Modeling Pollution Dispersi

8/19/2019 Modeling Pollution Dispersi

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Environmental Modelling & Software 17 (2002) 363–385www.elsevier.com/locate/envsoft

Review

Modelling pollution dispersion, the ecosystem and water quality incoastal waters: a review

I.D. James *

Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead CH43 7RA, UK

Received 10 May 2001; received in revised form 29 July 2001; accepted 11 October 2001

Abstract

This review is intended as a comprehensive but concise summary of present capabilities in coastal pollutant, ecosystem and waterquality modelling. It reflects the recent rapid developments in multidisciplinary modelling in shelf seas.

The behaviour of conservative pollutants that act as passive tracers is contrasted with those that have more complex behaviours,including oil spills. The importance of sediment modelling is emphasised, since contaminants commonly exist in both a dissolvedand a particulate state, or adhere to sediments.

Recently developed ecological models can have great complexity, reflecting the complexity of the real ecosystem. These modelsare now being linked to physical models of coastal waters and run with the same resolution. This has become possible only recentlybecause of increases in computer power, particularly the availability of parallel systems at reasonable cost.

The main advances in physical modelling are likely to come through greater understanding of turbulence and other sub-grid-scale processes as well as increased resolution.

In the coastal seas there is often a lack of oceanographic data, which is even greater for the many biological and chemicalvariables than it is for physical variables. This is probably the single most important factor limiting the progress of operationalwater quality models. © 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Coastal; Pollutant; Ecological; Water quality; Modelling; Multidisciplinary; Review

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364

2. Modelling pollutants in coastal waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3652.1. Pollutants as passive tracers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3662.2. Sediment and SPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3672.3. Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3682.4. Oil spills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368

2.5. Chemicals and toxins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

3. Ecosystem modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

4. Physical modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3744.1. Diffusion and dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

4.1.1. Vertical diffusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3744.1.2. Retinoic acid syndrome: a report of two casesLateral dispersion . . . . . . . . . . . . . . 375

* Tel.: +44-151-653-1533; fax: +44-151-653-6269. E-mail address: [email protected] (I.D. James).

1364-8152/02/$ - see front matter © 2002 Elsevier Science Ltd. All rights reserved.

PII: S 1364- 8152 ( 01) 00 080- 9


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364 I.D. James / Environmental Modelling & Software 17 (2002) 363–385

4.1.3. Quasi-two-dimensional turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376

4.1.4. Lagrangian chaos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

4.1.5. Numerical diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

4.2. Further requirements for the physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

5. A model system for coastal water quality applications . . . . . . . . . . . . . . . . . . . . . . . . 379

6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

1. Introduction

A general review paper covering the modelling of pol-

lution, the ecosystem and water quality in coastal waters,

and the prospects for making this modelling operational,

is timely for at least two reasons. One is the increase insuch multidisciplinary modelling in the last decade, and

the need for an introductory review for those modellers

who previously were limited to a single discipline. The

other is the increase in computer power, involving the

use of parallel processing, which has made it possible

for the first time to run linked physical and ecologicalmodels on the same high resolution. Multidisciplinary

modelling is therefore coming of age, and moving to the

stage where it is feasible to contemplate running a modeloperationally to provide real-time predictions of water

quality in coastal waters.

The intention here has been to cover this very wide

and active field comprehensively but concisely to givean accurate picture of present capabilities. To explore

individual topics in greater depth the reader is referred

to the bibliography.This subject is essentially multidisciplinary: to attempt

to understand the whole system demands knowledge of

disciplines ranging over ecology, biogeochemistry, toxi-

cology, sedimentology and fluid dynamics, while model-ling the system involves numerical analysis and, for

complex simulation models, coding techniques for high-

performance computers such as massively parallel

machines. The total coastal system is extremely compli-

cated and includes many variables and processes includ-

ing highly non-linear interactions. Most modelling todate has therefore tackled only part of the system, or

very simplified systems, in order to make progress andgain insight. Only recently have high-resolution hydro-

dynamic models and complex ecological models been

combined. The effectiveness of such deterministic mod-

els for making useful predictions about the ecosystem isnot yet completely proven and can still be controversial:

Nuttle (2000) argues in favour of the more traditional

empirical approach.

In this paper the view is taken that it is the physical

system and the physical conditions that are fundamentaland “set the stage” for the chemical and biological sys-tems. While there can be some influence of these on thephysics (for example, the effect on penetrating solar

radiation of a surface plankton bloom), in general a good

representation of the physics can be achieved in a model

without considering biology and chemistry. Conversely,

the physical conditions, which include currents, tides,

waves, turbulence, light, temperature, salinity, bed

materials and suspended particles, determine the trans-

port and dispersion of all suspended and dissolved

material in the sea, including contaminants and nutrients,

and affect all biological activity from the transport of larvae and bacteria and the growth of phytoplankton to

the behaviour of fish. Therefore it is a necessary con-dition for any model of an estuary or coastal region to

be used to help understand the present conditions and to

make useful predictions that the physics is properly rep-

resented.

Of course, no physical model can give information on

physical variables on all space and time scales: these

have to be appropriate to the problem in hand. For

example, a simulation of the spring phytoplankton bloom

in the North Sea can be achieved with a fairly coarse

horizontal resolution, so long as the vertical resolution

and reproduction of tidal mixing in the water column are

suf ficient to represent the onset of stratification, but thedetails of horizontal patchiness in phytoplankton and

zooplankton require much higher horizontal resolution

to include eddies and the details of stirring and mixing.

Several physical processes which are “sub-grid-scale”and which cannot be resolved by the physical model

have to be “parameterised”; that is, described by vari-ables which represent them more or less adequately. One

of these is “eddy viscosity”, which describes the effectof turbulence as if it behaved in the same way as an

increased molecular viscosity. A detailed model of tur-

bulence and sediment dynamics near the sea bed wouldbe needed to reproduce the processes seen in experi-

ments that can release material from the sea bed into the

water column, but this is often parameterised in a simple

resuspension term.

Despite the fundamental nature of the physical model

and the apparent simplicity of the physics in comparison

with the complexity of an ecosystem model or contami-

nant behaviour, it should not be assumed that the physics

is solved, easy to model or even well understood. It

involves non-linear equations which can lead to chaotic

or turbulent flow, a wide range of scales, and includes


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365 I.D. James / Environmental Modelling & Software 17 (2002) 363 – 385

dif ficult problems such as the behaviour of suspendedparticles of various shapes and sizes in fluid flow. Forprediction purposes, it is also critically dependent on the

boundary conditions that drive it. For example, a two-

dimensional model for sea level which resolves tides andsurges and which has been well tested over many years

is still dependent on accurate meteorological data forgiving good surge forecasts. Such surge models are the

archetype for successful operational application of

numerical modelling to coastal processes. Some reasonsfor their success are that they deal with relatively simple,

almost linear processes, long waves that are easily

resolved and energy dissipation that can be successfully

represented by a simple bottom friction term. The history

of surge modelling is the paradigm for the progress of

all coastal modelling: the original empirical methodsbased on statistical relationships between surge level and

meteorological and other variables have been replaced

by deterministic numerical models based on the equa-

tions of motion, which are time-stepped forward from

an initial state. Now this paradigm is being followed for

very much more complicated processes, and while

results may not be so reliable or accurate as for storm

surges, much progress has been made in recent years, as

this review will make clear. It is worth bearing in mindthat numerical surge modelling is still being refined aftera development period of nearly 40 years, and that

meteorological agencies can and do still keep the statisti-

cal methods available as a check on the results. For mod-

els of much more complex systems it is even more

important to use the models in conjunction with comp-

lementary information, possibly from empirical models.If the analogy with surge modelling is correct, we areat present in the initial stages of deterministic water

quality and ecosystem modelling in the coastal zone,

now made feasible by advances in computer power, with

many decades of development ahead.

The following two sections review pollutant and eco-

system modelling. Then follows a section on modelling

the physics which underpins the pollutant and ecosystem

models. Then an outline is given of the requirements

for a possible complete model system that would be aprototype for an operational water quality capability.

