STORM TIDE SIMULATIONS FOR HURRICANE HUGO (1989): ON THE SIGNIFICANCE OF INCLUDING INLAND FLOODING AREAS
by
DANIEL DIETSCHE B.S. Basle Institute of Technology, Switzerland, 1993
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Civil and Environmental Engineering in the College of Engineering and Computer Science at the University of Central Florida Orlando, Florida
Summer Term 2004 ABSTRACT
In this study, storm tides are simulated by performing a hindcast of water surface levels produced by Hurricane Hugo (1989). The region of interest incorporates inundation areas between Charleston and Shallotte Inlet (120 miles northeast of Charleston) and includes
Bulls Bay where the highest storm surge of about 20 feet occurred. The study domain also contains an important riverine system which is connected to the Winyah Bay: the
Waccamaw River up to Conway including all pertinent tributaries (Sampit River, Black
River, and Pee Dee River), and the Atlantic Intracoastal Waterway (AIW) within the
Grand Strand (Myrtle Beach).
Five different two-dimensional finite element models with triangular elements are applied in order to simulate the storm tides, allow for inundation, and provide a basis of comparison to assess the significance of including inundation areas and two extents of spatial discretization. Four computational regions comprise a semicircular mesh encompassing the South Carolina coast including all relevant estuaries and bays as well as the continental shelf. Two of these four computational regions include inland topography allowing the model to simulate inland flooding. One of the floodplain meshes is then incorporated into the Western North Atlantic Tidal (WNAT) model domain to produce a fifth computational region.
ii The computation of the water surface elevations is obtained from the long-wave hydrodynamic ADCIRC-2DDI numerical code, which solves the nonlinear shallow water equations. The code is driven by wind field information (wind velocities and atmospheric pressure) and by astronomical tide forcings at the open ocean boundaries. Short wave action (wave set-up and run-up) is not described by the code.
The primary focus of the study is the computation of two boundary conditions at Winyah
Bay inlet and Nixon’s Crossroad on behalf of the National Weather Service’s Southeast
River Forecast Center. Furthermore, the finite element meshes with and without inland topography exhibit whether incorporating inundation areas significantly improves the accuracy of the computed water elevations along the shorelines. A secondary product of this research is the assessment of near-inlet boundary locations with respect to forcings from storm surge hydrographs and astronomical tidal signals.
Assessments between historical data and the simulated storm tides based on the various model domains are presented. The simulated results show good consensus with historical data along the South Carolina coast. While the results show that including inland topography significantly influences the accuracy of the computed water elevations, it was determined that a limited extent with a coarse mesh resolution is sufficient. The boundary condition assessment indicates that storm tide hydrographs are very spatially dependent near inlets, whereas astronomical tides have minimal variance.
iii ACKNOWLEDGMENT
I would like to express my appreciation to those people whose assistance and guidance helped me to finalize this research. First, I would like to thank Dr. Scott C. Hagen for his exceptional support, advise, and guidance on this project as well as the many beneficial and pleasant conversations I had with him during my stay at the University of Central
Florida. I also would like to thank Dr. Gour-Tsyh Yeh and Dr. Manoj B. Chopra for agreeing to serve on my committee; Andrew T. Cox of Oceanweather Inc., for providing the wind field information; Yuji Funakoshi for his help on the mesh generation software
SMS and his excellent support by developing some of the meshes used in this thesis;
Mike Salisbury for his assistance with the Hydrology labs and updating the FORTRAN codes; and many thanks to the other lads in the lab: Peter Bacopoulos, Satoshi Kojima, and former colleague Ryan Murray. Last but not least, I am very thankful to the members of the Southeast River Forecast Center in Peachtree, Atlanta: Reggina Garza, Wylie
Quillian, Jamie Dyer, and John Feldt for their help in collecting data and providing vital information for the success of this project.
This study is funded in part from University Cooperation for Atmospheric Research
(UCAR) Subward No. UCAR S01-32794 pursuant to National Oceanic and Atmospheric
Administration Award No. NA97WD0082 to the University of Central Florida. The views expressed herein are those of the author and do not necessarily reflect the views of
NOAA, its sub-agencies, or UCAR.
iv TABLE OF CONTENTS
LIST OF TABLES viii
LIST OF FIGURES ix
ABBREVIATIONS xiii
CONVERSION FACTORS xv
CHAPTER 1. INTRODUCTION 1 1.1 Hurricane Impacts 1 1.2 Hurricane Hugo (1989) 3 1.2.1 The History of the Storm 6 1.2.2 Reported High Water Marks 8 1.3 Research Objective 9
CHAPTER 2. TROPICAL CYCLONES 12 2.1 Hurricane Origin 12 2.2 Hurricane Environment 14 2.3 Hurricane Development 18 2.4 Hurricane Classification 23 2.5 Hurricane Movement 23 2.6 Hurricane Weather 24 2.7 Hurricane Winds 25 2.8 Hurricane Land Impacts 26 2.8.1 Winds 27 2.8.2 Rainfall 27 2.8.3 Tornadoes 28 2.9 Hurricane Decay 28 2.10 Hurricane Modification 29 2.11 Hurricane Surveillance and Tracking 32
v 2.11.1 Aircraft Reconnaissance 33 2.11.2 Satellite Remote Sensing 34 2.12 Hurricane Prediction Models 35
CHAPTER 3. LITERATURE REVIEW 37 3.1 Pressure Surge, Long Wave, and Short Wave Processes 37 3.2 Short-wave Generation 41 3.3 Predicting Storm Surge 43 3.3.1 SLOSH Features 45
CHAPTER 4. NUMERICAL MODEL DOCUMENTATION 47 4.1 Tropical Wind Model 48 4.2 Meteorological Forcing Transformation into ADCIRC 53 4.3 Coastal Ocean Circulation Model 54
CHAPTER 5. DESCRIPTION OF STUDY AREA 60 5.1 Riverine System 61 5.1.1 Waccamaw River 61 5.1.2 Atlantic Intracoastal Waterway 62 5.1.3 Pee Dee River and Black River 63 5.2 Estuarine System 64 5.2.1 Winyah Bay 65 5.2.2 Bulls Bay 66 5.2.3 Charleston Harbor 67
CHAPTER 6. DEVELOPMENT OF THE FINITE ELEMENT MESHES 69 6.1 The open-ocean Boundary Placement 70 6.2 South Carolina Study Domain 72 6.2.1 SC-1 76 6.2.2 SC-1-FP 77 6.2.3 SC-2 80 6.2.4 SC-2-FP 83 6.2.5 Comparison South Carolina Meshes 91 vi 6.3 Western North Atlantic Tidal Domain 93
CHAPTER 7. MODEL PARAMETERS AND PERFORMANCE 99 7.1 Computational Model Parameters 99 7.1.1 South Carolina Domain 99 7.1.2 Western North Atlantic Tidal model domain 100 7.2 Computational Performance 102
CHAPTER 8. SIMULATION RESULTS AND DISCUSSION 104 8.1 Tidal Signal Verification 104 8.2 Inundation Areas 109 8.3 Storm Tide Hydrographs South Carolina Coast 115 8.3.1 Charleston Harbor 115 8.3.2 Bulls Bay 120 8.3.3 Winyah Bay Inlet 123 8.3.4 McClellanville 126 8.3.5 Awendaw 128 8.4 Winyah Bay Inlet Hydrograph Assessment 129
CHAPTER 9. CONCLUSION AND FUTURE WORK 139 9.1 Conclusion 139 9.2 Future Work 141
APPENDIX A. ADCIRC 2DDI INPUT FILE: MESH DESCRIPTION SC-2-FP 143
APPENDIX B. ADCIRC 2DDI PARAMETERS SC-2-FP 145
APPENDIX C. WIND FIELD DESCRIPTION SC-1 150
LIST OF REFERENCES 152
vii LIST OF TABLES
1.1 Deadliest U.S. Hurricanes 1900-1996 (NOAA, 1996) 2
1.2 Costliest U.S. Hurricanes 1900-2000, damages inflation adjusted to Year 2000 (NOAA, 2000) 4
2.1 Total Number of Storm for each Genesis Region, Period 1952-71 (Pielke, 1990, p. 35) 13
2.2 North Atlantic Tropical Cyclones (Elsner and Kara, 1999, p.16) 19
2.3 General Characteristics of North Atlantic Hurricanes (Elsner and Kara, 1999) 22
2.4 The Saffir/Simpson Scale. The Table shows the five defined Hurricane Levels and their Features (Elsner and Kara, 1999, p.22) 24
3.1 Physical Processes associated with Storm Event 43
4.1 Computed Wind Field Information Hurricane Hugo 52
5.1 Annual average Freshwater inflows to Winyah bay (Johnson, 1972) 64
6.1 Characteristics of the South Carolina Model Meshes 92
7.1 Tidal Constituents used to force the ADCIRC-2DDI model 102
7.2 Computational Model Setup and Performance (1.75 days) 102
8.1 Peak Elevations at Winyah Bay Inlet in meters above MSL, recorded
at Node 1 and Node 4 138
viii LIST OF FIGURES
1.1 Hurricane Hugo Track (NOAA). September 11 to 25, 1989 5
1.2 Hurricane Landfall Region Charleston 7
1.3 South Carolina, Waccamaw River, and AIW 10
2.1 Global Tropical Cyclone Source Regions, Period 1952-71 (Pielke, 1990) 13
2.2 Schematic of Wind Motion within a Hurricane 16
2.3 Tropical Disturbance, Gulf of Mexico (USACE, 2003) 18
2.4 Tropical Depression, West Coast Africa (USACE, 2003) 20
2.5 Tropical Storm Claudette, 1997, East Coast USA (USACE, 2003) 20
2.6 Hurricane Hugo Perspective (NASA) 22
2.7 Schematic of Hurricane Winds in the Eye Wall 25
2.8 Hypothesis Hurricane Modification, Project “Stormfury” (NOAA) 31
3.1 The Definition of the Storm Surge and the Storm Tide (BoM) 39
3.2 Schematic of the Storm Surge Composition (UCAR) 39
3.3 SLOSH Basins in the Atlantic (NOAA) 44
3.4 SLOSH Contour Surface Envelopes of Hurricane Hugo (NOAA) 45
4.1 Wind Field Extent with respect to the Western North Atlantic Tidal (WNAT) Model Domain 51
4.2 Computed Wind Field Vectors at Time of Landfall, Charleston Harbor 52
5.1 South Carolina Study Domain 60
5.2 Study Domain Waccamaw River and AIW (Drewes and Conrads, 1995) 61
ix 5.3 Winyah Bay (Maptech Terrain Navigator 2002) 65
5.4 Bulls Bay (Maptech Terrain Navigator 2002) 66
5.5 Charleston Harbor (Maptech Terrain Navigator 2002) 67
6.1 South Carolina Mesh location with respect to the State of South Carolina 70
6.2 Western North Atlantic Tidal (WNAT) Model Domain Boundaries 71
6.3 Bathymetry and Inland Topography South Carolina Study Domain 74
6.4 Scatter Point Set Resolution 74
6.5 South Carolina Mesh SC-1, without Floodplains 76
6.6 South Carolina Mesh SC-1-FP, with Floodplains 77
6.7 Boundary Development Stages for the SC-1-FP Mesh 78
6.8 Boundary Development Stages for the SC-1-FP, Inset Winyah Bay 78
6.9 South Carolina Mesh SC-2, without Floodplains 80
6.10 Mesh Structure at the Confluence of the Waccamaw River and the AIW 82
6.11 River Depth and River Slope Schematic, Waccamaw River and AIW 82
6.12 South Carolina Mesh SC-2-FP, with Floodplains 83
6.13 Boundary Development Stages for the SC-2-FP Mesh 84
6.14 Locations of Insets in the SC-2-FP Mesh 85
6.15 Locations of Insets along the Waccamaw River and the AIW 86
6.16 Bulls Bay, (a) Mesh Detail and (b) Bathymetry and Inland Topography 87
6.17 Winyah Bay, (a) Mesh Detail and (b) Bathymetry and Inland Topography 88
6.18 Winyah Bay, (a) Mesh Detail and (b) Bathymetry and Inland Topography 89
6.19 Confluence Waccamaw and AIW, (a) Mesh Detail and (b) Topography 90
x 6.20 Mesh Distinction Bulls Bay (a) SC-1, (b) SC-1-FP, (c) SC-2, and (d) SC-2-FP 91
6.21 Mesh Distinction Winyah Bay (a) SC-1, (b) SC-1-FP,
(c) SC-2, and (d) SC-2-FP 92
6.22 The relaxed Western North Atlantic Tidal Model Domain based on a
localized truncation error analysis (Hagen and Parrish, 2004; Funakoshi,
Hagen, Zundel, and Kojima, 2004) 94
6.23 Bathymetry WNAT-SC-1-FP 95
6.24 Locations of Insets within the WNAT-SC-1-FP 96
6.25 U.S. Southeast Coast, (a) Mesh Detail and (b) Bathymetry 97
6.26 South Carolina Coast, (a) Mesh Detail and (b) Bathymetry 98
8.1 Springmaid Pier, resynthesized and simulated tidal Signal (Murray, 2003) 106
8.2 Charleston Harbor, resynthesized and simulated tidal Signal (Murray, 2003) 106
8.3 Charleston Harbor Hydrograph, with and without River Inflow 107
8.4 Charleston Harbor Hydrograph Inset 107
8.5 Computed flooding extent Hurricane Hugo (a) SLOSH output
(USACE, 2004), and (b) ADCIRC output 110
8.6 Inundation at Winyah Bay, Sampit River, and Black River 112
8.7 Inundation Pee Dee River, AIW and Waccamaw River 112
8.8 Inundation AIW and Waccamaw River confluence 114
8.9 Inundation Waccamaw River at Conway 114
8.10 Locations of Storm Tide Hydrograph Recordings along the Coast and Inland 116
8.11 Storm Tide Hydrograph Hurricane Hugo at Charleston Harbor Tide Gage 117
xi 8.12 Storm Tide Computation WNAT-SC-1-FP Mesh 117
8.13 Storm Tide Hydrograph Hurricane Hugo at Bulls Bay Middle 120
8.14 Bulls Bay Water Stages at Time of Hydrograph Peak (SC-2 mesh) 122
8.15 Bulls Bay Water Stages at Time of Hydrograph Peak (SC-2-FP mesh) 122
8.16 Storm Tide Hydrograph Hurricane Hugo at Winyah Bay Inlet 123
8.17 Winyah Bay Water Stages at Time of Hydrograph Peak (SC-2 mesh) 124
8.18 Winyah Bay Water Stages at Time of Hydrograph Peak (SC-2-FP mesh) 124
8.19 Storm Tide Hydrograph Hurricane Hugo at McClellanville 127
8.20 Water Elevations at McClellanville and Awendaw (SC-2-FP mesh) 127
8.21 Storm Tide Hydrograph Hurricane Hugo at Awendaw 128
8.22 Recording Station Locations around Winyah Bay inlet 130
8.23 Bathymetry and Topography Winyah Bay Inlet 131
8.24 Hydrographs south of Winyah Bay inlet 132
8.25 Hydrographs South-East of Winyah Bay inlet 133
8.26 Hydrographs East of Winyah Bay inlet 134
8.27 Hydrographs North-East of Winyah Bay inlet 135
8.28 Hydrographs North of Winyah Bay inlet 136
xii ABBREVIATIONS
ADCIRC Advanced Circulation model
AIW Atlantic Intracoastal Waterway
BoM Bureau of Meteorology, Australia
DOC Department of Commerce
GPS Global Positioning System
GWCE Generalized Wave Continuity Equation
MEOW Maximum Envelop of Water
MSL Mean Sea Level
NAD North American Datum
NASA National Aeronautics and Space Administration
NGDC National Geophysical Data Center
NGVD National Geodetic Vertical Datum
NHC National Hurricane Center
NOAA National Oceanic and Atmospheric Administration
PBL Planetary Boundary Layer model
SERFC South East River Forecast Center
SMS Surface-water Modeling System
UCAR University Corporation for Atmospheric Research
UCF University of Central Florida
USGS Unite States Geological Survey
xiii USACE United Sates Army Corps of Engineers
SC-1 South Carolina Mesh 1, without floodplains
SC-1-FP South Carolina Mesh 1, with floodplains
SC-2 South Carolina Mesh 2, without floodplains
SC-2-FP South Carolina Mesh 2, with floodplains
SLOSH Sea, Lake, and Overland Surges from Hurricanes
WNAT Western North Atlantic Tidal
xiv CONVERSION FACTORS
SI units of measurement used in this thesis can be converted to Non-SI units as follows:
Multiply SI-Units by to obtain BC-Units
millimeter (mm) 0.0394 inch (in)
centimeter (cm) 0.394 inch (in)
meter (m) 3.281 foot (ft)
kilometer (km) 0.621 miles (mi)
square kilometer (km2) 0.3844 square miles (mi2)
meter per second (m/s) 2.232 miles per hour (mi/h)
kilometer per hour (km/h) 0.621 miles per hour (mi/h)
kilometer per hour (km/h) 0.540 Knots
cubic meter per second (m3/s) 35.311 cubic feet per second (cfs)
hecto Pascal (hPa) 1.0 millibars (mb)
Celsius (ºC) (ºC) 1.8 + 32 Fahrenheit (ºF)
xv CHAPTER 1
INTRODUCTION
A hurricane (or tropical cyclone) can be described as an awe-inspiring feature of tropical
weather, which is often referred to as the greatest storm on earth (Pielke, 1990). Powerful
hurricane winds cause tremendous damage to natural and man-made structures. Trees are
uprooted, properties are destroyed, and enormous waves rise and cause destruction to
coastal communities. Associated torrential rains create inundation to both coastal and
inland areas. In hilly and mountainous areas, hurricanes usually produce river flooding,
terrain erosion, and mud slides. Chaotic sea conditions threaten the safety of vessels. The
waves often reach elevations higher than 12 m. The interaction of strong winds, heavy
rainfall, storm surge, and tornadoes can be responsible for mass casualties.
1.1 Hurricane Impacts
Hurricanes are the single costliest and most devastating of all atmospheric storms on our planet (Pielke, 1990). In respect to property damages and lives lost during a storm event, hurricanes rank near the top of all natural hazards (Elsner and Kara, 1999). During the period from 1963 to 1992, the World Meteorological Organization estimated that hurricanes produced worldwide about three times as much damage as did earthquakes.
Total deaths caused by hurricanes are approximately 50% higher than those from seismic activity.
1 Table 1.1: Deadliest U.S. Hurricanes 1900-1996 (NOAA, 1996).
Rank Year Location Cat. 1 Deaths
1 1900 TX (Galveston) 4 8,000 2
2 1928 FL (Lake Okeechobee) 4 1,836
3 1919 FL (Keys), TX 4 600 3
4 1938 New England 3 600
5 1935 FL (Keys) 5 408
6 1957 Audrey (LA sw, TX n) 4 390
7 1944 U.S. ne 3 390 4
8 1909 LA (Grand Isle) 4 350
9 1915 LA (New Orleans) 4 275
10 1915 TX (Galveston) 4 275
1. Category (Cat.) refers to the Saffir/Simpson Hurricane Scale explained in Chapter 2 (see Table 2.4). 2. May actually been as high as 10,000 to 12,000. 3. Over 500 of these lost on ships at sea; 600 to 900 estimated deaths. 4. Some 344 of these lost on ships at sea.
Within the United States, tropical storms generated ten times as many deaths as compared with earthquakes (see Table 1.1) (NOAA, 2003). In November 1971, the biggest tropical cyclone disaster of the 20th century occurred in Bangladesh killing 300,000 to 500,000 people. In 1991, another cyclone struck Bangladesh causing over 158,000 casualties. As in 1971, most deaths were initiated due to catastrophic flooding caused by a hurricane
(NOAA, 2003).
2 The storm surge, produced during a hurricane event, is responsible for 90% of the deaths.
Most deaths are due to drowning (Elsner and Kara, 1999). On September 8, 1900,
approximately 8,000 people died in Galveston, Texas, as a result of a five-meter storm
surge associated with a Gulf of Mexico hurricane. In September 1928, hurricane driven
winds triggered the waters of Lake Okeechobee, Florida, to overflow its embankments
causing the deaths of an estimated 1,836 people. In 1944, an unnamed hurricane
generated a storm surge causing the death of 390 individuals in Louisiana. The storm
surge related with Hurricane Audrey (1957) was over 3.7 m and advanced about 40 km
inland.
