Ocean Mo delling and Prediction

Matthew H England and Peter R Oke

Intro duction

The o cean plays a vital role in our environment As such an ability to mo del

and predict its circulation can b e of enormous value Mo delling and pre

diction of o cean currents in coastal regions is imp ortant for many reasons

including inuences on recreation navigation algal blo om formation euent

disp ersion search and rescue op erations and oil spills Ocean currents near

the coast also aect b each conditions that impact up on the nearshore zone

Severe wave climates and storm surges can cause enormous destruction of the

built environment At larger scales vast o cean currents carry heat around the

glob e aecting climate and weather patterns such as those asso ciated with

the ElNino event and the North Atlantic Oscillation The o ceans also have a

vast capacity to absorb and redistribute gases such as carb on dioxide They

will therefore play a crucial role in determining our future climate

To understand and predict the way the o cean aects our environment a

numb er of o cean mo dels have b een develop ed during the past half century

Some are computationally simple and predict a limited numb er of o ceanic

variables such as tidal mo dels or a wave climate mo del Others such as

primitive equation o cean general circulation mo dels OGCMs are compu

tationally exp ensive and solve several equations in order to predict three

dimensional o cean currents and temp eraturesalinity T S In this chapter

we describ e the stateoftheart in o cean mo delling

What Is an Ocean Mo del

The Worlds o ceans can b e viewed as a turbulent stratied uid on a rotating

sphere with a multiplyconnected domain and an uneven b ottom bathymetry

More simply the rotating earth has an o cean system divided by land masses

and with varying water density and o cean depth The external forcing of

the o cean o ccurs through the mechanical forcing of the winds the socalled

thermohaline forcing via heat and freshwater uxes across the airsea in

terface and through planetary forces manifest in tides An o cean mo del is

Ocean Mo delling and Prediction

simply a computational solution to this problem using physical conservation

laws for mass momentum heat and so on and some estimation of the forc

ing elds the computer mo del predicts o cean currents and other prop erties

such as temp erature salinity and optionally chemical tracers or biological

parameters

Mean Largescale Ocean Circulation

The global scale o cean circulation can b e viewed in a numb er of ways In

the horizontal plane mean circulation is dominated in the upp er o cean by

winddriven ow Figure shows surface mean wind stress over the o ceans

and the upp er o cean circulation pattern Largescale gyres dominate at mid

latitudes with intensied western b oundary currents WBCs due to the

Earths rotation carrying tropical heat p oleward At the tropics easterly

trade winds and the doldrums drive a tropical currentcounter current sys

tem for more details see Tomczak and Go dfrey At higher latitudes

thermohaline circulation is manifest in the surface ow for example the

North Atlantic Current extends into the GreenlandNorwegian Sea to feed

North Atlantic Deep Water formation In the Southern Ocean a latitude

band free of continental land masses p ermits the eastward owing Antarctic

Circump olar Current ACC to circle the glob e

In the meridional plane a completely dierent view of the o cean circulation

is obtained Fig Water masses of dierent density classes ventilate the

interior of the o cean in a complex manner Around Antarctica dense b ottom

water is formed over the continental shelf by salt rejection during seaice

formation and wintertime co oling Further north Circump olar Deep Water

CDW is upwelled under the subp olar westerlies owing either northward

to form intermediate and mo de waters after the addition of freshwater via

precipitation or seaice melt or southward towards the Antarctic continent

In the Northern Hemisphere a saltier North Atlantic accommo dates deep

water pro duction whereas the North Pacic remains to o fresh to see deep

water convection The water masses formed in the World Ocean subsequently

recirculate and are either consumed by diapycnal mixing or when they

resurface in the upp er mixed layer In b oth cases T S prop erties are altered

or reset and the watermass is converted

Oceanic Variability

The dominant picture of o cean circulation at the largescale was one of steady

ow until drifting buoy technologies in the s revealed variability of ow

patterns at rather small spatial scales Nearshore variability was long known

to exist and was thought to b e controlled by uctuations in tidal ows and

lo cal winds At the largescale o ceanic variability is evident in phenomena

such as ElNino and the Antarctic Circump olar Wave as well as in western

Intro duction

Fig a Surface mean wind stress over the o ceans from Barnier and

b Schematic of upp er o cean circulation patterns from Thurman

b oundary current ow pathways In addition o ceanic eddies of size km

are seen near intense surface currents eg the ACC and WBCs and near the

Equator and play a key role in transp orting climate prop erties around the

glob e Figure shows the kinetic energy sp ectrum estimated for the o cean

and atmosphere as a function of horizontal wavenumb er revealing substantial

o ceanic energy at the length scale of these mesoscale eddies Unfortunately

most present day coupled climate mo dels do not resolve these scales of mo

Ocean Mo delling and Prediction

Fig Meridional latitudedepth o cean circulation schematics for the Pacic and

Atlantic Oceans from Thurman AAIW refers to Antarctic Intermediate

Water NPIW to North Pacic Intermediate Water and ANC to the Antarctic

Convergence

Intro duction

tion as computational requirements are to o high at subeddy scale resolutions

These mo dels adopt largescale eddy parameterisations to p ermit reasonable

mo del integration times Coastal or regional mo dels as well as global simula

tions over shorter integration p erio ds can resolve mesoscale eddy variability

see eg Semtner and Chervin Webb et al

Fig Kinetic energy sp ectrum estimated for the o cean and atmosphere as a

function of horizontal wavenumb er after Wo o ds

The Oceans Climate and Forcing

The o ceans play a vital role in the global climate system via their capacity

to absorb heat in certain lo cations transp ort this heat vast distances then

release some of it back to the atmosphere at a later time This is depicted

in Fig which shows the global mean transp ort of heat by the o ceans

This pattern of heat transp ort reects the eects of western b oundary cur

rents carrying warm water p oleward as well as the net ux of heat towards

deep water formation sites particularly NADW The o cean exhibits variabil

ity on a range of spacetime scales and some of this variability is at a large

Ocean Mo delling and Prediction

enough spatial scale to aect global weather systems For example the El

NinoSouthern Oscillation ENSO involves a massive redistribution of heat

in the tropical Pacic Ocean via anomalous surface circulation patterns see

Philander for details In the Southern Ocean the Antarctic Circum

p olar Wave ACW advects heat anomalies around the glob e aecting wind

patterns pressure systems and seaice extent Ocean mo delling for climate

studies has arisen from the need to understand and predict the way o cean

circulation can vary and aect weatherclimate Given that the o cean circu

lation is determined by b oth wind and thermohaline factors o cean climate

mo dels generally include b oth these forces whilst neglecting high frequency

waves such as tides and swell

Fig Global mean transp ort of heat by the o ceans from Mathieu using

observations of da Silva et al

Coastal o cean currents are aected by a numb er of dierent factors includ

ing winds surface heating buoyancy eects tides deep o cean forcing eg

WBCs and coastal trapp ed waves CTWs The time scales on which many of

these factors vary are from weatherband days to seasonal scales Winds

tend to b e the most dominant force lo cally aecting o cean currents temp er

ature and salinity through upwellingdownwelling and sealevel Buoyancy

eects often b ecome imp ortant in resp onse to winddriven events through

geostrophic adjustment in the presence of river outows or in regions where

a signicant amount of heat is gained or lost at the o cean surface In many

A Brief History of Ocean Mo delling

coastal regions tides are imp ortant eg the North West Australian shelf

Holloway and in others deep o cean forcing is predominant eg o

eastern Australia Oke and Middleton Mo delling the coastal o cean

is therefore a challenging task and consideration of what factors are most

imp ortant for any particular region is necessary in order to adequately repre

sent the true variability of the coastal o cean At smaller scales such as ows

in harb ours or bays circulation patterns are often dominated by tidal ows

so their mo delling can b e simplied somewhat

A Brief History of Ocean Mo delling

A numb er of simple analytic and linear vorticity mo dels of the basinscale

o cean circulation were develop ed prior to the proliferation of computing ma

chines including the socalled Sverdrup mo del of winddriven ow Welander

the StommelArons mo del of abyssal circulation Stommel and Arons

and Wyrtkis simple mo del of thermal overturning circulation

For a review of these early analytic mo delling eorts the reader is referred to

Weaver and Hughes Similarly analytic mo dels of winddriven coastal

jets Allen continental shelf waves Allen and stratied ows

over sloping top ography Chapman and Lentz have given mo dellers

great insight into the dynamics of coastal o cean ows

The rst real progress towards a primitive euqation o cean circulation

mo del came with the work of Kirk Bryan and Michael Cox in the s

Bryan and Cox in pioneering work towards a coupled climate

mo del They develop ed a mo del of o cean circulation carrying variable T S

and therefore density based up on the conservation equations for mass mo

mentum heat and moisture and the equation of state It is not surprising

this work was completed at an institution where atmospheric mo delling was

already wellestablished the GFDL as the o cean and atmosphere have a

numb er of similarities and their mo delling requires many analogous tech

niques BryanCox assumed the o cean had negligible variations in sealevel

ie the rigidlid approximation so that highfrequency gravity waves are

ignored in the mo del formulation and the depthaveraged comp onent of ve

lo city the barotropic mo de is solved using an iterative technique Their

mo del was congured in a variety of ways a D mo del a D basin mo del

and a full World Ocean mo del Cox

The computational requirements of this early mo del were relatively high

enabling only short integrations from initial conditions and therefore solu

tions that were not in thermo dynamic equilibrium with the mo del forcing

Nevertheless BryanCox achieved global simulations with realistic continen

tal outlines rough b ottom bathymetry prognostic equations for T S an

elimation of high frequency mo des and approximate closure schemes for the

eects of mixing friction and eddies Their work can b e seen as the genesis

of mo dernday o cean mo delling

Ocean Mo delling and Prediction

Since the early eorts of Bryan and Cox a great numb er of o cean mo del

developments have o ccurred for an outstanding review see Gries et al

These include the exploration of dierent grid systems The GFDL

mo del op erates on a Cartesian grid with geop otential ie horizontal lay

ers in the vertical Mo dels have now b een develop ed with terrainfollowing

Haidvogel et al and densitylayer co ordinates Bleck and Boudra

In the horizontal plane mo dels have b een develop ed with curvilinear

co ordinates to follow a lo cal coastline Blumb erg and Mellor

In addition to dierent grid systems a great variety of mo del options have

