The simulation of water quality in the Waikato and Tarawera rivers.

http://researchspace.auckland.ac.nz ResearchSpace@Auckland

Copyright Statement

The digital copy of this thesis is protected by the Copyright Act 1994 (New Zealand).

This thesis may be consulted by you, provided you comply with the provisions of the Act and the following conditions of use:

• Any use you make of these documents or images must be for research or private study purposes only, and you may not make them available to any other person.

• Authors control the copyright of their thesis. You will recognise the author's right to be identified as the author of this thesis, and due acknowledgement will be made to the author where appropriate.

• You will obtain the author's permission before publishing any material from their thesis.

To request permissions please use the Feedback form on our webpage.

http://researchspace.auckland.ac.nz/feedback

General copyright and disclaimer

In addition to the above conditions, authors give their consent for the digital copy of their work to be used subject to the conditions specified on the Library Thesis Consent Form.

THE SIMULATION OF WATER OUALITY

IN THE

WAIKATO AND TARAWERA RIVERS

A rh.esi.s subnitted in ;.:':ial fuLfitreit fcr the degree of Dcctor of Ph:10scphy, at t:-.e University of Auckland.

February

^1975.

Jarnes Christopher Rutherford

B.E.

^(Hons).

ABSTRACT

Th,e calre,es aqd

effeets of

watelr

pollutior:r

a're

Listed

and

tlre

^neehanisms

of

staeart sel-tr-ry,unifioation

des.oribed,

The paraneters

for

whleh nathena,tical,

rneidielj.E have been de,v,e].oped a:ne deecr.ib€d and the .suec€s,s

of the

variOus ^p,nevious s@de'Is f,oF

paedicting

thern

ts discussed.

Tlre eqr.ratiorls governing ta-e

eoncentretlen

of

dicqotved oxy€e,n Ln

a

pol,J.uted '*aterway

are

devElop,ed End h rtrev,j.ew :i.,s nEde

of

tlii€ vani.o,ue

f,inite

dif,fenenee ^seheFyeg w,biclr ane

avallable

^fo_1.

sotrv-ing then.

Models

are

deveLo5red

f,or pnedicting

diesolued ^px,ygen co$reentnations

in

two proll.,gted l{ew Z,ea1snd

riveFs, th€

ttaLkato a.n:d

the Tapawena. I*

tra,s f,,ound

that

the, -lhatdel. tis,ed, pr"evious,ly i.n

other

tdaterway6 rdere

not

ad€gtrate

fof; eith€F

o,f thes€

rivqne.

The nodel

of

the I{.ai}ato R.iven use,s

the

$elt+kRown S reeter-Fhelps:

cquatLon

tq

nnedel thef

exgrtion of

6OD

but

ineludes

the effeets

o.f

the

rnaerioeh)rt€

afid phy:l6,pLankton couuauni*ies on

th€

eonce,ntr.atlgn

of

dissolved roJy'geqd The

nodeL

of

ttre,tarasrer.a Riveq uses

t-te

!{onod equariohs Ge

gredict

rh€ concent-latlons

of

aeti've bi.6mass

in the

ipgrous p'unlee se-dinentg pn

the

Five,lr ^rbed

j

^,Eird. suceess.ftlllll

aecountB

fo.r thq high

r.ate <lf ^.ox5rge*r uptake whielir has been

observed.

The way ;ln whietl these ^,node.ls could

pro,fitabty

be developgd

is also

di.seuss,ed.

ACK NOWLED GEMENTS

There atrs serae,$al p€op],e w-lrro have made ualo,r

eontributions to the

sork de,eeribed i.ri

thi.s thesi:s,.

Mess)os

J.S. I{ietsen,

B.H-

PyIe,

rI .W.. Nagels ^and

G,€.

Bnyers, lilater QU4J.itJ L4bo.:tnatoryn

l4inist?y

^,of [.lcr,fte, liahiilLtori, ltessns 6.T.. Ridal.tr and 8..

eaelisle,

^gtraikato Val.ley

Authofity

Ha.lLiltont

Dr.:H.E.IJ. [6ylLor,, Auclrlatrd fiqgf.onatr

Autho!'ity,

,rqsk],and, H:o F..

toFe,

Steven and

Fitzdaulliee

L€di Auekla:ndn Dre

B.!.

Ooff,ey, I'les ^Zcralrand

Electr.ieity

Depantaentn HerqiLtorrr, D'

g

J,f,t;A. Btroiwt 6nd

t'l.rl.