2. Modelling pollutants in coastal waters

A pollutant may be defined as any substance thatreduces the water quality. It may or may not result from

human activity. It may have a well-defined source (suchas an oil spill) or a diffuse source (such as radioactivity

from the atmosphere or antifouling paints). It may be

dissolved in the water, be attached to particles, exist asparticles, float, or be mainly in benthic sediments ormud. Some pollutants may be partitioned (divided)

between several different phases (for example, metals

may exist in solution or as particulates). Some undergo

chemical reactions during dispersion in the sea; radioac-

tivity decays with time. Oil may behave in several ways

depending on its type and the prevailing conditions: it

can evaporate, spread out in a thin slick, becomeattached to sediments and form emulsions. The undesir-

ability of a pollutant may be measured by its biologicaleffect: it may be toxic; nutrients from fertilisers in river

discharges may cause excessive plant blooms

(eutrophication), killing animal life by deprivation of oxygen as the algae in the bloom decompose; it may

simply be aesthetically displeasing to humans. Distinc-

tion is sometimes made between contamination, definedas any artificial increase above a background level, andpollution, which implies harm to living things (for

example, Chapman, 1995), but this is not a distinctionmade in the dictionary, nor is it universally accepted by

ecologists (Taylor, 1993), since the level of contami-

nation that causes harm is not always easily identified.The variety of pollutant behaviours means that each

pollutant must have its own algorithm (that is, rule for

calculation) to describe its modelled behaviour. This

may take the form of either a time-stepping concen-

tration equation or a particle-tracking routine. The con-

centration equations are suitable for a widely dispersedsubstance, but care must be taken over the numerical

advection scheme used: more on this will be found in

Section 4. Advection merely describes the motion of a

substance with the water velocity, as a passive tracer.

Although this is a simple concept, simple numerical

advection schemes can cause either excessive diffusion

or “rippling” near sharp gradients. This is not a problemwith particle tracking, which is a natural method to use

with point sources, but once the substance is dispersed

a large number of particles may need to be used to retain

enough in each grid box to represent the concentrationthere.

The advection–diffusion equation

∂C

∂t ui

∂C

∂ xi

∂

∂ xiK ij∂C ∂ x j (1)

is the core of any equations determining pollutant con-centration C . K ij is the diffusivity tensor: usually for

shelf seas it is assumed that K ij 0 if i j and that

K 11 K 22 K H, a horizontal diffusivity, and K 33

K V, a vertical diffusivity. This equation alone would

describe a passive tracer. The diffusion part represents

tracer motion on scales too small for the model to rep-resent. If the flow is laminar, i.e. if there is no turbulence,the diffusion is on the molecular scale, with a thermal

diffusivity of the order of 1.4 × 107 m2 s1 in purewater. In coastal waters, the flow is almost always turbu-lent and the effective diffusivity is several orders of mag-nitude greater. Diffusion due to sub-grid-scale processes

in a model is often described by eddy diffusivity, often

determined by a turbulent energy equation, which,


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although much greater, nevertheless behaves like mol-

ecular diffusion: fluxes are always down-gradient andsharp changes are always smoothed out. This does not

necessarily represent the real processes of mixing that

may be taking place, and in reality there may be stirringof material into thin filaments of high concentration that

are ultimately diffused on the molecular scale. The dis-tinction could be important if the highest local concen-

tration of a pollutant is important, rather than the average

within a model grid box. The ability of a model to pre-dict concentrations from the advection–diffusion equ-ation is always limited by the resolution of the model as

well as the representation of sub-grid-scale mixing in the

diffusion term. This will be discussed further in Section

4. In a particle-tracking model, where advection is

straightforward, diffusion must be represented by ran-dom motion of the particles, determined by the value of

eddy diffusivity. However, convergence in the large-

scale velocity field can lead to narrow filaments of par-ticles that would not be so well resolved by a concen-

tration equation.

In addition to the advection–diffusion equation are theterms that describe the way the pollutant behaviour dif-

fers from a passive tracer. These must also be rep-

resented in a particle-tracking model, possibly by achange in the properties of each particle. For a dissolved

radioactive substance, this may simply be a decay of the

radioactivity with time. For a sediment, or other particu-

late matter, there may be a fall velocity. For large par-

ticles, there may be other differences between the par-

ticle velocity and the water velocity. For sediments there

may need to be terms representing deposition and resus-pension at the sea bed, cohesion and flocculation. Therecan be terms representing interaction, whether chemical

or biological, with other variables. The algorithm for

each individual pollutant variable needs to be derived

from a clear understanding of how that pollutant behaves

in coastal waters.

In the following subsections the simplest pollutants,

which behave most like passive tracers, are treated first,and then pollutants with more complex behaviours are

described.

2.1. Pollutants as passive tracers

A passive tracer is subject simply to advection and

diffusion and sources and sinks, possibly including

exchange across the sea surface and sea bed. The watermovement is independent of the tracer concentration, so

can be calculated separately. Quantities behaving in this

way include some dissolved metals (Prandle et al., 1993;

Charnock et al., 1994). Sources may typically include

rivers and the atmosphere; sinks for dissolved metalsmay include adsorption on to particulates. The latter pro-

cess is greater for some metals, for example lead, than

for others and for these the behaviour is less like a sim-

ple tracer. Nevertheless, Prandle et al. (1993) calculated

the distributions of salinity and metals in the southern

North Sea on the basis of residual flows from a two-dimensional model and river and atmospheric sources.

This process is most straightforward for conservativequantities, where there is no significant source or sink

term apart from perhaps a river input. In the case of salinity, its influence on density cannot usually be neg-lected when calculating currents, and certainly not near

river outflows, so it is not simply a passive tracer.One pollutant that approximates closely to a tracer is

a dissolved radioactive substance with a long half-life.

Radioactive decay adds only an exponential decay term

to the concentration predicted from the advection–dif-fusion equation. In fact, over a long period radioactive

substances have been useful for testing models of thelong-term circulation of shelf seas. Prandle (1984) used

residual currents from a two-dimensional shelf model to

simulate the transport of 137Cs from Sellafield in thisway. Recent discharges of technetium, which has a very

long half-life (2.13 × 105 years), from Sellafield(Leonard et al., 1997) and Cap de la Hague have pro-

vided more tracer information. Dahlgaard (1995), in an

overview of the EU MAST-52 project, discusses radio-

active tracers as a tool in coastal oceanography.The relative importance of advection and diffusion in

the dispersion of a tracer may be represented by the

Péclet number Pe UL / K , where K is (horizontal)

diffusivity, U the velocity and L a length scale. Prandle

et al. (1993) estimate that for the southern North Sea,

and this may be typical for tidal shelf seas in general,

advection dominates diffusion for a conservative traceron space scales O(10 km). This underlines the impor-tance of accurate numerical advection methods in pol-

lutant models as well as the need for a realistic represen-

tation of the mean circulation.

However, the less conservative the quantity of interest

is and the more it responds to local sources and sinks, the

less it can be regarded simply as a tracer. Temperature is

an example of a physical variable of this kind; over

much of the shelf a good simulation of the annual tem-

perature cycle can be achieved by one-dimensional mod-els of the water column, knowing heat input at the sur-

face and vertical mixing due to tidal currents. Here, the

critical factor is the specification of the vertical dif-fusion. Except near coastal plumes and strong persistent

residual currents, advection is of secondary importance.

As for salinity, temperature cannot be a passive tracersince it affects the water density and hence currents,

particularly near fronts and plumes.

The general conclusion is that for a pollutant to

behave as a tracer, it must be conservative and have

well-defined non-local sources and sinks. Pollutants thatapproximate most closely to this are dissolved radioac-

tive substances with long half-lives, metals with low

values of partition coef ficients (representing the ratio of


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particulate to dissolved phases) and low uptake by par-

ticles, and very fine particles with low settling velocities.Most pollutants, however, do not behave like simple tra-

cers and much of the emphasis in the following sections

is on the additional terms beyond advection and dif-fusion that are needed to model them.

2.2. Sediment and SPM

Here, SPM stands for “suspended particulate matter”,while sediment also includes those particles which lie on

or near the sea bed. Coarse material with grain size

larger than about 0.1 mm generally moves only as bed

load except during exceptional storms. Sediment may be

cohesive (particles, more often fine ones, may stick together) or non-cohesive. The modelling of sedimentand SPM is important not just for its own sake but

because pollutants may exist in a particulate phase or

adhere to or be adsorbed on to particles and because

particulates are an important part of ecological and water

quality models. For example, nutrients and detritus can

exist as particles, and SPM in turbid waters reduces

light levels.