b een develop ed In mo dels that do not explicitly resolve mesoscale eddies

their eects can b e parameterised in a numb er of ways eg Cox Redi

Gent and McWilliams Gent et al Gries et al

Free surface formulations were also develop ed to enable direct prediction of

the height and pressure of the o cean surface eg Killworth et al

Dukowicz and Smith This enabled direct comparison with satellite

derived data pro ducts as well as eliminating the need to solve the barotropic

streamfunction iteratively which b ecomes costly in higher resolution mo del

domains and when multiple islands are involved

Ocean mo del development has now proliferated due to improved numeri

cal techniques b etter global o cean data sets diversity of mo del applications

and p erhaps most dramatically faster computers with ever increasing pro

cessing capacity

Anatomy of Ocean Mo dels

Governing Physics and Equations

Ocean mo dels are capable of predicting a numb er of variables normally the

three comp onents of velo city u v w temp erature T salinity S and

therefore density They also usually predict either the depthintegrated

transp ort streamfunction or the sealevel pressure These predicted variables

are known as the mo del prognostic variables To build an o cean mo del re

quires a numb er of governing equations in order to solve for the prognostic

variables To have a welldetermined system requires the numb er of equa

tions to b e the same as the numb er of prognostic variables For largescale

or regional coastal o cean mo dels the governing equations are derived from

the conservation laws of mass heat and salt as well as the NavierStokes

equations for ow of uid on a rotating earth Typically mo dellers reduce the

latter to the socalled primitive equations by adopting the Boussinesq and

hydrostatic approximations meaning resp ectively that density variations do

not aect the momentum balance except via the vertical buoyancy force that

is density variations are much less than the total density and that the

buoyancy force is balanced solely by the vertical pressure gradient therefore

Anatomy of Ocean Mo dels

it is assumed that vertical velo cities are small compared to horizontal velo c

ities These assumptions are valid in almost all o ceanic circulation regimes

a notable exception b eing o ceanic convection of unstably stratied waters

discussed later wherein nonhydrostatic ow o ccurs

The primitive equations op erating in o cean mo dels are depicted in the

schematic diagram of Fig which shows how the equations are interrelated

as well as what surface forcing is required see also Sect

ATMOSPHERE

Air-sea heat flux Wind stress Evaporation-Precipitation

Conservation of heat Conservation of Conservation of salt momentum and mass S T u, v, w

OCEAN Equation of state

ρ = ρ (Τ, S, p)

Fig Schematic diagram showing the conservation laws prognostic variables

and airsea prop erty uxes used in o cean mo dels

The mo del equations can b e written in Cartesian co ordinates as follows

Horizontal momentum equations

du p u u u u

f v u v w f v F D

u u

dt t x y z x

p v v v v dv

f u u v w f u F D

v v

dt t x y z y

Hydrostatic approximation

p

g z

Ocean Mo delling and Prediction

Continuity equation

v w u

x y z

Conservation of heat

T T T T dT

u v w F D

T T

dt t x y z

Conservation of salt

S S S S dS

u v w F D

S S

dt t x dy z

where x y z is Cartesian space t is time u v w the three comp onents of

velo city f is the Coriolis parameter the mean o cean density p is pressure

is density g is gravity T is p otential temp erature and S salinity The terms

denoted by F and D represent resp ectively forcing and dissipation terms

discussed b elow The Coriolis parameter f sin where is the angular

velo city of the Earths rotation sec and is latitude T the

p otential temp erature often also denoted as is the temp erature a given

uid element would have if it were moved to a xed reference pressure nor

mally the sea surface This quantity is approximately a conserved prop erty

unlike in situ temp erature Density is a function of p otential temp erature

salinity S and pressure p through the nonlinear Equation of State see Gill

app endix for details

The conguration of an o cean mo del involves solving for u v

w p T and S over a given grid The spatialscale of the grid chosen determines

to what extent various pro cesses are resolved Motion in the o cean o ccurs at

a variety of scales from molecular diusion pro cesses scales of metres

right through to o ceanic gyres scales of metres

Figure shows these pro cesses as a function of spatial extent It turns

out that a signicant comp onent of o ceanic energy resides at the scale of the

external Rossby radius R which is the lengthscale at which rotation eects

are as imp ortant a restoring force on motion as gravitational or buoyancy

eects

p

g hjf j R

where h is the depth of the o cean Oceanic eddies are typically of the scale

of the external Rossby radius R varies from around km at tropical lati

tudes down to km at high latitude Coarse resolution o cean mo dels adopt

spatial grids of increment km well ab ove the Rossby radius of

deformation In such mo dels mesoscale eddy eects must b e parameterized

in some way discussed b elow

Anatomy of Ocean Mo dels

Time scale Unresolved Unresolved Unresolved Spectral window Micro-scale Medial-scaleMeso-scale of coarse OGCMs

1 century GENERAL CIRCULATION

thermohaline circulation 1 year fronts, gyres,

MESOSCALE 1 month EDDIES turbulence quasi-horizontal geostrophic

1 day Inertial Oscillations

Internal 1 hour waves

Mixed layer turbulence

1 min Surface gravity waves 3D molecular Internal Rossby turbulence Radius of deformation 1 sec Length scale R 1 mm 1 m 1 km 1000 km

STRATIFICATION EARTH ROTATION

EFFECTS EFFECTS

Fig Typ es of motion in the o cean as a function of spatial extent from Math

ieu

Mo del Choice of Vertical Co ordinate

Ocean mo dellers adopt a variety of numerical techniques for the treatment

of the vertical co ordinate The three most common vertical schemes used in

largescale o cean mo dels are depicted in Fig The rst one uses geop o

tential or horizontal z levels reducing the observed bathymetry to a series of

steps eg MOM DieCast The second uses isopycnal layers as the vertical

co ordinate system where the layeraveraged velo cities and layerthicknesses

are the dep endent variables eg MICOM The third uses a terrainfollowing

sigmaco ordinate system through the transformation of the water column

depth from z to the b ottom into a uniform depth ranging from to

eg POM SPEM

Each vertical co ordinate system has its own advantages and disadvan

tages The z level mo del is exible in a numb er of applications and lowest

in computational requirements although its grid orientation can result in

excessive diapycnal mixing In addition downslop e plume ows normally re

quire some form of parameterisation to preserve watermass signatures Sim

ilarly upwelling through thin b ottom b oundary layers in coastal regions is

Ocean Mo delling and Prediction

Fig The three most common vertical schemes used in largescale o cean mo dels

a Observed bathymetry b z level mo del top ography c isopycnal layer and

d sigmaco ordinate top ography from DYNAMO

not well resolved by z level mo dels Isopycnal layer mo dels are ideal for sim

ulating watermass spreading and eliminating unphysical diapycnic mixing

although the use of single p otential density values is dynamically inconsis

tent and can lead to errors in high latitude water mass distributions The

sigmaco ordinate with terrainfollowing levels is most likely to realistically

capture b ottom b oundary ows such as b ottom water plumes Its co ordi

nate is ideal for ow dominated by top ographic eects although it can result

in excessive diapycnic mixing near strong top ographic or isopycnal slop es

Sigmaco ordinate mo dels also require strongly smo othed bathymetry or high

horizontal resolution to avoid numerical errors asso ciated with the calculation

of the pressure gradient terms

Subgridscale Pro cesses and Dissipation

Given the enormous range of spatial scales apparent in o cean circulation

pro cesses order all o cean mo dels need to treat subgrid pro cesses to

Anatomy of Ocean Mo dels

some degree For coarse resolution mo dels this includes mesoscale eddies and

their eect on the largescale ow

The dissipation or mixing of momentum in the o cean is required to bal

ance the continual input of mechanical wind energy at the airsea interface

Kinetic energy in the o cean is transferred from largescales to smaller scales

eventually molecular The standard approach to parameterising the mixing

of momentum is to relate the subgridscale dissipation to largescale prop er

ties of the ow via a Fickian equation of the form

u u

A A D

H V u

x x z z

v v

D A A

v H V

y y z z

w

A D

V w

z z

where A A are the horizontalvertical eddy viscosity co ecients resp ec

H V

tively Typically o cean mo dellers adopt values for A A that greatly exceed

H V

their estimated magnitude to avoid numerical instabilities Under a hydro

static assumption as typically used in coastal and larger scale mo dels D is

w

considered negligible compared to g as p er The horizontal viscosity

terms represent a very adho c parameterisation for the exchange of horizontal

momentum from subgrid scales up to the mo del gridscale The term is re

quired to maintain numerical stability as the viscosity approximation acts to

dissipate energy without causing spurious sources of momentum The most

common approach is a Laplacian op erator

An example of a ow and resolutiondep endent parameterization for A

H

is

1

2

u v u v

A C xy

H

x x y y

where C is the Smagorinsky constant typically and x y are the

horizontal grid spacings This formulation determines A as a function of

H

grid resolution and horizontal velo city gradients eg Smagorinsky

For coastal applications with high horizontal resolution A is often set to

H

small constant values eg for x km A m s Allen et al

H

whereas for coarser horizontal resolution A can have magnitudes of

H

the order of to m s

For dierent applications the vertical eddy viscosity A must b e suitably

V

dened in order to adequately mo del factors such as the frictional eects

of the wind on the o cean surface and the frictional drag asso ciated with

ow over the o cean o or Many applications assume that A is constant V

Ocean Mo delling and Prediction

in space and time eg in most coarse global mo dels with A

V

m s Toggweiler et al England Others assume that A do es

V

not change with time but varies over the water column according to some

predened shap e function eg Lentz while still others parameterise

A as a function of the stability of the water column eg Pacanowski and

V

Philander Mellor and Yamada This asp ect of o cean mo delling

remains uncertain since mo dellers are trying to capture the eects of pro cesses

that o ccur on scales of the order of centimetres to metres using vertical grids

that have scales of the order of m

Viscosity pro cesses in the horizontal o ccur on scales of s to s of kilo

metres such as mixing by eddies whereas in the vertical they are dominated

by vertical shear instabilities convective overturning and breaking internal

waves over rough bathymetry This accounts for viscosity co ecient values

with A A This is to ensure numerical stability and given that mo del

H V

simulations are relatively insensitive to this parameter few other approaches

have b een tested An exception is the argument by Holloway that the

o cean in the absence of momentum input from the wind would spin down

not to a state of rest but to a state of higher system entrophy This is b ecause

eddies interacting with b ottom top ography can exert a largescale systematic

force on the mean o cean circulation Under this socalled top ographic stress

parameterisation the horizontal viscosity terms of are rewritten

with u v replaced by u u v v where u v represent the maximum

   

