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Development and Application of a Coastal and Estuarine Morphological

Process Modeling System

Yan Ding† and Sam S. Y. Wang‡

† Corresponding author, ‡ National Center for

Computational Hydroscience and Engineering, The

University of Mississippi, University, MS 38677

ABSTRACT

By means of the physical process-based modeling approache to computing coastal and estuarine hydrodynamic and

morphodynamic processes, an integrated model system was developed to simulate tides, waves, currents, winds, sediment

transport, and morphological changes in coastal and estuarine regions. This paper presents an overview of this integrated

morphological process modeling system consisting of modules for simulating random wave deformations, tidal and

shortwave-induced currents, sediment transport and morphological changes. The individual modules included in the

integrated model system were validated by simulating hydrodynamic and morphodynamic processes in laboratory

experiements and field study cases. An example for model application to an estuary is presented to demonstrate the model’s

effectiveness in simulating comprehensive impacts of combined storm waves, typhoons (or hurricanes), river floods,

sediment transport, and morphological changes in its coastal and estuarine area. This modeling system provides engineers

and researchers with an efficient and effective numerical software package to facilitate better coastal erosion protection,

flood and inundation prevention, coastal strom water management and infrastructure protection against hazardous storms,

typhoons, and hurricanes.

ADDITIONAL INDEX WORDS: Coastal and Estuarine Morphological Modeling, Model Validation, Coastal Flood,

Erosion.

INTRODUCTION

Coastal and estuarine waters are among the most

productive ecosystems on Earth, providing numerous ecological,

economic, cultural, and aesthetic benefits and services. They are

also among the most threatened ecosystems by flooding and

erosion, largely as a result of the extreme hydrological conditions

such as storm waves in typhoons/hurricanes, high tides, and

river floods. Rapidly increasing growth and development of

population and economy further makes the planning of flood

prevention and erosion protection more difficult than before.

The physical knowledge of hydrodynamics and morphology

in coasts and estuaries is very important to achieve coastal flood

protection, coastal sediment management, shoreline erosion

control, design and planning of coastal structures for different

engineering purposes, modeling of coastal/estuarine ecological

processes, and environmental impact assessment. The

hydrodynamic processes in large-scale coasts and estuaries are

highly complex, which are mostly driven by astronomical tides,

wind-induced waves, river flows, geotropic force, resulting in

multiple spatial and temporal scales of water motions. The

morphodynamic processes induced by these unsteady currents

cause changes of bed forms over coastal and estuarine regions

highly random and varied. In addition, due to different sand

sources from river upstream, longshore, and offshore, the

sediment properties over the regions are mixed up and in general

non-uniform. Therefore, understanding morphodynamic

processes well enough to develop a realistic coupled

waves-current-morphologic evolution model is a challenging

goal.

Induced by the combined dynamic forces of tides, waves,

river flows, and winds, sediment transport in coastal and

estuarine areas lead to shoreline erosion and accretion, scours

around structures, migration of sand bars, barrier island

breaching, etc. The significant bed changes in river mouths and

beaches will adversely impact the potential of currents, and may

cause unexpected inundations and structure failures due to

depositions and/or erosions induced by severe storm surges,

hurricanes, or typhoons. Therefore, as a traditional approach,

only to compute water elevations and currents in an idealized

hard sea bed is not sufficient to achieve flood management and

coastal infrastructure design/planning. In contrast, modeling of

these multi-scale and coupled hydrodynamic and

morphodynamic processes can give more accurate solutions of

water elevations, currents, and bathymetric changes. Therefore,

the systematical approaches to simulate hydrodynamic and

morphodynamic processes together can significantly facilitate

better planning of coastal projects and designing of coastal

structures for flood prevention, erosion protection, and coastal

environmental assessment.

Due to the complexities of multi-scale morphodynamic

processes, the mechanisms of sediment transport have neither

been fully understood nor described adequately by physical

principles and mathematical analyses. Direct simulation of

hydrodynamics and sediment transport over a full spectrum of

the scales has not yet been an applicable approach to solve

practical engineering problems of long-term (daily to yearly)

morphological evolutions in a real-scale coast coupled with tidal

currents, random waves and wave-induced currents. In the

past decades, significant progress has been made in the studies

of coastal processes by means of physical experiments and

Journal of Coastal Research Special Issue 52 127-140 Florida, USA ISSN 0749-0208

128

Coastal and Estuarine Morphological Process Modeling System

computational simulations (DE VRIEND et al., 1993; SHIMIZU ET

al., 1996; RENIERS ET AL., 2004). Especially, with the

process-based approach to development of coastal area

morphological model, simulations of morphological changes and

shoreline evolutions have become feasible. In general, this is

accomplished by computing tidal circulations, wave actions,

shortwave-induced currents, sediment transport, and seabed

changes sequentially (Figure 1). Then a newly computed

bathymetry is fed back to re-compute the wave and current fields

at the next time step. By this iterative procedure going through

the wave-current-morphological model, it is possible to compute

short- and long-term morphological changes using empirical

sediment transport models for simulating slowly varying

morphodynamic processes.

By means of developing and refining the state-of-the-art

numerical techniques for simulating physical processes in coasts

and estuaries, a process-based integrated coastal and estuarine

process model called CCHE2D-Coast has been developed at the

National Center for Computational Hydroscience and

Engineering (NCCHE) in The University of Mississippi, which

consists of three major modularized submodels for sequentially

modeling random wave deformations, tidal and wave- induced

currents, and morphological changes in a coast or an estuary.

First, the temporal/spatial variations of wave heights and

directions due to wave refraction, diffraction, and breaking are

computed by solving a multi-directional wave spectral equation.

Then, the two-dimensional (2-D) depth- and shortwave-

averaged momentum equations including the radiation stress

model are employed to simulate tidal and wave-induced currents.

In the sediment transport module, river sediment transport rate,

and cross- and longshore sediment transport rates are calculated

by utilizing a set of empirical sediment flux formulations; and

then the morphological changes are computed by a sediment

balance model with the downslope gravitational effect included.

