Modelling trace metal concentration distributions in estuarine waters

Estuarine, Coastal and Shelf Science 64 (2005) 699e709

www.elsevier.com/locate/ECSS

Modelling trace metal concentration distributionsin estuarine waters

Yan Wu a, Roger Falconer b,*, Binliang Lin b

a Hyder Consulting, UKb School of Engineering, Cardiff University, Queen’s Buildings, The Parade, Cardiff CF24 3AA, UK

Received 24 February 2005; accepted 25 April 2005

Available online 22 June 2005

Abstract

Details are given of a numerical model study of the fate and transport of trace metals in estuarine waters, with particular

application to the Mersey Estuary, located along the northwest coast of England. A dynamically integrated model was firstdeveloped, including a two-dimensional depth-integrated model and a one-dimensional cross-sectional averaged model. This modelwas then refined to predict the hydrodynamic and sediment and trace metal transport processes in the Mersey Estuary. Details are

given of the development of a governing equation of the total trace metal transport, including both dissolved and particulate metals.The model was first calibrated against field data, collected during spring and neap tidal cycles, for water levels, salinity andsuspended sediment. The calibrated model was then used to investigate the trace metal transport processes in the Mersey Estuary,with the partition coefficient between the dissolved and adsorbed particulate phases being modelled as a function of salinity.

Comparisons were also made between the model predictions and field-measured data along the estuary. Reasonable agreementbetween the model results and field data has been obtained, indicating that the novel approach to model metal concentrationdistributions is capable of representing the fate and transport of trace metals in estuarine environments and can be used as

computer-based tool for the environment management of estuarine waters.� 2005 Elsevier Ltd. All rights reserved.

Keywords: estuary; hydrodynamics; sediment transport; trace metals; numerical modelling

1. Introduction

Many UK estuaries have suffered environmentaldamage due to the discharge of effluents frommanufacturing processes and wastewater from centresof population over several decades. Although estuarinewater quality is generally improving, as a result of theremedial actions implemented over the past 20 years,many potentially harmful chemicals, such as trace metals,still remain embedded within erodable sediments. Tracemetals generally exist in two phases in estuarine waters,i.e., in the dissolved phase in the water column and in the

* Corresponding author.

E-mail address: [email protected] (R. Falconer).

0272-7714/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ecss.2005.04.005

particulate phase adsorbed on the sediments. Thebehaviour of trace metals in the aquatic environment isstrongly influenced by adsorption to organic and in-organic particles. The dissolved fraction of the tracemetals may be transported through the water column viathe processes of advection and dispersion, while theadsorbed particulate fractionmay be transportedwith thesediments, which are governed by sediment dynamics.The partition of a trace metal between its dissolved andadsorbed particulate fractions depends on the physicaland chemical characteristics of the suspended particles,together with various ambient conditions, such as:salinity, pH, type and concentration of dissolved organicmatter (Turner et al., 2001; Turner and Millward, 2002).

Fine sediments act as a source (or sink) for the organicchemicals and trace metals entering (or leaving) the water

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700 Y. Wu et al. / Estuarine, Coastal and Shelf Science 64 (2005) 699e709

column with sediments contaminated by trace metalsbeing a potential threat to the aquatic environment.Resuspension of contaminated bed sediments caused bystrong tidal currents or dredging operations may releasea significant amount of trace metals into the watercolumn, and this desorption of contaminants from theirparticulate phase can have a pronounced impact on theaquatic environment and ecosystem. Numerical modelsprovide a valuable tool for predicting the fate andtransport of trace metals in estuarine environmentsand are increasingly used for such hydro-environmentalmanagement studies of estuarine waters. However,computer-based tools for predicting such trace metalconcentration distributions and concentrations, althoughthey can support decision-making by the regulatoryauthorities, marine environment agencies and industry,are still used relatively infrequently (Ng et al., 1996).Coupled numerical models involving hydrodynamic andcontaminant geochemistry processes are very few innumber, and they are largely research oriented, ratherthan being applied tools for managing estuarine andcoastal waters.

The paper gives details of the development of a novelapproach in modelling trace metal concentration distri-butions and the application of the model to the MerseyEstuary, located along the northwestern coast of England,for the prediction of the fate and transport of tracemetals. Details are given of the development of a gover-ning equation for the total trace metal transport,including both dissolved and particulate metals asa combined flux, in contrast to previous model studiesreported in the literature where the dissolved andparticulate metal processes have been treated indepen-dently (e.g. Ng et al., 1996). Details are also given of theintegration of a two-dimensional depth-integrated estu-arine model and a one-dimensional cross-sectionalaveraged river model and the application of the modelto simulate the hydrodynamic and sediment and tracemetal transport processes in the Mersey Estuary. Themodel was calibrated against six sets of field measuredtime series data, collected during spring and neap tidalcycles, for water levels, salinity and suspended sedimentconcentrations. The calibrated model was then used toinvestigate trace metal transport processes in the estuary,with the partition coefficient between the dissolved andadsorbed particulate phases being modelled as a functionof salinity (Turner and Millward, 1994).

