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The effect of tidal inlets on open coast storm surge hydrographs

Michael B. Salisbury a,1, Scott C. Hagen b,⁎

a Water Resources Staff Engineer, Ardaman and Associates, Inc., 8008 South Orange Avenue, Orlando, Florida, 32809, USA b University of Central Florida, Department of Civil and Environmental Engineering, 4000 Central Florida Blvd., Orlando, Florida, 32816 – 2450, USA

Received 25 January 2006; received in revised form 11 September 2006; accepted 12 October 2006

Available online 29 November 2006

Abstract

Bridge scour modeling requires storm surge hydrographs as open ocean boundary conditions for coastal waters surrounding tidal inlets. These

open coast storm surge hydrographs are used to accurately determine both horizontal and vertical circulation patterns, and thus scour, within the

inlet and bay for an extreme event. At present, very little information is available on the effect that tidal inlets have on these open coast storm surge

hydrographs. Furthermore, current modeling practice enforces a single design hydrograph along the open coast boundary for bridge scour models.

This study expands on these concepts and provides a more fundamental understanding on both of these modeling areas.

A numerical parameter study is undertaken to elucidate the influence of tidal inlets on open coast storm surge hydrographs. Four different inlet –

bay configurations are developed based on a statistical analysis of existing tidal inlets along the Florida coast. The length and depth of the inlet are

held constant in each configuration, but the widths are modified to include the following four inlet profiles: 1) average Florida inlet width; 2) 100 m

inlet width; 3) 500 m inlet width; and 4) 1000 m inlet width. Results from these domains are compared to a control case that does not include any

inlet – bay system in the computational domain.

The Advanced Circulation, Two-Dimensional Depth-Integrated (ADCIRC-2DDI) numerical code is used to obtain water surface elevations for

all studies performed herein. The code is driven by astronomic tides at the open ocean boundary, and wind velocities and atmospheric pressure

profiles over the surface of the computational domains. Model results clearly indicate that the four inlet – bay configurations do not have a

significant impact on the open coast storm surge hydrographs. Furthermore, a spatial variance amongst the storm surge hydrographs is recognizedfor open coast boundary locations extending seaward from the mouth of the inlet.

In addition, a storm surge study of Hurricane Ivan in the vicinity of Escambia Bay along the Panhandle of Florida is performed to assess the

findings of the numerical parameter study in a real-life scenario. The main conclusions from the numerical parameter study are verified in the

Hurricane Ivan study: 1) the Pensacola Pass–Escambia Bay system has a minimal effect on the open coast storm surge hydrographs; and 2) the

open coast storm surge hydrographs exhibit spatial dependence along typical open coast boundary locations. The results and conclusions

presented herein have implications toward future bridge scour modeling efforts.

© 2006 Elsevier B.V. All rights reserved.

Keywords: Tidal inlets; Storm surge hydrographs; Bridge scour; Shallow water equations; Hurricane Ivan

1. Introduction

The design of coastal bridges is governed by a number of

factors: wind, moving (vehicular), and hydrodynamic loads, to

name a few. In particular, the coastal circulation patterns are

important in determining the amount of scour that occurs during

extreme flow events (e.g. hurricane storm surge). At present,

local three-dimensional models are used to estimate bothhorizontal and vertical circulation patterns, and thus bridge

scour, in the vicinity of coastal bridges. Typically, these models

encompass the bay system where the bridge is located and

extend seaward to shallow ocean regions beyond tidal inlets.

The magnitude for the design surge event (e.g. 50-yr, 100-yr,

or 200-yr surge event) used to force a local bridge scour model

(as used herein, the term bridge scour model refers to any high

resolution, three-dimensional circulation model that can be

applied to compute bridge scour) for a particular area is quite

varied between government agencies (Sheppard and Miller,

2003). As a result, it is necessary to elucidate the behavior of

Coastal Engineering 54 (2007) 377–391

www.elsevier.com/locate/coastaleng

⁎ Corresponding author. Fax: +1 407 823 3315.

E-mail addresses: [email protected] (M.B. Salisbury),

[email protected] (S.C. Hagen).1 Fax: +1 407 859 8121.

0378-3839/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.coastaleng.2006.10.002

mailto:[email protected]


http://dx.doi.org/10.1016/j.coastaleng.2006.10.002

http://dx.doi.org/10.1016/j.coastaleng.2006.10.002





2.1.2. Inlet – bay configuration

Four different inlet width profiles are used in the numerical

parameter study: an average inlet width (corresponding to the

average width identified in Table 2), a 100 m inlet width, a

500 m inlet width, and a 1000 m inlet width. This range of inlet widths encompasses the majority of Florida's tidal inlets. For

each inlet width configuration, the inlet length and depth are

held constant according to the average values determined in

Table 2. In contrast, the bay surface area varies between each

inlet width configuration according to a tidal prism–inlet cross-

sectional area relationship developed by Jarrett (1976). Con-

verted to the System International unit system, the relationship

is expressed as follows:

Ac ¼ 2:09 Â 10−5X0:95 ð3Þwhere, Ac=minimum cross-sectional area of the inlet (m2) and

Ω =tidal prism (m3

). This equation relates the minimum cross-

sectional area of the inlet to the tidal prism for stable tidal inlets.