entropy solution velo cities see Holloway Eby and Holloway for

further details

The mixing of scalars such as T S and chemical tracers has received

much attention in recent years The traditional formulation for subgridscale

tracer mixing adopted by Bryan and Cox was of the form

T T T

K K K D

H H V t

x x y y z z

with a similar equation for salinity Here K K are the eddy diusivities

H V

in the horizontalvertical directions Normally K K are taken to b e ei

H V

ther constant or some simple depthdep endent prole eg Bryan and Lewis

Like the viscosity co ecients K and K are typically chosen to en

H V

sure numerical stability with K m s and K

H V

m s In the real o cean however mesoscale eddies are known to diuse

scalars more eciently along surfaces of constant p otential density The work

involved in mixing tracers across density surfaces is order more than

that required to stir along density surfaces Thus high horizontal eddy diu

sivities will b e unrealistic in regions of steeply sloping density surfaces Eng

land Hirst and Cai and others have demonstrated the problems

of using strictly Cartesian mixing co ecients in regions such as the South

ern Ocean Mo del artifacts include unrealistic watermass blending spurious

vertical velo cities and excessive p oleward heat transp ort across the ACC

Anatomy of Ocean Mo dels

A solution to the problem of tracer mixing in o cean mo dels was rst pro

p osed by Redi and implemented by Cox wherein the eddy

diusivity tensor K was oriented along density surfaces rather than in

H V

a Cartesian system However to ensure numerical stability this socalled

isopycnal mixing scheme originally required a background horizontal dif

fusivity meaning that whilst it simulated increased isopycnal mixing it also

maintained some spurious horizontal diusion Theoretical developments in

more recent studies have identied solutions to this problem One solution

is to construct a mo del grid that orients its surfaces along isopycnals rather

than along a Cartesian co ordinate system eg Bleck et al Such mo d

els have now b een congured over global domains and have quite successfully

captured the o ceans thermohaline circulation and climate pro cesses eg

Bleck et al Sun

Mesoscale eddies aect tracers not only by increasing mixing rates along

density surfaces but also by inducing a largerscale transp ort rather like an

adiabatic advection term eg Rhines Gent and McWilliams

McDougall Gent and McWilliams and later Gent et al

prop osed a parameterization for this pro cess wherein the largescale den

sity eld is used to estimate the magnitude of the eddyinduced advection

u v namely

 

x

K u

e 

z z

y

K v

e 

z z

and since the eddyinduced advection eld is nondivergent Gent et al

w can b e derived from the equation



u v w

  