Hurricanes have a vast impact not only on the people but also on the economies of
nations. The costliest storm event ever, in the United States, was Hurricane Andrew in
1992 (see Table 1.2). Andrew produced about $35 billion (inflation adjusted damages to
year 2000) in damage to the states of Florida and Louisiana (NOAA, 2000).
1.2 Hurricane Hugo (1989)
In 1989, Hurricane Hugo (see Figure 1.1), which made landfall near Charleston, produced major inundation and destruction along the coast of South Carolina. The hurricane was the strongest storm to strike the United States since 1969 (DOC, 1990). It was also one of the costliest in U.S. history accounting for $9.7 billion in damage.
Although the number of casualties was kept low due to good weather information, planning and evacuations, the hurricane’s intensity directly caused 49 fatalities. 3 Table 1.2: Costliest U.S. Hurricanes 1900 to 2000, Damages Inflation adjusted to Year 2000 (NOAA, 2000).
Rank Year Hurricane Cat. Damage Location Damage in $
1 1992 Andrew 4 FL se, LA 34.9 billion
2 1989 Hugo 4 SC 9.7 billion
3 1972 Agnes 1 Northeastern U.S. 8.6 billion
4 1965 Betsy 3 FL, LA 8.5 billion
5 1969 Camille 5 LA, MS 7.0 billion
6 1955 Diane 1 Northeastern U.S. 5.5 billion
7 1979 Frederic 3 AL, MS 5.0 billion
8 1999 New England 3 Northeastern U.S. 4.7 billion
9 1999 Floyd 4 SC 4.7 billion
10 1995 Fran 3 FL nw 3.7 billion
South Carolina suffered the greatest number of deaths with 13 lives lost. More than
200,000 families were affected by the hurricane with homes destroyed or damaged
(DOC, 1990). However, it should be noted Hugo’s hazardous winds and storm surges had the potential of a heavy death toll.
4
South Carolina Florida
Bahamas
Virgin Islands Cape Verde Islands
Puerto Rico
St. Croix
Figure 1.1: Hurricane Hugo Track (NOAA). September 11 to 25, 1989 5 1.2.1 The History of the Storm
Hugo started as a cluster of thunderstorms. The storm was first detected on satellite pictures as it moved off the West Coast of Africa. On September 10, 1989, approximately
200 km south of Cape Verde Islands (see Figure 1.1), the storm became a tropical depression. The storm circulation gained full strength and was officially pronounced a hurricane one day later. By Thursday, September 14, Hugo’s wind speeds increased up to
184 km/h. The tropical storm reached maximum strength on September 15, with winds of
305 km/h at an altitude of 460 m, and surface wind speeds of 260 km/h.
On September 18, Hugo hit the southeast coastline of St. Croix. The 225 km/h-winds destroyed 90 percent of the buildings on the island. The telephone and water service broke down, the power supply failed. Hugo continued further west passing the island of
St. Thomas, the Virgin Islands and Puerto Rico. The storm caused huge precipitation amounts in Puerto Rico and the Virgin Islands. Rainfall amounts of 127 to 229 mm were reported (DOC, 1990). In northeastern Puerto Rico a maximum rainfall depth of 344 mm was observed. The hurricane weakened after its encounter with the island and continued traveling over the Atlantic where the storm regained strength heading northwest towards the Bahamas.
Reaching the Gulf Stream on September 21, Hugo developed a hurricane eye of more than 65 km in diameter. As a result, the U.S. Government ordered evacuation of beach
6 islands and coastal areas from Georgia up to North Carolina. Some 216,000 people
evacuated from the coasts before the storm struck (DOC, 1990).
At the zero hour on September 22, Hugo made landfall† on Sullivans Island just east of
Charleston (see Figure 1.2), South Carolina (DOC, 1990). The storm hit at an angle
nearly perpendicular to the coast (Schuck-Kolben and Cherry, 1995). The estimated
maximum sustained wind speed at the time of landfall was 220 km/h with a minimum
central pressure of 934 hectopascal (hPa). Heavy hurricane forces were recorded as far as
160 km northeast and 80 km south of Charleston.
-80º -79º
McClellanville Awendaw
+33º +33º
-80º -79º
Figure 1.2: Hurricane Landfall Region Charleston.
† Elsner and Kara (1999) define landfall as follows: “Landfall occurs when all or part of the hurricane eye wall passes directly over the coast or over the adjacent barrier islands.” Therefore, landfall can occur even if the exact center of low pressure remains offshore. 7 The hurricane continued its travel northward. With the overland movement, the winds started to decrease. The fast forward progress of the hurricane reduced the maximum rainfall potential and thus the risk of severe inundation. Rainfall of 102 to 152 mm was common along the coastline of South Carolina, depleting to 51 to 102 mm further inland.
At Edisto Beach, South Carolina, a maximum of 261 mm was measured. Some small river flooding occurred as far as southwest Virginia and western North Carolina where
Hugo approached hills and mountains producing local rainfall totals of more than 152 mm. The Appalachian Mountains caused a rapid storm weakening. Hugo turned northeastward across New York and left the United States less than 25 hours later (DOC,
1990).
1.2.2 Reported High Water Marks
The U.S. Geological Survey (USGS) and the U.S. Army Corps of Engineers (USACE) surveyed high water marks right after Hurricane Hugo. The storm-tide stages were the highest ever measured along the South Carolina coast. The highest water elevations happened at the mouths of inlets and bays and decreased inland.
The exceptions were Winyah Bay and Bulls Bay where the highest storm tides occurred inland. The strong hurricane winds blew directly into Bulls Bay inlet, generating a buildup of waves in the northwestern part of it. The water elevations reached a stage of approximately 6 m above mean sea level (MSL) (Schuck-Kolben and Cherry, 1995). At
McClellanville (see Figure 1.2), just northeast of Bulls Bay, high water marks of 5.0 to 8 5.5 m were measured. The highest surge of 6.2 m emerged at Awendaw, only a few kilometers southwest of McClellanville (DOC, 1990).
At Winyah Bay inlet, which is restrained by jetties, extending eastward from the inlet, the highest elevations (3.7 m) occurred near the middle of the bay. The high water elevation was a result of the storm surge entering the bay from its former entrance located in the northeast. The lowest stage was observed just inside of the inlet. Another reason for the high storm-tide stages was that Hurricane Hugo’s landfall coincided with the high astronomical tides. At Charleston harbor, the high water elevation (3.7 m) was estimated to have a recurrence interval of about 150 years (Schuck-Kolben and Cherry, 1995).
1.3 Research Objective
The unprecedented destruction along the South Carolina coast by Hurricane Hugo (1989) and later by Hurricane Floyd (1999), highlights the importance of developing a capability to model the interaction between storm surge, atmospheric tides, and river streamflow.
Hence, recent cooperative efforts between the University of Central Florida (UCF) and the Southeast River Forecast Center (SERFC) have resulted in the generation of several finite element meshes in order to conduct hydrodynamic computations along the South
Carolina coast. The region of interest (see Figure 1.3) includes the Winyah Bay northeast of Charleston, the Waccamaw River up to Conway and the Atlantic Intracoastal
Waterway (AIW) within the Grand Strand (Myrtle Beach). The riverine system is strongly influenced by astronomical tides. 9 The primary focus of our study is the computation of two boundary conditions at Winyah
Bay inlet and Nixon’s Crossroads. Finite element meshes with and without inland
flooding areas are employed in order to demonstrate whether incorporating inundation
areas significantly improve the accuracy of the computed boundary stages. The boundary
conditions will then be utilized by the SERFC for predicting river stages along the
Waccamaw River and AIW. A secondary outcome of our research is real time forecasting
of storm tides and the depiction of inundation areas. The information is computed by
applying a shallow water equation model (or ocean circulation model) that is driven by a
tropical wind model. The utilized ocean circulation model (ADCIRC) is capable of
calculating astronomical tides and storm surge stages at the same time.
o o o o -83o00' -82o00' -81 00' -80 00' -79 00' -78 00'
o 35o00' NORTH CAROLINA 35 00'
Lake Waccamaw Waccamaw o o 34 00' SOUTH CAROLINA River 34 00' Conway
Winyah Little River
Bay AIW
o GEORGIA o 33 00' Bulls Bay 33 00'
CharlestonCharelston ATLANTIC OCEAN
o 32o00' 32 00' -83 o00' -82o00' -81o00' -80o00' -79 o00' -78 o00'
Figure 1.3: South Carolina, Waccamaw River, and AIW.
10 Chapter 2 continues with a review on the physical process of tropical cyclones, the regions and the environment they entail in order to develop hurricane intensity. The chapter also emphasizes hurricane impacts, the feasibility of hurricane modification, i.e., measures to weaken the storm’s intensity, the surveillance of hurricanes, and hurricane prediction models. The literature review, in Chapter 3, explains the definition and generation of the storm surge and the storm tide, the wave set-up and wave run-up, and provides a brief explanation on the storm surge prediction model SLOSH used by the
National Hurricane Center in Miami, FL. Chapter 4 describes the numerical codes used in this thesis (tropical-wind model and ocean circulation model). The description of the study area is presented in Chapter 5. Chapter 6 provides explanations of how the different finite element meshes were developed. Information about the setting of model parameters and computer performance are presented in Chapter 7. Results are shown in Chapter 8.
Finally, in Chapter 9, conclusions are drawn and possible future work is discussed.
11 CHAPTER 2
TROPICAL CYCLONES
2.1 Hurricane Origin
There are only certain areas of the earth’s oceans where tropical cyclones can evolve (see
Figure 2.1). Based on these origins, hurricanes have different names. In the North West
Pacific and China Sea they are called Typhoons, Baguiose in the Philippines, Cordonazos on the west coast of Mexico, and Willy-Willy in northern Australia (Meyers, 1989).
Globally, about 80 tropical cyclones occur annually, one-third of which accomplishes hurricane status. The most active hurricane region is the North West Pacific that averages about 30 storms per year (see Table 2.1) over the period 1952 to 1971 (Pielke, 1990).
About 85 to 90% of hurricanes begin between the 20º N and 20º S latitude. In the North
East Pacific, ocean surface temperatures are usually too cold north of 25° N latitude, while over the North East Atlantic sea temperatures enable the genesis of tropical cyclones as far north as 35º N latitude (Elsner and Kara, 1999). Hurricanes do not develop in the South American region due to cold ocean water. In addition, tropical cyclones do not evolve at a location of about 4º to 5º latitude (North and South) since the
Coriolis force is too small to trigger a storm rotation. In the West Pacific and in the
Indian Ocean hurricanes can develop during the whole year, while hurricanes in the
North West Atlantic usually develop during the time between April to December.
12 Table 2.1: Total Number of Storms for each Genesis Region, Period 1952-71 (Pielke, 1990, p.35).
No. of Storms per Annual Mean Percentage of global Region 20 years Average total
North West Atlantic 234 11.7 12 %
North East Pacific 228 11.4 11 %
North West Pacific 593 29.7 30 %
North West Australia 144 7.2 7 %
South West Pacific 213 10.7 11 %
North Indian Ocean 287 14.4 15 %
South Indian Ocean 274 13.7 14 %
Figure 2.1: Global Tropical Cyclone Source Regions, Period 1952-71 (Pielke, 1990).
13 Over the North Atlantic region, intensified tropical disturbances, which later evolve into
storms with maximum sustained winds of at least 72 to 94 km/h, account for about 12%
of global activity (Pielke, 1990). More than 50% of these disturbances reach hurricane
intensity (Elsner and Kara, 1999). The “official” North West Atlantic hurricane season
defined by the U.S. National Weather Service is from June through November. Based on
observed hurricanes and tropical storms from 1886 to 1977, the frequency of hurricane
occurrence in the North West Atlantic usually peaks during the month of September.
2.2 Hurricane Environment
A cyclone is circular air rotation in a counterclockwise direction in the Northern
Hemisphere. In the Southern Hemisphere, a cyclone generates a clockwise rotation. Of
the many tropical waves‡ (or other pre-hurricane disturbances) each year, only a few develop into hurricanes. Although there is a lack of consensus regarding a theory of tropical cyclone development, there is an agreement on the requirements that are important for a hurricane genesis to occur. According to Pielke (1990) the requirements are as follows:
An underlying ocean with surface temperatures above 26.5º C.
A moist atmosphere (rich on water vapor).
‡ A tropical wave is a bend in the normally straight flow of surface air in the tropics that forms a low- pressure trough, or pressure boundary, and showers and thunderstorms.
14 An atmosphere for which the temperature cools sufficiently with height.
A location pole-ward of about 4º to 5º of latitude.
Small wind speeds and direction changes with height between the lower and upper
troposphere (weak vertical shear of horizontal winds).
Pre-existing low-level and/or upper-level disturbance.
Each of these necessities is quite common in the tropics, especially during hurricane season. The problem for the tropical cyclone forecast is that often one of the conditions stated above is missing (Pielke, 1990).
A hurricane evolves and spends most of its life within the relatively homogenous tropical atmosphere, i.e., the change of air temperature from place to place is minor. Water evaporates from the sea surface where it ascends and condenses inside cumulonimbus clouds. The latent heat release from the condensation, together with the sensible heat from the air in contact with the warm ocean, fuels the tropical cyclone (Simpson, 2003).
The thermodynamic heat engine starts working, i.e., drawn thermal and latent energy is converted into kinetic energy. The efficiency of this conversion process is about 2 to 4 percent (Simpson, 2003). This procedure must remain uninterrupted for at least a day or more for a cyclone to advance. At a later stage, significant condensation occurs not only within the eye wall but also in the hurricane’s feeder bands (Elsner and Kara, 1999).
The airflow aloft must provide enough outflow (divergence). At the same time, the rate of incoming air (convergence), in the lower region, has to drop to allow the pressure near 15 the surface to fall (low pressure zone). The outflow aloft conveys the extra heat by the
central condensation far from the storm center (Pielke, 1990). Therefore, no additional
warming of the air occurs except in the storm core (eye) in which air falls down. Figure
2.2 displays a schematic of air movement at an early stage of tropical cyclones. The moist
atmosphere produces rising parcels of air, which cool slower than their immediate
environments. As such, the air parcels will find themselves considerably warmer than
undisturbed surroundings all the way from the surface to about 10 or 12 km in the air.
This effect causes the vertical circulation inside the developing hurricane (Meyers, 1989).
It is not only essential that the sea water has to exceed 26.5º C, hurricane genesis requires
a substantial ocean area roughly the size of the United States. As stated earlier, over the
western North Atlantic, the ocean temperatures are warm enough to initiate hurricanes as
far north as 35º N latitude.
TRTROPOPAUSEOPOPAUSE Air f o
Upper Level Outflow Upper Level Outflow n ressio mp Co rd wa n Low Level Inflow w Low Level Inflow Do
Eye
OCEANSURF SURFACEACE
Figure 2.2: Schematic of Wind Motion within a Hurricane.
16 Another important issue for hurricane development is the effective force generated by the rotation of the earth. An area with numerous showers and thunderstorms near the equator will remain disorganized and fail to form a tropical cyclone. The horizontal component of the Coriolis force is too small to prompt a tropical cyclone on the Northern Hemisphere south of 8º N latitude (Elsner and Kara, 1999).
The consequences of wind shear on the development of a hurricane are complex and not fully understood. It is known that a circulation of low-level inflow of air coupled with upper-level outflow through strong rising currents can be disrupted by vertical shear of the horizontal winds (Simpson, 2003). Although complex, it can be inferred that the larger the shear the lower the probability of hurricane genesis.
An important ingredient for the formation of a hurricane is a pre-existing low-level atmospheric disturbance. The majority of North Atlantic hurricanes develop from convectively active tropical waves emerging from western Africa. The tropical wave is essentially a trough of low pressure near the ground embedded in the deep easterly flow on the equator-ward side of the subtropical high-pressure area (Pielke, 1990). The waves move westward at fairly regular intervals between 10º and 20º N latitude, primarily during August and September. Approximately 40 to 70 such waves occur in a season with the vast majority never reaching hurricane strength. The waves are relatively cool in the lower atmosphere but warm aloft. The associated shower and thunderstorm activity makes these atmospheric waves potential precursors to tropical storms and hurricanes.
17 The development of a tropical wave is indicated by the occurrence of low-level-westerly
winds against prevailing easterlies (Pielke, 1990).
2.3 Hurricane Development
Tropical cyclones form through different stages of development from a disturbance to a mature hurricane. The life of a hurricane is divided into four stages displayed in Table
2.2. The first sign of hurricane development is the appearance of a cluster of thunderstorms over the tropical oceans (Pielke, 1990). This phenomenon is called a tropical disturbance (see Figure 2.3).
Mississippi Alabama
Florida
Louisiana
Tropical Disturbance
Figure 2.3: Tropical Disturbance, Gulf of Mexico (USACE, 2003).
18 Table 2.2: North Atlantic Tropical Cyclones (Elsner and Kara, 1999, p.16).
Category Development and Intensification Criteria
Small pressure drop (less than 3 hPa) along a latitude. To the west of the trough surface winds are divergent and air is mostly cloud free, Tropical Wave while to the east of the trough there is enhanced cloudiness. Sometimes called easterly waves or African waves. This stage is absent in some developments.
The early stages of a tropical cyclone in which the maximum sustained (1-minute average) surface wind speed is below 62 km/h. Tropical Depression Also, the decaying stages of a tropical cyclone in which the maximum sustained surface wind has dropped below 62 km/h.
A warm-core tropical cyclone in which maximum sustained surface Tropical Storm winds range between 63 and 118 km/h.
A warm-core tropical cyclone in which maximum sustained surface Hurricane winds are at least 119 km/h.
A hurricane in which maximum sustained winds are at least Major Hurricane 180 km/h. Also called an intense hurricane.
The formative phase starts with a closed rotation known as a tropical depression (see
Figure 2.4). Minimum central pressures fall to 1,000 hPa or even lower (Elsner and Kara,
1999). The term intensification is used when the storm develops to tropical storm intensity (see Figure 2.5), i.e., winds stronger than 63 km/h but less than 118 km/h. Table
2.2 indicates that the early mature stage of a tropical cyclone starts at hurricane intensity and prolongs until winds reach maximum strength and central pressures drop to their lowest values.
19
Cape Verde Islands West Coast Africa
Atlantic Ocean Tropical Depression
Figure 2.4: Tropical Depression, West Coast Africa (USACE, 2003).
United States
Atlantic Ocean Tropical Storm
Figure 2.5: Tropical Storm Claudette, 1997, East Coast USA (USACE, 2003).
20 When a tropical cyclone exceeds 119 km/h of maximum sustained one-minute wind speeds near the surface (10 m above surface) it is considered a hurricane. Another special feature of the early stage of hurricane intensification is the emergence of narrow feeder bands of clouds forming a spiral that looks like a galactic star system (see Figure 2.6).
Looking from above a hurricane is a nearly circular mass of deep clouds. The hurricane continues to grow farther in size and the strongest winds extend beyond from the center of rotation. This part of the hurricane is referred to as the central dense overcast (Elsner and Kara, 1999). A distinct asymmetry of the storm may evolve. The fastest winds develop on the right side of the storm. Hurricanes are also characterized by relatively symmetric inflow of air near the ground and anticyclonic (clockwise, Northern
Hemisphere) outflow high in the air.
In the center of the hurricane appears a hole called the eye. The eye is surrounded by a wall (eye wall) that consists of cumulonimbus clouds. The remotest band can be located
1,000 km from the hurricane center. Within the eye wall the heaviest rains and strongest winds occur (Pielke, 1990). The small percentage of intense rising motion takes place in the eye wall. The eye usually is free of clouds and contains warm and dry air aloft and is one of the most distinguishing features of a mature hurricane.
Warmer ocean temperatures provide a greater potential for hurricane intensification. Due to the presence of wind shear, the actual intensity of a hurricane is limited. Table 2.3 presents the general features of mature hurricanes in the North Atlantic and summarizes the previous paragraphs. 21 Table 2.3: General Characteristics of North Atlantic Hurricanes (Elsner and Kara, 1999).
Characteristic Range
Storm Diameter 200 to 300 km
Surface Winds ≥ 119 km/h (1-minute averaged)
Lifespan 1 to 30 days
Eye Diameter 16 to 70 km
Direction of Motion Westward then northward
Energy Source Latent heat release
Figure 2.6: Hurricane Hugo Perspective (NASA).
