation........................................ 32
4.3.2 Superelevation Effect.................................... 35
4.4 EXAMPLES............ ........................................... 36
4.5 RESEARCH NEEDS .................................. .............. 40

5. STORM SURGE AND WIND-WAVE RESPONSE. ................................. 42
5.1 INTRODUCTION....... ..................... .............. 42
5.2 STORM SURGE......................................... ......... 42
5.4 WAVE CHARACTERISTICS.............................................. 48
5.5 RESEARCH NEEDS ................................. ............. 50

6. INTERACTION WITH NATURAL FEATURES AND CONSTRUCTED WORKS............... 52
6.1 INTRODUCTION.................................................... 52
6.2 NATURAL FEATURES.................... ............................ 52
6.3 CONSTRUCTED WORKS ... ........................................... 58
6.4 COST OF COASTAL WORKS........................................... 72
6.5 RESEARCH NEEDS.................................................. 74

7. SHORELINE RESPONSE MODELING....... ........... ........................ 76
7.1 INTRODUCTION...... .............................................. 76
7.2 LITERATURE REVIEW........ ....................................... 76
7.3 PHYSICAL PRINCIPLES............................................. 90










7.3.1 Kinematic (Sediment Budget) Considerations.............. 90
7.3.2 Dynamical Considerations................................. 92
7.4 RESEARCH NEEDS ................................................. 94
7.4.1 Analysis of Existing Data................................ 94
7.4.2 New Data................................................. 96
7.4.3 New Technology.......................................... 97

8. SALTWATER INTRUSION......................... ..................... 98
8.1 INTRODUCTION..................... .......................... 98
8.2 LITERATURE REVIEW.............................................. 98
8.3 PHYSICAL PRINCIPLES AND SOLUTIONS TO IDEALIZED PROBLEMS......... 101
8.3.1 General...... ............ .............................. 101
8.3.2 Discharge through an Unconfined Aquifer.................. 104
8.3.3 Oceanic Islands............................................ 106
8.3.4 Upconing................................................. 107
8.3.5 Single Extraction Well Near a Coast..................... 108
8.3.6 Saltwater Barriers...................................... 108
8.4 CASE STUDIES.................................................. 108
8.4.1 Long Island, NY......................................... 110
8.4.2 Miami, FL................................ ........... ..... 110
8.4.3 Los Angeles, CA.. ....................................... 112
8.4.4 The Potomac-Raritan-Magothy Aquifer System............... 112
8.4.5 Okinawa-jima Island.................... .............. 113
8.5 RESEARCH NEEDS.............. ............ ..................... 113

9. UPRIVER SALTWATER PENETRATION........................................ 115
9.1 INTRODUCTION........ so.* .................................... 115
9.2 LITERATURE REVIEW.............................................. 116
9.3 PHYSICAL PRINCIPLES .......................... .... 117
9.4 EXAMPLES ........................................................ 122
9.5 RESEARCH NEEDS ............................................... 125

10. SEDIMENTARY PROCESSES IN THE ESTUARINE REGION................. ....... 126
10.1 INTRODUCTION .... ........ ................. .................... 126
10.2 SHORELINE CONFIGURATION.... .................................... 126
10.3 ESTUARINE SEDIMENTATION... ................................... 129
10.4 WETLAND RESPONSE.................... ......................... 136
10.5 RESEARCH NEEDS ............................................... 142

11. COASTAL ECOSYSTEMS.. .......... ........ .................... ........... 144
11.1 INTRODUCTION..... .................. ...... ..... ... ...... ....... 144
11.2 ECOSYSTEM RESPONSE.............................................. 144
11.3 RESEARCH NEEDS................................................ 146

12. SUMMARY OF RESEARCH NEEDS.......................................... 149

13. BIBLIOGRAPHY.. ........ ..... .. ... ..... .. .............................. 162










LIST OF TABLES


TABLE PAGE

2.1. Estimates of Eustatic Sea Level Rise Based on Tide Gage Data
(adapted from Barnett, 1983; and Hicks, 1978).................... 6

4.1. Representative Bay Superelevations (after Mehta and Philip,
1986)................................................. 36

4.2. Secular Trends in Mean Tidal Range in the German Bight (after
FUhrbBter and Jensen, 1985)....................................... 37

8.1. Methods for Controlling Saline Water Intrusion (after
Todd, 1980) ................. ....... .......... .. ....... ... ...... 99

10.1. Rates of Marsh Accretion and Relative Sea Level Rise (adapted
from Stevenson et al., 1986)....................... ............. 138

12.1. Estimates of Eustatic Sea Level Rise.............................. 152

12.2. Compaction Effects............. ................................ 153

12.3. Tidal Range Effects............................................... 154

12.4. Storm Surge and Wind-Wave Response............................... 155

12.5. Interaction with Natural Features and Constructed Works........... 156

12.6. Shoreline Response Modeling....................................... 157

12.7. Saltwater Intrusion........ .................. ...................... 158

12.8. Upriver Saltwater Penetration ............................... 159

12.9. Sedimentary Processes in the Estuarine Region...................... 160

12.10. Coastal Ecosystems ........... ...... ............................. 161


I










LIST OF FIGURES


FIGURE PAGE
2.1. Cross-Spectral Characteristics between Sea Level at San
Francisco and Honolulu: Yearly Data, 1905 through 1971 at San
Francisco and Beginning 1907 at Honolulu (after Sturges, 1987).... 7

2.2. Mean Annual Relative Sea Level Changes During 40 Year Record.
Lines Define Three Main Segments of East Coast with Differing
Sea Level Trends (after Aubrey and Emery, 1982)................... 8

2.3. Characteristics of Tide Gage Data by 30 Longitude and Latitude
Sectors. The Lower Values Represent the Number of Tide Gages in
Each Sector. The Upper (Signed) Numbers Represent the Linear
Long-Term Relative Sea Level Change Resulting from those Gages
(after Pirazzoli, 1986) .............................................. 10

2.4. Distribution by 50 Latitude Belts of a) Tide Gage Stations, and
b) Median Values of Linear Long-Term Trends of Relative Sea Level.
Note the Tendency for a Relative Drop in Sea Level for the Higher
Latitudes (after Pirazzoli, 1986).............................. .. 10

2.5. Long-Term Tide Gage Trend Results, n, versus Latitude, <.
Continental United States and Alaska. Based on Hicks et al.
(1983)...................................................... ... 12

2.6. Average Annual Sea Level Variations for Pensacola, Florida
(adapted from Hicks et al., 1983)................................... 16

2.7. Use of Two Compacting Gages to Obtain Compaction Distribution
over Depth Zones hA, hB, and hB-h................................ 18

3.1. Results of Centrifuge-aided Compaction in Comparison to Two
Theories (after Schiffman et al., 1985)........................... 22

3.2. Device for Monitoring Compaction and Groundwater Elevation
(after Murayama, 1970)................................ ...... ... 23

3.3. Isolines of Total Subsidence (in cm) from 1935-1968 in Osaka,
Japan (after Murayama, 1970)...................................... 26

3.4. Monthly Record of a) Groundwater Level and b) Rate of Subsidence
in Osaka, Japan (after Murayama, 1970)............................ 27

4.1. Tidal Wave Envelope in an Estuary in which the Wave is Reflected
at the Upstream Closed End................. ........................... 34

4.2. Locations of Four Tide Gages in the German Bight.................. 34

4.3. Response of a Shallow Inlet/Deep Bay System to Sea Level Rise:
Changes in Mean Bay Level and Tidal Amplitudes (based on
computations by Mann, 1987)....................................... 39


I










5.1. Measured Storm Surge in Galveston, Texas Area during Hurricane
Carla (adapted from Army Corps of Engineers, 1984)................. 43

5.2. Isolines of Non-Dimensional Significant Wave Height for
Hurricane-generated Wind-waves (after Bretschneider, 1959)........ 44

5.3. Idealized Geometries for the Continental Shelf: a) Uniform Depth,
b) Uniform Slope................................................ 45

6.1. Historical Shoreline Changes at the Isles Dernieres, Mississippi
(after Penland et al., 1985)...................................... 54

6.2. The Shoal System at Cape Canaveral, Florida (after Field and
Duane, 1974) ... ................. ................... ..... ........... 55

6.3. Bathymetric Chart of Nassau Sound, Florida Showing Ebb Shoals.
Depths are in Feet (from NOS Nautical Chart 11489)................ 57

6.4. Shoreline Between Two Headlands at Wreck Bay, Vancouver Island,
with Observed Wave Patterns (after Bremmer and LeBlond, 1974)..... 59

6.5. Examples of Design Cross-sections for Sea Dikes (after Kramer,
1971) ..... ........ ............ ....... ........ .... ..... ........... 61

6.6. Shoreline of Holland if There Were No Dikes, Showing a 50% Loss
in Land Area (after Lingsma, 1966)................................ 63

6.7. Typical Cross-sections of a) Seawall, b) Bulkhead and
c) Revetment (adapted from Shore Protection Manual, U.S. Army
Corps of Engineers 1984)........................... .............. 64

6.8. Planview of the Galveston Seawall (after Davis, 1952)............. 65

6.9. Breakwater Project and Shoreline Response at Presque Isle,
Pennsylvania...................................... ..........**.** 67

6.10. Groin Field at Long Branch, New Jersey (after Army Corps of
Engineers, 1964).......................... ....... ........ ......... 69

6.11. Shoreline Response to Jetty Construction at Ocean City, Maryland
(after Dean et al., 1979).................................. ....... 71

6.12. Beach Nourishment Project at Harrison County, Mississippi (after
Army Corps of Engineers, 1984) ................................. ... 73

7.1. The Rise of Sea Level as Obtained from Carbon 14 Dates in
Relatively Stable Areas (after Shepard, 1963). Break in Slope
some 6000 Years BP may have Provided Basis for Barrier Island
Stability........................... ............. ............. ..... 77

7.2. Components of Sand Volume Balance Due to Sea Level Rise and
Associated Profile Retreat According to Bruun Rule................ 79










7.3. The Bruun Rule with Only Seaward Transport of Sediment and
Trailing Ramp Seaward of Active Profile........................... 80

7.4. Comparison of Predicted and Measured Shoreline Changes Due to
Water Level Increases, Eastern Shore of Lake Michigan (after
Hands, 1983) .................................................. ... 80

7.5. Generalized Shoreline Response Model Due to Sea Level Rise.
Applicable for a Barrier Island System which Maintains its Form
Relative to the Adjacent Ocean and Lagoon (after Dean and
Maurmeyer, 1983).................................................. 83

7.6. The Role of Shoreward Sediment Transport, Qs, Across the Shelf
and Rate of Sea Level Rise in Causing Barrier Island Formation
(after Dean, 1987)................................................ 85

7.7. Possible Mechanism of Sedimentary Equilibrium (after Dean, 1987). 87

7.8. Effect of Cutting Entrance to St. Andrews Bay in 1934 on
Downdrift Shoreline (after Dean, 1987)............................ 88

7.9. Effects of Establishment of Cape Canaveral Entrance and Subsequent
Nourishment Project on Downdrift Beaches (after Dean, 1987)....... 89

7.10. Dominant Forces Acting on a Sediment Particle Resting on the
Bottom............ .......................................... ...... 93

7.11. Isolines of Non-dimensional Average Bottom Shear Stress T'
Relative Depth h/Lo, and Wave Steepness, H/Lo (after Dean,
1987)............................................................. 95

8.1. Example of Unconfined and Confined Aquifers....................... 100

8.2. Balance between Fresh Water and Salt Water in a Coastal Aquifer
in which the Salt Water is Static (after Cooper, 1964)............ 102

8.3. Circulation of Salt Water from the Sea to the Zone of Diffusion
and Back to the Sea (after Cooper, 1964).......................... 102

8.4. Idealized Characteristics for Unconfined Flow to a Shoreline
(after Glover, 1964).............................................. 105

8.5. Effect of Sea Level Rise on Equilibrium Groundwater, Highly
Exaggerated Vertical Scale.................................. ...... 105

8.6. Freshwater Lens Under a Circular Oceanic Island Under Natural
Conditions (after Todd, 1980)..................................... 107

8.7. Flow to a Single Well Along a Seacoast............................ 109

8.8 Profile through Aquifer at Far Rockaway, Nassau County, Long
Island, Showing Location of Salinity Front as a Result of Pumping
(after Todd, 1980)................................................ 111


viii


i










8.9. Progressive Saltwater Intrusion in the Vicinity of Miami, FL,
1904 to 1959 (after Todd, 1980)..................... ............ ... 111

8.10. Piezometric Pressure Profiles Perpendicular to the Seawater
Intrusion Barrier in Los Angeles County for Various Times after
Commencement of Injection in the Fall of 1963 (after Todd,
1980) .............. *.0........... ............... ...... ........... 112

9.1. Mechanism of Salt Penetration: a) Development of a Gravity
Current, b) Arrested Saline Wedge................................ 119

9.2. Monthly Salinity (ppt) Distribution in Cumbarjua Canal, Goa,
India; -- Ebb; ---- Flood (after Rao et al., 1976).............. 119

9.3. Longitudinal Salinity Distribution in a Model Tidal Channel:
a) Test No. 2, b) Test No. 16 (after Harleman and Abrahams,
1966) .................. ......... ................... *.. ........... 121

9.4. Salinity (Chlorinity) Variation with Years in Lake Maracaibo
(after Partheniades, 1966)......................... ................. 121

9.5. High and Low Water Salinity Profiles through St. Marys Entrance,
Florida and Cumberland Sound, Georgia (after Parchure, 1982)...... 124

9.6. Effect of Channel Deepening on the Duration of Wedge Intrusion in
the Lower Mississippi River (after Johnson et al., 1987).......... 124

10.1. East Frisian Islands in 1750 and in 1960 (after Kunz, 1987)....... 130

10.2. Sediment Transport in the Estuarine Mixing Zone................... 130

10.3. Time-Rate of Subaerial Land Growth in Atchafalaya Bay, Louisiana,
Calculated by Different Approaches (after McAnally et al.,
1984)......................................... ....... .... .. .. 135

10.4. Time-History of Bottom Sediment Movement in Savannah Harbor
Estuary, Georgia (after Ariathurai, et al., 1977)................. 135

10.5. Relationship between Sea Level Rise and Marsh Level Rise Rates
(based on data compiled by Stevenson et al., 1986)................ 139

10.6. Marsh Evolution with Sea level Rise (after Titus, 1986)........... 139

10.7. Effect of Suspension Concentration on Marsh Elevation Rise and
Sea Level (after Krone, 1985)................ *..*................. 142










ABSTRACT


The effects of potential sea level rise on the shoreline and shore
environment have been briefly examined by considering the interactions between
sea level rise and relevant coastal processes. These interactions have been
reviewed beginning with a discussion of the need to reanalyze previous
estimates of eustatic sea level rise and compaction effects in water level
measurement. This is followed by considerations on sea level effects on
coastal and estuarine tidal ranges, storm surge and water level response, and
interaction with natural and constructed shoreline features. The desirability
to reevaluate the well known Bruun Rule for estimating shoreline recession has
been noted. The mechanics of ground and surface water intrusion with
reference to sea level rise are then reviewed. This is followed by
sedimentary processes in the estuaries including wetland response. Finally
comments are included on some probable effects of sea level rise on coastal
ecosystems.

These interactions are complex and lead to shoreline evolution (under a
sea level rise) which is highly site-specific. Models which determine
shoreline change on the basis of inundation of terrestrial topography without
considering relevant coastal processes are likely to lead to erroneous
shoreline scenarios, particularly where the shoreline is composed of erodible
sedimentary material.

