Yusuke UCHIYAMAREPORT OF THE PORT AND AIRPORT RESEARCH INSTITUTE, Vol.44, No.1
Copyright © 2005, the Port and Airport Research Institute. All Rights Researved.

Modeling three-dimensional cohesive sediment transport
and associated morphological variation in estuarine intertidal mudflats

Yusuke UCHIYAMAMarch 2005

Littoral Drift Division
Port and Airport Research InstituteYokosuka, JAPAN-20-

REPORT OF THE PORT AND
AIRPORT RESEARCH INSTITUTE
Vol.44, No.1 (Mar., 2005)

Modeling three-dimensional cohesive sediment transport
and associated morphological variation in estuarine intertidal mudflats

Yusuke UCHIYAMA*

Synopsis
A numerical model has recently been developed with incorporating a wetting and drying scheme into
the Princeton Ocean Model (POM; Blumberg and Mellor, 1983) to simulate tidal currents in San Francisco
Bay, CA, USA (WD-POM; Uchiyama, 2004). San Francisco Bay is encompassed by extensive intertidal
area including mudflats and salt marshes where flooding and draining are predominant for overlaying hydrodynamics.

Intertidal sediment transport and associated topography changes are of interest for coastal

engineers (e.g., Dyer, 1986) as well as marine biologists (e.g., Kuwae et al., 2003), whereas no threedimensional numerical models have been developed thus far to calculate the intertidal sediment transport
properly. In the present study, cohesive sediment transport and bed elevation changes are modeled andadapted to WD-POM to assess intertidal morphodynamics in San Francisco Bay.
The cohesive sediment transport model contains settling speeds of cohesive flocs (Burban et al., 1990)
and the sink/source terms due to deposition (Partheniades, 1992) and resuspension (Krone, 1962) at the seabed. The governing equation is transformed into the horizontal orthogonal curvilinear coordinate and thevertical sigma coordinate as used in WD-POM.

The bed elevation model is also developed based upon thevolume conservation of the deposited/suspended sediments and is capable of considering consolidation
through sediment porosity.
Astronomical tidal oscillations are imposed onto the open boundary condition off Golden Gate (the bay
mouth). Neither fluvial sediments nor surface wind stresses are assumed in the computation for the simplicity.

The model outputs exhibit that cohesive sediments are suspended dominantly in the deeper chan-nels while being transported and deposited on intertidal areas fringing the bay.

The morphological change

due to tidal currents during two spring-neap cycles shows that intertidal mudflats tend to slightly be accreted
yet channels seem rather eroded. These results demonstrate that the intertidal areas play an important rolein the sediment budgets in the estuary, acting as ‘sink’ of the suspended cohesive sediments under action of
the tidal currents.
Key Words: cohesive sediment transport, morphological change, intertidal mudflat, numerical model* Senior Researcher, Littoral Drift Division, Marine Environment and Engineering Department
3-1-1 Nagase, Yokosuka 239-0826, Japan
phone: +81-46-844-5045, facsimile: +81-46-841-9812, email: uchiyama@pari.go.jp-1-港湾空港技術研究所報告
第44巻第1号（2005.3）

内湾干潟海域における3次元凝集性土砂輸送
およびそれに伴う地形変動のモデリング内山 雄介*
要旨

代表的な 3 次元海洋流動モデルである Princeton Ocean Model（POM; Blumberg and Mellor,1983）に適用可能な冠水・干出スキームが著者によって開発され，米国サンフランシスコ湾の潮流シミュレーションに適用された（WD-POM; Uchiyama, 2004）．WD-POM では新たに拡張対数則が導入され，潮間帯周辺において水深が極めて浅くなった場合であっても，海底面境界層内外の流速分布構造，および底質再懸濁に対して重要な底面シアをより正確に再現することが可能となっている．サンフランシスコ湾は広大な潮間帯・干潟により沿岸部を囲まれた典型的な閉鎖性内湾であり，干出・冠水現象が湾内流動に対して重要な役割を果たしている．このような潮間帯域における底質輸送とそれに伴う地形変化の機構と実態にいては，海岸工学分野（例えば，Dyer,
1986）だけではなく，海洋生物分野（例えば，Kuwae et al., 2003）においても注目されている．しかしながら，潮間帯域の底質輸送を精緻に再現する 3 次元モデルはこれまで提案されていなかった．そこで本研究では，WD-POM に適用可能な 3 次元凝集性土砂（cohesive sediment）輸送モデ
ルおよび地形変化モデルを開発し，それらをサンフランシスコ湾に適用して湾内の底質移動，海底地形変動特性を検討する．
土砂輸送モデルは沈降速度を考慮した 3 次元の移流拡散方程式を基礎式とし，水塊のシアと凝集性土砂のフロック形成を考慮した沈降速度（Burban et al., 1990），海底面における沈降堆積速度（Partheniades, 1992）および再懸濁侵食速度（Krone, 1962）の各サブモデルが含まれている．
基礎方程式は WD-POM に適合するように 3 次元デカルト座標系から水平直交曲線座標系および鉛直σ座標系へと変換されている．海底地形変動モデルは底質の沈降，再懸濁を考慮した海底面における土砂の体積保存則に基いており，底質の間隙率を通じて圧密沈下を考慮できるように定式化されている．
湾口部（Golden Gate 西側）の開境界において，天文潮のみを与えて湾内の潮流分布およびそれに伴う土砂輸送と地形変化に関する計算を行った．本研究では潮流成分による土砂輸送の効果を検討するため，湾北東部の Sacramento-San Joaquin デルタからの淡水流入や，海表面における風応力の作用（吹送流および風波）は考慮していない．モデルによる計算結果から，凝集性土砂の再懸濁は湾中央に形成された水深の深い水路部において卓越しており，下げ潮流によって潮間帯周辺を含む浅海域方向に土砂が輸送されて沈降するというメカニズムが卓越することが明らかとなった．これに対応して，二朔望周期（約 28 日間）における潮流による地形変化結果から，水路部では侵食が，潮間帯干潟では堆積が卓越していることが分かった．すなわち，潮間帯干潟域は
内湾全体の流動だけではなく土砂収支の観点からも非常に重要な役割を果たしており，潮流に対しては土砂の“シンク”として機能していることが示された．
キーワード：凝集性土砂輸送，地形変化，潮間帯干潟，数値モデル* 海洋・水工部〒239-0826