22 2.4 Hurricane Classification
In order to measure the storm’s structural effects a scale was developed in 1970 by the
U.S. National Weather Service called the Saffir/Simpson Scale (see Table 2.4). The idea was to provide comparisons of the effects of tropical cyclones of various intensities in different locations on the globe (Simpson, 2003). Saffir and Simpson relied their scale on maximum sustained wind speeds, central pressure, and storm surge height. The scale is descriptive and represents a crude estimate of what a hurricane could possibly do to a coastal area if it hit directly (Elsner and Kara, 1999).
2.5 Hurricane Movement
Tropical cyclone motion results because the storm is embedded in a large body of moving
air, referred to as the steering current (Pielke, 1990). Weaker storms are steered by lower-
level winds. The strongest storms move with winds higher up. Hurricanes of low latitudes
will track to the west. The driving forces are the northeasterly trade winds. Hurricanes of
higher latitude move more to the northwest and north steered by the anticyclonic flow
around the subtropical high-pressure system. Another force that often occurs is a strong
upper tropospheric trough extending to low latitudes, which steers the hurricane north out
of the tropics. The absence of deep middle-latitude troughs allows low latitude hurricanes
to maintain a more westerly motion (Pielke, 1990).
23 Table 2.4: The Saffir/Simpson Scale. The Table shows the five defined Hurricane Levels and their Features (Elsner and Kara, 1999, p.22).
Max. Sust. Peak Central Storm Hurricane Damage 1-min Wind Example Pressure Surge 1 Wind Gust
[Cat.] [-] [hPa] [km/h] [km/h] [m] [Name]
1 Minimal > 980 119-151 148-191 1 Agnes
2 Moderate 965–979 151-180 191-223 2 Cleo
3 Extensive 945–964 180-209 223-259 3 Betsy
4 Extreme 920–944 209-248 259-310 4–5 Andrew
5 Catastrophic < 920 > 248 > 310 > 5 Camille
1. The storm surge development is explained in Chapter 3.
2.6 Hurricane Weather
Hurricane weather starts off with a torrential but short rain and sudden gusts of wind, followed by a phase of partial clearing until the next band arrives and stormy weather returns. As the hurricane center approaches the intensity of gusts increases. While the eye passes winds become light before strength of the storm increases again as the storm pulls away (Simpson, 2003).
24 2.7 Hurricane Winds
Winds in the hurricane increase from their lowest speeds within the eye to their highest
rate instantaneously beyond the edge of the eye, in the eye wall. Winds decrease more
gradually away from the eye wall. The distribution of the wind field around the storm is
often asymmetric. Usually, the strongest winds are located in the right front quadrant,
looking toward the direction of motion (Elsner and Kara, 1999). This is because the
winds on the right hand side have an additional forward motion added to the velocity of
rotation around the hurricane eye (see Figure 2.7).
Shoreline
Storm Path
FRONT 200 km/h
150 km/h EYEEYE 250 km/h
REAR 200 km/h
Storm Speed: 50 km/h Wind Speed around Eye: 200 km/h
Figure 2.7: Schematic of Hurricane Winds in the Eye Wall.
25 One of the more difficult tasks faced by analysts and forecasters has been the determination of near surface (10 m above surface) maximum sustained winds based upon the winds measured at reconnaissance aircraft’s flight level (Simpson, 2003). These flights are discussed in Section 2.11. Based on former flights to buoy data, i.e., data collected in the open ocean, Powell and Black (1990) suggested that a ratio of 63% to
73% should be used to reduce those flight level winds to the standard near surface winds.
In contrast, the National Hurricane Center suggested using a ratio of 80% to 90% for surface wind estimation. The release of well over 400 Global Positioning System (GPS)
Sondes in hurricanes and their environment, since 1997, helped to understand the horizontal wind distribution better. Franklin, Black and Valde (2000) verified upon 183 dropped sondes in the eye-wall that the horizontal wind speeds are generally greatest at about 500 m and 800 m above the surface. They also showed that, on average, surface winds would be about 91% to 78% of 3,000 m level wind speeds within the eye-wall.
2.8 Hurricane Land Impacts
Along the coast, the biggest impacts of either a landfalling hurricane or one paralleling the coast are storm surge, winds, precipitation, and hurricane tornadoes. Much of the hurricane damage results from the storm surge that will be discussed in more detail in
Chapter 3.
26 2.8.1 Winds
Another major hazard associated with hurricanes are the strong winds that produce considerable structural damage and risk to life from flying debris (Pielke, 1990). Even though winds start to decay after landfall, damaging winds can still occur far inland. The damage from winds is proportional to the kinetic energy of the flow. Maximum gusts, of course, are even stronger than the recorded one-minute average sustained winds.
2.8.2 Rainfall
Intense precipitation rates and abundant rainfall amounts accompany most tropical cyclones. Rainfall is often excessive at and after a hurricane makes landfall, leading to major flooding problems especially along the coast (Schuck-Kolben and Cherry, 1995).
Usually, the intensity of rainfall lessens quickly with distance from the shoreline. In addition, heavy rainfall can occur where very moist air is forced up and over mountain barriers. Some of the worst floods in the eastern United States were produced by hurricanes (Pielke, 1990). Frequently, the heaviest rainfall amounts accumulate when a hurricane stalls its forward motion. On the other hand, the rainfall can sometimes be beneficial to agriculture when the rains end an extreme period of drought.
27 2.8.3 Tornadoes
Tornadoes are the fourth danger associated with tropical cyclones near the coast. A tornado is a relatively small (approx. 100 m), but powerful vortex of winds in the shape of a funnel (Pielke, 1990). The funnel extends from the base of a cloud to the ground while rotating at tremendous speeds. Usually they evolve in the front right quadrant of the hurricane, within 150 km of the center. “In brief, the declaration of the hurricane force winds due to friction over land, coupled with rapidly rising air inside the thunderstorms, can generate tornadoes as hurricanes makes landfall” (Elsner and Kara,
1999). Usually, these tornadoes are not as severe as the springtime tornadoes. However, loss of life and property damage does occur as a result of them.
2.9 Hurricane Decay
As a hurricane moves inland, larger aerodynamic roughness of the land surface causes an increase in friction. A first approximation, the over-land wind speed dissipation rate is proportional to wind speed at landfall (Elsner and Kara, 1999). The flow of air toward the hurricane center is deflected and increased, which leads to rising surface pressures and a weakening of rotation. In addition, surface friction may alter the track movement of hurricanes at landfall. Over land the hurricane is removed from its essential source of warm seawater that fuels the convection. Without the rising of warm and moist air parcels the storm starts to decay. Tropical cyclones usually lose hurricane intensity within
28 12 hours after landfall. Torrential rainfall is often the last impact of a decaying hurricane.
The decay of hurricane intensity continues if the following occurs:
The source of heat and moisture is reduced as a result of travel over land or relatively
cold water.
Dry, cool air, which does not favor deep cumulonimbus convection, is transported
into the system.
Anticyclone (outflow) aloft is replaced by a cyclonic (inflow) circulation, which adds
mass to the hurricane heat engine. Larger scales of atmospheric circulation changes
are required to remove such an outflow region.
The requirements for the maintenance of a hurricane life cycle are less restrictive than
those for its genesis (Elsner and Kara, 1999).
2.10 Hurricane Modification
Hurricane modification is the general term that refers to all human attempts to exercise some weakening of a storm (Simpson, 2003). There have been actual efforts to modify hurricanes within the United States in the past. Many more ideas have been conveyed by scientists some ridiculous, others infeasible, and some with rather devastating consequences to the environment and human beings if performed.
29 The hypothesis of one attempt was that large amounts of super-cooled liquid water existed (above the freezing level) in clouds within and just outside of the eye-wall
(Simpson, 2003). In fact, this phenomenon of super-cooled liquid water was several times experienced during high altitude surveillance flights. Seeding of silver iodide crystals into those clouds on the outer edge or just outside of the eye-wall could convert the water to ice crystals (see Figure 2.8). The change in phase would release latent heat, resulting in increased growth of cumulus clouds and establishing the eye wall at a greater radius from the center of the cyclone (Pielke, 1990). The larger radius would cause a reduction in wind strength and a reduction in storm surge generation. Convinced about these ideas, experiments were commenced under the National Hurricane Research Project in the
1960’s. The cloud seeding program was called “Stormfury”. In the following years several hurricanes were seeded but did not show any relevant modification effect. The project finally was aborted in 1980 due to the lack of real evidence of storm alterations. It was decided that more had to be known about the internal process of a hurricane before modification experiments were resumed, if ever (Simpson, 2003).
Another suggestion by a “scientist” was to “blow the storm apart” using a nuclear bomb.
A mature hurricane of moderate strength and size releases as much condensation heat energy in a day as the nuclear fusion energy of about 400 20-megaton hydrogen bombs
(Simpson, 2003). Looking at the energy comparison alone makes this idea infeasible without even considering the damage to the environment.
30 Several researchers and scientists proposed the introduction of very small, sub-micron
carbon black particles into the hurricane boundary layer§. The particles would absorb solar radiation and warm the boundary layer. As a result, the outer radius cumulus convection would enhance while reducing the convection near the cyclone center.
Finally, the strongest winds within the eye-wall would deplete. It was suggested using large military aircrafts in order to disperse the particles. This turned out to be infeasible.
Another idea was using surface ships for burning the dispensing agent (Simpson, 2003).
Stormfury Hypothesis Seeding
Old Eye Wall Weakening as New One Grows
New Eye Wall Dominant
Figure 2.8: Hypothesis Hurricane Modification, Project “Stormfury” (NOAA).
§According to Simpson (2003): “The layer of atmosphere near the Earth’s surface in which frictional forces are important, typically the lowest 1,000 m of the atmosphere.”
31 Another effort was cutting off the hurricane’s surface energy supply by placing a chemical component on the ocean surface. The chemical retardant film would have to be very thin. Ocean winds and wave action would prevent its maintenance (Simpson, 2003).
Other schemes have been proposed all of them turned out to be infeasible.
2.11 Hurricane Surveillance and Tracking
Most of the time hurricanes spend over the open-ocean waters. Therefore, before airplane reconnaissance and weather satellites tracked hurricanes, the detection was largely a chance event (Elsner and Kara, 1999). If a cyclone did not affect a population or was not discovered by a vessel it never made it into the records. The epoch of major technological advanced hurricane detection started during and after World War II. A helpful accomplishment was the invention of the ground based radar observation, which enabled the first observation of the structure of the hurricane core. On July 27, 1943 the first intentional flight into a hurricane was completed (Simpson, 2003). With the development of geostationary satellites, by the late 1960s, a continuous monitoring was established. By the end of the 1960s the U.S. Navy initiated the use of oceanic buoys, which proved to be another dependable part of hurricane warning system. Within the following years, further technological advances helped to understand and predict hurricane tracks better.
32 2.11.1 Aircraft Reconnaissance
The use of aircrafts for hurricane exploration is one of the most vital tools for hurricane forecasters (Elsner and Kara, 1999). Initially, the U.S. Air Force and Navy participated in the first flight missions in 1943. The Navy discontinued operations after 1974. In 1983, the Office of Aircraft Operations was created to consolidate all of the aviation assets operated by NOAA. The first jet aircraft was acquired in 1996. Since the first flight into a cyclone, it has become a routine to fly at frequent intervals and different levels into hurricanes.
Reconnaissance flights provide information on the storm location, details of the wind, temperature fields surrounding the storm, and inner structure of a tropical cyclone. The aircrafts are equipped with radar devices to derive the wind speeds and directions. During surveillance flights, GPS dropwindsondes are launched from the aircraft in various hurricane locations. The sonde is a meteorological instrument with a parachute attached that descends from the aircraft to the sea surface, transmitting information back to the aircraft while in the air (Simpson, 2003). The dropwindsonde measures air temperature, dewpoint, and atmospheric pressure. It also utilizes the GPS to record horizontal and vertical wind speed. These data are measured and transmitted twice per second while the probe is in the air. NOAA’s jet aircraft primary mission during hurricane season is to fly into a hurricane, releasing the dropwindsondes in order to gather information on the steering currents that will determine a hurricane's future track and likely landfall location
(Simpson, 2003). 33 Surveillance flights are generally slightly above 3,000 m in strong hurricanes. Flights below about 350 m are dangerous to manned aircrafts due to very turbulent winds
(Simpson, 2003). Therefore, the operation of Unoccupied Aerial Vehicles (also known as drone aircrafts) is under discussion in order to collect data within these altitudes. The
Australian Bureau of Meteorology has already successfully operated these aircrafts. Such flight information can help to improve construction practices of the future, but also for determining appropriate responses before and after hurricanes strike (Simpson, 2003).
2.11.2 Satellite Remote Sensing
Remote sensing satellites have enabled a further enhancement in tropical cyclone monitoring and prediction. The first hurricane picture taken by a satellite (TIROS 1) was in 1961. In 1966, another major improvement in hurricane detection was established with the development of the first geostationary weather satellite (ATS-1) (Simpson, 2003).
Since then satellite observation became the main source of information on cyclones around the globe. Surprise hurricanes are highly unlikely anymore. The current technology allows the discovery of the tropical storms that lead to hurricanes in any ocean region from space (Simpson, 2003). Satellites provide information like multi- spectral information on clouds and water vapor fields, direct downward-looking radar images, microwave observations of the ocean surface temperature and derived surface winds, cloud-drift winds, vertical temperature profiles, and rainfall (NASA, 2003).
Today, the major global tropical cyclone forecast centers rely heavily on meteorological satellite surveillance (Simpson, 2003). 34 2.12 Hurricane Prediction Models
In order to forewarn and evacuate people safely several days before a hurricane makes landfall, the National Hurricane Center (NHC) in Miami, FL issues tropical cyclone track and intensity forecasts four times a day for storms in the north Atlantic and eastern north
Pacific. The forecasts include the latitude and longitude of the storm center (track model), and the intensity on the one-minute maximum sustained surface wind (intensity model) both at 12, 24, 36, 48 and 72 hours.
In the first half of the 20th century, forecasts were mainly based on subjective judgments and extrapolation of current trends. In the second half of the century, researchers developed objective models for estimating future storm track and intensity (Simpson,
2003). The early models were based on empirical relationships between storm properties and the storm’s future movement. Track prediction models based on physical principles were accomplished in parallel with empirical models. Later, these models were generalized to predict intensity as well as track (Simpson, 2003).
During the last 20 years, the performance of track forecast models show significant improvement (Simpson, 2003). It is likely that this trend will sustain. Advancement in computer technology and the number and accuracy of new observation techniques
(dropsondes, unmanned aircrafts, very high-resolution infrared sounders, etc.) available for hurricane analysis are increasing. Improvement in intensity forecast models should be
35 possible as well but remains a considerably more difficult task than track forecasts
(Simpson, 2003).
36 CHAPTER 3
LITERATURE REVIEW
The literature review includes three main topics: 1) the definition and generation of pressure surge as well as long and short wave processes, 2) explanations on the generation of short waves associated with hurricanes, and 3) brief description on the numerical storm surge code SLOSH employed by the National Hurricane Center (NHC) in Miami, FL, for storm tide predictions
3.1 Pressure Surge, Long Wave, and Short Wave Processes
The most destructive element of a hurricane is the flooding. Storm surge is defined as the difference between the storm tide and the normal tide (Elsner and Kara, 1999) (see Figure
3.1). The normal (astronomical) tide is the regular and predictable movement of water caused by astronomical phenomena, i.e., the way the earth, moon, and sun move in relation to each other and the force of gravity. Simpson and Riehl (1981) define it as: “a shoal of water process generated by hurricanes resulting in a super-elevation due to the combination of direct wind driven water and uplift induced by the pressure drop (see
Figure 3.2); at an ocean or bay-shore.” As noted in Chapter 2, the highest wind-driven surge occurs in the front right quadrant of a landfalling hurricane, when the onshore winds are the most powerful (Elsner and Kara, 1999). The high water associated with the storm surge lasts from 6 hours to several days (Elsner and Kara, 1999). Heights may
37 exceed 4 to 5 m and the large dome of water often sweeps 70 to 150 km wide from where the hurricane makes landfall.
There are four basic mechanisms for storm surge generation at or near the shoreline: 1) inverted barometric effect (pressure surge), 2) a wind-driven surge caused by strong onshore winds, 3) geostrophic tilt, a result of alongshore currents, and 4) set-up from short waves (Reid, 1990). The wind-driven surge usually has the largest impact for a landfalling hurricane on a coastline with a wide shelf (Reid, 1990).
ADCIRC is capable of simulating the pressure surge, the wind-driven surge, geostrophic tilt, and astronomic tides. Short wave set-up, and run-up are not described by the code and are explained below. However, ADCIRC can incorporate output information from a short-wave model (in form of radiation stress terms). Therefore, a coupling between the two codes is possible.
The inverted barometer effect causes the water surface to be sucked upwards in the zone of low atmospheric pressure (see Figure 3.2); it can account for not more than about one meter of rise centered at the storm center and depends directly on the central pressure deficit relative to normal sea-level pressure (Reid, 1990). It is equally effective over deep or shallow water (Simpson 2003).
38 Wave Run-Up
Figure 3.1: The Definition of the Storm Surge and the Storm Tide (BoM).
Figure 3.2: Schematic of the Storm Surge Composition (UCAR).
39 The wind-driven surge is caused by onshore wind stress and is most effective in shallow water. It depends directly upon the wind stress, the distance over which it acts, and inversely on the depth (Reid 1990). Elsner and Kara (1999) give the following explanation regarding its size development: the extent of the surge depends very much on
1) the shape of the coastline, 2) the angle between coastline and moving hurricane direction, 3) bathymetric depth, and 4) the duration of the strongest winds. Simpson
(2003) explains that high surge elevations occur along coastlines where the bottom topography inclines more smoothly as it is the case for the continental shelf **, e.g., along the east coast of the United States. While moving towards the coastline, the storm surge does not break (Reid, 1990). The wave runs up the coast and can act as a pathway for short-gravity waves (e.g., surf and swell) farther inland (Jelesnianski, 1972). Huge amounts of water are carried toward the coast and eventually onto the beaches and inland areas. A large surge occurring in flat terrain will inundate the land for several kilometers inland.
In bays and inlets the situation is intricate and often intense. Observations of water levels within bays and estuaries showed that they exceed open coast elevations by as much as
50% or even more for a slow moving hurricane (Pielke, 1990). Hurricane-driven tides in inlets may reach 6 to 8 m with the short wave run-up on top of that. Tides are complicated in estuaries, lagoons, and bays due to the fact that inlets and outlets to these
** The continental shelf is conventionally defined as being that part of the ocean floor above a depth of 100 fathoms (182.88 m) (Runcorn, 1967) and having a gentle slope (about 1º).
40 basins are not arranged in a regular way (Simpson, 2003). Tidal effects in an estuary can further be complicated by freshwater inflows of rivers.
The geostrophic tilt results in sea level rise that is caused by alongshore currents due to alongshore wind stress. Reid (1990) explains this phenomenon as follows: alongshore wind stress can generate alongshore currents, whose upper limit is governed by the wind stress and the opposing bottom stress. Therefore, if the wind is directed with the land to the right then the tilt of the sea surface caused by the Earth rotation (Coriolis force or geostrophic effect) will raise the sea level along the shore. This situation occurs in the early stages of a hurricane whose track is directed towards the coast in the northern hemisphere.
3.2 Short-wave Generation
One shortcoming of the governing equations used in this study is that short waves are not simulated. The code computes long waves only (astronomical tides, geostrophic tilt, and surge). The short waves cause wave set-up, and wave run-up prior to and during hurricane landfall. This absence of short wave capturing can have significant effects on the computation of the storm tides, i.e., usually the calculated water elevations are lower than the expected stages. It has to be noted that there is always wave movement, which is purely wind generated that makes accurate prediction of sea level stages almost impossible (Reid, 1990).
41 Wave set-up is triggered by the radiation stress (i.e., flux of excess momentum carried by the wave) associated with short waves that are also generated by the storm winds. The waves usually travel much faster than the tropical storm itself (Holman, 1990). This phenomenon produces a sea-level anomaly (increased sea elevations) along the shoreline well before other effects of the hurricane arrive. The wave set-up is confined to the near- shore zone where the waves break (i.e., surf zone) as they approach the shore, typically in water depth of 5 to 10 m. These waves can be as much as one meter (Holman, 1990).