With some exceptions, present day knowledge of shoreline response to
hydrodynamic forcing is inadequate for long-term quantitative predictions. A
series of inter-related basic and applied research issues must be addressed in
the coming decades to determine shoreline response to sea level change with an
acceptable degree of confidence.










1. INTRODUCTION


The complexities of shoreline response to sea level rise are contingent
upon a very wide range of inter-relationships between physical/ecological
factors. The focus of resource analysis for the present purpose must
ultimately be on predictive capability, since we are principally dealing with
the question of how shorelines and shore environment will change with future
sea level rise. Prediction in turn requires an understanding of process
fundamentals and adequate data. Therefore, much of what follows pertains to
these aspects, which in many cases have more to do with the basics of resource
response to hydrodynamic and meteorologic forcing than to sea level rise. If
this can be elucidated, then imposing and evaluating the effect of sea level
rise becomes a far less difficult task.

Organization of basic knowledge is intertwined with the question of
resolution of spatial and temporal scales. The desired resolution for the
evaluation of a resource is set by criteria which are dependent upon many non-
technical factors. At a built-up shoreline, a 10 m recession could severely
damage a structure, while at a natural shoreline the concerns will be less
stringent. Then again, in low lying areas such as the Florida Everglades,
just a few centimeter rise in sea level would prove to be disastrous to water
management, and would cause extensive ecological changes associated with
salinity intrusion. A rapidly rising sea level can generate a materially
different response than a slow one, an example being the fragile barrier
island shoreline. Finally, there is the question of absolute sea level rise
and the associated shoreline scenarios. By keeping the issues focused on the
coastal processes themselves, we have in the most part stayed clear of
centering on specific temporal and spatial scales explicitly, even though such
considerations are inherent in evaluating the degree of uncertainty in the

state-of-the-art knowledge and in future research needs.

The interactive nature of coastal processes renders it difficult to
isolate resource issues and place them under well-defined "umbrellas" for
descriptive purposes. We have selected ten headings (sections 2 through 11)
within which a range of topics has been referenced. The first of these -
Estimates of Eustatic Sea Level Rise does not deal with process description
in a general way, but highlights a fundamental issue, namely the quality of


I










the data base that has been used to calculate past secular trends in sea level
change, and what needs to be done to improve this base. Following this is the
section Compaction Effects, which is directly associated with problems in
water level measurement.

Sections 4 though 11 deal with coastal processes. In section 4 the
effect of sea level rise on tidal ranges is discussed, and section 5 deals
with non-astronomical factors including storm surge and waves. The next two
sections are concerned with shoreline response. While section 6 deals with
physical processes in shoreline response in broad categories, section 7
focuses on specific issues relative to the scope and limitations of the well
known Bruun Rule for estimating shoreline recession rate. Physical
considerations upon which this rule must be re-examined have been noted.

Section 8 describes problems with saltwater intrusion in groundwater as a
result of sea level rise or analogous effects, while the same problem in
surface waters is highlighted in section 9. Sedimentation problems in tidal
entrances, estuarine mixing zone and wetlands is described in section 10.
Finally, ecological changes, including research needed to quantify these
better, have been noted in section 11.

Some overlap between the various sections is inevitable. This extends to
both the physical description and research needs. Also, by and large, the
coastal processes have been reviewed from an engineering perspective, and
evaluation of present day knowledge has been made from the viewpoint of the
availability of quantitative (as opposed to qualitative) criteria.

In general it appears that with the possible exception of tidal
hydrodynamics and salinity intrusion, considerable further research is
required for assessing shoreline and shore environmental response in a
confident manner. Strides made during the past decade have been impressive,
but for example where sediment transport is a key factor, we are significantly
limited in long-term predictive capability. This is partly due to the lack of
good quality synoptic hydrodynamic/meteorologic data. This problem in turn
has an impact on ecological modeling, which is contingent upon a knowledge of
flows and sediment movement.

Section 12 is essentially a summary of future research needs. There is a
table for each of the ten broad research issues described in sections 2










through 11. A special issue ranking procedure has been used for the ultimate
purpose of a numerical ranking of research areas in terms of their importance
to the sea level rise problem.

Bibliography is contained in section 13. Division is by sections. In
some cases, additional references not cited in the text, but considered to be
of potential interest to the reader, have been included.









2. ESTIMATES OF EUSTATIC SEA LEVEL RISE


2.1 INTRODUCTION

Eustatic sea level rise is the global average sea level rise primarily
due to: 1) additional water mass in the oceans through release of water
contained in polar ice caps and alpine glaciers, and 2) steric expansion of
water presently in the oceans due to increased temperature, thereby increasing
the volume of an existing water mass. Sea level change data from 20,000 years
before present (BP) to 1,000 years BP have been obtained from radiometric
dating of plants and animals that lived only in intertidal or shallow marine
waters. Data from the last 100 or so years are based on measurements from
long-term tide gages. Both of these sources include not only the "signal" of
eustatic sea level change, but the "noise" or contamination by local vertical
movement of the land where the measurements are made. Additionally, local and
temporal oceanographic and meteorological factors may contribute to
anomalously high or low water levels for periods of many years. The degree of
contamination in any one tide gage record may be severe with the annual
contamination exceeding up to 40 years of eustatic trend. Much of the
contamination is spatially and temporally coherent over fairly long distance
and time scales and the physics of this contamination is poorly understood.
If the available tide gage data provided a representative distribution over
the world's oceans, the noise could be eliminated by simply averaging over
these gages. However, the available tide gage data are heavily concentrated
in the northern hemisphere and along continental margins.

Tide gages measure the local relative sea level which is important and is
the water level relevant to that area. However, an understanding of recent
eustatic sea level rise is critical, because models developed for predicting
future sea level rise are calibrated based on estimates of recent rise. Most
of these estimates suggest a rate of 10-15 cm/century (1 to 1.5 mm/yr) with
some investigators inferring an increase in the rate of rise over the past 40
or so years. Most of the studies leading to the above estimates have been
based on gages located in reasonably stable low- to mid-latitude areas.
Clearly the most significant neotectonic contribution to relative sea level
rise is the earth's rebound from the ice loading in the polar regions during
the last (Wisconsin) ice age. This rebound is causing uplift in the high










latitudes on the order of 1 meter per century and land subsidence at the lower
latitudes on the order of 5 cm per century. There have been suggestions that
most of the studies of eustatic rates, in excluding the high latitudes of
relatively rapid uplift, have yielded overestimates. A very preliminary
analysis presented here based on United States data tends to support this
contention.

Areas in which future studies appear warranted include: 1) understanding
the physics of the noise in tide gage records with the objective of extracting
this portion of the record, 2) revisiting the question of extracting recent
eustatic sea level rise rates from the tide gage records with an emphasis on
proper recognition of the contribution from glacial rebound at all latitudes,
and 3) if the changes resulting from 2 are significant, recalibrating the
models employed for predicting future sea level rise based on scenarios of
future changes in C02, other trace gases and a gradual warming trend.


2.2 LITERATURE REVIEW

There has been a wide range of techniques and degree of sophistication
applied in an attempt to extract eustatic sea level (ESLR) rise from tide gage
records. One of the first comprehensive published studies on ESLR based on
tide gages was by Gutenberg (1941). A total of 69 gages was analyzed
encompassing the period 1807 to 1937. Gutenberg excluded tide gages known to
be in areas of crustal uplift, yet gages were included in areas known to be
sinking, some at fairly high rates. Gutenberg concluded that ESLR was
approximately 1 mm per year.

Many investigations following those of Gutenberg have tended to adopt his
data selection procedures with similar results, i'.e. rates of 1 to 1.5 mm/yr,
see Table 2.1. Emery (1980) concluded that ESLR has been accelerating with a
rate up to 3 mm/yr over the past 40 years. Subsequent studies by Aubrey and
Emery (1983) and Barnett (1983) conducted specifically to examine the change
in rate concluded there was no convincing evidence for such a conclusion.

The difficulties of extracting the sea level rise (SLR) "signal" from a
record containing substantial noise has been studied carefully by Sturges
(1987). The coherency of spatially separated tide gage records was
investigated with the hypothesis that coherent signals with no lag could be
interpreted as global sea level rise whereas lags with a certain character


I










Table 2.1. Estimates of Eustatic Sea Level Rise Based on Tide Gage Data
(adapted from Barnett, 1983; and Hicks, 1978)



Author(s) Estimate
(cm/100 yr)

Thorarinsson (1940) > 5
Gutenberg (1941) 11 8
Kuenen (1950) 12 to 14
Lisitzin (1958) 11.2 3.6
Fairbridge and Krebs (1962) 12
Hicks (1978) 15 (U.S. only)
Emery (1980) 30
Gornitz et al. (1982) 12 (10 cm excluding long-term trend)
Barnett (1983) 15



could be interpreted as due to atmospheric forcing or long water wave (Rossby
wave) motions. As an example, the records at San Francisco and Honolulu were
found to be coherent at periods of 5 to 10 years and longer, although with a
phase lag. A comparison of the energy spectra obtained from these two
stations is presented as Fig. 2.1a and other spectral information is presented
in Figs. 2.1b,c,d. The amplitudes of these coherent components are 5-15 cm.
Similar coherence results were found for tide gage records located on both
sides of the Atlantic. Sturges concluded that the available records are
contaminated by substantial energy with periods up to 40 to 50 years, thus
exacerbating the problem of identifying any change in the rate of SLR. The
ability to extract the SLR signal may possibly be enhanced through an analysis
which recognizes the probable cause of the noise components, thereby guiding
their removal from the record.

Aubrey and Emery (1983) applied the method of eigenanalysis to United
States tide gage data in an attempt to identify fluctuations that were
spatially and temporally coherent. This method, among the most sophisticated
applied to date, has the potential advantage of retaining in the first few
temporal eigenfunctions, those fluctuations that have the same form and that
are either exactly in or exactly out of phase. The principal disadvantage is
that the method is purely statistical and does not recognize the physics of
the phenomenon, although it may isolate features that will assist in
identifying physical components. A particular drawback is that the method








PERIOD,years
101


2 80


UJ 0
o) 60
cox
40

ZE
Lu -20
0
uJ
m 0
u. 1(


10 1
FREQUENCY,cycles/year
c) Coherence Squared


100


10 2
100 l


1111 II I 1111 II I I I
SSan Francisco







J"

Honolulu
I I s I ar t Ie Iss I


-100L
10


100


100


PERIOD,years
101


10 -1
FREQUENCY,cycles/year


10 2


100












-_
100
100


Phase Spectra with 90% Confidence Intervals
PERIOD,years
102 101 100


0 0o
u 10
z
O'
0.
c)
UI

a
n-

W

SU
Sln"


100


10-2 10 -1 100
FREQUENCY,cycles/year
Frequency Response Function, Honolulu to San
Francisco


Fig. 2.1. Cross-Spectral Characteristics between Sea Level at San Francisco and Honolulu: Yearly Data, 1905
through 1971 at San Francisco and Beginning 1907 at Honolulu (after Sturges, 1987).


0
0
z
'O
In

z2
o m
m m
0
m
Z
m
<
I-


-90


0-2


10-1
FREQUENCY,cycles/year

a) Energy Spectra

PERIOD,years
101


10
1.00


0.75


0.50


0.25


0.00
10


I II I I I -- 1111111 I I

-




~

I- II I I I II


2


-2


-2
1 : ________


I









only recognizes correlations which are either in phase or exactly out of phase
as "signal". Thus a very long and slowly propagating wave would be rejected
as noise whereas a pure standing wave would be recognized as "signal". Aubrey
and Emery first applied the technique to 12 U.S. gages each of which
encompassed 61 years of data and secondly to 41 tide gages with a common time
base of 40 years of data. Different rates of rise were found for the East and
West coasts. From the longer term data set of 12 stations, the eustatic
values on the West and East coasts were found to be rising by averages of 1.4
mm/year and 1.3 mm/year, respectively. For the shorter term (40 years) of 41
stations, the rates of change for West and East coasts were -0.3 mm/yr and
+2.5 mm/yr, respectively. It was found that the long-term rates of sea level
rise are increasing from Cedar Key on the Florida west coast to Cape Hatteras,
decreasing from Cape Hatteras to Cape Cod and increasing from Cape Cod to
Eastport, Maine. These results are presented in Fig. 2.2. Finally, it was
concluded that there is no evidence from this analysis that rates of SLR are
increasing over the past 10 years.

Pirazzoli (1986) has analyzed the results from 1,178 tide gage stations
provided primarily by the Permanent Service for Mean Sea Level. This appears
to be the largest data set considered in an individual analysis. The analysis
method was straightforward, first taking averages for each station over five


LU 0.4 RK tIo AC YSH
> Cedar Key to Eastport Ph *NY

I- 0.3- S.As Pda 0
nE en Pd
0.2 Mt I z
Ew U K Fa N Ph
S0.O Bn
u 0

c100
w


C 200
0 500 1000 1500 1800
KILOMETERS

Fig. 2.2. Mean Annual Relative Sea Level Changes During 40 Year Record.
Lines Define Three Main Segments of East Coast with Differing Sea
Level Trends (after Aubrey and Emery, 1983).










year periods, then averaging over the two ends of the resulting data to obtain
a change in sea level from which the rate is determined. The results are
presented regionally and on a global basis. The effects of glacio-eustatic
adjustment to the last ice age are very apparent in the data with relative sea
level (RSL) rising and lowering in most low and high latitudes, respectively.
The possible effects of earthquakes in causing sudden displacements and
altering the trend after the earthquake are illustrated. As an example, the
tide gage at Messina, Italy recorded an abrupt increase in RSL of 57 cm during
the earthquake of 1908. Anthropogenic effects, primarily the extraction of
water and hydrocarbons, causing compaction are noted with Venice, Italy
particularly evident as a consequence of ground water pumping. In attempting
to infer global rates from the available data, it is noted that if the earth
is divided into 30 latitude and longitude sectors, a total of 72 compartments
result of which 71 have marine coasts. The data distribution in these
compartments is very non-uniform. Most of the tide gages (70%) are situated
in only 4 compartments whereas there are no data in 70% of the compartments.
Long-term tide gage data in the southern hemisphere are particularly sparse
with over 97% of the stations examined by Pirazzoli in the northern
hemisphere. Without the assumption that the results from the northern
hemisphere are globally representative, the available data are clearly
inadequate. Fig. 2.3 presents a distribution of the tide gage locations
according to the longitude-latitude compartments noted earlier. Fig. 2.4,
also from Pirazzoli, presents the distribution of tide gages and median trend
of RSL by 5 increments of latitude. The earlier noted effect of relative
rises in the mid-latitudes and lowering RSL in the higher latitudes is
evident.

Pirazzoli concludes that the results presented by most investigators (( 1
mm/yr) probably are an overestimation of the ESLR. Local and regional factors
including tectonic movements and oceanic factors are generally larger than
eustatic factors. The bias due to downwarping as a result of loading of the
continental shelves by sediment transport and deposition is noted. Finally,
when centimeter accuracy is attainable from satellite altimetry, the potential
to contour the open ocean is regarded as a major advance in our general
knowledge of eustatic sea level rise rates which have both good geographic
coverage and are free from much of the contamination which attends
measurements of tide gages located along the coastline.


I







LONGITUDE (deg)
180 120 60 0 60


Characteristics of Tide Gage Data by 300
Sectors. The Lower Values Represent the
Each Sector. The Upper (Signed) Numbers


Longitude
Number of
Represent


and Latitude
Tide Gages in
the Linear Long-


Term Relative Sea Level Change Resulting from those Gages (after
Pirazzoli, 1986).


