Modeling sand-mud transport induced by tidal currents and wind waves inshallow microtidal basins: Application to the Venice Lagoon (Italy)

L. Carniello*, A. Defina, L. D’Alpaos

Department IMAGE, University of Padova, Via Loredan 20, 35131 Padova, Italy

a r t i c l e i n f o

Article history:

Received 3 May 2011

Accepted 11 March 2012

Available online 19 March 2012

Keywords:

microtidal lagoons

sediment transport

cohesive sediments

bed composition

a b s t r a c t

In this study we present a mathematical model for sediment entrainment, transport and deposition

caused by the combined action of tidal currents and wind waves in shallow micro-tidal basins. The

model uses a bi-granular mixture made up of cohesive and non-cohesive sediments thus considering

clay, silt and sand, all of which commonly characterize the sediment bed composition of estuaries and

tidal basins. The model also describes the evolution of bed elevation and evaluates the variation of bed

sediment composition distinguishing cohesive from non-cohesive behavior.

A stochastic approach is proposed to evaluate sediment entrainment close to incipient sediment

motion. Particular attention is also given to the problem of reconstructing a reliable initial bed

composition as this has a significant impact on sediment entrainment.

The model was applied to the test case of the Venice lagoon (Italy) and good agreement was found

when comparing model results to a series of turbidity measurements collected inside the lagoon. The

model was then used to predict the actual net amount of sand and mud flowing through the inlets and

the bottom evolution in terms of elevation and composition.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Worldwide, many estuaries and coastal lagoons have been

experiencing a dramatic deterioration during the last decades

primarily due to i) reduced sediment supply from the watershed

mainly caused by sediment being trapped by dams in the upland

drainage basin, and ii) apparent erosion caused by a rise in the sea

level which is a result of climate change and land subsidence

(Fagherazzi et al., 2006; Marani et al., 2007; Gedan et al., 2009;

Kirwan et al., 2010). Many efforts have been made recently to

counteract this erosive trend and two fundamental aspects

contributing to these efforts are recognizing the morphological

features which are most fragile and identifying the mechanisms

which are responsible for the deterioration processes.

Wind waves are recognized to be the main cause of marsh-edge

retreat (Mariotti and Fagherazzi, 2010; Mariotti et al., 2010; Tonelli

et al., 2010; Marani et al., 2011) and sediment resuspension over

tidal flats (Carniello et al., 2005; Fagherazzi et al., 2006, 2007;

Defina et al., 2007). Sediment resuspended from tidal flats is then

transported by tidal currents which further influence entrainment

and deposition processes in deeper areas and within channels.

Tidal currents, occasionally enhanced by wind forcing and wind

waves, are therefore the key processes whichmust be considered to

describe the morphological evolution of estuaries and tidal basins.

Numerical models able to describe these physical processes are

useful tools in planning and designing effective restoration activi-

ties and in evaluating their impact. There are several models in the

literature that are constantly updated and improved, and used to

study hydrodynamics, wave propagation and sediment transport

in coastal areas (e.g., MIKE21, Delft3D, SWAN (Booij et al., 1999),

TELEMAC, SHYFEM (Umgiesser et al., 2004) coupled to SED-

TRANS05 (Neumeier et al., 2008)). Each model has both distinctive

features and limits, mainly depending on the context in which it

was developed.

The model we propose and discuss in the present study is

specifically designed to study the morphodynamics of very shallow

micro-tidal basins with highly irregular topography. Particular

attention is devoted to accurately representing the physical

processes that drive the morphological evolution of these envi-

ronments; these processes are modeled through the development

of specific and suitable subgrid models. The model couples WWTM

(Wind Wave Tidal Model), which is a two-dimensional finite

element model for hydrodynamics and wind-wave generation and

* Corresponding author.

E-mail addresses: carniello@idra.unipd.it (L. Carniello), defina@idra.unipd.it

(A. Defina), dalpaos@idra.unipd.it (L. D’Alpaos).

Contents lists available at SciVerse ScienceDirect

Estuarine, Coastal and Shelf Science

journal homepage: www.elsevier .com/locate/ecss

0272-7714/$ e see front matter � 2012 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ecss.2012.03.016

Estuarine, Coastal and Shelf Science 102-103 (2012) 105e115

propagation (Carniello et al., 2011), with a sediment transport and

bed evolutionmodule, which describes resuspension, transport and

deposition of a two size-class mixture of sediments which makes it

possible to consider the simultaneous presence of cohesive and

non-cohesive sediments as well as their mutual interaction.

In this paper, first we present the morphodynamic model briefly

summarizing the wind-wave tidal model (hereinafter WWTM) fol-

lowed by a description of the proposed sediment transport and

bottom evolution module. We then present the application of the

model to the case study of the Venice Lagoon. First we address the

problem of estimating a reliable initial bed composition for this

specific tidal environment given the limited available information

regarding the significant variability of the bed composition. Thenwe

compare model predictions of suspended sediment concentration

underdifferentmeteorological conditions and tidal forcing to a set of

turbidity data collected at different stations distributed throughout

the Lagoon. This is followed by an estimation of suspended sediment

rates in the three inlets connecting the Venice Lagoon to the Adriatic

Sea in order to assess the actual net export of fine sediment, which is

one of the main causes of the ongoing deterioration of the Lagoon.