2. Mathematical model

2.1. Hydrodynamic model

In modelling estuarine and riverine processes, themodelling domain often covers areas of different physicalcharacteristics, e.g. large water basins with a two- or

three-dimensional flow structure and narrowmeanderingchannels with a predominately one-dimensional flowstructure. When a two-dimensional numerical model isused for such cases the detailed bathymetric features ofa narrow meandering channel may not be well repre-sented unless a very fine grid system is used, therebyincreasing the computing time significantly. Similarly, ifa one-dimensional model is used then the two-dimen-sional flow features in the wider part of an estuary or rivermay not be well resolved. For many engineeringproblems these physical features are prevalent in manyestuarine and riverine waters. Therefore, a combined 2-Dand 1-Dmodel has been developed in this study to predictaccurately the hydrodynamic and water quality processesin the estuarine and riverine waters.

The hydrodynamic model used to predict the waterelevations and velocity fields in coastal, estuarine andriverine waters initially involves the solution of thegoverning equations of fluid flow. The two-dimensionalhydrodynamic equations are generally based on thedepth-integrated 3-D Reynolds equations for incom-pressible and unsteady turbulent flows, with the effectsof the earth’s rotation, bottom friction and wind shearbeing included to give (see Falconer, 1993):

vz

vtC

vqxvx

Cvqyvy

Z0 ð1Þ

vqxvt

CbvUqxvx

CbvVqxvy

Zfqy � gHvz

vxC

txw

r� txb

r

C�3H

�v2U

vx2C

v2U

vy2

�ð2Þ

vqyvt

CbvUqyvx

CbvVqyvy

Z� fqx � gHvz

vyC

tyw

r� tyb

r

C�3H

�v2V

vx2C

v2V

vy2

�ð3Þ

whereHZ zC hZ total water column depth; zZwaterelevation above (or below) datum; hZwater depthbelow datum; U, VZ depth-averaged velocity compo-nents in x, y directions; qxZUH, qyZVHZ unit widthdischarge components (or depth-integrated velocities) inx, y directions; bZmomentum correction factor;fZCoriolis parameter; gZ gravitational acceleration;txw, tywZ surface wind shear stress components in x, ydirections; txb, tybZ bed shear stress components in x, ydirections; and �3Zdepth average eddy viscosity.

The components of the wind stress at the free surfaceare given as (Falconer et al., 2001):

txwZCdraWsWx; tywZCdraWsWy ð4Þ

where CdZ resistance coefficient; raZ air density; Wx,WyZwind velocity components in the x, y directions,

701Y. Wu et al. / Estuarine, Coastal and Shelf Science 64 (2005) 699e709

respectively; and WsZwind speed at an elevation of10 m above the free surface.

The components of the bed shear stress are calculatedas:

txbZrgU

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiU2CV2

p

C2z

tybZrgV

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiU2CV2

p

C2z

; ð5Þ

where CzZChezy coefficient, which has been deter-mined in the current model using the ColebrookeWhiteequation for a given bed roughness length since thisformulation takes account of Reynolds number effectsover shallow water columns (Falconer et al., 2001).

The one-dimensional governing hydrodynamic equa-tions describing flow and water elevations in rivers arebased on the St Venant equations, applicable to 1-Dunsteady open channel flows. Various forms of StVenant equations have been formulated in the field ofunsteady open channel flow since the 1950s when thenumerical model simulations were first developed. Themost widely used form in practice is generally written as(Cunge et al., 1980):

TvzRvt

CvQR

vxZ0 ð6Þ

vQR

vtC

v

vx

�bQ2

R

A

�CgA

vzRvx

CgQRjQRjC2

zARZ0 ð7Þ

where TZ top width of the channel; zRZwaterelevation above (or below) datum; QRZ discharge;bZmomentum correction factor due to the non-uniform velocity over the cross section; AZwettedcross-sectional area; RZA/PZ hydraulic radius andPZwetted perimeter of the cross-section.

2.2. Transport model

2.2.1. Salt transportSalinity, i.e. the salt content within a water column, is

an important factor in the spatial dynamics of estuarineprocesses. This solute plays an important role in tracemetal partitioning between the dissolved and particulatephases and, in turn, influences the distribution of tracemetals along estuaries. Salinity may also affect theflocculation processes of cohesive sediment particles.As a conservative tracer, salinity distributions inestuaries can be modelled by the advectionediffusionequation.