The main additional terms in the equation for SPM

concentration are those that account for sinking, erosionand deposition at the sea bed. Sinking is represented by

a fall velocity, which can be an addition to the vertical

advection in the model. The fall velocity varies accord-

ing to the size of the particle, so a model needs to have

separate SPM variables for a range of particle sizes.

Sediment is deposited on and eroded from a separate

benthic layer. This layer in turn can be modelled indetail, including the effects of bioturbation. Erosion maybe supposed to occur if the bed stress is greater than a

critical value, and then increases as the stress increases,

while deposition occurs if bed stress is less than another

critical value. For particles of finite size and density dif-ferent from the water, the assumption that they behave

as a passive tracer with the addition of a fall velocity is

of course a simplification of their complete dynamics(Maxey, 1990). The interaction of particles in suspension

is also often neglected in SPM transport models.Results shown by Holt and James (1999) for SPM

from coastal sources in the southern North Sea show

how the addition of the extra sinking, erosion and depo-

sition terms can result in a considerable difference from

the dispersion predicted for a passive tracer. SPM trans-

port can depend strongly on the sequence and timing of erosion and deposition together with the variable wind-

driven circulation. The bed stress, which is a critical

quantity in the model formulae, is strongly influencedby storms (partly through enhancement due to waves in

shallow areas) as well as tidal currents, varying throughthe spring-neap cycle.

As an alternative to the concentration equations a par-

ticle-tracking method can be used (Puls and Sün-

dermann, 1990; Pohlmann and Puls, 1994; Sündermann,

1993). For both methods, the calculation increases as the

number of particle types and sizes increases. If the SPM

is passive, the hydrodynamic equations are unaffected

by the SPM concentrations. In this case, calculating theresidual flow and tidal currents once means they can be

used several times in different SPM runs (Sündermann,1993). The total flow, not residual only, is needed tocalculate the bed stress at any time. When concentration

of SPM is very high, however, it affects the apparentdensity of the water and very turbid water may flow asa density current (Simpson, 1987). Self-stratification of the boundary layer by resuspended fine sediment duringstorms may limit further resuspension (Jago et al., 1993).

The need for separate equations for each SPM fraction

is an example of the increase in the number of variablesand calculation load necessary for water quality model-

ling when compared with the hydrodynamic model

alone. Ideally, SPM modelling also has a requirement

for high resolution in the vertical to cover stratificationand boundary layers and in the horizontal to resolve tur-

bidity fronts and plumes.

The requirement for wave information in shallow

areas to provide an enhanced bed stress (Grant and

Madsen, 1979) suggests also that, if this effect is to beincluded accurately, a wave model needs to be run sim-

ultaneously. Some of the effect of enhanced bed stress

can, however, be represented by a simplified assumptionof wave activity (Jones and Davies, 1998).

Some effects not included in the Holt and James

(1999) model that are more dif ficult to parameterise are

those of flocculation, which increases the effective par-ticle size and affects the fall velocity; biology, which

may change cohesiveness, affect resuspension and alter

the bed sediments by bioturbation; and trawling and

dredging, which can be significant in many areas. Wil-lows et al. (1998) consider the modelling of biological

effects on the erosion of intertidal sediments.

The parameterisations in the SPM equations are them-

selves only simplifications of detailed processes at thesea bed and in the turbulent bottom boundary layer.

These include bursting phenomena and the effect of bedforms, including rippling of the bed. Detailed measure-

ments of sediment resuspension (for example, Williams

et al., 1998) show many complex processes that are only

approximately accounted for in the shelf-wide models.

The application of models to coastal morphodynamics

(change of bathymetry due to sediment movement) often

requires high resolution so as to include banks, channels

and the effect of structures. Near beaches, longshore cur-

rents driven by waves are important. Bedload, which

may be due to ripple movement, needs to be taken into

account. Despite the complexity of the problem, modelpackages are available for the prediction of changes in

coastal morphology (for example, DELFT 3D-MOR

from WL|Delft Hydraulics). These changes may need to


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be taken into account if a water quality model is used

to predict the consequences of new structures or dredg-

ing and dumping. Areas of tidal flats such as MorecambeBay can have very variable bathymetry because of the

movement of channels, which is very dif ficult or imposs-ible to predict. However, for many water quality appli-

cations, even involving sediment transport, changes inbathymetry may be neglected.

2.3. Metals

As noted above, metals can exist in both dissolved

and particulate forms. The partition coef ficient K d (Balls,1988) is defined as the ratio of metal concentration inparticulates (mg/kg) to the dissolved concentration

(mg/l). The concept of partition coef ficient is heavilyused in modelling, but is essentially a simplification of complex underlying processes. If K d is known, assuming

equilibrium existing between the dissolved and particu-

late phases, a knowledge of the total metal concentration

and the SPM concentration in a model grid box deter-

mines the fraction in solution. The greater the concen-

tration of SPM for a given K d, the greater the percentage

of metal that is particle-bound. Burton et al. (1993) give

curves demonstrating this for four trace metals (Mn, Pb,Cu and Cd) in the Thames estuary. These curves show

also that K d is not a constant for a given metal and that

it varies between metals: it is much larger for lead than

for copper. For copper, the dissolved fraction dominates

for all but the highest concentrations of SPM. Lead is

much more readily adsorbed on to particles and so may

be quickly removed from the dissolved phase. This is anexample of “particle scavenging”. Part of the variationin K d can be attributed to particle type: biological par-

ticles such as plankton may have high values for some

metals (Huthnance et al., 1993).

The dissolved fraction of a metal may be modelled as

a tracer, while the particulate fraction may be modelled

in the same way as SPM. If K d were known and a con-

stant and if there were a state of equilibrium, it would

be simple to calculate an instantaneous transfer between

the phases as indicated above. However, this is compli-cated by variations in K d and finite transfer timesbetween dissolved and particulate phases (Turner et al.,

1992). If significant, these transfer time scales mustappear in source and sink terms in the separate equations

for dissolved and particulate metal concentrations.

Because K d is relatively small for Cd and Cu, Prandleet al. (1993) had some success in modelling these as

tracers, given various coastal, boundary and atmosphericsources. For metals with a greater particle af finity suchas lead, significant amounts may be stored in sea bedsediments and benthic recycling, as these sediments areresuspended in the water column, may be an important

source.

Tappin et al. (1997) have presented a transport model

(NOSTRADAMUS) for metals (Cd, Cu, Ni, Pb, Zn) in

the southern North Sea. The currents are based on a two-

dimensional 35 km hydrodynamic model (from the Pro-

udman Oceanographic Laboratory). Exchange between

dissolved and particulate phases is driven by distributioncoef ficients K d taken from observations and changing

seasonally. Part of this change is due to changes in par-ticle type. Sediment is divided between organic and inor-

ganic, so a biological transport model is included. Esti-

mated uncertainties in the inputs of metals arehighlighted, but these apparently make relatively little

difference to the results.

The modelling of metal concentration in coastal wat-

ers is therefore feasible now, the main uncertainties lying

in inputs and partition coef ficients. However, fundamen-tal progress beyond the use of K d awaits improved under-standing of the spatio-temporal variation of the rates at

which biogeochemical transfer processes take place. A

move to three-dimensional models of higher resolution

is likely to improve results, particularly in regions strati-

fied by temperature or salinity, as in coastal plumes thatmay be carrying metals from rivers.

2.4. Oil spills

Oil spills are an area of pollution modelling that has

attracted a great deal of attention because of the immedi-

ate and catastrophic results of major accidents. Because

of the emphasis on accidental spills, it is also an area

where operational modelling is needed to provide real-

time predictions of the movement and fate of the oil. For

this to be effective, a high-resolution model of the areaat risk needs to be already set up, or needs to be easilyset up as part of a relocatable model system.

There have been several review papers summarising

the extensive literature on oil-spill modelling, including

Spaulding (1988), ASCE (1996) and Reed et al. (1999).

Here the main features will be outlined as far as they

affect algorithms for oil transport in the models.

Oil has a range of physical and chemical properties

that need to be considered when setting up a model.