The paper ends with a set of conclusions.

2. The morphodynamic model

The morphodynamic model is made up of three modules: i) the

hydrodynamic module, ii) the wind-wave module, and iii) the

sediment transport and bed evolution module (hereinafter STA-

BEM: Sediment Transport And Bed EvolutionModule). The first two

modules make up the WWTM, which is only briefly summarized

here (for details see, e.g. Carniello et al., 2011), while the STABEM

module is presented and discussed in detail.

2.1. The wind-wave tidal model (WWTM)

The hydrodynamic module solves the two-dimensional shallow

water equations suitably adapted to deal with flooding and drying

in very irregular domains. The equations are solved using a semi-

implicit staggered finite element method based on Galerkin’s

approach (see Defina (2000) and D’Alpaos and Defina (2007) for

a detailed description of the hydrodynamic model). The hydrody-

namic model yields water levels that are used by the wind-wave

model to compute the wave group celerity and to assess the wave

processes affected by flow depth (e.g., energy dissipation by friction

and wave breaking).

The wind-wave model is based on the solution of the wave

action conservation equation parameterized following the

approach proposed by Holthuijsen et al. (1989). The zero-order

moment of the wave action spectrum in the frequency domain is

chosen for the parameterization while spatial and temporal

distribution of the wave period is determined through an empirical

correlation function relating the mean peak wave period to the

local wind speed and water depth (Young and Verhagen, 1996;

Breugem and Holthuijsen, 2007; Carniello et al., 2011). The model

also assumes that the direction of wave propagation adjusts

instantaneously to the wind direction, thus neglecting refraction,

and neglects wave-current interaction given the relatively low flow

velocity over tidal flats where wave-induced bottom shear stress is

the main factor contributing to sediment resuspension.

Carniello et al. (2011) have shown that spatial non-uniformity of

wind climate over large basins may have a non-negligible impact

on the description of the wind-wave field and, therefore, on wave-

induced sediment resuspension. Accordingly, in the present study,

we improve the WWTM to account for the spatial variability of the

wind field which is determined through a suitable interpolation

procedure of the available wind data. We adopt the interpolation

technique proposed by Brocchini et al. (1995), which is an

improvement of the standard and long-used technique in meteo-

rological data interpolation proposed by Cressman (1959).

The WWTM has been widely tested comparing results to

hydrodynamic and wind-wave data both from the Venice Lagoon

(Carniello et al., 2005, 2011; D’Alpaos and Defina, 2007) and a series

of lagoons at the Virginia Coast Reserve, USA (Mariotti et al., 2010).

2.2. The sediment transport and bed evolution model (STABEM)

When modeling sediment transport and bed evolution in tidal

estuaries and lagoons, it is crucial to consider both cohesive and

non-cohesive sediments and the behavior of mixtures as a function

of the clay content. It is then important to distinguish cohesive from

non-cohesive sediment and to schematize the bed composition; we

decided to use two size classes of sediments: non-cohesive sand

and cohesive mud, which is the sum of clay and silt. The transition

between the non-cohesive and cohesive behavior of a mixture is

mainly determined by the clay content. However, since the clay-to-

silt ratio is approximately constant for a specific estuary or tidal

basin (Van Ledden, 2003, 2004), we use a threshold mud fraction,

pmc, to discriminate between non-cohesive and cohesive behavior.

The sediment transport model is based on the solution of the

advection diffusion equation

vCiY

vtþ VqCi � VðDYVCiÞ ¼ Ei � Di i ¼ s;m (1)

where C is the depth averaged sediment concentration, q ¼ (qx, qy)

the flow rate per unit width, Y the equivalent water depth (i.e. the

volume of water per unit area as defined by Defina (2000)), D the

two-dimensional diffusion tensor, E and D the entrainment and

deposition rates, and the subscript i (i ¼ s, m) the sand and mud

fraction respectively. Eq. (1) is simplified by assuming that diffusion

can be neglected compared to advection (e.g. Pritchard and Hogg,

2003).

In the model, the deposition rate of sand is computed as

Ds ¼ �wsr0Cs (2)

where ws is the sand settling velocity and r0 is the ratio of near-bed

to depth averaged concentration which is here assumed constant

(r0 ¼ 1.4) as suggested by Parker et al. (1987).

Deposition of pure cohesive mud is given by the Krone’s

formula:

Dm ¼ �wmCm max f 0; 1� sb=sdg (3)

Here wm is the mud settling velocity, sb the bottom shear stress,

and sd the critical shear stress for deposition.

The settling velocitiesws andwm are computedusing theVanRijn

(1984) formulation for solitary particles in clear and still water thus

neglecting the flocculation process which affects settling velocity

when grain diameter is greater than 20 mm (Mehta, 1989). Eqs. (2)

and (3) can also be applied in the presence of sand-mud mixture

provided that the mud concentration is below the so-called “gel

point concentration”which is the concentration beyondwhich sand

particles get trapped in the mud matrix (Winterwerp, 2002).

