ULTIMATE QUICKEST scheme being used to represent the ...Modelling hydrodynamic, sediment and contaminant transport processes in coastal and estuarine waters R.A. Falconer, B. Lin Cardiff

Modelling hydrodynamic, sediment and

contaminant transport processes in coastal

and estuarine waters

R.A. Falconer, B. Lin

Cardiff School of Engineering, Cardiff University, Cardiff, CF2 3TB, UK

Abstract

Details are given of the development, refinement and application of 2-D depthintegrated and 3-D layer integrated numerical models for predicting waterelevations, depth integrated and layer integrated velocity componentsrespectively, water quality indicator distributions, cohesive and non-cohesivesediment fluxes and the fate of trace metals in coastal and estuarine waters. Themodels involve solving the governing equations of mass, momentum and solutetransport, with the hydrodynamic equations including: the effects of the earth'srotation, bed friction, wind shear and turbulence. The transport equationincludes: (i) advection and diffusion of sediments, and contaminants in thedissolved phase, (ii) partitioning of contaminants,between the dissolved andabsorbed phases, (iii) input of adsorbed contaminants to the water column dueto re-suspension of bed sediments, (iv) accumulation of contaminants onsuspended sediments, and (v) loses due to volatilisation and biodegration oforganic contaminants. The models use a regular or curvilinear co-ordinatefinite difference or finite volume scheme to solve the equations, with theULTIMATE QUICKEST scheme being used to represent the advective terms inthe solute transport equation and with the aim being to represent these keyterms accurately and without the occurrence of grid space oscillations. Themodels outlined herein have been applied extensively to a wide range ofestuarine basins including, in particular, the Humber Estuary in the UK.

Transactions on Ecology and the Environment vol 26, © 1999 WIT Press, www.witpress.com, ISSN 1743-3541

4 Water Pollution

1 Introduction

The transport of water quality indicator organisms and suspended sediments hasbeen of increasing interest to scientists and engineers involved in coastal andestuarine water management, primarily for a range of hydro-environmentalconcerns relating to water quality, erosion, deposition and flood defence.Furthermore, in recent years, there has also been a growing interest in otheraspects relating to coastal and estuarine sediment dynamics, including: longterm morphological processes, estuarine and coastal inlet stability, and inparticular, the transport of heavy metals and toxic waste, via adsorption ontosediment particles and re-suspension into the water column. Coastal andestuarine waters are favourable sites for industrial and urban development butare physically and chemically highly complex aquatic environments. Hence,more stringent legislation relating to industrial discharges has been increasinglyintroduced (e.g. Commission of the European Communities, 1993) andshoreline managers have therefore sought accurate hydroinformatics tools topredict the flux of water quality indicator organisms, the transport of sedimentsand the fate of trace metals and organic contaminants in coastal and estuarinewaters.

In addition to water quality processes and suspended sediment dynamics beingcomplex phenomena, the transport of heavy metal contaminants, either insolution or via suspended sediment particles, is even more complex. Thepartitioning of trace metals between these two phases is dependant upon anumber of estuarine water column variables, including: salinity, pH, availabilityof complex species and the physical and chemical characteristics of suspendedparticles (Ng et al, 1996). Thus, heavy metal fluxes are difficult to predict fromtheoretical considerations alone.

Details are given herein of the refinement of 2-D and 3-D numerical models forpredicting water quality indicator constituents, suspended sediment fluxes andheavy metal concentration distributions in estuarine waters. For the 2-D modelan orthogonal boundary fitting curvilinear co-ordinate grid system has beendeployed to replicate complicated and irregular estuarine geometries. Likewise,for the 3-D model, an operator splitting algorithm has been used to split the 3-Dtransport equation into two main parts; one for solving the vertical diffusiontenns and the other for solving the horizontal transport terms, with the ratio ofthe vertical to the horizontal length scale being small for most estuarine studies.The model predictions have been tested against analytical tests and laboratorymodel results, as well as comprehensive field data sets for a range of estuarinebasins, including in particular the Humber and Mersey estuaries and the BristolChannel.


2 Model Equations

2.1 General

In order to predict the governing hydrodynamic, water quality, sedimenttransport and trace metal processes in coastal and estuarine waters, theequations to be solved include: the fluid mass and momentum conservationequations, including appropriate turbulence closure equations, and the solutetransport equation for water quality indicators, suspended sediments - bothcohesive and non-cohesive - and trace metal concentration distributions.