x y z

yielding

x y

K K w

e e 

x z y z

It turns out that the Gent et al mixing scheme results in a p ositive

denite sink on the global mean of available p otential energy This means

that mo del runs of coarse resolution can b e integrated with zero background

horizontal diusion and yet remain stable as the Gent et al advection

terms act as a viscosity or dissipative term on the mo del scalar prop erties

Successful simulations with zero K have b een achieved with minimal nu

H

merical problems see Hirst and McDougall England and Hirst

Ocean Mo delling and Prediction

Recent estimates of vertical diusion rates show very low values

cm s in the upp er o cean elevated values near regions of rough b ot

tom bathymetry up to cm s and much weaker values in the o cean

interior over regions of smo oth b ottom bathymetry such as abyssal plains

Ledwell et al Polzin et al Mo dels have traditionally adopted

constant or simple depthdep endent proles of K Unfortunately key o cean

V

mo del parameters such as the meridional overturn and p oleward heat trans

p ort are controlled to a large extent by the magnitude of K eg Bryan

V

Recent eorts have b een made to estimate K as a function of b ottom

V

bathymetry roughness and o cean depth in global o cean mo dels eg Hasumi

and Suginohara It turns out the meridional overturn and p oleward

heat transp ort in an o cean mo del can b e vigorous with zero K over the

V

o cean interior and only enhanced K over rough terrain eg Marotzke

V

This gives increased condence in the capacity of o cean mo dels to

realistically capture the largescale o cean circulation without fully resolving

smallerscale physical pro cesses

In most applications of coastal and tropical o cean mo dels owdep endent

vertical mixing schemes are used to represent enhanced mixing in the fric

tional surface and b ottom b oundary layers These schemes are typically de

p endent on the lo cal Richardson numb er

N

R i

u z

g

is the buoyancy frequency and u the mean horizontal where N

z

ow sp eed As such R i quanties the vertical stability of the water column

in relation to the velo city shear Examples of Richardson numb er dep endent

schemes are describ ed in detail by Mellor and Yamada Pacanowski

and Philander and Kantha and Clayson to name a few

It is now known that signicant vertical mixing o ccurs over rough b ottom

bathymetry as barotropic tides agitate internal wave breaking eg To ole et

al Future parameterizations of K should take account of global tidal

V

ow elds and bathymetry roughness in order to incorp orate these eects in

some way

Another subgridscale o ceanic pro cess is vertical convection wherein sur

face buoyancy loss via co oling evap oration or seaice formation leads to

vertically unstable waters and overturn to depths up to m or so Ex



amples include Mo de Waters McCartney C water in the North

Atlantic Worthington and Weddell Sea Bottom Water Since con

vection is intimately tied to watermass formation representing it in o cean

mo dels is critical Because the horizontal scale of convection is order kilome

tres no greater than its vertical scale nonhydrostatic pro cesses are involved

Present parameterisations of vertical convection simply mix T S and other

Anatomy of Ocean Mo dels

scalars completely over the unstable p ortion of the water column remov

ing the vertically unstable layer outside any calculation of vertical motion

Mo del simulations of nonhydrostatic convection by Send and Marshall

indicate that to rst order this vertical mixing approach approximates the in

tegral eects of vertical convection on the simulated T S elds The problem

remains however that the horizontal extent of convection in coarse resolu

tion mo dels is necessarily at least the dimension of a mo del grid b ox which

can b e ab out km

Boundary Conditions and Surface Forcing

Ocean mo dels have to b e given explicit b oundary conditions for motion and

temp eraturesalinity see also Fig These include b oundary conditions at

the airsea interface b ottom b oundary conditions for momentum as well as

lateral b oundary conditions for regional mo dels Side b oundary conditions at

land masses are the most simple including noslip nonnormal ow and zero

uxes of heat and salt In coarse mo dels b ottom b oundary layers normally

adopt some simple relationship to approximate the eects of frictional drag

on the deep o cean ow see for example Toggweiler et al

Surface forcing is a crucial asp ect of b oundary conditions in o cean mo dels

Firstly for motion mo dellers may cho ose b etween a rigidlid approximation

and a free surface condition Under the rigidlid approximation the vertical

velo city w is zero at the sea surface thereby excluding surface gravity waves

and allowing a longer mo del time step Bryan This means further that

the total volume of the o cean remains constant and that freshwater uxes

across the airsea interface must b e represented as eective salt uxes Other

surface pressure gradients such as those due to large scale geostrophic ow

are allowed under a rigidlid approximation but not predicted directly The

free surface condition on the other hand carries sealevel height or pressure as

a prognostic variable thereby eliminating the need to predict the barotropic

velo city eld which b ecomes costly in a domain of high resulution Dukowicz

and Smith Techniques have emerged to handle a free surface condition

without signicantly shortening the mo del time step either by using many

small steps in time for solving the freesurface during each single timestep

of the full D mo del Killworth et al or by solving the freesurface

equations using an implicit metho d Dukowicz and Smith Benets

of adopting these approaches include improved computational eciency in

high resolution domains an ability to mo del o cean ow over unsmo othed

top ography and a natural prognostic variable for assimilation of satellite

height data into o cean mo dels see eg Stammer et al

Surface forcing elds are required in o cean mo dels for momentum temp er

ature and salinity for an excellent review on these topics see Barnier

Surface pressure and barotropic motion will adjust freely to the mo del simu

lated T S and D motion so direct surface forcing elds are not required

Ocean Mo delling and Prediction

Tidal forcing is also required when subdiurnal scales of motion are imp or

tant such as for coastal o cean mo dels or for ow in harb ours and bays

Momentum input into the o ceans is via mechanical wind forcing normally

expressed as a wind stress vector where

c jU U ju

a D W

with the density of air c a turbulent exchange drag co ecient U

a D

the wind sp eed at anenometer height m ab ove the o cean surface U

W

the o cean current sp eed at the sea surface and u the wind velo city at

anenometer height This windstress is then converted into a forcing term in

the momentum equations via the expression

at z F

uv

z

Direct observations of wind stress over the o cean are relatively sparse

though a numb er of longterm global climatologies exist eg Hellerman and

Rosenstein as well as others derived from more recent remote sensing

technologies eg Bentamy et al Another technique for mo del wind

forcing is to adopt output from numerical weather prediction mo dels NWPs

normally these pro ducts are derived from a combination of observations and

forecasts via data assimilation eg Kalnay et al Gibson et al

The advantage of NWP pro ducts is that they have global high density cov

erage use available observations and are dynamically consistent They are

in addition provided in real time which facilitates o cean hindcasting

Surface forcing conditions for temp erature T salinity S in o cean mo d

els can b e formulated in a numb er of ways The equations are refer to

and

Q

net

F

T

z c

p

S

F E P R

S

z

where Q is the net heat ux into the surface layer W m z is the

net

upp er mo del level thickness density of seawater c the sp ecic heat of

p

seawater S mean o cean salinity E evap oration rate P precipitation rate

and R river runo rate E P and R are all in m s The value S is

required to convert the net freshwater ux into an equivalent salt ux in

rigidlid mo dels see Barnier for further details So in formulating

heat and salt uxes o cean mo dellers require some knowledge of Q E P

net

and R Q is comprised of several comp onents

net

Q Q Q Q Q Q

net SW LW LA SENS PEN

Anatomy of Ocean Mo dels

where Q is the net shortwave radiation entering the o cean Q is the net

SW LW

longwave radiation emitted at the airsea interface Q is the latent heat

LA

ux Q is the sensible heat ux and Q the p enetrative heat ux

SENS PEN

from the base of mo del level into mo del level

The Q term can generally b e neglected except when shallow surface

PEN

layers are adopted eg Go dfrey and Schiller Bulk formulae can b e

used to estimate the heat ux comp onents of eg Barnier

in particular Q dep ends on latitude time of year cloud cover and sur

SW

face alb edo Q dep ends primarily on o cean surface temp erature Q and

LW LA

Q dep end on surface wind sp eed humidity for Q and airsea tem

SENS LA

p erature dierence Satellite and in situ observations of these variables can

b e used to construct bulk estimates of heat and freshwater uxes across the

airsea interface

Unfortunately many of these quantities are only sparsely observed over

the o cean and in addition they are characterised by highfrequency variabil

ity making it extremely dicult to construct longterm climatologies Also

variables such as precipitation and evap oration are not easily quantied using

satellite technologies Nevertheless a numb er of global heat and freshwater

ux climatologies exist eg Esb enson and Kushnir Josey et al

Baumgartner and Reichel Unfortunately direct forcing with these

uxes can lead to signicant mo del errors eg Mo ore and Reason as

small errors in uxes can accumulate into large errors in mo del T S over a

sucient p erio d of integration time Because of this largescale o cean mo d

ellers have commonly adopted grossly simplied formulations of thermohaline

forcing for example restoration to observed surface T and S

F T T

T T obs mo del

F S S

S S obs mo del

where are timeconstants determining how long heatsalinity anoma

T S

lies p ersist b efore they are damp ed by airsea forcing T S are the

obs obs

observed climatological T S and T S the mo del surface T S

mo del mo del

Haney justied this style of formulation for temp erature so long as

T is replaced by T where T is the temp erature the o cean would

obs EFF EFF

obtain if there were no heat transp orted by it Various techniques exist to

estimate the distribution of T eg Rahmstorf and Willebrand Cai

EFF

and Go dfrey There is however no such justication for salinity as

salinity at the seasurface has no signicant role in controlling airsea fresh

water uxes This lead many mo dellers to use socalled mixed b oundary

conditions eg Bryan Weaver et al wherein a mo del run is

integrated with restoring salinity conditions diagnosed for the eective salt

ux distribution and rerun with this ux condition on S thereby allowing

the mo del to exhibit variability in S indep endent of the surface forcing elds

More recently the Haney heat ux formulation has b een extended to

Ocean Mo delling and Prediction

include simple parameterizations for the atmospheric disp ersion of o cean heat

anomalies Rahmstorf and Willebrand Power and Kleeman to

allow for example the simulation of o ceanic variability otherwise suppressed

by a b oundary condition of the form in

Data sets for surface thermohaline forcing include ux climatologies refer

to citations ab ove and Wo o dru et al DaSilva et al reanalyses

of NWP simulations eg Barnier et al Beranger et al Garnier

et al and satellite derived data pro ducts eg Darnell et al

However in practical terms any direct ux forcing technique can lead to

substantial errors in simulated T S b ecause of p ossible mo del bias and

errors in the ux elds themselves For example an error in heat ux as

small as W m which is at least an order of magnitude less than the

typical error asso ciated with heat ux climatologies would result in an error



in upp er level T of C after years of run time assuming a surface level

of thickness m To address this problem it is b ecoming common practice

for mo dellers to adopt surface thermohaline forcing of the form

Q

net

Q F

CORR T

z c

p

and

S

E P R S F

CORR S

z

with

Q T T

CORR T obs mo del

S S S

CORR S obs mo del

corresp onding to the Newtonian restoring terms describ ed earlier in

Typically these heat ux and salt ux correction terms adopt timescale

values for that give weak restoring towards observed T S thereby

T S

enabling thermohaline variability see also Wo o d et al

Lateral b oundary conditions in regional o cean mo dels represent a ma jor

area of uncertainty in o cean mo delling In order to resolve o ceanic features

with scales of the order of kilometres to s of kilometres high horizon

tal resolution is required However limited computational resources mean

that global coverage at such resolution is not feasible Therefore either re

gional mo dels have to b e nested inside global mo dels where the global mo del

provides b oundary conditions for the regional mo del or op en b oundary con

ditions must b e incorp orated into the regional mo del Op en b oundary con

ditions generally assume limited physics at the b oundary There are several

detailed studies on op en b oundary conditions eg Orlanski Chapman

Palma and Matano where most attempt to represent the advec

tion or prop ogation of mo delled disturbances into or out of the domain These

Some Commonly Used Ocean Mo dels

conditions are referred to as passive conditions since they are designed to have

minimal impact on the mo del solution Often sp onge layers Chapman

which are designed to slow mo del disturbances down near op en b oundaries

are employed in order to further reduce any unwanted reection For cases

where a typical state at the b oundary is known or assumed eg tidal ows

nonpassive b oundary conditions are often used where a relaxation term is

added to the passive conditions mentioned ab ove eg Flather Blum

b erg and Kantha Many applications relax temp erature and salinity

to their climatological values eg Stevens Gibbs et al Oke and

Middleton with velo cities b eing relaxed to their geostrophic b oundary