The shoreline evolutions are simulated synchronistically by

monitoring the wetting-and-drying processes in the seabed

change computations. To develop a numerical analysis tool for

end-users with a user-friendly interface, these physical process

submodels have been built in a software package called

CCHE2D (NCCHE, 2005), which is a comprehensively verified

and validated tool to analyze 2-D shallow water flows,

morphodynamic processes, water quality, etc. The user interface

and the non-orthogonal mesh generator previously developed for

the CCHE2D model (ZHANG AND JIA, 2005) can be used for

mesh generation and post-processing for the application of the

coastal process model. It therefore makes this coastal modeling

system much effective and convenient to handle a coastal zone

with complex shorelines.

In the paper, a brief description of the coastal and estuarine

morphological model is given at first. Several numerical

examples for validation of individual process submodels in the

integrated model are presented. An application of the model to

simulate coastal morphological changes driven by historical

typhoons, tides, storm waves, and river floods in a real-scale

estuarine engineering project is examined. Conclusions from this

study and scope of future research are finally summarized.

DESCRIPTION OF COASTAL AND

ESTUARINE MORPHOLOGICAL PROCESS

MODELING SYSTEM

The coastal morphological process model (CCHE2D-

Coast) has integrated systematically three major submodels for

simulating random wave properties (i.e. significant wave heights,

periods, and mean wave directions), hydrodynamic variables (i.e.

water elevations and velocities), sediment transport (bed load

and suspended sediment) fluxes, and morphological changes

(Figure 1). The modular models, for adding into the CCHE2D

models (NCCHE, 2005) have been developed to utilize the

capabilities of the mesh generation and the user interface of the

previously developed CCHE2D models to study hydrodynamic

and morphodynamic processes for engineering applications. The

main features included in the model are as follows:

Flexible non-orthogonal mesh capable of simulating

complex coastlines;

Random wave deformations including refraction,

diffraction, transmission through coastal structures, wave

breaking, etc.;

Tidal currents and river flows;

Coriolis force;

Surface winds and bottom friction stresses;

Wave-induced currents and wave set-up induced by wave

radiation stresses;

Sediment transport due to combination of wave and

current,

Morphological change;

Description of a variety of coastal structures, e.g., groin,

offshore breakwater, artificial headland, jetty, artificial

reef (submerged dike).

The wave module is a multi-directional spectral wave

transformation model built in a non-orthogonal mesh. It

provides users with several options for input wave spectra at

offshore boundary. This module has been extensively validated

(DING ET AL., 2003 AND 2004; DING AND WANG, 2005ab; DING

ET AL., 2006ab). The hydrodynamic module based on the

shallow water equations is used to simulate the depth-averaged

velocities driven by tidal waves, shortwave radiation stresses,

turbulence stresses, bottom friction, and geotropic force. It

provides users with a surface roller model as an option to take

into account the effects of undertow current and wave breaking

inside the surf zone.

DING ET AL. (2006b) found that the consideration of three-

dimensional flow structure in computation of currents can

improve further the accuracy of morphological process

modeling. The offshore wave climate process can be

parameterized by incident wave spectra and an adjustable

feedback frequency. By implementing the wave-current-

morphological feedback cycle, the modeling of short- and

long-term coastal processes with multi-scales can be achieved.

Wave Model

(Refraction,

Diffraction,

Breaking, etc.)

Current Model

(Radiation Stress,

Surface Roller Effect,

Bed Friction,

Turbulence)

Sediment

Transport Model (Sediment flux due to

wave and current)

Morphological

Change Model (shoreline evolutions)

Tidal Model

(Tidal Incident Wave,

Colioris Force, Storm

Surge, etc)

Figure 1. Flow chart of an integrated coastal and estuarine morphological model system.

129


Similar to the CCHE2D hydrodynamic model (JIA et al.,

2002), in CCHE2D-Coast, a time-marching implicit algorithm

was used to compute tidal flows and wave-induced currents in a

computational domain subject to boundary conditions on

offshore tides and river inflows. A validated algorithm for the

treatment of wetting and drying in the computational area was

used for predicting tidal flat variations and coastal inundations.

This integrated process model has been extensively validated by

simulating waves, wave-induced currents, and morphological

changes in coastal applications in various laboratory and field

scales (e.g., DING et al., 2004; DING AND WANG, 2005a; DING et

al., 2006abc, and DING et al., 2007). A hurricane model

integrated into the tidal module takes into account the effects of

surface pressure, wind fields, and the route of a hurricane or

typhoon (DING AND WANG, 2005b). The three modules in the

model, i.e., multi-directional spectral wave transformation model

(MDSWT), depth- and shortwave- averaged hydrodynamic

model, sediment transport and morphological change model, are

briefly described as follows:

Multi-Directional Spectral Wave Transformation

(MDSWT) Model

By means of a spectral energy balance equation, the model

produces statistical variables of random waves such as

significant heights, periods, and mean directions due to wave

transformation and deformation such as refraction, diffraction,

and wave breaking. The variation of wave energy density

S(x,y,,f) in a temporal-spatial-frequency domain under the

attack of multi-directional incident waves is written as

Qy

SCC

y

SCC

y

Sv

y

Sv

x

Sv

t

Sgg

yx

2

222 cos

2

1cos

2

(1)

where t is time; x and y are the horizontal coordinates; θ is the

wave angle related to the x-direction; Q is a source term which

represents generation, wave-wave interaction, and energy

dissipation due to wave breaking and bottom friction; v is the

energy transport velocity, of which three components are:

y

C

x

C

C

CvCvCv

g

gygx cossin,sin,cos

(2)

where C is wave celerity and Cg is wave group celerity. The first

term in the right hand side, introduced by Mase (2001),

represents the energy dissipation due to the diffraction effect in

the alongshore y-direction, which is implicitly perpendicular to

wave direction; is wave angular frequency; is empirical

coefficient. Mase (2001) suggested this empirical coefficient has

a possible value within a range of 2.03.0. Ding et al. (2006b)

however suggested even a wider range of the value dependent

on problems with laboratory and field scales. To specify the

offshore random wave spectrum in offshore, the TMA spectrum

(Bouws et al., 1985) (Texel- Marsden-Arsloe, named after the

three data sets used in the development) and the

Bretschneider-Mitsuyasu (B-M) spectrum (Mitsuyasu, 1970) can

be selected by users.

Figure 2. Transmission through and over a rubble mound break-

water.