As a comparison, the data of Florida tidal inlets are compared to

the solutions obtained from Eq. (3). Overall, Eq. (3) provides an

excellent fit to the raw data (Fig. 1). Thus, Jarrett's relationship

is deemed appropriate for Florida's tidal inlets.

Additionally, the tidal prism is related to the bay surface area

through the following relationship (USACE, 2002):

X ¼ 2a b A b ð4Þwhere, a b= the bay tide amplitude, and A b=the bay surface

area. The bay tide amplitude is defined as one half the tidal

range; thus, Eq. (4) relates the tidal prism to a product of the

tidal range (2a b) and the bay surface area. Substituting this

relationship into Eq. (3) yields the following solution:

Ac ¼ 2:09 Â 10−5 2a b A bð Þ0:95: ð5ÞFurthermore, it's assumed that the tidal range (2a b) is 1 m,

which is archetypical of the tidal range along the coast of

Florida [see Kojima (2005) for a detailed tidal analysis along the

United States coast]. Substituting this assumption into Eq. (5),

and rearranging for the bay surface area, leads to the following

equation:

A b ¼ Ac

2:09 Â 10−5

1=0:95

: ð6Þ

This expression is used to develop the inlet – bay configura-

tions in the finite element meshes of the numerical parameter

study. A rectangular cross-sectional profile is assumed for the

entire length of the inlet; thus, the inlet cross-sectional area ( Ac)

can easily be determined based on the desired inlet width

Fig. 1. Comparison of Jarrett's relationship to Florida tidal inlet data.

Fig. 2. Inlet – bay configurations for the idealized finite element meshes: a) average inlet width; b) 100 m inlet width; c) 500 m inlet width; and d) 1000 m inlet width.

380 M.B. Salisbury, S.C. Hagen / Coastal Engineering 54 (2007) 377 – 391



(average, 100 m, 500 m, and 1000 m) and the constant inlet

depth (3.7 m). Following this procedure for each inlet width

yields a unique bay surface area for each inlet configuration.

The result of this process leads to the following inlet – bay

configurations (Fig. 2).

The nodespacingranges from50 m intheinletto 100 m inthe

bay for the average, 500 m, and 1000 m inlet width config-

urations, and 25 m in the inlet to 50 m in the bay for the 100 m

inlet width configuration. This level of resolution ensures that

the inlet is represented by at least 4 elements across its width for

Fig. 3. a) Finite element mesh for the idealized domain; b) bathymetry for the idealized domain. Thick dashed lines represent locations of open boundaries.

Fig. 4. a) Finite element discretization for the ocean-based domain; b) bathymetry for the ocean-based domain; c) finite element discretization near Escambia Bay; andd) bathymetry for coastal areas near Escambia Bay.




all inlet – bay configurations. Furthermore, the domain measures

150 km alongshore with the ocean boundary placed 100 km

seaward from the coastline. A depth of 73 m is set at the ocean

boundary and a linear transition is applied to the bathymetry

profile between the ocean boundary and the coastline. Fig. 3a

shows the finite element mesh for the idealized domain, and

Fig. 3 b displays the associated bathymetry profile.

2.2. Escambia Bay domain

2.2.1. Study location

For the Hurricane Ivan analysis, a large-scale, ocean-based

domain is employed with higher mesh resolution in the

Escambia Bay region. The study area is located along the

Panhandle of Florida in the northwestern portion of the state of

Florida. The main focus of this study is an inlet – bay system that

was devastated by storm surge from Hurricane Ivan in

September 2004. The system includes the Pensacola Pass,

Pensacola Bay, Escambia Bay, Blackwater Bay and East Bay(Fig. 4). The system is connected to two adjacent bay systems via

a Gulf Intracoastal Waterway: Perdido Bay to the west and

Choctawatchee Bay to the east.

Pensacola Pass is a relatively deep inlet that connects the

Pensacola Bay to the Gulf of Mexico. The inlet is part of

Escambia County, and is bordered by two low-lying, sandy

barrier islands: Perdido Key to the west and Santa Rosa Island

to the east. The inlet became a federal navigation project in 1881

and is regularly dredged to a depth of approximately 15 m to

accommodate U.S. Navy aircraft carriers (Carr de Betts, 1999).

2.2.2. Model domain

An ocean-based domain is used to simulate storm surge dueto Hurricane Ivan in the vicinity of Escambia Bay. The domain

encapsulates portions of the Atlantic Ocean found west of the

60° West Meridian, the Gulf of Mexico, and the Caribbean Sea.

The mesh was developed by incorporating the Escambia Bay

coastline features into an existing 52,774 node mesh for the

Western North Atlantic Tidal model domain [see Hagen et al.

(in press) for verification of the existing mesh]. The new mesh

includes 88,318 nodes and 165,137 elements, and covers a

horizontal surface area of approximately 8.347×106 km2.