Sitrvesten, afld l.tiss

C,

Lan, Botany DeFart$erti Uni.versity' of, A.ueklan4,

l{r F,a. Leighton,

l{ew, Zealand Co;-operative

Dairy

^Conpan5r

Ltd"

^ruatAngl, lfi:, C.F. Densread, lt€.at Res6ancb

Institu-t€, llanilton,

^nelUbers

of

^the

Teehntcgl Gonqri-ttae, tf,aikata Rl.va:r Resowoe.s FFojeqt, Dn

!.l.J. l,titchell"

Tasm44 .FuLg aad FaEer Oonpa$gr Kawerau, and ntrrmerrous Otlrers"

f

^wquld

liRe tg

e,raplae$s

ny sincere

thariks

to

^my supervisorrr

Dtr

l{-.I.

Or8.u11luern., r.tho }ra.s given ne

a

co-nsiderable ^ano,unt

of

},lelp and. guidattee..

thtrough.o,ut.

the Droiectr

^:alld

in the

pr€pa,ratien

of thie

scniBt.

I

worlld

also

Ii-ke

tp

thank ury mothen and

ny sisten, fon thgiF

rassistgr.lo€

r{th

proof, r€adlngn ray wif,er. Susanl

folr,her

errt}ruaiasn and support thtougltout the ppoJectt a-nd

to

lfarnie Lolrg

fot the

enduotis

task

she performe.d

in ttrping

the nanusesipt.

I

^weu.ld

likp tg

e4pr.ess my €rFatitude

to the

^{f,asna.n Fulp} and Faperi cotipanyt Kireerau,

tlie

llew Zealah(t Co-;0.peiative Daitsy Company, l,tatangir dnd

the

^Auar(land

Farners.r freea:lng Conpa4y, AuckLand, whq h.ave gtven ne aeeess

to their files, I

^q4

also

^{deePtry {-ndebted}

te the riinisEry of

Worts en4 9evelopraent, _,b}

ttttorn

I

harie baen eraployed f.sr ^-the

last

eightee,n ^mom-ths n

for

araking

it

possi-bIe fon

!tre

tE

e.e-rilpil,Ft9

the

^wqrrk dEsenibed

in this, thesis at the

t:lrlivers-.1-ty gf, Aucklald.

I

a'[

als6

gratefutr

to the

trln,iverslty of, Aucklan'd

f,or

allowLng me paiat-time statrrE urLng

thiF

p€niod aRd

to the Un,iversitf

Olrants Co,rulitte€

tror the flnancial

as.s:lstqnge

of a

post-gSadg4te pehol,a:rghip betr.r€.en Marah 1972 a,nd

*lullt

1.973.

TABLE OF CONTENTS

Fage No, trIIf,ROEUCTI.ON

CtsAFTSR

1

PO'LLUTION AND I{ATER I'AE

1.1, Follutiorr

and

the

Gerteral Fubli.e

X.

2

lf,at€r Use

1. ?.

1

Done,s,tic Supply

7..2.2 Agnlcultural

Supply 1. ?.

3 Industrlel

^lJ-se

L.2.4

Reereatior,r

:1.2..5

G,eneration o.f

El.e.ctricity 1.2.6

Eisposa.l od ^Waste Maittef

1.3

Typ€s

of

Pollutants

1. 3

.1

Fhysieal P-ollut.rntg

1,. 3.

2

Chen.iea.i_ Poll.uta,nts 1.3.

A Eiological

PoLltrtsnt-s

l.jlr

^lfu.tef Qua.lity Letgislation

1.5

lletherdatical Hod.elling

of

l{ateF Quality

1.

5.1

Intr,'o.d.uet'ion

1.5.2

Parametetas

of

^Wdter

Quality

^MOdelE

I.5.3

Lin{.tatione

,ot

Mathenatieatr l{odels qtAPrER

2

['lEeI{4NISHs AND }{EA$'rilREf{ {T

or

P0LLUTISN

2.L

Intnoduction

l2

2'.2 Dilrrrtion,

Dispersion, arnd

Adveetiori

¹²

. Z.g

^Oxygen

Deptetion

¹³

2.3.

I

Intnoduction

2.9,2

Oxygen De:na,nd

of Polluted

^Waten

2.3.3

oxygen Uptake

in tlrc

l{atenray

2.3r.rt

^Oxygen Pnoduction and eonsump€.ion by Aquatic ?-lan:ts

2.1+

Kin,etics

of

P.eDulafion ^rghan.geE

in

FolLuted

t$aten

¹⁹

2.4.1

Intnoduct.ion

' 2.$.?