漂砂研究室 主任研究官

神奈川県横須賀市長瀬3-1-1

電話：046-844-5045，FAX：046-841-9812，Eメール：uchiyama@pari.go.jp-2-

CONTENTS

Synopsis·············································································································································1
1. INTRODUCTION························································································································5
2. STUDY SITE·······························································································································6
3. NUMERICAL MODELING·········································································································73.1. Cohesive Sediment Transport····································································································73.2. Boundary Conditions and Empirical Submodels·········································································83.3. Bed Shear Stress and Vertical Mixing Parameterization·······························································83.4. Bed Elevation Modeling···········································································································94. RESULTS····································································································································94.1. Cohesive Sediment Concentrations····························································································94.2. Geomorphological Variations··································································································12
5. DISCUSSION·····························································································································146. CONCLUSIONS························································································································15
ACKNOWLEDGEMENTS···············································································································15
REFERENCES·································································································································15

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Modeling three-dimensional cohesive sediment transport and associated morphological response in estuarine intertidal mudflats

1. INTRODUCTION

1997). However, intertidal mudflats extend in the estuaries where baroclinic motion is effectively significant

Intertidal mudflats play a crucial role in the transport

for the hydrodynamics (Ralston and Stacey, 2004), andof land-sourced sediments and contaminants into estuar-thus three-dimensional prognostic models are requisite

ies.

Currents and waves interact to erode mudflats andfor exploring intertidal sediment transport. Among thevary with tidal range, seasons, and episodic events suchmodels referred to above, Inagaki (2000), Nakagawa

as storms.

Sedimentation occurs during relatively calm

(2003, 2005), and Bricker et al. (2004) developed theperiods, when accretion is higher than erosion (Christie

three-dimensional intertidal cohesive sediment transportand Dyer, 1998; Uchiyama et al., 2001; Talke and Sta-models.

cey, 2003). Mudflats are recognized to be an importantmodel based upon TRIM-3D (Casulli and Cattani, 1994;

component of the estuarine system, particularly with re-

Gross et al., 1998) which is originally capable of simu-

gard to sediments, contaminants, and organic matter be-

lating inundation and drainage occurred on intertidal

cause they provide an extensive boundary condition

mudflats. However, both of them paid no attention to(Dyer, 1998). Hydrodynamics, sediment transport andintertidal processes, whereas the simulations are done for

associated morphological variations have been investi-South San Francisco Bay which is fringed by extensive

gated mostly through field measurement programs par-intertidal areas and man-made salt ponds (Siegel andticularly during the late 1990’s (e.g., Wood et al., 1998;

Bachand, 2002). Nakagawa (2003, 2005) employed theInagaki (2000) and Bricker et al. (2004) used aWhitehouse and Mitchener, 1998; Widdows et al., 1998;

PHRI siltation model developed by Tsuruya et al. (1990)

Li and Parchure, 1998; Van der Lee, 1998; Van der Lee,with implementing a wetting and drying capability to

2000; Whitehouse et al., 2000).