NUMBER OF STATIONS

0 10 20 30 40
| i t


0'
I- ~
-J


MEDIAN TREND
OF RSL(mm/yr)
-6 -4 -2 0 2

drop re


-600



-30



-00



-300


Distribution by 50 Latitude Belts of a) Tide Gage Stations, and b)
Median Values of Linear Long-Term Trends of Relative Sea Level.
Note the Tendency for a Relative Drop in Sea Level for the Higher
Latitudes (after Pirazzoli, 1986).


120 180


660


3 0
w
0
I-.
- 30

- 60


Fig. 2.3.


Fig. 2.4.


+5.5 .-57
25.
-2 -0.2+2.6 0.0 18 +6.523 +3.6
17 5 32 1 17 85 1 10
+0.7 +5.9+3C +1.6 +33+06+5.0+1.8
1 3 1/ 7 5., 2


+0.1 0 51.3
3 1 2
a I 2Sk.


ww









Lambeck and Nakiboglu (1984) have carried out an analysis of the effect
of post-glacial adjustment on estimates of ESLR. For this purpose, a viscous
model of the earth was adopted with the assumption of a uniform mantle
viscosity. To quantify the effect of rebound on estimates of ELSR as
determined from tide gage records, the apparent or RSL rises predicted by the
model without any additional water mass or steric changes were computed for
the same eight long-term tide gage'stations selected by Barnett (1983). Two
values of viscosity, V, were used: Model 1, P = 5x1021p and Model 2, P =
1022p. for the eight stations, Models 1 and 2 predicted apparent (relative)
sea level rises of 0.5 and 0.8 mm/yr, respectively whereas Barnett found
1.5 mm/yr. Based on this comparison, Lambeck and Nakiboglu conclude that the
post-glacial rebound contribution may be as high as 30% to 50% of published
estimates of ESLR.

A limited analysis has been carried out here to attempt to determine the
effects of employing only the lower latitude tide gate data. The U.S. data
for the East and West coasts and Gulf of Mexico as published by Hicks et al.
(1983) were used. The trend estimates in Hicks et al. were simply plotted
against latitude as presented in Fig. 2.5. A problem is that the data only
encompass latitudes from approximately 250 to 580 and thus it is necessary to
extrapolate liberally. At the lower latitudes, the data were extrapolated
uniformly at approximately 3.2 mm/yr and at the higher latitudes, due to the
uncertainties, two extrapolations were adopted to determine sensitivity as
presented in Fig. 2.5. Based on the latitudinal variation, in(), estimates of
the ESLR, nE, were based on the following

/2 .
\E j 0 f n.(4) cos) d( (2.1)
j 0

where j = I,II represents the different high latitude extrapolations. The
resulting values were


*E = 0.32 mm/yr, Extrapolation I

E1 = 0.67 mm/yr, Extrapolation II


These results are qualitatively in agreement with those of Lambeck and
Nakiboglu.


























--------

\ Extrapolation II

Extrapolation I \
\


E



zE





I-
-1 0









w
n-
-)



LU

_J
<)


10 20 30


40 50


70 80


LATITUDE, 6 (0)


Long-Term Tide Gage Trend Results, n, versus Latitude, <. Continental United States and Alaska.
Based on Hicks et al. (1983).


+10


0 East Coast Gages
- A Gulf of Mexico Gages
West Coast Gages


I' *


-20 L
0


Fig. 2.5.


I II












2.3 THE NATURE AND ANALYSIS OF SEA LEVEL DATA


From the standpoint of extracting eustatic sea level change, it is useful
to represent the total RSL, ni(t), as measured by the ith tide gage as


ni(t) = E(t) + nNi(t) (2.2)


in which nE(t) is the eustatic sea level at time t and lNi(t) is the total
"noise" at the ith tide gage. The noise can contain many components including
vertical ground motion, effects of freshwater in the vicinity of the gage,
coastal currents, long waves, barometric pressure anomalies, wave effects,
etc. Several obvious results follow from Eq. 2.2. First, if there were a
uniform coverage of tide gages on the oceans, an average of the elevations
from all such tide gages would yield the eustatic sea level. Additionally,
the eustatic sea level change rate need not be constant, but could vary
substantially year-to-year with temperature, etc. Considering two or more
tide gages, the noise may be correlated in space and time positively,
negatively, with an arbitrary phase or uncorrelated. The more widely
separated the gages, the greater the likelihood that the noise will be
uncorrelated. Thus, there are advantages to averaging many records along a
coast, possibly with an appropriate coastal length weighting factor. Finally,
the best estimate of eustatic sea level (and thus eustatic sea level rise) and
one which yields the most understanding as to the stability of the results is
a progressive averaging in which larger and larger data bases are averaged,
i.e.
IK
I n(t)wi
i=1
IK(t) IK =(2.3)
I wi
i=l1
where wi is a distance weighting factor and IK is the total number of gages
along a selected coastal segment, perhaps a continent. The worldwide estimate
of eustatic sea level, E(t) could then be obtained by averaging over all
available coastal segments

S IKTOTAL
nE(t) = KTOTA K(t) (2.4)
IK=I










Other ways of extracting meaningful information relating to post-glacial
rebound could include averaging first over longitude for certain increments of
latitude.


2.4 RESEARCH NEEDS

In general, improvements in our understanding of eustatic sea level
change can come about through use of the existing data base or development of
new data. Extraction of more meaningful results from the existing data base
will require either more powerful analysis procedures or an improved under-
standing and application of the physics of relative sea level change,
including the noise present in the records. Enhancement of the existing data
base through new measurements will most likely occur through satellite
altimetry once this is proven to centimeter accuracy over the open ocean.
Additionally, in some cases much can be learned locally about anthropogen-
ically generated compaction in areas of tide gages through the installation of
rather simple compaction measurement devices. One feature of new data is the
length of time that will be required for such data to "mature" to yield
significant meaningful information.


2.4.1 Use of Existing Data

Analysis in light of the physics of RSL change appears to be the most
effective and productive use of existing data. In particular, accounting for
the contribution of long period waves as explored by Sturges (1987) would
allow interpretation and removal of a major portion of the noise in the RSL
measurements.

A second productive area is a more thorough analysis than presented
previously of the contribution of post-glacial adjustment of the earth
following the last ice age. As noted previously, Lambeck and Nakiboglu (1984)
have inferred from viscous models of the earth that the actual eustatic rise
is roughly one-half to two-thirds the value determined from analysis of
records based only on areas of relative stability. Improved estimates of
eustatic sea level rise could be based on either a more inclusive data set
with or without the use of a viscous earth model. Obviously more meaningful
results could be obtained with the combined approaches simultaneously. The
approach envisioned here is in general the same as applied in "physical









principles" with the addition that the global viscous model would be employed
for interpretation, guidance and confirmation of the results obtained.

Most approaches of direct analysis attempt to reduce the noise in a
record on a station-by-station basis through determining some sort of RSL
estimate through fitting to the data. Unfortunately, the noise in individual
records is such that at least 20 to 40 years of data must be available at the
individual gages before these results can be considered meaningful. An
approach that would make these results meaningful early after their
availability is the weighted averaging of many stations along a coastline to
establish a more stable value. This averaging length could encompass, for
example, the North American or North and South American shoreline(s). Thus,
if a wave with length exceeding the expanse of the stations encompassed were
contributing to the "noise", this process would tend to reduce or (in the very
fortuitous cases) eliminate its contribution. By first averaging over long
segments of the shoreline, weighting each station by its alongshore influence
length, then combining appropriately the results for various such shoreline
segments, a much more stable year by year value could be obtained, i.e.
Eqs. 2.3 and 2.4. This would allow effective use of such data as are
available for the east coast of South America where eight of the twelve
available gages are less than 30 years in duration. As is evident from Fig.
2.6 which presents the mean annual sea level variation of Pensacola, Florida,
30 years is not adequate to obtain a stable estimate from an individual gage.


2.4.2 Need for New Data

There are two types of new data that would contribute to improved
estimates of ESLR: those that contribute immediately and those that would
require a data base of at least several years before meaningful results could
be obtained. It is anticipated that even with the potential benefits of
satellite altimetry, at least one decade and possibly two decades will be
required before adequate confidence will be placed in these data to yield
accepted reliable estimates of eustatic sea level rise. Three research needs
in the category of "new data" are described below.

Compaction Gages As is well-documented by a number of studies,
withdrawal of ground water and hydrocarbons can contribute to substantial
subsidence and thereby a "relative sea level rise" (see also section 2 for a























3.0 I I i I I I
Yearly Mean Sea Level Station No. 8729840
Pensacola, FL

I 2.0

z
O -

> 1.0-


STrend Line of 0.3m per Century
(for Comparison Purposes)
0.0 -- I I I 1 I I
1850 1865 1880 1895 1910 1925 1940 1955 1970 1985
YEAR




Fig. 2.6. Average Annual Sea Level Variations for Pensacola, Florida (adapted
from Hicks et al., 1983) .










discussion of compaction effects). It is worth noting that this is probably
the only component that realistically can be controlled by humans. The
obvious general but not universal correlation of areas of tide gage locations
and ground fluid extraction near population concentrations justifies a
possible concern over this activity. Also the fact that these are the areas
that continued RSL rise may contribute most to the ultimate response cost
(relocation, defense, repair, etc.) makes it important that the significance
of anthropogenically induced subsidence be quantified and possibly controlled
as early as possible.

Very simple and sensitive compaction meters have been utilized in
quantifying this effect in the vicinity of Osaka and Niigata, Japan among
other locations. A schematic of two such gages is presented in Fig. 2.7.
Each installation consists of an outer casing lining a hole drilled to some
depth, h. The inner pipe of slightly smaller diameter is founded on the
stratum at depth h. Thus the relative vertical movement between the top of
the inner pipe and the general ground level represents the total compaction
over the upper sediment column of thickness, h. To establish differential
compaction, several such devices would be required at each location of
interest. Ideally installations would be made near tide gages and also remote
from cities but say inland and in the same geological formations as those near
the tide gages. These gages would commence yielding valuable data
immediately, and it may be possible to supplement the compaction data
collected with models using data representing the geological formations and
the history of past ground fluids extraction to estimate earlier compaction.
Such results would be invaluable in providing more reliable estimates of past
and future eustatic sea level rise.

New Tide Gage Data Referring to Figs. 2.3 and 2.4a, it is clear that
the southern hemisphere is especially deficient in long-term tide gage data.
A number of relative short-term tide gage records are available along the east
and west coasts of South America; however, there needs to be an effort on an
international basis to install and maintain additional gages to provide a
representative distribution. In addition to the southern hemisphere, more
insular tide gages and tide gages along the open coast are needed. A first
phase effort could be a survey to identify such sites.











Bench Mark


LLIJ
I.' .J


Outer Pipe
Lining
Inner Pipe
Founded on
Strata at
Depth,hA


Differential Compaction
Over Depth hA= ZA2 ZA


ZB2 ZB1 Bench Mark


Outer Pipe
Lining
Inner Pipe
Founded on
Strata at
Depth,hB

Differential Compaction
Over Depth hB= ZB2-ZB1

Differential Compaction Over Zone
hAtO hB=(B 2-ZB1 )-(A2-ZA1 )


Fig. 2.7. Use of Two Compacting Gages to Obtain Compaction Distribution over Depth Zones hA, hB, and hB-hA.


hA

I i










Satellite Altimetry This new technology should soon yield absolute
vertical accuracies of centimeter accuracy. Thus, sounding much of the ocean
surface would allow much broader coverage and very importantly does not
require reliance on coastal measurements. It would appear appropriate to
continue a dense network of tide gages for sea level rise purposes for several
decades after such accuracy is claimed to assure that future needs will be
met, and also to allow comparison of the broader satellite coverage and the
long-term tide gage results.










3. COMPACTION EFFECTS


3.1 INTRODUCTION

Compaction results in the subsidence of ground level due to reduction in
the void ratio of the underlying soil, and in coastal areas contributes to a
local relative rise in sea level. Reduction in void ratio is often the
natural response of a soil to an increase in loading, because an increase in
the interstitial stresses between solids is required. An increase in the
loading of a soil stratum can be the result of an increase in loading on the
ground surface (e.g. building construction or additional sediment deposition),
or due to removal of ground fluid (e.g. water, oil, or natural gas).
Compaction occurs in nature as mud is deposited on the beds of rivers and
estuaries, and especially in river deltas. Another example is the increase in
loading as a barrier island migrates over a stratum of peat, causing the peat
to compact and ground level to subside. Because compaction is a time-
dependent process, the relative rate between deposition and compaction will
determine whether bed elevation increases or decreases. Compaction of a
region can also be induced by man, due to 1) loading by the weight of
structures, 2) the extraction of oil and natural gas, and 3) depletion of the
groundwater table due to active pumping or by preventing recharge of aquifers.

The literature in soil mechanics and foundation design is too replete
with articles on the general topic of compaction to review in detail. The
proceedings of a symposium "Land Subsidence" held in Tokyo in 1969 (in
reference list in section 13) provides a thorough treatment of the causes of
compaction, its theoretical description, field measurement techniques and
analysis, physical consequences and remedial measures. Much of the subsequent
material is gleaned from this collection of studies. However, no
investigations have been found which identify any specific effects of the
inverse problem, i.e. the effect of sea level rise on compaction and
subsidence.

Shiffman et al. (1985) review the available theories regarding
consolidation (compaction). The simplest is Terzaghi's "Conventional Theory"
governed by


I










2 au
a2u au + o a8
Cv + (3.1a)
Sz2 at at at

k(l + e )
c= p (3.lb)
w v

where u is the excess pore water pressure, uo is the hydrostatic pressure, a
is the total stress applied to the system, k is the hydraulic conductivity, eo
is the initial void ratio, p is the mass density of the fluid (water), and av
is the compressibility of the soil skeleton. Solving Eq. 3.1 for u and
applying the continuity equation for conventional theory

a k au an
3z (kp ) (3.2)


soil porosity n is determined. Knowing the porosity as a function of time and
the initial thickness of the soil layer, the time history of ground level
subsidence can be calculated. Except for very idealized cases, this problem
must be solved numerically. Shiffman et al. (1985) also describe a nonlinear
finite strain theory, which removes several assumptions of conventional theory
but requires difficult numerical solution. Fig. 3.1 displays comparison of
the two theories to centrifuge experiments, with the finite strain theory
providing good results.


3.2 MEASURING COMPACTION

As noted in section 2, a simple yet effective device for measuring
compaction rates has been developed in Japan and has been widely used there
for at least the past 30 years, see Murayama (1970). This device, shown in
Fig. 3.2 (see also Fig. 2.7), consists of two concentric pipes that penetrate
to a desired non-compactable stratum. The outer pipe is perforated to allow
the groundwater table to move freely up and down in the casing. A float-type
gage monitors the water level. A strip chart and pen displacement gage,
mounted on a foundation that "rides" the ground surface, records the
subsidence as the pipes appear to protrude from the ground. Several of these
gages located in the same area, but penetrating to different strata, provide
information about the vertical distribution of compaction. A single gage
which penetrates to bed-rock will record the total subsidence.

































0.4 -



0.6-
0

o 0.8-



1.0 -
10













Fig. 3.1.


Prototype Time. tp (days)


Results of Centrifuge-aided Compaction in Comparison to Two
Theories (after Schiffman et al., 1985).





















steel pipe


outer steel pipe
Ground surfoce


cley y sftratum





cle y Stratum










Fig. 3.2. Device for Monitoring Compaction and Groundwater Elevation (after
Murayama, 1970).