values that match the T S climatology at the b oundary Barotropic b ound

ary ows may b e estimated using a Sverdrup relationship The uncertainty

asso ciated with the choice of op en b oundary condition means that a sub

stantial amount of testing and mo del validation should b e p erformed b efore

condence is shown in a regional simulation

The ab ove discussions of o cean mo del forcing are in the context of o cean

only mo del integrations However even when coupling to an atmospheric

GCM some integration of an o ceanonly mo del is required prior to coupling

In that case a numb er of spinup strategies are p ossible as discussed by

Mo ore and Reason This is detailed further in Chap

Some Commonly Used Ocean Mo dels

There are a vast numb er of o cean mo dels used around the world to day Some

of these mo dels are designed for a very sp ecic use limited to a certain geo

graphic region and only resolving the dominant comp onents of the equations

of motion Other more generalised mo dels have b een congured to b e op

erational over a range of space and timescales with a variable geographic

domain Such mo dels are b ecoming widely used with literally hundreds of

applications across many institutions A limited set of such o cean mo dels are

describ ed here

The GFDL Mo dular Ocean Mo del

The GFDL Mo dular Ocean Mo del MOM is the most widely used o cean

mo del in largescale coupled climate simulations It is a nite dierence reali

sation of the primitive equations governing o cean circulation These equations

are formulated in spherical co ordinates An identifying feature of the GFDL

mo del is that it is congured with its vertical co ordinate as level geop oten

tial surfaces ie socalled z level The MOM grid system is a rectangular

Arakawa staggered B grid Further mo del details can b e found in Pacanowski

and Bryan Applications range from global at coarse and eddy

resolving resolution down to regional and idealised pro cessoriented mo d

Ocean Mo delling and Prediction

els A full bibliography of MOMrelated pap ers app ears in an app endix in

Pacanowski

As an example Figure shows the upp er o cean circulation in the South

Pacic Ocean from such a mo del from England and Garcon This

mo del has resolution and geometry typical of stateoftheart coupled o cean

atmosphere mo dels used to study climate variability and anthrop ogenic cli

mate change The resolution is coarse degrees in longitude and de

grees in latitude so the eddy eld is not resolved explicitly There are

unequally spaced vertical levels with b ottom top ography and global conti

nental outlines as realistic as p ossible for the given gridb ox resolution The

mo del is driven by Hellerman and Rosenstein winds The mo del tem

p erature and salinity are relaxed to the climatological annual mean elds of

Levitus at the surface The gure shows vectors of o cean currents sim

ulated at m depth with top ography shallower than m depth shaded

Apparent is the bathymetric steering of the Antarctic Circump olar Current

ACC even in the upp er o cean well ab ove the main top ographic features in

the region

20 cm/sec

Fig Upp er o cean circulation in the South Pacic Ocean from England and

Garcon Top ography features shallower than m are shaded

The tendency for ow in the ACC to b e along constant depth contours

is not dicult to understand The reason for this is that the ow is mostly

barotropic so that the p otential vorticity

f

Q

h

Some Commonly Used Ocean Mo dels

will b e conserved where is the relative vorticity f the Coriolis parameter or

planetary vorticity h the o cean depth and is the relative sealevel elevation

At the latitude of the ACC apart from mesoscale eddies the largescale ow

is such that its relative vorticity f In addition sealevel variations

are of the order of metres compared with an o cean depth of h

metres So the conservation of p otential vorticity implies that

f h constant With the ACC ow b eing primarily west to east we can take

f as approximately constant so a uid column tends to have the same value

of depth h and is thus steered along isobaths

The Princeton Ocean Mo del

The Princeton Ocean Mo del POM adopts curvilinear orthogonal co ordi

nates and a vertical sigmaco ordinate to facilitate simulations of coastal zone

ows Mellor The horizontal timedierencing is explicit whereas the

vertical dierencing is implicit allowing a ne vertical resolution in the sur

face and b ottom layers This is imp ortant in coastal o cean mo dels as the

nearshore o cean can b e a region of substantial surface and b ottom b ound

ary gradients POM can b e integrated with a freesurface and using split

timestepping as in MOM Another p ositive feature of the POM is the

emb edded turbulence submo del Mellor and Yamada which is de

signed to provide realistic owdep endent vertical b oundary layer mixing

This submo del along with the terrainfollowing sigmaco ordinates allows

the mo deller to resolve b ottom b oundary layer ows that are often asso ci

ated with coastal upwelling a feature that z level mo dels cannot adequately

represent Applications of the POM range from coastal Mellor through

to regional Middleton and Cirano and basinscale studies Ezer and

Mellor

An example of the POM congured with idealised continental shelf and

slop e top ography and forced with constant Pa upwelling favourable

winds is shown in Fig taken from Oke and Middleton This gure

shows the evolution of a crossshelf slice of temp erature alongshelf velo city

and crossshelf streamfunction over a day p erio d This sequence shows the

initial resp onse to the wind in the streamfunction eld where an upwelling

circulation is generated By Day a coastal jet has formed in the direction

of the wind and isotherms have b een upwelled to the surface By Day the

upwelling is concentrated in the b ottom b oundary layer as indicated by the

concentration of the crossshelf streamlines over the top ography and the up

welling front has b een advected oshore This typ e of idealised conguration

mo delling has given o ceanographers great insight into the overall dynamics

of coastal upwelling eg Allen et al as it may enable the upwelling

dynamics to b e isolated from more complicated continental shelf pro cesses

such as the eects of top ographic variations

Ocean Mo delling and Prediction

Temperature Alongshelf Current Streamfunction 0 −50 ZERO FIELD ZERO FIELD −100

Depth (m) −150 Day 0 −200

−50 −100

Depth (m) −150 Day 1 −200

−50 −100

Depth (m) −150 Day 5 −200

−50 −100

Depth (m) −150 Day 10 −200

−50 −100

Depth (m) −150 Day 15 −200 0 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50

Distance (km) Distance (km) Distance (km)

Fig A sequence of crossshelf slices of temp erature alongshelf velo city

 1

and crossshelf streamfunction leftright contour intervals C m s

2 1

m s resp ectively showing their evolution in resp onse to constant Pa

upwelling favourable winds Oke and Middleton

Some Commonly Used Ocean Mo dels

The Miami Isopycnic Co ordinate Mo del MICOM

MICOM is a primitive equation isopycnic o cean mo del that uses equations

that have a co ordinate of p otential density in the vertical direction Fig c

instead of the traditional vertical co ordinate of depth That is whereas z level

and sigma co ordinate mo dels predict the density at a xed depth MICOM

predicts the depths at which certain density values are encountered Thus

the traditional roles of water density and height as dep endent and indep en

dent variables are reversed The surface mixed layer with dierent isopycnal

values sits over the subsurface isopycnic domain The horizontal co ordinate

system is the Arakawa C grid The mo del accommo dates a user sp ecied

horizontal geographic zone Further mo del details can b e found in Bleck et

al Recently MICOM has b een congured for global o cean simula

tions Bleck et al A map of the simulated surface o cean currents from

a degree by cosdegree global MICOM simulation Sun is shown

in Fig

MICOM global ocean model surface currents

60E 120E180 120W 60W

Fig Simulated surface o cean currents from a degree by cos degree

global MICOM simulation after Sun

The DieCast Mo del

The DieCast mo del is a z level mo del like the GFDL MOM only with dif

ferent numerical and horizontal grid schemes The DieCast mo del combines

asp ects of the Arakawa A and C grids DieCast uses fourth order interp ola

tions to transfer data b etween the A and C grid lo cations in order to combine

Ocean Mo delling and Prediction

the b est features of the two grids This pro cedure eliminates the Agrid null

space problems and reduces or eliminates the numerical disp ersion caused by

Coriolis term integration on the C grid The mo died A grid mo del includes

a fourth order approximation for the baro clinic pressure gradient asso ciated

with the imp ortant quasigeostrophic thermal wind Further discussion of

the DieCast grid system is given by Dietrich The mo del geometry

is in most ways identical to the GFDL MOM The key dierence b etween

DieCast and the GFDL MOM is that DieCast defaults to higher order nu

merical schemes and incorp orates a merged Arakawa A and C grid system

as describ ed ab ove

Ocean Mo del Applications

A Global Coarse Resolution Mo del

Perhaps the most widely applied global coarse resolution mo del over the past

two decades has b een that congured initially by Bryan and Lewis

based on the GFDL BryanCox primitive equation numerical mo del Bryan

Cox The Bryan and Lewis simulation has b een used in

a wideranging series of coupled climate mo dels eg Manab e and Stouer

o ceanonly mo dels used to understand watermass for

mation pro cesses eg England England et al Toggweiler and

Samuels and in mo dels of the o ceanic carb on cycle Sarmiento

et al It has also undergone extensive assessment using geo chemical

tracers such as radio carb on Toggweiler et al and chlorouoro carb ons

England et al England and Hirst

A particular example of the utility of the coarse resolution mo del of Bryan

and Lewis is exemplied in the England et al assessment of

the formation mechanism for mo de and intermediate waters in the South

ern Ocean Realistic representation of the lowsalinity tongue of Antarctic

Intermediate Water AAIW was achieved by England He found that

the AAIW tongue can quite successfully b e simulated provided appropriate

attention is taken to observed wintertime salinities near Antarctica and so

long as an isopycnal mixing scheme is incorp orated into the mo del A diagram

showing the observed and mo delled salinity is included in Fig

England et al found that AAIW is not generated by direct sub

duction of surface water near the p olar front as had b een the traditional

b elief eg Sverdrup et al Instead the renewal pro cess is concen

trated in certain lo cations particularly in the southeast Pacic Ocean o

southern Chile see Fig The outow of the East Australian Current

progressively co ols by heat loss to the atmosphere and assimilation of p o

lar water carried north by the surface Ekman drift and freshens due to

the northward Ekman transp ort of low salinity Subantarctic Surface Waters

during its slow movement across the South Pacic towards the coast of Chile

Ocean Mo del Applications

Fig Observed and mo delled salinity in the depthlatitude zonal mean Ob

servations from Levitus mo del simulation is that of England et al

This results in progressively co oler denser and fresher surface water leading

to deep er convective mixed layers towards the east O Chile advection of

warmer subsurface water from the north at m depth enables more

convective overturn resulting in very deep mixed layers from which AAIW is

fed into the South Pacic via the subtropical gyre and also into the Malv

inas Current via the Drake Passage This formation mechanism for AAIW

was rst prop osed by McCartney based on observations although a

detailed dynamical framework was not clear until the England et al

study

Ocean Mo delling and Prediction

p

Fig a Observed annualmean salinity at m depth redrafted from

Levitus be Simulated prop erties in the England et al o cean

2

mo del b salinity near m depth c net surface heat ux W m into the

o cean d maximum depth m of convective overturn and e horizontal velo city

near m depth

Ocean Mo del Applications

Global Eddyp ermitting Simulations

The rst global domain eddyp ermitting o cean mo del was integrated by Semt

ner and Chervin Presently several groups are moving in this direc

tion although the huge computational cost of an eddyp ermitting global

mo del limits applications to multidecadal runs Two prominent examples

of global eddyp ermitting mo dels include the Ocean Circulation and Climate

Advanced Mo delling Pro ject OCCAM de Cuevas et al and the

Parallel Ocean Climate Mo del Stammer et al Tokmakian

The OCCAM pro ject has develop ed two high resolution and de

gree mo dels of the World Ocean including the Arctic Ocean and marginal

seas such as the Mediterranean Vertical resolution has depth levels rang

ing from m near the surface down to m at m depth OCCAM is

based on the GFDL MOM version of the BryanCoxSemtner o cean mo del but

includes a free surface and improved advection schemes A regular longitude

latitude grid is used for the Pacic Indian and South Atlantic Oceans A

rotated grid is used for the Arctic and North Atlantic Oceans to avoid the

convergence of meridians near the p oles The mo del was started from the

Levitus annual mean T S elds The surface forcing uses ECMWF monthly

mean winds and a relaxation to the Levitus seasonal surface T S climatol

ogy This initial mo del run was integrated for mo del years The OCCAM

mo del has b een run with high resolution forcing using the sixhourly ECMWF

reanalysis data from onwards The OCCAM simulation in the region of

the Agulhas Retroection is shown in Fig Agulhas eddies are spawned

south of Africa transp orting heat and salt from the Indian Ocean into the

Atlantic contributing to the global transp ort of prop erties b etween o cean

basins This has b een linked with the global thermohaline transp ort of North

Atlantic Deep Water NADW Gordon Coarse resolution o cean mo d

els cannot explicitly resolve o ceanic eddies and so they do not include the

heat and salt uxes asso ciated with Agulhas rings

The Parallel Ocean Climate Mo del POCM has nominal lateral resolu



tion of Stammer et al Tokmakian The POCM domain

 