Experimental investigations with sand-mud mixtures indicate

that the erosion rate of a mixture cannot be described by existing

formulas for pure sand and pure mud since the rate strongly

depends on the degree of cohesion of the mixture (Williamson and

Ockenden, 1993; Torfs, 1995; Garcia, 2008).

For the case of non-cohesive mixture (pm < pmc) the Van Rijn

(1984) formula describes reasonably well the sand erosion rate

while visual observations suggest that the mud fraction is easily

washed out when the bed behaves non-cohesively (Murray, 1977).

L. Carniello et al. / Estuarine, Coastal and Shelf Science 102-103 (2012) 105e115106

Van Ledden (2003, 2004) proposed an erosion formula for non-

cohesive mud as a function of the bed load transport rate and the

saltation length of sand particles. For cohesive sediment mixture

(pm > pm, cr) both sand and mud entrainment can be evaluated

using Partheniades’ erosion formula (Williamson and Ockenden,

1993; Torfs, 1995).

Based on the above, the erosion rates for non-cohesive

(pm < pmc) and cohesive (pm > pmc) mixtures are written as:

Es ¼

8

<

:

ð1� pmÞws1:5

D50=Y

D0:3*

!

T1:5 for pm � pmc

ð1� pmÞMcT for pm � pmc

(4)

Em ¼

8

<

:

pm1� pm

MncT for pm � pmc

pmMcT for pm � pmc

(5)

Here D*

is the dimensionless grain size

(D� ¼ D50½ðs� 1Þg=n2�1=3, where s is the specific density and n the

kinematic viscosity) and Mc and Mnc are respectively the specific

entrainment for cohesive and non-cohesive mixtures given as

(Van Rijn, 1993; Van Kesteren et al., 1997; Van Ledden, 2003)

Mnc ¼ a

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðs� 1Þg D50

p

D0:9*

Mc ¼

�

Mnc

Mm$

1

1� pmc

�1�pm1�pmc

$Mm (6)

where Mm is the specific entrainment for pure mud, and T is the

transport parameter which is usually defined as T ¼ max{0; sb/

sc�1}. However, in shallow micro-tidal basins close to equilibrium,

bed shear stress assumes values close to the critical shear stress and

the above definition for the transport parameter, which describes

a sharp transition between T ¼ 0 and T ¼ sb/sc�1, is too rough.

Due to turbulence, the bottom shear stress is very unsteady and

not uniform because of the non-uniform flow velocity, wave char-

acteristics and small scale bottom topography within a computa-

tional element. Critical shear stress also is strongly non-uniform

because of the random grain exposure and bed composition in time

and space. Similar to the stochastic approach suggested by Grass

(1970), we assume that both bed shear stress and critical shear

stress are random and distributed according to a log-normal

probability density function (Grass, 1970; Bridge and Bennett,

1992). Therefore, we write:

T ¼1

sc

Z

N

0

2

6

6

4

Z

N

~sc

�

~sb � ~sc

�

pb

�

~sb

�

d~sb

3

7

7

5

pc

�

~sc

�

d~sc (7)

where pc(�) and pb(�) are the pdf for sc and sb respectively, and ~sb, ~scare the dummy variables of integration. Fig. 1 compares the

transport parameter computed as T ¼ max{0; sb/sc�1} and that

computed using Eq. (7) with different values of sb, sc and standard

deviation sb, sc chosenwithin a range of values commonly found in

the literature (e.g. Grass, 1970; Sarmiento and Falcon, 2006). The

effect of the stochastic approach is to smooth the transition

between T ¼ 0 and T ¼ sb/sc�1.

An adequate interpolation of Eq. (7) is given as

T ¼ �1þ

�

1þ

�

sb

sc

�

ε�1=ε

(8)

where ε is a non-dimensional calibration parameter.

Fig. 1 shows the good agreement between the transport

parameter computed using Eqs. (7) and (8) with different mean

values and standard deviations for the log-normal distributions.

The corresponding values for the parameter ε are also reported.

The influence of the stochastic approach in evaluating the

transport parameter on the estimation of the suspended sediment

concentration and the efficiency of the suggested approach in

describing the near-threshold conditions is discussed in the next

section.

In the model the bed shear stress (sb) is computed using the

empirical formulation suggested by Soulsby (1997) which accounts

for the non-linear interaction between the wave and current

boundary layers, whereas, following Van Ledden (2003, 2004) the

critical shear stress (sc) is assumed to vary monotonically between

pure sand (scs) and pure mud (scm) depending on the mud content:

sc ¼

8

<

:

ð1þ pmÞscs for pm � pmc

scsð1þ pmcÞ � scm

1� pmcð1� pmÞ þ scm for pm � pmc

(9)

It is worth noting that Eqs. (4) and (5) give the potential

entrainment of sand and mud since they are limited by the local

and temporal availability of each size-class of the mixture.

Given an initial bed configuration, the bed evolution module

computes the bed evolution both in term of bottom elevation and

bed composition as a consequence of different sand/mud deposi-

tion and erosion rates whereas bed porosity n of the mixture is

assumed to be constant (n ¼ 0.4) in time and space independent of

the mud content.

