Observations of oceanic potential vorticity and its relationship with other tracers

(1)

University of Southampton Research Repository

ePrints Soton

copyright owners. A copy can be downloaded for personal non-commercial

research or study, without prior permission or charge. This thesis cannot be

reproduced or quoted extensively from without first obtaining permission in writing

from the copyright holder/s. The content must not be changed in any way or sold

commercially in any format or medium without the formal permission of the

copyright holders.

When referring to this work, full bibliographic details including the author, title,

awarding institution and date of the thesis must be given e.g.

AUTHOR (year of submission) "Full thesis title", University of Southampton, name

of the University School or Department, PhD Thesis, pagination

(2)

UNIVERSITY

OF

SOUTHAMPTON

Observations of Oceanic Potential

Vorticity

and

its

Relationship

with

Other

Tracers

by

Anne

Inglis

Morrison

Doctor

of

Philosophy

School of Ocean and

Earth

Sciences,

Faculty

of

Science

(3)

ABSTRACT

FACULTY OF SCIENCE

OCEAN AND EARTH SCIENCES

Doctor

of

Philosophy

Observations of oceanic

potential vorticity

and its

relationship

with

other

tracers.

by

Anne

Inglis

Morrison

Driven

by

interest in

measuring

the oceanic

velocity

_{field from space,}sea surface

temperature

(SST)

has been

suggested

as a_{proxy for}

potential vorticity

(PV),

which may then be invertedto

give velocity.

However,

little isknown about the

relationships

between PV and otherwatermasstracers, asthese have not

previously

been

thoroughly

examined. In this

thesis,

the

inter-relationships

between

PV,

SST,

potential

temperature

and

salinity

in three

quite

different frontal

regions

of theocean are

investigated.

The

regions

studiedwere in the North-east

Atlantic,

the

Sargasso

Sea and the

Bellingshausen

Sea

(Southern Ocean).

The

only

earlier work known in this field was

by

Fischeretal.

(1989),

which found a

near-linear

relationship

between PV and

isopycnic potential

temperature

on ashallow

isopycnal

in the North Atlantic. This

relationship

wasalso evident in

climatological

values of PV and

temperature

in the North Atlantic. The results from the three

regions

considered in this thesis vary

considerably,

andarebelievedtobe dueto different frontal

dynamics

andwatermassformation mechanisms. All the North-east Atlantic results are

in close

agreement,

despite

differences inmeasurementscales and the_year_{of survey.}

Thereasons for different

relationships occurring

areexamined. Theories for

setting

PV

andtracervalues are

investigated,

and in

particular

the models of Woods

(1985)

and

Spall

(1995)

are foundto

explain

the

relationships

found in the North-east Atlantic and

(4)

CONTENTS

ABSTRACT i

CONTENTS ii

LISTOF FIGURES v

ACKNOWLEDGEMENTS

ix

LIST OF ABBREVIATIONS USED x

Chapter

1. INTRODUCTION 1

1.1 whatis this thesisabout? 1

1.2 whystudy therelationshipsbetweenpvandtracers? 3 1.3. Whatare thespecific objectives ofthisthesis? 5

1.4 howis this thesis laidout? 7

Chapter

2. BACKGROUND 9

2. l Introduction 9

2.2 physicaltermsused in this thesis 9

2.2.1 Potential

vorticity

9

2.2.2 Oceanic scales

of

motion 11

2.2.3 Ventilation andsubduction 12

2.3 historyofpvmapping 12

2.4 Mixedlayer and thermocline theories 14

2.4.1 Mixed

layer

_processes 14

2.4.2 Thermocline circulation 16

2.5

Fronts,

eddies andsubduction 20

2.5.1

Definition of

ocean

fronts

20

2.5.2

Frontogenesis

21

2.5.3 Subductionatocean

fronts

22

2.5.4 At the base

of

the mixed

layer

23

2.6 Choiceof data for this study 24

Chapter

3. VIVALDI'91 26

3.1 Introduction 26

3.2 Background 26

3.3 Datacollectionandprocessing 28

(5)

3.3.3 Three-dimensional

velocity field

29

3.3.4

Vorticity

29

3.4 Results 29

3.4.1 Watermass

analysis

29

3.4.2 Correlation

ofproperties

on

different surfaces

31

3.4.3

Comparison ofPV

with

temperature

and

salinity

measurements 32

3.5 DISCUSSION 34

Chapter^

FASINEX 50

4.1 Introduction 50

4.2 Background 50

4.3 Datacollection and processing 52

4.3.1. Three-dimensional

density field

52

velocity

field

53

4.3.3.

Vorticity

54

4.4 RESULTS 54

4.4.1. Watermass

analysis

54

4.4.2 Correlation

of

properties

on

different surfaces

56

4.4.3.

Comparison ofPV

with _temperatureand

salinity

measurements 57

4.5 DISCUSSION 60

Chapter

5. STERNA'92 72

5.1 Introduction 72

5.2 Background 73

5.3 Datacollection and processing 73

density field

74

velocity

field

74

5.3.3.

Vorticity

75

5.4 Results 75

5.4.1. Watermass

analysis

75

5.4.2. Correlation

of

properties

on

different surfaces

76

5.4.3.

Comparison

ofPV

with_temperature,

salinity

and

chlorophyll

a measurements

78

5.5 Discussion 81

Chapter

6. DISCUSSION 98

6. l Progresstowards objectives 98

6.2 HOWWELLDO THERESULTS SUPPORT THE HYPOTHESISOF A LINEAR

(6)

6.3 whydo theresultsvary from that offlw89? 101 6.4 howdo the results fit with theories ofthermoclineventilation? 106

6.5 Modificationsto theory suggestedby the results 110

6.6 Waysto test these ideas ill

Chapter?.

MIXEDLAYER MODELLING 112

7.1 Introduction 112

7.2 Historyandconceptof mixedlayer modelling 112

7.3 descriptionofUKmeteorologicaloffice mixed layer model 114

7.4 Implementationof model 117

7.4.1 Initialisation and control

of

the model 117

7.4.2

Running

the model

for

this

application

and

analysis techniques

118

7.4.3

Stability of

the model 119

7.5 ModeloutputforVivaldiregion 120

7.6 Discussion 121

7.7 Conclusions 121

Chapter

8. CONCLUSIONS 128

8.1 Achievements 128

8.2 Futurework 131

8.3 Finalcomments 131

Appendix

A. OCEAN VELOCITY FROMSATELLITES 133

A.I REMOTELY-SENSEDTRACERS OF SURFACEFLOW 133

A.2 Approachesto estimating surfacecirculationfrom satellites... 134 A. 3 Existingmethods for evaluating surface flow from satellite

IMAGES 135

Appendix

B. INVERTINGPVTO VELOCITY 138

B. 1 MODELTO BE USED FORPVINVERSION 138

B .2 Inversiontechniquesand preliminaryresults 141

Appendix

C. ATLANTICISOPYCNIC MODEL

(AIM)

144

C.I THEMODEL 144

C.2 COMPARISONOF SVERDRUP PVWITHISOPYCNICPOTENTIAL TEMPERATURE

AND MIXED LAYER TEMPERATURE 145

C.3 ComparisonofAIMresults withVivaldiresults 145

Appendix

D. DERIVATION OF ISOBARIC POTENTIAL VORTICITY

EQUATION (2.4)

149

(7)

Fig.

1-1

Chlorophyll image

from the Coastal Zone Color Scanner

(CZCS)

for 7

May

1979

showing

the Gulf Stream and associated

rings

3

Fig.

1-2 Potential

vorticity

field of the north-west Atlantic Ocean

(Gulf

Stream

area)

from

layer

5

(102.038 metres)

of the Ocean Circulation and Climate

Advanced Model

(OCCAM).

Figure by

M.-M.

Lee,

SOC 4

Fig.