Intertidal sediment

simulate cohesive sediment transport in Ariake Bay, Ja-transport and associated topography changes are of in-pan, still he mentioned nothing about effects of the inter-terest not only for coastal engineers and physical ocean-tidal mudflats surrounding the estuary on its hydrody-

ographers (e.g., Dyer, 1986) but also aquatic biochemists

namics and sediment transport.

and marine biologists (e.g., Kerner, 1993; de Jonge and

A wetting and drying scheme (WDS) has recently

van Beusekom, 1995; Asmus et al., 1998; Kuwae et al.,been developed and incorporated into the Princeton

1998; Cabrita and Brotas, 2000; Christensen et al., 2000;

Ocean Model (POM; Blumberg and Mellor, 1983, 1987)

Kuwae et al., 2003)

to simulate tidal currents in San Francisco Bay (WD-

Effort has also been made to develop numerical mod-

POM; Uchiyama, 2004). The WDS is different fromels for intertidal areas while wetting and drying (emer-

the other schemes proposed by Zheng et al. (2003), Xie

gence during high waters and immergence during low

et al. (2004), and Oey (2005) in representation of bed

waters) are essential to the intertidal hydrodynamics but

boundary layer since the extended logarithmic law was

it is generally difficult to implement the wetting/drying

newly introduced into the WDS so as to accurately esti-

capability into three-dimensional numerical models.

mate bed shear stresses and resultant sediment resuspen-

Nevertheless, a number of cohesive sediment transportsion and deposition in extremely shallow basins such asmodels have been developed involving Sheng and Lickintertidal mudflats.

(1979), Thomas and McAnally (1985), Zeigler and Lickverified by comparing the observed tidal surface eleva-(1988), Hayter and Pakala (1989), Barros and Baptista

tions and 3D current velocities to the model outputs.

(1989), Lee et al. (1994), Ziegler and Nisbet (1994,

The primary advantage of WD-POM over TRIM-3D and1995), McDonald and Cheng (1997), Shrestha et al.

the PHRI model is its ability to evaluate the 3D hydro-(2000), Inagaki (2000), HydroQual Inc. (2002), Naka-

dynamics and associated scalar (salinity, temperature,

The accuracy of WD-POM wasgawa (2003, 2005), Bricker et al. (2004), and others.

sediments, etc.) transport even though water depth ap-

Most of them are based on 2DH hydrodynamic models

proaches zero in response to tide. This is mainly due tosuch as TRIM (Cheng et al., 1993) which can readily be

the coordinate systems that these models employ.

applied to intertidal simulations (McDonald and Cheng,though TRIM-3D and the PHRI model are configured on

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Al-

Yusuke UCHIYAMA

Figure 1: Location of the study: San Francisco Bay & Sacramento-San Joaquin Delta system, California, USA.
marks correspond to the turbidity measurement sites by Buchanan and Ruhl (2001) summarized in Table 3.

Circlethe 3D Cartesian coordinate with a so-called the multi-

avoid this complexity, the model presented here simply

level vertical coordinate (where vertical grids are aligned

formulated by using the standard parameterizations suchparallel to a certain datum plane), WD-POM (and also its

as by Krone (1962) for the resuspension rate, by Parthe-original version of POM) is on the 2DH orthogonal cur-niades (1992) for the deposition rate, and by Burban etvilinear coordinate with the vertical terrain-following

al. (1990) for the settling speeds. Attempts are made tosigma-coordinate (Uchiyama, 2004).

The important

extract some crucial properties of sedimentary dynamics

conclusion of the study by Uchiyama (2004) is that infrom the computational results by paying careful atten-

San Francisco Bay the intertidal mudflats are found totion to effects of the intertidal shallow topography.

remarkably alter and control hydrodynamics of the em-

2. STUDY SITE

bayment since the intertidal sloping bathymetry apparently enhances refraction and shoaling of propagating
tidal waves while attenuating propagating speeds and

San Francisco Bay, California, USA (Figures 1 andconsequent phases owing to increasing bed friction in the2), consisting of South Bay, Central Bay, San Pablo Bay,shallow regions.

and Suisun Bay, is chosen for the study site. The bay is
a tidally-forced, semi-enclosed estuary encompassed by

The objectives of the present paper are to model cohe-wide-spreading intertidal area comprising mudflats andsive sediment transport and associated morphologicalsalt marshes, where flooding and draining are predomi-

variations, to incorporate them into WD-POM, and tonant for overlaying hydrodynamics.

examine effects of intertidal topography on estuarine hy-

has the surface area of about 1240km and the intertidal

drodynamics and resultant sediment transport processes.

mudflats of about 200km2.

Cohesive sediments are intricately influenced by ambient

The Sacramento-San Joa-quin delta system enormously supplies the freshwaterhydrodynamics, pore water dynamics, biostabilization,and bioturbation as reviewed in Black et al. (2002).