The change in bed level is a direct consequence of the erosion

and deposition fluxes of sand and mud: at each time step the

variation in bed elevation (dzb/dt) is evaluated as

ð1� nÞdzbdt

¼ ðDs þ DmÞ � ðEs þ EmÞ (10)

The model uses a well-mixed active layer just below the bed

surface (Hirano,1971,1972; Armanini and Di Silvio, 1988; Armanini,

1995). The active layer thickness Dzb can increase by local deposi-

tion but cannot decrease by erosion below a threshold value Dzb0; if

this tends to occur, the layer thickness is re-established incorpo-

rating part of the sub-layer into the active layer. The sub-layer

characteristics are constant and set equal to the initial bed

Fig. 1. Comparison between the transport parameter computed using: i) T ¼ max

{0; sb/sc�1} (bold line): ii) Eq. (7) considering different parameters of the log-normal

distribution of the total bottom shear stress (sb) and of the critical bottom shear stress

(sc) (symbols); iii) Eq. (8) (thin lines).

L. Carniello et al. / Estuarine, Coastal and Shelf Science 102-103 (2012) 105e115 107

composition. Themodel updates the bed composition by evaluating

the variation of the mud content (pm) as a consequence of sand and

mud fluxes between the active layer, the above-water column and,

if necessary, the sub-layer.

Using a sediment mixture requires a reliable reconstruction of

the initial configuration of the bed composition, which is known to

be a difficult and site-specific task. In fact, available field data are in

most cases insufficient compared to the spatial variability of bed

composition thus preventing the use of standard interpolation

techniques. Dastgheib and Roelvink (2009) and Van der Wegen

et al. (2010) have recently suggested a technique that attempts to

reconstruct a suitable initial condition for the bed composition

when data are lacking or insufficient. The technique consists in

performing long-term simulations starting from an approximate

description of the initial bed composition and letting it evolve

assuming a fixed bathymetry. The technique is based on the

assumption that if the main processes governing themorphological

evolution of a basin are correctly reproduced by the model, then

they should drive the bed composition toward a reliable configu-

ration. However, the non-linear feedback between bed composition

and morphological evolution can largely affect the solution,

limiting the reliability of the technique. For example, an incorrect

initial guess of bed composition influences the morphological

evolutionwhich in turn affects the changes in the bed compositions

leading to a solution that can largely differ from the actual one. At

present, the problem of reconstructing a reliable distribution of bed

composition based on a limited number of measured data is still an

open and challenging issue. In the next section we will present the

approach we used to address this issue for the case study of the

Venice Lagoon.

3. Application to the Venice Lagoon

A well-known example of micro-tidal environments is the

Venice Lagoon in Italy. The Venice Lagoon is a w550 km2 wide

shallow basin in the North East of Italy connected to the Adriatic

Sea by the three inlets of Lido, Malamocco, and Chioggia (Fig. 2a).

The average water depth of the Lagoon (excluding the main chan-

nels) is about 1.00 m with a semidiurnal tidal excursion of about

0.70 mwhich can suddenly be enhanced by meteorological forcing.

Many studies and field campaigns have shown that the Venice

Lagoon is under erosion with a net loss of fine sediment (e.g., Day

et al., 1999; D’Alpaos and Martini, 2005; Defina et al., 2007;

Carniello et al., 2009; Molinaroli et al., 2009). Nevertheless it is

difficult to estimate the net amount of fine sediments resuspended

within the lagoon and lost out to the sea and this has a significant

influence on the restoration activities which have been underway

for the last few decades.

A further important trend within the lagoon is the flattening of

the bottom topography, as proved by the gradual but persistent

areal reduction of salt marshes and by the silting of tidal channels.

Waves are the main process responsible for salt marsh retreat

(Mariotti and Fagherazzi, 2010; Mariotti et al., 2010; Marani et al.,

2011) and sediment erosion from tidal flats (Carniello et al., 2005;

Fagherazzi et al., 2007), while tidal currents enhance erosion and

drive suspended sediment through the inlets out to the sea.

The Venice Lagoon is a significant and challenging example of

a very shallow and topographically uneven basin. Indeed the large

amount of field data collected over many years makes it possible to

reliably calibrate and evaluate the assumptions and performance of

the model proposed here.

The sediment transport model was calibrated and tested against

turbidity measurements collected at different sites within the

Venice Lagoon (the position of the stations is shown in Fig. 2a). The

numerical simulations consider several events characterized by

different tidal and meteorological conditions. In the northern

part of the Adriatic Sea, and in the Venice Lagoon in particular,

a frequent meteorological condition called the ‘Scirocco’ is a wind

that blows from the South-East producing wind-drivenwater levels

which, combined with low atmospheric pressure, determine high

water conditions flooding the city of Venice. However, the most

intense, morphologically significant wind is the ‘Bora’ blowing from

the North-East generating the highest waves within the Lagoon.