Exogerrogs Ms:taboLlsrn

of

Baetefie-

?.4.3

Endogenous Hetabolisn

of

Seqteria

' 2..4r.4

Pnedatlorl

by

F:rotozoa

2.b..5

oxygen Uptalae

la

Co:nplex Systene

2

.5

!4ierobial rContaminatioo and Self-Funif

ieat:lon

²²

e.S.1

Inttroduet:lon

2.5.Z

Tndieaton 0rganigns

2.5.3

Mierrob:ial

Self-Purlfieatlon.

I

'

^{Fage l{o.}

e$AFTER

3

HATI{EI{ATXCAL I{CiDSLS 0F trATEn QUAl"ltY

3.

tr

Kineti.ee ,of Oxygen

Uptake

^?5

3.l,L

F:i-t,st Orden Models

3,1.2

Seeend Onden Models 3. 1..

3, the

llonsd Eqr,rations

3.l..ir

Frotoz,cal

Aetivi.ty . 3.1,5

End-oge.no-us Hetabo,li.sm

g.2

The Transpoi3t

Egu,Eti.on

^3r0

3.3

^The

Potlutioa fquatiorts

³²

3.3.L

^BOD=DO Equations

,3.

3.2

Secand OederF Equatloas

3.3.3,

Bo'und,ary and

ltiitial

&rnd.itior.re

3.4,

The 0perr ctlierinel Floir

Eg.uations

^3s

3.

5 Estination of the

^Rate

of tongitudinel Diepensirin

³⁶

3. S.

t

Inli.lpduetio,n

3.5"'2 Fredictioq of the

Rate

of

Dis,persion

3.5.,3,

P-as,slb,Le trna<reurEcies

in the

^l{ethocl

3.6

Estirnation of,

the

Sate

of

Reaeration

CInAFTER

4

SOLUTION 0,F THE POLI!UTI0!{ EQUATTOUS

t{.1

Introduation

4.2

^Efirors Ag:goelated.$rith

the

NunerriEal

Solution of

ttre FoJrl.uti'on Eguation.s

r+.5,

Nunerroie+L ,S-olu,tien of,

the

TFenspoi't ^Eqg-atrlon

11,3..1

6.iaple

Explielt

^l{ethod

tt.3.2 Inplicit

Methods

tt

.3.3

Lax=tlendroff

fype

lilethods

tr.s.,$

_{A General} Sesc:riptiori

of

^t-b€ A-cqqracy ^aad UsefuLne.s;s

of the

Numerie.al Pietldde

4.r!t

!e^slE' F:rob,lelne

u.f+.1

Introducti.on

r+.tl

.A Anaiytieal

SolutXorrs

to

^t-!ie

test

^Pnoblens

l+.tt.3

_{Results and} Cbtncl.trsl,ons

4.5

SoLution of, t.he Tr,ansport Equation

in a

Non-Uriiforn

'

Chann,el

l|'.6

SioLuttion

of tlre

Po,!!-utl6n Equation$

b.6.1 Explicit

Uethods

11.6,2

Trdo-Step !{ethods.

4.6.3 Iu5rli;cit

Methods

!+.,6"

rt

Diqe-uesion

4.7

sol-utieNr o.f

the

G,radua}ly V.atying H[Otr gqiuetion

CHAPTER,

5,

DESCNIPtrION OF T.T.IE IIIAIKATO RIVER

5,1

Desoeip.tion

af the

eatc iuent 6e

5.2

Ercletlng Sater

Qrlality ia the

U.p:per lCaikato River

and

La-kes

⁶⁷

- 9,3 Exleting

Slaten gualtt5r

in the

Lower" lrlaLkato

f,ive!

5.3.1

Ssui^see

of

Fotr,tutJ.on

5.i.2

ltleagu.rement

of

glater Quattty 5. 3.

g

;ELsEorlved Oxy:gen

5.3.4

Biocbenical Oxygen Denand

40

$,1

'50

6,8 5s

Faee_ No.

C'IiAPTER

5

(c<intinued)

5.3..5

Fa,ecal B'aster:la

5.3.6

Aquatic

Plant Life

9.3,? !/ater

Tenp.erature and othen Faragneters

5.4

,

I|3rdnaulie Charae€eristieg

5.4.1

Riven

flofi -

5 .4

.2

Tributar.i:es

5,t+.3

Chaonel CharasteF(stics

CTTAFTER

6

A WATER QTIALITY HODEL FOR TIIE WAIKIITO R TE8

6.1 Paranete.rxs,llode}led

^?8

6.2

llydrauli.e Eata Req-uirred

bJ the l{odel

¹⁵

6.2.1

Titre

of Travel

Predictions

6.