Bathymetry for the Escambia Bay region was obtained via the

National Geophysical Data Center (NGDC) Coastal Relief

Model, volume 3. The database consists of a combination of 3-arc second digital elevation maps (via the United States

Geological Survey) and hydrographic soundings (via the National

Ocean Service). For regions extending beyond the Escambia Bay

and Pensacola Pass, the bathymetry was interpolated from an

existing high resolution Western North Atlantic mesh. Fig. 4a

through d presents the finite element discretization and

bathymetry for the ocean-based domain with zoomed in views

of the Escambia Bay and Pensacola Pass.

In addition, a second computational domain is used that

includes the low-lying barrier islands as inundation areas. The

same ocean and Escambia Bay coastline features are used from

the previously described mesh, but Santa Rosa Island to the east

and Perdido Key to the west of Pensacola Pass are included as

inundation areas. Including the barrier islands into the model

domain allows the storm surge to inundate the barrier islands,

creating higher surge levels within the bay. Model results are

compared to historical data at a National Ocean Service (NOS)

tide gauge located in Pensacola Bay (Fig. 4d).

2.3. Storm surge model

The water surface elevations and circulation patterns are

computed by the Advanced Circulation model (ADCIRC) for

shelves, coasts, and estuaries (Luettich et al., 1992). In this study,

barotropic dynamics are predominant and density gradients are

assumed to be relatively small, as these conditions are common

near tidal inlets (Hench et al., 2002). These assumptions permit

the use of the fully nonlinear two-dimensional, depth-integrated

option of the model (ADCIRC-2DDI). Westerink et al. (1994)

present the basic governing continuity Eq. (7) and momentum

Eqs. (8) and (9) that are used in the model:

Af

At þ AUH

A xþ AVH

A y¼ 0 ð7Þ

AU

At þ U

AU

A xþ V

AU

A y− f V ¼ −

A

A x

ps

q0

þ g ðf−agÞ

þ 1

H M X þ sSX

q0 H −s⁎U

ð8Þ

AV

At þ U

AV

A xþ V

AV

A yþ fU ¼ −

A

A y

ps

q0

þ g ðf−agÞ

þ1

H

M Yþ

sSY

q0 H

−s⁎V

ð9Þ

where, t =time; x, y = horizontal coordinates, aligned in the East

and North directions respectively; ζ= free surface elevation,

relative to the geoid; U =depth-averaged horizontal velocity, x

direction; V = depth-averaged horizontal velocity, y direction;

H = total water column depth, h +ζ; h = bathymetric depth

relative to the geoid; f = 2Ω sinφ=Coriolis parameter; Ω =angu-

lar speed of the earth; φ= degrees latitude; ps=atmospheric

pressure at the free surface; g = acceleration due to gravity;

η= Newtonian equilibrium tide potential; α= earth elasticity

factor; ρ0= reference density of water; τ SX= applied free surface

stress, x direction; τ SY=applied free surface stress, y direction;

s⁎ ¼ C f ffiffiffiffiffiffiffiffiffiffiffi

U 2þV 2p H =bottom stress; C f =bottom friction coefficient;

M X= E h2

A2UH A x2 þ A

2UH A y2

h i= depth-integrated momentum disper-

sion, x direction; M Y= E h2

A2VH A x2 þ A

2VH A y2

h i= depth-integrated mo-

mentum dispersion, y direction; and E h2= horizontal eddyviscosity.

The governing equations are discretized in space by linear

finite elements and in time by a finite difference scheme

(Luettich et al., 1992). The finite element solution to the shallow

water equations gives rise to spurious modes and numerical

instabilities. Hence, it becomes necessary to reformulate the

equations into a form that provides a stable solution in its finite

element representation. Therefore, ADCIRC-2DDI employs the

Generalized Wave Continuity Equation (GWCE), together with




the momentum conservation equations, to eliminate this

problem (Westerink et al., 1994). The result is a noise-free

solution that is used to solve for the deviation from the geoid (ζ)

and the velocities in the x and y directions.

2.3.1. Hurricane Ivan wind field model

The state-of-the-art wind data (Fig. 5) for the hurricane storm

surge simulations was provided using a tropical wind model

developed by Cox and Cardone (2000). The model is a

derivative of the TC96 model that was first implemented in the

Ocean Data Gathering Program. The TC96 model provides

snapshots in time that are blended into a synoptic-scale wind

field using the Interactive Objective Kinematic Analysisalgorithm (Cox et al., 1995) of the Wind Workstation. Using

a numerical integration technique, the model solves the

vertically averaged equations of motion for a boundary layer

under horizontal and vertical stresses. Based on this principle,

the numerical model provides a fairly thorough description of

the time–space evolution of the wind speeds within the

planetary boundary layer (PBL) during a tropical cyclone

event (Thompson and Cardone, 1996).

The wind field model is driven by “snapshots” in time of the

storm's intensity and is based on the assumption that the

structure of the hurricane changes relatively slowly (Cox and

Cardone, 2000). In addition to the TC96 model, these snapshotsare also obtained from the Hurricane Research Division Wind

Analysis System, a distributed system that uses real-time tropical

cyclone observations as input (Powell et al., 1998). The slow

evolution of the storm's intensity is then interpolated from these

snapshots. In addition, the model is also controlled by several

input parameters: the storm's speed and direction, the geo-

strophic flow of the ambient PBL pressure field, a pressure

profile parameter, and a scaling factor for the exponential radial

pressure profile. The wind model is capable of simulating any

type of storm for any particular region, and has been verified and

validated for a number of test cases (Cox and Cardone, 2002).