These properties may vary considerably between differ-ent types of oil. For a particular spill, the oil type must

be specified. The values of viscosity, volatility and den-sity, for example, affect the rate of spreading, evapor-

ation and dispersion in the water column.

As for the other pollutants, oil is subject to advection

and diffusion. As it is less dense than water, much of the oil travels in a surface slick, which is affected by

wind, waves and the surface current in the water. Many

spill models assume an empirically based wind- and

wave-induced (Stokes drift) component for the drift of

a slick, which may be added together and are typicallyaround 3.5% of the wind speed. Both Elliott (1986) and

Reed et al. (1994) suggest the angle between the wind

and this wind-driven component is small, effectively


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zero. As the wind increases, oil droplets are dispersed

into the water column and the water current at depth

becomes a significant factor. Although Proctor et al.(1994a,b) use a two-dimensional numerical model to

hindcast tide and surge currents for the Braer and Gulf oil spills, the vertical variation — in wind-driven cur-

rents in particular — is important and a three-dimen-sional model of currents would have advantages, but it

needs to resolve strong current gradients near the sea

surface and preferably include wave–current interac-tions. The importance of the advection of oil dispersed

through the water column was shown in the Braer spill

off the Shetlands (Turrell, 1994): a southward transport

did not follow the wind direction.

Vertical diffusion of oil can be calculated by vertical

diffusivity in the water column, modified by the buoy-ancy of the oil droplets. Elliott (1986) uses a random

walk technique in the vertical as well as the horizontal

direction. Horizontal diffusion is often calculated by a

random walk, which is appropriate for particle tracking,

which is clearly preferable to concentration equations for

modelling oil spills. The properties of the particles may

change due to the effects of other processes acting on

the oil. The spill may be represented by a number of

parcels or droplets, which may have a size distribution(Elliott, 1986), or individual “spillets” may represent aspill that is released over a period of time or over a

wider area.

Some near-surface transport effects, such as those

induced by Langmuir circulation (Faller and Auer,

1988), are commonly neglected in models, but may have

important effects on dispersion of oil. Additional com-plexity is introduced if there is ice present (see, forexample, Yapa and Weerasuriya, 1997), and the

reliability of predictions is limited by the ability of sea-

ice modelling at the appropriate scale (Reed et al., 1999).

Spreading is important in the early stages of an oil

spill. This describes the increase in area of the oil slick

under the forces of gravity, viscosity and surface tension,

and is distinct from any expansion of the slick due to

turbulent diffusion. The spreading formulae now

described as “classical” (Reed et al., 1999) are reviewedby Hoult (1972). Eventually spreading will cease at

some terminal thickness, and the time taken to reach this

state depends on the properties of the oil. Most spreading

may be expected to take place in a matter of hours to

days after a spill. In practice, the slick may break up

into patches. Shear spreading, caused by the dispersioninto the water column and resurfacing of oil droplets

after being moved apart by vertical shear in the horizon-

tal currents (Elliott et al., 1986), is likely to describe the

main physics of spreading once the initial gravitational

spreading has ceased.Evaporation of oil is another important process that

needs to be included: in the first few days between 10%and 75% of the mass may evaporate depending on

whether the oil is heavy or light. The most commonly

used equations describing evaporation are those of Stiver

and Mackay (1984). The oil may be considered as con-

sisting of a number of different fractions, the evaporation

of each fraction being considered separately. An alterna-tive approach (Proctor et al., 1994b), in a model based

on the tracking of droplets, is to introduce an evaporationtime scale l1, giving the probability p 1e lt of adroplet being removed within a time step t . A similar

use of a time scale can also describe other decay pro-cesses, such as biodegradation. Further weathering

effects, including photochemical oxidation, can change

the character of the oil and cause decay.

Dispersion of the oil into the water column follows

the breakup of the slick into small droplets and the

spread and diffusion of these droplets in the vertical.Although the oil may be less dense than water, in certain

conditions turbulence and breaking waves may mix the

oil well below the surface. Oil dispersed below the sur-

face is not subject to evaporation, but the processes of

biodegradation and dissolution (transfer to a dissolved

phase) are enhanced. Usually much less than 1% of the

oil spilled will dissolve, so this process is often neg-

lected. Once oil droplets are dispersed below the surface

they are subject to advection and diffusion by the fluidflow, plus buoyancy (or “rise velocity”) and the possi-bility of adsorption on to SPM or the sea bed. The

methods of Delvigne and Sweeney (1988) are often used

to estimate the oil mass entrained into the water column

per unit area and unit time. Vertical dispersion followed

by resurfacing, by the process of shear spreading noted

above, tends to result in the elongation of the slick inthe wind direction.

Water-in-oil emulsions or “mousses” sometimes formwhen chemical conditions are right and there is enough

mixing energy. Algorithms for emulsification have beenformulated by Mackay et al. (1980a,b). Compared with

the original oil, the emulsion has a much greater volume,

is denser and more solid, and has a very much larger

viscosity. Evaporation and spreading are much reduced.

Of particular concern in relation to oil spills in the

coastal zone is the stranding of oil at the shoreline. Manymodels can predict the motion of oil until it reaches the

shore but cannot include beach and surf-zone processes.

One exception is COZOIL (Reed et al., 1989), which

includes such processes as a wave-induced longshore

current. Some simplifying concepts that have been used

to describe shoreline deposition are the “holdingcapacity” of the shoreline type, “removal rates” and“half-life” values. On many coasts, tide levels and thepossibility of a tidal cycle of deposition on the shore

are important.

The number and complexity of processes involved inthe oil spill problem are clearly very great. This brief

review has already touched on advection, diffusion,

spreading, evaporation, biodegradation, dispersion,


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weathering, photochemical oxidation, emulsification,adsorption on to sediment, interactions with ice and

shoreline stranding. The prediction of the biological

impact is a further step beyond the types of model dis-

cussed here. Models must introduce major simplifi-cations and may neglect some processes, but neverthe-

less they have become broadly successful in simulatingoil-spill trajectories. Among many applications that dem-

onstrate this are hindcasts of the Braer spill off Shetland

(Proctor et al., 1994a; Spaulding et al., 1994) and theGulf War spill (Proctor et al., 1994b).

2.5. Chemicals and toxins

The previous section on oil spills shows that for an

individual pollutant several complex behaviours specificto that substance may need to be included in a model.

The very many chemical contaminants released to the

coastal environment through river and outfall discharges

and via the atmosphere may therefore need to be con-

sidered individually. Some may be represented as pass-

ive tracers but many have complex and sometimes

poorly understood physico-chemical speciation, which

controls phase partitioning. Thermodynamic partition

coef ficients used to model particulate–water exchange of compounds can be inaccurate owing to the heterogeneity

of sorbants, which can alter the kinetics of partition to

such an extent that equilibrium is never attained. How-

ever, the partitioning between dissolved and particulate

phases and the possible scavenging of chemical pol-

lutants by sediment and organic particles are of critical

importance. Some pollutants may become bound to sedi-ments and are released from the sea bed to the watercolumn through bioturbation, resuspension in storms,

fishing and dredging. Several of these processes havealready been discussed in relation to metals: they can in

principle be modelled, but with large uncertainties over

partition coef ficients and over the realism of the rep-resentation of sediment and SPM. For example, there

may in reality be ef ficient scavenging by organisms orlarge flocculated organic material not included in themodel. As in the case of oil, chemical processes suchas oxidation and reduction, the effects of sunlight and

reactions with other substances present in the water may

need to be considered.

Estimates of the bioavailability and toxicity of chemi-

cal pollutants are needed to make predictions about their

ecological impact. To date this has not been included inthe complex predictive ecosystem models to be dis-

cussed in Section 3, and would be extremely ambitious.