is nearly global running from S to N The actual grid is a Mercator



grid of size in longitude yielding a square grid everywhere b etween the



Equator and latitude Stammer et al The resulting average grid



size is in latitude Mo del bathymetry was derived by a grid cell average



of actual o cean depths over a resolution of Unlike most coarse mo dels

the ne resolution mo del includes a free surface after Killworth et al

that treats the sea level pressure as a prognostic variable

The POCM is integrated for the p erio d through to June us

ing ECMWF derived daily wind stress elds climatological monthly mean

ECMWF sea surface heat uxes pro duced by Barnier et al and some

additional T S surface restoring terms The surface restoring of T and S

adopts the Levitus et al monthly climatology with a day relax

ation time scale Subsurface to m depth T S are also restored towards

Ocean Mo delling and Prediction

Fig OCCAM simulation of sea surface salinity in the region of the Agulhas

Current and leakage into the Indian Ocean from Semtner



Levitus along articial mo del b oundaries north of N and south of



S to approximate the exchange of water prop erties with those regions not

included in the mo del domain

An example of the POCM simulation is shown for the South Atlantic

upp er o cean in Fig Only velo city vectors at every third grid b ox are

drawn with no spatial averaging otherwise the current vectors are dicult

to visualise The BrazilFalkland conuence is close to the lo cation describ ed

from hydrographic and satellite observations Also the South Atlantic Cur

rent is simulated to the north of the ACC and separate from it unlike

coarser mo dels which tend to simulate a broad ACC and no distinct SAC At

the tropics the POCM resolves some of the meridional structure in zonal cur

rents observed as discussed in Stramma and England Eddyresolving

simulations capture much more spatial structure than their coarse resolution

counterparts including more realistic western b oundary currents frontal dy

namics and internal o ceanic variability

Regional Simulations in the North Atlantic Ocean

A large variety of simulations of the North Atlantic Ocean have b een carried

out within the World Ocean Circulation Exp eriment WOCE Community

Ocean Mo del Applications

Fig POCM simulation for the South Atlantic upp er o cean near m depth

from Stramma and England Only velo city vectors at every third grid b ox

are drawn

Mo deling Eort CME and more recently by other mo delling groups An

overview of some of the CME North Atlantic mo dels is given by Boning et

al with particular reference to the sensitivity of deepwater formation

and meridional overturning to a numb er of mo del parameters It turns out

that surface thermohaline forcing England mo del resolution Boning

et al mixing parameterisation Boning et al as well as the

resolution of certain subsurface top ographic features Rob erts and Wo o d

all control mo del NADW formation rates

More recently the Dynamics of North Atlantic Mo dels DYNAMO study

intercompared a numb er of simulations in the region using mo dels with dier

ent vertical co ordinate scheme namely a mo del with horizontal z levels an

other with isopycnal layers and thirdly one that used a dimensionless sigma

co ordinate as p er Fig The goal of the DYNAMO pro ject was to develop

an improved simulation of the circulation in the North Atlantic Ocean includ

ing its variability on synoptic and seasonal timescales The study included a

systematic assessment of the ability of eddyresolving mo dels with dierent

vertical co ordinates to repro duce the essential features of the hydrographic

 

structure and velo city eld b etween S and N

Ocean Mo delling and Prediction

Figure shows the p oleward heat transp ort in all three o cean mo dels

compared with observations The northward heat transp ort in the z level sim

ulation is markedly lower than the observations and the sigma and isopycnal



cases south of N This is due to mixing in the outow region and spurious

upwelling of NADW at midlatitudes DYNAMO On the other hand

the isopycnal run simulates a more realistic heat transp ort pattern although

its low eddy kinetic energy is comp ensated by an enhanced deep NADW out

ow Thus examination of the integral measure of p oleward heat transp ort

aliases more subtle dynamical discrep encies in that mo del The sigma mo del

also captures a realistic heat transp ort pattern although the formation site

for NADW is not concentrated in the subp olar region gure not shown

Overall the intercomparison of mo dels in the DYNAMO pro ject underscores

the relative merits and shortcomings of dierent vertical co ordinates in the

context of basinscale mo delling

Fig Poleward heat transp ort in the DYNAMO exp eriments with z level

isopycnal and sigma co ordinate vertical schemes from DYNAMO Observa

tions are included from McDonald and Wunsch

ENSO Mo delling

Mo delling the upp er o cean dynamics in tropical waters is crucial for an im

proved understanding of the ElNino Southern Oscillation ENSO ENSO

o cean mo dels are ultimately coupled to atmospheric GCMs in order to pre

dict the climate impact of changes in tropical SST Ocean mo dels used in the

Ocean Mo del Applications

context of ENSO simulations have ranged in complexity from shallow water

mo dels representing tropical upp er o cean dynamics eg Cane and Sarachik

McCreary and mo died shallow water mo dels eg Schopf and

Cane through to threedimensional general circulation mo dels eg

Philander and Pacanowski A similar hierarchy of atmospheric mo d

els also exists from those employing simple damp ed shallowwater dynamics

eg Gill through to full atmospheric GCMs In turn the coupled

o ceanatmosphere mo dels used can range from simple mo dels and intermedi

ate coupled mo dels through to D coupled GCMs for a review of the former

see Neelin et al

Ocean GCMs used to study ENSO dynamics are normally constructed

with enhanced horizontal resolution in the tropics and enhanced vertical

resolution in the upp er metres This is done to optimise mo del p er

formance in the equatorial zone without unduly increasing computational

costs Upp er o cean vertical mixing schemes are also generally more sophis

ticated than those used in standard global GCMs For a review of o cean

and coupled GCMs used to study ENSO dynamics the reader is referred to

Delecluse et al

A Regional Mo del of the Southern Ocean

The Fine Resolution Antarctic Mo del FRAM is a primitive equation numer

 