The wind speeds that are computed by the wind field model

are used as surface stress conditions in the ADCIRC-2DDI

model. In order to convert wind speed to wind stress, ADCIRC

employs a relationship developed by Garrett (1977). Further-

more, the wind model also provides a pressure gradient to

ADCIRC. A conversion is then performed within ADCIRC to

convert the pressure gradient to an equivalent water column

height through the transformation P / ρw g (Blain et al, 1994). In

the end, the wind stress and the equivalent water column height are linearly interpolated to each computational node of the finite

element mesh used by ADCIRC.

2.3.2. Synthetic wind field model

For the numerical parameter study, a synthetic hurricane

wind field model is used to force the ADCIRC-2DDI model.

The wind field model is parameterized according to the forward

velocity and pressure field of Hurricane Ivan, and simulates a

simplified, circularly symmetric version of the storm. Com-

pared to the wind field model used in the Hurricane Ivan study,

the synthetic wind field model is much less sophisticated.

However, the model does allow the user to specify the hurricane parameters and path of the storm, which makes it ideal for a

numerical study such as this.

In all cases presented herein, the wind field model is

initialized to represent a typical worst-case scenario for coastal

storm surge in the vicinity of the tidal inlet. First, the path of the

storm is setup to traverse the coastline in a perpendicular

manner. Additionally, the eye of the storm makes landfall at a

point 25 km left of the tidal inlet, placing the inlet in the upper

right quadrant of the storm (Fig. 6).

2.3.3. Model parameters for idealized domains

For the idealized study, the inlet – bay configurations are

isolated to examine their influence on the model results.Consequently, the model parameters are held constant for each

simulation and are specified according to the following: The

equations are solved in the Cartesian coordinate system.

Simulations are spun up from rest over a 2-day period via a

hyperbolic ramp function. Total simulation time is 4 days, with a

0.25 second time step used to ensure model stability. A hybrid

bottom friction formulation is employed with the following

specifications: C fmin=0.0025, H break =10 m, θ=10, and λ=1/3.

Fig. 5. Hurricane Ivan wind field just before landfall.

Fig. 6. Synthetic wind field used in the numerical parameter study.




The horizontal eddy viscosity coefficient is set to 5 m

2

/sec. Aconstant Coriolis parameter corresponding to 27.5°N (approxi-

mately the middle latitude of Florida) is used. One harmonic

forcing frequency corresponding to the M 2 (principal lunar)

constituent is applied to the system with an amplitude of 0.5 m

and 0° phasing. This produces a tidal range of approximately 1 m

near the coastline, which is representative of the tidal range

characteristics along the Florida coast. Meteorological forcings

(wind stress and surface pressure) are read into the simulation

every 30 min, with the eye of the synthetic hurricane making

landfall approximately 3 days into the simulation.

2.3.4. Model output locations for idealized domains

In lieu of the fact that previous bridge scour modeling effortshave incorporated open coast boundaries at varying distances

from the mouth of the inlet, a wide range of semi-circular arcs

are created with output stations located along each arc. These

arcs have radii ranging from 1 km to 15 km from the mouth of

the inlet, and are representative of typical open coast boundary

locations used in bridge scour modeling. Water surface

elevations are recorded at each of these stations over the entire

duration of the simulation at six minute intervals. Fig. 7 displays

the semi-circular arcs with the output locations for the different

radii.

2.3.5. Model parameters for the Escambia Bay domainAstronomic tides are included in the Escambia Bay domain

simulations; however, the astronomic tides and storm surge are

computed separately due to the differences in model parame-

terization and simulation length. The total hydrograph is com-

puted by superimposing the storm surge output with a

resynthesis of the astronomic tides. The results are then

compared to historical National Ocean Service (NOS) gauge

data located within Pensacola Bay to verify the model.

The model parameters for the astronomic tidal simulations

are set as follows: The coordinate system is set to spherical.

Total simulation length is 90 days with all runs begun from a

cold start. Seven harmonic forcings are applied simultaneously

along the ocean boundary ( M 2, K 1, O1, N 2, K 2, Q1, and S 2)

and are ramped over a 20-day period. The hybrid bottom

friction formulation is employed with the following settings:

C fmin=0.0025, H break =1 m, θ=10, and λ=1/3. The horizontal

eddy viscosity coefficient is set at 5 m2/sec, and a time step of

5 s is used to ensure model stability.

Similarly, the model parameters for the storm surge simu-

lations are set as follows: A spherical coordinate system isapplied. Simulations are begun from a cold start, and are run

over a ten day period (September 7, 2004 at 6 p.m. to Sep-

tember 17, 2004 at 6 p.m.) with a 2.5-day ramp time. Meteo-

rological forcings (wind stress and pressure) are read into the

model every 30 min. The wetting and drying of elements is

employed with the minimum depth set to 0.1 m. A 2.5 second

time step is used for each model domain to ensure stability. A

hybrid bottom friction formulation is used with the following

settings: C fmin=0.001, H break =10 m, θ=10, and λ=1/3, and

the horizontal eddy viscosity coefficient is set to 5 m2/sec.