To the uncertainties involved in the prediction of con-

taminant concentration must be added the poorly under-

stood mechanisms of uptake of a complex cocktail of chemicals by aquatic organisms, the resulting toxic

responses and the effect of bioaccumulation in the food

chain. Progress has been made on simulating responses

to contaminants at a cellular level (for example, Moore

and Willows, 1998), but the aim of scaling up such mod-

els to whole animals and embedding them in an ecosys-

tem model is some way from realisation. Ecotoxicology

is a relatively new term for the study of the ecologicaleffects of toxins, integrating ecology and toxicology

(Chapman, 1995). This considers rather more complex,subtle and long-term effects of the harm caused by pol-

lution than the crude concepts of the lethal dose and the

LC50 test (the concentration required to kill 50% of a

test species within a set time). Environmental Quality

Standards, which are set by national governments and

the EU, give what are regarded as safe levels based on

a range of biological assay tests. The standard is some-

times expressed as a PNEC (predicted no effect

concentration) level. There are uncertainties related tothe interpretation of the biological tests, to the effects of

a mixture of contaminants and to long-term ecological

consequences, but it remains the first-order aim of waterquality models to predict concentrations and make con-

clusions about safety based on these available quality

standards.

The ability of coastal models to predict these concen-

trations is still limited. For example, Stolwijk et al.

(1998) compared five water quality models of the NorthSea, one of the most heavily modelled shelf-sea areas in

the world. It was claimed in this paper that it was the

first time that water quality models of the North Sea hadbeen reviewed and compared with field data. Five sub-stances were selected for comparison: cadmium, PCB-

153, two PAHs (polycyclic aromatic hydrocarbons),

namely fluoranthene and benzo[a]pyrene, and atrazine (apesticide), but only cadmium was common to all fivemodels. These were from BSH (Hamburg),

NORWECOM from IMR (Bergen) (Skogen et al., 1995),

NOSTRADAMUS (Tappin et al., 1997) and SCREMO-

TOX and ZeeBOS-TOX from WL|Delft Hydraulics.

They vary in the processes represented in the pollutant

transport simulations. The BSH model could only rep-

resent passive conservative substances. In

NORWECOM, Cd and atrazine were modelled as dis-

solved passive tracers (neglecting adsorption to particu-late matter). An equilibrium model based on the octanol–water partition coef ficient was used to calculate the dis-tribution of PCB-153 and PAH between the dissolved

and particulate phase. NOSTRADAMUS was run for

metals only (as described in Section 2.3), so results for

Cd only were considered in this comparison. SCREMO-TOX is a model with limited physics, a steady-state

residual flow only, but includes among the chemical pro-cesses adsorption/desorption to inorganic silt and POC

(particulate organic carbon), volatilisation, degradation

and sedimentation/resuspension. ZeeBOS-TOX hasmore physics, from a two-dimensional hydrodynamic

model, while there can be adsorption to POC, DOC

(dissolved organic carbon) and inorganic matter, sedi-


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mentation and resuspension, volatilisation and degra-

dation. Pollutants such as heavy metals can adsorb to

inorganic suspended matter, while others such as organic

micropollutants can adsorb to POC or DOC, calculated

using equilibrium sorption equations involving K d andK poc. The intercomparison, which showed a considerable

deviation of the modelled from the measured values forCd (usually model values were lower), led to the con-

clusion that there was a lack of quality-controlled fielddata to calibrate and validate the models.

This lack of data is likely to limit the testability of

the most sophisticated models, and not only are monitor-

ing data needed for the interior of the model for testing

purposes, but input data are also required to give bound-

ary conditions. In the intercomparison above (Stolwijk

et al., 1998) the substances chosen were some for whichadequate boundary data and field data as well as processknowledge were thought to be available. For other sub-

stances there are even fewer data, and therefore there

is even less chance of accurate predictions, even if the

understanding of their behaviour is good and simulated

well by the models.

3. Ecosystem modelling

An ecosystem may be defined as a connected groupof organisms together with their environment. More

particularly, it involves a natural unit of living and non-

living components that interact to form a system in

which an interchange of materials and energy takes

place. Ecosystem or ecological modelling must describethe interactions between all elements of the ecosystemin either a deterministic or an empirical manner. Despite

some remaining controversy over the effectiveness and

usefulness of the deterministic numerical models (Nuttle,

2000), which follow the time-stepping approach of the

hydrodynamic models but may be much more complex

as shown below, these are the types of model that will

be discussed here.

All ecological models involve some form of simplifi-cation since it is not feasible to include every organismindividually or indeed every species. Many models

aggregate these biological components and abstract them

into functional groups or compartments. For example,

all phytoplankton may be considered together and within

this group associated state variables such as carbon and

nitrogen may be defined. These functional groups rep-resent the main functional roles of production (e.g.

phytoplankton), consumption (e.g. zooplankton, fish)and decomposition (bacteria). Individual organisms

within a functional group are assumed to be identical

and physiological processes and population dynamicsare described in terms of fluxes of carbon and nutrientsbetween functional groups and between organic and

inorganic material. Functional groups may be subdivided

into size classes to create a food web. A review of func-

tional group models may be found in Totterdell (1993).

However, the functional group models have limitations

when it comes to representing the larger, long-lived

organisms in the higher trophic levels. For example,biomass increase here may be by growth of individuals

rather than by increased numbers of identically sizedorganisms. Other approaches such as structured popu-

lation models and individual-based models can then be

used. Structured population models are appropriate forconsidering cohorts of particular species with multi-stage

development, and can be coupled with spatially resolved

models (e.g. Bryant et al., 1997). Individual-based mod-

els track individuals through time and consider their

interaction with the environment. Although this tech-

nique has been used with the larger animals such as wad-ing birds (Wolff, 1994), a similarly Lagrangian approach

has been applied to plankton (Woods and Barkmann,

1994). Multi-species models may be constructed from a

combination of hydrodynamic, functional group, struc-

tured population and individual-based models.

Functional group models are commonly used to simu-

late phytoplankton and nutrient cycling. Phytoplankton,

which is responsible for most marine primary pro-

ductivity, consists of microscopic floating plants (algae)and bacteria (cyanobacteria, or blue-green algae) which

by photosynthesis use sunlight to convert dissolved inor-

ganic substances to organic material: in a simplified formthis is represented by

6CO2 6H2O→C6H12O6 6O2 (2)

This process also requires nutrients: these are mainlynitrogen, as the ions nitrate (NO3 ), nitrite (NO

2 ) orammonium (NH 4 ), phosphorus, as phosphate (PO

4 ),

and silicate (SiO2). If any of these nutrients is not avail-

able, growth of phytoplankton may be limited. The

larger phytoplankton, which may be captured in nets,

occur mainly in two groups: diatoms, which are silicate-

dependent and are often the dominant type in temperate

and high latitudes, and dinoflagellates. However, thesmaller phytoplankton below 20 µm in size, namely nan-oplankton (2 to 20 µm) and picoplankton (0.2 to 2 µm),make a considerable contribution to total photosynthesis.

Zooplankton are the small drifting animals which feed

on phytoplankton and other animals. Copepods are often

the dominant larger zooplankton. The zooplankton in

turn provide food for larger animals such as fish, andalso break down some of the organic material into itsinorganic components: this process is known as reminer-

alisation. Detritus consists of both inorganic and non-

living organic particles resulting from excretion and

death of plankton, and tends to sink to the sea bed. The

“microbial loop” describes the process by which dis-solved organic matter is scavenged by bacteria, which

are then grazed by single-celled animals, which provide

food for larger zooplankton. This can be an important


10/23


part of the food chain in terms of energy transfer in cer-

tain circumstances. The small zooplankton also consume

the small phytoplankton, extending the microbial loop

to the “microbial food web”.The complexity of the biological system means that

there is less consensus on the basic equations describing

it than for the physical system. Models have been con-structed with varying levels of detail. One of the simplest

is the early model of Riley (1946), in which phytoplank-

ton biomass is represented by a single variable P, andits rate of change is given by

dP / dt P(Ph RG), (3)

where Ph is photosynthetic rate, R is respiration and G

is grazing by zooplankton. Quantities determining the

value of terms on the right-hand side, such as nutrient(phosphate), temperature, depth of mixed layer, trans-

parency and quantity of zooplankton, were given (as

monthly means). P, as given by the above equation, was

then found to agree well with the observed population.

Fasham et al. (1990), in a model of the oceanic mixed

layer, extended this concept from the one variable P to

seven compartments (phytoplankton, zooplankton, bac-

teria, nitrate, ammonium, dissolved organic nitrogen and

detritus), each of which has an ordinary differential equ-ation giving its rate of change. The right-hand sides of

the equations include intercompartmental exchanges.