3.3 IMPLICATIONS OF COMPACTION


Compaction enters the discussion of sea level rise in two distinct
places. First is the obvious effect that relative sea level will rise as
ground or bed level subsides, resulting in deeper water in rivers and
estuaries, and increasing the likelihood of erosion and flooding in coastal
communities. This will occur even without global sea level changes and
seismic activity. Second is the possible contamination of estimates of
eustatic rise due to compacting of regions where tide gages are located.
Although most such estimates as detailed in section 2 have avoided using
records from areas subject to "obvious" compaction, compaction rates
comparable to estimates of eustatic sea level rise (~ 1 mm/yr) are not obvious
without detailed measurements using devices such as that described. Because
tide gages are usually located near coastal cities where both loading by
structures and groundwater extraction/depletion are to be expected, the
potential for compaction contamination of the measurements exists.


3.4 REMEDIAL MEASURES

Of all types of subsidence, only that which is man-induced can be
prevented, arrested, and perhaps partially reversed. Extraction of oil and
gas can be accompanied by recharge of the soil stratum with water, as was the
case at Terminal Island, California to be discussed. Protection of the
surface recharge areas of aquifers, and water use management to avoid extreme
draw-down of the water table also can prevent or reduce compaction.


3.5 EXAMPLES

Mississippi River Delta A striking example of subsidence due to natural
compaction is the delta of the Mississippi River. According to May et al.
(1983), the Louisiana coast is retreating at an average rate of 4.2 m/yr, most
of which is attributed to erosion and inundation in response to relative sea
level rise induced by natural compaction. The levees built along the river
have cut off the source of sediment to the mud flats, and their natural rate
of compaction is causing some areas to sink at rates of 1 cm/yr or more (see
also Table 10.1). Only in a small area of delta formation is the rate of
deposition greater than the rate of compaction. This high rate of rise in
relative sea level is drowning salt marshes and causing existing small sandy









barriers to migrate over the backbarrier muds, further exacerbating the
compaction. Penland et al. (1985) predict that at present rates of sea level
rise, the Chandelieur Islands and Isles Dernieres will be lost during the next
100 years. Because the loading in this region is naturally-induced and the
affected area so large, the only functional remedial measure would be to
remove the levees in the delta region in hopes of restoring the sediment
supply and deposition rate. Although proven successful on a local scale, this
is not a cost-effective nor practical solution on a regional basis.

Terminal Island, California This classic example of the increase in
relative sea level due to man-induced subsidence demonstrates many of the
possible consequences of natural sea level rise. Due to withdrawal of oil and
gas from the Wilmington Oil Field, an area 5 km wide and 6.5 km long subsided
an average of about 1.5 m, and encompassed Terminal Island and a portion of
Long Beach, California. In some areas the overall subsidence reached 7 m and
resulted in considerable damage to harbor facilities as relative sea level
rose. This damage required substantial remedial efforts including diking in
areas of extreme subsidence, reconstruction of damaged facilities, and bridge
repair. The compaction was arrested by injecting water into several of the
existing wells in order to maintain pore pressure as the production wells
continued operation. It should be stressed that the rate of increase in
relative sea level in this instance was much greater than any expected rates
due to eustatic or neotectonic changes.

Japan Several regions of Japan have experienced large rates of
subsidence due to compaction, generally caused by overpumping of groundwater.
Ground elevations in Niigata Prefecture and the cities of Osaka and Tokyo have
dropped as much as 4 m in the past 40 years, sometimes reaching rates as high
as 16 cm/yr (Takeuchi et al., 1970). Fig. 3.3 displays the isolines of the
total amount of land subsidence in Osaka from 1935 to 1968. The subsidence is
greatest near the coast (280 cm) and small (40 cm) in the hilly region in the
center of the city where the compatible stratum is thin. Fig. 3.4a displays
monthly measurements of groundwater elevation and Fig. 3.4b shows the
corresponding monthly rates of compaction. The two are clearly correlated.
The period where subsidence stopped is due to destruction of the city during
the bombing of World War II when pumping of groundwater ceased. The
installation of an industrial water system and the reduction in pumping
































































Fig. 3.3. Isolines of Total Subsidence (in cm) from 1935-1968 in Osaka, Japan
(after Murayama, 1970).


26

















YEAR



0



20
o
010
LU
-j
cc
LU.
o
S20


z
S30
0







-10w
O 10
ww
< C)
crm
S20
C)















Fig. 3.4.


1968


Monthly Record of a) Groundwater Level and b) Rate of Subsidence in
Osaka, Japan (after Murayama, 1970).










started in 1961 have since raised the groundwater table and arrested the
subsidence. In Nilgata the most severe subsidence has also occurred right on
the coast. In all of these cases, regulations controlling groundwater pumping
have since been enacted, plus recharge has been practiced in several of the
regions where the subsidence is particularly acute. These measures have
always proved successful in at least slowing the rate of compaction. In the
Tokyo region however, 253 km of embankments, 41 sluice units, and 9 pumping
stations were required to protect against typhoon flooding and extreme tides,
and to provide drainage for rainwater (Ukena et al., 1970; Tagami et al.,
1970). These are precisely the types of measures that may be required in many
coastal cities within the next century.


3.6 RESEARCH NEEDS

One important aspect of compaction that requires investigation is its
effect on the tide gage measurements used to determine sea level rise, as
noted in section 2. Although gage elevations are often surveyed in relation
to bench marks that are anchored to bedrock, the error inherent in leveling
over possibly long distances would favor a more direct indication of any local
compaction. It is recommended that a few experimental groundwater
table/compaction devices be installed near selected tide gages. These would
be located in communities where demand for the local groundwater is high, and
compressibility of the underlying strata significant. If these devices prove
useful, more should be added until, ideally, every tide gage used in making
sea level rise estimates has at least one accompanying compaction device.

Another task necessary to resolve the eustatic component of sea level
rise is to survey each tide gage in relation to orbiting satellites. Once
each gage is tied-in to an absolute datum and compaction devices installed,
the relative rise (or fall) in sea level at any particular site can be
separated into its compaction, tectonic, and eustatic components.

A program is also needed to document compaction rates in those coastal
areas currently experiencing high rates of erosion and shoreline retreat to
see if compaction is playing a role, and to determine if remedial measures can
be implemented. Installing arrays of compaction measuring devices will also
permit study of the long-term behavior of the local subsidence as well as its
relation to fluctuations and secular depletion of the water table. By sinking










nearby devices to different depths, the vertical distribution of compaction
can be determined, and by placing arrays farther inland along a transect the
spatial behavior of compaction rates can be studied.










4. TIDAL RANGE EFFECTS


4.1 INTRODUCTION

The effect of sea level rise on the open coast and estuarine tidal ranges
is a matter of significance as far as the dynamics of shoreline response is
concerned, including such processes as coastal flooding, salinity intrusion
and sediment transport. An obvious question is whether a rise in the range,
should it occur, would overshadow the effect of the mean sea level rise
itself. The phenomenon is strongly site-specific, depending upon local
morphological and meteorological conditions, and also on remote forcing due to
macro-scale oceanographic phenomena.

Astronomical tides are shallow water waves even in the deepest ocean, and
therefore "feel the bottom". Conversely, therefore, the bottom topography and
frictional resistance influence tide propagation in the sea. Since shorelines
define the boundaries of the offshore shelf which is usually quite "shallow,"
nearshore tides are strongly influenced by the shelf topography. The
distinction between tide measured "along the open coast" and, for example, at
a bay entrance therefore becomes somewhat blurred. With reference to tide
measured inside a bay as opposed to outside, Mehta and Philip (1986) noted
that "the definition of 'outside' remains somewhat obscure in physiographic
terms...". However, they added that "restrictive dimensions of bays compared
to the sea impose water level oscillations whose range and frequency may be
partially unrelated to oscillations outside." Furthermore, from the point of
view of organizing data, the distinction between open coast tide and bay or
estuarine tide may be retained, as in the following description.


4.2 LITERATURE REVIEW

The principal tide-generating forces arise from the gravitational pull
exerted on the earth's surficial water mass (and to a much smaller extent on
the entire mass of earth; see, e.g. Hendershott, 1972) by the moon and the
sun. Darwin (1898) presented an "Equilibrium Theory of the Tides," which
provides a useful qualitative description of some of the main features of the
tide phenomenon based on a force balance involving gravitational attraction
and centrifugal reaction for the system comprising the earth, the moon and the
sun. This theory has been summarized by Dean (1966); it highlights the role









of the basic forces in generating periodic oscillations of the water surface,
and their dependence on such factors as the latitude, the declination of moon
and the relative effects of the moon and the sun.

During the 1920's, Proudman (see e.g. Proudman, 1925) published a series
of articles in which he investigated various aspects of tidal motion including
the Coriolis effect due to earth's rotation. The significant advance made
relative to the equilibrium theory was accounting for the actual motion of
water particles on the rotating earth. Computer technology has now made it
feasible to simulate tidal motion over entire oceanic masses. Early
computations were based on solutions of Laplace's tidal equations (LTE). A
review of numerical models of the sixties and the seventies has been provided
by Hendershott (1977). Subsequently, more general forms of the Navier-Stokes
equations of motion have been solved. A recent review of solutions of these
ocean tidal equations (OTE) has been provided by Schwiderski (1986).

Tides in the nearshore environment are considerably influenced by winds,
waves, bottom topography as well as temperature- and salinity-induced
stratification. Where astronomical tides are small, e.g. along U.S. Gulf
coast, non-tidal forcing often assumes overwhelming significance and modeling
of a purely deterministic nature becomes difficult. Physical considerations
along these lines have been reviewed by Csanady (1984).

Proudman's contributions also included considerations for tidal motions
in channels of various cross-sectional shapes, and the effect of coastal
configuration on offshore tidal features. A good review of simple analytic
approaches for tidal propagation in estuaries, without and with bottom
frictional effects, has been presented by Ippen and Harleman (1966). For the
fundamentals on numerical methods for estuarine hydrodynamics, the works of
Dronkers (1964) and Abbott (1979) may be cited. Nihoul and Jamart (1987) have
edited a series of contributions on the state-of-the-art modeling techniques
of marine and estuarine hydrodynamics using three-dimensional numerical
approaches.

A special class of tidal hydraulics pertains to the hydraulics of tidal
inlets or entrances connecting the sea to relatively small and deep bays. A
simple, coherent theory for predicting water level variation in the bay for a
given, sinusoidally forced, sea tide has been presented by Keulegan (1967).
Mehta and Ozsoy (1978) have reviewed various approaches including developments

previous and subsequent to Keulegan's contribution.
31










4.3 PHYSICAL PRINCIPLES
4.3.1 Tidal Propagation

According to the equilibrium theory of tides, the tidal amplitude can be
shown to be proportional (to leading order) to the fourth power of earth's
radius, considering the moon-earth system. Since this number (6,378 km) is so
large compared to any expected effect of sea level rise (i.e. increase in
earth's radius), the corresponding change in the tidal range on this account
would be negligible. In order to evaluate the effect of sea level rise on the
tidal range, the nature of propagation of tide in very shallow waters must be
considered.

The simplest description of tide in the dynamic sense is that of a
shallow water wave moving along the x-direction with a speed or celerity,
Co. If a frictionless bottom is assumed, the wave equation is

2 2
9n 2 2n
-= C 2 (4.1)
at2 o 2 2
at ax

where n(x,t) is the instantaneous water surface elevation. The celerity, C =
(gh) 12 where g is acceleration due to gravity and h is water depth.

The effect of friction can be accounted for by including an additional
term on the right hand side of Eq. 4.1. Thus, for example, this term under
the assumption of linearized friction is -gMln/at, where M is an empirical
coefficient accounting for the magnitude of bottom friction. Friction slows
down the speed of propagation (celerity), decreases the current speed and
reduces the tidal range compared with frictionless tide. The effect is depth-
dependent, and it can be shown that in fact it varies with h-1/3, which means
that increasing the water depth would decrease frictional damping, thereby
increasing the tidal range. Observations in the German Bight (southern North
Sea) suggest this type of a trend, as will be noted later.

Within the estuary itself, increasing the water depth can have a drastic
effect on the tidal range. The majority of present day estuaries are of
holocene origin, having been formed since the last ice age and accompanying
sea level rise. In some, sea level rise has caused the depths to increase
while in others, sedimentation rates have been high enough for the depths to
have "kept pace" with sea level rise. In a few cases, e.g. some estuaries in
China (Qitang, for example), sedimentation rates have essentially exerted an










overwhelming control, causing the depths to decrease inspite of sea level
rise, and thereby pushing the mouth seaward.

While, in general, increased water depth would increase the estuarine
tidal range, the opposite effect could occur, for example, in cases where
tidal resonance is a significant factor. This can be illustrated in a simple
way by considering the case of a tidal wave entering a frictionless channel
closed at the upstream end. In this case, considering complete wave
reflection at the closed end, the incident and reflected progressive waves
combine to form a standing wave, as shown in Fig. 4.1. The estuary is of
length Z, with the closed end at x=0 and the mouth at x=-L. If the range of
the progressive wave is H, the range of the standing wave at the closed end
will be 2H. The standing wave envelope is thus defined by an antinode at the
closed end and a node in the sea. It can be shown (Ippen and Harleman, 1966)
that the ratio, R, of the amplitude, nom, at the closed end to the amplitude,

n-Am, at the mouth will be (ignoring bottom friction)

n
om 1
R = = (4.2)
1n 1 C 2 1 It:
-Am |cos(kT)}

Since Icos(27r/L)I < 1, in general, the tide at the closed end will be higher
than that at the mouth. This type of a resonance effect is well known, and
occurs in such estuaries at the Bay of Fundy, Canada, and at Cambay in
India. Given such a behavior, a situation can arise whereby an increase in
water depth would in fact decrease the difference between the tide at the
closed end and that at the mouth.

Consider first the case of an estuary of mean water depth, h = 15 m.
Given an estuary length, A = 108 km, from Eq. 4.2 R = 3.7, for a semi-diurnal
tide. Now if h is increased, for example, by 2 m, R is reduced to 2.60
(assuming no change in the estuary length). Further suppose that as a result
of the 2 m sea level rise, the tidal range at the mouth increases by 10%, say
from 1 m to 1.10 m. Then, by virtue of Eq. 4.2, the range at the closed end
will decrease, from 3.2 m to 2.9 m.

A bay-like water body connected to the sea via an entrance will
experience range amplification as the frequency of tidal forcing approaches
the natural period of oscillation of the water body. The situation is
analogous to the response of a damped harmonic oscillation (Mehta and Ozsoy,



















-


4 .


.4 -~1


Tidal Wave Envelope in an Estuary in
the Upstream Closed End.


N







German Bight
(souther
North Sea)





Norderney o c
-b --_~c


which the Wave is Reflected at


List.


Federal Republic
of Germany


) 50 100 km
B. .. I


Fig. 4.2. Locations of Four Tide Gages in the German Bight.


x=- (-x)- x=0


MSL
--- MSL 2H





4 L


Fig. 4.1.


I
I


|-










1978). In a number of bays along the U.S. coastlines, for example, the tidal
range in the bay is greater than that outside (O'Brien and Clark, 1974).
Amplification becomes most pronounced when the forced and natural frequencies
are equal. If therefore an increase in water depth due to sea level rise were
such as to shift bay response away from resonance, the tidal range relative to
that at the mouth could, as illustrated previously, decrease in spite of the
opposing trend caused by decreasing bottom friction and increasing tidal
admittance with increasing water depth. In a great many inlet/bay systems,
however, bottom friction in the inlet channel controls the bay tide; hence in
these cases sea level rise will increase the bay range, as will be illustrated
later.