2.3.6. Model output locations for the Escambia Bay domainIn a similar manner to the idealized domain, semi-circular

arcs of varying radii are extended seaward from the mouth of

Pensacola Pass. The arcs range from 1 km to 15 km in radial

distance. Fig. 8 shows the observation points along each semi-

circular arc extending seaward from Pensacola Pass.

Observation points for locations due east and west from the

mouth of the inlet are not included as some of the points would

either be outside of the model boundaries or within the bay

system. In this case, seven output stations are located on each

semi-circular arc: east –southeast (1), southeast (2), south–

southeast (3), south (4), south–southwest (5), southwest (6), and

west –southwest (7). These output locations are used to compare

the effect that the Pensacola Pass has on the open coast stormsurge hydrographs and to examine the spatial variance of the

hydrographs along each arc.

3. Simulation results

Primary focus is given to the effect that inlet – bay configura-

tions have on the open coast storm surge hydrographs. Two

Fig. 7. Semi-circular arcs with output locations for idealized domain.

Fig. 8. Semi-circular arcs with output locations for Escambia Bay domain.




different studies are presented in this section to illustrate these

results: 1) a numerical parameter study, where the effect of four different inlet widths (average, 100 m, 500 m, and 1000 m

widths) on the open coast storm surge hydrographs are isolated

and compared; and 2) a storm surge study that focuses on the

effect of the Pensacola Pass and Escambia Bay system on the

open coast storm surge hydrographs produced from Hurricane

Ivan. Additional discussion is provided on the spatial variance of

the open coast storm surge along the observation arcs.

3.1. Numerical parameter study results

3.1.1. Inlet comparison

Ultimately, the results and conclusions from this study will

be used to determine whether an inlet and bay system (e.g. thePensacola Pass and Escambia Bay system) should be included

in a large-scale ocean circulation model (e.g. the Western North

Atlantic Tidal model domain) for generating open coast

boundary conditions for local bridge scour models. In order to

accomplish this, four inlet – bay configurations and a control

case are developed in an idealized setting. The control mesh

does not include an inlet – bay system along the coastline and

provides a test case for better determining the influence of the

inlet –

bay system on the open coast storm surge hydrographs.Model output is compared at each of the observation points

for all of the inlet – bay configurations. Figs. 9–11, show model

results for each of the inlet – bay configurations at point 3

(perpendicular to the coast) on the 1 km, 5 km, and 15 km radii

arcs, respectively.

It is evident from the plots that no appreciable difference

exists in the storm surge hydrographs between the inlet – bay

configurations. A difference of 5 cm is noticed in Fig. 9 (1 km

radius) for the 1000 m inlet width, but the difference is

practically negligible at the 5 km radius (Fig. 10) and the 15 km

radius (Fig. 11). Similar results are obtained at all of the other

model output locations, but are not included in the interest of

brevity. It is apparent from this analysis that the flow througheach of the inlets (velocity=3.1 m/s) does not produce a large

enough velocity head to draw down the water surface elevations

along the open coast when compared to one another.

Proper modeling practice dictates that the open coast

boundary be placed far enough from the inlet to allow for

appropriate circulation patterns to be generated within the

model (Militello et al., 2000). Thus, bridge scour modeling

studies would place the boundary farther than 1 km from the

inlet to avoid momentum flux problems. At locations further

Fig. 9. Storm surge hydrographs at point 3 on the 1 km radius observation arc for

each of the inlet – bay configurations.

Fig. 10. Storm surge hydrographs at point 3 on the 5 km radius observation arcfor each of the inlet – bay configurations.

Fig. 11. Storm surge hydrographs at point 3 on the 15 km radius observation arc

for each of the inlet – bay configurations.

Fig. 12. Storm surge hydrographs along the 1 km radius observation arc.




from the inlet, the open coast storm surge hydrographs are

nearly identical. Hence, the inlet – bay configurations do not

appear to create a significant difference in the open coast stormsurge hydrographs. Consequently, a large-scale model (e.g. the

WNAT domain) would not need to include an inlet – bay system

along the coastline when generating boundary conditions for a

local bridge scour model.

3.1.2. Spatial variance

Previous research has applied a single design hydrograph

along the open coast boundary for bridge scour modeling

studies. No consideration was given in these studies to the

spatial variance of the open coast storm surge hydrographs

along the boundary location. This was most likely due to the

unavailability of a large-scale model to produce boundary

conditions for a local, high resolution circulation model. Hence,stochastic formulations were developed for generating open

coast boundary conditions. The use of a large-scale model for

generating coastal boundary conditions allows for the spatial

variance of storm surge hydrographs to be incorporated into the

local circulation model.

Two different results are presented in this section: 1)

hydrographs along both the 1 km radius and 5 km radius arcs;

and 2) hydrographs for point 3 (perpendicular to the coast) on

each arc ranging from 1 km to 5 km (model results at the other

output locations show similar patterns, but are not included in

the interest of brevity). Water surface elevations are compared at the same open coast boundary locations as previously described

for the average inlet width. Analysis in the previous section

indicates that all inlet profiles produce nearly identical results as

the average inlet width; therefore, the results and conclusions

presented in this section can be extended to other inlet profiles

as well.