In addition, CCHE2D-Coast can take into account wave

transmission processes in case that offshore incident waves

penetrate through a permeable coastal structure (e.g. a detached

breakwater) which has water in the lee side (Figure 2). Wave

run-up and overtopping can cause wave transmissions by

regenerating the waves on the lee side. Meanwhile, waves

passing through the structures, if it is sufficiently permeable, can

transmit energy from the front side to the lee side. Due to the

complexities in wave transmission processes, the prediction of

the wave transmission heavily relies on experimental studies in

laboratories and field observations. However, the transmission

coefficient Kt, the ratio of transmitted to incident wave heights is

the principal parameter guiding the design of the breakwaters.

Notice that the ratio of transmitted to incident wave energy is

related to Kt2. Therefore, the portion of wave transmission can be

taken into account in the calculations of the wave energy in Eq.

(1) (DING et al., 2006a).

The Hydrodynamic Model

The hydrodynamic model contains the depth- and

shortwave-averaged two-dimensional (2-D) continuity and

momentum equations to simulate the currents driven by tides,

shortwave radiation stresses, river inflows, wind surface stresses,

and turbulence mixing in a large-scale coastal and estuarine

region, namely

? ) 0h

t

u (3)

1 1

晻 S b

t

corg ht h h h

u τ τu u τ R f

(4)

where is water elevation; h is water depth; u is depth- and

shortwave-averaged velocity vector in the horizontal

coordinates; g is the gravitational acceleration; is water

density; t is the depth- averaged Reynolds stress; S

is wind

stress; b is seabed friction stress; fcor is the Coriolis force term;

R is the radiation stress which represents the net

(shortwave-averaged) force that the shortwave exert on a water

column is defined as (Svendsen, 1984):

w wm pS S ρ

h

Q QR e I (5)

where I is the identity matrix; Qw is the wave volume flux

induced by the short wave motion; the tensor e is

2

2

cos sin cos

sin cos sin

θ θ θ

θ θ θ

e (6)

The scalar Sm and Sp, as well as the wave volume flux are

calculated respectively according to the different formulations

suitable for the region inside and outside the surf zone (Table 1).

However, the most existing hydrodynamic models only use the

radiation stress derived from the sinusoidal wave theory to

calculate the wave-induced forcing terms over the entire coastal

domain, although it is known that these sinusoidal formulations

could not generate accurately currents inside surf zone when

especially wave breaking occurs (SVENDSEN et al., 2003).

Therefore, this hydrodynamic model needs to identify the coastal

surf zone, and then uses the non-sinusoidal radiation stresses for

the region inside the surf zone, and the sinusoidal wave

formulation for the region outside the surf zone (deep water

region), respectively. Table 1 summarizes the different radiation

stress formulae inside and outside the surf zone. Because the

radiation stresses used for the surf zone take into account the

vertical variations of wave breaker structures, some 3D features

130


of the cross-shore movement mechanisms, e.g. undertow and

mass flux, are reflected accordingly in the hydrodynamic model.

By taking into account the influence of combined wave and

current on the bottom friction stress b, the friction law of the

combined wave and current proposed by Tanaka and Thu (1994)

is used to estimate the friction coefficient, namely

( )b

f b bC u u u u (7)

where the overbar means the time-averaged integration over a

typical short wave period; Cf = friction coefficient; ub=the wave

orbital velocity at the bottom. The friction law of the combined

wave and current is used to estimate the friction coefficient in

the different flow regimes, including rough turbulent flow,

smooth turbulent flow, and laminar flow. The combined friction coefficient fcw (=2Cf) is given as follows,

wwcccw fffff |cos|2 (8)

where fc and fw are the friction coefficients due to current and

wave, respectively; is the coefficient due to nonlinear

interaction of waves and currents; is the angle between wave

orthogonal and current vector. As far as the depth-averaged

Reynolds stress t in Eq. (4) is concerned, the present

hydrodynamic model provided users with two eddy viscosity

turbulence models pertaining to the characteristics of waves: the

Longuet-Higgins eddy viscosity model (LONGUET-HIGGINS,

1970) and the LARSON- KRAUS MODEL (LARSON AND KRAUS,

1991).

Table 1. Terms of radiation stresses inside and outside surf zone.

Inside surf zone Outside surf zone

Sm

LH

AhB

gh

CgH

20

22 )

2sinh

21(

16

1 2

kh

khgH

Sp 0

2

2

1BgH

kh

khgH

2sinh

2

16

1 2

Qw i)(20

22

LH

AhB

gh

c

C

gH

iC

gHB

2

0

Note: H is wave height; k is the wave number; A is the surface

roller area, =0.9H2; B0 is the wave shape parameter, =1/8

sinusoidal waves; L is the wavelength; i = (cos, sin).

Sediment Transport and Morphological Change

Models

The variation of seabed elevation Zb is calculated by

considering the local sediment balance and the downslope

gravitational transport:

晐 | | |b b bx y

Z Z Zq q

t x x y y

q (9)

where q= (qx,qy) is the local sediment transport rate, and is an

empirical coefficient. At the right hand side of Eq. (9), the bed

evolution is described by a divergence term and the other two

terms for the anisotropic downslope gravitational effect.

According to Watanabe et al. (1986), the local sediment

transport rate has two contributions from wave and current:

( | | )m cw D b cA F A

g

τ

q u i u (10)

where m = the maximum bottom shear stress which has been

modified to consider the difference of the stress in river flow and

nearshore current (see VAN RIJN (2007) for more discussions); c

is the critical shear stress; Aw is an empirical coefficient related

to grain size and fall velocity; iθ is the unit vector of wave

direction, equal to (cosθ, sinθ); FD represents the direction

function (=+1 for onshore, =-1 for offshore):

1 21 0.5 1 tanh 20( ) 1 tanh 20( )D m c m cF (11)

where m is the maximum Shields number; c1 and c2 are

respectively two critical Shields numbers at initiation of

suspension and at that of deposition of suspended sediments.

Ac is an empirical coefficient for sediment transport rate due to

current.