ical mo del of the Southern Ocean b etween latitudes S and S The mo del



was initialised with T C and S psu and relaxed to Levitus an

nual mean T S over years Surface wind forcing is that of Hellerman and

Rosenstein Various strategies for gradual imp osition of these uxes

is adopted to minimise numerical instability in the mo del spinup phase for

details see de Cuevas Mo del mixing schemes include a mixture

of harmonic and biharmonic terms and a quadratic b ottom friction stress

The total mo del run time is years The op en b oundary condition used in

FRAM is a combination of a Sverdrup balance in the barotropic mo de and

a simple quasigeostrophic balance and Orlanski radiation in the baro clinic

terms see Stevens for further details

In the nal seasonal cycle phase of the mo del run the Antarctic Circum

p olar Current transp ort through Drake Passage oscillates b etween and

Sv Sv m s This overly strong transp ort is a problem

chronic to globalscale high resolution mo dels The main regions of eddy for

mation in the FRAM are in the Agulhas Current and along the path of the

Circump olar Current The FRAM streamfunction simulated after the initial

spinup phase of the mo del run is illustrated in Fig Clearly apparent is

the resolution of the ACC and its asso ciated frontal dynamics and meanders

In addition a substantial amount of eddy kinetic energy gure not shown

is simulated in regions where the ACC encounters top ographic features such

as the Campb ell and Kerguelen Plateaus

Ocean Mo delling and Prediction

Fig Simulated barotropic streamfunction in the Fine Resolution Antarctic

Mo del FRAM after the initial spinup phase from Webb et al

A Coastal Ocean Mo del o Eastern Australia

An example of the POM congured for the EAC region is the NSW shelf

mo del which was develop ed at the UNSW Oceanography Lab oratory eg

Gibbs et al Oke and Middleton The mo del utilises a curvilin

ear orthogonal grid with horizontal resolution of km and extends along

the entire coast of NSW Observed surface and m temp erature elds are

combined with Levitus climatology to pro duce the initial density eld which

is then used to determine the initial velo city eld via dynamic height calcu

lations With a constant inow at the northern b oundary and op en b oundary

conditions which are relaxed to climatology at the east and south the mo del

has proved to b e very useful for investigating the role that the EAC plays in

nutrient enrichment of NSW coastal waters eg Gibbs et al Oke and

Middleton An example of the surface temp erature and velo city elds

mo delled by the NSW shelf mo del for a p erio d during January from

Oke and Middleton is shown in Fig The mo delled elds which

were qualitatively similar to observed temp erature elds at the seasurface

Ocean Mo del Applications

and at a depth of m indicate that over a p erio d of ab out a week the

EAC intensied over the continental shelf and extended southwards along

the coast to the south of Sydney A lo calised upwelling o ccurred immedi

ately to the south of Port Stephens indicated by the cold water mass near

the coast Through an analysis of the mo del elds it was hyp othesised that

the acceleration of the EAC over the narrow continental shelf near Smoky

Cap e resulted in uplifting of colder water which ultimately reached the sur

face in the vicinity of Port Stephens The January p erio d corresp onded

to a time when an algal blo om formed o Port Stephens As a result of the

mo delling study it was suggested that top ographically induced EACdriven

upwelling plays an imp ortant role in the nutrient enrichment of New South

Wales coastal waters

o 30 N −1 Jan. ’97 1.0 ms Smoky 24 31oN Cape

32oN Port Stephens 33oN 22

25 23 34oN Sydney 21 24 22 20 35oN 19

21 36oN 20 18

o W o W o W o W o W o W o W o W o W o W o W o W

150 151 152 153 154 155 150 151 152 153 154 155

Fig Simulated surface temp erature left and velo city right from the NSW

shelf mo del a conguration of the POM showing elds for January Oke and

Middleton

A Coastal Mo del of a River Plume

An example of a version of the POM utilised for a pro cessoriented study

of the resp onse of a river plume during upwelling favourable winds Fong

and Geyer is outlined b elow The mo del is congured for the north

ern hemisphere f s with a rectangular basin and idealized mo der

ately steep nearshore bathymetry that is typical of many narrow continental

Ocean Mo delling and Prediction

shelves Freshwater is discharged via a short riverestuary system at the coast

in the upp er left hand corner of the km km domain Fig In the

region of interest the resolution is less than metre in the vertical km

in the crossshore direction and km in the alongshore direction A mo d

ied MellorYamada turbulence submo del is utilized Mellor and Yamada

NunuzVaz and Simpson and a recursive Smolarkiewicz advection

scheme Smolarkiewicz and Grab owski is used to advect salt and tem

p erature A steady inow of m s is imp osed at the northern b oundary to

mo del the ambient continental shelf currents and a combination of clamp ed

and radiative b oundary conditions are employed at the oshore and southern

b oundaries The salinity was initially psu throughout the domain and the

river plume is simulated by discharging freshwater psu from a p oint source

at the coast at a constant rate of m s The plume is established in

the absence of wind over a month p erio d Fig a after which time

constant Pa upwelling favourable winds are applied over a day p erio d

The simulations demonstrate that in resp onse to upwelling favourable winds

the surfacetrapp ed river plume widens and thins and is advected oshore

by the crossshore Ekman transp ort Fig bd The thinned plume is

susceptible to signicant mixing due to the vertically sheared horizontal cur

rents Fong and Geyer utilise this conguration to investigate how the

advective pro cesses change the shap e of the plume and how these advective

motions alter the mixing of the plume with the ambient coastal waters

Exploiting Ocean Observations

Mo del Assessment

The assessment of o cean mo dels involves the comparison of a set of mo del

variables or diagnostics with observations Mo del assessment techniques range

from simple qualitative comparisons through to statistical signicance tests

It is convenient to lo ok at largescale and coastal mo dels separately as dif

ferent quantities and timescales are involved in such assessments

Largescale models For largescale mo dels those of an o cean basinscale

or greater much mo del assessment is fo cused on longterm climatological

hydrographic prop erties particularly T S as well as integrated transp ort

quantities like the net ow in the ACC This is particularly the case for

coarse resolution mo dels such as those incorp orated into climate simulations

In such noneddyresolving mo dels o cean current sp eeds are slow and have

none of the highfrequency variability asso ciated with eddies or tides in the

real o cean Thus direct comparison with observed current meter records is

inappropriate Instead integrated transp ort measures b oth in the horizontal

and meridional plane provide a more meaningful assessment of the mo del

Watermass formation is also most often assessed indirectly in coarse mo d

els that is by analysing mo del and observed T S rather than the mo del

Exploiting Ocean Observations

450 (a) t = 0 hrs (b) t = 24 hrs (c) t = 48 hrs (d) t = 72 hrs

400 30 30

30 30 350 28

300

30 250 28 30 y (km)

30 30 200

150

100

50 30 cm/s

0 50 0 50 0 50 0 50

x (km) x (km) x (km) x (km)

Fig Surface velo city and salinity for the evolution of a river plume during

upwelling favourable wind conditions a after month of buoyancy forcing with

no wind bd after and hours of Pa upwelling favourable winds

The scale for velo city is shown in panel d and the contour intervals are psu for

salinity adapted from Fong and Geyer

sub ductionconvection pro cesses This is partly b ecause the pro cesses that

are linked with watermass formation such as convection mixing and deep

currents are extremely dicult to measure directly In addition such pro

cesses are subgridscale to a coarse resolution mo del so assessment of them is

b est achieved by analysing their parameterised eects on mo del T S eg

England Hirst and Cai Hirst and McDougall

Because temp erature and salinity are prognostic variables in global o cean

mo dels and intrinsic in any denition of a watermass it is tempting to rely

solely on them in the assessment of mo del watermass formation However

they provide only limited information on mo del watermass formation rates

such as indicating the depth of rapid ventilation asso ciated with surface mix

ing Geo chemical tracers on the other hand provide detailed information

on the pathways and rates of watermass renewal b eneath the surface mixed

layer and therefore provide a stringent test of mo del b ehaviour The main

Ocean Mo delling and Prediction

tracers that have b een used in this context include tritium Sarmiento

chlorouoro carb ons England et al England and natural and

b ombpro duced radio carb on Toggweiler et al

Assessment of largescale eddyresolving o cean mo dels relies on quite dif

ferent data sets to those discussed ab ove These mo dels capture some degree

of highfrequency variability such as meanders in b oundary currents as well

as mesoscale eddy activity They are also only run over interannual to decadal

timescales so they do not simulate the longterm climatological watermass

prop erties of the o cean interior A more stringent test of mo del b ehaviour

in this situation is to compare prop erties such as the global eddy kinetic

energy density or meridional uxes of heatfreshwater Figure shows a

comparison of the surfaceheight variability observed by satellite with that



simulated in a mo del Maltrud et al The mo del and observed

eddy kinetic energy are in overall agreement with high eddy activity where

the ACC interacts with top ography and in western b oundary currents

Fig Comparison b etween the surfaceheight variability a observed Wun



sch with that b simulated in a mo del that of Maltrud et al

from IPCC

Exploiting Ocean Observations

Regional and coastal ocean models Many observational studies fo cus on con

tinental shelves and coastal regions since this is where most recreational and

commercial marine activities are fo cussed Such studies typically involve spa

tially and temp orally intense measurements of sp ecic o ceanic regions As a

result the validation of regional coastal o cean mo dels is feasible for p erio ds

when observations are available Typical observations of the coastal o cean

for any given exp eriment include in situ measurements of currents and T S

from an array of mo ored instruments at xed lo cations or from shipb oard

surveys Additionally remotely sensed sea surface temp eratures are often

available Together these data provide an incomplete picture of the coastal

circulation which can b e compared and contrasted with output from o cean

mo dels in order to either validate the mo del or gain insight into the dom

inant dynamical pro cesses that determine the circulation of the particular

region An example of a crosssection of temp erature salinity and p otential

density o Newp ort Oregon observed during the OSU NOPP summer eld

season of is shown in Fig Austin and Barth

These sections show the isohals and isopycnals outcropping near the coast



and a subsurface temp erature maximum eg the isotherm b eing sub

ducted under the shallow surface mixed layer The mechanism by which this

subsurface temp erature maximum is formed is unclear Mo del analysis needs

to b e undertaken to determine the dynamical balances op erating in the re

gion

Mo del validations usually involve a comparison b etween p oint source mea

surements and mo del output either qualitatively by identifying similarities

and dierences in mo delled and observed features or quantitatively through

statistical comparisons in the time domain eg means variances correla

tions empirical orthogonal functions and so on or in the frequency domain

eg coherence phase gain For a given application the validation require

ments may b e dierent For example if the timing and magnitude of temp er

ature uctuations are of interest in order to detect upwelling then prediction

of the mean temp erature may b e less imp ortant than the prediction of the

variance and it would b e imp ortant for the mo del to b e well correlated with

observations However if coupling with the atmosphere is a concern then the

magnitude of the surface heat ux will dep end on the mean surface temp er

ature compared to the atmospheric temp erature through the formulation of

the sensible heat ux dened in

A relatively recently develop ed metho d for observing the coastal o cean

environment is the use of landbased high frequency HF Coastal Ocean Dy

namics Application Radar CODAR arrays eg Paduan and Roseneld

CODAR measurements provide maps of nearsurface o cean currents

with high spatial km and temp oral minutes resolution The avail

ability of these measurements provides mo dellers with an ideal opp ortunity

to test the validity of their mo dels An example of a mo deldata comparison

b etween an idealised conguration of the POM with CODAR data on the

Ocean Mo delling and Prediction

25 km 20 km 15 km 10 km 5 km 0 km 0 15 1413 12 1011 9 20

40

8 60 depth, m 09/01/1999 80 Temperature, ° ∆ T=0.2 C (6−9) ° ∆ T=1 C (9−15) 100 0 32

20

40 33

60 depth, m 09/01/1999 80 Salinity ∆ S=0.2 PSU

100 0 24 25 20

40 26 60 depth, m 09/01/1999 80 Potential density ∆ σ =0.2 kg m−3 t 100 −124.4 −124.35 −124.3 −124.25 −124.2 −124.15 −124.1 −124.05 °