These two meteorological phenomena, and especially the Bora,

were therefore considered in the numerical simulations. A further

simulation characterized by low wind speed was performed and

the results of all the simulations were compared to the available

turbidity measurements.

In the simulations, the spatial and temporal evolution of the

wind field over the domain was interpolated from the wind data

collected at the stations shown in Fig. 2a.

The simulated events refer to the following periods of time: i)

2e5 April 2003 characterized by Borawindwith speeds up to 16m/

s; ii) 9e13 December 2005 characterized by Bora wind with speeds

up to 20m/s; iii) 29 Julye2 August 2007 characterized by Borawind

with speeds up to 20 m/s; iv) 21e25 November 2007 characterized

by Scirocco wind with speeds up to 9 m/s; v)10e18 April 2006

characterized by very low wind conditions (average wind speed of

about 2.5 m/s).

The model uses Eq. (8) with ε ¼ 2 to compute the transport

parameter. This value for ε, which corresponds for example to ssb/

sb ¼ 0.6 (Sarmiento and Falcon, 2006) and ssc/sc ¼ 1.2, is assumed

through a trial and error calibration procedure.

Fig. 2. The upper panel shows the Venice Lagoon bathymetry based on the most

recent (2003) bathymetric survey which was carried out using different techniques

(multibeam, single beam, GPS, orthophoto restitution, direct topographic survey) in

order to obtain precise results for each range of elevation (Consorzio Venezia Nuova-

Technital, 2007). The standard error in bottom elevation data is �5 cm for salt

marshes, �5 cm for subtidal flats and, �10 cm for tidal channels. Symbols mark the

position of the stations where turbidity data and wind data are collected. The lower

panel shows the bed composition in term of mean grain size used in the model and

reconstructed on the basis of field data (circles).

L. Carniello et al. / Estuarine, Coastal and Shelf Science 102-103 (2012) 105e115108

Fig. 3 shows the comparison of the measured and computed

suspended sediment concentrations at the LT7 station (see Fig. 2a)

for the intense Bora event in April 2003. In order to highlight the

effect of the proposed statistical approach to estimate the transport

Fig. 3. Comparison of measured (dashed line) and computed (solid lines) suspended

sediment concentration at the stations LT7. The computed suspended sediment

concentration has been obtained by estimating the transport parameter, T, (i) following

the probabilistic approach (black bold line e see Eq. (8)); (ii) considering the classic

formulation, T ¼ max{0; sb/sc�1}, without modifying the critical shear stress values

(black thin line); (iii) considering the classic formulation, T ¼ max{0; sb/sc�1}, and

reducing the critical shear stress values (scrS ¼ 0.3 Pa; scrM ¼ 0.6 Pa - gray line). In the

simulations using the classic formulation for T the parameter of the sediment transport

model have been modified through an ad hoc calibration procedure.

Fig. 4. Comparison of measured (dashed line) and computed (solid line) suspended sediment concentrations at the stations LT1 to LT8 within the lagoon during intense Bora wind

events.

Table 1

Parameters used in the sediment transport model.

Parameter Description Value

D50S Mean grain diameter for pure Sand 200 mmD50M Mean grain diameter for pure Mud 20 mmscrM Critical shear stress for pure Sand 0.5 Pa

scrS Critical shear stress for pure Mud 0.8 Pa

sDEP Critical shear stress for deposition 1.0 Pa

Mm Specific entrainment parameter

for pure mud

5$10�2 gm/s

a Parameter in eq (6) to define the

specific entrainment parameter

for non-cohesive mixture

1$10�5

Dzb0 Initial active layer thickness 0.02 m

L. Carniello et al. / Estuarine, Coastal and Shelf Science 102-103 (2012) 105e115 109

parameter, numerical simulations were performed either by

computing T using Eq. (8) (black thick line) or considering the

classic formulation (i.e. T ¼ max{0; sb/sc�1}; black thin line). In

each simulation the sediment transport parameters (i.e. Mm and a)

were adjusted in order to achieve the best agreement with

turbidity data. The agreement between measured and computed

data is quite good when using Eq. (8). On the contrary, using the

classic formulation to estimate the transport parameter, the model

is not able to correctly predict the time evolution of the local

turbidity at near-threshold conditions.

We then performed a simulation using the classic formulation to

estimate the transport parameter reducing the critical shear stress

of both sand and mud (scrS ¼ 0.3 Pa; scrM ¼ 0.6 Pa e gray line). In

this way the prediction of the suspended sediment concentration

during decay was improved but no improvement was obtained

observing the near-threshold conditions at the beginning of the

wind event.