!.2

Goef

ficient qf

l.otrgttudi.-nar DisPqrs:ion

6.3

Data on

th€ PallutloB So.urc€s

⁸⁰

6.

9,'J

^{Domestic ise$age}

6r.3

.;?

^Da.i.ry f.'aqtory

Efftu€nt

6.3.3 Abattoir

and l"r.eezing

liorks Effluent

6 ! 3 .

r{

Agrie. un

tlrr,al

^Ef

flqeot

and Fasture ^Ru,noff

6.lr

Bate

ebeffioients for the l-{odel

^g'P

6.

$.1,

EOD E:certiOn Rhte

6.ft.z .

BeaeFation Rate

6 .4 ^r

5

^O4ige-n Prroduetion and Consunption ^by

{quatic

^PlaEt€

6.!r,r+

Ef,fects

of

Sur.rlight

IntensitJr

aiid

['l*tef -_

'Feurpq'natune oril ^,Or$f,gan Produetion ^and Consumption Rates

cIiaPrER

7

PREDICTIoIfS OF T,JATER QUALIty IH THE r{ArKATo RMR

'l.L

Cornputation

Procedunes 190

I

1.1"1

Des'cr{pti.on

of the

Mathenatieal l4odeL 7.1

.2

.Discr*ssion

of

^t-he flethods usied t@ FF.edlct,

,Eiseol.ved ^{Oxy, ge-n} Ooncentratlons

7.?

?-r:'edieti.sn$,

of

E'*'is,ti.nB Conce'ltrnatlsns

of

Dib€olved

Oxygen

^lq1

7.2.L

Pe:riod

of

Sunner Low Flort

7,?"2

^Peried

df

Peak Daiklr Produetion

7.3 Prediction of

Changes

in the

Concentrations

of

Dissolved

Or.Jrg-ed

^1,13

7.3.1 Effects of

Increasing F,opulation and X,ndustry

7.3t2

Ef,feote

of

Dischange

of

,Co'elirlg _Eatejr-

7,4 Csnclnqlgn€

12q

_

7. !l .

L

^Mo€e].

flor

D:Lesolved Oxygen

'1,.t,2

Steps Neo€ssany

to

Maintain Eigh Coneentratlo&s

of

Dissolved Or.ygen.

? "

lt.3

Suggeoti;ons

for

^{Furthen l{srih}

-

_T

-S Predictioh of

Rateo

of

Fnush.i.ng

of Pollutan.t€

^L2'7

7.5 .

I

fntnoduc'tion

'?

.6,2

Nume:rieal ltethodc

7,5.8

nesultE

?.5.4

Dissussion and Propqsed llonk

CHAPTER, 8 S'IMIIIATION 0F I.IATER QUALITY

IN

THE TARA{,IERA nrPEfl trnt-?odrletiion,

Hydrau.Lie Character.lstics

8 . ?,

1

R.lver Flow

8.2.12

'f,he Riven Bed

8.1.,3

Lo,ngitud:lnaL Disperslon

8.2.4

Rate sf, Reaepati6n

8

-3;

Th,e t{eo=hanis.ms

of

oxygen

tJptake

¹³⁶

8.4

Uathe&atioal. ModeL

of

Di.sso.ve{ Oxy,gen

Go.neentna,tion

^13?

I .4 r

1

In.trFoduet iorj

8.4.?

^{Model ,ef}

the River

Bad

8.$!3

.Eguatioas €ovot'niag

the

Coneentr*tio,n sf, Dissol,ved 0xygen

Pqge Nq.

13s L3?

l4I

lq6

$a

1s,tr

1.5.5

156

158

183

18lt 185

1E ,8.1

a.2

8.5

The

Fplluting

[.oed

9.s.1

chortric-al c-onstituen_ts o,f

pulp MlIl Effluant 8.5.2 Estination of

Rate Parametens

8,5.3

Erstii'nation

sf

Rates

sf

Additi.on

L 5.4

.Pii.6to,zoal .Aetivi.ty

8,5,,5

Endogenor:rs HetaboJ.ls.lo

9.6

Reer.lXts .and DiserlssLen

8.8.f

_. Dinensions

of the

Sedisrent ^Layerns I

.6.2

Rates

of

Di€pers i.oir

9.8.3 laitial

Concenrration

of

^giorlras,s

$.6.+ Effects sf

^protozoa

d.8.S

Eff,eicte o.f Endogerou,s Hetabolisr[

8.€.'6r

eompari.son

of the

One and Twos8u$.stnate. lttgdeJs

8.T

Concl.us:loRs

8.8

SuggestJ"ons

fbr

Fupth€r ifork

EEAPTIR

9

S['r+tARY AND COI{CLUSIOIi}S

S.l,

$unErary: and Conelusigns.