San Francisco Bay2and associated sediment influx sourced by the Sierra

To

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Modeling three-dimensional cohesive sediment transport and associated morphological response in estuarine intertidal mudflats

Figure 2: The bathymetric map of San Francisco Bay, California, USA (left) and the computational grid alignment using the horizontal orthogonal curvilinear transformation (right). The bathymetry is relative to the MLLW level.
Mountains and Central Valley to the northeastern part ofeddy coefficients, and a Smagorinsky-type parameteriza-

the bay, i.e., Suisun Bay, San Pablo Bay and Centraltion for horizontal mixing with the Boussinesq approxi-

Bay. (Conomos et al. 1985).

mation and hydrostatic assumption.

By contrast, South Bay,The governing

the southernmost part of San Francisco Bay, is often de-equations are converted from the 3D Cartesian coordi-

scribed as "a tidally oscillating lagoon with density-

nate into the orthogonal curvilinear coordinate (horizon-

driven exchanges with the northern reach" (Gross et al.,Limited number of numerical simulations havetal) and σ−coordinate (vertical) to smoothly follow complex terrain geometries and marine bathymetries as

been performed for San Francisco Bay by Cheng et al.

shown in Figure 2. A wetting and drying feature is(1993) and McDonald and Cheng (1997) using TRIM-

implemented by Uchiyama (2004) to deal with hydrody-

2D, by Gross et al. (1998), Inagaki (2000) and Bricker etnamics in extremely shallow basins composed of inter-al. (2004) with TRIM-3D, and by Uchiyama (2004) withtidal flats and salt marshes.

WD-POM, since emersion and immersion are indispen-transport model to be coupled with WD-POM is devel-

sable to hydrodynamics of the embayment although gen-oped here as expressed in Eqn. (1).

1999).

erally laborious to incorporate into 3D hydrodynamic

The cohesive sediment∂CD ∂UCD ∂VCD ∂ (ω - Ws ) C
+
+
+
∂t
∂x
∂y
∂σ

models.

,(1)∂ ⎡ K H ∂C ⎤+ FC∂σ ⎢⎣ D ∂σ ⎥⎦3. NUMERICAL MODELING=

3.1 Cohesive Sediment Transport

where (U, V, ω): 3D velocity vector, D: total depth(=H+η, H: depth, η: surface elevation), C: cohesive
sediment concentration, Ws: settling velocity, KH: verti-

Princeton Ocean Model (Blumberg and Mellor, 1983,
1987) consists of a set of the 3D primitive equations,cal eddy diffusivity, and FC: the horizontal diffusion

Mellor-Yamada level 2.5 turbulent closure model (Mel-terms.

lor and Yamada, 1982; Galperin et al., 1988) for vertical

Equation (1) is converted from the regular Car-tesian coordinate into the 2D horizontal curvilinear and-7-

Yusuke UCHIYAMA

Table 1: Summary of the hydrodynamic and numerical parameters used in the San Francisco Bay-simulation.
definition
time step for external mode (2D)time step for internal mode (3D)
Smagorinsly constantdensity of seawaterroughness height
critical depth used in WDS*
minimum depth used in WDS*
scaling factor used in WDS*

parameter

∆te
∆ti
AM

ρ

z0
dcr
dmin

δ

value
5s
50 s
0.2
1025 kg/m3
1 cm
20 cm
5 cm
1 cm

(* see Uchiyama, 2004)

Table 2: Sedimentological parameters used in the San Francisco Bay-simulation.
definition
initial sediment concentration
roughness height for sediments
dry density of sediments
porosity of sediments
minimum τb for erosion
minimum τb for deposition
constant erosion probability

parameter
C|t=0
zb

ρs
λs
τbe
τbd
Pe

value
0 mg/l
0.5 cm
2.0 kg/m3
0.5
0.15 Pa
0.03 Pa
5×10-6 kg/m2/s

the bed shear stress τb and a constant erosion probability
Pe (Krone, 1962; Ariathurai and Krone, 1976).

vertical sigma coordinate as used in WD-POM. Settling velocity, Ws, is unchanged in Eqn. (1) after the conversion into a σ-coordinate system (Wang, 2001; 2002).
The horizontal advection terms (the second ant third⎧⎛ τ −τ ⎞⎪ Er = Pe ⎜⎜ b be ⎟⎟⎨⎝ τ be ⎠⎪E =0⎩ r

terms in the left hand side) are calculated with the Smolarkiewicz’s iterative upstream scheme (Smolarkiewicz,

when τ b ≥ τ be(4)

when τ b < τ bewhere Pe: the constant erosion probability, τbe: the critical bottom shear stress for erosion. Similarly, the sink1984). All the terms in Eqn. (1) are solved explicitly
except the vertical diffusion term.

term, Dp, in Eqn. (3) can be calculated by using the

3.2 Boundary Conditions and Empirical Submodels

parameterization by Partheniades (1992).
D p = Ws C Pd ,The boundary conditions for Eqn. (1) at the surface