The 2-D depth-integrated advectionediffusion equa-tion is given as:

v

vtðHSÞC v

vxðqxSÞC

v

vy

�qyS

�� v

vx

�HDx

vS

vx

�

� v

vy

�HDy

vS

vy

�Z0 ð8Þ

where SZ depth-averaged salinity; Dx, DyZ depth-averaged dispersion coefficients in x, y directions,respectively, which can be expressed as (Falconeret al., 2001):

DxZ

�klU

2CktV2�H

ffiffiffig

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiU2CV2

pC

CDW;

DyZ

�klV

2CktU2�H

ffiffiffig

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiU2CV2

pC

CDW ð9Þ

in which klZ longitudinal dispersion constant; ktZ lat-eral diffusion constant and DwZwind induced disper-sion coefficient. The values of the constant kl and kt aregiven as 5.93 and 0.15, respectively, in the literature(Elder, 1959; Fischer, 1973). However, in practicalstudies these values tend to be rather low (Fischeret al., 1979), with measured values for kl and kt rangingfrom 8.6 to 7500 and 0.42 to 1.61, respectively.

The 1-D cross-sectional averaged advectionediffu-sion equation is generally written as:

v

vtðASÞC v

vxðQRSÞ �

v

vx

�AKx

vS

vx

�Z0 ð10Þ

whereSZ cross-sectional averagedsalinity;URZQR/AZcross-sectional averaged velocity and KxZ longitudinaldispersion coefficient.

2.2.2. Sediment transportThe heavily contaminated sediments in many estuar-

ies, resulting from industrial and municipal effluents,accidental oil spills etc, could release trace metals,mineral oils and other toxic contaminants. The de-sorption of contaminants from their particulate phasecan have a significant impact on the ecological balanceof estuarine and riverine waters. Therefore, all un-derstanding and representation of sediment dynamics isof vital importance for the environmental managementof estuaries and rivers.

The two-dimensional governing equation describingsediment transport processes can be written as:

v

vtðHSPMÞC v

vxðqxSPMÞC v

vy

�qySPM

�

� v

vx

�HDx

vSPM

vx

�� v

vy

�HDy

vSPM

vy

�

Z

�qeroCqdep; cohesive sediment

wsðSPMae � SPMÞ; non-cohesive sedimentð11Þ

where SPMZ depth-averaged sediment concentration;qdep, qeroZ cohesive sediment deposition and erosionrates, respectively, which may be obtained usingempirical expressions given by Krone (see Raudkivi,1998); wsZ sediment settling velocity and SPMaeZequilibrium reference sediment concentration, which can


be calculated from the expressions given by van Rijn(1984).

The one-dimensional cross-sectional averaged sedi-ment transport equation can therefore be written as:

v

vtðASPMÞCvðQRSPMÞ

vx� v

vx

�AKx

vSPM

vx

�

Z

�qeroCqdep; cohesive sediment

wsðSPMae � SPMÞT; non-cohesive sediment ð12Þ

where SPMZ cross-sectional averaged sediment con-centration; qdep, qeroZ deposition and erosion rates ofunit length of the channel and TZ top width of thechannel.

2.2.3. Trace metal transportTrace metals can exist in both the dissolved or

adsorbed particulate phases in estuaries. The distribu-tion between these two phases can be described bya partition coefficient KD, defined as:

KDZP

Cð13Þ

where PZ concentration of trace metals adsorbed onsuspended sediments and CZ concentration of tracemetals dissolved in the water column.

The partition coefficient KD, determining the amountof adsorbed and dissolved fractions, depends on thephysical and chemical characteristics of the suspendedparticles and the ambient conditions, such as salinity,pH, etc. Due to the complexity in determining thepartition coefficient, a mean value for the partitioncoefficient has often been used in such applications. Inthis paper an exponential relationship with salinity(Turner and Millward, 1994) was used as given by:

ln KDZblnðSC1ÞCln K 0D ð14Þ

whereKDZ partition coefficient as a function of salinity,SZ salinity, bZ constant andKD