4.3.2 Superelevation Effect

In most bays, the tidal mean water level is usually different, often
higher than mean sea level. The difference, referred to as bay super-
elevation, results from a number of physical factors. Mehta and Philip (1986)
reviewed these factors, and the physical mechanisms by which they generate
superelevation. Representative maximum superelevation corresponding to each
cause, as might be found from measurements, were suggested; Table 4.1 gives a
summary of the findings. Among the listed causes, sea level rise will
directly or indirectly influence inlet/bay geometry, sea tide, salinity, wave
penetration and some other factors. Since these in turn influence the mean
bay level, in the evaluation, for instance, of the change in tidal range due
to sea level change, the associated change in superelevation must be
additionally considered in calculating the net water change.

Mann (1987) examined the superelevation effect resulting from inlet/bay
response to tidal forcing. Tide-averaged hydrodynamic equations were
developed and it was shown that bottom friction in the inlet channel is the
primary cause of superelevation. Stokes drift, tidal current asymmetry and
river runoff were identified (in the absence of such effects as those arising
from salinity, wind waves, etc.) as the major governing physical processes.
Mann considered the case of a small, deep bay connected to the sea via a long
inlet channel. The combined effects of tide and superelevation resulting from
sea level rise were evaluated, as will be noted in the next section.










Table 4.1. Representative Bay Superelevations (after Mehta and Philip, 1986)


Cause Superelevationa Comment
(cm)

Inlet/Bay Geometry 5-30 Effect of shallow bar is more
important than changing geometry
with tide; hence seasonal and
episodic response

Sea Tide 10 Theoretical estimate; no
verification; believed to be a small
contribution compared to others

Runoff 50 Major factor; strong seasonal
variation

Salinity 15 Important in estuaries rather than
bays (no runoff); seasonal variation

Wind 10-15 Local forcing and remote forcing can
both be equally important; seasonal
and episodic response

Waves 5-10 Induced pileup behind reefs may be
important; seasonal and episodic
response

Other Factors 1-30 Modification of tide during upland
propagation and Coriolis effect are
significant


a0nly positive values are indicated.
i.e. lower bay level than sea, e.g.


Superelevation can also be negative,
due to offshore wind.


4.4 EXAMPLES

Fiihrboter and Jensen (1985) evaluated long-term sea level trends at ten
gages in the German Bight. The evaluation was based on records obtained over
a 100 year period from 1884 to 1983. Trends relevant to the present purpose
may be illustrated by considering four gages, at Norderney, List, Cuxhaven and
Bremerhaven, shown in Fig. 4.2. Of these, the gages at Norderney and List may
be considered as "open coast" gages, while Bremerhaven is decidedly up estuary
(Weser). Cuxhaven is at the mouth of estuary (Elbe). Table 4.2 gives
relevant results.










Table 4.2. Secular Trends in Mean Tidal Range in the German Bight (after
Fihrbdter and Jensen, 1985)


Rate of Change of Mean Range (m/100 yr)
Location
N = 100 N = 25

Norderney -a 0.431
List -a 0.369
Bremerhaven 0.380 1.293
Cuxhaven 0.065 0.949

alnsufficient data


The rate of change of mean tidal range has been calculated in two
different ways for each location. The first is the average rate based on the
entire 100 year period (no values were computed for Norderney and List due to
insufficient data). The second is based on the last 25 year (=N) record,
converted to an equivalent 100 year rate. Comparing Norderney and List to
Bremerhaven, it is observed that the tidal rise (N=25) has been far more
significant (three-fold) within the estuary than on the open coast. The rise
at the estuary mouth is intermediate in magnitude. One likely reason is the
effect of reduced bottom friction due to sea level rise. This effect is more
pronounced in the shallow estuary than in the deeper sea.

It is also interesting to observe from Table 4.2 (for Bremerhaven and
Cuxhaven) that the increase in tidal range has been considerably more
significant in recent years (N=25) than what is obtained based on a 100 year
record (N=100). At Bremerhaven, the mean tidal range 100 years ago was
~ 3.30 m. Thus the range increased there by ~ 9% during the subsequent
75 years. During the next 25 years the range increased again by about the
same percentage.

Fihrbiter and Jensen noted a trend of rising tidal range approximately
over the past century at all ten locations examined. They concluded that this
trend is not due to any long-term changes in meteorological conditions, but is
possibly due to the morphology of the North Sea, a very shallow water body in
which the global rise of the mean water level effect is amplified via a
standing wave effect. This possibly suggests a situation in which the natural










frequency of the water body approaches the tidal forcing frequency with
increasing water depth and changing boundaries.

Mann (1987) theoretically simulated the response of inlet/bay systems of
assumed geometries to a total sea level rise of 1.3 m, corresponding to a
0.3 m rise over the past century and a 1.0 m projected rise. The bay was
assumed to be relatively small and deep, with a surface area of 5x106m2. The
inlet channel was 1,800 m long and 150 m wide. It is illustrative to consider
here the case of an initially 1.5 m deep channel. For this shallow system,
the ratio of the (semi-diurnal) tidal frequency to the natural frequency is
0.16, which is << 1, thus signifying a friction-dominated (as opposed to
resonance-dominated) system.

In Fig. 4.3, the resulting changes in the mean bay level and bay tidal
range are shown. A 1.3 m rise in sea level decreased bay superelevation (head
above mean sea level), from 0.27 m to 0.11 m. On the other hand, reduced
friction resulted in an increased tidal range. Initially, the high water (HW)
and low water (LW) amplitudes of tide relative to mean bay water level were
0.28 m and 0.25 m, respectively. The tidal range was thus 0.53 m. After a
1.3 m sea level rise, the amplitudes became 0.66 m and 0.56 m, i.e., range
1.22 m.

These data on the effect of sea level rise enable the determination of
the high water level within the bay initially, and following sea level rise.
Let S = sea level rise, aHW = HW tidal amplitude in the bay relative to mean
bay level and B = bay superelevation. Let AaHW and AB represent changes in
aHW and B, respectively. Then, initially, the HW level with respect to the
initial mean sea level will be aHW + B. After sea level rise, it will be S +
aHW + AaHW + B + AB. Note that in the example considered, AB is a negative
quantity. Relevant quantities in the present case are: S = 1.3 m, aHW =
0.28 m, AaHW = 0.38 m, B = 0.27 m and AB = 0.16 m. Thus the initial HW
level relative to initial sea level was 0.55 m, which rose to 2.07 m
subsequent to sea level rise.

The significance of the above result is self-evident; sea level rise
could, in addition, increase the tidal range so that, in spite of a decrease
in bay superelevation, high water level rise within the bay would become
greater than that corresponding to sea level rise alone.





















0.6




0.4




0.2



0.0



-0.2



-0.4


0


SEA LEVEL RISE (m)


Response of a Shallow Inlet/Deep Bay System to Sea Level Rise:
Changes in Mean Bay Level and Tidal Amplitudes (based on
computations by Mann, 1987).


0.8


LU
-J





w
LU
CO
0

LU
w
I-

LU



-j
LU


0.2 0.4 0.6 0.8 1.0 1.2


Fig. 4.3.










A noteworthy conclusion based on the result of Fig. 4.3 is that the
secular rate of water level rise would be lower in the bay than in the sea, on
account of the decrease of bay superelevation. Hicks (1984) selected 19 pairs
of gages, one inside the bay and the other at the closest location outside the
entrance, for which long-term data were available. For each pair, the
difference (outside minus inside) in the secular rate of change of mean water
level (mm/yr) was calculated. In 12 cases, this difference was positive,
which means a greater water level rise outside than inside the bay. With the
exceptions of the Long Branch (NJ)/New York (NY) and Springmaid Pier/
Charleston (SC) pairs, where the differences were large (13.1 and 13.6 mm/yr,
respectively), the mean of the remaining 10 pairs was 2.6 mm/yr. If bay
superelevation changes were the sole effect involved (which is not by any
means certain, since the gage data were probably contaminated by any number of
physical phenomena), this 2.6 mm/yr change would be indicative of the rate of
decrease of superelevation.

Mann (1987) showed that the changes in bay response are greater in
shallow inlets than in deep ones. He also found that considering, for
example, the bay to have a gentle boundary slope as opposed to a vertical
wall-like perimeter would reduce the changes in superelevation and tidal range
compared with the vertical wall case (Fig. 4.3). In general, however, it was
concluded that due to an increase in sea level, "additional coastal flooding
may occur beyond that due merely to the changes in sea level." Observations
by FUhrboter (1986) in the German Bight estuaries seem to corroborate such a
trend.


4.5 RESEARCH NEEDS

Fast computers with large memory storage have made numerical modeling of
tides rather sophisticated. In many cases, it seems, modeling capabilities
have "outstripped" data quality such that inaccuracies in collected data limit
the accuracy of mathematical prediction. Data limitations arise from many
causes; it suffices to note two factors.

One pertains to a lack of physical understanding, on a micro-scale, of
phenomena which ultimately affect water level prediction. An example is our
understanding of bed forms, the manner in which they change with flow, and the
precise relationship between their occurrence and the flow resistance they










generate. Such forms may be as small as ripples to large, migratory sand
waves found in estuaries and in nearshore waters.

The second factor is related to historic tide records. Many records are
highly contaminated by such unaccounted for effects as arising from land
subsidence, poor leveling between gages, shifting gage locations, and a
general lack of knowledge of the physical surroundings and variations in
parameters characterizing these surroundings over the duration of tidal
record. Thus, an accurate, quantitative evaluation of superelevation effects
would require the deployment of better monitored gages. In addition, Mehta
and Philip (1986) noted that our understanding of bay response and its
relation to response outside would be considerably enhanced by: 1)
establishment of additional primary stations along the open coast, 2)
collection of long-term records at several presently designated secondary
stations in bays, 3) accurate geodetic leveling connecting additional outside
and inside stations, and 4) publication of relevant data in a user-oriented
format. National Ocean Service initiated marine boundary programs and tidal
datum survey programs appear to be directed towards this type of effort,
particularly with respect to the first three items.










5. STORM SURGE AND WIND-WAVE RESPONSE


5.1 INTRODUCTION

Storm surge is the response of mean water level to the high winds,
pressure differential, and rainfall associated with tropical (hurricane) and
extratropical (northeaster) storms. The forces which appear to elicit the
greatest responses are wind-induced shear, which tends to push water onto the
beach, and the inverse barometer effect, which elevates the water level under
the eye of a hurricane. For example, Fig. 5.1 displays the observed tides and
storm surge associated with Hurricane Carla in the Galveston, Texas area. A
complete discussion of all the relevant forces and the equations governing
flows induced by storms can be found in the Shore Protection Manual, U.S. Army
Corps of Engineers (1984). Solutions to idealized cases are given by
Bretschneider (1966a) and Dean and Dalrymple (1984). The dependence of these
solutions on nominal water depth will be examined in order to postulate some
of the possible effects of long-term sea level rise.

The stress applied to the water by the high winds associated with storms
is also responsible for wave generation. Bretschneider (1959) developed a
family of curves from non-dimensional significant wave height induced by a
hurricane, shown in Fig. 5.2. Wind waves are affected by sea level (water
depth) both in their generation and as they propagate over the continental
shelf. Shallow water limits the height a growing wave can attain due to
steepness-induced breaking and bottom friction, while bottom friction
continues to drain energy from the waves as they propagate out of the
generation region. Wave generation in shallow water and losses due to bottom
friction will be briefly examined in order to identify effects of depth, and
hence the consequences of long-term sea level rise. Reference can be made
again to the Shore Protection Manual and Bretschneider (1966b) for information
on these topics.


5.2 STORM SURGE

For the idealized situation shown in Fig. 5.3a where the continental
shelf is uniform in depth, we consider a spatially and temporally uniform
surface shear stress due to the wind associated with the storm. According to
Dean and Dalrymple (1984) the set-up, n, for steady-state conditions is given

by

























S,.26 I__


0.6

S0.6 car~~e isia 2.
- 0 pe1r 2.7:



0.6 pleasure
0.6 Pleasure P er Predicted-

















Carla (adapted from Army Corps of Engineers, 1984).
Caria (adapted from Army Corps of Engineers, 1984).


































































Isolines of Non-Dimensional Significant Wave Height for Hurricane-
generated Wind-waves (after Bretschneider, 1959).


Fig. 5.2.














a) Uniform Depth

!- ---- -


b) Uniform Slope






ho 71 (X )


















Fig. 5.3. Idealized Geometries for the Continental Shelf: a) Uniform Depth,
b) Uniform Slope.


i











n = + 12 (5.1)
h 2 Z
o h
o
where B includes the wind induced shear stress and ho is the original water
depth. Note that at the shoreline (x=A), the set-up increases with the
expanse of the shelf. Rearranging slightly and evaluating this expression at
the shoreline yields


n(A) = (h 2 + 2BA) 2- h (5.2)


Taking the derivative with respect to ho, the dependence of n(A) on ho can be
examined:


a_=- [h (h2 + 2BA)-I2_ 1] (5.3)
9h o 0
o



an(a) 1
= 1 (5.4)
h0 ( + 2B 1/2

h
o

Because Eq. 5.4 is always negative, n decreases as h increases. This
indicates that according to this simple model, as long-term sea level rises
(ho increases) the set-up induced by a given wind shear will decrease.

Consider the following situation:


average depth ho = 10 m

shelf width A = 150 m

average wind
shear "head" B = 3.3 x 10-5m (wind speed = 12.5 m/s)


and using Eq. 5.2 the wind-induced set-up at the shoreline is calculated: n(A)
= 0.49 m. For the same shear and shelf width, but including a 1 m rise in sea
level yields n(A) = 0.45 m. There is 4 cm less set-up with sea level rise,
but of course the total water level would be 96 cm higher than without the 1 m
rise in sea level.










Another relevant idealized geometry for the continental shelf and
nearshore region is that of a uniformly sloping bottom, as shown in Fig.
5.3b. Dean and Dalrymple (1984) present an implicit solution for wind-induced
set-up

h+Tn BY
h 2
x h+n B_ 0 ho
S= F -- n Bt (5.5)
o h 1--
o 2
So -


where


h = h (1 -) =ho(1 ) (5.6)
o

where m is the shelf slope. If we attempt to follow the same procedure as
before, n(A) is given by the transcendental expression

B
0 = n(a) + B n (n(a m (5.7)
m h B
o -
m

Taking the derivative of Eq. 5.7 with respect to h yields


1 B
an(a) mn()
S= h Zm (5.8)
-h hm
o o
B

from which it is difficult to immediately draw firm conclusions. However, for
positive n(A), from Eq. 5.7 we know that



0 m(< (5.9)
hm
B h o m
mn() ) B

Quite sophisticated 2-D (planform) and multiple layer numerical models
have been developed since the mid-1950's, which treat more realistic bottom
topography and boundary geometry, see e.g. Jelesnianski (1965), Reid and
Bodine (1968), Heaps and Jones (1975), Wang and Connor (1975), Wanstrath









et al. (1976), Forristall et al. (1977), Chen et al. (1978) and Thacker
(1979). The caliber of these models has outrun the quantity and quality of
available field data with which to verify them. Complicated numerical models
also do not lend themselves easily to examining the general interaction of the
forcing mechanisms and surge response, and it may be necessary to look for
ways to parameterize and scale the models to extract the effects of sea level
rise on storm surge.