2-1 Model of

layers

_{in the upper}ocean. The convection

layer

is

statically

unstable,

while the remainder of the mixed

layer

is

weakly

stable. The flow is

predominantly

laminarin the seasonal and

permanent

pycnocline.

(After

Woods

(1985))

18

Fig.

3-1 Sea surface

temperature

during

Vivaldi '91 withcruise tracks overlaid...36

Fig.

3-2 e-S

plots

for 0.02

kg

m"3

isopycnal

data 37

Fig.

3-3 e-S

plots

for0.15

kg

rn3

isopycnal

data 38

Fig.

3-4 Potential

density

vertical sections 39

Fig.

3-5 Potential

temperature

Fig.

3-6 Potential

Vorticity

Fig.

3-7

Comparison

of

potential

temperature

on different

isopycnals

42

Fig.

3-8

Comparison

of IPVondifferent

isopycnals

43

Fig.

3-9

Comparison

of

properties

on different isobaric surfaces 44

Fig.

3-10

Relationship

between Potential

Vorticity

and

temperature

on

isopycnals

of

0.15

kg

m"3

gridded

data 45

Fig.

3-11

Relationship

between PV and

salinity

on

isopycnals

of 0.15

kg

m'3

gridded

data 46

Fig.

3-12

Relationship

between PV and

temperature

onisobaric surfaces 47

(8)

Fig.

3-14

Maps showing climatological

values for

May

of

(a)

temperature,

(b)

salinity

and

(c)

Sverdrup

PVon

isopycnal

27.00

kg

m"3

in the North Atlantic,

(a)

and

(b)

taken from Bauer and Woods

(1984). (c)

taken from

Stammer and Woods

(1987)

49

Fig.

4-1 30 dbar

potential

temperature

during

FASINEX SeaSoar Run 2 with cruise

tracks overlaid 61

e-S

plots

62

Potential

density

Potential

temperature

Potential

Vorticity

Relative

vorticity

Comparison

of

properties

ondifferent surfaces 67

Relationship

between IPV and

temperature

onvarious

isopycnals

68

Relationship

between IPV and

salinity

onvarious

isopycnals

69

Relationship

between IPV and

temperature

onvarious pressure surfaces. 70

Relationship

between IPV and

salinity

on _{various pressure surfaces} 71

5 dbar

potential

temperature

during

STERNA SeaSoar Run lEl with cruise

tracks overlaid 83

e-S

plots

84

Potential

density

Potential

temperature

Salinity

Chlorophyll

Potential

Vorticity

Relative

vorticity

(9)

Fig.

5-10

Relationship

between PV and

temperature

onvarious

isopycnals

92

Fig.

5-11

Relationship

between PV and

salinity

onvarious

isopycnals

93

Fig.

5-12

Relationship

between PV and

chlorophyll

a onvarious

isopycnals

94

Fig.

5-13

Relationship

between PV and

temperature

onvarious_pressure surfaces..95

Fig.

5-14

Relationship

between PV and

salinity

on various pressure surfaces 96

Fig.

5-15

Relationship

between PV and

chlorophyll

a on_{pressure surfaces} 97

Fig.

6-1 Schematic

diagram

of IPV

generation

andthe establishment of IPV-water mass correlation. The

spring

rise of the mixed

layer depth (heavy

line)

and the subductionof

isopycnals

intothe seasonal thermocline areshown.

Region

1 is

representative

of the

subtropical

_{gyre, and}

region

2 of the

subpolar

gyre. Fora

pair

of

isopycnals

the 9-S

relationship

is determined

by

the

region,

while the

spacing

is determined

by

the time of subduction.

(After

Fischeretal

(1989))

102

Fig.

6-2 Schematic

diagram showing

aconfluence

moving

waterintoan areaof

increasing (decreasing)

absolute

vorticity

onthe

cyclonic (anticyclonic)

sideofa

front,

causing

the

separation

of

isopycnals

toincrease

(decrease).

Since the surface is

fixed,

avertical circulation is set_up as shown.

(After

Pollard and

Regier

(1992))

105

Fig.

7-1 Section

plots

from

model,

day

137 year5 123

Fig.

7-2 Time series of

potential

temperature

and PV from model at selected

latitudes 124

Fig.

7-3 PV

against potential

temperature,

from model

day

_{140 year}

5,

for 4

isopycnals

125

Fig.

7-4 PV

against potential

temperature,

from model

day

_{161 year}

5,

for 4

isopycnals

126

Fig.

7-5 PV

against potential

temperature,

from model

day

_{203 year}

5,

for 4

(10)

Fig.

B-l Two

layer

model of different

density

fluids, top

layer

much shallower than

lower

layer,

with flow

only

in

top

layer

139

Fig.

B-2 Simulated

QGPV

field

produced

from AVHRR SST

imagery

ofaGulf Stream

ring,

overlaid with

velocity

vectors derived

by inverting

the

QGPV

using

scale

length

10.0 and

boundary

conditions ofzerostreamfunction.

143

Fig.

C-l Mixed

layer

temperature,

layer

11

potential

temperature

and

layer

11

Sverdrup

PV fromrun

AW,

_year

30,

month 8

(May)

of AIM 147

(11)

I would liketo thank Prof. Ian Robinson and Dr Meric Srokosz for their

supervision

and

encouragement

during

the courseof this work.

This thesis couldnothave been carried outwithout the

data,

whichwerecollected

during

three

cruises,

and I would liketo_{record my thanks} tothose scientists and

ships'

crew and technicians who did this. I amalso

grateful

to

Meric,

andtoDavid Turner

(Principal

Scientist),

for

allowing

me totake

part

in

Discovery

Cruise 198.

Many

other

people

_gave me

help,

advice and

information,

andwere

generally willing

to

discuss various

aspects

of the work. The most

significant

of thesewere

Raymond

Pollard,

Jane

Read,

George

Nurser,

Ian Totterdell and Yanli Jia. Other members of the James Rennell Division of

Southampton Oceanography

Centre also

helped

_me, and I

apologise

fornot

listing

them all

by

_name,but itwas much

appreciated.

(12)

LIST OF ABBREVIATIONS USED

e-s ACC ADCP ATSR AVHRR CTD CWB CZCS ENAW FASINEX FLW89 GPS IPV LPS83 MLD NAC NACW PF PV PVU RRS RY82 SFZ SPF SST STERNA '92 STCZ TSG Vivaldi '91 WNAW WOCE

Potential

temperature

-

Salinity

Antarctic

Circumpolar

Current

Acoustic

Doppler

Current Profiler

Along-Track Scanning

Radiometer

Advanced

Very High

Resolution Radiometer

Conductivity-Temperature-Depth

Continental Water

Boundary

Coastal Zone Color Scanner

Eastern North Atlantic Water

FrontalAir-SeaINteraction

Experiment

Fischer,

J.,

H. Leach and J. D. Woods

(1989)

A

synoptic

_{map of}

isopycnic

potential vorticity

in the seasonal thermocline. J.

Phys. Oceanogr.,

19,

519-531.

Global

Positioning System

Isopycnic

Potential

Vorticity

Luyten,

J.,

J.

Pedlosky

and H. Stommel

(1983)

The ventilatedthermocline. J.

Phys. Oceanogr.,

13(2),

292-309.

Mixed

Layer Depth

North Atlantic Current

North Atlantic Central Water

Polar Front

Potential

Vorticity

Potential

Vorticity

Unit,

equivalent

to

lO'9 m"1

s1

Royal

Research

Ship

Rhines,

P. and W.

Young

(1982a)

Homogenization

of

potential vorticity

in

planetary

gyres. /. Fluid.

Mech., 122,

347-367.

Subtropical

Frontal Zone

Southern Polar Front

Sea Surface

Temperature

Bellingshausen

Sea survey

(not

an

acronym)

Sub-Tropical Convergence

Zone

ThermoSalinoGraph

North-east Atlantic Ocean survey

(not

an

acronym)

Western North Atlantic Water

(13)

1.1

WHAT

IS THIS THESIS

ABOUT?