ω 2

and seabed are defined as:
K H ⎛ ∂C ⎞⎜⎟ = 0, σ → 0D ⎝ ∂σ ⎠K H ⎛ ∂C ⎞⎜⎟ = E r − D p , σ → −1
D ⎝ ∂σ ⎠0Y −12
Pd = 1 −ed ω0 ,
2π ∫− ∞

at sea surface,

(2)

⎤
⎡
⎞
⎛τ
Y = 2.04 ⋅ log ⎢0.25⎜⎜ b − 1⎟⎟e1.27⋅τ bd ⎥ ,⎠⎝ τ bd⎦⎣at seabed, (3)

(5.2)
(5.3)

where Pd: the deposition probability, ω 0: a dummy variable and τbd: the bottom shear stress below which Pd=1
(dyne/cm2).

where Er, Dp: erosion and deposition rates at the seabedempirically formulated.

(5.1)

The source term, Er, is sim-plistically evaluated to represent resuspension of cohe-Settling velocity, Ws, of cohesive flocs is calculated

sive sediments from the bed in accordance with the con-with the parameterization by Burban et al. (1990) in

ventional formulation using the threshold stress, τbe, for-8-Modeling three-dimensional cohesive sediment transport and associated morphological response in estuarine intertidal mudflats

which flocculation is dependent on the product of local

3.4 Bed Elevation Modelingconcentration and vertical shear stress in water column.
Ws = α (CG ) ,βBathymetry changes can be evaluated from the vol-(6.1)⎡⎛ ∂U ⎞ 2 ⎛ ∂V ⎞ 2 ⎤G = ρ s K M ⎢⎜⎟ +⎜⎟ ⎥⎢⎣⎝ ∂z ⎠ ⎝ ∂z ⎠ ⎥⎦ume conservation of sediments at the bed varying witherosion and deposition rates computed in the model.

1/ 2

,

(6.2)

1
d hb
(Er − Dp )=λs ρ sdt

in which ρs: dry density of suspended medium, KM: ver-where hb: bed elevation, λs: porosity of the bed sediments. Although the previous studies have often intro-

tical eddy viscosity, α, β: the empirical non-dimensional
constants, Ws, C and G are expressed in m/day, mg/L,
and dyne/cm2, respectively.

(9)

duced a “layered” bed model (Hayter, 1983; McDonald

The above equation im-

and Cheng, 1997; HydroQual, Inc., 2002) to incorporate

plicitly incorporates the effect of internal shear stress, G,consolidation of deposited sediments and vertical distri-on aggregation and settling. For saltwater suspensions,bution of the dry density of sediments in the bed and the

Burban et al. (1990) estimated values of α and β to be
2.42 and 0.22 (HydroQual, Inc., 2002).

critical shear stress into the numerical models (Tsai andLick, 1987; MacIntyre et al., 1990), it contains many
unknown, tuning parameters.

3.3 Bed Shear Stress and Vertical Mixing
Parameterization

In the present study, thebed elevation model is simplistically formulated to avoid
intricate uncertainty.

Bed shear stress for sediments is formulated with

4. RESULTS

slightly being modified based on the extended logarithmic law to be:

4.1 Cohesive Sediment Concentrationsr r
τ b = ρ s C d ub ub ,⎡ 1 ⎛ z + z 0 ⎞⎤⎟⎟⎥C d = ⎢ ln ⎜⎜⎣ κ ⎝ z b ⎠⎦(7.1)
The horizontal grid alignment of San Francisco Bay isdisplayed in Figure 2. A total of 45 x 160 horizontal

−2

,

(7.2)

cells and 10 vertical σ-layers are defined in the simulation as used by Uchiyama (2004). Astronomical tidal

where κ: the von Karman constant, Cd: bed friction coef-

oscillations are imposed on the open boundary condition
off Golden Gate (the bay mouth). Neither fluvial sedi-

ficient, ub: the bottom-most horizontal velocity vector,
z+ z0: height of ub relative to the bed, z0: the roughness
height, and zb: the roughness height for sediments.

ments nor surface wind stresses are assumed in the computation for the simplicity. The elevation condition isTo-

applied to the open boundary; a spatial gradient (the firstgether with Eqn. (7), leaving the determination of l un-

order differentiation) of elevation, velocities, q2, q2l, andchanged, where l is turbulent macroscale, KM and the

C are set to be zero.

vertical eddy diffusivities KH and Kq must be slightly al-

tological and numerical parameters used in the simula-tered as proposed in Uchiyama (2004) so that:K M = S M q (l + κz0 )⎫⎪,K H = S H q (l + κz0 )⎬K q = S q q(l + κz0 ) ⎪⎭The hydrodynamic, sedimen-tion are listed in Tables 1 and 2. The sedimentologicalparameters employed here are generally standard values,
not calibrated with field data since the simulation solely(8)

considers tidal currents, so it would have almost no
meaning to compare with the observed data quantitatively. Nevertheless, the computed spatial distribution

where SM, SH, and Sq are the stability functions, and q isof sediment concentrations and morphological variations

the square root of TKE multiplied by 2, used in the Mel-

indicate a fairly reasonable agreement with the observed

lor-Yamada level 2.5 sub-model in POM.

results as demonstrated later.