As stated in the previous section, knowledge of the initial bed

sediment distribution is crucial to correctly predicting suspended

sediment concentration as well as bottom evolution. Based on the

analyses of the available bed composition data for the Venice

Lagoon (Amos et al., 2004; Umgiesser et al., 2006; Guerzoni

and Tagliapietra, 2006), we suggest the following empirical

relationship between mean grain size D50 and both the local

bottom elevation and the distance from the inlets (Carniello et al.,

2008)

Dhf ¼

(

maxn

300; 50�

�hf �0:8�0:75o

if hf <�1:0ma:m:s:l:

15 if hf>�1:0ma:m:s:l:

D50 ¼ Dhfþ100 e�0:0097L3

(11)

where bottom elevation hf is in m a.m.s.l., the linear distance from

the closer inlet L is in km and the grain diameter Dhf and D50 are in

mm and the deeper the bottom, the coarser the grain size distri-

bution and the further the point from the sea, the finer and more

cohesive the bottom sediment. This behavior can partly be ascribed

to a landward reduction of flow velocity and thus to the capacity of

the current to carry into suspension sand coming from the sea

(Wang et al., 2011). We used this correlation to reconstruct the

distribution of mean grain size D50 which is compared to measured

diameters in Fig. 2b.

The mud content (pm) is then computed from the D50 distribu-

tion using the following correlation relationship derived by fitting

pm�D50 data reported by Umgiesser et al. (2006):

pm ¼ 1�lnðD50=DmÞ

lnðDM=DmÞ(12)

where Dm ¼ 20 mm and DM ¼ 200 mm are the mean grain size that

the model assumes to characterize mud and sand respectively.

The model parameters used in the simulations (Table 1) were

determined through a calibration procedure through which

parameter a and the specific entrainment rate for mud (Mm) were

adjusted to give the best fit to the data while the critical shear

stresses for sand (scrS) and mud (scrM), the critical shear stress for

deposition (sDEP), and the mean grain size (D50S, D50M) were

assumed on the basis of a recent field campaign (Amos et al., 2004).

The initial active layer thickness was set to Dzb0 ¼ 0.02 m

(a sensitivity analysis was performed which demonstrates that this

parameter does not significantly influence the solution).

In order to show and quantify the model’s performance, the

results of the simulations were visually compared to field data. We

also estimated model efficiency by using conventional statistic

parameters, namely the Percentage Model Bias (PB) which

evaluates the model error normalized by the data and the Scatter

Index (SI) defined as the rms error normalizedwith themean of the

observational data (e.g. Allen et al., 2007; Moriasi et al., 2007).

The results obtained from simulations with Bora wind (i.e. 2e5

April 2003, 9e13 December 2005, 29 July-2 August) are shown in

Fig. 4. The comparison with measured data is provided for each of

the stations located within the Lagoon (i.e. LT stations) and

considers the total suspended sediment concentration computed

by the model, i.e. the sum of sand and mud. The model results

compare favorably with themeasured data in most of the cases: the

model correctly predicts not only the magnitude of the suspended

Table 2

Capability of the model to reproduce observed turbidity at the stations within the

lagoon during Bora events (upper part: April 2003eDecember 2005eJuly 2007) and

during a Scirocco event (lower part: November 2007), evaluated on the basis of the

Percentage Model Bias (PB) and the Scatter Index (SI). The different categories for

the PB index are: PB < 10 excellent; PB ¼ 10e20 very good; PB ¼ 20e40 good;

PB > 40 poor (Allen et al., 2007).

STATION PB SI

LT1 (April 2003) 4.6 (excellent) 0.639

LT2 (April 2003) 17.6 (very good) 0.474

LT3 (July 2007) 7.4 (excellent) 0.825

LT4 (December 2005) 1.7 (excellent) 0.558

LT5 (December 2005) 11.7 (very good) 0.738

LT6 (July 2007) 9.2 (excellent) 0.397

LT7 (April 2003) 4.1 (excellent) 0.329

LT8 (July 2007) 0.94 (excellent) 0.796

LT3 (November 2007) 13.5 (very good) 0.458

LT6 (November 2007) 19.0 (very good) 0.322

LT8 (November 2007) 16.1 (very good) 0.552

Fig. 5. Comparison of measured (dashed line) and computed (solid line) suspended

sediment concentrations at three stations (LT) within the lagoon during a Scirocco

wind event.

L. Carniello et al. / Estuarine, Coastal and Shelf Science 102-103 (2012) 105e115110

sediment concentration but also its modulation induced by tidal

level and wind-wave variations.

Since the eight turbidity stations are well distributed

throughout the lagoon and located in places with different initial

bed composition, depth, andwind exposure, the comparison can be

considered a stringent test.

The estimation of the model’s efficiency considering the

Percentage Model Bias (PB) and the Scatter Index (SI) is provided in

Table 2. Based on the categories suggested by Allen et al. (2007) for

the PB parameter, the model’s performance was consistently

excellent or very good and the scatter index was reasonably small

in most of the cases.

Fig. 5 compares measured versus computed suspended sedi-

ment concentration at three stations during a Scirocco event (i.e.

21e25 November 2007). The three stations were located respec-

tively in the Southern part of the lagoon (LT8), in the middle part

(LT6) and in the central-northern part (LT3) close to the city of

Venice (see Fig. 2a). We observed that during Scirocco events, the

suspended sediment concentration was considerably smaller (one

order of magnitude) than during Bora events thus confirming the

greater impact of the Bora wind on the morphological evolution of

the Venice Lagoon. The model in the case of Scirocco wind also

compared reasonably well with measured data reproducing the

magnitude of the suspended sediment concentration and the main

features of its modulation especially at LT8 station. The model

slightly underestimated the suspended sediment concentration at

the LT3 station which is located leeward the city of Venice. We also

observed (not shown) that sand contribution to the total sediment

concentration was negligible (i.e. two or three order of magnitude

lower than mud concentration) for all the stations located within

the Lagoon. The model performance, estimated by means of the

Percentage Model Bias (PB) and the Scatter Index (SI) as given in

Table 2 was very good.