Interest inocean

dynamics

has

developed

for many reasons, notleast of which is that the

ocean

plays

an

important

role in

setting

the weather and climateover land and sea

(Apel,

1987).

Commercial

shipping

uses

knowledge

of the

velocity

and

position

ofcurrents to

make their

operations

safer,

cheaper

and

quicker,

while scientific researchers needto

know aboutcurrents tounderstand the

transport

of

heat,

nutrients and

pollutants.

These

applications require knowledge

ofclimaticocean

dynamics,

and short-to

medium-range

forecasts of the ocean's state, while studies of

global

environmental

change require

forecasts on

longer

time-scales.

In the last few

decades,

oceanmodels have been

developed

to

study

the ocean's effect on

long-term

climate

change,

andto look at

dynamics

onvarious

temporal

and

spatial

scales

(Bryan,

1969,

Cox and

Bryan,

1984, Oberhuber, 1990).

Theseoceanmodelsuse

approximate

forms ofthe basic

equations

_{that govern}ocean

dynamics,

andare

integrated

forward in time froma setof initial

conditions,

to

give

anestimate of the

physical

stateof

theocean at alater time. The

equations

used in these modelsare

gradually developing

towards

being

more

representative

of the observed

dynamics

in the _ocean, whicharenot

yet

fully

understood. The initial

conditions,

suchasthe initial

velocity

field,

needtobe as

accurate and

precise

as

possible,

because

subsequent integration

ofamodel is

dependent

on these. As

computer

technology improves

and models are

developed, they

arebasedon

grids

of finer

resolution,

and theinitialisationfieldsmust

adequately

represent

the

dynamics

atthese finer resolutions

(Robinson,

1996).

Initial

velocity

fieldsare

mainly

derivedfromhistorical

hydrographic

datacollected 'in

situ' from

ships

or

buoys

in the

region

ofinterest

(Smeed,

et

at., 1991,

Smeed,

et

at.,

1992).

Hydrographic

dataare_{sparse in location and}

time,

more soin some

regions

than

others,

and aretherefore notideal foruse in initialisation of models. Satellite data have introduced the

possibility

of

improving

the initial

fields,

by specifying

the initial

velocity

field inmore detail thancanbe derivedfrom

hydrographic

data. Satellite-borne

instrumentscan _survey

large

areasofocean, atleast

quasi-synoptically,

and a

single

satellitecan achieve

global

_{coverage in} a

fairly

shorttime. Satellites follow

repeated

orbits,

meaning

thata

particular patch

ofsea canbe

surveyed regularly,

_say

monthly

or

seasonally,

fora

length

of time up to thelifetimeof the satellite. That isto _{say, data may}

be availableover allareasof the _{ocean, at}all times of the year, over _{many years:} a

situation whichcannotbe achieved

by hydrographic

_{surveys alone.}

However,

current

(14)

Chapter

1 Introduction

The

velocity

field of the oceancannot

directly

be measured from satellites andmustbe inferred from someothermeasurementsuch as seasurface

temperature

(SST)

or sea surface

height. Although

it is

possible

tomeasure the

varying

part

of the surface

geostrophic

currentwith asatellite

altimeter,

themean ocean circulationcannotbe

easily

separated

from the

geoid signal (Marshall,

1985).

Until this

happens through determining

the

geoid directly by measuring

the Earth's

gravitational

field,

other

techniques

have been

developed

to

get

round the

problem.

One such methoduses

hydrography

atthe time of

one satellite pass todetermine the absolute_current, whichcanthen be inferred

by

subsequent

passes whichmeasure the

variability

of the current

(Challenor,

et

al,

1996).

For many

applications, velocity

variability

is all that is

required,

and

using

satellite

altimetry,

relative

velocity

canbe derived frommeasurements ofsea surface

height

on

scales of less than about 2000 km where

geoid

models arebelievedtobe

good. Accuracy

of better than 5 cm

s"1

has been claimed for such measurementsof

variability, resolving

scales of 50-80 km

along-track

(Strub,

et

al,

1997).

The assimilationof altimeter data

into oceancirculation models is an active research field

(e.g.

Wunsch, 1996, Haines,

1991,

Haines,

et

al,

1993).

Satellite

images

ofSSTand Ocean Colour often have finer resolution

(e.g. pixel

size of order 1 km for SST data from the AVHRRorATSR

instruments),

and so

present

the

possibility

of

forming

moreaccurate initial

velocity

fields for models.

However,

the conversion from measured

quantity

to

velocity

is not

straightforward

and has beenan area of much research inrecent_years.

Appendix

A of this thesis

presents

a_{summary of the} status of research into

deriving

the

velocity

field from satellite

imagery. Generally,

a_{sequence of}twoor more

images

overthe same areais

required

toderive the

velocity

field,

and such a_{sequence is}often difficultto obtain dueto

cloudcover and satellite orbit

pattern.

It has been

proposed by

other researchers

(Marshall

and

Williams, 1989)

that

velocity

could be derivedfroma

single

satellite

image

ofa suitable_tracer,

by using

it as a_proxy for the

potential vorticity

(PV)

atthe base of the oceanic mixed

layer.

PVis the fluid

equivalent

of

angular

_momentum, and

comprises

a

planetary

component

(i.e.

dueto

planetary

rotation)

andalocal

component

(i.e.

duetolocal

forces).

Before

attempting

to

implement

aschemeto derive

velocity

from SST treated as a_{proxy for}

PV,

it is necessary

tounderstandbetter the

relationship

between PV and othertracers. Oceanic PV on small scales

(order

10

km)

has notbeen studied

extensively

because of the

difficulty

of

measuring

it 'm situ' andso

present

understanding

is limited.

However,

it is now

possible

to

study

these

inter-relationships

because methods for

mapping

oceanic

potential vorticity

have

improved

with the increased

deployment

of

undulating

towed

hydrographic

instruments suchas SeaSoar

(Fischer,

et

al., 1989, Allen,

et

al, 1992,

Pollard and

Regier,

(15)

The main

objective

of this thesis isto considerthe

inter-relationships

of

PV, SST,

potential

temperature

and

salinity

inthree

quite

different frontal

regimes.

The areas of

study

are the North-eastAtlantic

Ocean,

the

Sargasso

Sea and the

Bellingshausen

Sea

(west

ofthe Antarctic

Peninsula).

It _emergesthat these

regions

show

quite

different inter¬

relationships

between PV and_tracers, and the reasons forthis are

examined,

concentrating

onfrontal _{processes and}watermassformation. Theories for the

setting

of

PV and tracervalues are

put

forward and

investigated, using

a 1-dimensional model

running

atdifferent

geographical positions

to followthe

development

of the PV-tracer

relationship.

This thesis is

unique

in

examining

the PV-tracer

inter-relationship

and in

comparing

these

relationships

in such different

regions.

Itwas

hoped

atthe outsetthata clearfunctional

relationship

_{between PV and SST} _would be

established,

_{and that this could then be used}_to _{derive the}

velocity

field froma

single

SST

image.

Some

preliminary

workwas carriedout todemonstrate howto

implement

such a

scheme,

by

inverting

the PVfield to

yield

velocity

measurements. This work is

presented

in

Appendix

B. As it_{turned out,} and will be shown in later

chapters,

the results ofthe PV-tracer

comparison

showedthat the

relationship

is

complicated

and

variable,

so theinversionofthePV fieldwas not

pursued

further in this work.

In thenext section ofthis

chapter,

the motivationbehindthe

study

of the PV-tracerinter¬

relationship

is

explained

in moredetail.

Specific

objectives

forthe workare setout inthe

following

section. It is the intention ofthis thesisto show thatthese

objectives

are

achieved. In thefinal

section,

the

layout

ofthis thesis is described.