-9-

Yusuke UCHIYAMA

Figure 3: Bihourly evolution of the cohesive sediment concentrations (black-white colors) and 3D horizontal velocity
vectors (white arrows) at the first σ-layer (surface) during a ebbing phase in a spring tide on the 108th and 109th Julian
day in 2003 (UTC). The contour intervals are set to be 50mg/l.

The starting date of the simulation coincides withthe simulation starts with zero concentration in the whole

March 29, 2003 (the 88th Julian day in 2003) and adomain at t=0s.

simulation spin-up (McDonald and Cheng, 1997) is con-cycles) are utilized in the following analysis, and thus

ducted for the first 12 days to attain a dynamically equi-the total duration of the computation is 40 days. Water

librium distribution of the sediment concentrations since

surface elevations and 3D tidal current velocities at mul-

-10-

The last 28 days (i.e., two spring-neap

Modeling three-dimensional cohesive sediment transport and associated morphological response in estuarine intertidal mudflats

Figure 4: Same as Figure 3, but during a flooding phase.

tiple locations along the coast line of San Francisco Bay

Figures 3 and 4 show the bihourly development of

have already validated with the observed data to repre-

the sediment concentrations and the 3D horizontal cur-sent that WD-POM is able to accurately reproduce therent velocity vectors at the first σ-layer for 14 hours on
the 108th to 109th Julian day in 2003 in UTC. The

hydrodynamics in the whole bay (Uchiyama, 2004).

model outputs exhibit that during a spring tide, cohesive-11-

Yusuke UCHIYAMA

Table 3: Statistical summary of the near-bottom suspended sediment concentrations measured in San Francisco Bay observed by USGS (Buchanan and Ruhl, 2001). The locations of the measurement sites are plotted in Figure 1. The
concentrations are measured by optical backscatterance sensors (OBSs) calibrated with sampled turbid waters.

Site
Mallard Island
Carquinez Bridge
Mare Island Causeway
Channel Marker 9
Point San Pablo
Pier 24
Channel Marker 17
Dumbarton Bridge
San Mateo Bridge*

mean (mg/l)
46
203
186
213
81
33
171
150
60

median (mg/l)
58
297
235
263
99
38
215
190
73
* mid-depth concentration

sediments are suspended dominantly in the deeper chan-model presented here is capable of realistically reproduc-

nels while being transported and deposited on the inter-ing the cohesive sediment concentrations in San Fran-tidal areas fringing the bay at flooding phases. Thiscisco Bay.

tendency can also be observed during neap tides

significantly increase in response to riverine discharges

although magnitude of the variations is much smaller

and wind condition, it is necessary to implement these(not shown here) than those for the spring tides. In

effects into the model in the future.

South San Francisco Bay, the concentrations are not as

The incoming tidal waves are propagating as anti-high as those in San Pablo Bay as weaker tidal currents

clockwise Kelvin waves but significantly refracted on

are generated in South Bay. The sediment concentra-

the intertidal slopes in San Francisco Bay (Uchiyama,tions in San Pablo Bay are estimated from the simulation

2004) presumably to boost the instantaneous, as well as

to range from 0 to 300 mg/l while those in South Bay
vary about 0-200 mg/l.

residual, velocity component normal to the isobaths par-These ranges of the fluctuations

ticularly in the intertidal areas. Figures 3 and 4 also

reasonably agree with the observed data as listed in Table 3 and displayed in Figure 5.

exhibit that in San Pablo Bay the bed cohesive sediments

The measured con-begin to be resuspended in the channels during an ebbing

centrations range from 0 to 150 mg/l in the whole bay,phase (at 14h), and subsequently being carried in the di-indicating higher concentrations in San Pablo Bay andSuisun Bay while lower in South Bay.

rection of ebb tidal currents (at 16h through 18h). Next

The medianthe resuspended sediments appear to be transported onto

concentrations fluctuate from 99 (Point San Pablo) to

the intertidal areas in response to the rising tides and to297 mg/l (Carquinez Bridge) in San Pablo Bay althoughapproach the shoreline during floods (at 18h throughin South Bay ranging from 38 (Pier 24, Central Bay) to22h), and finally the sediments are diluted perhaps by

215 mg/l (Channel Marker 17, South Bay) as indicatedin Table 3 (after Buchanan and Ruhl, 2001).

deposition (at 22h though 2h).