DATA REQUIREMENTS, BOUNDARY/INITIAL

CONDITIONS, AND EXTERNAL FORCING

INPUTS

For numerical applications, various data sets are required in

order to set up the integrated models, which can be mainly

categorized into bathymetric data, hydrological data, and

metrological data. Bathymetric data are measured bed elevations

or DEM (Digital Elevation Model) data covering an objective

domain of engineering project in a coastal and estuarine region.

The coastal infrastructures, e.g., breakwaters, dikes, harbors,

inlets, etc., should be identified in the bathymetric data. The

numerical models presented in the paper for simulating waves,

currents, and morphological changes are based on a

non-orthogonal mesh grid. The integrated models support a

mesh created by a non-orthogonal mesh generator for the

CCHE2D model (ZHANG AND JIA, 2005).

Boundary conditions for simulating wave deformation over

a computational domain covering ocean, coast and estuary are

comprised of offshore wave heights, periods, and directions. The

random incident wave properties can be represented by an

empirical spectrum of offshore random waves. The present wave

spectral model supports two kinds of offshore wave spectrum

inputs, i.e., the TMA spectrum (BOUWS et al., 1985) and the

Bretschneider-Mitsuyasu (B-M) spectrum (MITSUYASU, 1970).

To simulate hydrodynamics in the computational domain, the

boundary conditions, i.e., offshore tidal elevations, surface wind

speeds and directions, upstream river inflow hydrographs are

needed. Sediment properties on the bed of ocean, coast, estuary,

and rivers are needed in order to simulate morphodynamic

processes. According to the measured grain sizes, a median size

d50 is a typical input of sediment property for the sediment

transport model. The bed roughness is another important

parameter to represent the bottom friction forcing, of which the

Manning’s roughness values are based on field observations.

NUMERICAL APPROACHES

To simulate morphodynamic processes in a coastal and

estuarine region, the integrated numerical models were

developed to solve the abovementioned four partial differential

equations, i.e. (1), (3), (4) and (9). The so-called Efficient

Element Method (EEM) proposed by JIA AND WANG (1999) was

used for discretizing the four equations in a non-orthogonal

mesh. This numerical model is therefore convenient to simulate

the morphodynamic processes in a coast with complex

coastlines. The morphodynamic modeling was implemented

sequentially. First, the energy balance equation (1) was solved

by means of the parabolic approximation, in which the waves

were assumed to have a principal propagation direction from

offshore toward onshore. Second, a time-marching algorithm

proposed by JIA et al. (2002) was employed for computing

currents. Then, the bed level evolution equation (9) was solved

by using the implicit Eulerian backward scheme. The bed levels

were calculated at each morphodynamic time step by updating

131


the local sediment transport rate due to the variations of bed

levels and bottom frictions. Finally, after having gone through a

computational duration for simulating morphological changes,

wave and current were updated according to the computed new

bed levels. Therefore, by adjusting the frequency of the feedback

morphodynamic processes, this integrated model system takes

into account the interactions of wave, current, and sediment

transport.

In general, a typical computational domain in a coastal and

estuarine region is surrounded by the four boundaries: a

shoreline, an offshore boundary, two open cross-sections in the

cross-shore direction, and river inflows at upstream. Inside the

domain, island shorelines or offshore structure boundaries may

be present. The known values of velocities or discharges can be

imposed on the corresponding cross-sections in the cross-shore

boundaries. The impermeable condition of currents was used on

shorelines. The known tidal elevations are specified at offshore

boundary. For the initial conditions for velocities and water

elevations, the cold start (starting from a static state) is generally

utilized to initiate the simulations of the tidal and wave-induced

currents. In addition, to predict the shoreline changes due to

morphological changes, a moving boundary treatment is applied

to handle the dynamic wetting-and- drying process.

VALIDATION OF MODELS

Validations of Wave-Current-Morphology Models

The integrated submodels for modeling wave, current,

morphological change can be validated individually or

combined. For instance, the performance of wave transformation

processes (e.g. refraction, diffraction, wave breaking, etc) in the

wave model may be confirmed separately by using a set of

simplified laboratory experimental data. However, coastal and

estuarine morphodynamic processes should be validated

systematically, because coastal sediment transport cannot be

solely simulated without information of wave and current.

The experiments of wave deformation over an elliptical

shoal conducted by VINCENT AND BRIGGS (1989) were utilized

for validating the multi-directional spectral wave transform-

ation model in Eq. (1) to confirm the effectiveness of

refraction-diffraction terms in the model. In the paper, only the

results for the case of the narrow directional spreading spectrum

are presented, in which the incident wave height H0 was 7.75

cm, the period 1.3 s. Figure 3 compares (a) two narrow wave

frequency spectra and (b) a narrow directional spreading

function with the measurements, respectively. These wave

frequency spectra, i.e., TMA and Bretschneider- Mitsuyasu

(B-M) spectra, reproduced very well the experimental offshore

wave conditions. Figure 4 depicts the wave height profiles along

three transects behind the shoal with the corresponding measured

values. In Figure 4 (a), the solid lines stand for the wave height

computed with the TMA spectrum, and the dash lines by the

B-M spectrum, in which all the results were computed with the

diffraction effects with the diffraction coefficient κ=1.5. The

negligible discrepancies between the two lines imply that the

two wave spectra can produce almost the same results. Figure

4(b) shows a calibration process by comparing the wave height

profiles along the middle transect computed by the B-M

spectrum with different κ values. It was found that a calibrated κ

value of 1.5 was indeed suitable for the simulation of the wave

deformations over the shoal.

Frequency (Hz)

Fre

qu

en

cy

Sp

ectr

um

(Cm

2s)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2

4

6

8

10

12

14

16

18

20

Measured Spectrum

TMA Spectrum

B-M Spectrum

(Deg)

D(f

,

)(1

/rad

)

-90 -60 -30 0 30 60 900

0.5

1

1.5

2

2.5

3

TMA Spectrum

Measurement

(a) Wave Frequency Spectra (b) Narrow Directional Spreading (σm=10)

Figure 3. Comparison of frequency spectra and directional spreading functions between measurements and simulations

X (m)2 4 6 8 10 12 14 16

TMA

B-M

Measurement

Simulations(=1.5)

0.6 1.41.0

HS/H

0

y (m)

HS

/H0

0 3 6 9 12 15 180.6

0.8

1

1.2

1.4

1.6

Exp.