9..2

Sug8es.tions

fori

FuFttr€r l{ork

APSENETX

r

AFPENDIX 2

d,FPENOTX ₉

AFFIX'|-DIX ^q.

APPENDIX 5

AtFEREIfCES

E€tiln€tioo

of

'luongitrldlnal _D,ii spe:'s,.ion,Coef f,

ieisnts Detailed

De'script:i.on

of the

,t{unenical Sol.ut:isus

to

tb,e Te,slt Prerblems

Rate.g

of

Qxyg.en Frolduotl.on by Helos.i)ia ^Epecies

Ffedic-lion

of,

^gtege arrd Me:an VeXocitll in: t-he Wai]<atE

l,iver

^1?9

ExPerlurents on 0xygen lJptake

in the

Tarallera Rirren, 1c€5

LIST OF FIGURES

CHAPTER

4

Page No'

r+.1

Computational- Net f

or the

t,ax-i{endrof

f

Two-Step

Scheme

^r+5

4.2

Conputational Net

fon the

Cnowley Two-Step

Scheme

⁴⁷

CHAFTER 5

5.1

^Hap

of the Locality of the

Viaikato

Riven

⁶⁴

5.2

Seasonal Vaniation

of

tlaten TemDerature

in the

Waikato

River.

⁷⁵

CHAPTER 6

6.1

Diurnal- Vaniation

of Effluent

Flow and Composition

fron

^a

Septic Tank

in Hamilton

⁸²

6.2

Seasonal- Va::iation

of

Production

at

Te Rapa and

Taupiri

Dairy

Factonies

⁸³

6.3 Diurnal Variation of Effluent

Flow from

the

Horotiu

Abattoin

⁸⁷

6.1+ Correlation

between

Effluent

Flow and Pnoduction

at

the

Horotiu

Abattoir

⁸⁸

6.5

^SeasonaL

Variation of

Production

at the Horotiu Abattoir

⁸⁹

6.6 Algal

Counts

at

Tuakau

Bridge, 1971-1973

⁹⁵

6.7 Algal

Counts

at the

Road Enidges,

19?4

⁹⁶

6.8

Assur:led

Diurnal

Vaniation

of

tlxygcn Pncduction and

Consunption by Aquatic

Plants

⁹⁹

CHAPTER 7

7,1 Daily

Average Dissolved Oxygea Concentrations Predicted Using

Three

Dif.ferent

Values

for

BOD Decay

Rate

¹⁰²

?.2

Predicted Diunnal

Variations in

Dissolved ^Oxygen and ^BODU

concentrations

¹⁰⁴

7.3

Predicted Dissolved Oxygen Concentrations

including the Effect

of Hacrophytes

¹⁰⁵

7.4

Predicted Dissolved Oxygen Ccncentrations

including the

^Effects

of a Uniforn

concentration

of

Phy-topl-ankton, 5

Bgl1

¹⁰⁷¹

7.5

Predicted Dissolved Oxygen Concentrations Incl,uding

the

^Effects

of

an Increasing Concentration

of

Fhytoplanktont 5-10

ngll

¹⁰⁹

?.6

Predicted Dissolved oxygen Concentrations

Includiig

the

Effects of

an Increasing Coneentration

of

PhytoPlankton

7.s -

¹⁵

ngl1.

¹¹⁰

?,7

Pnedicted Dissolved oxygen Concentrations Assuming

that

the

PhytopLankton

are active only in the

Euphotic Zoner

l

metre

deep

¹¹¹

7.8

A Comparison Between 0bserved and Predicted Dissolved Oxygen

Concentrations

during the

Period

of

^Peak

Dairy

Production

7.9

A Compar"ison

of

Predicted Dissolved Oxygen Concentrations

during

Surnmen Low Flow

Periods,

1975 and

1985 Utl 7.10

Dissolved Oxygen Coneentrations Predicted Assuming

that

the

Disehar:ge

of

Chlorinated

Effluent

from Hamilton Severely

Damages Phytoplankton

Populations

^LL7

7.lL

A Comparrison

of

Dissolved Oxygen Concentnations Predicted

.