In addi-around the deeper channels although lower on the inter-

analysis gave us the instantaneous surface sediment con-tidal shallow areas.

centrations as displayed in Figure 5 (after Ruhl et al.,This spatial distribution of thesediment concentrations is most likely induced by the

The image was taken on March 25, 1995, at

tidal current component normal to the isobaths and may

13:00, and the concentrations are inferred from theprovoke specific topography variation in the bay as dis-

bands-1 and -2 of the NOAA-14 AVHRR, and calibrated

cussed later.

with the measured data using optical backscatterance
sensors.

Figure 5 shows a simi-

lar pattern in which higher concentrations appear to betion to the in situ measurements, the satellite image

2001).

However, because the concentrations may

These observed results clearly support that the-12-Modeling three-dimensional cohesive sediment transport and associated morphological response in estuarine intertidal mudflats

Figure 5: A NOAA-AVHRR image corresponding to the instantaneous sediment concentrations in San Francisco Bay
on March 25, 1995, at 1300h (after Ruhl et al., 2001).

4.2 Geomorphological Variations

The channel is eroded by about 2.4m for 29 years between two surveys to yield ~10cm/y as shown in Figure

The morphological changes due to the tidal currents

7 (a). The simulated maximum erosion rate is about

during two spring-neap cycles (28 days) in San Pablo

10-20 cm/y, demonstrating the model can qualitatively

Bay and South Bay are estimated as shown in Figure 6.

replicate the geomorphological behavior in San Pablo

Intertidal mudflats tend to slightly be accreted whereas

Bay realistically.

deeper channels seem rather eroded in the both subembayments.

the sediment transport and associated bathymetry varia-

This result is obviously consistent with thetions are largely controlled by tidal currents.

temporal development of the cohesive sediment concen-

However,the locations of the most accretive regions inferred bytrations as sequently indicated in Figures 3 and 4.

the model outputs are slightly different from those by the

Sediment resuspension is predominant in the deeper

surveys, probably because the model neglects the surface

channels to generate suspended cohesive sediments, resulting in significant erosion.

This consistency also suggests thatwind stress, waves and fluvial discharges, and employs

The sediments are thenthe simplified sediment submodels. Similar compari-transported and deposited onto the intertidal areas to en-son can be done by examining Figures 6 (b) and 7 (b)hance accretion.

which exhibits bathymetry changes between 1931 andThis computed geomorphological pattern is next

1956 in South Bay on the basis of the surveys (after

compared with surveyed topography variations. Figure

Foxgrover et al., 2004).

7 (a) shows the bathymetry-change rate in San Pablo

at around ±2-3cm/y in the simulated results although

Bay calculated with the historical bathymetry surveys
conducted by COOPS-NOS-NOAA in 1922 and 1951

about ±1-2cm/y calculated from the surveys. The
model-generated morphological pattern is much different

and summarized by USGS (after Jaffe et al., 1998).

from that evaluated by the surveys.

-13-

The bathymetry tends to vary

Accretion pre-

Yusuke UCHIYAMA(a) San Pablo Bay – Central San Francisco Bay(b) South San Francisco Bay

Figure 6: Model-estimated bathymetry changes in (a) San Pablo Bay and (b) South San Francisco Bay.

(a) San Pablo Bay – Central San Francisco Bay(b) South San Francisco Bay

Figure 7: The erosion and accretion rate estimated for the historical bathymetric surveys conducted by CO-OPS, NOSNOAA in (a) San Pablo Bay (after Jaffe et al., 1998) and (b) South San Francisco Bay (after Foxgroverl et al., 2004).

dominantly occurs in the whole South Bay according to

5. DISCUSSION

the surveyed results, while the model output shows thatthe intertidal areas are largely eroded. This inconsistency may also be caused by the neglecting hydrody-

The model is qualitatively able to estimate the cohe-namic components such as wind and waves which gen-sive sediment transport and resultant bathymetry varia-

erally enhance erosion.

tions with having a realistic agreement with the observed-14-Modeling three-dimensional cohesive sediment transport and associated morphological response in estuarine intertidal mudflats

Figure 8: Long-term accretion on an intertidal sloping topography. Only a sinusoidal tidal oscillation is considered at
the open boundary (the left side).

results. An important finding here is that the tidal cur-with more simplified 1D models proposed by Roberts etrents have a key role in the sediment resuspension, andal. (2000) and Pritchard et al. (2002). This result also

the subembayment or inter-embayment scale dispersion

suggests that tidal currents evidently influence to raiseof the resuspended sediments to induce erosion in thethe sediment deposition on the intertidal areas and todeeper channels and accretion in the intertidal areas. In

create the flat topography near the shoreline.

order to verify this accretive effect of tidal currents on

6. CONCLUSIONS

intertidal topography, a 2D-vertical long-term simulationof sediment transport and morphological response on a
The initial beach

Cohesive sediment transport and resultant bathymetry

slope is set at 1:500, and monochromatic sinusoidal tidal

response in estuaries encompassed by intertidal area are

oscillations with amplitude of 1.2m and at a period ofdeveloped on the basis of WD-POM. The primary ad-