2.2 Hydrodynamic Model

The governing equations for the hydrodynamic models were obtained byintegrating the Reynolds equations over the depth and layers of the watercolumn for the 2-D and 3-D models respectively. The equations were written intheir full conservative form and included the effects of the earth's rotation, windaction, bed friction and turbulent diffusion. For the turbulent diffusion ofmomentum two turbulence models were included in both models, namely a zeroequation two-layer mixing length model - refined to include free shear layerturbulence, and a two-equation k-e turbulence model (Rodi, 1984). For the 2-Dmodel an additional turbulence model was included to solve for the Reynoldsstresses directly, namely the algebraic stress model (Hakimzadeh, 1997). Thebed resistance stress was represented in the form of Darcy's equation, with thefriction factor being evaluated using the Colebrook-White equation, and withReynolds number effects being included and found to be particularly significantfor shallow water flood plain or wetland flows (Falconer and Chen 1996). Thesurface wind stress was represented using a quadratic friction law, with theresistance coefficient being represented in a piecewise manner (Wu, 1969).

The 3-D hydrodynamic model was solved using a combined explicit andimplicit difference scheme. An alternating direction implicit scheme was usedto solve the depth integrated hydrodynamic equations to give the waterelevation (or pressure) field. The layer-integrated equations were then solvedimplicitly to obtain the layer-averaged velocities, using the pressure fieldpredicted from the depth integrated equations. After solving the depthintegrated hydrodynamic equations, the layer-averaged velocities wereintegrated over the depth to obtain the depth averaged velocity. The Crank-Nicolson scheme was used to solve the layer-integrated hydrodynamicequations, with the vertical diffusion terms being treated implicitly and theremaining terms treated explicitly. Two iterations were performed to solve thecoupled depth and layer integrated equations. The flooding and dryingprocesses were modelled using a robust scheme developed by Falconer andChen (1991) and with full details of the hydrodynamic model being given byLin and Falconer (1997a). More recently, the 2-D depth integrated model has


Water Pollution

been re-formulated using a triangular unstructured finite volume approach andthis model is currently being verified against laboratory and field data for theBristol Channel.

2.3 Solute Transport Model

For the 3-D model predictions of water quality indicator, suspended sedimentand trace metal fluxes in coastal and estuarine waters, the generalised 3-Dsolute transport equation was expressed as:

where <J) = solute concentration; u, v, w = layer averaged velocity components

in x, y, z directions; W% = apparent sediment settling velocity (= 0 for water

quality indicators and trace metal concentrations); e^, By, 8^ = layer-

averaged dispersion-diffusion coefficients in x, y, z directions; (^ = direct or

diffuse loading rate; (j)g = boundary loading rate (including: upstream,

downstream, benthic and atmospheric inputs); and (j)̂ = total kinetic

transformation rate. The formulations used for the various kinetictransformation rates, for the individual water quality indicators modelled usingequation (1) in the 2-D and 3-D models, were based on the US EPAformulations included in the QUAL2D model (Brown and Barnwell, 1987).

In solving equation (1), four different boundary condition types were needed.These included:

(i) Open boundary condition: For an inflow boundary condition theconcentration profiles were prescribed using either available field data orassumed conditions, or for suspended sediment fluxes equilibriumconcentration profiles were assumed to be related to the local bed shearstress. For an outflow boundary condition, the concentration profiles wereobtained by extrapolation using a first order upwind difference scheme.

(ii) Bank boundary condition: At bank boundaries the normal solute fluxeswere set to zero, i.e. normal concentration gradients were set to zero.


Water Pollution 7

(iii) Surface boundary condition: At the free surface the net vertical solute fluxwas assumed to be zero, giving zero gradient with respect to z for the water

quality indicators (where W,. = 0), and for sediment and trace metal fluxes

we get:

W,(|> + s — =0 (2)fej^

where £ = water surface elevation above datum.