Assulning

that the

Discharge

cf

Cooling Water

at

Huntly

Affects

the

Phytoplankton Populations

in Different ways

¹¹⁹

7.L2

Dissolved Oxygen and BOD Concentrations Predicted Assurning

that

the

Dischange

of

Cooling Water

at

Huntly Causes Severe ^Damage

to the

Phytoplankton

Populations

^12L

Page No.

7.L3 Pollutant

Concentrations

after the

^Reled,se

of a

Slug Load

fron Fainfield Eridge

¹²⁸

7.L4

PolLutant Concentrations Passing

the

Proposed

Intake

Site Following

the

Discharge

of a

Stug Load

at a

^llumber

of

Different Loeaticns

¹²⁹

7.15

Tirne

fon

which

the Pollutant

Concentration

at the

Proposed

Intake is

above

the

Detection

Limit.

¹³⁰

CHAPTER 8

8.1

ltap

of the Locality of the

Tarawena

Riven

¹³³

8.2

Predicted FIow Ccnditions and Rate

of

^Sediment

TransDort

¹³⁵

8.3

Dime.nsions

of the

Sediment

Layens

¹³⁹

8.4 Effects of

Variati.ons

of the

Dirnensions

of the

Sediment ^Layens on Pnedicted Dissolved Oxygen Concentrations, One Substrate

MoCeL

¹⁴⁷

8.5 Effects of Variations of the Initial

Concentration

of

Baeteria on Predicted Dissolved oxygen Concentratj.ons, One Substrate

Model

¹⁴⁷

8.6 Effects of

Var"iations

of the

Dinensions

of the

Sediment Layens

on Pr^edicted Dissolved oxygen Concentrations, T..-ro Substrate

HodeJ., Simultanecus Substrate

Assi:nilation

^lqg

8.7 Effects of

Var:iations

of the Initial

Concentration

of

^Bacteria,

on ?redicted Dissolved oxygen Concentrations, Two Substrate

Hodel, Sinultaneous Substrate

Assinilation

^1\9

8.8 Effects of Variations of the

firnensions

of the

Sediment layers

on Predicted _Dissolved Oxygen Concentrations, Two Substrate

Mo<iel, Sequential Substrate

AssiniLation

^l'51

8.9 Effects of

Vaniations

of the Initial

Concentration

of

Eactenia

on ?redicted Dissolved 0xygen Concentrations, Tvro Substrate

Hodel, Sequential Substrate

Assinilation

¹⁵¹

8.1C

Comparison

of

Predicted

Dissolvei

Cxygen Concentrations, Two

Substrate

llodels,

Simultaneous and Sequential Substnate

Assinilation

^1S3

8.11

Conparison

of

Predicted Dissolved Oxygen Concentrations, Trro

Substr"ate Models,

at

two

Different

Flow

Rates

¹⁵³

APPENDIX 1

- A1.1. Definition

Sketch

of the Variables

Used

to

Evaluate

the Integral in

^(3.31)

41,2 Longitudinal

Dispersion

Coefficients in the

^Lowen hlaikato

Riven

¹⁵¹

APPENDIX 2

42.1

Nurae:rical and Anal5rtieal Solutj.ons

to the

Advection

of a

Sl.ug'

in a

Uniforrn

Channel

^L68

}.2.2

Numerical and Analytical-

Solutions to the

Advection ^and

Dispersion

of a

Slug

in a

Unifor:m

Channel

¹⁷¹

42.3

Numerical and AnalyticaL

solutions to the

Advection

of

^a

Pollutant

below

a Sinusoidally

Varying Source

in a Uniforn Channel

^l'73

A2.r+

Numerical and

Analytical Solutions to the

Advection and Dispersion

of a Pollutant

below

a Sinusoidally

Varying Source

in a

^Unifonrn

channer

¹⁷⁶

APPENDIX 3

A3.L Definition

Sketch

of the

Channel

Characteristics

¹⁸⁰

43,2

Conparison

of the

Observed. and preCicted _Ratings

at

Several

Sites

on

the

^Lol;erl' Waikato

River.

¹⁸¹

LIST OF TABLES

Page No.