Jelesnianski (1972) explains the short wave action as follows: when a wave breaks on a coast, the chaotic mass of water runs up the coast (wave run-up). The mass of water should flow back to the sea but is prevented from completing the action by following breaking waves. After some time, an equilibrium state is formed in which the mean water level is other than normal. This situation is referred to as wave set-up.
Table 3.1 summarizes the previous sections and this one on wave generation. The table indicates physical processes ADCIRC can simulate and what is currently not captured by the code.
42 Table 3.1: Physical Processes associated with Storm Event.
Wave Name Wave Type ADCIRC included Caused by
Wind-driven Surge Long Yes Storm Winds
Pressure Surge N/A Yes Low Pressure
Geostrophic Tilt Long Yes Alongshore Currents
Astronomic Tides Long Yes Gravity
Short Wave Set-up Short No Wave Radiation
Short Wave Run-up Short No Non-breaking Waves
3.3 Predicting Storm Surge
The National Hurricane Center (NHC) in Miami, FL, uses a numerical-dynamic model called SLOSH (Sea, Lake and Overland Surges from Hurricanes) in order to produce
real-time, operational forecasts of storm surges on continental shelves and along
coastlines. The NHC currently runs SLOSH for 38 domains in the Atlantic and Pacific
Oceans (see Figure 3.3).
Over the past few years, SLOSH has been used for conducting hurricane simulation
studies as an initial phase for comprehensive hurricane evacuation planning. The NHC
has run several hundred hypothetical hurricanes with the SLOSH model. The resulting
flooding for each run is recorded and displayed in maps for each basin. These maps,
43 called the Maximum Envelope of Water (MEOW) (see Figure 3.4), indicate land area that could be inundated, i.e., the MEOW gives the maximum amount of flooding possible from a given hurricane. The MEOW's are utilized for evacuation planning and preparedness.
Figure 3.3: SLOSH Basins in the Atlantic (NOAA).
44 3.3.1 SLOSH Features
SLOSH is a two-dimensional, depth averaged velocity computer program, covering water
bodies and expected inundated areas. The calculations are applied to a specific local
shoreline, incorporating the unique bay and river configurations, water depths, major
bridges and roads, and other prominent physical features. If the model is being used to
estimate storm surge, forecast data is put in the model every 6 hours over a 72-hour
period and updated as new forecasts become available (Jelesnianski et al., 1992).
The main difference from ADCIRC is that SLOSH applies a finite-difference scheme in
order to approximate the shallow water equations. For the computation, a polar grid
system (see Figure 3.4) is employed. According to Jelesnianski et al., (1992), such a grid
system overcomes many of the problems associated with specifying boundary conditions.
Figure 3.4: SLOSH Contour Surface Envelopes of Hurricane Hugo (NOAA).
45 The meteorological driving forces onto the oceans surface, e.g., surface stress and a pressure gradient body force, are described by a storm wind model that is integrated into the SLOSH model (note that ADCIRC employs pressure and wind velocities from a detached wind model). The driving forces are determined with a “straightforward” model
(Jelesnianski et al., 1992). The storm input parameter is comprised of the following information: 1) central pressure, 2) radius of maximum winds (i.e., distance from the storm center to maximum winds), 3) storm path, and 4) speed along track.
SLOSH includes overtopping of barrier islands, levees and roads as well as inland inundation. The incorporation of simple hydraulic procedures allows flow through barrier breaches, adverse river flow, and deep passes between bodies of water. SLOSH enables the inclusion of river flow upstream as a boundary condition (Jelesnianski et al., 1992).
The program does not take into account the actual astronomical tide level. Only an initial tide elevation is superposed upon the computed storm surge. Furthermore, short wave action is ignored.
For the final result, the storm tide (storm surge plus approximated astronomical tide) is presented as color-coded contour surface envelopes at different time steps within the domain (see Figure 3.4). The contour lines are usually displayed in feet above the model's reference level, the National Geodetic Vertical Datum (NGVD), in elevation steps of 1 ft
(0.305 m).
46 CHAPTER 4
NUMERICAL MODEL DOCUMENTATION
In order to compute tropical wind fields and storm tides, generated by hurricanes, numerical methods can be used to approximate the differential equations that describe the physics. Numerical methods enable the replacement of the differential equations by employing approximation sets of algebraic equations or matrix equations, which are solved by using the method of linear or nonlinear algebra and requiring the use of computers (Yeh, 1999).
In this project, the ADCIRC-2DDI program (Advanced Circulation Model for Oceanic,
Coastal, and Estuarine Waters – Two Dimensional Depth Integrated option) solves the shallow water equations over a finite element mesh a) along the South Carolina coast only and b) over the Western North Atlantic Tidal model domain (WNAT) (Luettich,
Westerink, and Scheffner, 1992). The model has been proven successful for tidal and storm surge studies in coastal waters throughout the world. Oceanweather Inc.
(wwww.oceanweather.com) generously provided the computed tropical wind fields for
Hurricane Hugo (1989). The wind fields are used in conjunction with the ADCIRC code in order to create the forcing for the storm surge generation.
47 4.1 Tropical Wind Model
The lowest layer of the atmosphere is called the troposphere. This stratum can be divided into two sections a planetary boundary layer (PBL) extending upward from the surface to a height that ranges anywhere from 100 to 3,000 m and above it the free atmosphere
(Meyer, 1989). Within the PBL the whole energy flux takes place. The boundary layer is directly influenced by the presence of the Earth's surface, responding to frictional drag, solar heating, and evapotranspiration (Meyer, 1989). Each of these forces generate turbulence of various-sized eddies, which can be as deep as the boundary layer itself, lying on top of each other. The wind model used to generate the wind fields for this study simulates the airflows within this layer.
The U.S. Army Corps of Engineers (USACE) extensively employs the Hurricane
Planetary Boundary Layer model that computes the wind velocity and pressure. It has been a very useful tool for ocean response modeling (Thompson and Cardone, 1996), i.e., wave or storm surge modeling. Originally, Chow (1971) developed the theoretical formulation of the code at the University of New York. In recent years, Cardone,
Greenwood, and Greenwood (1992), Thompson and Cardone (1996), and Cox and
Cardone (2000) upgraded the original model. The same researchers also provide a detailed description of the wind model used in this study.
48 The wind field model is an application of a theoretical model of the horizontal airflow in the boundary layer of a moving vortex (Cox and Cardone, 2000) vertically averaged through the depth of the planetary boundary layer. It can provide a quite complete description of time-space development of the surface winds in the PBL of a hurricane.
The model relies on parameters that are derived from data in meteorological records and the ambient pressure field. New upgrades are available where reconnaissance data can be incorporated as well (Cox and Cardone, 2000).
The wind field scheme uses the concept that a hurricane usually changes its structure relatively slowly. A tropical cyclone traveling over the open ocean can normally be well represented by parameters that are collected every 6 to 24 hours (Thompson and Cardone,
1996). These representative states of the hurricane are called the “snapshots” of the wind field. According to Cox and Cardone (2000) the following input parameters have to be defined or known in order to generate these “snapshots”:
Relative storm motion
Storm intensity
Geostrophic flow of the ambient PBL pressure field in which the vortex propagates
Scale radii of the exponential radial pressure profile (Holland, 1980)
Pressure profile parameter
While storm structures change slowly, the hurricane position can change rather quickly.
Therefore, the center of the storm is specified at every hour. The hourly information 49 includes latitude and longitude of the storm’s eye. The relative storm motion and intensity are taken from best track data or possibly from forecasts released by warning agencies. Some parameters like the scale radii of the exponential radial pressure profile have to be estimated unless aircraft reconnaissance data is available for verification purposes (Cox and Cardone, 2000). The whole wind field is then calculated from knowledge of the variation of those input parameters along the storm path by computing solutions in a moving coordinate system.
The eye of the storm is the center of this constantly transferring computational grid, which is a system of rectangular nests. The grid, moving with the hurricane throughout the domain, provides relatively fine grid spacing near the hurricane eye and coarser spacing in the outer region. The mesh point spacing is doubled with each successive nest
(Thompson and Cardone, 1996). The discretization in time and space of the governing differential equations is based on a finite difference scheme (Blain et al., 1994). Figure
4.1 shows the extent of the Hurricane Hugo wind field (applied to the South Carolina meshes only) with respect to the Western North Atlantic Tidal model domain. Figure 4.2 illustrates an inset of the wind field vectors (15-min. averaged), around the time of landfall, between Winyah Bay and Charleston harbor. In addition, Table 4.1 provides further information about the computed wind field.
Despite the more realistic theoretical approximation of the used wind field model there are still some shortcomings. The major limitation is that the model does not take into account transitional stages of the boundary layer across roughness discontinuities, e.g., a 50 hurricane passing from water to land (Thompson and Cardone, 1994). In reality, winds on the right quadrant of the hurricane are reduced from full strength as they flow overland.
Winds on the left side of the cyclone coming off the land are much less than simulated.
The winds are reduced due to the increased roughness of the land. The PBL model does not adequately represent these processes associated with a hurricane making landfall. As a consequence, this restriction of the wind model leads to drying of coastal elements on the left of the hurricane and over prediction of the surge on the right of the storm (Blain et al., 1994).
South Carolina Mesh 60º Meridian
Wind Field Extent Florida
Atlantic Ocean Gulf of Mexico
Figure 4.1: Wind Field Extent with respect to the Western North Atlantic Tidal (WNAT) Model Domain.
51 Table 4.1: Computed Wind Field Information Hurricane Hugo.
Description South Carolina Study Domain
Duration 1.75 days
Start Storm Animation September 20, 1989, 18:00
Landfall September 22, 1989, 0:00
End Storm Animation September 22, 1989, 12:00
Sustained averaged wind 15-minute
100 km/h
18:00, Sept. 20, 1989
12:00, Sept. 22, 1989
Figure 4.2: Computed Wind Field Vectors at Time of Landfall, Charleston Harbor.
52 4.2 Meteorological Forcing Transformation into ADCIRC
The computed wind field drives the shallow water equation model ADCIRC. The wind field values (velocity and atmospheric pressure) are interpolated from the nested grid of the planetary boundary layer model onto the hydrodynamic model grid and subsequently stored for use by ADCIRC (Scheffner and Carson, 2001). In order to read in the wind velocities, ADCIRC has to convert the wind velocities to wind stress. This conversion is accomplished for this study by applying the following relationship proposed by Garratt
(1977):
τ sφ ρ = C air W W [1] D φ ρO ρ O and
τ ρ sλ = C air W W [2] D λ ρO ρO
where:
τ , τ = wind stress in the φ and λ directions sφ sλ
ρair / ρo = ratio of air density to average density of seawater, 0.00129
CD = computed frictional drag coefficient (0.75 + 0.067W) 0.001
| W | = magnitude of wind velocity
W , W = components of the wind velocity vector in the φ and λ directions φ λ
53 The PBL model also determines a pressure gradient. ADCIRC requires as input a pressure field expressed as an equivalent column height of water. The conversion from pressure gradient to height of water is realized by applying the transformation P/(ρw g). In the end, wind stress and water column values are linearly interpolated from the nested grids onto the finite element grid of ADCIRC (Blain et al., 1994).
4.3 Coastal Ocean Circulation Model
The computation of the water-surface elevations and currents during Hurricane Hugo
(1989) are obtained from the long-wave hydrodynamic model ADCIRC-2DDI. The model originated under the U.S. Army Corps of Engineers Dredging Research Program in the early 1990s. ADCIRC facilitates high computational efficiency, which allows for long numerical simulations using large computational grids and very large numbers of nodes (Scheffner and Carson, 2001). A finite element mesh is utilized in order to approximate the governing equations. ADCIRC uses the vertically averaged equations of mass and momentum conservation, subject to incompressibility, hydrostatic pressure, and the Boussinesq approximation (Luettich et al., 1992).
Linear, triangular elements facilitate spatial discretization, while, like in most finite element applications, finite difference schemes accomplish the forward marching in time
(Yeh, 1999). The model grew as a group of two-dimensional and three-dimensional programs. For this study, only the two-dimensional depth integrated feature is used.
54 According to Scheffner and Carson (2001), the capabilities of the two-dimensional option model can be summarized as follows:
Simulating tidal circulation and storm surge propagation over large computational
domains while simultaneously providing high resolution in areas of complex
shoreline and bathymetry. The targeted areas of interest include continental shelves
near-shore areas, and estuaries.
Representing all pertinent physics of motion. These include tidal potential, Coriolis
effect, and all non-linear terms of the governing equations.
Providing accurate and efficient computations over time periods ranging from
month to years.
ADCIRC-2DDI solves the fully nonlinear shallow water equations: continuity [3], and momentum [4], [5]. This leads to the following set of conservation statements in primitive non-conservative form of equations in a spherical coordinate system (Blair et al., 1994):
∂ζ 1 ∂UH ∂(VH cosφ ) + + = 0 [3] ∂t R cosφ ∂λ ∂φ
∂U 1 ∂U 1 ∂U tanφ + U + V − U + f V = ∂t R cosφ ∂λ R ∂φ R
1 ∂ ps 1 τ sλ − + g()ζ −αη + M λ + −τ ∗U [4] R cosφ ∂λ ρ 0 H ρ 0 H
55 ∂V 1 ∂V 1 ∂V tanφ + U + V + U + f U = ∂t R cosφ ∂λ R ∂φ R
1 ∂ ps 1 τ sφ − + g()ζ −αη + M φ + −τ ∗V [5] R ∂φ ρ0 H ρ 0 H
where:
t = time
λ = degrees longitude, east of Greenwich
φ = degrees latitude, north of Equator positive
ζ = free surface elevation, relative to the geoid
U = depth averaged horizontal velocity, λ direction
V = depth averaged horizontal velocity, φ direction
R = radius of the Earth
H = total water column, h + ζ
M λ = momentum dispersion, λ direction
M φ = momentum dispersion, φ direction
h = bathymetric depth, relative to the geoid
f = 2Ωsinφ = Coriolis parameter
Ω = angular speed of the Earth
ps = atmospheric pressure at the free surface
g = acceleration due to gravity
ρ0 = reference density of water
56 α = earth elasticity factor
τ sλ = applied free surface stress, λ direction
τ sφ = applied free surface stress, φ direction
U 2 + V 2 τ = C = bottom stress ∗ f H
Cf = bottom friction coefficient
The effective Newtonian equilibrium tide potential by Reid (1990) is given as follows:
2π (t −t0 ) η ()λ,φ,t = ∑ α jn C jn f jn (t0 )L j (φ )cos [6] n, j T jn + jλ + v jn ()t0 where:
C jn = Constant characterizing the amplitude of tidal constituent n of species j
α jn = effective earth elasticity factor for tidal constituent n of species j
f jn = time-dependent nodal factor
v jn = time-dependent astronomical argument
j = 0, 1, 2 = tidal species (j = 0, declinational; j = 1, diurnal; j = 2, semidiurnal)
2 L0 = 3 sin φ - 1 [7-1]
L1 = sin (2φ ) [7-2]
2 L2 = cos (φ ) [7-3]
t0 = reference time
T jn = period of constituent n of species j
57 The finite element solution is more readily obtained when the equations are first converted to the Carte-Parallelogramatique (CP) projection. Solving equations [3] to [5]
(CP projection of equations) gives rise to numerical instability. Therefore, it is necessary to reformulate the equations to provide stable solutions. Hence, ADCIRC-2DDI solves the Generalized Wave Continuity Equation (GWCE) together with the equations of momentum conservation. The GWCE is derived by first writing the primitive non- conservative momentum equations into conservative form. Then spatial derivatives are taken of these results. The spatial derivatives are substituted into a time-differentiated
primitive continuity equation. To this result, a weighting parameter, τ 0 , is applied and multiplied by the primitive continuity equation; this yields the GWCE [8]. The GWCE is then solved in combination with the momentum equations in either conservative or non- conservative form (Parrish and Hagen, 2002).
For all domains the wetting and drying feature is employed. A hybrid bottom friction function is used. This function proves to be more accurate in shallow water and when wetting and drying of elements are allowed (Murray, 2003).
58 The Generalized Wave-Continuity Equation, in spherical coordinates (Kolar, Gray,
Westerink and Luettich, 1994) is:
∂ 2ζ ∂ζ 1 ∂ 1 ∂UUH ∂UVH cosφ tanφ +τ − + − U + f VH 2 0 ∂t ∂t R cosφ ∂λ R cosφ ∂λ ∂φ R
E 2 H ∂ ps h2 ∂ ζ τ sλ − + g()ζ −αη + + − (τ ∗ −τ 0 )UH R cosφ ∂λ ρ 0 R cosφ ∂λ∂t ρ 0
1 ∂ 1 ∂HUV ∂HVV cosφ tanφ H ∂ ps − + + U + f UH − + g()ζ −αη R ∂φ R cosφ ∂λ ∂φ R R ∂φ ρ0
E 2 τ h2 ∂ ζ sφ tan φ ∂VH + + − ()τ ∗ −τ 0 VH − +τ 0VH = 0 [8] R ∂φ∂t ρ 0 R ∂t
59 CHAPTER 5
DESCRIPTION OF STUDY AREA
The study area is located in the northern region of the South Atlantic Bight along the southeast coast of the United States (Bennett, 1999). The main focus of our study is on a riverine system along the South Carolina coast that is strongly influenced by astronomical tides. It includes the Waccamaw River, northeast of Charleston, from Conway down to the confluence with the Atlantic Intracoastal Waterway (AIW), and the AIW from
Shallotte inlet and Little River inlet to Winyah Bay inlet. The study domain also includes portions of the shoreline between Charleston and Winyah Bay. Figure 5.1 shows the extent of the area of interest.
o o o o o o -83 00' -82 00' -81 00' -80 00' -79 00' -78 00'
o 35 o00' NORTH CAROLINA 35 00'
Lake Waccamaw
Waccamaw o o 34 00' SOUTH CAROLINA River 34 00' Conway Little River Winyah Bay AIW
GEORGIA o o 33 00' 33 00' Bulls Bay CharlestonCharelston ATLANTIC OCEAN
o 32 o 00' 32 00' -83 o00' -82 o00' -81 o00' -80 o00' -79 o00' -78 o00'
Figure 5.1: South Carolina Study Domain.
60 5.1 Riverine System
5.1.1 Waccamaw River
The Waccamaw River is a slow moving, black-water river with wide floodplains (Drewes and Conrads, 1995) situated within the Coastal Plain. It originates from Lake Waccamaw in extreme southeastern North Carolina (see Figure 5.1). From its origin, the river runs southward into South Carolina passing Longs, Conway, and Georgetown before flowing into the Atlantic Ocean at Winyah Bay inlet (see Figure 5.2). The river drains the coastal areas of southern North Carolina and northern South Carolina (Bennett, 1999).
Figure 5.2: Study Domain Waccamaw River and AIW (Drewes and Conrads, 1995). 61 For the period 1995 to 2000, the annual average recorded discharge at Marina, Conway, was 63 m3/s (USGS, 2000). The entire Waccamaw drainage area covers approximately
36,000 km2. The bulk of the land comprising the river’s watershed is forest or forested wetland. Roughly equal portions (6 to 7%) have been converted to agricultural and urban uses, the later consisting mostly of the area around Conway and Georgetown. However, the percentage of watershed land remaining in a relatively undisturbed condition is declining (Drewes and Conrads, 1995).
The Waccamaw River forms a confluence with the AIW about 68 km upstream from
Winyah Bay inlet and about 58 km from Little River inlet (see Figure 5.2). The river stretching from the confluence down to Winyah Bay is presently referred to as the
Atlantic Intracoastal Waterway (Drewes and Conrads, 1995).
5.1.2 Atlantic Intracoastal Waterway
The AIW is a shipping route, extending for about 4,800 km along the U.S. east coast and the Gulf of Mexico. In 1938, the River and Harbors Act authorized the construction of the AIW stating that a 3.65-meter channel depth be maintained in order to allow the use of larger vessels and private carriers. Despite the 3.65-m authorization, the project depth along the Waterways varies between 3.65 m to as little as 1.50 m. The actual controlling depth in portions of the Intracoastal is often 2.40 m to 2.75 m or less (AIWA, 2004). For much of its length, the system consists of naturally deep estuaries, rivers and sounds.
62 These natural stretches are connected by man-made cuts through land areas and shallows, many of which require periodic dredging to maintain their depths (AIWA, 2004).