(iv) Bed boundary condition: At the bed the flux for most water qualityconstituents (including trace metals) was zero, whereas for sediment fluxesthe bed boundary was specified at a small height 'a' (i.e. the referencelevel) above the bed. For suspended sediment transport modified forms ofthe van Rijn (1984) formulations were used and, likewise, for cohesivesediment transport, the bed boundary fluxes used in the models were basedon formulations outlined in Raudkivi (1990).

Finally, for heavy metals the distribution of contaminants between the dissolvedand adsorbed particulate phases was defined according to empirically derivedequilibrium partition coefficients, of the form:

V _ Ta x~x

where ((\ and <{),, = concentrations of contaminants adsorbed on suspended

particles and in solution respectively. The partition coefficient K^ was

assumed to vary in one of two ways:

(i) Using the relationship of Turner and Millward (1994), that is:

InKp =bln(s + l)+lnK^ (4)

where b = constant, s = salinity and K^= partition coefficient for fresh

water, i.e. S = 0.

(ii) Using explicit tabulations of measured values of K^ as a function of

salinity.

For the 2-D and 3-D solutions of equation (1), the velocity field was used fromthe hydrodynamic model, together with the operator splitting technique for theunknown solutes ({). This approach divides the transport equation according to

the physical meaning of the various terms and also splits the terms up along thevarious directions of motion. The advection terms were solved using the


8 Water Pollution

ULTIMATE QUICKEST scheme in both models (Lin and Falconer, 1997b),which is a third order accurate scheme, enabling high concentration gradients tobe solved with no overshoot or undershoot. The finite volume method was usedin the vertical plane to accommodate variations in the bed topography. For the2-D boundary fitting model, the orthogonal co-ordinate system was conformallymapped onto a regular Cartesian grid.

3. Model Applications

3.1 General

The numerical models have been tested extensively against analytical solutionsand controlled laboratory measurements for a range of hydrodynamic conditionsand topographic geometries. These tests primarily include a range of analyticalsolutions for the development of vertical sediment concentration profiles andwind induced circulation in rectangular basins, and tidal velocity andconcentration distributions in rectangular harbours with a range of aspect (orlength to breadth) ratios and for various hydrodynamic boundary conditions andturbulence models (Hakimzadeh, 1997).

3.2 Humher Estuary

The numerical models outlined herein were also applied to a number of sitespecific studies by the authors, with each having a particular research objectivein mind. The example described herein is for the Humber Estuary, UK, whereparticular emphasis has been focused on refining models for predictinghydrodynamic processes (e.g. flooding and drying), water quality concentrationdistributions (e.g. BOD, DO, nitrates, phosphates), cohesive and non-cohesivesediment fluxes and trace metal concentration distributions.

The Humber Estuary is a large and well mixed estuary, situated along the north-east coast of England and providing an outlet to the North Sea for the riversTrent and Ouse, and shipping access to a number of ports. It has the largestcatchment in the UK, draining over 20% of England. The main estuarystretches from Spurn Head in the east to Trent Falls in the west, a distance ofapproximately 62km (see Figure 1). There are numerous sewerage andindustrial effluent inputs along the estuary, with some being metal bearing. Ithas a relatively large tidal range, of up to 7m, giving well mixed waters andextensive flooding and drying. The inter-tidal mudflats are environmentallysensitive areas, supporting naturally rare bird and plant populations. There arealso five sites of special scientific interest (SSSI) along the estuary. The mainpurpose of the most recent study was to investigate the spatial and temporaldistributions of both suspended sediments and dissolved and paniculate tracemetals along the estuary.


Water Pollution 9

In applying the 3-D numerical model to the Humber Estuary, a regular finitedifference grid of 118 x 56 cells, equally spaced at 500m intervals, was set upover the horizontal plane, covering the estuary from Trent Falls at the head ofthe estuary to about 6km seawards of Spurn Head. Fifteen layers were includedin the vertical. During flood tide the flow was in a southerly direction, with asection of the flow separating from the main current and flowing into theestuary. In contrast, during ebb tide the flow pattern was reversed, with theseaward boundary parallel to Spurn Head effectively acting as a streamline.Hydrodynamic data were also taken from a coarser grid model of the North Sea.Full details of the estuary and boundary locations are given in Figure 1.