0 Z partition coefficientas a function of salinity.

The transport in the dissolved phase can be describedby the following two-dimensional advectionediffusionequation:

v

vtðHCÞC v

vxðqxCÞC

v

vy

�qyC

�� v

vx

�HDx

vC

vx

�

� v

vy

�HDy

vC

vy

�ZH

�SdoCSd

t

�ð15Þ

where SodZ source or sink of dissolved trace metal; and

StdZ transformation term defining adsorbed or desorbed

particulate fluxes to or from the sediments.The adsorbed particulate phase is transported with

the sediments, and this process may be described by thefollowing equation:

v

vtðHPSPMÞC v

vxðqxPSPMÞC v

vy

�qyPSPM

�

� v

vx

�HDxP

vSPM

vx

�� v

vx

�HDyP

vSPM

vy

�

ZH�SpoCSp

tCSpb

�ð16Þ

where SopZ source or sink of adsorbed particulate trace

metal; StpZ transformation term defining metal flux

from, or to, dissolved phase in the water column; andSbpZ source term defining particulate flux from or to the

bed, for sediment erosion or deposition, respectively.The transformation processes between the dissolved

and adsorbed particulate phases are very complex.However, noting that Sd

tZ� Spt , we can avoid calculat-

ing the transformation rate between the dissolved andadsorbed particulate phases by first calculating the totaltrace metal concentration distributions, and then di-viding the dissolved and adsorbed particulate phasesusing a partition relationship of the form given inEq. (14). The evaluation of the total trace metal concen-trations in this form is thought to be novel, with thecorresponding equation derived by summing Eqs. (15)and (16), and re-arranging the diffusion terms to give:

v

vtðHCTÞC

v

vxðqxCTÞC

v

vy

�qyCT

�� v

vx

�HDx

vCT

vx

�

� v

vy

�HDy

vCT

vy

�C

v

vx

�HDxSPM

vP

vx

�

Cv

vy

�HDySPM

vP

vy

�ZH

�SdoCSp

oCSpb

�ð17Þ

where CTZ concentration of total trace metal, i.e.:

CTZCCSPMP ð18Þ

Substituting Eq. (13) into Eq. (18) gives:

CZCT

1CKDSPMð19Þ

Likewise, the 1-D cross-sectional averaged equationdescribing the total trace metal transport processes canbe written as:

v

vtðACTÞC

v

vxðQRCTÞ �

v

vx

�AKx

vCT

vx

�

Cv

vx

�AKxSPM

vP

vx

�ZA

�SdoCSp

oCSpb

�ð20Þ

3. Numerical methods

To predict both predominantly 2-D and 1-D hydro-dynamic, solute and particulate transport processes in


estuarine and riverine waters at the same time, a 2-Dand 1-D overlapping approach is normally adopted.Models using an overlapping approach explicitly ex-change data between the 2-D and 1-D models, providingboundary conditions for each model over the over-lapping zone (Lin et al., 2001). The models based on thiskind of explicit algorithm are generally mass non-conservative and may be subject to numerical instabil-ities. In this paper, a model dynamically integratinga two-dimensional depth-integrated model and a one-dimensional cross-sectional averaged model is described.The present integrated model, which implicitly solvesthe 2-D and 1-D system as a whole, eliminates theexplicit exchange of data between the 2-D and 1-Dmodels at their overlapping fictitious boundary and thescheme is both fully mass and momentum conservative.

3.1. Hydrodynamic models

The dynamically integrated 2-D and 1-D model isconstructed on a combined 2-D and 1-D grid system.The one-dimensional grid is connected to the two-dimensional grid in the x or y direction. To solveimplicitly the two-dimensional and one-dimensionalsystems together, one of the grid rows in the two-dimensional grid system is chosen as a principal gridrow, which connects with the one-dimensional gridsystem. During the calculations the principal row, i.e.the row connecting with one-dimensional grid system, isalways calculated first, with the other rows in two-dimensional grid system being calculated after (Wuet al., 2001).

The two-dimensional depth-averaged hydrodynamicEqs. (1)e(3) are discretised using an alternatingdirection implicit scheme based on the finite differencemethod. A space-staggered grid is used, with thevelocities and depths being located at the centre of thesides of the grid cell and the other variables located atthe centre of the grid cell. Similarly, a space-staggeredgrid, with the discharges being located at the sides of thegrid cell (segment) and the water elevation located at thecentre of the cell, is used to discretise the one-dimensional cross-sectional averaged hydrodynamicEqs. (6) and (7). The finite volume approach is used toderive the discretised equations.

3.2. Water quality model

The QUICKEST scheme, originally developed byLeonard (1979), was used in the present model to predictthe advective transport processes. Even though thethird-order QUICKEST scheme greatly reduces thenon-physical oscillations caused by numerical disper-sion, this scheme still suffers from numerical oscillationsnear discontinuities. Thus, the universal limiter designedfor one-dimensional problems by Leonard (1991) has

been used to suppress the non-physical numericaloscillations. However, it was found that local disconti-nuities were distorted when the one-dimensional univer-sal limiter was directly used at each control volume facefor the two-dimensional problem. A modified one-dimensional ULTIMATE algorithm for the two-di-mensional problem has been constructed to avoid anyvariations in local discontinuities (Wu and Falconer,1998).