5.4 WAVE CHARACTERISTICS

The characteristics of waves generated in deep water should not change in
response to sea level rise. However, for the same wind speeds and fetch
lengths, waves generated over the continental shelf and shallower water will
be higher and longer due to the reduced effects of bottom friction and
steepness-limited breaking. From the Shore Protection Manual, U.S. Army Corps
of Engineers (1984) the wave height H generated by wind speed U blowing over a
fetch length F in water depth h is given by the expression

0.42
^5 ~ 0.025(1)
0.75 {tz) }
H = 0.238 tanh[0.53 (hh) ]tanh U (5.10)
2 U2 U 75
U U tanh[0.53( 0) ]
U

In shallow water this reduces to

0.75
= 0.126 (Uh) (5.11)
U2 U

It follows that

-0.25
9-= (0.126)(0.75) (- = 0.75 (5.12)
U

and it is clear that wave height will increase with water depth. Wave period
follows an expression similar to Eq. 5.10
0.25
0.375 0.077 1
y.h 0.375 U 2
gT = 1.20 tanh[0.833 (35-) ] tanh U (5.13)
U tanh[0.833 (gh) ]
S/









which in shallow water becomes


T A) 0.375 (5.14)
2nU = (5.14)
U

so that
-0.625
T -(2-)(0.375) = 0.375 T (5.15)
ah U 2 h
U

and it is apparent that waves become longer as sea level rises.

After a wave leaves the storm area where it was generated, bottom
friction will drain energy and reduce its height, but should not alter wave
period. The losses due to friction can be expressed by the equation


ECg b (5.16)


where E is energy density, Cg is group velocity, Tb is the bottom shear stress
and ub the water particle velocity. The overbar denotes time-averaging over
one wave period. Defining the instantaneous shear stress as


T f ublubl (5.17)


performing the time average and integrating Eq. 5.16 yields


H(x) = H(o) (5.18a)
1+r

where

fa H(o)x
r 3 (5.18b)
3ig Cg sinh3kh

The effect of rising sea level will depend on the geometry of the continental
shelf. For a uniform depth where the rise in sea level does not affect the
shelf length, r will decrease and H at the shoreline will increase. However,
if the geometry is such that a rise in sea level results in a wider shelf, r
may tend to increase and H at the shoreline will then decrease, because bottom
friction has had a longer time to drain energy.










Consider a storm on the continental shelf that results in the conditions:


wind speed U = 30 m/s (g/U2 = 0.01089 m-1)
fetch length F = 50 km
average water depth ho = 10 m


so that gF/U2 = 544.4 and gh/U2 = 0.1089. According to Eq. 5.10 waves will be
generated whose heights are 2.06 m, and according to Eq. 5.13 the period will
be 6.3 s.

Next consider the same storm after a 1 m rise in sea level. Following
the same procedure as before yields H = 2.18 m and T = 6.4 s, or an increase
in wave height and period of 5.8% and 1.6% respectively. If the continental
shelf is 150 km wide and has a friction coefficient f=0.01, the loss in wave
height due to bottom friction is calculated using Eq. 5.18 and the wave height
in the nearshore is found to be H = 0.82 m for the case without sea level
rise. With the initial wave conditions for the 1 m sea level rise, the wave
height on the inner shelf is found to be 0.96 m, or a 16.6% increase in wave
height due to the combined effects of sea level rise during generation
(slight) and reduced bottom friction on the shelf (marked).

More detailed numerical models for wind-wave generation have been
developed, e.g. Cardone et al. (1976) and Resio (1981). Several models have
been intercompared by the Sea Wave Modeling Project (SWAMP, 1985) but without
definite conclusions due to lack of data. Cardone (1986) concludes that the
level of error in wave height, period, and direction is on the order of 10% if
high quality wind data are available. However, such data seldom are, and for
predictive purposes the use of less accurate models for representing winds is
often necessary.


5.5 RESEARCH NEEDS

The aspects of storm surge and wind-wave generation that require research
have less to do with long-term sea level rise, than with the basic phenomena
themselves. Storm surge has received intensive theoretical and numerical
study over the past three decades, and several sophisticated numerical models
exist. However, there is a conspicuous lack of field measurements of
hurricane and extratropical storm surge with which to calibrate and verify










these models. Required are concurrent time series from devices placed along
the coast at intervals small enough to resolve the behavior of the surge as a
storm moves out of the open ocean and makes landfall. The ability to model
and predict storm surge cannot improve significantly without such data. Also,
several phenomena associated with storms such as the superelevation of water
level before arrival of the storm (often referred to as a forerunner) are
still a mystery.

Research on wind-wave generation in deep and shallow water has progressed
well. However, as noted there is a lack of detailed, high quality wind and
wave data with which to verify these models. The basic process of damping of
wind-waves as they cross the continental shelf due to bottom friction and
breaking induced by wave-wave interaction are other areas in which research is
needed. Theoretical work has progressed, but accurate field measurements are
lacking. It is also necessary to stress the spectral approach to damping, as
most methods available to date are limited to the assumption of monochromatic
waves. Basic research on the directionality of wave spectra, in both deep and
shallow water, is also necessary before a better understanding of the effects
of sea level rise on ocean waves can be assessed accurately.










6. INTERACTION WITH NATURAL FEATURES AND CONSTRUCTED WORKS


6.1 INTRODUCTION

Assuming that sea level will rise a significant amount over the next
century, and that shorelines will generally respond in some manner, the
question arises as to by what means can (or will) this response be modified or
prevented. Natural features such as shoals, headlands, inlets and even
barrier islands themselves will cause the neighboring shorelines to respond in
a manner different from that of the typical "open" coast. Man-made
engineering works, e.g. breakwaters, jetties, and beach fills, by their very
purpose alter shoreline response from that of nature, and so can modify
shoreline response to sea level rise. Alternatively, the design,
construction, and cost of coastal projects is highly dependent on local water
depth. Relative sea level rise must therefore be addressed for a project
having a long design-life.

On a sandy coast, sea level rise generally invokes shoreline response by
two mechanisms. First is simply the retreat due to flooding or inundation,
which is often small because natural beach profiles are usually concave
upwards in shape. However, the rise in sea level builds a large potential for
additional erosion and shoreline retreat induced by wave action, which can be
quite severe. The only means of preventing shoreline retreat due to
inundation is by constructing dikes and seawalls. All other features which
modify shoreline response, both natural and man-made, do so by altering or
reducing the wave climate and have little effect on the inundation
component. These features/structures are now discussed individually.


6.2 NATURAL FEATURES

Barrier islands are the elongated natural islands composed of sandy
material, which front a substantial portion of the mainlands of the world.
These islands block out the wave activity to which the mainland shoreline
would otherwise be subjected, essentially acting like large breakwaters.
Although the mainland shorelines are still vulnerable to flooding due to sea
level rise and wind-waves generated locally in the bays, barrier islands are
the paramount safeguard against realization of the full erosional potential of
sea level rise in the back-bay region. This potential is especially strong










because the sediments found here are often fine sands, silts, clay and peat,
all highly erodible.

If sea level rise causes local barrier islands to deteriorate and "drown
in place" rather than migrate landward, progressively more wave energy will
penetrate through the chain and attack the mainland shoreline. This can
result in enlargement of the bay area as the mainland erodes. An example is
the Isles Dernieres on the coast of Louisiana, see Penland, et al. (1985). As
shown in Fig. 6.1, since 1853 the large barrier has deteriorated drastically
to become a series of five small islands, which have retreated about 2 km in
125 yrs. Most of this is due to inundation and erosion accompanying the rapid
subsidence of the delta region. Concurrently, Lake Pelto has been greatly
enlarged by erosion of both the isles and the mainland. As the isles continue
to disappear, erosion of the mainland should accelerate.

Shoals are large deposits of sediment, usually associated with relict
barrier islands, inlets, and large headlands. They serve to naturally limit
the wave energy that impacts a shoreline, as a result of dissipation due to
bottom friction and breaking, as well as partial reflection. As sea level
rises, shoals become less effective unless their natural response is to grow,
as is the case at inlets as described subsequently. Such growth of course
requires sediment and may demand it from neighboring shorelines or inlets. An
example of the effects of offshore shoals on the neighboring shoreline is Cape
Canaveral, Florida, shown in Fig. 6.2. This cape has an extensive system of
offshore and shore-connected shoals, which generally protect the cape from
storm wave activity out of the northeast. Little protection is afforded from
the southeast. The regional direction of net longshore drift is from north to
south, and the offshore shoals A, B, C and the Hetzel Shoal have afforded
enough protection for the Chester Shoal and False Cape to form utilizing this
supply of sediment. The entire shoal system is responsible for the formation
and protection of Cape Canaveral and Southeast Shoal. Farther to the south
the shoreline assumes a crenulate shape as is common for such features. Field
and Duane (1974) report that since 1878 Chester and Southeast Shoals have
become broader and thicker, and the offshore shoals have migrated slightly to
the southeast. Since 1898 accretion has occurred on the southern sides of
Chester and Southeast, while the shoreline between these shoals and to the
south of the cape have experienced erosion. This seems to indicate that as

































































Historical Shoreline Changes at the Isles Dernieres, Mississippi
(after Penland et al., 1985).


Fig. 6.1.













































































The Shoal System at Cape
Duane, 1974).


Canaveral, Florida (after Field and


Fig. 6.2.


i










sea level has risen the protected areas at False Cape-Chester Shoal and Cape
Canaveral-Southeast Shoal have continued to be maintained, apparently at the
expense of the region to the south which has become more crenulate in shape
due to blockage of longshore drift from the north.

Natural inlets are the breaches between barrier islands, usually cut
during storms. They generally affect neighboring shorelines as they migrate
alongshore, which causes the updrift side to accrete and the downdrift side to
erode. After a natural or man-made inlet is cut, ebb shoals along the mouth
of the inlet grow and shunt sediment across the inlet and partially maintain
the supply of sand to the downdrift beach. Sea level rise will tend to
trigger a chain of events which could result in larger shoreline retreat than
would occur if the inlet were not present. A rise in mean water level
increases the depth of a bay and increases the hydraulic efficiency of an
existing inlet, thereby increasing the tidal prism. An increase in tidal
prism increases the velocities in an inlet which in turn may deepen or enlarge
the throat. The ebb shoal then demands more sediment from the neighboring
shorelines as the inlet grows in size.

Natural tidal inlets also trap sediment in shoals on the bay side of the
inlet (called flood shoals). Because of the reduced wave climate in the bay,
these shoals are usually left behind as the inlet migrates and thus become a
sink for sediment. As is the case with ebb shoals, the size of these shoals
generally increases with the size of the inlet, and an increase in inlet size
due to sea level rise will tend to remove more sediment from the beaches and
store it in flood shoals.

A good example of the effect of long-term sea level rise on a natural
inlet is Nassau Sound, Florida, shown in Fig. 6.3. Calculations of the volume
of sediment contained in the ebb shoals by Marino and Mehta (1986) indicate
addition of 6.3 x 106m3 of material from 1871-1970. The shoal volume is
currently about 40.5 x 106m3. During this 99 year span, relative sea level
rose 0.3 m. Long-term sea level rise will also promote creation of additional
inlets, each with their own demand for sediment to maintain shoals.

Headlands are natural intrusions of hard material on an otherwise sandy
shoreline. These less-erodible features act as natural groins or breakwaters
and compartmentalize a shoreline. A large single isolated headland usually
causes a crenulate embayment to form on its downdrift shoreline, as is the

































































Fig. 6.3. Bathymetric Chart of Nassau Sound, Florida Showing Ebb Shoals.
Depths are in Feet (from NOS Nautical Chart 11489).


57










case at Cape Canaveral. A series of two or more headlands spaced closely
enough to act as a system will cause formation of embayments that are more
semi-circular in shape.

The role that a headland or series of headlands will play in modifying
shoreline response to sea level rise will depend on the amount of incident
wave energy dissipated or reflected by the headland(s), and the aspect ratio
(ratio of width to length) of the embayment(s). Those with broad faces
parallel to the coast block significant amounts of energy, and their
embayments have larger aspect ratios. This means they significantly increase
the length of shoreline available to "resist" a given amount of wave energy -
the amount being controlled by the fixed distance between headlands. Because
of the reduced energy density at the shoreline, less of the potential erosion
takes place as sea level rises. This situation is analogous to the
performance of offshore breakwaters. However, narrow headlands do not block
significant amounts of wave energy and although the shoreline in between may
be reoriented, it is not lengthened substantially. Because the energy density
at the shoreline is not reduced, little is done to affect on/offshore
transport and therefore the full potential for erosion associated with a rise
in sea level can be realized. This situation is analogous to a groin field,
to be discussed subsequently along with offshore breakwaters.

An example of the effect of headlands on shoreline evolution is Wreck Bay
on the west coast of Vancouver Island, British Columbia, shown in Fig. 6.4.
Quisitis Point and Wya Point are two natural headlands responsible for the
large embayment inbetween. Although historical shoreline changes for the bay
are not readily available, the general behavior in response to future sea
level rise is expected to be as described. Part of the erosive potential of
the rise will be spent on lengthening the shoreline of the bay as it
enlarges. So, the average retreat of the shoreline will be less than on the
open coast.


6.3 CONSTRUCTED WORKS

Dikes and levees are free-standing, elongated mound-like structures
used to prevent coastal and riverine flooding and to create usable land from
low-lying, previously inundated wetlands. They are usually constructed of
earth or sand (armored by clay, asphalt, rubble or vegetation), masonry, and



























































Fig. 6.4. Shoreline Between Two Headlands at Wreck Bay, Vancouver Island,
with Observed Wave Patterns (after Bremmer and LeBlond, 1974).








59










concrete, and are often assisted by pumps to remove seepage. A few typical
design cross-sections are shown in Fig. 6.5. Although costly to construct and
maintain, dikes are the only means of totally preventing shoreline retreat
(both inundation and wave-induced) due to a rise in relative sea level. They
"modify" shoreline response essentially by creating a new shoreline at the
structure location, and have been successful in many places throughout the
world, more notably the Netherlands. If long-term sea level rise is
significant, dikes may be the only workable means of protecting coastal
cities.

The effect of sea level rise on existing dikes and the design of new ones
is manifested predominantly in the required crest elevation of the structure.
This is the elevation that prevents significant overtopping during the design
storm. Crest elevation in turn determines the cross-sectional area of the
structure and the volume requirements for material. A crude relationship is
that the height increases directly with the rise in sea level and area
increases with the square of the increase in sea level. More precise
estimates depend on the actual design cross-section. The major sea level
related question confronted in the design of new dikes and levees is whether
to include projected long-term estimates or not. Answers depend on the site
specific estimate of the rate of sea level rise, the type and method of
construction to be used, the expected lifespan of the structure, and the
expected frequency of maintenance. In regions where relative sea level is
rising rapidly due to ground subsidence or tectonics, a projected estimate of
suitable length (on the order of 10-50 years) may be most appropriate. "Hard"
structures such as dikes built with masonry, concrete, and rubble are usually
very expensive to maintain or improve, and should be designed using the
maximum long-term sea level estimate projected during the design life of the
structure. "Soft" structures built with sand or earth and armored with
vegetation usually require frequent (but relatively inexpensive) maintenance
and are more easily altered and improved. This permits raising of the crest
elevation in response to actual sea level rise, rather than designing for a
perhaps uncertain projection of sea level.