Fig. 12 shows computed sea stages along the 1 km radius

observation arc for the average inlet profile. The highest peak

(recorded at point 5) is 2.16 m above mean sea level (MSL),

whereas the lowest (recorded at point 3) is 2.04 m above MSL, a

difference of 0.12 m. The peaks reveal that the points (4 and 5)

closest to the eye of the storm produce the greatest surge.

Overall, the behavior of the storm surge hydrographs shows that a spatial variance exists along this observation arc during the

surge event. However, the hydrographs also show that the

astronomic tide signals are identical prior to hurricane landfall

(i.e. before day 2.75 of the simulation), thus indicating that the

spatial variance is limited to the surge event.

Similarly, Fig. 13 presents computed water elevations along

the 5 km radius observation arc. The highest peak (recorded at

point 5) is 2.18 m above MSL, whereas the lowest (recorded at

Fig. 13. Storm surge hydrographs along the 5 km radius observation arc.

Fig. 14. Storm surge hydrographs at point #3 on radii extending from 1 km to5 km.

Fig. 15. Astronomic tide comparison at the NOS station in Pensacola Bay.

Fig. 16. Astronomic tide comparison along the 5 km radius observation arcextending seaward from the mouth of Pensacola Bay.




parameter study, historical water elevation data is available tocompare model results as a means of verification. First, an

astronomic tide verification and a storm surge study of Hur-

ricane Ivan are performed to validate the model domain in the

coastal region of Pensacola Pass and Escambia Bay. Next, the

effect of the Pensacola Pass–Escambia Bay system on the open

coast storm surge hydrographs and the spatial variance of the

storm surge hydrographs along the open coast are evaluated.

The width (980 m) of Pensacola Pass and the size (6.8× 108 m2)

of the adjoining bay indicate that the domain is similar to the

inlet – bay configuration with the 1000 m inlet width used in the

numerical parameter study.

3.2.1. Astronomic tide verification

First the model domain is verified through an astronomic tide

comparison. A National Ocean Service tide gauge located

within Pensacola Bay (see Fig. 4) provides historical tidal

constituent data. A 14-day resynthesis of model results is com-

pared to a resynthesis of historical constituents at the NOS tide

gauge in Pensacola Bay (Fig. 15). The 14-day resynthesis

period is chosen to allow for a complete spring–neap tide cycle.

The results indicate that the model performs reasonably well at

this location. A slight discrepancy is recognized in phasing

between days 8 and 14, as well as the troughs through most of

the resynthesis. Overall, however, the model domain faithfully

simulates the tidal dynamics within the Pensacola Pass–EscambiaBay system.

In addition, the astronomic tide variance is examined along

the open coast observation arcs extending seaward from the

mouth of Pensacola Pass. Similar to the tide verification at the

NOS station in Pensacola Bay, a 14-day resynthesis is per-

formed at each of the model output locations along the obser-

vation arcs. Fig. 16 shows a resynthesis of the astronomic tide

signal along the 5 km radius observation arc.

The results indicate that the tide signal is nearly identical at

each of these locations. Similar results are obtained along the

other semi-circular observation arcs, indicating that the astro-

nomic tides do not display a spatial variance near the inlet. As a

result, the spatial variance recognized amongst the storm surge

hydrographs in the following sections is a result of the storm

surge phenomenon rather than the astronomic tides.

3.2.2. Historical comparison

Both model domains (barrier islands as model boundaries

and barrier islands as inundation areas) are used to simulate

storm surge within Escambia Bay for a ten day period: Sep-tember 7, 2004 at 6 p.m. through September 17, 2004 at 6 p.m.

Fig. 17 compares model results to historical gauge data at the

NOS station for the domain that treats the barrier islands as

model boundaries.

Two noticeable results are obtained from this figure. First,

the NOS tide gauge appears to have stopped recording close to

the time of hurricane landfall. As a result, the peak surge level

and the set-down behavior at this location are not shown in the

historical data, making a comparison throughout the entire

hurricane event impossible. In lieu of this, it is difficult to

accurately compare model results to historical data; however,

high water marks in Escambia Bay suggest a peak water level of 3–4.5 m near the Interstate 10 Bridge in Escambia Bay

(Douglass et al., 2004). A plot of the maximum surge elevations

within the bay (Fig. 18) for the model results that treat the

barrier islands as model boundaries indicates that the model

produces peak surge levels that are slightly less (2.5–3 m) than

the high water marks near the bridge.

Second, a difference in the rising limb behavior is noticed

between the model results and the historical data (between 9/14

and 9/15). This difference can be attributed to several factors

that are not included in this study. First, short-wave (wind

waves) processes are not included in the modeling process.

Typically, wind-induced waves travel ahead of the storm surge,

creating water elevations to rise before the hurricane makeslandfall. In order to perform a true storm surge hindcast (which

is not the objective of this study), wind waves would have to be

included in the modeling process.

Additionally, the difference may also be attributed to the

model parameter (bottom friction coefficient, wind drag co-

efficient, and horizontal eddy viscosity) values used in this

study. However, the model parameter values used are con-

sidered standard values and a sensitivity analysis is outside the

Fig. 21. Storm surge hydrographs at point #4 along the 5 km radius observation

arc for the model domain that does not include the Pensacola Pass and the model

domain that does include the Pensacola Pass.