In applying the universal limiter a criterion was usedto check that the solute concentration maintainedmonotonicity. In estuarine and riverine flows the waterdepth or cross-sectional area may vary rapidly, thus themonotonicity of the depth-integrated concentration orcross-section integrated concentration may be differentfrom the monotonicity of the solute concentration.Therefore, when applying the modified ULTIMATEQUICKEST scheme a conservative form of the advec-tionediffusion equation for the depth-average concen-tration should be used. For details of the numericalmethod, see Wu and Falconer (2000).

4. Model application to the Mersey Estuary

The Mersey Estuary is one of the largest estuaries inthe UK, with a catchment area of some 5000 km2 overthe north western part of England, and includes themajor conurbations of Liverpool and Manchester. TheUpper Estuary, between Warrington and Runcorn Gap,is a narrow meandering channel of about 15 km inlength (see Fig. 1). Below the Gap, the estuary opens upinto a large shallow basin to form the Inner Estuary ofabout 20 km in length, with extensive inter-tidal banksand salt marsh on its southern margin. Furtherdownstream of the Inner Estuary, the estuary convergesto form the Narrows, a straight narrow channel of up to30 m depth, even at low water. Seaward of the Narrows,the channel widens again to form the Outer Estuary,consisting of a large area of inter-tidal sand and mudbank (Jones, 2000). The Mersey Estuary is a well-mixedmacrotidal estuary with tidal ranges at Liverpoolvarying from 10.5 m (extreme spring) to 3.5 m (extremeneap) over a typical springeneap cycle. Freshwater flowfrom the River Mersey into the Mersey Estuary variesfrom 10 m3 s�1 to 600 m3 s�1 at the extremes, withtypical flows being in the range of 20e40 m3 s�1.

4.1. Model set up

The numerical model was set up and applied tosimulate the tidal flow field and the salt, sediment andtrace metal concentration distributions in the MerseyEstuary from New Brighton (seaward) to Howley Weir(landward). The water elevation recorded at theGladstone tide gauge was chosen as the seaward


Fig. 1. Map of the Mersey Estuary showing 1- and 2-D boundary and location of sampling sites.

boundary condition to drive the tidal currents and thedaily flow rate recorded at Howley Weir was used forthe upstream flow boundary condition. The modeldomain was represented horizontally in two gridsystems, i.e. the 2-D and 1-D grids. The 2-D grid,covering the region from New Brighton to Hale, wasrepresented horizontally using a mesh of 216! 116uniform grid squares, each with a length of 100 m. The1-D grid covering the region from Hale to Howley Weirwas represented using 80 segments, with extensivebathymetric data at each cross-section being collectedduring the most recent bathymetric surveys conductedby HR Wallingford Ltd and APB in 1997. The reasonfor ending the 2-D grid at Hale is that there is a lowwater channel upstream of Hale, which can be betterrepresented by the 1-D model. Fig. 1 is a map of theMersey Estuary showing the location of sampling sitesand the internal boundary of the 1- and 2-D model.

4.2. Model calibration

The integrated model was calibrated against six setsof data provided by the UK Environment Agency. Fourof these data sets were collected during spring tides andtwo were collected during neap tides. The freshwater

input from the River Mersey for these sets of datacovered both wet and dry season conditions. Thesampling stations are shown in Fig. 1. All model runsstarted at high water with the initial velocities being setto zero. The time step was set to 10 s, and the model wasrun for three tidal cycles, to reduce the effect of theinitial conditions, before predictions were considered.

4.2.1. Water levelsThe main hydrodynamic parameter used for the

hydrodynamic calibration was the bed roughness. Thebed roughness was calibrated by trial and error based onthe above six sets of data. Calibration of waterelevations was carried out only due to the lack of dataon velocities. For the present Mersey Estuary model, thebed roughness was defined in terms of the roughnesslength, which can be related to bed features such asripples and dunes, over the two-dimensional modeldomain. For the one-dimensional model domain, theManning’s roughness coefficient was used. Differentroughness lengths were assumed in the two-dimensionalmodel domain, with the roughness length downstreamof Eastham being bigger than that upstream of East-ham, due to the fact that fine sediments were found inthe upstream reaches of the estuary. The calibrated


roughness lengths were 50 mm and 20 mm for these tworegions covering the two-dimensional part of theestuary, respectively. For the one-dimensional part ofthe estuary, the optimum calibrated Manning’s rough-ness coefficient was found to be 0.02.