The best example of the use of dikes and levees to prevent coastal
flooding, and their interaction with long-term sea level rise, is the
Netherlands. Dikes have existed in the Netherlands since pre-Roman times and























.A" SEADIKE WITH FORELAND

,g 5.50m DESIGN STORM rIDE
^^ ---- ^ 1 FORELAND
ROAD 110 XL50
RA SAND C-J 1,U
_7r3M PLANEMSL BT
&6.00-I -450-- I1
---3.-0 L--~-d---------- ------


..B"SEADIKE WITHOUT FORELAND


ROAD


65,40 --- -- --


.C" RIVERDIKE 800
15 s 6.70m DESIGN STORM TIDE

DRAIN ROA^D SAND FORELAND .5so

SDATUM PLANE MSLrOOm
K 59.00


Fig. 6.5. Examples of Design Cross-sections for Sea Dikes (after Kramer,
1971).










over 1,000 km now exist (Lingsma, 1966). However, several catastrophic
failures during storms have served to periodically demand a review of their
use and design, the most recent being the flood of February 1, 1953 where
1,783 people were killed and total damage was estimated at 250 million dollars
(Wemelsfelder, 1953). This disaster prompted construction of the massive
Delta Project, whose large storm surge barriers were just recently completed
(see Kohl, 1986). As shown in Fig. 6.6, almost half of the Netherlands is
below mean sea level and protected by dikes. The situation here is a clear
microcosm of the future of many regions around the globe if the greatest
estimates of sea level rise prove accurate.

Seawalls bulkheads, and revetments are structures of concrete, masonry,
steel sheet pile, or rubble used to armor the shoreline and prevent retreat
due to the combination of wave activity and sea level rise. Although
performing much like dikes, they usually are not free-standing and are always
"hard" features, with vertical or steeply sloping faces. They generally are
used on a local rather than regional basis and are built to protect the upland
along a limited section of beach. Besides their cost, the major drawback to
seawalls is that as sea level rises progressively less sandy beach is
available for recreation and additional storm protection. Periodic beach
nourishment is often required as mitigation. Typical cross-sections for a
seawall, bulkhead and revetments are shown in Fig. 6.7.

Sea level rise affects the design, construction, and maintenance of these
structures in the same general manner as with dikes. As sea level rises,
higher crest elevations are required, but because the structures are not free-
standing the required cross-sectional area increases more linearly than
quadratically with sea level. As with dikes, a seawall, bulkhead or revetment
can either be designed with enough crest elevation to account for projected
sea level rise, or else the crest elevation can be periodically raised in
response to sea level. Because these are hard structures, it is usually
difficult and expensive to exercise the second option.

Galveston, Texas is fronted by a seawall constructed after the city was
demolished during a major hurricane in 1900, in which more than 6,000 people
were killed. The wall, whose cross-section was shown in Fig. 6.7a and
planform is displayed in Fig. 6.8, is 4.9 m high and over 16 km long. Nine
million cubic meters of fill were placed behind the wall and much of the city
































































Fig. 6.6. Shoreline of Holland if There Were No Dikes, Showing a 50% Loss
in Land Area (after Lingsma, 1966).


63



























b) A splash apron may be added next to
coping channel to reduce damage
due to overtopping

Coping Channel Top of Bulkhea
Top of Bulkhead


t -
Tide Range


Dredge Bottom
:v-


Dimensions and details to be
determined by particular
site conditions



Sand Fill -


Former Ground Surface b i^
Tie Rod -.*-^S ^ ^ r Timber Block


Timber Wale
SSteel Sheet Piles


- Round Timber Pile


1.4m Rounding

0.5m -


C) Elev. 2.7m ...

Stone Rip-Rap 0.6m Thick,
(25%> 130kg, 25%< 15kg
'50%wt.>70kg) 2
listingg Beach 1
Elev. 0.00 MSL


Topsoil and Seed


'0.3m
Poured Concrete
(Contraction Jt. every 3.1m)
Gravel Blanket 0.3m Thick
(200 sieve to 7.6cm, 50%>3.8cm)
Over Regraded Bank
'Elev. -0.3m


Typical Cross-sections of a) Seawall, b) Bulkhead and
c) Revetment (adapted from Shore Protection Manual, U.S.
Army Corps of Engineers, 1984).


Fig. 6.7.







































0 1 2 3km
I I I


Fig. 6.8. Planview of the Galveston Seawall (after Davis, 1952).


6^










was raised in elevation. The seawall has been subjected to seven major storms
since 1915, during which overtopping and toe scour have required additional
fill and rubble toe protection. Subsidence of the wall has also been a
problem, especially in places where it is located over a soft clay stratum.
Relative sea level at Galveston has risen approximately 24 cm since 1904
(Leatherman, 1984), and during that time most of the original beach fronting
the wall (up to 90 m wide) has been lost. Leatherman also indicates that
diking will be necessary in the future to preserve the city.

Breakwaters are free-standing structures, usually of rubble mound
construction, attached to the shoreline or seaward (detached) of the
shoreline. Breakwaters cannot prevent inundation by sea level rise, but can
modify shoreline response by blocking some of the incident wave energy. The
resulting shoreline (for detached breakwaters) has a bulge associated with
each structure, and holds the mean shoreline at a more seaward position.
Effective in preventing beach erosion due to both longshore and on/offshore
transport, offshore breakwaters have been used for shore protection in the
U.S., Canada, Europe, and quite extensively (over 2,500) in Japan. Although
initial construction costs can be high, proper design usually ensures low
maintenance. The shoreline response and functional design of offshore
breakwaters is extensively discussed in Dally and Pope (1986).

As sea level rises, an existing breakwater project will lose sediment
from its salient(s) as its relative position moves offshore and overtopping
becomes more frequent. In order to maintain shoreline position and a
prescribed level of protection, the structure will need to be lengthened and
its crest elevated. Otherwise, projected sea level must be used in both
structural and functional design, with the margin of safety diminishing as sea
level rises during the life of the project.

An example of a segmented breakwater project installed to provide
shoreline protection and a recreational beach is found at Presque Isle,
Pennsylvania. The project, shown in planform in Fig. 6.9, consists of three
segments, each 38 m long and placed 46 m offshore of a beach fill. There is a
substantial longshore drift (from left to right) from which the structures
have entrapped additional sand to form a series of salients which
progressively diminish in size in the drift direction. These salients erode
during storms and accrete in calm weather, but the placed fill has remained
relatively unscathed.





















Direction of Longshore Drift --


- --Pre-Construction Shoreline
Nourished Shoreline (July, 1978)
Shoreline (September, 1978)


0 50 100m
I I I


Fig. 6.9. Breakwater Project and Shoreline Response at Presque Isle,
Pennsylvania.










Groins are shore-perpendicular structures made of timber, steel or
concrete sheet pile, or rubble, whose purpose is to entrap sediment moving
alongshore. The shoreline accretes on the updrift side and erodes on the
downdrift until sand is able to pass around the end of the structure and
restore the longshore drift. If the fillet is placed artificially during groin
construction, much of the downdrift erosion can be prevented. For long
stretches of beach, a groin "field" of many structures is used, examples of
which are found at Rehoboth Beach, Delaware; West Hampton Beach, Long Island,
New York; and Madeira Beach, Florida. It is stressed that groins are only
useful if local erosion is due to spatial variation in the longshore drift,
and have little positive impact if erosion is due to on/offshore sediment
transport. Consequently, the use of groins will do little to modify shoreline
response to sea level rise.

Sea level rise will generally result in a loss of efficacy of existing
groin projects. Increased water level will allow more overtopping by waves,
and eventually flanking could occur at the landward end of the structure as
the shoreline retreats. Groins with long useful lives may require lengthening
and raising, while those with shorter lifespans should be replaced with
redesigned structures.

Fig. 6.10 shows the groin field at Long Branch, New Jersey, where the
longshore drift is from south to north. This project has succeeded in
trapping sand and building a beach, but apparently at the expense of the North
Long Branch shoreline.

Jetties are shore-perpendicular structures, usually of rubble mound
construction, placed at tidal inlets in order to stabilize their position and
maintain a navigable channel. Shoreline response to construction of jetties
is similar to that of groins, but on a larger scale as jetties are usually
very long. A large fillet is formed on the updrift side of the inlet, with
the downdrift shoreline often subject to severe erosion. Jetties serve to
increase the velocities in a tidal inlet, which deepens the cross-section and
pushes the ebb shoals offshore, entrapping even larger amounts of sediment.
Without mechanical bypassing of sand from the updrift to downdrift side of an
inlet, the downdrift beach will erode until the updrift fillet and ebb shoals
are large enough to shunt sand across the inlet.


I


































































Fig. 6.10. Groin Field at Long Branch, New Jersey (after Army Corps of
Engineers, 1964).

69










Jetties may exacerbate shoreline retreat as sea level rises in the
following manner. A rise in mean water level increases the depth of a bay and
increases the hydraulic efficiency of an inlet, thereby increasing the tidal
prism. An increase in tidal prism increases the velocities through the inlet
which in turn pushes the ebb shoal offshore into deeper water. The shoal then
demands more sediment from the neighboring shorelines until the regional
longshore transport rate is restored (if possible). As noted previously,
long-term sea level rise will also promote creation of additional inlets,
which if stabilized will each demand sediment to maintain ebb shoals.

As with groins, sea level rise will tend to reduce the efficacy of
jetties due to overtopping and possible breaching at the shoreward end.
Because jetties usually have long lifespans, they may require lengthening and
raising of the crest of the structure.

A typical example of the shoreline response to jetties is the inlet at
Ocean City, Maryland shown in Fig. 6.11. A hurricane cut the inlet in August,
1933 and jetties were constructed shortly thereafter. By 1976 the updrift
shoreline had advanced 245 m while the downdrift had retreated 335 m. The
shoreward end of the south jetty has had to be rebuilt and extended several
times. It is doubtful that in the 50 years since "stabilization", the
shorelines have regained a state of dynamic equilibrium, so the effects of 50
years of sea level rise cannot be deduced accurately.

Beach nourishment is the mechanical placement of sand on a beach to
advance the shoreline. It is a "soft" protective and remedial measure that
leaves a beach in a more natural state than hard structures, and preserves its
recreational value. Beach fills cannot "modify" shoreline response to sea
level rise because the natural littoral processes remain unaltered, and thus
fills can only be regarded as a temporary measure. Although requiring
maintenance at regular intervals and after severe storms, beach fills have
been successful in many instances such as Miami Beach, Florida; Virginia
Beach, Virginia; and Wrightsville Beach, North Carolina.

The greatest effect of long-term sea level rise on beach fill design is
to increase the volumetric requirements of the fill and so increase costs.
Attempting to hold the shoreline in one location will necessarily require a
steeper beach profile as sea level rises. This means increased volumes of
placed sand are necessary to satisfy the offshore transport demand, or else
placing material of coarser grain size than the native sediment.
70




















Shoreline Dates


- -- -Sept 18, 1933



June 27, 1976




0 300m
I I I


Isle of Wight
Bay


'.. A



..
C5S *-
*, .J~


*1

:"1










-L :
: I









:'* .:.
-i






* I

:1* ..:


, 1 .teL .'tBJ~aigU Pi^


Ocean City Inlet


Assoteague
Island


Fig. 6.11.


Shoreline Response to Jetty
(after Dean et al., 1979).


Construction at Ocean City, Maryland


I-- = .. .- .










An example of a successful beach nourishment project is that at Harrison
County, Mississippi, shown in Fig. 6.12. Constructed in 1951-1952 of 4.6
million m3 of fill, the project provided 280 hectares of new beach which was
90 m wide with a berm height of 1.5 m, and fronted the seawall constructed in
1925-1928. The project has performed well, with annual losses on the order of
76,500 m3, and has provided upland protection during several major
hurricanes. Several islands provide some shelter to the project from the Gulf
of Mexico and may be partially responsible for its longevity. It was
renourished with 1.5 million m3 of fill in 1972-1973, following the effects of
hurricane Camille (1969), which caused storm tides locally in excess of 6 m.
Relative sea level is estimated to have risen only 8 cm during the life of the
project (Hicks et al., 1983), forestalling conclusions of the fill's stability
in response to sea level rise.


6.4 COST OF COASTAL WORKS

Although the effect of a rise in relative sea level on the cost of a
coastal structure or beach nourishment project can only be accurately
determined on a case-by-case basis, several crude indicators are available.
For rubble mound structures, the cost increases with the required individual
weight of the armor stone. Using the well known Hudson formula, found in the
Shore Protection Manual (Army Corps of Engineers, 1984), the weight (W)
increases with the cube of wave height. From section 5, expression 5.10 for
the generated wave height and 5.18 for the height after bottom friction can be
used to determine the relative increase in stone weight. For the example
presented (sea level rise of 1 m, wind speed of 30 m/s, fetch length of 50 km
and shelf depth of 10 m), the ratio of weights is

W (after s.l.r.) (0.96)3
S = 1.60 (6.1)
W (before s.l.r.) (0.82)3

or a 60% increase in stone size. We see that sea level rise may have a
significant impact on the design and cost of rubble mound structures.

For beach nourishment projects, the increase in the rate of losses can be
examined by assuming the transport rate (Qs) to be proportional to wave height
to the 2.5 power (Dean, 1976). For the same example of section 5 reiterated
above, this means that





























kSS CHRISTIAN


HENDERSON P I
POINT S S P P
S S


CAT ISLAND






GULF OF MEXICO


SOUND


SHIP ISLAND


I I I I I I
2 0 2 4 6 8m


Profile of Beach


Fig. 6.12.


Beach Nourishment Project at Harrison County, Mississippi (after
Army Corps of Engineers, 1984).










Q (after) (0.962.5
= = 1.48 (6.2)
Q (before) (0.82)25

or a 50% increase in the rate of losses from a beach fill.

Using two different methods, the approximate cost of maintaining the
existing shoreline of Florida with beach nourishment was examined in the NRC
report "Understanding and Responding to Sea Level Rise" (National Research
Council, 1987). For the three different scenarios of sea level rise examined,
the annual costs range from $33 to $204 per linear meter of shoreline, or
between 0.1 and 3.4% of the present day value of beachfront property in
Florida. The amount varied by a factor of 2.5 between the two methods -
highlighting the need for research in this area.


6.5 RESEARCH NEEDS

Research needs in the area of modifying shoreline response to sea level
rise and the effects of sea level rise on the design of protective works lie
in the realm of ongoing basic studies of natural shoreline processes, and have
little requirement for specific treatment of sea level rise. If engineers had
a surf zone sediment transport model capable of reproducing and predicting
beach response to storms and structures, including the effects of sea level
rise would mean an almost trivial matter of increasing the mean water depth in
the model. However, until the knowledge of basic processes has grown
considerably and such models are developed, there is little reason to expect
accurate prediction of the response of beaches to sea level rise to be
possible, and that cost-effective techniques for modifying the response will
be available.

There are four major areas requiring research in basic physical
processes: 1) wave refraction/diffraction, 2) wave breaking, 3) undertow and
longshore currents nearshoree circulation) and 4) sediment entrainment under
shoaling and breaking waves. The knowledge gained from research in these
areas would then be used as input to beach profile and planform response
models.

Once a reasonable expertise in shoreline modeling has been reached, the
greatest research need is for the engineering community to analyze and
quantify the performance and costs of the available alternatives for dealing









with sea level rise, and to then determine their cost-effectiveness. Studies
should be implemented that are specifically devoted to dikes and artificial
dunes, offshore breakwaters, and beach fill design. These measures appear to
be the most promising for confronting sea level rise.










7. SHORELINE RESPONSE MODELING


7.1 INTRODUCTION

A potential dominant effect of relative sea level rise is shoreline
erosion. An erosional trend on a developed coastline always requires a
decision to: 1) retreat, 2) stabilize through coastal structures, or 3)
stabilize through nourishment. Each of the above can be costly; accepting
that under a given scenario of relative shoreline stability, sea level rise,
etc. there is an "optimal" choice, it follows that an inappropriate choice
could be inordinantly expensive. Given that eustatic sea level rise affects
shorelines on a global basis, that the human rate of shoreline development is
increasing and that some projections of future sea level rise are much greater
than in the past, it becomes important to attempt to predict the shoreline
response to such a rise.