An additional test was also carried out considering an event

characterized by very low wind. In this case turbidity data were

available at six stations (IT stations) located close to the three

inlets. At these locations the bed composition is richer in sand

content than at the other stations within the Lagoon (LT stations);

this is confirmed by the fact that sand contribution to the

computed suspended sediment concentration is relatively large

and of the same order of magnitude as mud contribution. (i.e.

mud concentration w10 mg/l and sand concentration w2e3 mg/

l). The absence of wind clearly influenced the erosion processes

since the suspended sediment concentration was considerably

smaller than during wind events. Fig. 6 compares measured and

computed suspended sediment concentrations at the six IT

stations. Both computed suspended sediment concentrations and

the modulation induced by ebb and flood alternation compare

favorably with measured data. It is interesting to note that the

highest peaks in turbidity correspond to maximum ebb phases

which means that those peaks are mainly due to sediment flowing

out to the sea.

The model’s efficiency estimated using the Percentage Model

Bias (PB) and the Scatter Index (SI) is summarized in Table 3. The

small PB and scatter index values suggest that the model perfor-

mance is always very good or excellent, even in no-wind conditions.

Given the relatively good performances provided by the model

in reproducing the suspended sediment concentration at different

Fig. 6. Comparison of measured (dashed line) and computed (solid line) suspended sediment concentrations at the stations located close to the three inlets (IT) during an event

characterized by very low wind. The upper-left plot also shows the tide oscillation at the three inlets.

L. Carniello et al. / Estuarine, Coastal and Shelf Science 102-103 (2012) 105e115 111

locations and under different meteorological conditions, we then

analyzed the numerical results considering solid transport

discharge at the three inlets in order to obtain information

regarding the Lagoon’s budget of sediment. In particular we were

interested in identifying the processes responsible for the erosive

trend that the Venice Lagoon has been experiencing since the

beginning of the last century (Defina et al., 2007; Carniello et al.,

2009; Molinaroli et al., 2009).

Fig. 7 compares the sediment discharge computed at the three

inlets for the 2006 no-wind event and for the 2003 Bora wind

event. In both cases the tidewas similar, so that we can assume that

the tidal current contribution to the sediment transport processes

is about the same; this means that the differences can be ascribed

to resuspension by wave.

First, we notice the asymmetric behavior of the inlets: Fig. 7

clearly shows that most of the sediment carried outside the

lagoon during the ebb phase (positive values in the plot) are not

re-introduced in the lagoon during the following flood phase (see

also Martini et al., 2004; D’Alpaos and Martini, 2005). Moreover,

the jetties go far beyond the surf zone thus preventing any

sediment supply from the coastline. The only exception is the

Lido inlet: because of the progressive accretion of the beach north

of the inlet during the last century, the present coastline is very

Table 3

Capability of the model to reproduce observed turbidity at the stations at the three

inlets during a no wind event, evaluated on the basis of the Percentage Model Bias

(PB) and the Scatter Index (SI). The different categories for the PB index are: PB < 10

excellent; PB¼ 10e20 very good; PB¼ 20e40 good; PB> 40 poor (Allen et al., 2007).

STATION PB SI

IT1 (April 2006) 2.3 (excellent) 0.245

IT2 (April 2006) 16.9 (very good) 0.358

ITS (April 2006) 17.5 (very good) 0.429

IT4 (April 2006) 10.4 (very good) 0.222

IT5 (April 2006) 1.9 (excellent) 0.351

IT6 (April 2006) 13.3 (very good) 0.214

Fig. 7. Computed total suspended solid transport discharge at the three inlets for the 2006 no wind simulation (upper panels) and the 2003 Bora wind simulation (lower panels).

48 hours within the simulations characterized by a similar tide (dashed line) were considered. For both the events wind speed at two stations (W1 in northern lagoon andW4 at the

Chioggia inlet, see Fig. 2) is reported.

L. Carniello et al. / Estuarine, Coastal and Shelf Science 102-103 (2012) 105e115112

close to the head of the northern jetty (see Fig. 2) so that the

long-shore sand transport can bypass the jetty and enter the

Lagoon during flood tide. This process is not reproduced in our

simulations because swell waves in front of the Lagoon and long-

shore currents are not considered in the model. However, recent

studies and measurements (Umgiesser et al., 2006; Defendi et al.,

2010) suggest that the net import of sand from the sea through

the Lido inlet is not particularly significant since sandy sediment

remains close to the inlet. Indeed, in the long term, the average

solid flux indicates a tendency for loss of sediments from the

lagoon.

We also observed a significant increase of the sediment

discharge peak during Borawind conditions both at theMalamocco

inlet (about 7 times greater than the case with no wind) and at the

Chioggia inlet (about 6 times greater than the case with no wind).