=0.0

=0.5

=1.0

=1.5

=2.0

=2.5

(a) H/H0 in three transects (b) Calibration of diffraction at the second transect (B-M spectrum)

Figure 4 Comparisons of normalized wave heights with and without diffraction term.

132


The integrated coastal morphodynamic model was validated

systematically by simulating waves, currents, and morphological

evolutions sequentially in a movable bed laboratory experiment

conducted by MIMURA et al. (1983). This experiment was carried

out in a wave basin being 14-m long, 7.5-m wide, and 0.42-m

deep. A beach with 1/20 slope was initially covered with 10-cm

thick sand, which had a uniform diameter of 0.2 mm. The still

water depth in the experiment was 25 cm. The incident random

waves with 5.7 cm significant height and 0.9 s period attacked

normally the beach for approximately 12 hours. Then, an

offshore breakwater of an iron plate with 1.5 m long and 0.5 m

height was installed at 1.8-m offshore from the initial shoreline.

The experiment of the morphological changes lasted more than

twelve hours after the installation of the offshore breakwater.

The measured beach topography at the time of the breakwater

installation was used for generating a computational mesh with

0.1m uniform spatial increment. The morphodynamic simulation

was started just from the measured bathymetry at the installation

of the structure and finally terminated after six hours.

5.5

54.5

43.532.5

2

1.5

5

4.5

4

3.5 3 2.5 2

Figure 5. Computed wave heights (unit: cm) and directions at 6h.

The wave deformation processes were computed by the

wave model with the B-M spectrum specified at the offshore.

The diffraction coefficient κ was set up to 2.5 to take into

account the diffraction effect by this iron breakwater. A

snapshot of the distribution of significant wave heights and

mean wave directions at t = 6h is shown in Figure 5. A further

comparison of breaking wave heights between the measurement

and simulation was discussed in DING et al. (2006b). The

wave-induced current fields for driving the morphodynamic

processes were thus computed by solving the shallow water

equations with the modified radiation stresses in Eq. (5) by

which the surface rolling effect of breaking waves in the surf

zone was considered. The simulations of waves and currents

were repeated after every 12 min of the morphodynamic

computations. Figure 6 compares (a) the computed currents at 6

h with (b) the measurements at the same time. The computed

currents reproduced the circulations and currents in front of the

breakwater.

Figure 7(a) presents the final bed elevations computed after

6-hour continuous wave attacks; and Figure 7(b) shows the bed

elevation changes at the final time step (6 h) relative to the

initial bathymetry. It was found that the integrated model

reproduced the sand depositions behind the breakwater, the

scours at the tips of the breakwater, and offshore bars.

Moreover, Figure 8 compares the contour lines of simulated and

measured bed elevations at -4.0cm behind the breakwater at t=6

hour. Figure 9 presents a comparison of the bed elevation

profiles along the cross-shore section cutting through the center

of the breakwater. Although the current model is

two-dimensional depth-averaged, the computed vertical profile

of beach was found to be close to the measurement. Thus, a

reasonable agreement in the morphological change results

between the simulation and the observation was obtained.

20cm/s

20cm/s

(a) Simulation (b) Observation (Mimura et al., 1983)

Figure 6. Comparison of wave-induced currents at t=6 h between simulation and observation.

-16.0

-14.0

-12.0

-10.0

-8.0

-6.0

-4.0-2.0

0.0

2.0

-2.8-2.8

-2.4

4.0

3.6 -0.4

-1.2

-1.2

2.0 1.6

0.80.4

2.0 2.0

-0.8

0.8

0.4

0.0

Zb

(cm)4.0

3.2

2.4

1.6

0.8

0.0

-0.8

-1.6

-2.4

-3.2

-4.0

(a) Computed bed elevations (unit: cm) (b) Computed bed changes

Figure 7. Computed bed elevations and bed changes at t = 6h.

133


Bed Level = -4.0cm

Simulation

Observation

Initial Level

Figure 8. Comparisons of a contour line of bed elevation at t=6 h.

Distance offshore (m)

Bed

Ele

vati

on

(m

)

-0.5 0 0.5 1 1.5 2 2.5 3-0.2

-0.15

-0.1

-0.05

0

0.05

Simulation at Y= 0.0m

Observation at Y=0.0m

Initial Bed at Y=0.0m

Figure 9. Comparison of bed elevations in a cross-section along the

cross-shore direction going through the middle of the breakwater.

Validations of Tidal Flow Module

The validation of the tidal flow module was done by using

the real-time data provided by the USGS sites in the Hudson

River, New York. The computational domain covered the tidal

river reach from HASTING (USGS Site# 01376304) to GREEN

ISLAND (USGS Site# 01358000). The validation of the tidal

model was carried out by simulating the tidal flows during a

10-day period from 0:00am, 05/29/2004 to 0:00am, 06/08/2004.

The tidal elevations at the Hastings-on-Hudson cross section

were used as the downstream boundary condition as an incident

tidal wave, which were downloaded from the USGS website. The

upstream discharge at Green Island was estimated as 6,000ft3/s

(169.92m3/s) based on the historical data during the same days in

2003. The average wind velocity and direction, 5.73mph and

NNW, collected at Poughkeepsie during the 10-days

computational period, were used in the tidal model as a steady

wind field. The simulations of the tidal flows in the area were

started from a status of still water at the initial condition. The

tidal elevations, discharges, and stream velocities at the other

three sites, Albany, Poughkeepsie, and West Point, were used for

comparisons between the numerical and the measured values.

The computed tidal currents around the Hastings-

on-Hudson are shown in Figure 10 for an ebb tide at 7:30am,

6/07/2004, and for a flood tide at a lower water level (LWL) at

10:30am, 6/07/2004. The computed tidal elevations above the

National Geodetic Vertical Datum (NGVD) at Albany are

compared with the observations in Figure 11. The simulated

discharges at Poughkeepsie are compared with the observed ones

and presented in Figure 12. Excellent agreement for both tidal

elevations and discharges was obtained.

Figure 10. Computed tidal currents in the lower Hudson River, NY (Left: Ebb tide at 7:30am, 06/07/2004; Right: Flood tide at 10:30am,

06/07/2004).