Prior to the 1930s the Waccamaw River only ran to the south towards Winyah Bay. Since the U.S. Army Corps of Engineers constructed the canal, between Enterprise Landing and
Little River inlet (see Figure 5.2), portions of the Waccamaw discharge, at the confluence, flows east towards Little River and Shallotte inlets. Like the Waccamaw the
AIW is affected by tides throughout its entire reach. Drewes and Conrads (1995) report a mean tide range of 1.22 m at Nixon’s Crossroads and one of 1.07 m at Hagley Landing.
5.1.3 Pee Dee River and Black River
After the confluence with the Waccamaw, the Intracoastal receives freshwater from two major tributaries: the Pee Dee River and the Black River (see Figure 5.2). Both rivers are tidally affected (Drewes and Conrads, 1995). The Pee Dee River basin contributes the largest portion of freshwater inflow to Winyah Bay, in general about 60% of the average inflow (Johnson, 1972). The Pee Dee River receives freshwater from the Lynches River and the Little Pee Dee River. The annual average Pee Dee streamflow is about 400 m3/s
(see Table 5.1) that includes the discharge from the Lynches River, approx. 30 m3/s, and the Little Pee Dee River, approx. 90 m3/s (Drewes and Conrads, 1995). The downstream stretch of the Pee Dee River branches into three small creeks; Bull Creek, Thoroughfare
Creek, and Schooner Creek (see Figure 5.2). The majority of freshwater from the Pee
Dee basin moves through Bull Creek to the AIW (Johnson 1972). 63 Table 5.1: Annual average Freshwater Inflow to Winyah Bay (Johnson, 1972).
River / Location Annual Mean Inflow Percentage to total Inflow
Waccamaw River 110 m3/s 25 %
Pee Dee River 190 m3/s 42 %
Lynches River 20 m3/s 4 %
Little Pee Dee River 60 m3/s 13 %
Black River 70 m3/s 16 %
Winyah Bay 450 m3/s 100 %
The Black River contributes approximately 16% of the annual average freshwater inflow to Winyah Bay (Drewes and Conrads, 1995). Table 5.1 displays estimated annual average freshwater inflows to Winyah Bay, based on the research by Johnson (1972).
5.2 Estuarine System
According to Johnson’s (1972) definition, an estuary generally extends from the river mouth upstream to that point at which tidal fluctuations no longer affect the water-surface elevation of the river. Pritschard (1967) defines an estuary as a semi-enclosed coastal body of water that has a free connection with the open sea and within which seawater is measurably diluted with freshwater derived from land drainage.
64 5.2.1 Winyah Bay
The Winyah Bay (see Figure 5.3) estuary is about 7 km across at its widest location near the middle of the bay and about 1.5 km wide at the ocean’s inlet. Within the bay, there are several large islands and a shallow area, called Mud Bay. The distance from the
Winyah Bay entrance to Georgetown is about 23 km. In order to assure ship navigation a channel is maintained at a minimum depth of 9 m throughout the bay (Bennett, 1999).
Near its mouth, the bay is protected by a massive barrier island, which has dunes as high as 12 m (Schuck-Kolben and Cherry, 1995). A former entrance to the bay is located to the North; refereed to as North Inlet. The former entrance is now part of the National
Estuarine Research Reserve System.
Georgetown
North Inlet
Figure 5.3: Winyah Bay (Maptech Terrain Navigator 2002). 65 5.2.2 Bulls Bay
Another estuary of major interest is Bulls Bay (see Figure 5.4). The bay is situated about
40 km northeast of Charleston harbor and approximately 40 km southwest of Winyah
Bay. Several small marsh islands engulf the 12 km-long and 6 km-wide bay. Within the bay, the average water depth is about 2.5 m. The Atlantic Intracoastal Waterway passes immediately inland from the West shore of the bay. Note that during Hurricane Hugo, the highest water elevations occurred inland at Awendaw (6.2 m) and McClellanville (5.0 to
5.5 m) (see Figure 5.4).
McClellanville
Awendaw
AIW
Figure 5.4: Bulls Bay (Maptech Terrain Navigator 2002).
66 5.2.3 Charleston Harbor
The most densely populated localities in the study area are Charleston, Mount Pleasant,
Sullivan Island, and Isle of Palms (see Figure 5.5). Sullivan Island and Isle of Palms are barrier islands and were severally inundated during the 1989 hurricane event. Within the bay shipping channels are maintained at a project depth of 6 to 11 m. Three rivers stream into the harbor: the Cooper River, the Wando River, and the Ashley River. In general, the riverine system within the bay is highly canalized. A sea wall, approx. 2.5 m, at the southern shoreline of Charleston protects the city from wave overtopping during rough sea. Tidal Station Sullivan Island Figure 5.5: Charleston Harbor (Maptech Terrain Navigator 2002). 67 The harbor also accommodates a water level station on the eastside of Charleston (see Figure 5.5). The National Oceanic and Atmospheric Administration (NOAA) have operated a station since 1899. Fortunately, the tidal station was able to record water elevations during Hurricane Hugo. Other stations, e.g., Springmaid Pier, SC, were destroyed by the hurricane. The recorded historical data at Charleston Harbor proved to be the only available data for verification of the computed sea level stages. 68 CHAPTER 6 DEVELOPMENT OF THE FINITE ELEMENT MESHES A numerical model for storm tides must resolve the physical equations that affect storm surge generation and propagation as well as the astronomical tides. The period, wavelength, and amplitude features of a storm surge rely on geometric properties of the water body (i.e., bathymetry and topography) and characteristics of the meteorological forcing (Blain et al., 1994). Therefore, in order to obtain reliable simulation results a model domain has to incorporate complex coastal geometries, account for quickly changing bathymetry in the continental slope and shelf areas, and permit reasonable boundary condition specification. The ideal formulation for satisfying these kinds of requirements is a finite element mesh (Blain et al., 1994). Five different two-dimensional finite element models are applied in order to evaluate the surge-tide-streamflow interaction within our study domain. The water elevations are computed by applying triangular finite elements to all domains. Four computational domains comprise a semicircular mesh encompassing the South Carolina coast and the continental shelf including the Winyah Bay, AIW, and portions of the Waccamaw River (see Figure 6.1). Previous work by Bennett (1999) and Murray (2003) helped to establish the meshes that include inland topography. One of the four meshes (SC-1-FP) is then incorporated into a newly generated Western North Atlantic Tidal (WNAT) model domain (see Figure 6.2) to produce an additional computational region. 69 6.1 The open-ocean Boundary Placement Several studies in the past have proven that extending the open-ocean boundary in deep water is advantageous as compared to placement on the continental shelf or the shelf break. The complicated shelf topography (or bathymetry) causes nonlinear constituents, phasing errors, and rapidly changing gradients in surface elevation and velocity (Kolar, et al., 1994). Furthermore, hurricane storm surge typically builds up significantly on the continental shelf (Feyen, Atkinson, and Westerink, 2004). NORTH CAROLINA Conway, SC Cape Fear, NC GEORGIA Hilton Head, SC Figure 6.1: South Carolina Mesh location with respect to the State of South Carolina. 70 Therefore, placing the open-ocean boundary in deep ocean regions can have several advantages (Kolar et al., 1994): 1) the prediction of amplitude and phase can be accurately accomplished by coupling it to a global ocean model; 2) nonlinear processes are insignificant; 3) geometric simplicity of a boundary and 4) regional wind fields do not dramatically affect sea surface elevations. United States 60º West Meridian Florida South Carolina Study Domain Gulf of Mexico Atlantic Ocean Central America Figure 6.2: Western North Atlantic Tidal (WNAT) Model Domain Boundaries. 71 The open-ocean boundaries for the South Carolina domains are located within the continental shelf break and the continental shelf (see Figure 6.3). The open-ocean boundary for the WNAT model is placed in the deep ocean. Hence, the open-ocean boundary conditions for the shelf-based South Carolina meshes are computed by using the WNAT model domain. A result comparison between the computational results by using the South Carolina meshes and the WNAT model domain is presented and discussed in Chapter 8 (Simulation Results). 6.2 South Carolina Study Domain Four different South Carolina meshes (SC-1, SC-1-FP, SC-2, and SC-2-FP) are used in order to compute the storm tide stages. Two meshes (SC-1-FP and SC-2-FP) include inland topography that is employed through the wetting and drying of elements. The different study domains all accommodate important inlets along the South Carolina coast. All meshes include the same semi-circular arc at the open-ocean boundary. The endpoints are located at Hilton Head Island, South Carolina and Cape Fear, North Carolina (see Figure 6.1). The arc extends about 100 km into the Atlantic Ocean. The mesh elements within the Atlantic Ocean and the majority of the continental shelf remain the same for all domains. Slight grid alterations had to be made along the coast and estuaries, insignificant to the computational results. The maximum element size for all meshes is 14 km. Digitized shoreline and riverbank information is retrieved from the Coastline Extractor at: http://www.ngdc.noaa.gov/mgg/shorelines/shorelines.html (National Geophysical Data Center; NGDC). 72 A state-of-the-art mesh generation software (Surface-water Modeling System; SMS) is utilized in order to incorporate the inland topography. SMS (2002) is a pre- and post- processor for surface water modeling and analysis. The software facilitates reading in background images, e.g., USGS contour-elevation maps (topographic maps). It proved to be very useful to have these maps available on CD-ROM (http://www.maptech.com). SMS also allows reading in bathymetric and topographic data within the Atlantic Ocean, Waccamaw River, AIW, and inland areas. The elevation data (called scatter points) is obtained from the NGDC Coastal Relief CD- ROM, Volume 2, Version 1.0 (1999). The NGDC collects the data from several sources. Land elevations come from the United States Geological Survey/National Image Mapping Agency 1:250,000 or 1-degree Digital Elevation Models of the states. Soundings for each volume of the Coastal Relief model series are compiled from hydrographic surveys conducted by the National Ocean Service and from various academic institutions. The CD-ROM provides a database of 3-arc-second (approx. 90 m) resolution elevations in 1-degree grids for the U.S. coastal areas. One is able to specify grid boundaries to the nearest minute of longitude and latitude, grid resolution from 3- seconds to 1-minute, a water datum reference, and file download formats (Bennett, 1999). For all South Carolina meshes, the water datum reference is Mean Sea Level (MSL), and a precision of 1/10 of a meter is used. A scatter point resolution of 3-arc-second and 6- arc-second is used. Figure 6.3 shows the ocean’s bathymetry and the inland topography within the area of interest. Figure 6.4 shows the associated scatter point resolution of the inland topography. 73 Bathymetry and Inland Topography (m) Continental Shelf Inland Topography Shelf Break Charleston Continental Slope Figure 6.3: Bathymetry and Inland Topography South Carolina Study Domain. Legend: 3-arc-second Resolution 6-arc-second Resolution Figure 6.4: Scatter Point Set Resolution. 74 The NGDC elevation information is retrieved from the CD-ROM and read in to SMS by means of an “Import Wizard” that converts scatter points into a Shoals File (*.pts). Within SMS, scatter points (Horizontal Datum: North American Datum of 1983; NAD 83) can be easily transformed to any commonly used datum, in our case the North American Datum of 1927 (NAD 27). It has to be noted that the elevation data on the Coastal Relief CD-ROM (1999) is negative below MSL and positive above MSL. In ADCIRC-2DDI, the bathymetry is considered to be positive below MSL and negative above MSL, i.e., the opposite than the NGDC convention. Therefore, after the elevation points are read in they have to be converted from positive to negative and vice versa. This can be easily accomplished by using the SMS integrated “Data Calculator” in the map module. After building the mesh, the converted scatter points are then interpolated onto the mesh nodes. In the following four sections, the development of the four South Carolina domains is explained. Special attention is drawn on the development of the two “Floodplain Meshes”: SC-1-FP, and SC-2-FP. Brief explanations are also given on the generation of the SC-1 and SC-2 mesh. 75 6.2.1 SC-1 Bennett developed the SC-1 mesh (see Figure 6.5) and provides a thorough explanation on the mesh development in his thesis (Bennett, 1999). Again, the mesh accommodates all important inlets and bays along the South Carolina coast. The Winyah Bay region includes small portions of the AIW, and the Black River. The assigned boundary type for the shoreline boundary and the river boundary is a no-flow boundary condition. This means that the boundaries act like vertical walls by not allowing any flow through it. The same type of boundary condition is applied to river islands and ocean islands. SC-1 Node No.: 10,400 AIW Element No.: 19,000 Black River Winyah Bay Bulls Bay Charleston Figure 6.5: South Carolina Mesh SC-1, without Floodplains. 76 6.2.2 SC-1-FP The SC-1-FP (see Figure 6.6) mesh is an adaptation of the SC-1 mesh. The appending of the mesh is accomplished by defining a preliminary inland boundary, far enough inland from the river and coastline boundary that covers the observed inundation areas (see Figure 6.7). Information regarding inundated areas, during Hurricane Hugo, is retrieved from anecdotal records, depicted inundation areas, surveyed high water mark maps and topographic maps from the U.S. Geological Survey (USGS). Within the study area, barrier islands as well as river islands are “meshed over” allowing for wetting and drying of elements. SC-1-FP Node No.: 14,500 Element No.: 27,600 Figure 6.6: South Carolina Mesh SC-1-FP, with Floodplains. 77 Preliminary Boundary SC-1 Boundary Final SC-1-FP Boundary (approx. 6 m contour line) Figure 6.7: Boundary Development Stages for the SC-1-FP Mesh. Deleted Nodes > 6.0 m SC-1 Boundary Final SC-1-FP Boundary (approx. 6 m contour line) Figure 6.8: Boundary Development Stages for the SC-1-FP, Inset Winyah Bay. 78 Large portions of pertinent tributary basins (Black River, Sampit River, and Santee River) are included within these boundaries as well. In addition, the boundaries should not restrict the water-flow and allow the storm surge to spread out into floodplains and inundation areas. Islands within the riverine system of the AIW are also incorporated in the mesh. The same applies for barrier islands along the shoreline between Charleston harbor and Winyah Bay inlet. A node spacing of 600 m is determined along the preliminary boundary. The next step is the development of the new mesh portion covering the area between the SC-1 no-flow boundary and the preliminary boundary, referred to as inland topography. Prior to the meshing of the inland topography a new feature polygon has to be created in the map module of SMS. The mesh type “Paving” is selected in the “Polygon Attributes” window that subsequently triggers SMS to build triangular finite elements within the specified polygon. The next step is to retrieve elevation data from the NGDC CD-ROM (1999). The selected data has a resolution of 6-arc-second (approx. 180 m). In order to ensure the same bathymetry the new scatter points that overlap with the SC-1 mesh are deleted. Scatter points outside the preliminary boundary are deleted as well. Next, the new scatter point set is merged with the existing SC-1 mesh elevation data. Now, the merged data can be used for interpolation onto the nodes of the entire mesh. The final SC-1-FP mesh boundary is accomplished by deleting all nodes with elevations exceeding 6.0 m (see Figure 6.8). 79 6.2.3 SC-2 Murray (2003) extended the SC-1 mesh’s river boundary by including the AIW from Hagley Landing to Little River inlet and Shallotte inlet. He also integrated the Waccamaw reach from its confluence with the AIW up to Conway. The highly refined “Murray mesh” (with 65,000 nodes and 115,000 elements) includes too many nodes for storm surge simulations. As a result, a new mesh (see Figure 6.9) has been generated based on the river boundaries outlined by Murray (2003). The number of nodes was reduced by about 50% to 34,000 nodes. SC-2 Waccamaw River AIW Little River Inlet Node No.: 34,000 Element No.: 56,300 Figure 6.9: South Carolina Mesh SC-2, without Floodplains. 80 One feature of the newly developed mesh is that only three elements are used across the river (see Figure 6.10). Three elements across assure a good approximation of the parabolic or trapezoidal shape of the river cross-sections. Furthermore, three elements across enables proper generation and propagation of the storm surge wave throughout the scheme. This especially proves important to a riverine system with an extended upstream body like the Waccamaw River and AIW. At the same time, an artificial riverbed slope is pronounced along the Waccamaw River from Conway down to the confluence and along the AIW from Shallotte inlet and Little River inlet down to Winyah Bay inlet (see Figure 6.11). Depth and riverbed gradients are determined based on surveyed river cross-sections and information retrieved from Nautical Chart No. 11536 (1994). The starting depth at Conway is 3.0 m below MSL. At the confluence a depth of 4.0 m below MSL is defined. From the confluence a gradual slope is applied towards Little River inlet and Shallotte inlet. A steeper slope is forced towards Winyah Bay inlet. Little River inlet maintains a depth of 4.5 m while Winyah Bay inlet has a depth of 6.5 m. 81 Waccamaw River Island AIW Confluence AIW Figure 6.10: Mesh Structure at the Confluence of the Waccamaw River and the AIW. Conway: 3.0 m below MSL 24 km Confluence: 4.0 m below MSL 58 km 68 km Little River inlet: 4.5 m below MSL Winyah Bay inlet: 6.5 m below Figure 6.11: River Depth and River Slope Schematic, Waccamaw River and AIW. 82 6.2.4 SC-2-FP The SC-2-FP (see Figure 6.12) mesh is built based upon the SC-2 mesh. For the generation of the SC-2-FP mesh, the same procedure is applied as for the SC-1-FP as discussed (above in Section 6.2.2). Hence a preliminary inland boundary is established that covers inundation areas, floodplains, and significant river basins (Figure 6.13). Storm tide simulations prior to the generation of the SC-2-FP mesh, utilizing the SC-1-FP mesh, helped to reduce the size of the preliminary boundary. Furthermore, the extension of the riverine system, in the SC-2 mesh, allows incorporating large portions of the downstream floodplains of the Sampit River, the Black River, and the Pee Dee River. SC-2-FP Node No.: 118,000 Element No.: 227,000 Figure 6.12: South Carolina Mesh SC-2-FP, with Floodplains. 83 Due to a high mesh resolution of the SC-2 domain a node spacing of 500 m is chosen along the preliminary boundary. After building the necessary inland topography polygon SMS automatically meshes the selected area. The generated mesh is composed of 244,000 nodes and 485,000 elements. In order to minimize the vast amount of elevation information a 3-arc-second resolution is employed adjacent to the Waccamaw River, AIW, and along the ocean’s shore. A 6- arc-second resolution is used far inland, where the mesh size is coarser (see Figure 6.4). Again, scatter points that overlap with the SC-2 elevation points are deleted as well as the points outside the preliminary boundary. Preliminary Boundary SC-2 Boundary Final SC-2-FP Boundary (approx. 