1.2

WHY

STUDY THE

RELATIONSHIPS BETWEEN

PV

AND

TRACERS?

Satellite

images

of SST and oceancolourshow

strong

frontal

features,

suchas the Gulf Stream and its associatededdies and

rings

(see

Figure 1-1).

Phytoplanktort PigmentConcentration(mgftn3) rr

1.5 30.

Figure

1-1

Chlorophyll

image

fromthe CoastalZoneColor Scanner

(CZCS)

for7

May

1979

(16)

Chapter

1 Introduction

These

images

are also reminiscent of fields of

potential vorticity

(PV)

from

eddy

resolving

ocean

models,

an

example

of which is shown in

Figure

1-2

(Holland,

et

al,

1984,

Marshall and

Williams, 1989, McDowell,

et

al, 1982).

Potential

vorticity

can

describe the motion ofa

geophysical

fluid suchas theocean, because it is aconserved

quantity following

afluid

parcel (Hoskins,

et

al., 1985).

Mesoscale

features,

which have a

horizontal

length

scale of order 100

km,

suchaseddies and

rings,

areunderstoodto have

strong

PV

signals

associated with them

(Apel,

1987).

Figure

1-2Potential

vorticity

field of thenorth-westAtlantic Ocean

(Gulf

Streamarea) from

layer

5(102.038 metres)ofthe Ocean Circulationand Climate Advanced Model

(OCCAM).

Figure by

M.-M.

Lee,

SOC.

Such observations

suggest

that afunctional

relationship

_{may exist between PV and}a surface tracer

field,

such asSST or ocean colour.

However,

while PV may be considered

tobe a conserved

quantity,

SST and ocean colourarebetterdescribed as

quasi-conservativetracerswhich areadvected

by

the

underlying velocity

field. Neither SSTnor

oceancolour is

exactly

conservedbecause

changes

in SSToccurwhen heatis

exchanged

between the

atmosphere,

the

sea-surface,

and theocean

interior,

and oceancolour varies as

phytoplankton

_{grow and}

decay

with the seasons.

Nevertheless,

onthe

length-scales

of

mesoscaleocean features and overtime-scales of the order ofafew

days,

SST andocean colourare

approximately

conserved

(Stow,

1987).

Evidence foraconnection between PV and

temperature

was

presented by

Fischeret

al,

(1989) (henceforth

referredto as

FLW89).

They

found that PV and

isopycnic

potential

temperature

fields canbe

functionally

related,

identifying

a near-linear

relationship

on a shallow

isopycnal

in afrontal

region

of the North Atlantic

during

the summerof 1981.

They

also demonstratedthat when

studying

mesoscale

dynamics,

relative

vorticity

is

significant

andmustbe

evaluated,

although

it contributes

negligibly

to PVon the gyre-scale

(of

order 1000

km).

Climatological

values of PV and

temperature

in the north-east Atlantic _appearto have asimilar near-linear

relationship

(Bauer

and

Woods,

1984,

(17)

Undersomecircumstances surfacefields andsub-surface fields have been showntobe

strongly

linked. For

example,

SST and

isopycnal potential

temperature

in the Gulf Stream are

strongly

correlated in the vertical

(Open

University,

1991).

It _maybe

possible

to

exploit

this tofind afunctional

relationship

betweena surfacetracer field detectable

by

satelliteinstruments and sub-surface PV values.

In

strong

frontal

regions,

orwhere there is

strong

eddy activity,

PV and surfacetracer

fields

(such

asSST and ocean

colour)

_{may be}influencedmore

by

horizontaladvection of

properties

from distant

sites,

than

by

local

forcing

or

dissipation.

Thiscan

happen

because PV and othertracerfields are setwhenwater is subducted from the surface intothe

thermocline,

andarethen

conservatively

transported

along isopycnals

(Woods,

1985).

Hence,

it may be feasible touse surfacetracers as

proxies

for

PV,

which is a subsurface

property

defined

only

within stratified

regions

of the_ocean,below themixed

layer.

Because therearevarious circumstanceswhichcan leadto _strongvertical coherence of

properties

of thewater

column,

different

relationships

_may occurbetweenthe PVand the surface field. That isto _{say, it is}

expected

thatthe

relationship

_{may vary with} seasonand

geographical region.

The

inter-relationships

between observed_upper oceanPV and othertracershavenotbeen

thoroughly

examined

before,

although

several researchers have commented that

anomalies occurin PV andtracers atthe same locations

(McDowell,

et

al,

1982,

Voorhis and

Bruce,

1982,

Arhan and Colin de

Verdiere,

1985, Marshall, 1995,

Talley,

1985).

Investigators using

modelsto

study

_{frontal processes have also mentioned the}

relationship

between PV and other_tracers,but have not studiedthem

closely,

_{e.g. Samelson and}

Chapman

(1995).

It isnow

timely

to considerthese

inter-relationships

as

they

_{may shed}

light

onthe mechanisms offrontal processes _{and may prove useful} in

deriving dynamical

informationfrom satellites.

1.3.

WHAT

ARE THESPECIFIC

OBJECTIVES

OF THIS

THESIS?

Having

established thatit is worthwhileto examine the

relationships

between PV and

tracer

fields,

because of their

importance

infrontal

dynamics

andocean

modelling,

itis

necessary todefine more detailedand

specific objectives

to achieve this.

* _{The first}

step

isto define

PV,

as itsdefinition

depends

onthe

simplifying assumptions

which aremade in

studying

ocean

dynamics.

Next,

it is necessary toassess what is thebest_way to_{derive and map PV from}

hydrographic

data. This leadsus toexamine the

development

of PV

mapping,

the

(18)

Chapter

1 Introduction

Thenext

objective

is tofindout whetherFLW89's

relationship

between PV and

isopycnic

temperature

is found in other datasets from the same

region

andother

regions.

In other

words,

is this auniversal

relationship?

To do

this,

the datafromthree frontal_surveys areexamined.

Comparisons

of the PV fields with

temperature,

and other measured

quantities,

show that the

inter-relationships

are

quite complex

anddifferent for each data set. From this

result

emerged

the

major objective

of

describing

the results and

explaining why

the datasets show different

PV-temperature relationships.

To

explain why

the data

give

different

results,

_{it is necessary}toexamine theoriesfor the

setting

of PV and

temperature

_{in the upper}ocean and consider how thesecan

accountfor the resultsfound in the data.

It is also desirabletoconsider whether the datacan

suggest

modificationsto the

currenttheories.

To

study

the

development

of the

temperature

and PV

fields,

and their inter¬

relationship, using

aone-dimensional mixed

layer

model which is run

using

initial

fields

appropriate

tovarious locations within theVivaldi '91

region.

This allowsusto

lookatwhetherthe

resulting PV-temperature relationship

is similartothatfromthe observed

data,

andto consider

why

_{it agrees}or

disagrees.

The

analyses

ofthe datasets show that the

relationship

between PV and SST atafrontal site areinfluenced

by

the conditions andcircumstances which have ledto the formation

of the front. The

complexity

of these results weakens the

possibility

of

reliably recovering

PV from

SST,

butat thesametime

provides

new

insights

into the frontal _processes which

produced

them. Some

preliminary

workwascarriedout to

investigate

how to

proceed

fromaPV field

through

inversion ofamodel of PV toobtain the

velocity

field,

and this is

presented

in

Appendix

B. Plans totakethis

further,

by using

the derived

PV-temperature

relationships

in the data sets,were setaside in favourof

examining

thefrontal

dynamics

that led tothese different

relationships.

However,

this could be taken forward atsome other time.

This

study

is

unique

in

looking

at_{three very} different

regions through high quality

surveys. The datasetswerefrom three different

regions,

where the fronts haddifferent

histories andwereformed

by

different

mechanisms,

_{and the surveys had been carried} out

(19)

1.4

HOW

IS THIS THESISLAID

OUT?