134


Figure 11. Comparison of tidal elevations between simulation and observation at Albany in the upper Hudson River, NY.

Figure 12. Comparison of stream discharge between simulation and observation at Poughkeepsie in the middle Hudson River, NY. ( some

observation data were missed). Sign of discharge: (+) ebb tide, (-) flood tide.

0 1km 2km

(a) Overview of the domain

BED (m)

5

4

3

2

1

0

-1

-2

-3

-4

-5

-10

-15

-20

N

Touchien

Fengshan

Offshore

Rivermouth Bar Head

Mid of Island

0 1k m

(b) Close-up view of the estuary

Figure 13. A non-orthogonal mesh covering the estuarine area

MODEL APPLICATIONS

Model Set-up and Simulations

An application case study reported herein is the simulation

of morphological changes in an estuary which is located at the

west coast of Taiwan. As shown in Figure 13, this estuary has a

1.0-km wide river mouth, a rivermouth bar, two islands inside

the bay, and two rivers upstream. This type of medium-sized

estuary has equally important coastal and estuarine processes

driven by tides, waves, river inflows, and winds. The sediments

can be transported into/through the estuary conveyed by river

flows, tidal currents, wave breaking across the surf zone, and

lower frequency infragravity wave motions by typhoons or

storm surges. The morphodynamic processes in the estuary are

of multiple-scale motions and therefore very complex.

To investigate the hydrodynamic and morphodynamic

responses to typhoon and flood events in the estuary, a

computational domain, as shown in Figure 13 (a), was set to

cover the two rivers, the estuary, a harbor, and the coastal areas

facing to Taiwan Strait. Figure 13 (b) shows a close-up of the

non-orthogonal grids covering the estuary. The numerical

investigations of the morphological changes in the estuarine area

were carried out by applying the model to several selected

historical typhoons and flood events (DING et al., 2006c), as

external forcings. In this paper, two sets of numerical results of

hydrodynamics and morphological changes, which corresponds

to one historical typhoon and a hypothetical 100-year flood

event are reported as follows: One typhoon event, called

Typhoon Mindulle, was formed in the east of Taiwan on the

north side of the equator in 6/24/2004, of which the track is

shown in Figure 14. The simulation period for the typhoon event

was chosen from 23:00, 6/29/2004, to 11:00, 7/3/2004. The two

hydrographs during the events at the inlet crosssections of the

two rivers were provided by one-dimensional flood simulations.

For the 100-year flood event, the maximum peak discharges

reached 7,775 m3/s in Touchien River (Figure15). The boundary

Hours

Dis

char

ge(m

3 /s)

48 96 144 192 240-15000

-10000

-5000

0

5000

10000

15000Simulated Discharge

Observed Discharge

Hours

Tida

lEle

vatio

nab

ove

NG

VD

(m)

48 96 144 192 240-1

-0.5

0

0.5

1

1.5

2

Simulation

Observation

Comparison of Tidal Elevations in the Albany

135


conditions of tidal elevations at the offshore were computed by a

two-dimensional regional tidal flow model. The wind speeds and

directions were obtained from local meteorological stations. As

an example, the tidal elevations at the offshore during Typhoon

Mindulle are shown in Figure 16. The wave properties, i.e.,

significant wave heights, periods, and wave mean directions, in a

large regional grid including Taiwan Strait were computed by

SWAN wave model (SWAN, 2007). These wave properties on

the offshore boundary of the estuary were extracted from the

results of the large regional model. The wave heights at the

offshore computed by the SWAN model in Typhoon Mindulle

are plotted in Figure 17. The wave heights in the event were

found to have varied in a range from 0.5 m to 1.5 m.

Figure 14. Track of Typhoon Mindulle.

0

2000

4000

6000

8000

10000

7/21/05

0:00

7/21/05

6:00

7/21/05

12:00

7/21/05

18:00

7/22/05

0:00

7/22/05

6:00

Dis

cha

rge

(m3/s

)

Touchien Creek Fengshan Creek

Figure 15. Hydrographs of the two rivers in the 100-year flood

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

6/29/04

12:00

6/30/04

12:00

7/1/04

12:00

7/2/04

12:00

7/3/04

12:00

Tid

al

Ele

va

tio

ns

(m)

Figure 16. Tidal elevations at the offshore in Typhoon Mindulle.

0.0

0.5

1.0

1.5

2.0

6/30/04

0:00

7/1/04 0:00 7/2/04 0:00 7/3/04 0:00 7/4/04 0:00

Wa

ve

Hei

gh

t (m

)

Figure 17. Wave heights at the offshore in Typhoon Mindulle

To simulate the random waves propagating through the

ocean to the estuary, the Bretschneider-Mitsuyasu (B-M) spectra

were used to specify the spectral wave inputs at the offshore.

The lower and upper frequency bounds were set to 0.1 Hz and

10 Hz, respectively. The frequency interval 0.495 Hz (i.e. 21

frequency bins) and the angle interval 5.0O (i.e. 37 directional

bins between –90O and +90

O) were adopted. The effects of wave

breaking and wave diffraction were considered in the

simulations of random wave deformations, in which the

coefficient k for including the wave diffraction was set to 2.5.

The time interval for the hydrodynamic and morphodynamic

modeling was 2 s. A critical shallow water depth, 5 cm, was

used to define the dry cells if the local wave depth was less than

this criterion. The wave field was updated after every 1.0-h of

hydrodynamic and morphodynamic computations. According to

the grain size measurements, a uniform grain size, d50 = 0.2 mm,

was used to represent the coastal sediments in the area. A

modified Watanabe’s total load sediment transport formulation

was used to calculate sediment fluxes at coast, estuary, and

river. The bottom roughness coefficient was set to 0.025 on the

sea bed, and 0.033 on the river bed, which were based on the

observations in the region. The wind surface friction coefficient

was 0.0015.