6 m contour line) Figure 6.13: Boundary Development Stages for the SC-2-FP Mesh. 84 After reading in the merged scatter points onto the mesh, the nodes with elevation exceeding 6.0 m are deleted. The final mesh comprises of 118,000 nodes and 227,000 elements, including riverine and barrier islands. The nodes and elements are reduced by about 50% with respect to the starting mesh. The following pages display detailed insets of the mesh and bathymetry at Bulls Bay (Figure 6.16), Winyah Bay (Figure 6.17), Winyah Bay islands (Figure 6.18), and the confluence AIW and Waccamaw River (Figure 6.19). Note that the stated meter values, in the mesh detail, refer to the mesh size in the surrounding area. Figure 6.17 Figure 6.16 Figure 6.14: Locations of Insets in the SC-2-FP Mesh. 85 Figure 6.19 Figure 6.18 Figure 6.15: Locations of Insets along the Waccamaw River and the AIW. 86 (a) 500 m 700 m 2,000 m (b) Bathymetry/Topography (m) Figure 6.16: Bulls Bay, (a) Mesh Detail and (b) Bathymetry and Inland Topography. 87 (a) 2,000 m 500 m (b) Bathymetry/Topography (m) Figure 6.17: Winyah Bay, (a) Mesh Detail and (b) Bathymetry and Inland Topography. 88 (a) 450 m 25 m 50 m 180 m (b) Figure 6.18: Winyah Bay, (a) Mesh Detail and (b) Bathymetry and Inland Topography. 89 (a) 25 m 15 m 40 m (b) Topography Figure 6.19: Confluence Waccamaw and AIW, (a) Mesh Detail and (b) Topography. 90 6.2.5 Comparison South Carolina Meshes The following eight insets illustrate the mesh differences between the four South Carolina meshes at Bulls Bay (Figure 6.20) and at Winyah Bay (Figure 6.21). The insets clearly show the increased mesh-resolution within the Winyah Bay region, while for the Bulls Bay area the mesh resolution remains about the same for all meshes. In addition, Table 6.1 shows the characteristic of the four South Carolina meshes engaged in this study. (a) (b) (c) (d) Figure 6.20: Mesh Distinction Bulls Bay (a) SC-1, (b) SC-1-FP, (c) SC-2, and (d) SC-2-FP. 91 Table 6.1: Characteristics of the South Carolina Model Meshes. Smallest Domain Floodplain Nodes Elements Element Figure Page Size SC-1 No 10,400 19,000 65 m 6.5 76 SC-1-FP Yes 14,500 27,600 65 m 6.6 77 SC-2 No 34,000 56,300 9 m 6.9 80 SC-2-FP Yes 118,000 227,000 9 m 6.12 83 (a) (b) (c) (d) Figure 6.21: Mesh Distinction Winyah Bay (a) SC-1, (b) SC-1-FP, (c) SC-2, and (d) SC-2-FP. 92 6.3 Western North Atlantic Tidal Domain In order to verify whether the South Carolina domain is sufficient for approximating the storm surge and the astronomical tides one of the floodplain meshes is incorporated into a large computational domain: the Western North Atlantic Tidal (WNAT) model domain. Preliminary simulation results showed that the SC-1-FP mesh produces results with the same accuracy as the SC-2-FP mesh. Hence, the more efficient SC-1-FP mesh is included in the WNAT model domain. The coastal boundaries of the WNAT mesh are composed of the South, Central, and North American coastline. The entire domain covers an area of about 8.4 million km2 (Parrish, 2001). The following pages display figures of the entire WNAT-SC-1-FP finite element mesh (Figure 6.22), the related bathymetry (Figure 6.23), as well as two insets showing the southeast coast (Figure 6.24 and 6.25). In the insets, the rectangular box represents the extent of the wind field and the semi-circle delineates the South Carolina study domain. 93 United States 60ºWest Meridian Florida Atlantic Ocean Gulf of Mexico Central America Figure 6.22: The relaxed Western North Atlantic Tidal Model Domain based on a localized truncation error analysis (Hagen and Parrish, 2004; Funakoshi, Hagen, Zundel, and Kojima, 2004). 94 Figure 6.23: Bathymetry WNAT-SC-1-FP. 95 Figure 6.25 Figure 6.26 Figure 6.24: Locations of Insets within the WNAT-SC-1-FP. 96 (a) 40 km 70-100 km 25 km (b) Figure 6.25: U.S. Southeast Coast, (a) Mesh Detail and (b) Bathymetry. 97 (a) 10 km 8 km 35 km 6 km (b) Figure 6.26: South Carolina Coast, (a) Mesh Detail and (b) Bathymetry. 98 CHAPTER 7 MODEL PARAMETERS AND PERFORMANCE 7.1 Computational Model Parameters Storm tide simulations using two significantly different study domains (the South Carolina domain and the Western North Atlantic Tidal model domain) requires that parameters in the ADCIRC input file (fort.15) be set differently. This includes, for instance, parameters that control the wetting and drying process, the selection of different time-steps, running simulations with the advection terms on or off, etc. Accordingly, the selected computational model parameters are presented for each study domain separately. 7.1.1 South Carolina Domain The model parameters for the ADCIRC-2DDI, South Carolina, simulations are as follows: The GWCE is solved in conjunction with the conservative form of the momentum equations. The chosen coordinate system is spherical. The simulations are begun from a cold start and the advective terms are included. Eight tidal elevation forcings (K1, M2, M4, M6, N2, O1, S2, and Steady) are applied at the open-ocean boundaries (see Table 7.1). Boundary forcings are ramped over a period of 0.5 days. Meteorological forcings (wind speed and surface pressure) are read into the mesh every 15 minutes. The total simulation time is 1.75 days (September 20, 1989, 6 p.m. to 99 September 22, 12 p.m.). For the two “Floodplain Meshes” the minimum depth of wetting and drying elements is set at 0.01 m; this means that if the computational mesh possesses bathymetric points less than 0.01 m, ADCIRC sets the bathymetry to 0.01 m at the corresponding node (ADCIRC Manual). The two other meshes (SC-1 and SC-2) have a minimum depth of wetting and drying elements of 0.05 m. The bottom friction term selection parameter is set to operate with the hybrid formulation, i.e., in deep water the friction coefficient is constant and a quadratic bottom friction law is employed, where in shallow water the friction coefficient increases as the depth decreases (similar to a Manning-type friction law). The specified hybrid friction parameters are: minimum friction coefficient, Cfmin = 0.0025, break depth, Hbreak = 1 m, and the two dimensionless parameters θ = 10 and λ = 1/3 (Murray, 2003). The eddy viscosity is set at 5.0 m2/s. The GWCE weighting factor, τ 0 , is set to 0.020. The time steps, applied to the different domains, are displayed in Table 7.2. The ADCIRC-2DDI parameter input file (fort.15) is shown in Appendix B. 7.1.2 Western North Atlantic Tidal model domain Over the large model domain, astronomical tides and storm surge elevations are computed separately due to the difference in finite element mesh size and wind field extent. The storm tide is calculated by adding the two stages. 100 The model parameters for the ADCIRC-2DDI, astronomical tides, simulations are as follows: The GWCE is solved in conjunction with the non-conservative form of the momentum equations. The chosen coordinate system is spherical. The simulations are begun from a cold start. Advective terms are not included. Seven tidal potential forcings (K1, K2, M2, N2, O1, Q1, and S2) are applied simultaneously over the entire domain. At the same time, the open-ocean boundary is depth forced with amplitude and phase of the same seven constituents. Boundary forcings are ramped over a period of 20 days for stable solutions. The total simulation time is 35 days (August 20, 1989, 0 a.m. to September 25, 1989, 0 a.m.). The minimum depth of wetting and drying elements is set at 0.05 m. The hybrid formulation is employed. The specified hybrid friction parameters are: minimum friction coefficient, Cfmin = 0.0025, break depth, Hbreak = 1 m, and the two dimensionless parameters θ = 10 and λ = 1/3. The eddy viscosity is set at 5.0 m2/s. The GWCE weighting factor, τ 0 , is set to 0.020. The time step is five seconds (see Table 7.2). The model parameters for the ADCIRC-2DDI, storm surge, simulations are as follows: The GWCE is solved in conjunction with the non-conservative form of the momentum equations. The chosen coordinate system is spherical. The simulations are begun from a cold start. Advective terms are not included. Boundary forcings are ramped over a period of 0.5 days. Meteorological forcings (wind speed and surface pressure) are read in to the mesh every 15 minutes. The total simulation time is 1.75 days (September 20, 1989, 6 101 Table 7.1: Tidal Constituents used to force the ADCIRC-2DDI model. Symbol Name Period Frequency K1 Luni-solar diurnal 23.93 hr 0.000072921165921 K2 Luni-solar semidiurnal 11.97 hr 0.000145842317201 M2 Principal lunar semidiurnal 12.42 hr 0.000140518917083 M4 Shallow water overtides of principal lunar 6.21 hr 0.000281037834166 M6 Shallow water overtides of principal lunar 4.14 hr 0.000421556751249 N2 Larger lunar elliptic 12.66 hr 0.000137879700000 O1 Principal lunar diurnal 25.82 hr 0.000067597751162 Q1 Larger lunar elliptic diurnal 26.87 hr 0.000064958541129 S2 Principal solar semidiurnal 12.00 hr 0.000145444119418 STEADY STEADY ∞ 0.000000000000000 p.m. to September 22, 12 p.m.). The minimum depth of wetting and drying elements is set at 0.05 m. The hybrid formulation is employed. The same hybrid friction parameters are used specified in the astronomical tides run. The eddy viscosity is set at 5.0 m2/s. The GWCE weighting factor, τ 0 , is set to 0.020. The time step is five seconds. 7.2 Computational Performance The storm tide simulations are performed in the Compaq Water Resources Simulations Laboratory, at the University of Central Florida, Orlando (http://cwrsl.cecs.ucf.edu/). The 102 laboratory is equipped with a twelve-node Compaq-ALPHA cluster; each unit contains a 600 MHz processor. These machines can be run either in serial or as a high-speed parallel system. Running simulations on all twelve processors splits the mesh into twelve sub- domains that are post-processed to one domain after computation. A 1.4 GHz Myrinet switch establishes the communication between the processors. For each finite element mesh, Table 7.2 shows the recorded run time in serial (1 processor) and in parallel (12 processors). Table 7.2: Computational Model Setup and Performance (1.75 days). Run Time Run Time Domain Node No. Time Step 1 Processor 12 Processors SC-1 10,400 6 s 48 min 1 4 min 2 SC-1-FP 14,500 6 s 1 hr 21 min 1 7 min 2 SC-2 34,000 0.6 s 21 hr 2 1 hr 45 min 1 SC-2-FP 118,000 0.6 s 90 hr 2 7 hr 30 min 1 WNAT-SC-1-FP 109,000 5 s 12 hr 2 57 min 3 1. Recorded run time. 2. A linear speedup relationship between run time and number of processors is achieved and therefore applied to these calculations. 3. Recorded run time for the computation of the storm surge only. The computation of the tides only (35-day simulation, 25-day ramp) takes 23 hr (on 12 processors). 103 CHAPTER 8 SIMULATION RESULTS AND DISCUSSION First, a comparison between computed and resynthesized tide stages is shown at Springmaid Pier and Charleston harbor in order to verify that the finite element meshes are accurately simulating the tides at known tidal stations. Furthermore, sea elevation outputs (with and without river inflows) are evaluated at Charleston harbor. The comparison confirms that the river inflows have no significant effect on the computed water stages (amplitude and phase) for the time period from September 20th to 22nd, 1989. The three main simulation results are presented in Section 8.2 to 8.4: 1) inundation areas along the AIW and within the region of Bulls Bay, 2) five storm tide hydrographs along the South Carolina coast at Charleston harbor, Bulls Bay, Winyah Bay inlet, Awendaw, and McClellanville, and 3) several hydrographs recording the sea elevations at the entrance to the Winyah Bay. 8.1 Tidal Signal Verification The South Carolina meshes used in this thesis have been subject to several model verifications (Bennett, 1999 and Murray, 2003). The studies emphasized whether the models simulate the tides at the shoreline accurately. Both studies showed an apparent phasing error of the tidal signal at Charleston harbor. 104 Bennett (1999) examined the SC-1 mesh’s performance by comparing recorded historical data at Charleston harbor. Murray (2003) validated the SC-2 mesh’s performance by using resynthesized data that was based on information obtained from Charleston harbor and Springmaid Pier. He compared resynthesized data with simulated model results (see Figure 8.1 and 8.2). Both of them used five constituents (M2, N2, S2, K1, and O1) for their assessment. Bennett (1999) concluded that the SC-1 mesh simulates “the tidal elevations reasonably well” at Charleston harbor. Murray (2003) found that the SC-2 mesh “does a very good job” at Springmaid Pier (Figure 8.1) but shows only good to fair simulation results at Charleston harbor due to a shift in phase (Figure 8.2). He suggested that the phasing error could be overcome by inputting a “large number of freshwater inflows” at Charleston. Two steady river inflow events (average flow: 500 m3/s, and extreme flow: 5,000 m3/s) are read in to the SC-2 mesh in order to see whether the simulated tidal signal is improved (see Figure 8.3 and 8.4). Historical USGS streamflow data is used from the Tailrace Canal (Cooper River) at Moncks Corner. The gaging station is located 50 km upstream from Charleston harbor, just downstream of Lake Moultrie. The recording period from 1979 to 2000 shows streamflow data as follows: annual mean = 230 m3/s, highest daily mean = 953 m3/s (USGS, 2000). Between September 21 and September 22, 1989, the recorded average freshwater inflow was about 100 m3/s (USGS, 1989). While the extreme flow event helps to examine whether a significant change in the tidal signal occurs, the increased average freshwater inflow considers lateral inflows between Lake Moultrie and Charleston harbor. 105 1.50 Resynthesized Tidal Signal 1.00 Simulation Result (SC-2) 0.50 L [m] MS 0.00 Deviation from -0.50 -1.00 -1.50 0 6 12 18 24 Time into Resynthesis [Hours] Figure 8.1: Springmaid Pier, resynthesized and simulated tidal Signal (Murray, 2003). 1.50 Resynthesized Tidal Signal 1.00 Simulation Result (SC-2) ] 0.50 [m L 0.00 form MS viation -0.50 De -1.00 -1.50 0 6 12 18 24 Time into Resynthesis [Hours] Figure 8.2: Charleston Harbor, resynthesized and simulated tidal Signal (Murray, 2003). 106 3.50 Historical Data 3.00 Charleston (No Inflow) 2.50 Charleston (Q = 500 m3/s) 2.00 Charleston (Q = 5,000 m3/s) L [m] 1.50 1.00 Deviation from MS 0.50 0.00 -0.50 -1.00 9/21/1989 9:00 9/21/1989 12:00 9/21/1989 15:00 9/21/1989 18:00 9/21/198 9 21:00 9/22/1989 0:00 9/22/1989 3:00 9/22/1989 6:00 9/22/1989 9:00 Time [Date and Time] Figure 8.3: Charleston Harbor Hydrograph, with and without River Inflow. 3.50 Historical Data 3.00 Charleston (No Inflow) 2.50 Charleston (Q = 500 m3/s) 2.00 Charleston (Q = 5,000 m3/s) ] L [m S 1.50 M tion from 1.00 via De 0.50 0.00 -0.50 -1.00 9/21/1989 9:00 9/21/1989 12:00 9/21/1989 15:00 9/21/1989 18:00 9/21/1989 21:00 9/22/1989 0:00 9/22/1989 3:00 Time [Date and Time] Figure 8.4: Charleston Harbor Hydrograph Inset. 107 Both computational results (see Figure 8.3 and 8.4) reveal that an increase in water elevations occurs only during low tides but a shift in phase is not evident. Hence, including freshwater inflow (at Charleston) does not cause a shift of the tidal signal. The phasing discrepancy has other reasons, e.g., the model does not adequately describe the actual bathymetry within Charleston harbor. The findings lead to the conclusion that including average freshwater inflows, for the time of storm surge simulation, are not going to affect the computational results significantly. However, it has to be noted that other events (e.g., Hurricane Floyd in 1999) may have different effects on the rising limb. 108 8.2 Inundation Areas This section focuses on presenting the extension of the computed flooded areas along the Atlantic Intracoastal Waterway, the Waccamaw River and Winyah Bay. Inundation figures of the Bulls Bay region are shown in Section 8.3 (see Figure 8.14 and 8.15). All inundation figures (Figure 8.5b, 8.6 to 8.9) show a snapshot around 12.00 p.m. on September 22, 1989. On the following page, an output comparison is presented between an ADCIRC generated output (Figure 8.5b) and a SLOSH output developed by the USACE (Figure 8.5a). Note that when Hurricane Hugo made landfall it was a Category 2 storm. Therefore, in the SLOSH output the blue colored areas have to be compared with the ADCIRC output. It is not known on what assumptions the USACE generated the SLOSH data, i.e., topographic information; forward speed of the storm; hurricane landfall region; and at what angle did the hurricane hit the coastline, etc. Both figures show about the same extent of flooding. At the Winyah Bay inlet, SLOSH indicates the overtopping of a large barrier island. Clearly this was not the case during Hurricane Hugo (Schuck-Kolben and Cheery, 1995). Another difference is shown in the Pee Dee River Basin. The ADCIRC computed surge extends further up the basin. Also, it seems ADCIRC does a better job in predicting the flooding along the AIW and the Waccamaw River. The SLOSH figure does not depict any inundation along the two rivers 109 (a) (b) Bull Creek Pee Dee River Basin Black River Basin Sampit River Basin Open Sea Category 1 Category 2 Category 3 Category 4 Category 5 100yr Flood Figure 8.5: Computed flooding Extent Hurricane Hugo (a) SLOSH Output (USACE, 2004), and (b) ADCIRC Output. 110 due to a Category 2 storm. However, SLOSH indicates inundation between the AIW basin and the Pee Dee River basin, i.e., the location of the Bull Creek. Both figures reveal about the same extent of flooding within the Sampit River basin and the Black River basin. The inundated areas southwest of Winyah Bay show similar patterns. Figures 8.6 and 8.7 show the inundation extent, in more detail, at Winyah Bay as well as within the river basins of the Sampit River, Black River, and the Pee Dee River. Note that the black line within each figure describes the boundary of the SC-2-mesh. Certain elements appear white (dry) in the figures immediately surrounded by blue (wet) elements. This means that the white element has a higher elevation than the surrounding elements and therefore causing the element sometimes to dry out. The inundation maps show that the determined mainland boundaries are well placed allowing the necessary flooding without interfering with the boundaries. It is also indicated that most of the river islands are flooded. Figure 8.7 shows the flooding within the Pee Dee River basin and nicely depicts the wetted areas within Bull Creek (between the Pee Dee River and the AIW). The channel of Bull Creek is not included in the SC-2-FP mesh, though a nice river channel is illustrated due to the topographic information that was read in. 111 Black River Basin Sampit River Basin dry element Winyah Bay Figure 8.6: Inundation at Winyah Bay, Sampit River, and Black River. Pee Dee River Basin Waccamaw River Basin Bull Creek AIW Basin Figure 8.7: Inundation Pee Dee River, AIW and Waccamaw River. 