Fig. 22. Storm surge hydrographs along the 1 km radius observation arcextending seaward from Pensacola Pass.




realm of this study. Lastly, inaccuracies in the wind field and

pressure field may have also led to errors in the storm surgeresults.

Furthermore, when the barrier islands are treated as

inundation areas, the surge levels within the bay increase by

almost half a meter compared to treating the barrier islands as

model boundaries. Fig. 19 compares the storm surge hydro-

graphs between the two model domains (barrier islands as

model boundaries and barrier islands as inundation areas) to

historical data at the NOS tide gauge. The results clearly

indicate that allowing the storm surge to flood over the barrier

islands creates greater water elevations within the bay. In this

case, the highest surge value for treating the barrier islands as

inundation areas is 2.12 m, whereas the highest surge value for

treating the barrier islands as model boundaries is 1.66 m, adifference of 0.46 m.

Similarly, comparing the maximum storm surge contours

within Escambia Bay to high water marks (3–4.5 m) recorded

near the Interstate 10 Bridge indicates that including the barrier

islands as inundation areas creates maximum surge levels that are

more consistent with historical records (Fig. 20). The results

shown in this figure (3–4 m near the bridge) compare more

favorably with the high water marks than the results shown in

Fig. 18 (barrier islands treated as model boundaries). Thus, in-

cluding the barrier islands as inundation areas creates more

realistic surge levels within the bay than treating them as model

boundaries.Model results still indicate a discrepancy when compared to

the historical data during the rising limb period. It's important to

note, however, that this is not a true storm surge hindcast study for

two reasons: 1) wind–wave processes are not included in the

modeling process; and 2) standard, not necessarily optimal,

values for model parameters (i.e., bottom friction coefficient,

wind drag coefficient, and horizontal eddy viscosity) were used.

In order to identify optimal model parameter values a sensitivity

study would be required, but that is outside the realm of this study.

The important conclusion from the results presented thus far is the

model reproduces the overall long-wave behavior reasonably

well, which is paramount to the open coast storm surge hydro-

graph analysis presented in the following sections.

3.2.3. Pensacola Pass

The main conclusion from the numerical parameter study is

that the effect of tidal inlets on open coast storm surge

hydrographs is negligible. The implication of this conclusion is

that a large-scale ocean circulation model does not need to include

an inlet – bay system in the computational domain when gen-

erating open coast boundary conditions for a local bridge scour model. This section verifies this conclusion for the case of

Pensacola Pass during Hurricane Ivan.

Two computational domains are used in this analysis: 1) a

finite element mesh of the Western North Atlantic Tidal model

domain that does not include the Pensacola Pass–Escambia Bay

system; and 2) a finite element mesh of the same region that does

include the Pensacola Pass–Escambia Bay system (previously

described). The domain that does not include the Pensacola Pass–

Escambia Bay system has been optimized in previous research for

storm surge applications (Hagen et al., in press; Kojima, 2005),

and is representative of a model domain that would be used to

generate open coast boundary conditions for a local bridge scour model if the inlet – bay system is not included in the domain. In

contrast, the domain that does include the Pensacola Pass–

Escambia Bay system is typical of a model domain that would be

used to generate the open coast boundary conditions if the inlet –

bay system is included in the domain. Model output is generated

along the semi-circular observation arcs extending seaward from

the mouth of the inlet.

Fig. 21 shows sea stages at point 4 (due south) on the 5 km

radius observation arc. Model results for the domain that does

not include the Pensacola Pass indicate a peak surge level of

1.79 m; whereas model results for the domain that does include

the Pensacola Pass indicate a peak surge of 1.71 m (a difference

of 8 cm). Similar results are obtained at the other open coast observation locations.

At this point, it is impossible to state that this difference would

or would not have an appreciable effect on the performance of a

bridge scour model. However, clearly it is unlikely that a differ-

ence of 8 cm (4.5% relative to the peak value) would significantly

alter the model's performance, especially since the rising and

falling limbs of the hydrographs are nearly identical. These results

are consistent with the conclusions from the numerical parameter

Fig. 23. Storm surge hydrographs along the 5 km radius observation arc

extending seaward from Pensacola Pass.

Fig. 24. Storm surge hydrographs at the same location (point 4, due south) oneach observation arc from 1 km to 5 km in radius.




study, i.e. tidal inlets do not appear to have a significant influence

on the open coast storm surge hydrographs.

3.2.4. Spatial variance

This section verifies the spatial variance results shown in the

numerical parameter study with a real-life scenario (e.g.

Pensacola Pass). The 1 km radius and 5 km radius observationarcs are used to verify these findings. Fig. 22 displays the storm

surge hydrographs along the 1 km radius extending seaward

from the mouth of Pensacola Pass. The plots indicate that a

minimal difference exists between the hydrographs along this

observation arc. The highest peak surge value is 1.87 m at point

7 (west –southwest), whereas the lowest peak value is 1.83 m at

point 3 (south–southeast), a difference of only 4 cm.