Numerical Results

Computed Wave Fields

Typhoon Mindulle considered in the studies was formed in

the east of Taiwan; and its first landing was in the east coast of

Taiwan. When the typhoon arrived at the estuary area in the

west coast of Taiwan, the wind strength was decayed due to the

resistance of the central mountains in the island. Figure 18 (a)

shows the computed significant wave heights and the mean

directions in the estuarine area before Typhoon Mindulle arrived

at the site, while the offshore wave direction was NE. Figure

18 (b) shows the two wave properties right after the typhoon eye

passed over the site, while the offshore wave changed its

direction from N to W. Although the tidal elevations were

included in the simulations of the waves, the wave breaking in

the surf zone and the wave diffraction behind the harbor were

well simulated. When the upstream river floods were small such

as the discharges in Typhoon Mindulle, the offshore waves

could not invade inside the river mouth due to the obstruction of

the rivermouth bar. However, if the floods were large enough to

overflow the rivermouth bar, the offshore waves can come over

the bar and invade into the bay. As shown in Figure 19, the

offshore waves invaded into the island inside the river mouth

because the rivermouth bar was inundated.

136


0.1

0.1

0.1

0.2

0.2

0.3

0.3

0.4

0.5

0.5

0.5

0.6

0.7

N

0 1 2km

Touchien

Fengshan

(a) t = 37 h (Offshore wave: NE)

0.1

0.1

0.1

0.2

0.2

0.2

0.2

0.3

0.3

0.4

0.4

0.5

0.5

0.5

0.6

0.6

0.7

0.7

0.8

0.8

0.8

0.9

1

1

1

1.1

1.1

1.1

1.2

1.2

1.3

1.3

N

0 1 2km

Touchien

Fengshan

(b) t = 83 h (Offshore Wave: SW)

Figure 18. Computed wave heights and mean directions in Typhoon Mindulle

0.1

0.1

0.1

0.1

0.1

0.2

0.2

0.20.3

0.3

0.4

0.4

0.40.4

0.5

0.5

0.5

0.6

0.6

0.6

0.7

0.7

0.8

0.8

0.8

0.9

0.9

1

1

1.1

1.1

1.2

1.2

1.2

1.3

1.4

1.4

1.5

1.5

N

0 1 2km

Touchien

Fengshan

Figure 19. Wave heights and directions in a case the rivermouth bar

inundated (Offshore wave: N).

Computed Currents

The hydrodynamic model includes all major hydrodynamic

forcing terms existing in coastal and estuarine waters, e.g.

offshore wave radiation stresses, tidal flows, river inflows, the

Coriolis forces, winds, bottom roughness resistance, turbulence

mixing, and interaction with bed elevation changes. Therefore,

this model is capable of simulating the currents at coasts and

estuaries driven by these combined forces. Then, the simulated

currents and water elevations can be much closer to the realistic

coastal/estuarine flows, than those produced by only a tidal flow

model or a nearshore current model. Furthermore, when the

flood flows meet with high tide waters in the estuarine region, it

is most likely that coastal inundations, sand bar overflows and

breaches will take place. To reproduce these complex flow

phenomena is a challenge to numerical coastal/estuarine models.

In the simulations of the currents caused by Typhoon Mindulle,

no inundations and overflows in the rivermouth bar were

produced, due to the small flood discharges from the two rivers.

However, the coastal inundations were predicted in the 100-year

flood event. This 100-year flood could cause coastal inundations

over a large area of the estuary; and further breach the river

mouth sand bar. Figure 20 presents four snapshots of the

predicted overflowing and breaching process in the rivermouth

bar due to the 100-year flood from upstream and the tidal waters

from ocean. Figure 20 (a) shows the computed currents before

the breaching; (b) the breaching started at the middle of the bar;

(c) the coastal inundation over the rivermouth; and (d) flood

receding. In addition, the model predicted that the sands in the

bar were flushed out to the offshore; and consequently the

rivermouth was widened. The detailed morphological changes

are presented below.

The time histories of the computed water elevations for the

two events at five monitoring stations, of which the locations are

shown in Figure 13 (b), are plotted respectively in Figure 21 (a)

and (b). The tidal elevations at the offshore station show that the

tidal waves are approaching to the estuary. The computed water

elevations at the two upstream stations responded to the flood

waters from the two rivers and the tides at the river mouth. The

flood waters by Typhoon Mindulle shown in Figure 21 (a) were

much less than those in the 100-year flood event in Figure 21

(b). The water elevations at upstream stations due to Typhoon

Mindulle, as shown in Figure 21(a), have almost no changes.

But, the water elevations at the stations due to the 100-year

flood reached up to their highest levels because the peak

discharge took place at a high tide as shown in Figure 21(b) (see

Figure 20 (c) for the high flood in the estuary).

Morphological Changes

Actually, the two islands inside the estuary split the river

flows from the Touchien River into three branches (Figure 13).

Therefore, together with the Fengshan River flow, three river

courses join at the river mouth (e.g. Figure 20 (a)), which lead to

complicated hydrodynamic conditions with unstable bathymetric

changes in the estuary and the rivers. As shown in Figure 22 (a),

Typhoon Mindulle can cause a limited amount of erosion in the

head of the rivermouth bar, and mostly the deposition on the two

river beds. But it can not cause overtopping the river banks and

the breaching in the rivermouth bar. However, for the 100-year

flood event, flood waters may overtop the left bank, flow into

the island inside the estuary, and thus inundate the surrounding

areas as shown in Figure 22 (b). By comparing with the

hydrodynamic results of the breaching process shown in Figure

20, the numerical model predicted a large-scale breaching

process occurring in the rivermouth bar and rivermouth

widening due to the hazardous 100-year flood waters together

with tides and offshore waves. Although the flood period (28

hours) was short, severe erosion and breaching were predicted in

the rivermouth bar. Therefore, the estuarine morphology may be

changed drastically. Due to the extreme flood, a large amount of

sediment from upstream may be deposited in the rivers inside

the estuary.

137


Vel (m/s)

4

3.6

3.2

2.8

2.4

2

1.6

1.2

0.8

0.4

0

1

N

0 1 2km

Touchien

Fengshan

m/s

Vel (m/s)

4

3.6

3.2

2.8

2.4

2

1.6

1.2

0.8

0.4

0

1

N

0 1 2km

Touchien

Fengshan

m/s

(a) t = 12 h (b) t = 13 h

Vel (m/s)

4

3.6

3.2

2.8

2.4

2

1.6

1.2

0.8

0.4

0

1

N

0 1 2km

Touchien

Fengshan

m/s

Vel (m/s)

4

3.6

3.2

2.8

2.4

2

1.6

1.2

0.8

0.4

0

1

N

0 1 2km

Touchien

Fengshan

m/s

(c) t = 20 h (d) t = 35 h

Figure 20. Computed currents in the 100-year flood.