In order to drive the hydrodynamic model, water elevation data recorded byABP Research and Consultancy Ltd were used at both the seaward andlandward boundaries, i.e. just beyond Spurn Head and Trent Falls. Fieldmeasurements of water elevations, velocities, water quality indicators, andsuspended sediment fluxes were also available at several sites along the estuaryfor model calibration and verification. For the various effluent and industrialdischarges along the estuary, mean daily rates were input at the outfall cells andlinear interpolation assumed to obtain intermediate values. For the waterquality constituent, suspended sediment and heavy metal fluxes from the riversWharfe, Aire, Don, Trent and Ouse, the boundary values used were obtained bysumming the individual water quality components and field data by Edwards etal (1987) for heavy metals. The predictions of the hydrodynamic parameters,i.e. water elevations and velocities, and the salinity and suspended sedimentfluxes agreed well with field data along the estuary. Full details of thehydrodynamic model are given in Lin and Falconer (1997a) and with typicalcomparisons of the velocity field and non-cohesive and cohesive sedimentpredictions being given in Figures 2, 3 and 4 respectively.

The performance of the contaminated transport module for heavy metals wasassessed by running the model for the following partitioning scenarios, under atypical spring tide and high river discharge: (i) no partitioning of contaminantsbetween the dissolved and adsorbed phases, i.e. KD = 0, (ii) no salinitydependence of KD (i.e. by setting b in Eq. 4 to zero), (iii) salinity dependence ofKD based on empirically derived partitioning results, and (iv) increasing thesalinity dependence of KD (i.e. by increasing b to -1.5). The boundary values ofdissolved contaminant concentrations were based on measured values ofdissolved cadmium and were 0.5ug/l at the freshwater gauging station on theRiver Ouse and 0.06jig/l at the seaward boundary. The heavy metal module wascalibrated against dissolved and participate trace metal data at Bull Fort, i.e. ata site as remote as possible from the input sites. The model results and observeddata are continuing to be compared, with observed distributions of dissolvedcadmium and zinc being reasonably well-produced by the models.


10 Water Pollution

4. Conclusions

Details are given of the increasing application of hydroinfonnatics softwaretools for predicting hydrodynamic, water quality, sediment and contaminanttransport processes in coastal and estuarine waters. Particular emphasis hasbeen focused herein on the refinement of 2-D boundary fitting and 3-D modelpredictions, with emphasis being focused on treatment of the closed boundaryconditions, accurate modelling of the advective processes and the inclusion ofhigher order turbulence models. The models have also been extended to includetrace metal flux predictions, with emphasis being focused on including adynamic salinity based partition coefficient, defining the proportion of tracemetal in the dissolved and participate phases. The models have been applied toanalytical and laboratory test cases, for which idealised data exist and to anumber of estuarine and coastal basins. In the study reported herein, details aregiven of the application of the models to the Humber Estuary, in northernEngland, for which extensive hydrodynamic, water quality, suspended sedimentand trace metal data exist. The model predictions agreed well withindependently acquired data for both the regular (3-D) and curvilinear (2-D)grid models, and for a range of hydrodynamic, water quality indicators andsuspended sediment fluxes along the estuary, with the models now being used asmanagement tools to predict the hydro-environmental and ecological conditionsalong the estuary. For the heavy metal predictions along the estuary, a novelsalinity dependant partition coefficient has been included in the models and hasbeen shown to give good qualitative agreement with field data, with the modelspredicting higher trace metal levels in the dissolved phase at the seaward end ofthe estuary. Research is now continuing on improving the model accuracy inpredicting cohesive sediment and trace metal predictions, with the model beingapplied to the Mersey Estuary in the UK.

Acknowledgements

The paper outlines briefly a number of research projects funded by the NaturalEnvironment Research Council, LOIS programme, the Engineering andPhysical Sciences Research Council, BP Chemicals Ltd., Yorkshire Water picand BMT Ports and Coastal Ltd. The authors are also grateful to theEnvironment Agency (North East Region) and ABP Research and ConsultancyLtd. for the provision of field data.

References

1. Brown, L.C. and Barnwell, T.O., The enhanced stream -water qualitymodels OUAL2E-UNCAS: documentation and user manual, Report No.EPA/600/3-87/U007, Environmental Research Laboratory, US EPA,Athens, GA, pp.189, 1987.