In thenext

chapter,

various terms aredefined.

Ways

to derive and_map PVare

examined,

and themost

appropriate

methods selected for the chosen datasets.

Three

hydrographic

_survey data sets wereexamined in this

work,

andthe results of these

investigations

are

presented

in

Chapters

3 to_{5. Each survey} collectedmeasurementsof

temperature,

salinity

and pressure, and

independent

measures ofcurrent. These

measurements should be sufficienttoestimate the PV fields

according

tothe methods

established in

Chapter

2. Thethree datasets examinedareVivaldi

'91,

FASINEX and Sterna '92. Thesewere selected for

study

because

they

were

readily

available

locally

and are _{surveys of}

quite

differentfrontal

systems.

Additionally,

Vivaldi '91 datacome froma similarlocation tothe_survey examined in FLW89. It should be noted that the author

participated

in the Sterna '92

cruise,

andwasinvolved in the initial

collection,

processing

andcalibrationof these data.

The Vivaldi '91

data, presented

in

Chapter

3,

werecollected

during April

toJune 1991 and

comprise

a

hydrographic

_{survey of the}

top

450mof theocean

spanning

part

of the Azores Currentin thenorth-east_{Atlantic Ocean. The survey} was of sixnorth-south

sections between 39N and54N

separated by approximately

300 km

zonally.

In this

chapter,

the Vivaldi '91 datasetis

described,

andthe

analysis

of the

PV,

temperature,

salinity

and other fields is

presented

and

compared

with the resultsofFLW89.

The FASINEX

data,

presented

in

Chapter

4,

werecollected

during February

1986 and

comprise

a

hydrographic

_{survey of the}

top

300m of theocean

spanning

afront in the

Sargasso

Sea,

south-west of

Bermuda,

_{in the north-west Atlantic Ocean. This survey} was

of

eight

north-southsectionsbetween 27N and29N

16 km

zonally.

In this

chapter, descriptions

of the datasetand results of the

analyses

are

presented

for the FASINEX data set, ina similar

layout

tothe

analyses

of Vivaldi data in the

previous chapter.

The Sterna '92

data,

presented

in

Chapter

5,

werecollected

during

Novemberto

December 1992 and

comprise

a

hydrographic

_survey of the

top

400m of theocean

spanning

afrontin the

Bellingshausen

Sea,

inthe Southern Oceanto thewestof the Antarctic Peninsula. This _surveywas ofsevennorth-southsections between 66.5S and 68S

15 km

zonally.

In this

chapter,

descriptions

of the data

set and results of the

analyses

are

presented

for the STERNA data set, in a similar

layout

(20)

Chapter

1 Introduction

These are

followed,

in the sixth

chapter, by

discussion of the results from the three data

sets. This

chapter

also containsareviewofcurrenttheories ofoceancirculation and frontal

dynamics

with

particular

referencetowatermass formation and PV. These theories areconsidered

alongside

the data results.

To

explore

how the

PV-temperature relationships developed,

a

simple

one-dimensional

mixed

layer

modelwas usedto simulate the circumstancesof the Vivaldi data set, and this work is

presented

in the seventh

chapter.

Finally,

in the

eighth chapter,

the overallconclusions are

presented.

Three

appendices

tothis workarealso

attached,

describing

several

pieces

ofwork which werecarriedout

during

thecourseof the

thesis,

but which donotbear

directly

onthe

specific objectives

of the thesis.

Appendix

A contains areview of methods for

deriving

ocean currents fromsatellite data.

Appendix

B illustrates how aPVfieldcanbeinverted

to

yield

velocity

estimates.

Appendix

C containsa

comparison

between PV and

(21)

2.1

INTRODUCTION

The main

objectives

ofthis

chapter

areto define what ismeant

by

Potential

Vorticity

(PV)

in thecontextof this

thesis,

and toassess the best wayto _{derive and map PV from}

hydrographic

data. To do the

latter,

the

development

of PV

mapping

will be examined.

Following

this,

a short review of the maintheoriesof mixed

layer

_{processes and} thermocline circulation is

presented,

to setthecontextwithin which the

relationship

between PV and otherwatermasstracers will be examined. In section

2.5,

the

characteristics and theories are discussedof what

happens

in frontal and

eddying regions

of theocean with

respect

to subduction. These arerelevant when

considering

the

FASINEX and STERNA data in

particular,

whichare _surveysat themesoscale.

Finally,

in section

2.6,

the motives for

studying

these

particular

data setsare

explained.

2.2

PHYSICAL

TERMS USED IN THIS THESIS

2.2.1 Potential

vorticity

Potential

Vorticity

(PV),

which is a measureofawatercolumn's

tendency

to rotate, is very

important

totheories ofoceancirculation

(Holland,

et

al, 1984,

Rhines, 1986,

Pedlosky,

1990,

Marshall and

Nurser,

1992).

The definition of PV varies in different

dynamical

situations. The PV definitions

appropriate

to mesoscale and submesoscale processes atocean fronts aredescribed in this section.

The PV ofa watercolumn bounded

vertically by density

surfaces is the

isopycnic

potential vorticity

(IPV).

The vertical

component

of IPV withina

region

where_{x, y} increase eastand

northwards,

respectively,

is defined

(Apel,

1987,

Pedlosky,

1987)

by

q=

C+f

Ap

AP

A)

(2.1)

where

f

=

{dv/dx

-

du/dy)

and

/are

the vertical

components

of relative and

planetary

vorticity respectively

(w

and varethe

components

of

velocity

in thexand_y

directions,

respectively),

Ap

is the vertical

spacing

definedin terms_{of the pressure difference}

(22)

Chapter

2

Background

/

= 2Q.sinX

n

2)

whereQis the earth's

angular speed

of rotation of

approximately

7.292x

10~5

s"1,

and X is the latitude. The relative

vorticity, ,

is the

component

of

vorticity

caused

by

local forces such aswindstressorfrictional forces. The sumof the

planetary

and relative

components

(/

+

)

is the total

vorticity,

which is more

usually

known asabsolute

vorticity.

From

equation

(2.1)

it is seenthat the IPV is the

product

of the vertical

component

of absolute

vorticity

and the

density

structure of thewatercolumn. It is defined

only

in the

statically

stableocean

interior,

including

the seasonal

thermocline,

butnot _{in any mixed}

layer,

because the mixed

layer

has

homogeneous

vertical

density

structure.

For gyre- or

large-scale

motions,

/(Pedlosky,

1987),

and IPV reducesto the

Sverdrup isopycnic potential vorticity (Woods, 1985)

which contains

only

the

part

of the PV due tothe

planetary vorticity,

definedas

AP

A)

(2.3)

Following

Pollard and

Regier

(1992),

analternate formulation to

(2.1)

for

evaluating

PV

on isobaric surfaces is

(see

Appendix

D for

derivation)

(2.4)

whereNis the Brunt-Väisälä

frequency

(iV2

=

-gp"'pz),

F=

(u2

+

v2)/iV2

is the Froude

number and =

C,

+

Ff

is the relative

vorticity

calculatedonisobaric surfaces. In

(2.4),

-Fis a

twisting

term,

expressing

the conversion ofhorizontal

vorticity

to vertical

vorticity

by

the vertical shear. The

equivalent expression

to

(2.3)

onisobaric surfaces is

qs =

fli2/g.

(2.5)

Both forms of the IPV

equations,

(2.1)

and

(2.4),

and

Sverdrup

IPV

equations,

(2.3)

and

(2.5),

wereused in this thesis

depending

onthe dataset. The formulation used will be indicated in the text. Forease of

reference,

the

potential

vorticity

unit

(PVU)

will be defined

throughout

this thesis such that 1 PVU is

equivalent

to

10~9 m's1

(sometimes

(23)

2.2.2 Oceanicscales of motion

There isa continuous

spectrum

of

interacting

oceanic motions across different

time,

_space and energy scales.