12h are imposed on the open boundary condition locatedvantage of the model is its ability to simulate the verticaluniform intertidal slope is performed.

at the cross-shore distance of 0km in Figure 8. The

hydrodynamics (vertical profiles of 3D velocities, turbu-

sedimentological parameters and the other boundary

lence, sediments, and other passive scalars) even thoughconditions are same as those used in the 3D simulation

the water surface descends to become extremely shallow.

for San Francisco Bay except the open boundary condi-

The model employs the widely-used parameterizations

tion for the sediment concentration. In the 2D simula-involving the erosion rate submodel by Krone (1962),

tion, a constant value of C0 (C0 is set 100 mg/l here) isthe deposition rate submodel by Partheniades (1992),

used for the sediment concentrations when the direction

and the settling speed submodel by Burban et al. (1990).

of currents at the open boundary is landward. The nu-

The model is applied to San Francisco Bay, CA,

merical parameters are set here as ∆ te = 2s, ∆ ti = 60s, ∆ xUSA, which is fringed by extensive intertidal mudflats.

= 100m, 5 vertical σ-layers are used, and the Coriolis
terms are eliminated.

The model outputs are compared to the observed results

The computed long-term morphological evolution is

et al. (1998), and Foxgrover et al., (2004) to exhibit aby Buchanan and Ruhl (2001), Ruhl et al. (2001), Jaffe

found to be similar to the results of the 3D simulation.

reasonable agreement.

The flooding tides evidently amplify the shorewardthat the sediments are remarkably suspended in thesediment transport to be deposited near the shoreline,

deeper channels while deposited on the intertidal fringes.

and accordingly enhance the accretion in the intertidal

This sediment transport induces significant erosion in theareas. As a consequent, the intertidal topography is de-channel and visible accretion in the intertidal mudflats.

veloped gradually near the high water mark. The cross-

The intertidal areas play an important role in the sedi-

shore topography after 100 years is resemble the results

ment budgets in the estuary, acting as ‘sink’ of the sus-

-15-

The simulated results indicate

Yusuke UCHIYAMA

pended cohesive sediments under action of the tidal currents.

Blumberg, A.F. and Mellor, G.L., 1983: Diagnostic and

A supplemental 2D vertical simulation with aprognostic numerical circulation studies of the South

simplified numerical setting also supports the results

Atlantic Bight, J. Geophys. Res., 88: 4579-4593.

educed from the 3D simulation to demonstrate that tidal

Blumberg, A.F. and Mellor, G.L., 1987. A description ofcurrents have evident influence on transporting the re-a three-dimensional coastal ocean circulation model,

suspended sediment shoreward and enhancing accumula-

In: Three-dimensional Coastal Ocean Models, Vol.4,

tion to create mudflat topographies.

Heaps, N. (ed.), Ameri. Geophys. Union, Washington
D.C., pp.208.
Bricker, J.D., Inagaki, S. and Monismith, S.G., 2004.

ACKNOWLEDGEMENTS

Modeling the effects of bed drag coefficient variabil-This research project was partially supported by Ja-

ity under wind waves in South San Francisco Bay,pan Society for Promotion of Science and is a part of theProc. 8th Int’l Conf. Coastal and Estuarine Modeling,

author’s work during his stay at University of California,

ASCE, Monterey, CA, USA. (in print, Pers. Comm..)Berkeley, USA, since March 2002 till March 2004.

Buchanan, P.A. and Ruhl, C.A., 2001. Summary of sus-

The author would like to express sincere appreciation topended-sediment concentration data, San Francisco

Professor Mark T. Stacey of UC Berkeley, Professor

Bay, California, Water Year 1999, Open-File Report

Rodney J. Sobey of Imperial College of London, UK,

01-100, U.S. Geological Survey, Sacramento, CA,

and Mr. Yasuyuki Nakagawa of Port and Airport Re-

USA, 40pp.

search Institute, Japan, for their helpful comments on the

Burban, P.Y., Xu, Y., McNeil, J. and Lick, W., 1990:

manuscript. Thanks are also due to Mr. Satoshi Inagaki

Settling speeds of flocs in fresh and sea waters, J.

of Kajima Corporation, Dr. Jeremy D. Bricker of Kobe

Geophys. Res., 95, 18213-18220.

University, Dr. Stefan A. Talke and Dr. David K. Ral-

Cabrita, M.T. and Brotas, V., 2000. Seasonal variation inston of UC Berkeley for their discussion on the numeri-

denitrification and dissolved nitrogen fluxes in inter-cal modeling and help with searching for the literatures.

tidal sediments of Tagus estuary, Portugal, Mar. Ecol.

(Accepted on November 10, 2004)

Progress Ser., 202: 51-65.
Casulli, V. and Cattani, E., 1994. Stability, accuracy and

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