Only selected results are shown herein for thecalibration undertaken using the survey data collected.However, these data sets and comparisons are typical ofa wide range of comparisons. Comparisons of theobserved and predicted water elevations were made atWaterloo, Eastham, Runcorn and Fiddlers Ferry, withthe calibration details given for a spring tide from 6:30to 19:30 on 18 September 1989. Good agreement wasobtained between the model predicted water levels andfield data at Waterloo and Eastham, with the differencein tidal range generally being less than 5%. The modelpredicted water levels agreed reasonably well with theobserved water levels at Runcorn and Fiddlers Ferry,except that the model gave slightly higher water levelsduring the period of ebb tide. Fig. 2 shows a comparisonbetween the model predicted and surveyed water levelsat Fiddlers Ferry. The discrepancy was possibly causedby using the bathymetry surveyed during 1997 to modelan event in 1989, with the bathymetry of the MerseyEstuary known to change frequently and especiallyaround Runcorn Gap.

4.2.2. SalinityThe main parameter for the calibration of the salt

transport module is the dispersion coefficient. In thepresent model the dispersion coefficient has beencalculated according to the formula (9), where twoempirical constants were used, namely, longitudinaldispersion constant and lateral diffusion constant. Sixsets of salinity data provided by the UK EnvironmentAgency were used to calibrate the dispersion constants.These data sets were collected on the same dates as thewater levels used in the calibration of the hydrodynamicmodel. The longitudinal dispersion and lateral diffusion

6:30 7:30 8:30 9:30 10:3011:3012:3013:3014:3015:3016:3017:3018:3019:30

18-9-89

0

2

4

6

8

10

12

Water elevatio

n (m

)

Fiddlers Ferry

Model ResultsField Data

Fig. 2. Comparison of predicted and measured water elevations at

Fiddlers Ferry.

constants were calibrated by trial and error, based onthe salinity data collected along the estuary at PrincesPier, Eastham, Runcorn, Randles Sluices, FiddlersFerry, Monks Hall and Bridge Foot, as shown in Fig. 1.

Again only selected calibration results for the field-measured salinity, taken during the same survey periodas for the hydrodynamic calibration, are presentedherein. Good agreement was obtained between thepredicted and measured salinities at all of the sitesconsidered, with the tidal pattern also being wellrepresented. Oscillations were observed in the field dataobtained at Princes Pier and Eastham during the firsthalf tidal cycle, which were thought to be caused by theRiver Weaver flowing into the estuary, both at the riverconfluence below Runcorn and at Eastham Locksthrough the Manchester Ship Canal; these inputs werenot included in the present model. Towards theupstream the model results were very encouraging, withthe predicted salinity generally agreed well with the fielddata of a complex pattern. The predicted and observedsalinities at Randles Sluices on 18 September 1989 areshown in Fig. 3, with the predicted salinities agreeingwell with the observed values, except that the modelpredicted slightly higher salinities during the period ofebb tide. This over-estimated salinity during ebb tide isconsistent with the conclusions of the hydrodynamiccalibration, in that the bathymetry of the MerseyEstuary undergoes frequent changes especially aroundRuncorn Gap and this may have caused less ebb flow inthe model through Runcorn Gap. At Fiddlers Ferry, themodel predicted almost identical minimum salinities tothose obtained from measurements, although it slightlyunder-predicted the maximum salinity. At Monks Hall,the predicted and measured salinities again agreedreasonably well, with the predicted minimum salinitybeing similar to the field data. As before, at high tide,the model again over-estimated the peak salinity. Fig. 4shows a comparison of the tidally averaged salinitybetween the predictions and measured values along theestuary from 6:30 to 19:30 on 18 September 1989. As

6:30 7:30 8:30 9:30 10:3011:3012:3013:3014:3015:3016:3017:3018:3019:30

18-9-1989

Salin

ity

0

5

10

15

20

25

30

35

Randles Sluices

Model Results

Field Data

Fig. 3. Comparison of predicted and measured salinity at Randles

Sluices.


can be seen the model predictions have generally agreedwell with the field data.