Large-scale

or

gyre-scale

motions have horizontal scales of the order

of 1000

km,

which includes the

general

circulation of the

sub-polar

and

sub-tropical

ocean _gyres.

Large-scale

motions make_upthemean motion of theoceanand arethe

oceanic

equivalent

of "climate"

(Open University,

1991).

Motions atintermediate scales of the order of 100

km,

more

commonly

called

mesoscale,

are theoceanic

equivalent

of "weather". Mesoscale motions aredominated

by

eddieswith

length

scales of 50-200 km and

periods

ofoneto afew months. These eddiesare believedto

gain

_{their kinetic energy from the relaxation of}

sloping

isopycnals

which

releases

potential

_{energy from the oceanic} meanflow. Mesoscale eddies aremost

commonly

generated

at

density

discontinuities where flow

perturbations

called "baroclinicinstabilities" _{may form and}evolveinto

eddies,

although

thereare other mechanismswhichcan _generate mesoscale eddies

(Apel,

1987).

Such eddies are an intrinsic

part

of the oceanic circulation andare found

throughout

the world's oceans. It is

thought

thatmost _{of the ocean's kinetic energy is contained in these mesoscale motions}

(Open University,

1991).

Smaller scale

motions,

known as sub-mesoscale

motions,

of the order of 10 kmalsooccur in theocean. Most mid-ocean

fronts,

whichare somefewtens of kilometres _across, fall

withinthis_range

(Open University,

1991).

The

Rossby

radius of

deformation,

_R, is an

approximation

tothe distance that a_wave, or other

perturbation,

cantravel before

being

significantly

affected

by

the Coriolis

force,

or in other

words,

the

length-scale

atwhich rotation effects balance

buoyancy

effects. Itcan be shown

(Gill,

1982,

Pedlosky,

1987)

that in thecontext of

quasigeostrophic

motion,

the

Rossby

radius isthe scaleatwhich the relative

vorticity

and the vortex

stretching

make

equal

contributions tothe

potential vorticity.

When

examining

the contributionof relative

vorticity

to

PV,

it is usefulto examine the

Rossby

radius of the observed oceanic

region.

There aredefinitions of

barotropic

and baroclinic

Rossby

radii,

and thebaroclinic

Rossby

radii includeone for each baroclinic internal mode

(Pedlosky,

1987).

In this

work,

the relevant

quantity

is the baroclinic

(or internal)

Rossby

radius,

/

(2.6)

(24)

Chapter

2

Background

,

AP

P

(2.7)

The three

hydrographic

data setswhich are

analysed

in this thesis will be described in

moredetail in later

chapters,

but the scales resolved

by

the surveys areconsidered here.

All three data setshave

along-track spatial

_{resolution of around 4 km. Two of the surveys,}

STERNA and

FASINEX,

had between-track

separation

of around 15

km,

so some sub-mesoscale features will have been resolved

by

_{these surveys,}

though

the smallest features

may well have been aliased. The Vivaldi survey hadabetween-track

separation

ofsome

300 km.

Hence,

this survey was almost ableto resolve mesoscale features between

track,

andsome sub-mesoscale features may be discernible in the

along-track

direction.

2.2.3 Ventilationand subduction

Inthecourse of this

thesis,

the

properties

of the oceanin the mixed

layer

and seasonal

thermocline areexamined. These

properties

_{may be} setand

changed by

the transfer of

waterbetween the mixed

layer

and the thermocline

below,

soit is

important

toconsider the mechanisms

by

which fluid transferoccurs, and howwater

properties

are affected. Ventilation is the transfer ofwaterfrom the mixed

layer

to the

thermocline,

while subduction is the motion of fluid

along

an

isopycnal

from the mixed

layer

into the

thermocline,

which meanstheterms areoften

interchangeable

(Udall, 1993).

Fluid from the mixed

layer

ventilates the thermocline

temporarily

in the seasonal

thermocline,

from where it is later re-entrained into the mixed

layer,

or is

permanently

subducted

beyond

the

maximum mixed

layer depth

into the

permanent

thermocline

(Woods, 1985).

2.3

HISTORY

OF

PV

MAPPING

Fluid circulation and

vorticity

have been

recognised

as

important

concepts

in

meteorology

and

oceanography

since the end of the 19th

century,

but the theories wereso

complex

that itwas difficulttomakeuse of them in studies of the environment

(Hoskins,

et

al.,

1985).

Thiswas the situation until

Rossby

made advances in the late

1930s,

by

recognising

that the vertical

component

of absolute

vorticity

is the most

significant

for

large-scale atmospheric

flow,

and that it could be assumedtobe conserved in horizontal motion.

Rossby developed

this notion further

by using

the

concept

of PV to describe the interaction ofvortex

stretching

and horizontal advection of absolute

vorticity,

and extended itto surfaces ofconstant

potential

temperature

(isentropes).

From this time

onwards,

atmospheric

researchers embraced theuse of

isentropic

chartsto look at

(25)

paper

published

in

1942,

Ertel

independently

extended

Rossby's

results tofull

hydrodynamical generality.

Over the

following

decades the

utility

of

atmospheric

PVhas been

gradually exploited

(Hoskins,

et

al.,

1985).

In the late

1940s,

PVwasusedto

study

the

Lagrangian

behaviour of the

atmosphere.

In the

1950s,

the idea of PV anomalies wasusedto

explain

events in the upper

troposphere.

Around this

time,

researchers also

began

to_map out

atmospheric

PV structures inmore

detail,

and lookedatits

adequacy

as anair-mass tracer.In the

1960s

mapping

of PVwasmade easier with the advent of

computers,

and the 1970ssaw these maps

being

usedmore

routinely

to

diagnose atmospheric

behaviour.

By

the 1980s PV had takena

leading

role in the

diagnostics

of

atmospheric

models.

Meanwhile,

similar

developments

were

taking place

in

oceanographic

studies,

but ata slower

place,

because of the

difficulty

of

obtaining

datasetswith sufficient resolutionto

produce

maps. Parr

(1938)

and

Montgomery

(1938)

were the firstto

publish plots

of

large-scale

scalar

properties

on

isopycnic

surfaces. It tooka

long

time for the

utility

of

this

concept

tocatch on! In the

1960s,

several atlaseswere

published

of

gyre-scale

distribution of pressure,

temperature,

salinity

and other

properties

onselected

isopycnals

in the Pacific Ocean

(e.g.

Reid,

1965)

and since then it has been

accepted

that

isopycnic

maps arevaluable in the discussion of the oceanic

general

circulation. Motion is

expected

to be

approximately

in the

plane

of

isopycnals

onboth the

gyre-scale

and the mesoscale

(McDowell,

et

al., 1982).

However,

itwasconsidered difficultto_{map mesoscale}

hydrographic

data because traditional

hydrocast

CTD dataare

widely spaced

geographically

and

temporally.

However,

in the 1970s and 1980s instruments

(e.g.

Batfish, SeaSoar)

were

designed

tobe towed behind

ships,

and these could carry CTD

equipment

fromnearsurfaceto400 metres

depths

andmore. The first recorded

attempt

to

map mesoscale scalar

properties

on

isopycnals

_{away from}oceanfronts appears tobe Woods and Minnett

(1979),

who used data

gathered

withaBatfish

system.

Their aim was

to deduce the circulation

pattern

indirectly

rather than

using

directmeasurementsfrom

current meters which would be

swamped by

other motions. The data from such

systems

is then

vertically linearly interpolated

onto

isopycnals,

andsome errorfields _{may be}

estimated

during

_{this process}to

give

anidea of confidence in the

interpolated

values.