On the contrary, the Lido inlet experienced only a slight increase

(less than 2 times).

The different behavior between the Lido inlet and the other

two inlets when Bora wind was blowing can be explained by the

fact that the Northern part of the Lagoon is fetch limited because

of the presence of salt marshes and therefore, on average, the

wave height and thus its erosive capacity decreases in this part of

the Lagoon which pertains to the Lido inlet basin. Moreover, in the

northern Lagoon, the path that suspended sediments must follow

to reach the Lido inlet is, on average, much longer than the paths

to the Chioggia and Malamocco inlets in the central southern

Lagoon.

We then evaluated the net loss of sediments in the two above

cases in a 48-h time interval considered about 1600m3 of sediment

are lost to the sea during the no-wind condition whereas with the

Bora wind the volume of lost sediment increases to 5700 m3. In

particular, if we consider separately the contribution of the Lido

inlet and that of the two other inlets, we notice that there is a slight

reduction in the net loss through the Lido inlet from 616 m3

without wind to 540m3 with Borawind. This can be ascribed to the

fact that, because of the wind, the divide between the Lido and

Malamocco basins slightly moves upwind (i.e. closer to the city of

Venice). On the contrary the loss through the Malamocco and

Chioggia inlets increases more than 5 times when the Bora wind is

blowing (i.e. from 980 m3 to 5135 m3).

This result is in agreement with the extensive tidal flat erosion

and salt marsh deterioration experienced, in particular, by the

central southern part of the lagoon during the last century as

pointed out by Carniello et al. (2009) and Molinaroli et al. (2009)

through the analyses of different bathymetric surveys.

Finally, Fig. 8 shows the net evolution of the bottom elevation at

the end of the 2005 simulation characterized by a long and intense

Bora wind. The crucial role of wind waves in reworking the lagoon

bathymetry which, in the case of Bora wind, mainly impacts the

central southern part of the basin clearly emerges. A single Bora

event lasting about 24 h produced a net erosion of the tidal flat

which, in some locations, is greater than 2 mm. This is followed by

a net deposition within the main channels that is indirectly

confirmed by the dredging of the navigable channel periodically

performed by the local authorities.

4. Conclusions

In this paper we presented amorphodynamic model made up of

a sediment transport model and a bottom evolution model (STA-

BEM) that were developed in order to be coupled with the two-

dimensional finite element model (WWTM) which reproduces

the tide propagation and the wind-wave generation and propaga-

tion in shallow tidal basins. The WWTM was improved in order to

take into account the spatial variability of the wind field which is

now interpolated over the domain on the basis of the available

wind measurement.

The sediment transport model and the bottom evolution model

consider both cohesive and non-cohesive sediments and schema-

tize the bed composition using two size-classes of sediments, i.e.,

non-cohesive sand and cohesive mud. Based on the analyses of the

available bed composition data a reliable initial configuration of the

bed composition has been obtained for the case study of the Venice

Lagoon.

In the sediment transport model, in order to better evaluate

the sediment resuspension rate, both the total bottom shear

stress sb and the critical shear stress sc are treated as random

variables. The stochastic approach gives a transport parameter

which varies gradually at near-threshold conditions and

improves the description of the initiation of the erosion process.

The sediment transport model was tested against turbidity

measurements collected at different stations within the Venice

Lagoon. The sediment transport model correctly reproduced not

only the magnitude of the suspended sediment concentration but

also its modulation induced by tidal currents and wind-wave

variations.

The model testing was performed considering several events

characterized by different tidal and meteorological conditions. The

model performed well in all the situations and, in particular, during

intense Borawind events. Since the turbidity data were collected at

stations that are distributed throughout the Lagoon and charac-

terized by different depths, initial bed composition and wind

exposure, the comparison with such data can be considered a very

stringent test.

The analysis of the numerical results in term of solid transport

discharge at the three inlets confirms the net loss of sediments

Fig. 8. Net evolution of the bottom elevation computed by the bed evolution model at

the end of the simulation reproducing the long and intense Bora wind event occurred

in December 2005.

L. Carniello et al. / Estuarine, Coastal and Shelf Science 102-103 (2012) 105e115 113

from the Lagoon as suggested by recent studies andmeasurements.

The main factors responsible for this net loss of sediments are the

asymmetric behavior of the inlets due to the presence of the jetties

and bed erosion by wind waves, in particular during Bora wind

events.

The net variation of the bottom elevation provided by the model

clearly shows the crucial role of wind waves in driving the lagoon

bathymetry evolution and the net erosion of tidal flats, in particular

in the central southern part of the basin. Furthermore we can

observe the deposition within the main channels, which periodi-

cally need dredging.

Acknowledgements

This research has been funded by Comune di Venezia “Mod-

ificazioni morfologiche della laguna, perdita e reintroduzione dei

sedimenti”. The authors wish to thank the Ministero delle Infra-

strutture e dei Trasporti, Magistrato alle Acque di Venezia, through

its concessionary Consorzio Venezia Nuova for the field data,

collected within the VeniceLagoon, essential to validate the model.

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