Hours

Wa

ter

Ele

va

tio

ns

(m)

0 6 12 18 24 30 36 42 48 54 60-2

0

2

4

6

8

10

Touchien Inlet

Offshore

Rivermouth Bar Head

Mid of Island

Fengshan Inlet

Hours

Wa

ter

Ele

va

tio

ns

(m)

0 6 12 18 24 30 36-2

0

2

4

6

8

10

12

14

16

18

20

Touchien Inlet

Offshore

Rivermouth Bar Head

Mid of Island

Fengshan Inlet

(a) Typhoon Mindulle (b) 100-year flood event

Figure 21. Time histories of computed water elevations at five monitoring stations.

Breaching

138


-30

-25

-20

-20

-15

-10

-10

-5-5

-5

-3

-3

-3

-1

-1

-1

1

1

1

11

1

1

3

3

3

DZ (m)

1

0.8

0.6

0.4

0.2

0.01

0

-0.01

-0.2

-0.4

-0.6

-0.8

-1

N

0 1 2km Touchien

Fengshan

(a) Typhoon Mindulle

-30

-25

-20

-20

-15

-10

-10

-5

-5

-3

-3

-3

-3

-1

-1

1

1

1

1

1

3

DZ

1

0.8

0.6

0.4

0.2

0.01

0

-0.01

-0.2

-0.4

-0.6

-0.8

-1

N

0 1 2km Touchien

Fengshan

(b) 100-year flood

Figure 22. Comparisons of morphological changes at the end of

the two events.

Discussions about Numerical Results in the

Application Case Study

Using the integrated coastal and estuarine process model, a

number of numerical simulations were carried out successfully to

predict highly-nonlinear hydrodynamic and morphodynamic

processes in the estuary driven by combined external forcings of

tide, wave, wind, typhoon, and river flood. These results revealed

complex flow patterns and significant morphological changes in

the estuarine area, which are characterized by unsteady flows,

spatial/temporal variations of water elevations, coastal

inundations, breaching of the rivermouth sand bar, and

erosions/depositions of sediments. The findings are important to

the understanding of the nonlinear interactions among tides,

waves, and river floods, as well as sediment transport and

morphodynamic processes due to typhoons/storms and floods in

the area. Furthermore, they can be used in the planning of coastal

flood prevention, sediment movement management, and

shoreline stabilization structure designs in the region.

The extreme high flood used in the test was a 100-year

flood event, which has a highest peak discharge of 7,775 m3/s.

Due to the lower peak discharge, Typhoon Mindulle caused a

limited amount of erosion on the rivermouth sand bar, and

sediment deposition in the two paths of the river beds. But it can

not cause overtopping of the river banks and the breaching of

the rivermouth bar. However, for the 100-year flood event, the

peak flood water happening in a high tide may cause

overtopping in the left bank and inundation on the low land

areas much severer than that by Typhoon Mindulle. The

numerical model also predicted that a large-scale breaching

process and a river mouth widening may take place due to the

100-year flood event.

This integrated coastal and estuarine process model has

proved its capability in simulating both hydrodynamic and

morphodynamic evolutions driven by waves, storms, tidal

currents and flood flows; and the results are consistent with the

physical principles as well as field observations qualitatively.

Even without the benefit of field measurements to calibrate the

model parameters, this model was still able to provide excellent

preliminary results which show a strong feasibility that this

model after having been validated by the accurate and sufficient

amount of field data, the quantitatively accurate and reliable

results were obtained. This numerical model will be a

cost-effective and powerful tool to facilitate preventing flooding

and protecting shoreline erosion in the estuary and its adjacent

coasts. The same approach can be applied to better designs in

other river estuaries as well.

CONCLUSIONS

This paper presents an integrated coastal and estuarine

morphological process model which was developed for

simulating the coastal and estuarine morphodynamic processes

consisting of random wave deformations, wave-induced

currents, tidal currents, sediment transport, and morphological

changes. The modularized submodels for simulating the

corresponding physical processes were systematically validated

by simulating hydrodynamics and morphological changes due to

the nonlinear interactions of waves, currents, and seabed

changes for laboratory and field cases. The offshore wave

climate process can be parameterized by an incident wave

spectrum and an adjustable feedback frequency. Therefore, by

adjusting the wave-current-morphological feedback cycle, the

modeling of coastal and estuarine morphodynamic processes

can be better performed; morphological changes can be

predicted more accurately.

The success of the application of the model to a

medium-sized estuary and the numerical results of

hydrodynamics and morphological changes indicate that the

model can simulate complicated coastal morphodynamic

processes such as coastal inundation, erosion/deposition,

breaching of rivermouth bar under the combined forcings of

tides, storm waves, typhoons, and river floods. The simulation

of the time-dependent hydrodynamic and morphodynamic

processes driven by the combined external forcings, has

demonstrated another important capability of the model to

capture the peak water elevations in the estuarine region when

the peak upstream river flood coincides with a high tide and a

high wave in the estuary near the coast. This capability enables

the model to reproduce the worst case of scenarios for coastal

water emergency management when a storm occurs during a

high tide and a peak upstream river flood. Therefore the model

is especially useful for coastal hazardous flood management and

infrastructure protection planning for extreme and complex

hydrological conditions during the season of tropical storm

invasion. In addition, this numerical tool is also capable of

assisting researchers and engineers for the marine environmental

impact assessment.

Erosion

Erosion

139


It is generally known that in a large-scale coastal and

estuarine region, the nature of sediment composition is

heterogeneous, because the sediment sizes in coasts may be

different from those in river bed. Therefore, in the near future,

this model is to be further updated to include the non-uniform

sediment transport mechanism with multiple grain size classes

for bed materials, so that the results shall be more realistic.

ACKNOWLEDGEMENTS

This work was done at the National Center for

Computational Hydroscience and Engineering in The University

of Mississippi. The application case study for the estuary was a

collaborative research with the National Chiao Tung University,

Shinchu, Taiwan.

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