In the shelf seas, a key component of ecological mod-

elling has been the linking with physical models. As dis-

cussed above in connection with tracers, the relative

importance of diffusion, horizontal advection and local

forcing can vary with the location and scales of the pro-cesses concerned. In areas where advection is relativelyunimportant but local sources — for example, resuspen-sion of material that may contain nutrients from the sea

bed — have a major influence, a one-dimensional modelsuch as SEDBIOL (Smith and Tett, 2000) can reproduce

seasonal cycles and give estimates of annual production.

This model includes a Mellor and Yamada level 2 turbu-

lence closure scheme to determine values of vertical

eddy diffusivity and it also includes a sediment resus-

pension model that takes particles from a finite “fluff layer” on top of the sea bed. It has eight state variablesin the biological sub-model; microplankton carbon and

nitrogen, detrital carbon and nitrogen, concentrations of

dissolved nitrate, ammonium and oxygen, and zooplank-

ton nitrogen. Each of these has source and sink terms

that are added to the advection–diffusion equation foreach variable (the advection in the one-dimensional

model being entirely due to fall velocity). Chlorophyll

is derived from microplankton carbon and nitrogen so is

not a state variable. Physical driving terms include solar

radiation, tidal pressure gradients and wind stress.Other one-dimensional models have had some success

in reproducing primary production in areas such as the

central North Sea (Radach and Moll, 1993; but this is

based on an upper-layer model that does not include tidal

stirring, and also has a single nutrient, phosphate). How-

ever, a three-dimensional model is necessary where hori-

zontal advection is significant and inputs are non-local,for example where nutrients are introduced by river run-off. Several of the biological models have now been

linked to three-dimensional hydrodynamic models, or atleast have included estimates of horizontal transports,

with horizontal resolution of varying scales. The SED-

BIOL model has been linked with the Belgian MUROFIshelf-sea model (described in Ruddick et al., 1995) to

form COHERENS (Luyten et al., 2000). A development

of the Radach and Moll (1993) model has been com-

bined with the Hamburg three-dimensional model

(Pohlmann, 1996; Moll 1997, 1998; Skogen and Moll,

2000) to form ECOHAM1. The Princeton Ocean Model(POM; Blumberg and Mellor, 1987) provides the physi-

cal module for NORWECOM (the Norwegian Ecologi-

cal Model System), described by Skogen et al. (1995).

The biological module in NORWECOM contains as

prognostic variables inorganic nitrogen, phosphorus and

silicate, two types of phytoplankton (diatoms and

flagellates) and detritus, as well as light and turbidity.These biological modules all contain considerable

simplifications, and the choices clearly differ; severalhave just one type of phytoplankton and some have just

one nutrient. A deliberately more complex ecosystem

model in terms of numbers of variables is ERSEM (the

European Regional Seas Ecosystem Model), which

attempts to include all significant processes necessary toproduce a realistic representation of the cycling of car-

bon and nutrients in the European shelf seas (Baretta etal., 1995). ERSEM includes several kinds of phytoplank-

ton, a microbial loop and explicit mesozooplankton. It

incorporates a benthic submodel, which describes the

complex processes within the seabed including bioturb-ation: these have an important effect on the exchange

of nutrients between the sea bed and the water column.

Benthic processes are of course also important for con-

taminants, but this was not the focus for ERSEM. The

EU-funded ERSEM programme ran in two parts:

ERSEM-I from 1990 to 1993 (Baretta-Bekker, 1995) andERSEM-II, which included many detail developments,

from 1993 to 1996 (Baretta-Bekker and Baretta, 1997).

In ERSEM-I the model had been applied to a very

coarse box model of the North Sea. In the horizontal,

these were the ICES boxes (10 covered the whole North

Sea) and in the vertical there was either one box or two,

where thermal stratification occurs, making 15 boxes inall. Transport between boxes was estimated from the

Hamburg three-dimensional circulation model (Lenhart

et al., 1995). The reason for such a coarse box approach

was the complexity of the biological model combinedwith the limitations of computer power at the time. A

few years later, in ERSEM-II, the North Sea model had

been refined to 130 boxes, the horizontal resolution


11/23


being 1° × 1°. It had also been applied to a 4.5 km resol-ution grid, with hydrodynamics from a two-dimensional

model, around the Humber estuary, with 359 biologi-

cally active cells (Allen, 1997).

The enormous computational demand of a biologicalmodel such as ERSEM, in comparison with the hydrody-

namic model alone (there are some 100 extra variables,around 30 to 40 of which need to be advected and

diffused), requires the power of a massively parallel

computing system if it is to be run with the resolutionin both space and time of a typical three-dimensional

shelf-sea physical model. This has now been achieved

in the coupling of ERSEM with the POL3DB model

(Allen et al., 2002). This hydrodynamic model is

described by Holt and James (2001), and includes s-

coordinates in the vertical, to maintain a resolved uppermixed layer across the shelf edge in a terrain-following

coordinate system, and an advanced piecewise parabolic

advection scheme (see Section 4). Despite the compu-

tational demands of using this scheme with many vari-

ables, the performance of parallel systems means that

the calculation of annual cycles in three dimensions with

ERSEM on a shelf-wide grid with 12 km horizontal res-

olution and 20 levels in the vertical is readily achieved,

and higher resolutions are feasible. The parallel schemeis based on domain decomposition in the horizontal, with

the use of the MPI (Message Passing Interface) standard

for communication between processors (Proctor et al.,

1999). The POL3DB model has been developed with the

assistance of funding from the UK Met. Of fice, and anearlier version is running operationally there (from June

2000), so in principle the physical variables for thecoupled model are available operationally. All of theelements for an operational shelf-wide ecosystem model

would be present if the necessary inputs and boundary

conditions for the ecological variables were also avail-

able in real time.

As the resolution of models increases and they

become eddy-resolving, they will be able to address

problems such as the observed patchiness of phytoplank-

ton (Powell and Okubo, 1994; Abraham, 1998). The res-

olution required for an eddy-resolving model in shelf seas is the order of 1 km or better (see Section 4).

As was remarked in the previous section, the ecologi-

cal models have not generally included any direct effect

of contaminants such as oil or toxic chemicals. However,

an important aspect of water quality they have been used

to study is that of eutrophication, the effect of excessnutrient supply, which may come from sewage outflowor agricultural fertilisers in river run-off. The resulting

excess plant and phytoplankton growth is followed by

decay, in which bacteria use dissolved oxygen in the

water. These bacteria also decompose organic matter thatmay be in the original outflow; sewage is a particularlylarge source of this in coastal and estuarine waters. The

capacity of a volume of water to consume oxygen is

known as its biological oxygen demand (BOD). If this

is too high, oxygen will be depleted and animals includ-

ing fish will die. The concentration of dissolved oxygen(DO) is often taken as a key measure of the health of

the aquatic ecosystem. For example, measurements of DO show the considerable recent improvements in the

water quality of the Mersey estuary, a large part of thisbeing a result of the ending of untreated sewage out-

flows: the BOD load has been reduced from over 300t/day in 1972 to around 50 t/day in 2000 (Jones, 2000).

One of the main challenges for an operational ecosys-

tem model would be to predict the timing and extent of

blooms of plankton, not only the normal spring and aut-

umn blooms but also those due to an excess of nutrients,

which may result in rapidly growing toxic algal blooms

and “red tides”. Hindcasts of the spring bloom have beensuccessfully demonstrated in models (Ruardij et al.,

1997; Allen et al., 1998). At a longer time scale, one of

the uses of the model would be to predict the improve-

ment in water quality to be expected by a reduction in

discharges. This would involve running the model to

give an “environmental assessment”, in which thedetailed meteorological input is unimportant, rather than

to give a prediction of conditions over the next few days.

This type of assessment has been made with several eco-logical models, for example scenarios of the effect on

the North Sea of reductions in the nutrient transport in

rivers, using ERSEM (Lenhart et al., 1997).