4.2.3. SedimentsIn simulating sediment concentration distributions in

the Mersey Estuary, both cohesive and non-cohesivesediment fractions were considered. Three sets ofsuspended sediment data, provided by the EnvironmentAgency, were used to calibrate the sediment transportmodule. From these data and the two sets of axialmeasurements to be described in the next section, it wasfound that finer sediments exist primarily towards theupstream end of the estuary and coarser sedimentsdownstream of the estuary. Therefore, two sediment sizeregimes were assumed in the model simulations. In theUpper Estuary, between Warrington and Runcorn Gap,the bed sediments were considered as cohesive, whiledownstream of Runcorn Gap, the bed sediments wereconsidered as non-cohesive. The main reason choosingRuncorn Gap as the boundary dividing the two regionswas that a clear difference could be observed in thebathymetric characteristics at this point. The grain sizeof the sediments used in the model for non-cohesivesediment in the Inner Estuary, i.e., downstream ofRuncorn Gap, was provided by the UK EnvironmentAgency. Based on these field data D16Z 12 mm,D50Z 75 mm, D84Z 195 mm and D90Z 225 mm wereused in the model. A cohesive sediment size of 20 mmwas assumed for the cohesive sediment module. Thesediment transport modules were calibrated by trial anderror, based on the suspended sediment concentrationsalong the estuary at: Princes Pier, Eastham, Runcorn,Randles Sluices, Fiddlers Ferry and Monks Hall. Thecalibrated critical shear stresses for erosion and de-position and the erosion constant were found to be1.0 N/m2, 0.25 N/m2 and 0.00004 kg/m2 s, respectively.

The sediment transport module was calibratedagainst the three sets of data provided, but comparisonsare given only for one data set herein. This data set was

0 5 10 15 20 25 30 35 40 45

Distance from Howley Weir (km)

0

5

10

15

20

25

30

35

Sa

lin

ity


Fig. 4. Comparison between model predicted and measured tidally

averaged salinity levels along the estuary.

collected during a spring tide from 6:30 to 19:30 on 18September 1989, with an interval of 30 min. Compar-isons of the measured and predicted sediment concen-trations were made at: Princes Pier, Eastham, Runcorn,Randles Sluices, Fiddlers Ferry, and Monks.

Fig. 5(a) shows good agreement between the pre-dicted and measured suspended sediment concentrationsat a downstream site, Princes Pier. The model repro-duced the two peaks corresponding to the flood and ebbtides. The predicted maximum suspended sedimentconcentration at Princes Pier was 0.69 kg/m3, i.e.0.1 kg/m3 higher than the measured value of 0.59 kg/m3.At Eastham, the predicted suspended sediment con-centration also agreed well with the field data, with themaximum concentration being accurately predicted.Fig. 5(b) shows predicted and measured suspendedsediment concentrations at an upstream site, FiddlersFerry. The predicted maximum suspended sedimentconcentrations agreed well with the measured values,with the general pattern of the suspended sediment overthe tidal period being reasonably well predicted by themodel. The level of agreement between the modelpredictions and the field data is not so close at MonksHall in comparison with the other sites, although themodel did pick up the second peak observed in the field

6:30 7:30 8:30 9:30 10:3011:3012:3013:3014:3015:3016:3017:3018:3019:30

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Fig. 5. Comparison of predicted and measured sediment concen-

trations at: (a) Princes Pier and (b) Fiddlers Ferry.


data. In view of the complexity and uncertainties insediment transport modelling, the model is consideredto be generally well calibrated and appropriate for theapplication of investigating the trace metal concentra-tion distributions in the Mersey Estuary.

4.3. Trace metal transport

In order to gain a better understanding of the tracemetal transport processes in the Mersey Estuary, theEnvironment Agency carried out intensive field surveysin the Estuary during 1998. High- resolution data ondissolved and adsorbed particulate trace metals, sus-pended particulate matter, salinity, and other variablessuch as pH and DO along the estuary were collectedduring the surveys. For all surveys the vessel startedfrom the Outer Estuary at about high water and tookabout 3.5 h to reach the upper Estuary. Two sets ofsurvey data (25 June 1998 and 20 October 1998) wereused to verify the model capability in predicting thetrace metal transport processes in the estuarine waters.Only the model predictions using the data collectedduring the first survey will be shown herein.

The survey on 25 June 1998 was undertaken fora spring tide, of range 8.47 m, with the high tidereaching Liverpool at about 12:45. The freshwater inputfrom the River Mersey during this period was about3.6 million m3. The survey boat started from the BuoyC1 in the Outer Estuary at 10:56 and traversed toMonks Hall in the Upper Estuary. Samples werecollected at 20 locations along the estuary and thetravel time was about 3.5 h.

A comparison was made of the salinity between themodel predictions and the field data along the estuary.The model results were tidally corrected to enable thepredicted concentrations to be compared directly (i.e. atthe same time) as the sample collection times. It wasfound that the model predictions were in goodagreement with the observed data, particularly at thehead of the estuary where salinity is an importantparameter in influencing the partitioning of trace metals.The comparison between the model predicted andobserved suspended sediment distribution along theestuary was also made. The predicted suspendedsediment distribution agreed reasonably well with thefield data, although the model underestimated the peaksuspended sediment concentration, with the predictedmaximum suspended sediment concentration at MonksHall being 483.5 mg/l, which is about 16.8% lower thanthe observed value of 581 mg/l.