Water Pollution 11

2. Commission of the European Communities., Proposal for a Councildirective on integrated pollution prevention and control, COM (93), 423final, Brussels, Belgium, 1993.

3. Edwards, A., Freestone, R. and Urquhart, C, The Water Quality of theNumber Estuary, Report of Humber Estuary Committee, Yorkshire Waterpic, 1987.

4. Falconer, R.A. and Chen, Y., An improved representation offloading anddrying and wind stress effects in a 2-D numerical model, Proceedings ofInstitution of Civil Engineers, 91, pp.659-687, 1991.

5. Falconer, R.A. and Chen, Y., Modelling sediment transport and waterquality processes on tidal floodplains, Floodplain Processes, ed. MG.Anderson et al, John Wiley and Sons Ltd, 1996.

6. Hakimzadeh, H., Turbulence Modelling of Tidal Currents in RectangularHarbours, PhD Thesis, University of Bradford, UK, pp.336, 1997.

7. Lin, B. and Falconer, R.A., Three-dimensional layer integrated modellingof estuarine flows with flooding and drying, Estuarine, Coastal and ShelfScience, 44, pp.737-751, 1997a.

8. Lin, B. and Falconer, R.A., Tidal flow and transport modelling using theULTIMATE QUICKEST scheme, Journal of Hydraulic Engineering, ASCE,123, (4), pp.303-314, 1997b.

9. Ng, B., Turner, A., Tyler, A.O., Falconer, R.A. and Millward, G.E.,Modelling contaminant geochemistry in estuaries, Water Research, 20 (1),pp.63-74, 1996.

10. Raudkivi, A.J., Loose boundary hydraulics, Third Edition, Pergamon Presspic, Oxford, 1990.

11. Rodi, W., Turbulence models and their application in hydraulics, IAHRPublication (Second Edition), Delft, 1984.

12. Turner, A. and Millward, G.E. The partitioning on trace metals in amacrotidal estuary: implications for contaminant transport models,Estuarine, Coastal and Shelf Science, 39, pp.45-58, 1994.

13. van Rijn, L.C., Sediment transport part 2: Suspended load transport,Journal of Hydraulic Engineering, ASCE, 100 (10), pp.161301641, 1984.

14. Wu, J., Wind stress and surface roughness at air-surface interface, Journalof Geophysical Research, 74, pp.444-455, 1969.


12 Water Pollution

S*«w«rd boundaryKINGSTON UPON HULL

Spurn HeadSunk Channel f .• ==Oso23(Hawi<e Anchorage)o Middle. Shoa. ..' .•• y —v o .,:; —̂•» •<:••f'Jr Halton MkJdle '':.-.•.•. ' '

Immingham

Landward Boundary

Tidal GuagaField SiteMeteorological StationHigf> water levelLow water level

Figure 1 Map of Humber Estuary and location of field observation stations

field data51 52 63 54 55 56 57 56 59 60 61 62 63 64

2000 H 1 1 1 1 1 1 1 1 1 1 1 1 h 2000

51 52 53 54 55 56 57 SB 59 60 61 62 63 64

model prediction51 52 53 54 55 56 57 56 59 60 61 62 63 64

2000 H 1 ' 1 1 1 1 1 1 1 1 I I I 200Q

I

-i 1 1 i—=*-T"—̂ \ ' i "i i ^'r—i r^51 52 53 54 55 56 57 58 59 60 61 62 63 64

time (hr)

Figure 2 Comparison of Predicted and measured non-cohesive sediment concentrationsat Middle Shoal


Water Pollution 13

40

35

.£* 30

25

20

I Model Results' o Field Data

-o O Q O

7 8 9 10 11 12 13 14 15 16 17 18 19 20Time (hour)

Figure 3 Comparison of predicted and field measured salinity at Hawke AnwkeAnchorage, taken on 8 June 1995

120

? 100 -_— ModelO 2m (data)o 6m (data)

X im(data)A 4m (data)O 8m (data)

7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00Time (hour)

Figure 4 Comparison of predicted and field measured cohesive sediment concentrationsat Hawke Anwke Anchorage, taken on 8 June 1995


Documents

ULTIMATE QUICKEST scheme being used to represent the ...Modelling hydrodynamic, sediment and contaminant transport processes in coastal and estuarine waters R.A. Falconer, B. Lin Cardiff