ERSEM has also been used in models of fish popu-lations in combination with structured population mod-

els, including a larval stage. Fish are predators for zoo-

plankton and zoobenthos, while fish excretion andmortality can be returned to ERSEM from the fish modelas dissolved and particulate organic matter (Bryant et al.,

1995; Heath et al., 1997). Humans of course enter the

picture here as predators for fish as well as producers of sewage and contaminants. Such models can be a step

towards an ecological modelling approach to fisheriesmanagement which includes the potential impact of the

physical environment on fish populations. This com-plexity goes well beyond that of traditional fishery mod-els (for example, Beverton and Holt, 1957) and couldform the basis of more accurate predictions to guide

fisheries policy in the future.The complexity of biological models with their many

variables and parameters raises the question of how they

may be compared with measurements and hence vali-

dated and improved. Some data sets for a selection of

variables are obtainable from individual experiments and

more extensively for relatively well-monitored seas; for

example, climatological cycles of nutrients and chloro-

phyll in the North Sea (Radach and Pätsch, 1997). These

data sets can be used for a straightforward comparisonwith model data (for example, Moll, 1998). But it is not

always clear whether a poor fit with data is due to themodel structure or to the selection of model parameters,


12/23


as pointed out by Vallino (2000), and as we have noted

above there are many models with somewhat different

structures aimed at describing the same phenomenon,

such as phytoplankton growth, and it would be useful to

have some way of deciding which is superior. Vallino(2000) describes the use of mesocosm experiments and

data assimilation for parameter estimation. A mesocosmis an enclosed experimental ecosystem which, being

generally “well-mixed”, can reduce the number of dimensions to that of time only, allows controlledexperiments to explore several regions of state space,

and allows intensive sampling. If parameter uncertainty

can be reduced, then model comparisons can concentrate

on differences in structure. However, model results may

still lack robustness through sensitivity to parameter

values, which may not in reality be constant. Mesocosmscannot include all of the processes found in the open

sea, where there is a need for comprehensive data sets

including estimates of fluxes across the open systemboundaries. If such a data set were available, data assimi-

lation may be able to determine whether the model is

able to fit it well by adjustment of parameters, and if notit may be concluded that there is some structural

deficiency in the model. Spitz et al. (1998) applied dataassimilation to the Fasham et al. (1990) mixed layermodel and concluded in this way that some of the

assumptions needed to be carefully reconsidered. In most

circumstances, though, the use of data assimilation will

be limited by the availability of data.

4. Physical modelling

As stated in the Introduction, a good representation of

the physics is the necessary basis for a water quality

model. Physical modelling will not be reviewed compre-

hensively here; an overview of coastal models may be

found in Greatbatch and Mellor (1999). We concentrate

first on the modelling of diffusion and dispersion andthen outline some further topics that are important for a

physical model underpinning a water quality model.

4.1. Diffusion and dispersion

While present physical models may be expected to

give reasonable results for sea level, currents, tempera-

ture and salinity at medium (10 km) resolution, given

good boundary forcing information, it is not completelyclear that they are able to predict accurately the disper-

sion of pollutants. One of the main reasons for this is the

central importance of the advection–diffusion equation,which involves turbulence, which is generally unre-

solved in these models and remains a challenging prob-lem in itself. So we review here the physical processes

of dispersion of material in the sea and the ability of

present models to reproduce them. It was noted in Sec-

tion 2 that diffusivity on a molecular scale, which will

always be unresolved by the models, is very much less

than the effective diffusivity in a turbulent flow on themodel grid scale but that the use of an effective “eddydiffusivity” implies neglect of the details of the stirringdue to turbulence, which is ultimately followed by mol-

ecular diffusion.

4.1.1. Vertical diffusivity

In the coastal ocean, the disparity between horizontaland vertical scales means that horizontal and vertical dif-

fusion are usually considered separately and have very

different values. There is an extensive literature on the

parameterisation of vertical eddy viscosity and diffusiv-

ity, reviewed by Davies et al. (1995), and this will not

be covered again in detail here. Most shelf-sea modelsuse some form of turbulence closure scheme, whether

based on equations for turbulence energy and dissipation

(k , ) or for turbulence energy q2 2k and q2l, where l

is a length scale known as the mixing length, to deter-

mine vertical eddy viscosity and diffusivity. Many mod-

els use a turbulence energy equation but have an

algebraic form for mixing length. Some ocean models,

however, involve “large eddy simulation” (LES), inwhich there is suf ficient resolution to include explicitlythe most energetic turbulent eddies: this implies a verti-

cal and horizontal resolution of the order of metres in

the upper ocean (Large and Gent, 1999; Wang, 2001)

but still requires parameterisation of the effect of smaller

eddies, and the resolution needed is prohibitive for wide-

area models. This approach has been very useful for the

study of Langmuir circulation and convection cells, bothof which are neglected in the usual turbulence energyapproach and which may be strong generators of mixing

in the surface layers (Skyllingstad and Denbo, 1995;

Wang et al., 1998).

The LES models do not indicate a simple parameteris-

ation of Langmuir circulation or convection, which,

together with the effects of internal waves, can explain

some of the shortcomings of the turbulence energy clos-

ure schemes particularly in stratified flow. In the mostcommonly used schemes, vertical diffusivity oftendefaults to an arbitrary minimum value in a strongly

stratified region such as the thermocline, which thendetermines cross-thermocline exchange. Convection

caused by surface cooling, when handled by instan-

taneous stabilisation of unstable density profiles or bylarge values of mixing given directly by the turbulenceenergy schemes, is still not always enough to explain

observed deepening of the surface mixed layer. Wind

waves also introduce effects that are not explicitly

included in the turbulence energy equations, whether

through wave breaking and wave-induced shear in theupper layers (Craig and Banner, 1994) or additional

wave-induced bed stress in shallow water (Grant and

Madsen, 1979). Internal waves induce additional mixing


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both by increasing shear across the thermocline (as do

inertial currents, but they may be resolved by the model)

and by breaking (Woods, 1968; Thorpe, 1994).

Models have problems in satisfactorily reproducing

mixing due to these processes, which are unresolved onthe model grid and are dif ficult to parameterise. Mellor

(1989) suggested an extra term in the turbulent energyequation to account for the extra shear due to long

internal waves, but this does not account for the breaking

of short internal waves. Burchard et al. (1998) show thatboth the k – and the q2–q2l models require modificationthrough the inclusion of an internal wave parameteris-

ation to predict correctly the observed levels of turbulent

dissipation: this was done through setting a minimum

value of k and also applying a limiting condition to

(or l). Kantha and Clayson (1994) use results from LESsimulations to try to improve terms in the Mellor–Yam-ada closure scheme, applied to the surface mixed layer,

while Large and Gent (1999) use LES and observations

to validate vertical mixing in an equatorial ocean model.

4.1.2. Lateral dispersion

Mixing in the vertical is not entirely detached from

mixing in the horizontal; in fact there are at least two

ways in which lateral dispersion is determined by verti-cal mixing. One is boundary mixing in the deep ocean,

the other is shear dispersion, which is particularly effec-

tive in shelf seas with strong currents, including tidal

currents. Boundary mixing in the ocean, reviewed by

Garrett et al. (1993), refers to mixing near the sloping

sea bed, at continental slopes or on shelves, which pro-

duces water that can spread preferentially along iso-pycnals into deeper water. This has been suggested(Munk, 1966) as a source of the mixing required to

explain the overall heat balance in ocean basins. This

paper has been updated by Munk and Wunsch (1998),

who propose that the mixing required to maintain the

abyssal stratification against global upwelling associatedwith deep water formation is concentrated in only a

small portion of the oceans, and is driven mainly by

wind and tides.

Dispersion from the shelf or slope into the deep oceanmay take place along isopycnal surfaces once mixing on

the shelf or in the boundary layer on the slope has

occurred, so it is determined by this mixing. It may

firstly include cascading down the slope for shelf waterthat is denser than oceanic water at the same depth. Gent

and McWilliams (1990) introduced a parameterisation of eddy-induced isopycnal mixing that can be used in non-

eddy-resolving ocean models. Diapycnal (cross-

isopycnal) mixing in the deep ocean is relatively

inhibited by buoyancy forces and low levels of turbu-

lence away from the surface and sea bed. This behaviouris a challenge to ocean models in which the vertical

coordinate is not based on isopycnals (as it is in the

MICOM model: Paiva et al., 1999 describe a recent

eddy-resolving application of this isopycnal coordinate

model to the North Atlantic) but on horizontal surfaces

( z-levels) or terrain-following systems (s - or s-coordinates). Then the numerical scheme may introduce

false diapycnal mixing because of its tendency to mixin the horizontal or along coordinate surfaces rather than

along isopycnals. In s -coordinates, where the coordinatesurfaces are not horizontal, an imposed horizontal diffu-

sivity may induce spurious vertical diffusivity (Mellor

and Blumberg, 1985; Stelling and van Kester, 1994), buteven if the numerical formulation is suitable for bottom

boundary layers and minimises artificial vertical dif-fusion, a truly horizontal diffusivity in the ocean interior

will still give incorrect diapycnal mixing. However, on

the shelf the advantages of isopycnal coordinates are no

longer evident because of the prevalence of tide- andwind-mixed layers and the large areas of vertically well-

mixed water.