112 Figures 8.8 and 8.9 represent flooded areas at the confluence of the AIW with the Waccamaw River, and the Waccamaw River at Conway. Figure 8.8 shows that only small portions of the AIW are flooded. Adjacent inland areas along the AIW are relatively steep compared to the large floodplains along the Waccamaw River (mainly marshland). The larger flooding process within the Waccamaw River basin confirms this fact. Flooding is obvious all along the meandering Waccamaw River especially around river bends. Along the AIW, the only large inundation occurs southwest of the confluence on the right hand side (looking downstream) just before the AIW turns south. Again, all islands within the riverine system are inundated. Figure 8.9 illustrates the extensive flooding south of Conway. The floodplain boundaries allow the inundation process without restricting the flow. The figure also shows the wetted channel around Thorofare Island. An actual lateral inflow location (Pitch Lodge Lake) is observed that was not included in the SC-2 mesh, but was generated when reading in the elevation data to the mesh. As expected, flooding is more evident around river bends. 113 Waccamaw River AIW Confluence Figure 8.8: Inundation AIW and Waccamaw River confluence. Conway lateral Inflow Waccamaw River Thorofare Island Figure 8.9: Inundation Waccamaw River at Conway. 114 8.3 Storm Tide Hydrographs South Carolina Coast The calculated storm tide hydrographs within the Atlantic Ocean include simulation results from all five meshes utilized in this study (SC-1, SC-1-FP, SC-2, SC-2-FP and WNAT-SC-1-FP). Inland storm tides are computed by using the floodplain meshes only. Figure 8.10 illustrates the location of the five recording stations. 8.3.1 Charleston Harbor Figure 8.11 displays the results at Charleston harbor. Deviation from mean sea level (MSL) in meters is plotted against time (Date and Time). The thin black line represents historical data recorded at the Charleston harbor tide station. The five other graphs (see legends for colors) allow distinction to be drawn between the five separate meshes. The water elevations for the South Carolina meshes are calculated by simultaneously including surface pressure and stresses from the hurricane winds, and the astronomical tides. The WNAT-SC-1-FP mesh results are computed separately: first sea stages due to winds only, and then sea stages due to astronomical tides only (see Figure 8.12). The total storm tide is calculated by adding the two stages. The reason for the separated computation lies in the extent of the utilized wind field and the much larger finite element mesh. The tides are computed over the entire WNAT-SC-1-FP mesh. In order to accomplish a stable tide signal, a simulation time of 35 days with a 20-day ramp is chosen. The storm surge is 115 computed by using the winds and interpolating it onto the finite element mesh within the boundaries of wind field only. The simulation time is 1.75 days with a 0.5-day ramp. -80º -79º McClellanville Awendaw Winyah Bay Inlet +33º +33º Bulls Bay Charleston Harbor -80º -79º Figure 8.10: Locations of Storm Tide Hydrograph Recordings along the Coast and Inland. 116 3.50 Historical Data 3.00 SC-1 (Winyah Bay Only) 2.50 SC-1-FP (Winyah Bay and Inland Topography) SC-2 (Waccamaw River and AIW) 2.00 SC-2-FP (Waccamaw River, AIW, and Inland Topography) 1.50 WNAT-SC-1-FP (Winyah Bay and Inland Topography) 1.00 Deviation from MSL [m] 0.50 C A 0.00 -0.50 B -1.00 9/20/1989 18:00 9/21/1989 0:00 9/21/1989 6:00 9/21/1989 12:00 9/21/1989 18:00 9/22/1989 0:00 9/22/1989 6:00 9/22/1989 12:00 Time [Date and Time] Figure 8.11: Storm Tide Hydrograph Hurricane Hugo at Charleston Harbor Tide Gage. 3.50 Historical Data 3.00 WNAT-SC-1-FP (Total Signal) WNAT-SC-1-FP (Winds Only) 2.50 WNAT-SC-1-FP (Tides Only) 2.00 [m] 1.50 m MSL fro n o 1.00 i at i Dev 0.50 0.00 -0.50 -1.00 9/20/1989 18:00 9/21/1989 0:00 9/21/1989 6:00 9/21/1989 12:00 9/21/1989 18:00 9/22/1989 0:00 9/22/1989 6:00 9/22/1989 12:00 Time [Date and Time] Figure 8.12: Storm Tide Computation WNAT-SC-1-FP Mesh. 117 Since the storm surge occurred at nearly high tide (see Figure 8.12) it is important to point out that all meshes accurately simulate the tidal signal leading up to the storm surge event. The WNAT-SC-1-FP mesh (using a 35-day run simulation with a 20-day ramp) clearly represents a more stable and smooth tidal signal solution than the South Carolina meshes (using a 1.73-day run simulation with a 0.5-day ramp). Still a phasing error is evident that is applicable to all the meshes used. The two meshes that do not allow inland flooding (SC-1 and SC-2) result in the highest peak of the storm tide (approx. 3.0 m). Due to the no-flow boundary conditions (equivalent to a infinite vertical wall) specified at all shorelines these results seem reasonable. The no-flow boundary constrains the water mass within the vertical walls. It also can be noted that the SC-1 and the SC-2 domains result in an artificial second peak (indicated by letter A in Figure 8.11) due to a sloshing effect caused by the no-flow boundary. The three domains that allow inland flooding (SC-1-FP, SC-2-FP, and WNAT-SC-1-FP) produce lower peak surge than the SC-1 and SC-2 meshes. The large domain mesh has a significantly higher sea elevation at the beginning of the storm peak’s rising limb (see B, Figure 8.11). One explanation could be that the larger domain results in more water pushed towards the shoreline that, in addition, causes an interaction with the shelf break. Another reason could be that the large domain captures the geostrophic tilt effect better. Clearly, the separated calculations of the storm surge (winds-only) and astronomical tides 118 (tides-only) have an effect on the end results, i.e., the nonlinear interaction between tides and storm surge is not simulated. None of the models accurately capture the rising limb of the storm tide hydrograph. At the zero hour on September 22, 1989 the gauge stages are above MSL (see letter C, Figure 8.11). This shortcoming is due to the absence of short wave action, which could be included in future efforts by incorporating wave radiation stress terms from short wave calculations in order to produce setup. The storm surge peak may also increase as a result of including short wave output. 119 8.3.2 Bulls Bay Figure 8.13 shows the calculated hydrograph at Bulls Bay. Recorded station data is not available for this location. After Hurricane Hugo, the U.S. Army Corps of Engineers (USACE) surveyed high water marks along the coast of South Carolina. The USGS reports sea elevations of about 6.0 m above MSL within Bulls Bay (Schuck-Kolben and Cherry, 1995). 5.50 5.00 SC-1 (Winyah Bay Only) 4.50 SC-1-FP (Winyah Bay and Inland Topography) 4.00 SC-2 (Waccamaw River and AIW) 3.50 SC-2-FP (Waccamaw River, AIW, and Inland Topography) 3.00 A 2.50 WNAT-SC-1-FP 2.00 1.50 Deviation from MSL [m] 1.00 0.50 C B 0.00 -0.50 -1.00 -1.50 9/20/89 18:00 9/21/89 0:00 9/21/89 6:00 9/21/89 12:00 9/21/89 18:00 9/22/89 0:00 9/22/89 6:00 9/22/89 12:00 Time [Date and Time] Figure 8.13: Storm Tide Hydrograph Hurricane Hugo at Bulls Bay Middle. Close examination of Figure 8.13 reveals that all meshes produce about the same tidal signal. A slight distinction in amplitude is noticed between the large domain and small domains. Again, the two meshes without inland topography produce higher peaks (approximately 5.1 m) than the SC-1-FP, SC-2-FP, and WNAT-SC-1-FP meshes (4.4 m, 120 4.3 m, and 4.5 m). The lower peak computation of the floodplain meshes is reasonable, since the inland areas allow the water to flow into the floodplains (see Figure 8.14 and 8.15 that show contour plots of the water elevations at Bulls Bay, with and without floodplain). A discrepancy is noticed for the recession curves (see letter A, Figure 8.13). The graphs representing the floodplain meshes have a higher recession limb due to inland areas that hold the storm tide longer. A small artificial second peak (see letter B, Figure 8.13) produced by the SC-1 and SC-2 domain is shown. As before, these peaks are caused by a sloshing effect from the no-flow boundary conditions at the shoreline. The large domain (WNAT-SC-1-FP) produces higher water elevations prior to the rising limb (see letter C, Figure 8.13). Reasons for the higher sea stages could be: a) the wind-driven surge begins outside of the smaller domain and therefore is larger when it reaches the boundaries of the smaller domain, b) the interaction of the wind-driven surge with the shelf break, c) capturing the geostrophic tilt effect better, and d) the piecewise computation of the storm tides that does not take into account the nonlinear interaction between the storm surge and astronomical tides. None of the meshes produce sea elevations of 6 m above MSL at the center of Bulls Bay. Again, this shortcoming is due to the absence of short wave action that produces setup. Therefore, including the short wave action and the associated setup could likely produce peak elevations of 6 m above MSL within the Bulls Bay. 121 Water Stages above MSL (m) No-Flow Boundary Mainland Boundary Bulls Bay Figure 8.14: Bulls Bay Water Stages at Time of Hydrograph Peak (SC-2 mesh). Water Stages above MSL (m) Bulls Bay Figure 8.15: Bulls Bay Water Stages at Time of Hydrograph Peak (SC-2-FP mesh). 122 8.3.3 Winyah Bay Inlet Figure 8.16 presents the generated hydrographs at Winyah Bay inlet. High water mark information is used in order to assess the computed sea stages. At Winyah Bay inlet and within the middle of the bay elevations of 3.7 m above MSL were reported (Schuck- Kolben and Cherry, 1995). Again a clear distinction can be made between the meshes with and without inland topography at the time of peak. Unlike the two previous locations, the storm peaks are now higher when they include floodplain areas. The SC-1- FP and the SC-2-FP meshes produce water stages of 3.3 m to 3.4 m above MSL. The WNAT-SC-1-FP domain generates an even higher peak of 3.7 m above MSL. While the SC-1 and SC-2 meshes show peaks of 3.0 m above MSL. 4.00 3.50 SC-1 (Winyah Bay Only) SC-1-FP (Winyah Bay and Inland Topography) 3.00 SC-2 (Waccamaw River and AIW) 2.50 SC-2-FP (Waccamaw River, AIW, and Inland Topography) 2.00 WNAT-SC-1-FP 1.50 A 1.00 Deviation from MSL [m] 0.50 B 0.00 -0.50 -1.00 9/20/89 18:00 9/21/89 0:00 9/21/89 6:00 9/21/89 12:00 9/21/89 18:00 9/22/89 0:00 9/22/89 6:00 9/22/89 12:00 Time [Date and Time] Figure 8.16: Storm Tide Hydrograph Hurricane Hugo at Winyah Bay Inlet. 123 North Inlet Water Stages above MSL (m) No-Flow Boundary Mainland Boundary Winyah Bay Inlet Figure 8.17: Winyah Bay Water Stages at Time of Hydrograph Peak (SC-2 mesh). Water Stages above MSL (m) Barrier Island Winyah Bay Inlet Figure 8.18: Winyah Bay Water Stages at Time of Hydrograph Peak (SC-2-FP mesh). 124 The two meshes without floodplains (SC-1 and SC-2) are not able to capture these extensive inundation processes (see Figure 8.17) due to no-flow boundaries at the shorelines. Note that the incorporation of inland topography does not always create lower water elevations (see Charleston harbor and Bulls Bay). Including inundation areas can also have an opposite effect on the water stages (Winyah Bay region). The floodplain meshes are able to allow extensive inundation that leads up to higher water elevations within the bay and its entrance. The high storm tide at the bay’s center is a result of the water surging in from its former North inlet (see Figure 8.17 and 8.18). The North inlet comprises of barrier islands of low elevations and therefore allows the storm surge to enter the bay from the northeast. In addition, large amounts of water stream in overland from the southwest causing an additional increase in water stages. At the same time, water is entering the bay from its present inlet and piles up against the elevated water body at the bay’s center. This pilling-up effect is strengthened due to a massive barrier island at the entrance to the bay (see Figure 8.13). The water is restricted from flowing back into the ocean. The small domains produce the same tidal signal (phase and amplitude). An unusually large amplitude distinction is noticed between the large domain and small domains (see letter A, Figure 8.16) that also leads up to a much higher peak computation. Reasons for the elevated sea stages are: a) the wind-driven surge begins outside of the smaller domain and, therefore, is larger when it reaches the boundaries of the smaller domain, b) the interaction of the wind-driven surge with the shelf break, c) capturing the geostrophic tilt 125 effect better, and d) the piecewise computation of the storm tides that does not take into account the nonlinear interaction between the storm surge and astronomical tides. Another feature to become aware of is an increase in water stages at the end of the recession limb (see letter B, Figure 8.16). The elevated stages are produced due to water backflow that surged into the bay from the northeast and the southwest. The SC-2-FP hydrograph shows a relatively small increase in water stage (around MSL). While the WNAT-SC-1-FP and the SC-1-FP mesh produce much higher water elevations (about 0.9 m above MSL). The reason for the difference in sea stages is caused by the domain size of the SC-1-FP and the SC-2-FP. The SC-2-FP domain incorporates extensive reaches of the AIW and the Waccamaw River. Therefore, the storm surge propagates further inland and the relevant water backflow occurs much later in time than with the SC-1-FP mesh. Note that this is the only downside to using SC-1-FP in WNAT. 8.3.4 McClellanville Figure 8.19 shows computed water elevations at McClellanville. The village is located northeast of Bulls Bay (see Figure 8.20), inland and was subject to severe flooding (Metts, 1989). High water marks reached elevations of about 4.9 to 5.5 m above MSL (DOC, 1990). Figure 8.19 shows only a short time-period of the computed hydrograph. Water starts to rise around 4 a.m. The peak of the storm surge occurs around 4:45 a.m. and produces water elevations between 5.2 to 5.5 m above MSL. Figure 8.15 represents the size of inundation around 4 o’clock in the morning of September 22, 1989. The 126 depicted elevations are computed by using the SC-2-FP mesh. The SC-2-FP domain generates a slightly lower peak (5.2 m) than the two other meshes (5.4 to 5.5 m). Also, a slight time discrepancy is noticed between the rising limbs of about 10 minutes. 6.00 5.75 SC-1-FP (Winyah Bay and Inland Topography) 5.50 SC-2-FP (Waccamaw River, AIW, and Inland Topography) 5.25 5.00 WNAT-SC-1-FP (Winyah Bay and Inland Topography) 4.75 ] m 4.50 [ L 4.25 MS m o 4.00 r 3.75 viation f e 3.50 D 3.25 3.00 2.75 2.50 2.25 2.00 9/22/89 4:00 9/22/89 5:00 9/22/89 6:00 9/22/89 7:00 9/22/89 8:00 Time [D ate and Time] Figure 8.19: Storm Tide Hydrograph Hurricane Hugo at McClellanville. Water Stages above MSL (m) McClellanville Awendaw Figure 8.20: Water Elevations at McClellanville and Awendaw (SC-2-FP mesh). 127 All three meshes simulate the storm’s peak well. It is noted that the domains are not built for simulating accurate water elevation within populated areas (McClellanville or Awendaw), therefore, the computed results seem reasonable compared with the reported high water marks. 8.3.5 Awendaw Figure 8.21 illustrates a computed hydrograph at Awendaw. The village is situated northwest of Bulls Bay, about 15 km southwest of McClellanville (see Figure 8.20). The highest surge appeared to be at Awendaw (DOC, 1990) where a value of 6.2 m above MSL was measured. Awendaw is located outside of the SC-1-FP and WNAT-SC-1-FP domain. Hence results are only obtained from the SC-2-FP mesh. 6.00 5.50 SC-2-FP (Waccamaw River, AIW and Inland Topography) 5.00 4.50 4.00 ] m L [ 3.50 MS m o 3.00 r 2.50 Deviation f 2.00 1.50 1.00 0.50 0.00 9/22/89 3:00 9/22/89 4:00 9/22/89 5:00 9/22/89 6:00 9/22/89 7:00 Time [Date and Time] Figure 8.21: Storm Tide Hydrograph Hurricane Hugo at Awendaw. 128 The computed peak surge is about 4.9 m above MSL. Again, a peak under-prediction (about 1 m) is observed due to the missing wave set-up in Bulls Bay. The result seems reasonable taking into account that better information about topographical feature would further lead to better computational results. 8.4 Winyah Bay Inlet Hydrograph Assessment Because many two-dimensional and three-dimensional models employ open-water boundary conditions near inlets, an exploration was undertaken into how far the floodplain and the no-floodplain boundaries affect the storm surge and the astronomical tide signal on the continental shelf near the inlet of the Winyah Bay. Recording stations are placed on four semicircles with radii of 2,500 m (1), 5,000 m (2), 7,500 m (3), and 10,000 m (4). The center of the semicircles coincides with Winyah Bay inlet. Each radius accommodates five stations: south (s), southeast (se), east (e), northeast (ne), and north (n) (see Figure 8.22 and 8.23). The following five hydrograph-figures are based on computational results obtained from the SC-2 and SC-2-FP meshes. Note that within one figure several hydrographs are presented that follow the nomenclature stated in the last paragraph and are illustrated in Figure 8.22. Special importance is given to the variation of the recorded sea stages in an axial direction: south, southeast, east, northeast, and north. Preliminary examination showed that all peaks stages gradually decreased from node (1) to node (4). Therefore, investigation results are drawn based on peak stages on node (1) and node (4). 129 Winyah Bay n 4 3 ne 2 1 e se s Figure 8.22: Recording Locations around Winyah Bay Inlet. 130 Bathymetry and Inland Topography (m) n 4 3 ne 2 1 e se s Figure 8.23: Bathymetry and Inland Topography Winyah Bay Inlet. 131 Figure 8.24 shows recorded sea stages along the “south radius”. Close examination indicates that both meshes produce about the same tidal signal. A discrepancy is observed when the storm starts to affect the sea stages. The highest peak (computed with the SC-2 mesh at node 1s) is about 3.45 m above MSL, the lowest (SC-2-FP, 4s) is about 3.15 m above MSL. The peaks reveal that the mesh without floodplain produces higher elevations, dissimilar to the observation at Winyah Bay inlet (see Section 8.3.3) but similar to the one at Bulls Bay (see Section 8.3.1). The incorporation of the floodplain causes lower sea stages due to the inundation process. The extensive flooding within the center of Winyah Bay does not affect the sea stages south of Winyah Bay inlet. The hydrograph peaks fall from north to south. Discrepancies are shown at the end of the simulations caused by the different boundary types (e.g., sloshing effect). Note also that all nodes are located within a relatively shallow area (see Figure 8.23) that causes high peaks. 3.50 3.25 1s (SC-2) 4s (SC-2) 3.00 2.75 1s (SC-2-FP) 4s (SC-2-FP) 2.50 2.25 ] 2.00 m L [ 1.75 MS 1.50 om 1.25 on fr 1.00 viati e D 0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 9/20/89 18:00 9/21/89 0:00 9/21/89 6:00 9/21/89 12:00 9/21/89 18:00 9/22/89 0:00 9/22/89 6:00 9/22/89 12:00 Time [Date and Time] Figure 8.24: Hydrographs south of Winyah Bay Inlet. 132 Figure 8.25 represents computed sea elevations along the “southeast radius”. Again, both meshes produce about the same tidal signal. A slight recession limb discrepancy is noticed prior to the storm surge. It can be observed that the peak-difference between nodes (1se) and nodes (4se) (about 0.40 m) is much larger than on the previous hydrographs (south radius: about 0.15 m). The highest peak (computed with the SC-2 domain at node 1se) is about 3.30 m above MSL, the lowest (SC-2-FP, 4se) is about 2.80 m above MSL. All computed peaks are lower than the hydrographs on the “south radius” (by about 0.1 to 0.2 m). Peak elevations are increasing the closer the node is to the inlet. Clearly, the larger the distance between the node and the shoreline, the smaller the peak elevation, i.e., the remote nodes are not influenced as much by the boundaries. Therefore, hydrographs drop from node (1se) to node (4se). Still, a slight sloshing effect is evident at the end of the run. 3.50 3.25 1se (SC-2) 4se (SC-2) 3.00 2.75 1se (SC-2-FP) 4se (SC-2-FP) 2.50 2.25 2.00 1.75 MSL [m] 1.50 om 1.25 ion fr t a 1.00 vi De 0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 9/20/89 18:00 9/21/89 0:00 9/21/89 6:00 9/21/89 12:00 9/21/89 18:00 9/22/89 0:00 9/22/89 6:00 9/22/89 12:00 Time [Date and Time] Figure 8.25: Hydrographs southeast of Winyah Bay Inlet. 