Fig. 23 shows the water elevation recordings along the 5 km

arc radius. In contrast to the 1 km radius, a noticeable spatial

variance is evident in the plots. The greatest peak surge value is

1.94 m (point 7) and the lowest peak surge value is 1.65 m

(point 3), a difference of 0.29 m. The spatial variance along the5 km radius is much greater than the spatial variance along the

1 km radius, which is consistent with the results from the

numerical parameter study.

In addition, spatial variance is also recognized as the radius

of the observation arc is increased. Fig. 24 shows hydrographs

at the same location (point 4, due south) along the 1 km and

5 km observation arcs. Similar to the numerical parameter study

results, the peak storm surge increases nearer to the coastline.

4. Conclusions

Presented herein is a numerical parameter study focusing on

the effect that tidal inlets have on open coast storm surgehydrographs. Four different inlet – bay configurations are con-

structed based on a statistical analysis of existing Florida tidal

inlets. The inlet – bay configurations allow for a number of test

cases to elucidate the influence that tidal inlets have on open

coast boundary conditions. A secondary focus of this study is

the spatial variance of the storm surge hydrographs along near-

inlet boundary locations. Results from the numerical parameter

study are compared with results from a Hurricane Ivan storm

surge study in the vicinity of Escambia Bay. The conclusions

from this study have implications toward future bridge scour

modeling efforts.

4.1. Numerical parameter study conclusions

Two primary conclusions are drawn from the numerical

parameter study: 1) the effect of tidal inlets on open coast storm

surge hydrographs is minimal; and 2) a noticeable spatial var-

iance of storm surge hydrographs exists along the open coast

boundary locations.

The effect of including inlet – bay systems on the open coast

storm surge hydrographs is negligible. Comparing model output

for all four inlet – bay configurations to the control mesh indi-

cates that including an inlet – bay system in the model domain

does not significantly alter the open coast hydrographs. Taking

this into account, a large-scale model domain (e.g. the WNAT

model domain) would not need to include the inlet – bay system

in the computational domain to generate open coast boundary

conditions for a local inlet-based model (a significant time-

saving benefit for coastal modelers).

Another significant finding in this study is the spatial

variance of the storm surge hydrographs along the open coast

boundary locations. Nearer to the inlet, the spatial variance of the hydrographs is minimal; however, the spatial variance

increases further from the inlet (i.e. going from the 1 km radius

to the 15 km radius). This suggests that it is more appropriate to

apply spatially varying hydrographs along the open coast

boundary, instead of the single design hydrograph method used

in previous bridge scour modeling studies (as a point of

reference, the open coast boundary in these studies appeared to

be several kilometers offshore). If the open ocean boundary is

placed close to the inlet so that a single hydrograph can be used

at each node, then momentum flux problems may arise from the

boundary being placed near the area of interest. By placing the

boundary further from the inlet and applying individualhydrographs at each node, the cross-basin hydrodynamics of

storm surge propagation can be artificially incorporated into the

inlet-based model. The results from this study imply that current

bridge scour modeling practices can be improved upon by

incorporating spatially varying hydrographs along the open

coast boundary.

4.2. Hurricane Ivan conclusions

The primary focus of the Hurricane Ivan storm surge study is

the verification of the numerical parameter study conclusions in

a real-life scenario. The effect that the Pensacola Pass–Escambia

Bay system has on the open coast storm surge hydrographs wasexamined. The results are consistent with the conclusions from

the numerical parameter study, such that including the Pensacola

Pass–Escambia Bay system in the model domain does not have a

significant impact on the open coast storm surge hydrographs.

Furthermore, a spatial variance is also recognized along obser-

vation arcs extending seaward from the mouth of Pensacola

Pass. Similar to the behavior recognized in the numerical pa-

rameter study, the magnitude of the spatial variance increases as

the open coast boundary locations are extended farther from the

mouth of the inlet. Thus, it is apparent that applying a single

design hydrograph along the open coast boundary is inappro-

priate and may lead to erroneous results.A corollary to this study is the significance that the low-lying

barrier islands had on the storm surge within Escambia Bay

during Hurricane Ivan. In this case, the storm surge increased by

half a meter in the bay when the barrier islands were treated as

inundation areas compared to treating the barrier islands as

model boundaries. This is an important conclusion for future

storm surge studies in areas that have barrier islands prevalent in

the coastal system.

Acknowledgments

This study was funded in part by Award UFEIE-

S0404029UCF as a subcontract from the Florida Department




of Transportation (FDOT) via the University of Florida (UF);

Award N00014–02–1-0150 from the National Oceanic and

Atmospheric Administration (NOAA), U.S. Department of

Commerce; and by National Oceanographic Partnership

Program (NOPP) Award No. N00014–02–1-0150 administered

by the Office of Naval Research (ONR). The views expressed

herein are those of the authors and do not necessarily reflect those of the FDOT, UF, NOAA, Department of Commerce,

ONR, or NOPP and its affiliates. The authors also wish to thank

Vince Cardone and Andrew Cox of Oceanweather Inc. for

providing the wind field used in the Hurricane Ivan study, and

Don Slinn at the University of Florida for providing the

synthetic wind field code used in the numerical parameter study.

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