CHAPTER 5

5.L

Areas unden

Cultivation

ano Stocking Areas

in the

Waikato

Valley

⁶⁶

5.2

Population ^j.n

t}e

Waikato

Valley, 1956-1976

⁶⁷

5.3

Sewage Treatment Systems

in the

l.laikato

Valley, 1955-1974

⁶⁸

5.k

Dair.y Factories

in the

Waikato

Val1ey

^?o.

5.5

l'tajon Tnibutanies

of the

Lor*er 'rlaikato

River

⁷⁶

CHAPTER, 6

6.

L Effluent

Volune and BOD Load from

a

Septic Tank

in Hamilton

⁸¹

6.2

^Volurne and Cornposition

of Efftuent

Associated

with

the

Manufacture

of

Various

Dairy Products

⁸⁶

5.3

Composition

of Effluent

frorn

the

AFFCo Works

liorotiu, 1970-19?3

⁸⁶

6.r.1

^BOD Exertion Rate j.n _Sarnples

of

Waikato River

!'later

⁹¹

6.5

Rates

of

0xygen Pr.oduction and Consumption by Macnophytes,

after

Sculthor:pe

⁹³

6.6

Areas

of the

Predominant Species

of

Hacrophytes

in the

Waikato

River, 1969-?3

^9r+

6.7

Rates

of

Oxygen Production and Consumption by

Phytoplankton

⁹⁸

CHAPTER 7

?.1 Effluent

Loads,

Tributary

Flow and Conposition Used

to Predict

¹⁰³

Dissolved Oxygen Concentrations

during a

Current February ^Low

Flow

period

103

7.2 Effluent

Loads,

Tributary

Flow and Composition Used

to

Predict Dissolved Oxygen Concentrations

during a

Current Cctober Low

-_'

Flow

peniod

¹¹³

7.3

EffLuent Loads,

Tributary

FIo', and Composition Used

to

Predict Dissolved Oxygen Concentrations ciuring

a

Februar.y Low FIow

Period

in 198r+

¹¹⁶

CTNPTER

8

^'

8.1

Chemieal Conposition

of

^pulp

llill Effluent

^1r+2

8.2

Rate Parameters Used

to Predict

Dissoh,ed Oxygen

Concentrations

¹⁴⁵

APPENDIX ].

AL.L

Predi.cted

Longitudinal

Dispersion

Coefficients in the

Waikato

Riven

¹⁶⁰

AL.z

Published

Longitudinal

Di.spersion

Coefficients

¹⁶²

A1.3

Fublished

Lateral

Dispersion

Coefficients

¹⁶²

APPENDIX 3

A3.1 Friction Coefficients in the

Vlaikato

Riven

¹⁸³

APPENDTX

Aq.1

'{ Rates

of

Oxygen Production Estimated using Magadzats

data

from

Lake

Karapino

¹⁸⁴

Att.2

Rates

of

^Oxygen Froduction Estimated using .Iavornicky and

'

Kornarkovat

s data

¹⁸⁴

A4.3

Dimensions

of the

Thnee Predonlinant Species

of Diatoms

¹⁸⁵

APPENDIX 5

A5.1

Rate

of

Deoxygenetion

of

Surface Waters of,

the Tar-.era Rive::

¹⁸⁷

A5.2

Deoxygenating

Activity of

Sanples

of

^Purnice

fron the

Tarauera

River

¹⁸⁷

NOTATION

S{E8!|[|trIIC ANE C0MFUTATtr0NAL PARAIIETERS

A(xot)

ehanrrel a,rea

[i{l ar ,,crd

tridi.agona). o.oef,fioie,nt nat}irilc and

its

eomp-o'nent vector3s

b(xry)

channel

Fidth

d(a)

ahrartnel depth

drt

drfunensj.orrs

of the

s€dirDg.rt laye!.3

ErFrF longitudinal

dLspe:rs,ion coefficLents

t oF

nrrrmerica.l- crr pd.eudo-dispeis,ion boe.ff:ioientreofi^Ect€A cOeffioierrt

E giravitetional

aoceleratj.on

hod

dineneilotris e,f

the

sed:irnerrt lpyers

J;n

^{slraee and}

tine indiciee in finlt€

diiffe,Tence

notation k.rkt

non-di&ensionatr disBersion cOefftcients

K(xty)

.eharrnpl conyeJance

n

l..lanning

friction

eoeff,:i.c.lent

Q(xrt)

ehannef, df.soharge

g(xrtt)

l,etoraL lnf-low

per rrnlt

l.ength o,f, ohannell

$(x:ry)

ohannel hydi'aullrc nadiu€

SI

sr!il ^<rf, eddy lo,sses

TfCl transport

^opeinator

f,(xrt)

wate:. tedpeiFature

t tiae

u(x,yrAnt)