Shear dispersion, which we have met before in Sec-

tion 2.4, occurs when vertical diffusion and a vertical

shear in the horizontal current occur together: it is there-

fore significant in the shelf seas, where there may bestrong, vertically sheared, wind-driven and tidal currents.

An initially vertical column of any substance is stretched

horizontally by the shear in the currents; vertical mixingwill then have the net effect of distributing this substance

over a wider region horizontally, which is a similar

effect to horizontal diffusion, except that it occurs in the

current direction (Bowden 1965, 1983). This occurs in

an oscillatory tidal flow as well as in a steady current.Shear dispersion would occur in a three-dimensional

model even with no imposed horizontal diffusivity, butwould not be reproduced in a two-dimensional model,which of course includes no effects of vertical shear. A

two-dimensional model would need an imposed dif-

fusion coef ficient to achieve the same result. The effectcan be increased by horizontal shear in the currents,

which strains the initial distribution further.

In this view of shear dispersion, horizontal currents

stretch or distort an initial patch of material by advec-

tion, while mixing is taken to occur by vertical diffusion.

This is an example of stirring increasing the rate of mix-ing, just as turbulent eddies themselves stir a substance

into thin sheets and filaments with a large surface areaover which molecular diffusivity can act effectively.

Classical results on dispersion were obtained by Rich-

ardson (1926), who proposed that the coef ficient of eddydiffusion should increase with length scale l as l4/3, fromobservations in the atmosphere. This was deduced from

the rate of increase of distance between balloons. Itagrees with Kolmogorov’s (1941) theory for the inertialrange of three-dimensional turbulence, in which kinetic

energy is transferred in a cascade from larger to smallerscales, eventually to be dissipated at the smallest scales,

in the viscous range. If the rate of dissipation is and

wavenumber is k , this leads to a power spectrum


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E (k ) 2/ 3k 5/ 3, and if a pair of particles is released a

distance l apart, the rate of increase of the square of their

distance apart varies as 1/ 3l4 /3. Richardson and Stommel

(1948), in a paper beginning “We have observed therelative motion of two floating pieces of parsnip”, sug-gested the 4/3 law of diffusivity applies also to horizon-

tal diffusion in the sea. Applied to a patch of materialreleased at r 0 at time t 0 and spreading in the hori-

zontal plane, an eddy diffusivity proportional to r 4/3 leads

to a variance of the distribution varying as t 3 and a cen-

tral concentration at r 0 varying as t 3: a constant

diffusivity would lead to a variance t and a central con-

centration t 1, while a diffusivity r would lead to

variance t 2 and central concentration t 2 (Bowden,

1983). Some support for diffusivity obeying a power law

of 4/3, or near this value, is given by results from the

spreading of dye patches (Okubo 1971, 1974). However,

the apparent power law is affected by energy being put

in at intermediate scales, equivalent to a variation of .Also, Zimmerman (1986) rejects the possibility of a

5/3 power law for the energy density in a shallow tidal

sea in the interval between 10 m (a scale set by the water

depth) and 10 km (a scale set by tidal excursion), in

which any real turbulence should be quasi-two-dimen-

sional (see Section 4.1.3). In this range and in these con-

ditions, vertical and then horizontal shear dispersion

should take over to spread a dye patch.

Both advection and diffusion can cause particles that

were initially close together to separate; however, advec-

tion is in principle reversible by reversing the velocity

field, but diffusion is not. Advection by eddies wouldcause a patch of red dye to be sheared into thin red

streaks, while diffusion would result in a pink patch of

dyed water. The streakiness of a dispersing tracer in both

two- and three-dimensional turbulence is discussed by

Garrett (1983). In comparison with the deep ocean,

streakiness may be reduced in many areas of tidally

mixed shelf seas because of the magnitude of shear dis-

persion.

The difference between advective stirring by eddies

and diffusion may be significant for some polluting sub-stances that do not mix well with water. In Section 2.4

on oil spills, it was noted that horizontal diffusion was

generally modelled by a random walk procedure appliedto particle tracking, which simulates the spreading of

particles while mixing with the water is not necessarily

implied. For a pollutant, the maximum concentration

may be important, and this is much higher within a

streak than in a diffused patch. If a model is based on

the concentration equations and so is unable to cover

scales smaller than the grid scale, the model concen-

tration is the mean over a grid box, even if in reality

complete mixing over that volume has not occurred, and

the maximum concentration in streaks will not be repro-

duced. This is an example of artificial diffusion intro-

duced by the numerical method; more on this topic is

discussed below in Section 4.1.5.

4.1.3. Quasi-two-dimensional turbulence

As eddy scales become larger, in comparison with thewater depth or a stratification scale, the turbulence

becomes more two-dimensional. Because of the additionof another constraint, the conservation of enstrophy (half

squared vorticity), two-dimensional turbulence behaves

in a quite different way from three-dimensional turbu-

lence. As shown by Kraichnan (1967), if turbulence is

forced at a certain wavenumber, there will be an inverse

energy cascade to larger scales, or smaller wavenumber

k , in which E k 5 /3 as for the three-dimensional spec-trum, and an enstrophy cascade to larger k , in which

E k 3. In the case of freely decaying two-dimensional

turbulence the inverse cascade means that an initially

disordered flow becomes more ordered, into larger-scalecoherent vortex structures, that can be very stable. These

were modelled by McWilliams (1984). Similar results to

those for strictly two-dimensional turbulence are

obtained for geophysical flows: both rotation and strati-fication can make the flow more two-dimensional incharacter. A consequence of the behaviour of geos-

trophic turbulence, i.e. turbulence in fluids that are nearto geostrophic and hydrostatic balance (Rhines, 1979),

and therefore typical of geophysical fluids, is the preva-lence of long-lived mesoscale eddy motion in the deep

ocean and the smaller-scale eddies in the stratifiedshelf seas.

Laboratory experiments by Linden et al. (1995) dem-

onstrate the inverse energy cascade in a rotating stratifiedfluid forced by an array of sources and sinks. The Rossbydeformation radius, which for the lowest baroclinic

mode is RD NH / f , where N is the buoyancy fre-

quency, H the depth and f the Coriolis parameter, is a

key length scale: when this scale exceeds the size of the

tank the inverse cascade is seen to occur, but for smaller

values of RD baroclinic instability acts to reduce the size

of any flow structures that form on a scale larger than RD. The inverse energy cascade is therefore modified bya cascade to smaller scale due to baroclinic instability.This result was also found by Grif fiths and Hopfinger(1984) in a laboratory experiment on turbulence gener-

ated by the instability of a front in a two-layer rotating

fluid. Narimousa et al. (1991) also show baroclinic insta-bility at a front in a laboratory experiment and conclude

from the energy spectra that the dynamics is that of

quasi-two-dimensional turbulence, forced at the scale of

the most unstable frontal eddies. Numerical experiments

by Cushman-Roisin and Tang (1990) and Tang andCushman-Roisin (1992) were conducted in a reduced-

gravity model, for which RD (gh)1/ 2 / f , where g is

the reduced gravity and h the layer depth, and in a two-

layer model, for which RD (gh)1 /2 / f , where g

g( r2 r1) / r2 and h h1h2 / (h1 h2), where upper-


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and lower-layer depth and density are h1, r1 and h2, r2respectively. They show in the reduced-gravity model,

for flow evolving from scales smaller than RD, that theinverse energy cascade towards larger scales can halt at a

statistical equilibrium beyond RD, while energy at scaleslarger than RD cascades to smaller scales and halts at a

scale just greater than RD. In the two-layer model, similarresults are obtained for flow evolving from

Modeling Pollution Dispersi

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