Fig. 6(a) shows a comparison between the modelpredicted and measured dissolved cadmium concentra-tions along the estuary. The empirical constants KD

0 andb were set to 41,700 and �0.45, respectively in themodel, to evaluate the partitioning of the cadmiumbetween the adsorbed and dissolved phases. The

predicted dissolved cadmium distribution agreed rea-sonably well with the field data, with the desorptionprocess generally being well reproduced in the model.

To investigate the impact of the input loads on thedistribution of the trace metal concentrations along theMersey Estuary, the model was run both with andwithout input metal loads from the river Weaver and thesewage works at Liverpool and Warrington. The metaldistribution on the bed sediments was estimated fromspot data provided by the Environment Agency. Theempirical constants KD

0 and b, which affect the value ofthe partition coefficient, were provided by PlymouthUniversity (Martino et al., 2002). For the case of zincthe empirical constants for KD

0 and b were 6000 and0.299, respectively. The dissolved and particulate metalconcentration distributions that were used as observa-tions for determining these constants can also be foundin Martino et al. (2002). Fig. 6(b) shows the modelpredicted and measured dissolved zinc distributionalong the estuary. It can be seen that the predictedvalues of the peak concentration of dissolved zinc agreewell with the measured data, but the location of the peakdissolved zinc concentration is different between both

0 5 10 15 20 25 30 35 40 45


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Fig. 6. Comparison of predicted and measured axial distributions on

25 June 1998 for: (a) dissolved cadmium and (b) dissolved zinc.


sets of results. Similar simulations were also undertakento predict zinc distribution along the estuary butwithout bed load inputs into the model and it wasfound that the discrepancy between the model predic-tions and the measurements increased significantly. Thishighlights the importance of the contaminated bedsediments on the dissolved zinc concentrations and thatthe contaminated bed sediments contribute noticeablyto the axial dissolved zinc concentrations along theestuary.

It was also noted that the positive value of theconstant b used in the partitionesalinity relationship forzinc did not follow the trend found elsewhere (Turneret al., 2002). Alternative KD-salinity relationships havebeen proposed for zinc from more recent investigations(Martino et al., 2004). Further research has beenplanned to implement these new relationships into thenumerical models developed for this study and toinvestigate the impact of the modifications on the modelpredictions.

5. Conclusions

An integrated 1-D and 2-D numerical model has beendeveloped to predict the hydrodynamic and sedimentand trace metal transport processes in estuarine andcoastal waters. A new approach has been developed topredict metal concentration distributions in thesemodels. This approach involves first calculating thetotal trace metal flux in the water column and thenseparating this flux into the dissolved and particulatemetal constituents. This sub-division of the total metalflux into its constituents is based on a salinity-dependentpartition coefficient. This modelling approach differsfrom other model studies reported in the literaturewherein the dissolved and particulate metal concentra-tion distributions are calculated separately. The newapproach has the advantage of efficiency and the factthat separate source and sink terms are not neededbetween the two sets of equations for particulate anddissolved transport.

In modelling estuarine and river processes, themodelling domain often covers areas of a significantlyvarying width, as in the case of the Mersey Estuary. Toovercome this problem the 2-D model was extended to1-D, to enable the narrower channels at the head of anestuary to be modelled more accurately. The model hasbeen set up and applied to simulate the hydrodynamicprocesses and the salinity, sediment and trace metalconcentration distributions along the Mersey Estuary,from New Brighton (seaward) to Howley Weir (land-ward). The most recent bathymetric data were used andthe 2-D model was set up from New Brighton to Hale,with a uniform grid spacing of 100 m. The 1-D reachcovered a region from Hale to Howley Weir and

included 80 segments. The refined model was firstcalibrated against extensive field data collected for theMersey Estuary by the Environment Agency. The modelwas then tested to investigate the partitioning of tracemetals with sedimentary particles and applied to studythe impact of contaminated bed sediments on the waterquality of the estuary. The model generally showed goodagreement between the predicted and measured concen-tration distributions of dissolved zinc and cadmium andfurther showed that the contaminated bed sedimentshad a marked impact on the metal concentrations alongthe estuary.

Acknowledgements

The authors are grateful to the National Environ-ment Research Council for supporting this study and toDr. Peter Jones of the Environment Agency for theprovision of data. The authors are also grateful toProfessor Geoff Millward of the University of Plymouthfor his collaboration on this project and, in particular,for his advice on the use of partition coefficient.

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Documents

Modelling trace metal concentration distributions in estuarine waters