Shoreline response to sea level change depends not only on the rate of
change, but also on antecedent conditions and the degree and type of
disequilibrium of the shoreface. The dominant engineering approach to
predicting shoreline response is the so-called "Bruun Rule" which considers
only cross-shore conditions and an offshore "closure depth" seaward of which
there is no sediment exchange. The Bruun Rule yields a simple relationship
resulting in horizontal shoreline retreat of approximately 50-100 times the
rise of sea level. This chapter presents a more complete consideration of the
sediment budget on the shoreface and attempts to remove some of the
limitations of the Bruun Rule. Specific cross-shore components not included
by Bruun but which could be of significance are: 1) shoreward transport of
sediment across the shoreface, 2) deposition of suspended sediment, and 3)
biogenetic production of sediment. An important factor relating to shoreward
sediment transport is the history of sea level change over the past ~ 20,000
years, with the last 6,000 years or so representing a relative still stand.


7.2 LITERATURE REVIEW

Prior to discussing the models for shoreline response, it is instructive
to review estimates of sea level rise over the last 20,000 years or so, shown
in Fig. 7.1. Sea level rose rapidly (about 0.8 m/century) from 20,000 years
before present (BP) to about 6,000 years BP. Over the last 6,000 years, sea























25- &

.E










75 \
Texas Shelf
+ Holland
x Australia
Southwest Louisiana
Eastern Argentina
100 West Louisiana Shelf
a Western Mexico
a-a









5 10 15 20

THOUSANDS OF YEARS BEFORE PRESENT










Fig. 7.1. The Rise of Sea Level as Obtained from Carbon 14 Dates in
Relatively Stable Areas (after Shepard, 1963). Break in Slope
some 6000 Years BP may have Provided Basis for Barrier Island
Stability.










level has risen at the greatly reduced rate of 0.08 m/century, which is
roughly consistent with estimates of 0.11 m/century based on tide gage data
over the last century. As will be discussed later, the earlier much more
rapid rise of sea level may still be having an effect.

The most widely applied engineering approach to predicting shoreline
response to sea level rise is the so-called Bruun Rule. This rule considers:
a) the active profile to always be in equilibrium, and to retain its relative
position to sea level, and b) the active portion of the profile to be limited
by the "depth of effective motion" seaward of which no sediment exchange
occurs. With the above assumptions, when sea level rises a vertical distance,
S, the entire active profile must rise also by S, requiring a volume 'R, of
sand per unit beach length


A_ = SL (7.1)


in which L is the offshore length of active profile. This required sand is
provided by a profile retreat, R, over a vertical distance, h*+B, (see
Fig. 7.2). The volume generated by this retreat is


AV = (h*+B)R (7.2)


and equating the two volumes, the retreat R can be shown to be

L S
R = S (7.3)
(h*+B) tan6

in which 6 is the average slope of the active profile out to its limit of
active motion, Fig. 7.3. From Eq. 7.3, it is clear that beach profiles with
mild slopes would experience greater recessions due to a given sea level rise
than would steeply sloping profiles.

Several laboratory and field studies have been carried out to evaluate
the Bruun Rule, usually with confirmation claimed. Schwartz (1965) conducted
small-scale laboratory model studies to determine whether an increase in water
level caused an offshore deposition equal to the rise in water level as
predicted by the Bruun Rule. The wave basin was quite small using medium
sized sand of 0.2 mm. Following the development of an equilibrium profile,






















AV = R(h +B) )- Depth of Effective Motion h,




a) Volume of Sand "Generated" by Horizontal Retreat, R, of
Equilibrium Profile Over Vertical Distance (h, +B)


b) Volume of Sand Required to Maintain an Equilibrium Profile
of Active Width, L, Due to a Rise, S, In Mean Water Level


Fig. 7.2. Components of Sand Volume Balance Due to Sea Level Rise and
Associated Profile Retreat According to Bruun Rule.


















tane =B+h*
W Erosion

R 1
S tan


sport Deposition

"Ramp" if Bruun Rule
Strictly Applicable


Fig. 7.3.


The Bruun Rule with Only Seaward Transport of Sediment and Trailing
Ramp Seaward of Active Profile.


E
- 20
w
'0


0
4, 10


Ultimate
Agreement


Yeor


Fig. 7.4. Comparison of Predicted and Measured Shoreline Changes Due to Water
Level Increases, Eastern Shore of Lake Michigan (after Hands,
1983).










the water level was increased by 1.0 cm and the test program resumed with the
same wave conditions. Following profile equilibration, it was found that the
offshore profile had increased in elevation by 0.9 cm which Schwartz
considered as confirmation of the Bruun Rule. Schwartz (1967) also conducted
a second series of tests with slightly larger facilities, but following the
same general experimental framework. Again good agreement with the Bruun Rule
was reported. Field measurements were also carried out by Schwartz at Cape
Cod, MA in which the shoreline response between spring and neap tides was
evaluated in terms of the Bruun Rule. Although "a recognizable upward and
landward translation of the profile was noted in the interval between neap and
spring tides" was reported and the results were generally regarded as
confirmatory, examination of the results is not convincing as to their
significance to and agreement with the Bruun Rule. Also, it is not clear that
spring tides, which of course have water levels both higher and lower than the
average, should be equated to a sea level rise since the average water level
is unchanged. Moreover, it is not clear that the Bruun Rule was meant to
apply on such a short-term basis especially recognizing that short-term
changes in wave climate and convergences of longshore sediment transport can
play an important role in beach profile changes.

Dubois (1975, 1976, 1977) has reported on shoreline changes in Lake
Michigan in association with a 30 cm rise over a 35 week period. The
shoreline recession of 7 m was regarded as substantiation of the Bruun Rule.

Rosen (1978) has evaluated the Bruun Rule on the Virginia shoreline of
Chesapeake Bay. Using 14 beach profiles, Rosen found that the errors in
predicted erosion rates on the eastern and western shores were +58% and -7%
with the positive percentages indicating that the predicted erosion exceeds
the measured. As expected, considering smaller groups of profiles, the errors
were larger.

Hands (1983) has evaluated the Bruun Rule employing a series of 25
profiles along 50 km of the Lake Michigan eastern shore over a 7 year
period. During this period, the water level rose by 0.51 m and then fell by
0.31 m. Fig. 7.4 from Hands shows that the shoreline responded to the changes
in water level, although with a lag. Hands recommends that in the absence of
other information the "depth of limiting motion" be taken as twice the
significant wave height.










Everts (1985) presented a sediment budget approach which encompassed and
extended beyond the Bruun Rule. The method was applied to Smith Island, VA
and a 75 km segment of the Outer Banks of North Carolina to determine the
portion of the shoreline retreat explainable by sea level rise. It was found
that 55% and 88% of the measured shoreline retreat was attributable to sea
level rise at Smith Island and the Outer Banks, respectively. The remaining
component was interpreted to be due to gradients in longshore sediment
transport. The sediment budget approach applied by Everts recognizes the
limitations of the Bruun Rule and the need to consider a more complete
framework for representing and interpreting shoreline response to sea level
rise.

Dean and Maurmeyer (1983) have generalized the Bruun Rule to barrier
island systems that retreat as a unit filling in on the bay side to maintain
their width as they erode on the ocean side. Employing the notation of
Fig. 7.5, the shoreline recession, R, due to a sea level rise, S, is

(LL + W + L )
R= S (7.4)
hb hb.
o L
It is clear from Eq. 7.4 that the recession will always predict a greater
erosion than the Bruun Rule because: a) a greater horizontal dimension is
being elevated with sea level rise (the entire active barrier island width),
and b) the portion of the profile now being "mined" to yield compatible
sediment is the difference between ocean and bay depths, hbo hbL, i.e.
smaller. This equation simplifies to the Bruun Rule if only the ocean side of
the barrier system is active. Finally it is noted that as the bay depth hbL
approaches the active ocean depth, hbo, Eq. 7.4 predicts an infinite retreat
rate. This may explain in part the phenomenon of "overstepping" in which
barrier islands, rather than migrating landward retaining their identity in
the process, are overwashed and left in place as a linear shoal, see, e.g.
Sanders and Kumar (1975).

It is noted that Eqs. 7.3 and 7.4 both consider the portion of the
profile being "mined" for sand as containing 100% compatible material. If a
portion of the profile contains peat or fine fraction that will not remain in
the active system, a rather straightforward modification of the equations is
required.

















L---. o ---- --
Barrier Island
B h
h L Position After Response .- b0
L in Sea Level Rise -
Original Position (Upward and Landward Migration)


Fig. 7.5. Generalized Shoreline Response Model Due to Sea Level Rise.
Applicable for a Barrier Island System which Maintains its Form
Relative to the Adjacent Ocean and Lagoon (after Dean and
Maurmeyer, 1983).


Kriebel and Dean (1985) have described a dynamic cross-shore transport
model in which the input includes the time-varying water level and wave
height. In addition to predicting long-term responses, this model accounts
for profile response to very short-term events such as hurricanes. Thus an
equilibrium profile is not assumed and, in addition to a sand budget
volumetricc equation", a "dynamic equation", is required which was
hypothesized as

Qs = K()-DV) (7.5)

in which Qs represents the offshore sediment transport per unit length of
beach, K is a universal constant (K = 2.2 x 10-6m4/N in the metric system) and
V and D* represent the actual and equilibrium wave energy dissipation per unit
water volume. Eq. 7.5 is suggested following the determination by Bruun
(1954) and later by Dean (1977) that most equilibrium beach profiles are of
the form

h = Ax2/3 (7.6)

in which A is a dimensional profile constant depending primarily on sediment
size but secondarily on wave climate. Dean (1977) found that Eq. 7.6 is
consistent with uniform wave energy dissipation per unit volume. The
quantities A and VD are related by











24 2/3
A 2] (7.7)
pg/g K

in which p is the mass density of water, g is the gravitional constant and K
is the ratio of spilling breaking wave height to water depth (K 0.8).

All models of beach profile response described earlier require the
identification of a limiting depth of motion h* in Eq. 7.3 and hbo and hbL
in Eq. 7.4. Hallermeier (1981) has proposed an approximate method for
predicting this depth, h*, based on average annual significant deep water wave
height, H and period Ts and sediment size D,

0.5
h, = (H 0.3a) T (g/5000D)0.5 (7.8)
s S

in which a is the standard deviation of the significant wave height.

The models presented heretofore invoke the concept of a limiting depth of
motion, a depth seaward of which conditions are static or at least there is no
substantial exchange of sediment with the more active shoreface. This
assumption seems innocent and quite natural, yet the consequences are very
substantial. If no interchange with the shelf profile occurs, erosion is the
only possible shoreline response to sea level rise, i.e. there can be no
shoreward transport contributions from the continental shelf. There is
evidence that shoreward sediment transport is a major contributor to shoreline
stability in many areas. The erosion along the south shore of Long Island and
at Montauk Point is clearly too small to provide the well-documented westward
net transport at Fire Island (Dean, 1986; Williams and Meisburger, 1987).

Dean (1987) has suggested that during the more rapid rate of sea level
rise up to 6,000 year BP, the shoreward shelf transport was not sufficient to
maintain a stable shoreline. However, with the relative sudden sea level rise
reduction by an order of magnitude, the same rates of shoreward sediment
transport generally led to reduced erosion rates and in some cases to stable
or accreting shorelines; Fig. 7.6 illustrates the concept. The equilibrium
mechanics associated with this concept are much different than those employed
by Bruun. Recognized are the natural variability of waves and sediment sizes
with sorting resulting in coarser sediment close to shore. It is hypothesized
that a particle of a given size is in equilibrium when it is in a certain
water depth at a particular distance from shore. With sea level rise and















dtS 0.8m/century



a) Sea Level Rise Too a "s
Rapid for Barrier to
Form (>6000 Years BP)

Sediment Accumulates
at Shoreline Forming
Beach and Dune
dS
S0.08m/century
"..- dt


b) Sea Level Rise
Lessens Allowing
Sand to Accumulate
at Shoreline
(<6000 Years BP)


Lagoon


dS
0.08m/century
dt


c) Barrier Grows and
Traps a Lagoon
(<6000 Years BP)


The Role of Shoreward Sediment Transport, Qs, Across the Shelf and
Rate of Sea Level Rise in Causing Barrier Island Formation (after
Dean, 1987).


Fig. 7.6.










assuming that the wave climate remains the same, the sediment particle would
tend to move landward rather than seaward as required by the Bruun Rule.
Fig.- 7.7 illustrates this mechanism of sedimentary equilibrium.

With greater and greater sea level rise, the general situation will shift
toward erosion. Of primary importance is that to predict the response to sea
level change, each shoreline segment must be considered on a case-by-case
basis with due consideration of the sediment budget. The components of the
sediment budget are difficult to quantify. The best basis for developing an
appropriate response model for a shoreline segment is an analysis of past
response, including a focus on possible anthropogenic effects.

In discussing shoreline response models to sea level change and their
development and calibration, it is important to recognize and respect the
amount of "noise" in the system including that introduced anthropogenically.
Coastal structures and sand management practices at navigational channel
entrances are undoubtedly the main contributors to shoreline perturbation by
humans. The special attention to documentation following storm activity
should also be noted. Along the east coast of Florida, in excess of 38
million cubic meters of beach compatible material has been dredged from
channel entrances and disposed at sea. Based on the Bruun Rule, this amount
is enough to offset 70 years of shoreline retreat using a eustatic sea level
rise of 1.2 mm/year and a retreat/rise multiplier of 100. Data provided by
the Jacksonville District of the U.S. Army Corps of Engineers for the period
1980 to 1985 indicates that approximately 50% of the east Florida coast
material dredged was still being disposed at sea during this period. This
amount (38,000 m3), again using the Bruun Rule, is sufficient to more than
offset their retreat due to the eustatic sea level rise rate employed in the
preceding example.

The role of inlets in Florida has been well documented in two cases. The
entrance to St. Andrews Bay was cut in 1934 on a previously stable beach.
Over the next 50 years, the beach receded at a maximum rate in excess of
2 m/yr where accretion of 1 m/yr had occurred prior to cutting the inlet,
Fig. 7.8. The second example illustrates both the adverse effect of cutting
the entrance to Port Canaveral in 1951 and the beneficial effects of a beach
restoration project carried out in 1974. Again as shown in Fig. 7.9, a

















Increased Sea Level








0 Particle


"Subjected to a Given Statistical Wave Climate, A Sediment
Particle of a Particular Diameter Is in Statistical Equilibrium
When in a Given Water Depth"

Thus When Sea Level Increases, Particle Moves Landward
Thus When Sea Level Increases, Particle Moves Landward


Possible Mechanism of Sedimentary Equilibrium (after Dean, 1987).


Fig. 7.7.











< I

w




z
,0 -.



0 10 20 30

DISTANCE EAST FROM BAY COUNTY LINE (km)


a) Shoreline Change Rates
1934 (79 Years).


n-
LLU


L.I




O




I
-)
Wi


Prior to Cutting Entrance to St. Andrews Bay, 1855-


DISTANCE EAST FROM BAY COUNTY LINE (km)
b) Comparison of Shoreline Change Rates Prior to Cutting Entrance to St.
Andrews Bay, 1855-1934 (79 Years) and Subsequent to Cutting Entrance,
1934-1984 (50 Years).


Fig. 7.8.


Effect of Cutting Entrance to St. Andrews Bay in 1934 on
Downdrift Shoreline (after Dean, 1987).


Entrance to St. Andrews Bay
1855-1934- __.




1934-1984
Direction of Longshore Sediment Transport
-! !,




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