:lnstantanecus vetro.e.lty

U(xrt),V(x,tlrlf(x"t)

€roes-rse€tional average

veloeltiee

ut(rt' r.Zrt) differetrce

betrre€n ine.,taita'neous a$a.!re-'d'n veLoelt-y ilr

(xrsr:t)

_6epth elrepaged:

velocitlr

diff,qrenee

'rsy

>z

Eu,le:ntan di€paaccneflte, _-y

veriti.ealr ,(

down,Ett'ea!0

V6(x)

alrelage d"pth

z(x)

eharlnel bed

elevation,,

abolre datur.

o(x:t)

,

$(x't )

vsloeJ.tsr coBff,icients

AxoAt .

^{Eedh EXze and}

tirne

Etep

in fiaite

Etiff,erence

notation

e latefaL

addy

diffusivity

lrlr tise

_'and ^.epace dlff.erenci.og pairameters

P

advection pa'rAaeteir, U AtlAx

o

dispension pa?amster, E At/Axz

E

tag-rangian displaeenent

variable

ru\TER QUAL]TV ^FARASETERS BrBn

9gtB6. ^. .

c,irEi,..

DtD*

k1

k, plpt

S,8n 'onFrYrd

.

^GrCrDrF

11K 1l

$rvnt

$rPr.ulrX 0(c l'

eoneentration of, heterotrotrlhie bactenia

pdll.utant

esneent-tration

i.nitial,qoncentratiotns

eolrcentfations

in tnibutary

^in'flo;ws

diss€ v€d oxygen coneeltt'?atioa'gat.qration eonoentlatLpn

BOD decay

fate

nea€ratioft nate

eonoentr?atibn

of

^g.rotoa-oa concentration

of

substrate

aubstrate ^a

sslnila lion/bastcr !a

gnowth para&€ters

bacteria

eons umpt ^:LoD /p.r'otozoa gngwth Par*meterf ^g

bacteria decline

^parametePs Ilrotozoa ^dee,lir

e

lEnaret€rs

atop

funetionc

biological rate

oper€to-r

BIOLOGICAL TERMS

aerobic occurring in the

Pnescence of

'

making use

of

oxygen

aLgae

conmon name

for a

wide nange

of aquatic

^plants

anaerobic

occunring

in the

absence

of, without

making use

of

^oxygen

bactenia prirnitive nicro-organisns,

abundant

in

erater and

the soil benthic inhabiting the

sedi.nents on

the

^bed

of a

wateruay

biota total

PoPulation

of

animals and

plants in a locality

coliform a type of

bactenia cornmonly found

in the digestive

^systems

of

^nammalst

and

also

found

in the soil

enzJrme catalyst

neleased by an organism, ^conmonly

to

incnease

the rate of

br.eakdown

of a

substrate

endogenous utilization of

food stored

within the cell

netabo].ism

epiphyte a

pLant which adheres

to Parts of

another largen

plant

e.utr:ophic

enniched

with nutrients,

capable

of

suppor"ting extensive

plant

and animal populations

exogenous utilization of

food obtained fFom outside

the cell

netabolisn

heterotrophic obtaining

noupishment frorn organic Substancesr

Parasitic

^on saproPhytic

indicaton bacteria typically of enteric origin

^{whose pnesence}

in large

^nunrbens

in bacteria in

waterway

indicates recent

^sewage contamination

lysis celL

r.upture

following starvation

maerophytes

I'ooted vascular

aquatic plants'

water weed

nutnient inorganic

^compound nequined by

plants for the

synthesis

of

carbohydrate and protein

oligotnophic deficient in

one or' rnone

nutrients,

^incapable

of

suPPorting extensive

plant

and animal populations

periphyton plants or

anirnals

adhering to parts of

rooted

aquatic plants

photcnespiration respiration

which occurs

in sunlight, at a higher rate than in the

dark

photosynthesis

process whe:reby

plants

manufactune carbohydrate fnom

inorganic

^conpounds

in the presence of sunlight,

oxygen being neleased as

a

by-product

phytoplankton plant plankton,

smal1

plants

which

d:rift gtith the

surrounding water

protozoa uni-cellular or non-cellular

anirnals which

often

^{feed on} bactenia

substrate

^source

of

nourishment

for

heterotroPhic organisms

turbidity

absorbance

of light

by suspended

natter, usually over a

^{wide nange}

of

wavelengths