Horizontally,

"radiator" surveys areoften

used,

consisting

of

parallel

_survey

sections,

whichare more

easily interpolated

onto a

regular

horizontal

grid.

At

large (gyre)

scales the PV canbe

represented by

the

Sverdrup

PV,

as relative

vorticity

is

negligible

atthese

scales,

andcanbe calculated from

hydrographic

measurements

without

knowledge

of the local

velocity

_{field. The first recorded maps} ofPV on

isopycnals

arethose in

Behringer

(1972),

which used data collected in the South Atlantic

(26)

Chapter

2

Background

sooner, other than that noone

thought

to doso.

During

the

1980s,

therewas

quite

a

flurry

of papers

containing

isopycnic

maps of PV. McDowell etal

(1982)

produced

PV maps of the North Atlantic

using

data from 1957-58 and

1962,

and thesewereusedtovalidate theories

put

forward for the

general

circulation

(Rhines

and

Young, 1982b).

Meanwhile others used Levitus

climatological

data

(Levitus, 1982)

to

produce

maps of PV in their

areas of interest

(e.g.

Sarmiento,

et

al, 1982, Holland,

et

al, 1984).

As the usefulness of

such mapswas

becoming

more

evident,

Stammer and Woods

(1987)

mapped

the seasonal

cycle

of the

Sverdrup

PV in the North Atlantic

using climatological

data,

foruse in

studies of the

general

circulation and its links with

atmospheric

fields.

All of these_maps werefor

Sverdrup

PV

only.

McWilliams

(1976)

also calculated the relative

vorticity

_componentof

PV,

and

produced

_{maps of}

this,

along

withan

analysis

of

the

complex

errorstatistics of the

mapping

method

used,

in orderto

study

the conservation of PV. This

study

used float

trajectories

and vertical

density profiles

to

generate

the PV field. More

frequently,

in the

1980s,

_maps

began

to _{appear of full PV}

calculated

using

measurementsof the

velocity

field

independent

of the

hydrographic

data

(e.g.

Arhan and Colinde

Verdiere, 1985,

Hua,

et

al,

1986,

Fischer,

et

al,

1989,

Pollard and

Regier,

1992).

Few of these studies

explicitly

state the estimatederrors in the PV

field,

although they

describe measurestouse

only

data within confidence constraints. As an

example

of the level of accuracy which has been

achieved,

the PVfields

presented by

Fischeretal.

(1989)

havemeanvalues around 1.04

PVU,

withstandard deviation of 0.45 PVU and a_rangeof 2.33 PVU. A confidence level of 0.4 PVUwas usedto select which datawere includedin the

analysis.

Errors

(both

over- and

under-estimates)

in PV values of the order of8% wereintroduced when relative

vorticity

wasexcluded.

These

developments

in the

mapping

of PV on

isopycnals

has ledto an

increasingly

clear

picture

of the

gyre-scale

PV

field,

which is

important

asthe interactionof PV

dynamics

and

thermodynamics

is

largely

unsolved. Theoretical and

modelling

work

suggest

that

mapping

the PV field should be of

high priority

(Rhines, 1986).

The

picture

is

certainly

not

yet

clearat smaller scales.

2.4

Mixed

layer and thermocline theories

2.4.1 Mixed

layer

_processes

The surface

layer

of the oceanhas low vertical

gradients

of

temperature,

salinity

and

momentumas aresult of turbulent

mixing

generated

by

mechanical and

buoyancy

forcing,

and for thisreason is referredto as the "mixed

layer"(Niiler

and

Kraus,

1977).

This thesis concentrateson

examining hydrographic

data

gathered

from the mixed

layer

(27)

properties

of data

gathered,

and for this reasonit is relevantto this thesisto consider what factors may haveinfluencedthe

properties

of the mixed

layer

in the datasets.

However,

it isnotthe intention hereto

investigate

mixed

layer dynamical

_{processes themselves.} The mixed

layer

canbe definedin various ways, but is most

commonly

defined

by

requiring

that the vertical

gradient

of

temperature

or

density

should be less than a threshold value.

However,

such definitions of mixed

layer

donot

always yield

the same

depths

for theextentof the mixed

layer, especially

in

regions

where the

salinity

makes a more

significant

contributionto the

density

value

(Lukas

and

Lindstrom,

1991).

It is usual foraresearcherto select the method whichmost_{suits their purpose.}

The energy flux between the mixed

layer

and the

atmosphere

is balanced

by

viscous

dissipation

and

by changes

in the

depth

of the mixed

layer.

For

example,

_{increased energy}

in the mixed

layer

lifts denser waterfrom below and mixes

it,

deepening

the mixed

layer

as wateris entrained into it

(Kraus

and

Turner,

1967,

Udall,

1993).

Mixed

layer

deepening,

and the

corresponding shoaling

which occurswhen energy is reduced in the

mixed

layer,

follows a diurnal

cycle

anda seasonal

cycle.

These variations

depend

inturn

onthe

cycles

of the

forcing

fields which affectthemixed

layer

kinetic energy. Inmore

strongly

stratified

fluids,

the entrainmentrateis reduced

by

internalwaves and

by

eddies

inhibiting

the advance of the

boundary

between the mixed

layer

and the stratified fluid.

Detrainment is

governed by

the influences of the surface wind _stress,which enables

mixing,

and the

buoyancy

flux,

which enables

restratification,

onthe mixed

layer.

Water which is detrained from the mixed

layer

into the denser

layers

below will retain the

temperature,

salinity

and

potential vorticity

values of the mixed

layer

atthe time of detrainment.

Windstress acts across the mixed

layer

totransfermomentum_{and energy into the}ocean and varies with the wind

speed,

swell andwave field

(Kraus

and

Turner,

1967).

Wind

stressinduces waves onthe sea

surface,

whichbreakandintroduceturbulence into the mixed

layer.

This is the mechanism

by

which wind stresscontributestothe total kinetic energy of thewater

column,

andcan overcome

buoyancy

effects

during daylight

hours

(Woods, 1980).

This direct influence of the wind

penetrates

to the

depth

of the Ekman

layer, generating

anEkman driftcurrent

(Pedlosky,

1987).

Other mechanisms which alter the

buoyancy

of themixed

layer

include

evaporation

and

precipitation,

which leadtofreshwaterfluxes

(Niiler

and

Kraus,

1977).

Buoyancy

is also forced

by

_{heat fluxes which may result from latent heat of}

evaporation,

sensible heat

transfer due to air-sea

temperature difference,

and solar and terrestrial

penetrative

radiant heat fluxes.

Throughout

the

day,

solar radiation adds heat into the mixed

layer

while it is

(28)

Chapter

2

Background

causesconvective

overturning

in

just

the

top

few millimetres of the mixed

layer.

In

contrast, at

night

convection dominates the totalkinetic_energy

production,

and

penetrates

to much

greater

depths

(Woods, 1980).

Studiesof the

sensitivity

of mixed

layer

modelsto

surface fluxes have

suggested

that models are more sensitiveto

buoyancy

fluxes than to

windstress

(Woods, etal, 1984).

Internal processes suchas the

production

of internal wavesand shear-induced instabilities

are

generally

consideredtohave little effectonthe mixed

layer (Niiler

and

Kraus,

1977),

butsome research

suggests

that such processes may be

important

oncertain time-scales

(Oakey

and

Elliott, 1982).

Some

modelling

results indicate that

only

asmall

proportion

(10%)

of mixed

layer

_{kinetic energy contributes}to mixed

layer deepening,

with the

majority being

used in the

production

of internalwaves and

dissipation,

sothese

mechanisms should therefore be included in mixed

layer

models

(Denman

and

Miyake,

1973,

Kraus and

Turner,

1967).

2.4.2 Thermocline circulation

Below the mixed

layer

andto about 1000metres

depth

in the oceanthere are

strong

vertical

gradients

of

temperature

and

density.

This

region

is labelled the

thermocline,

or

the

pycnocline.