Longitude, E

Fig Crossshelf section of temp erature top salinity middle and p otential

density b ottom o Newp ort Oregon observed during the OSU NOPP summer

eld season of Austin and Barth

Exploiting Ocean Observations

Oregon continental shelf for the summer of is shown in Fig from

Oke et al This gure shows a comparison b etween the mo delled and

observed mean surface currents A and B which indicates that the mean

mo del elds are similar in structure and magnitude to the observed means

A comparison is also shown b etween the dominant spatial mo des obtained

from an empirical orthogonal function EOF analysis of the mo delled and

observed elds CF The spatial mo des of an EOF analysis represent the

structures of the variance elds The p ercentage of the variance represented

by each mo de is shown in each panel indicating that of the mo delled

variance and of the observed variance is represented by these two EOFs

The rst mo de represents the acceleration of the coastal jet in resp onse to

upwelling favourable winds The second mo de represents the ow asso ciated

with upwelling relaxation Gan and Allen where a northward counter

current is generated in resp onse to the alongshore pressure gradients induced

by the wind Although the details of the mo delled and observed means and

the EOF mo des dier it is clear that the mo del is capturing a substantial

amount of the true variability of the o cean in this region

Inverse Metho ds and Data Assimilation

Data assimilation refers to the metho ds by which the inverse problem of the

o cean circulation can b e addressed The inverse problem for the o cean circu

lation is the problem of inferring the state of the o cean circulation through

a quantitative combination of theory and observations Wunsch Con

sider the system of equations that approximately and incompletely describ es

the o cean

D dt F f

with

Initial Conditions I i

i

Boundary Conditions B b

b

o

Observations D d

m m

m

where represents the mo del state space which consists of every mo del

variable eg u v w T S at every mo del grid lo cation F I B and

D represent the mo del forcing initial conditions b oundary conditions and

observations resp ectively and f i b and d represent the errors in the mo del

forecast initial conditions b oundary conditions and observations resp ectively

Bennett The inverse problem is to combine this information to obtain

the most accurate and complete depiction of the o cean circulation that we

can given the resources available

The forecast error f may b e due to the approximations made by dis

cretising the governing equations or due to missing physics if for example

Ocean Mo delling and Prediction

MODEL DATA

A 200 B 44.7oN YH

44.5oN 150 WLP 100 44.3oN 0.5 m/s 0.5 m/s 50

C D 44.7oN

44.5oN

44.3oN 51% 38% 124.6 124.4 124.2 124 124.6 124.4 124.2 124 o o W W

o E o o o F o o o 44.7 N W W W W W W

44.5oN

44.3oN 22% 10% 124 124 124.2 124.2 124.4 124.4 124.6 124.6 o o W W o o o o o o

W W W W W W

Fig Mo delled left and observed right elds of surface currents o Oregon

during the summer of showing the means AB and the dominant spatial

mo des CF calculated from an EOF analysis Oke et al

the nonlinear terms in the equations are neglected The error in the initial

conditions i is a consequence of the fact that we can not know the precise

state of the o cean at any moment in time A mo dels initial condition will

typically b e derived from climatological data or from an interp olation from

sparse observations The error in b oundary conditions b may b e due to the

uncertainties in the applied wind or heat ux forcing or in the case of re

gional mo dels due to the uncertainty in the lateral b oundary conditions as

well

Finally the observation error d represents the system noise which is

m

the result of instrument error measurement error and uncertainties in the

observability of a particular o ceanic variable In order to pro duce the b est

Exploiting Ocean Observations

p ossible depiction of the o cean circulation the metho d of leastsquares is

employed where one attempts to nd the solution to the governing equations

given the initial conditions b oundary conditions and observations that is

within the given error b ounds of each comp onent

The simplest metho d for solving this inverse problem involve the applica

tion of sequential metho ds namely optimal interp olation eg Cohn et al

or the Kalman Filter eg Miller These metho ds attempt to

optimally combine the observations and the dynamics to pro duce an analysis

a

of the o cean The analysis is pro duced by combining the mo dels forecast

f

and the observations d using the socalled analysis equations

m

a f f

Kd H

m

with

f T f T

K P H HP H R

where K is the Gain matrix and H is an interp olation matrix that interp olates

the mo del state onto the space of observations The Gain matrix dep ends on

f

the forecast error covariance matrix P and the observation error covariance

matrix R For sequential metho ds f i and b are considered together and

f

lab elled the forecast error The forecast and observation error covariances

are given by

T

f f f

P h i

and

T

o o

i R h

o

resp ectively where hi denotes a time average and is the observation error

For sequential metho ds an analysis of the mo del state is pro duced at each

assimilation cycle which will dep end on the time scales of the problem that

is under investigation In addition to the analysis equations presented ab ove

f

the Kalman Filter also solves an equation for the time evolution of P The

implementation of the analysis equations involves the estimation of the fore

f o

cast and observation error covariance matrices In practise b oth and

and hence their covariances are unknown The estimation of these covariance

matrices involves assumptions ab out decorrelation length and time scales

and often ab out the homogeneity and isotropy of the mo del error elds

These matrices must b e estimated prior to assimilation and their validity

tested through a series of ob jective statistical tests after each assimilation

Bennett

As an alternative to sequential metho ds the generalized inverse metho d

eg Bennett et al Errico may b e used This approach involves

the formulation of a quadratic p enalty functional or cost function J

Z Z Z Z

X

J W f dtdx W i dx W b dt W d

f i b d m

Ocean Mo delling and Prediction

where W W W and W are p ositive weight functions for each comp o

f i b d

nent of the system describ ed ab ove These weights are related to the ab ove

mentioned forecast and observation error covariances and must also b e chosen

prior to assimilation The cost function J is a single numb er for each depic

tion of The cost function must b e minimized by identifying the smallest

values for f i b and d in the weighted leastsquares sense Once the global

m

minimum of J is obtained the optimal solution to is obtained For a de

tailed discussion of the generalized inverse metho d and other metho ds for

data assimilation the interested reader is referred to Bennett or Wun

sch

The development and implementation of practical data assimilation tech

niques is vital if op erational forecasting of the o cean circulation is going to

b ecome a reality The development and maturity of remote sensing and in

situ observing systems the advances in scientic knowledge of the global and

regional o cean circulation and the development of sophisticated o cean mo d

els has made realtime observing and forecasting systems feasible As out

lined ab ove data assimilation enables available observations derived either

remotely from satellites or radar systems or in situ from mo ored instru

ments drifters or shipb oard surveys to b e combined with o cean mo dels in

order to pro duce a complete depiction of the o cean circulation at time scales

of a few days and space scales of several tens of kilometres The Global Ocean

Data Assimilation Exp eriment GODAE is an exp eriment that is designed

to demonstrate the practicality and feasibility of routine realtime global

o cean data assimilation and prediction Smith and Lefebvre

All weather forecasting systems that are presently in op eration utilise data

assimilation in some form through either initialisation to an ob jective map of

the atmospheric state or through more sophisto cated assimilation techniques

Forecasting the o cean circulation presents all of the same diculties and

challenges as weather forecasting except that o cean observations are much

more sparse compared to observations of the atmosphere Consequently the

development of reliable and practical data assimilation systems for o cean

forecasting is more crucial since we must endeavor to take full advantage of

the limited observations that are available

Applications of Data Assimilation to Coastal Ocean Mo dels

One application of suboptimal sequential data assimilation to a regional

primitive equation mo del of the Oregon continental shelf circulation is out

lined b elow This application involved assimilation of surface velo city data

obtained from a landbased HF CODAR array during the summer of

Oke et al The surface information was pro jected over the entire wa

ter column in order to correct velo cities and density at depth In order to

demonstrate how well the surface information was pro jected over depth the

depthaveraged velo city in m of water obtained from a mo ored acous

tic doppler proler ADP is compared with the mo del hindcast with and

Exploiting Ocean Observations

without assimilation Fig The magnitude of the complex correlation

b etween the observations and the mo del without assimilation is and

with assimilation is indicating that the assimilation improved the hind

cast by approximately demonstrating its p otential for coastal o cean

mo deling

Application of Data Assimilation to Largescale Mo dels

An example of a pro ject that is endeavouring to develop a forecast system

for the global o ceans is the GODAE This development is a very challeng

ing task b oth from a scientic and technical p ersp ective Issues that must

b e overcome include development of advanced mo dels development of e

cient and eective assimilation schemes estimation of error statistics data

management and quality control and access to large computer facilities and

communication systems The main b enets of a global nowcast and forecast

system include the availability of reliable initial conditions for coupled o cean

atmosphere mo dels which are used for climate and seasonal forecasting reli

able b oundary conditions for high resolution regional o cean mo dels as well

as applications to marine safety sheries oshore industry and management

of continental shelf and coastal areas

Variational Data Assimilation Example

Table Comparison of various solutions for the M and K surface elevation in

2 1

the Barents Sea RMS errors cm from Kurap ov and Kivman

Mo del Resolution M RMS K RMS

2 1

Domain error cm error cm

Gjevik et al  km

Nonlinear no assimilation Barents Sea

Kowalik and Proshutinsky  km

Nonlinear no assimilation Arctic Ocean

 

Kivman 

GIM nite dierence Arctic Ocean

Kurap ov and Kivman km

GIM nite element Barents Sea

The generalised inverse of a highresolution nite element mo del of the

Barents Sea which is a part of the Arctic Ocean based on the linearised

shallow water equations was develop ed by Kurap ov and Kivman

Ocean Mo delling and Prediction

(a) 0.04

0 (Pa) y τ −0.04

−0.08

(b) 0 −0.05 −0.1 −0.15

ADP (m/s) −0.2 −0.25 −0.3

(c) 0 −0.05 −0.1 −0.15 −0.2 Assim (m/s) −0.25 −0.3

(d) 0 −0.05 −0.1 −0.15 −0.2 Model (m/s) −0.25 −0.3

170 175 180 185 190 195 200 205 210

days

Fig a Alongshore wind stress from Newp ort Oregon vector stick

o

plots of depthaveraged velo cities from b a mo ored ADP v at m depth c

a

mo del simulation with assimilation of surface velo city data v and d mo del sim

m o m o a

ulation with no assimilation v Correlations C v v C v v

from Oke et al

Concluding Remarks

This inverse mo del involved assimilation of tidal constituents from coastal

tide gauges The resulting assimilation was validated by a comparison of the

analysed tidal elevations with indep endent tide gauges in the interior of the

domain and near the op en b oundaries The results indicate that with a low

weight given to the op en b oundary conditions in the cost function the gener

alised inverse is capable of repro ducing tidal elevations of the dominant tidal

constituents with greater precision than other more complicated mo dels with

larger domains that did not utilise data assimilation These comparisons are

summarised in Table While the linear mo del clearly has signicant errors

due to the neglected physics particularly in the shallow waters these com

parisons demonstrate that its generalised inverse provides a very eective

dynamically based interp olator for this region This example demonstrates

the p ower of inverse metho ds for o cean mo deling particularly for hindcasting

and nowcasting

Concluding Remarks

Ocean circulation mo dels form an imp ortant comp onent of o ceanographic

and climate research Applications range from simulations of ow in bays

and harb ours through to coastal regional and globalscale mo dels In this

chapter we reviewed the governing equations mo del grid systems b oundary

conditions and the parameterisation of subgridscale pro cesses We also gave

sp ecic examples of a numb er of mo dels from largescale climate related

simulations to coastal exp eriments river plume mo dels and tidal ows The

use of observational data was also reviewed from mo del assessment to data

assimilation and inverse mo del techniques The future directions of o cean

mo delling research are farreaching they include renements of subgridscale

parameterisations use of higher resolution mo dels development of improved

numerical schemes applications of data assimilation towards predictive sys

tems and coupled mo delling with climate and biological mo dules

Ocean Mo delling and Prediction