133 Figure 8.26 shows the calculated hydrographs along the “east radius”. Both meshes produce the same tidal signal. The hydrographs show similar results as obtained on the “southeast radius”. The highest peak (computed with the SC-2 mesh at node 1e) is about 3.30 m above MSL, the lowest (SC-2-FP, 4e) is about 2.80 m above MSL. The hydrograph peaks fall from node (1e) to node (4e). A slight sloshing effect is recognized at the end of the simulation. 3.50 3.25 1e (SC-2) 4e (SC-2) 3.00 2.75 1e (SC-2-FP) 4e (SC-2-FP) 2.50 2.25 ] 2.00 m [ L 1.75 1.50 om MS r 1.25 ion f at 1.00 vi De 0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 9/20/89 18:00 9/21/89 0:00 9/21/89 6:00 9/21/89 12:00 9/21/89 18:00 9/22/89 0:00 9/22/89 6:00 9/22/89 12:00 Time [Date and Time] Figure 8.26: Hydrographs east of Winyah Bay Inlet. 134 Figure 8.27 illustrates the computed hydrographs along the “northeast radius”. Both meshes produce the same tidal signal. The rising limbs of the surge show a slight discrepancy between node (1ne) and node (4ne). However, the graphs demonstrate a similar behavior as the “south radius” hydrographs. The computed peak elevations show smaller peak differences than observed on the two previous locations. The peak- difference between node (1ne) and node (4ne) is about 0.20 m. The computed peaks are lower than the one on the “south radius”: the highest peak (computed with the SC-2 mesh at node 1ne) is about 3.30 m above MSL, the lowest (SC-2-FP, 4ne) is about 3.00 m above MSL. As expected, the peaks drop from node (1ne) to node (4ne). A slight sloshing effect is recognized at the end of the run. 3.50 3.25 1ne (SC-2) 4ne (SC-2) 3.00 2.75 1ne (SC-2-FP) 4ne (SC-2-FP) 2.50 2.25 ] 2.00 m [ L 1.75 1.50 om MS r 1.25 ion f at 1.00 vi De 0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 9/20/89 18:00 9/21/89 0:00 9/21/89 6:00 9/21/89 12:00 9/21/89 18:00 9/22/89 0:00 9/22/89 6:00 9/22/89 12:00 Time [Date and Time] Figure 8.27: Hydrographs northeast of Winyah Bay Inlet. 135 Figure 8.28 shows computed elevations along the “north radius”. Both domains generate the same tidal signal. With respect to the other four locations, the peaks on the “north radius” are the highest: the peak (computed with the SC-2 at node 4n) is about 3.55 m above MSL, the lowest (SC-2-FP, 1n) is about 3.30 m above MSL. Note that this time the highest peaks are recorded on node (4n). The two different domains produce a slight peak drop node (1n) to node (4n). Figure 8.23 (bathymetry and inland topography) reveals that the barrier island, situated in front of Winyah Bay, acts like a vertical wall. The boundary of the no-floodplain mesh almost coincides with the shoreline of the barrier island. Therefore, it seems reasonable that both meshes produce about the same peak elevations. The computed hydrograph at node (4n) (floodplain mesh) is also influenced by the surge that enters the Winyah Bay from the North Inlet and causing an additional peak increase. As before, a slight sloshing effect is recognized at the end of the run. 3.75 3.50 3.25 1n (SC-2) 4n (SC-2) 3.00 2.75 1n (SC-2-FP) 4n (SC-2-FP) 2.50 2.25 2.00 L [m] 1.75 1.50 1.25 1.00 Deviation from MS 0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 9/20/89 18:00 9/21/89 0:00 9/21/89 6:00 9/21/89 12:00 9/21/89 18:00 9/22/89 0:00 9/22/89 6:00 9/22/89 12:00 Time [Date and Time] Figure 8.28: Hydrographs north of Winyah Bay Inlet. 136 Close examination of all figures (8.24 to 8.28) reveals that both meshes (SC-2 and SC-2- FP) show good agreement on the simulated tides (approx. between 0.00 and 18.00 on September 21, 1989). This indicates that astronomical tides have minimal variance near inlets. As a result, an open-ocean boundary near an inlet could be forced by the same hydrograph at each node. The hydrograph could be computed by using a large computational domain, e.g., the South Carolina domain. However, it has to be noted that different bays and estuaries may show different results that lead to different conclusions. The storm tide hydrographs reveal that the hydrographs are very spatially dependent near the inlet, i.e., the storm tide elevations show large variance between node (1) to node (4) (see Table 8.1). The different shoreline boundary conditions and the spatially varying bathymetry significantly affect the computed storm tide stages. For a storm surge simulation (e.g., a two- or three-dimensional bridge scour study) employing a small local model, each boundary node requires an independent storm surge hydrograph that will then force the local model. However, it is noted that even this procedure might not realize reliable simulation results, since flux terms are desirable in addition to elevations for near-inlet boundaries. 137 Table 8.1: Peak Elevations at Winyah Bay Inlet in meters above MSL, recorded at Node 1 and Node 4. Radius No Floodplain Mesh Floodplain Mesh Node 1 Node 4 |1-4| Node 1 Node 4 |1-4| n 3.45 3.55 0.10 3.30 3.45 0.15 ne 3.30 3.10 0.20 3.20 3.00 0.20 e 3.30 2.90 0.40 3.15 2.80 0.35 se 3.30 2.90 0.40 3.20 2.80 0.40 s 3.45 3.35 0.10 3.30 3.15 0.15 138 CHAPTER 9 CONCLUSIONS AND FUTURE WORK The primary focus of this study is to assess the inclusion of inland topography thereby allowing inundation of areas along shorelines and within the Winyah Bay and Waccamaw/AIW riverine system. The floodplain meshes are compared with meshes that include no-flow boundary conditions (not allowing any flooding processes) in order to examine whether including inland topography significantly improves the predicted storm tide stages. The aim is to accomplish a computationally efficient mesh (i.e., small number of nodes) with a good prediction accuracy of water elevations. A secondary product of this research is the assessment of near-inlet boundary locations with respect to forcings from storm surge hydrographs and astronomical tide signals. 9.1 Conclusions Two main conclusions may be drawn from this thesis. 1. Inundation areas near the coastal shoreline must be included 2. Present storm tide studies lack critical short wave components All plotted hydrographs related to the five different meshes (SC-1, SC-1-FP, SC-2, SC-2- FP, and WNAT-SC-1-FP) show clear distinction between the models including inland 139 topography (SC-1-FP, SC-2-FP, and WNAT-SC-1-FP) and the models without inland topography (SC-1, and SC-2). The inland topography meshes obviously achieve better results where inundation occurred. Inundation either causes a decrease in water elevations, at Bulls Bay, or an increase, at Winyah Bay inlet. In addition, simulated sea elevations all show lower storm tide elevations when compared with historical data. The fact that the applied numerical code, ADCIRC-2DDI, does not include short wave action explains the reduced sea stages. In the final analysis, incorporation of inland topography is significant and should be included for predicting near-shore storm tides, and at a minimum, wave radiation stress terms from a short wave model should be incorporated. Another important fact to draw attention to is that the SC-1-FP mesh (with 14,500 nodes) produces virtually the same results as the SC-2-FP mesh (with 118,000 nodes) near the shorelines. Therefore, storm tides can be predicted with good accuracy with a less computationally expensive mesh and still include pertinent inland topography. The only drawback noted is in the recession limb of the storm tide hydrographs, however, the peak is unaffected. It is noted that SC-2-FP incorporates a larger riverine body than the SC-1-FP mesh and much of the increased node number is a result of the incorporation of these river reaches. It is also recognized that including extensive river reaches makes it necessary to include at least three elements across a river channel in order to approximate the cross-section. Besides describing the usually trapezoidal shape of the river channel, a good propagation of the storm surge is facilitated, which results in less simulation instabilities. 140 The evaluation of the Winyah Bay entrance boundary condition indicates that storm tide hydrographs are very spatially dependent near inlets, whereas astronomical tides have minimal variance. The large discrepancy of computed storm surge hydrographs, between the inner and outer radius, showed that an open-ocean boundary for storm surge simulation has to be properly specified. In order to force the model, storm surge hydrographs have to be produced at each node of the open-ocean boundary. A large model domain is desired to compute the appropriate storm surge hydrographs. A forcing at the boundary by a single hydrograph, as is common practice (e.g., bridge scour studies) is inappropriate and may lead to erroneous results. 9.2 Future Work Future work will need to be addressed in several ways to improve this study. The first is a shortcoming of the governing equations used in this thesis in that short waves are not simulated. ADCIRC-2DDI computes long waves only (astronomical tides, geostrophic tilt, and surge) but does not take into account short wave action. The short waves result in wave set-up prior to, and wave run-up during hurricane landfall. This absence of short wave capturing can have significant effects on the accuracy of the storm tides. Therefore, future work has to ultimately explore coupling a short wave model with ADCIRC-2DDI and should immediately incorporate wave radiation stress terms in present modeling efforts. 141 The simulation time of 1.75 days should be extended to about three to five days. As a result, the backflow of the storm surge within the SC-2-FP mesh could be observed. In addition, high freshwater inflows that started one day after the hurricane made landfall could be included in the computer simulations and permit an assessment of widespread river flooding. In addition, more effort has to be made in collecting and obtaining river and bathymetry data along these two rivers. In particular, reliable bank elevations (e.g., by conducting a field survey) would help to correctly simulate the overtopping of the riverbanks and further enhance the prediction of the inundation extent. At the same time, a good photo documentation including important land features along the Waccamaw River, AIW, Winyah Bay, Bulls Bay, Charleston harbor, and other important tributaries and bays would help to better understand future simulation results. The WNAT-SC-1-FP mesh should be used for predicting storm tide stages caused by Hurricane Floyd (1999). After Hurricane Hugo (1989), the USGS decided to operate more streamflow gaging stations along the Waccamaw River and the Atlantic Intracoastal Waterway. A much larger quantity of historical data should be available in order to validate the performance of a Hurricane Floyd hindcast. Because of the nature of Hurricane Floyd, its track paralleled the East coast of the U.S., a hindcast of its flooding effects will permit a future substantiation of the two main conclusions drawn herein. 142 APPENDIX A ADCIRC-2DDI INPUT FILE: MESH DESCRIPTION SC-2-FP 143 SC-2-FP 228022 118194 1 -80.7168080000 32.1616280000 2.8050000668 2 -80.7122070000 32.1545040000 2.8150000572 3 -80.7080580000 32.1482790000 2.9900000095 # This portion of the input has been eliminated # 118193 -79.0444329982 33.8335990000 1.0000028610 118194 -79.0442549982 33.8336100000 3.0000038147 1 3 1 106 107 2 3 2 106 1 3 3 108 106 2 # This portion of the input has been eliminated # 228020 3 118185 118194 118193 228021 3 118185 118186 118194 228022 3 118186 118187 118194 1 = Number of open boundaries 105 = Total number of open boundary nodes 105 = Number of nodes for open boundary 1 1 2 3 # This portion of the input has been eliminated # 103 104 105 13 = Number of land boundaries 8288 = Total number of land boundary nodes 1639 1 = Number of nodes for land boundary 1 71344 71424 71503 # This portion of the input has been eliminated # 4921 4683 4457 144 APPENDIX B ADCIRC-2DDI PARAMETERS SC-2-FP 145 STEADY/K1/O1/N2/S2/M2/M4/M6 ! ALPHANUMERIC RUN DESCRIPTION SC-2-FP WD WT ! 24 CHARACTER ALPHANUMERIC RUN IDENTIFICATION 0 ! NFOVER - NONFATAL ERROR OVERRIDE OPTION 0 ! NABOUT - ABREVIATED OUTPUT OPTION PARAMETER 0 ! NSCREEN - UNIT 6 OUTPUT OPTION PARAMETER 0 ! IHOT - HOT START PARAMETER 2 ! ICS - COORDINATE SYSTEM SELECTION PARAMETER 0 ! IM - MODEL TYPE (0 INDICATES STANDARD 2DDI MODEL) 2 ! NOLIBF - BOTTOM FRICTION TERM SELECTION PARAMETER 2 ! NOLIFA - FINITE AMPLITUDE TERM SELECTION PARAMETER 1 ! NOLICA - SPATIAL DERIVATIVE CONVECTIVE TERM SELEC. PARAM. 1 ! NOLICAT -TIME DERIVATIVE CONVECTIVE TERM SELEC. PARAM. 0 ! NWP – VAR. BOTTOM FRICTION & LATERAL VISC. OPTION PARAM. 1 ! NCOR - VARIABLE CORIOLIS IN SPACE OPTION PARAMETER 0 ! NTIP - TIDAL POTENTIAL OPTION PARAMETER 4 ! NWS - WIND STRESS AND BAROMETRIC PRESSURE OPTION PARAM. 1 ! NRAMP - RAMP FUNCTION OPTION 9.81 ! G - ACCELERATION DUE TO GRAVITY - DETERMINES UNITS -0.020 ! TAU0 - WEIGHTING FACTOR IN GWCE 0.6 ! DT - TIME STEP (IN SECONDS) 0.0 ! STATIM - STARTING TIME (IN DAYS) 0.0 ! REFTIM - REFERENCE TIME (IN DAYS) 900 ! WTIMINC 1.73 ! RNDAY - TOTAL LENGTH OF SIMULATION (IN DAYS) 0.5 ! DRAMP - DURATION OF RAMP FUNCTION (IN DAYS) 0.35 0.30 0.35 ! TIME WEIGHTING FACTORS FOR THE GWCE EQUATION 0.01 1 1 0.05 ! H0 - MINIMUM CUTOFF DEPTH 265.5 29.0 ! SLAM0,SFEA0 - CENTER OF CPP PROJECTION 0.0025 1.0 10 0.3333333 ! FFACTOR, HBREAK, FTHETA, FGAMMA 5.0 ! ESL - LATERAL EDDY VISCOSITY COEFFICIENT; IGNORED IF NWP =1 0.0 ! CORI - CORIOLIS PARAMETER - IGNORED IF NCOR = 1 0 ! NTIF – NO. OF TIDAL POTENTIAL CONSTITUENTS FORCED 8 ! NBFR - TOTAL NO. OF FORCING FREQU. ON OPEN BOUNDARIES STEADY ! ALPHA DESCRIPTOR FOR CONSTITUENT NO. 1 0.000000000000000 1.0 0.0 ! CONST. FREQ., NOD. FACTOR, EQUIL. ARG. K1 ! ALPHA DESCRIPTOR FOR CONSTITUENT NO. 2 0.000072921165921 1.096 184.244 ! CONST. FREQ., NOD. FACTOR, EQUIL. ARG. O1 ! ALPHA DESCRIPTOR FOR CONSTITUENT NO. 3 0.000067597751162 1.156 225.857 ! CONST. FREQ., NOD. FACTOR, EQUIL. ARG. N2 ! ALPHA DESCRIPTOR FOR CONSTITUENT NO. 4 0.000137879700000 0.970 12.793 ! CONST. FREQ., NOD. FACTOR, EQUIL. ARG. S2 ! ALPHA DESCRIPTOR FOR CONSTITUENT NO. 5 0.000145444119418 1.0 180.0 ! CONST. FREQ., NOD. FACTOR, EQUIL. ARG. M2 ! ALPHA DESCRIPTOR FOR CONSTITUENT NO. 6 0.000140518917083 0.970 51.982 ! CONST. FREQ., NOD. FACTOR, EQUIL. ARG. 146 M4 ! ALPHA DESCRIPTOR FOR CONSTITUENT NO. 7 0.000281037834166 0.941 103.964 ! CONST. FREQ., NOD. FACTOR, EQUIL. ARG. M6 ! ALPHA DESCRIPTOR FOR CONSTITUENT NO. 8 0.000421556751249 0.913 155.947 ! CONST. FREQ., NOD. FACTOR, EQUIL. ARG. STEADY ! ALPHA NUMERIC DESCRIPTION OF OPEN BOUNDARY 0.19196E-02 0.000 ! BNDRY FORCING CONSTITUENT NO. 1 AT FIRST NODE 0.18488E-02 0.000 0.17777E-02 0.000 # This portion of the input has been eliminated # 0.29036E-02 0.000 0.30063E-02 0.000 0.31199E-02 0.000 !BNDRY FORCING CONSTITUENT NO. 1 AT LAST NODE K1 0.11117E+00 190.794 !BNDRY FORCING CONSTITUENT NO. 2 AT FIRST NODE 0.11118E+00 190.750 0.11118E+00 190.712 # This portion of the input has been eliminated # 0.10085E+00 183.370 0.10087E+00 183.363 0.10089E+00 183.354 ! BNDRY FORCING CONSTITUENT NO. 2 AT LAST NODE O1 0.82243E-01 202.436 ! BNDRY FORCING CONSTITUENT NO. 3 AT FIRST NODE 0.82247E-01 202.417 0.82249E-01 202.399 # This portion of the input has been eliminated # 0.74570E-01 195.786 0.74587E-01 195.776 0.74605E-01 195.764 ! BNDRY FORCING CONSTITUENT NO. 3 AT LAST NODE N2 0.20080E+00 349.483 ! BNDRY FORCING CONSTITUENT NO. 4 AT FIRST NODE 0.20070E+00 349.389 0.20060E+00 349.303 # This portion of the input has been eliminated # 0.14785E+00 338.217 0.14806E+00 338.198 0.14830E+00 338.177 ! BNDRY FORCING CONSTITUENT NO. 4 AT LAST NODE 147 S2 0.15960E+00 18.899 ! BNDRY FORCING CONSTITUENT NO. 5 AT FIRST NODE 0.15952E+00 18.807 0.15943E+00 18.724 # This portion of the input has been eliminated # 0.11639E+00 8.210 0.11658E+00 8.181 0.11678E+00 8.149 ! BNDRY FORCING CONSTITUENT NO. 5 AT LAST NODE M2 0.88290E+00 359.856 ! BNDRY FORCING CONSTITUENT NO. 6 AT FIRST NODE 0.88233E+00 359.806 0.88181E+00 359.760 # This portion of the input has been eliminated # 0.63691E+00 350.612 0.63788E+00 350.580 0.63894E+00 350.545 ! BNDRY FORCING CONSTITUENT NO. 6 AT LAST NODE M4 0.19039E-01 275.053 ! BNDRY FORCING CONSTITUENT NO. 7 AT FIRST NODE 0.18520E-01 275.841 0.18055E-01 276.613 # This portion of the input has been eliminated # 0.73156E-02 355.151 0.72941E-02 356.690 0.72768E-02 358.405 ! BNDRY FORCING CONSTITUENT NO. 7 AT LAST NODE M6 0.11321E-01 37.818 ! BNDRY FORCING CONSTITUENT NO. 8 AT FIRST NODE 0.11360E-01 37.433 0.11404E-01 37.067 # This portion of the input has been eliminated # 0.13035E-01 104.562 0.13123E-01 104.906 0.13220E-01 105.274 ! BNDRY FORCING CONSTITUENT NO. 8 AT LAST NODE 45.0 ! ANGINN - INNER ANGLE THRESHOLD 1 0.0 1.73 1000 !NOUTE,TOUTSE,TOUTFE,NSPOOLE:ELEV STATION OUTPUT 71 ! TOTAL NUMBER OF ELEVATION RECORDING STATIONS -79.9231 32.7818 ! Charleston, SC (Tide Station Location) 148 -79.5972 32.9416 ! Bulls Bay Old (West location) -79.552098 32.98405 ! Bulls Bay New (center of bay) # This portion of the input has been eliminated # -78.552 33.8696 ! Little River AIW -79.4667 33.0903 ! Mc Clellanville -79.58769 33.02485 ! Awendaw 0 0.0 0.0 0 !NOUTV,TOUTSV,TOUTFV,NSPOOLV:VEL. STATION OUTPUT INFO 0 ! TOTAL NUMBER OF VELOCITY RECORDING STATIONS 0 0.0 0.0 0 ! NOUTM, TOUTSM, TOUTFM, NSPOOLM 0 ! TOTAL NUMBER OF METEOROLOGY RECORDING STATIONS 1 0.0 1.73 2000 !NOUTGE,TOUTSGE,TOUTFGE,NSPOOLGE:GLOBAL ELEV 1 0.0 1.73 2000 ! NOUTGV,TOUTSGV,TOUTFGV,NSPOOLGV:GLOBAL VEL 0 0.0 0.0 0 ! NOUTGM,TOUTSGM,TOUTFGM,NSPOOLGM 0 ! NHARFR - NUMBER OF CONSTITUENTS INCLUDED IN HARM. ANALYSIS 0.00 0.00 0 1.0 ! THAS,THAF,NHAINC,FMV - HARMONIC ANALYSIS PARAM. 0 0 0 0 ! NHASE,NHASV,NHAGE,NHAGV - CONTROL HARMONIC ANALYSIS 0 0 ! NHSTAR,NHSINC - HOT START FILE GENERATION PARAMETERS 1 0 2.98E-5 25 ! ITITER, ISLDIA, CONVCR, ITMAX – ALGE SOLU. PARAM. 12 ! MNPROC 149 APPENDIX C WIND FIELD DESCRIPTION FOR SC-1 150 OWI WINDS INTERPOLATED ONTO SC-1 MESH 1 -0.15477E+02 -0.11810E+01 0.10104E+04 2 -0.15479E+02 -0.11918E+01 0.10104E+04 3 -0.15480E+02 -0.12013E+01 0.10104E+04 4 -0.15481E+02 -0.12080E+01 0.10103E+04 5 -0.15482E+02 -0.12163E+01 0.10103E+04 6 -0.15483E+02 -0.12234E+01 0.10103E+04 # This portion of the wind field input has been eliminated # 10375 -0.16795E+02 -0.15901E+01 0.10102E+04 10376 -0.16796E+02 -0.15907E+01 0.10102E+04 10377 -0.16794E+02 -0.15897E+01 0.10102E+04 10378 -0.16794E+02 -0.15882E+01 0.10102E+04 10379 -0.16795E+02 -0.15869E+01 0.10102E+04 OWI WINDS INTERPOLATED ONTO SC-1 MESH 1 -0.15775E+02 -0.22413E+01 0.10102E+04 2 -0.15776E+02 -0.22557E+01 0.10102E+04 3 -0.15777E+02 -0.22684E+01 0.10102E+04 4 -0.15778E+02 -0.22773E+01 0.10102E+04 5 -0.15778E+02 -0.22883E+01 0.10102E+04 # This portion of the wind field input has been eliminated # 10374 -0.67230E+00 0.26979E+02 0.10091E+04 10375 -0.68435E+00 0.26985E+02 0.10091E+04 10376 -0.70323E+00 0.26987E+02 0.10091E+04 10377 -0.67555E+00 0.26984E+02 0.10091E+04 10378 -0.68058E+00 0.26990E+02 0.10091E+04 10379 -0.69679E+00 0.26998E+02 0.10091E+04 151 LIST OF REFERENCES ADCIRC Manual. 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