_{In many}

parts

of the world's oceanthe

temperature

dominates the

density

value,

and sotheterms "thermocline" and

"pycnocline"

areoften

interchanged.

The data

sets whichare examined in this thesis are_{surveys of the}

top

300to400metres of the

ocean,which encompasses the

top part

ofthethermocline. For thisreason it is relevantto

consider here the processes whichdeterminethe

properties

of the waterwithin this

part

of

theocean. The thermocline consists oftwo

parts.

_{There is the seasonal upper}

part

which

is re-entrained into the mixed

layer

each

winter,

where its

properties (temperature,

salinity, potential vorticity,

oxygen content,

etc.)

arereset to the mixed

layer

values. And there is the

permanent

deeper

part

which is

deeper

than the annual maximum mixed

layer

depth

and,

therefore,

is not

directly

influenced

by

the mixed

layer.

The datasetsexamined here were all

gathered

in

springtime

andso thethermocline which is examined is

likely

to

be that

part

known asthe seasonal thermocline. There is little diabatic

forcing

in the

thermocline,

soflow there isnear

geostrophic.

Various theorieshave been

proposed

for circulation

through

the

thermocline,

but inrecent_yearsmostinterest has restedon the theories of

"homogenisation

of thethermocline"

(Rhines

and

Young,

1982a)

and "the ventilated thermocline"

(Luyten,

etal,

1983).

(29)

unventilated

isopycnals

and within these

loops

the

potential vorticity

is

homogenised.

At

the

edge

of the closed

region,

there is aconcentrated

region

of

high gradients

of

potential

vorticity.

Beyond

this transitionzonelies motionless

fluid,

or adifferentflow

regime

in

which the

planetary gradient

of

potential vorticity

_{may be dominant. Potential}

vorticity

is

homogenised

within the closed

geostrophic

contours in subsurface

isopycnals

if the dominant

dissipative

mechanism is lateral

diffusivity

of

potential

vorticity,

perhaps

dueto

mesoscale

eddies,

anddirect

forcing by

external stress or

heating

is

negligible.

This

homogenisation

of

potential vorticity

has been

supported by

oceanobservations

(McDowell,

et

al, 1982).

Luyten

etal.

(1983) (henceforth LPS83)

describedatheoretical model for the thermocline which addressed the

problem

of theocean

conserving

its

density

and

potential vorticity

fields far fromthe

regions

in which

they

were set. This model is known asthe "Ventilated Thermocline". The model consists ofan

arbitrarily large

numberofin

viscid,

homogeneous

fluid

layers

each withadifferent

density. Sverdrupian dynamical

balances

are assumed

throughout,

and the surface

density

is

specified

in

regions

where the Ekman

pumping

is

negative

(downward).

This means thatsome

isopycnals

outcrop

in certain

regions

andwater_pumps downtothe thermocline

stirring

_up

deep

motion evenin

locations far from the

outcrop

where the

layer

is shielded from the directinfluence of the wind. A

major

differencebetween this

approach

and that of RY82 is that the ventilated thermocline modelallows

significant deep

flowson _open

potential vorticity

contours that

return tothe ocean surface rather than the eastern

boundary.

It alsomeansthat distinct flow

regimes

canbeidentified. In

downwelling

areasthereareventilated

regions

in which all

isopycnals

arein

motion,

whileatthe

edge

of this there areshadowzoneswhere

potential vorticity

contours meetmeridional boundaries and these shadowzones _may bound uniform

potential vorticity

or

stagnant

areas.

Meanwhile,

in

upwelling

areas

isopycnals

will

outcrop.

Processes which take

place

above the

permanent

pycnocline

are notconsidered

explicitly

by

either the RY82

"homogenisation

of the thermocline" model orthe LPS83 "ventilation of the thermocline" model. In these

models,

the

density

and vertical

velocity

are

specified

at the

top

of the

permanent

pycnocline

which is assumed tobe atthebase of the Ekman

layer.

This,

according

toWoods

(1985),

is

unsatisfactory

because this treatment of the surface

layer

_{is wrong, and the models}cannotbe used in

regions

where the surface

density

distribution is unknown and

changing.

The

problem

is that

pycnocline

depth,

which is definedasthe annual maximum

depth

of the mixed

layer,

does notcoincide in the realocean with the base of the Ekman

layer.

Between the Ekman

layer

and the

permanent

pycnocline

lies the seasonal

pycnocline,

within which waterflows

(30)

Chapter2 Background

being pumped

down

vertically

from the mixed

layer

asmostmodels

prescribe

(Lukas

and

Lindstrom,

1991).

Woods

(1985)

offersan alternativemodel of the

pycnocline

which is ventilatedfrom the

seasonal

boundary layer

in_responseto the surface fluxes. The theoretical form of the near-surface

layers

of the oceanis summarised

by Figure

2-1,

which shows amixed

layer

consisting

ofa

statically

unstable convection

layer overlying

the

weakly

stable

part

of the mixed

layer. Daily

variation inthe

penetration

of the convective

layer,

and

daily

variation in the

depth

and

temperature

of the mixed

layer

occurs in responseto the

daily

pattern

of solar

heating

whichcauses convectionto be

quenched

during

the

day,

andtorecur

just

before sunsetand

through

the

night.

This variation leadstothe

layer

definedasthe diurnal

pycnocline.

Seasonal variations in the

length

of

day,

maximumsolar

elevation,

cloudcoverandsurfacefluxes leadsto variations in the extentof the mixed

layer,

and the

layer

which is defined

by

this variation is knownas the seasonal

pycnocline.

The annual maximum

depth

of the mixed

layer

is where the

permanent

pycnocline begins.

Density

H_max

(31)

Woods'

(1985)

model wasusedto_{demonstrate the role of advection in the upper} ocean. In

winter,

the mixed

layer

is

deeper

than the Ekman

layer,

and convection controls the mixed

layer

depth.

Increases in the

depth

of the diurnal

pycnocline depend

onthe

daily

meansurface

buoyancy

flux and the

density gradient

atthe

top

of the seasonal

pycnocline.

The

depth

of the diurnal

pycnocline

reaches tothe

top

of the

permanent

pycnocline

when the

daily buoyancy

flux

changes sign

atthe startof

spring,

when

warming

occurs. If there isno advection in the

model,

the annual maximum

depth

of the mixed

layer

_{will increase each year.}

However,

this

depth

is

approximately

constantin

nature. This means that thenetannual

buoyancy

flux dueto

heating

mustbebalanced

by

a

divergence

of advective

buoyancy

flux,

which is to _{say, advection is necessary}to

predict

the annual maximum mixed

layer depth.

Most one-dimensionalmodelshave

neglected

advection

(Woods, 1985).

Isopycnic potential vorticity

isnot definedin the mixed

layer

andso this

layer

acts as a

source

(sink)

of

potential vorticity

forwater

flowing

out

(in).

The mechanism for the

input

of

potential vorticity

into the seasonal

pycnocline suggested by

Woods

(1985)

is

that the

top

of the diurnal

pycnocline

rises

rapidly

in

spring leaving

behind itawater

column witha

density profile

that setsits

potential vorticity profile.

The

potential

vorticity

"sinks" tothe seasonal

pycnocline during

the autumnand winter whenthe mixed

layer deepens, entraining

water from the

underlying pycnocline.

_{In this way,}

changes

in the mixed

layer

affect the sourceof

potential vorticity

in the seasonal

pycnocline

and in

turn this affectsthe flux of

potential vorticity

intothe

permanent

pycnocline.

Woods

(1985)

foundthat

potential vorticity

therefore flows from the seasonal

pycnocline

into the

permanent

pycnocline

at

places

where the annual maximum mixed

layer depth

decreases

downstream,

and viceversa.

LPS82,

RY83 and Woods

(1985)

_{agree in that the}

properties