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AOKAUTERE BASINS: A STUDY IN MORPHOMETRY 

A thesis presented in partial fulfilment 

of the requirements for the Degree of 
Master of Arts in Geography at 

Massey University 

by 

NANYANG LEE 

1973 



ACKNOWLBDGMENTS 

I gratefully acknowledge the following individuals 

and organisations Dr. J.L. McArthur who supervised 

and offered valuable advice and criticism throughout 

the study; Geography Department of Massey University 

for providing a field work vehicle and equipment; farm 

owners of the study area for giving permission to carry 

out field work on their farmlands; Aerial Mapping Ltd. 

of Hastings, City Council of Palmerston North · and the 

Manawatu Catchment Board for supplying information and 

topographic maps; Wellington Meteorological Office for 

providing the required climatic data; Messrs. C.T. Liew 

and A. Fleming for assistance in field work; and all 

the people who have assisted in the course of study. 



TABLE OF CONTENTS 

ACKNOWLEDG~~MENTS 

TABLE OF CONTENTS 

LIST OF TABLES 

LIST OF FIGURES 

LIST OF PLATES 

CHAPTER I 
I. 1 

I. 2 

I. 3 
I.4 
I. 5 

CHAPTER II 
II. I 

INTRODUCTION 
Location Of The Study Area 
Aim 
Data 
Techniques 
Previous Research 

CLIMATE AND GEOLOGY 
CLIMATE 

II.I.1 Temperature 
II.I.2 Rainfall 
II.I.3 Wind 
II. II GEOLOGY 
II.II.1 Stratigraphy 
II.II.2 Relief And Geomorphol ogical 

His+,ory 

CHAPTER III BASIN CHARACTERISTICS - AREAL 
AND LINEAR 

III.1 
III.2 

Stream Numbers 
Stream Lengths 

III.3 · Rasin Areas 

iii 

page 

ii 

iii 

v 

vi 

vi: ii 

1 

1 

1 

2 

2 

3 

6 

6 

6 

7 
7 

10 

10 

12 

17 

18 

20 

21 



III.4 Frequency Distributions Cf Lengths 
And Areas 

III.5 Rela ti on Between Area And Length 
III.6 Drainage Density And Constant Of 

Channel Maintenance 
III.7 Basin Shapes 
III.8 Summary 

CHAPTER IV BASIN CHARACTERISTICS - RELIEF 
IV.1 Drainage Basin Relief 
IV.2 Erosional Surfaces 
IV.3 Total Relief 
IV.4 Relief Ratio 
IV.5 Relation Between Drainage Density 

And Relief Ratio 
IV.6 Channel Gradient 
IV.7 Maximum Slope Angle 
IV.8 Hypsometric Integral 
IV.9 Correlation Of Relief 
IV.10 Summary 

CHAPTER V CONCLUSIONS 

REFERENCES 

Variables 

page 

23 

26 

29 
32 

36 
36 
38 

39 
40 

42 

45 
46 

47 
52 
55 

58 

61 

iv 



LIST OF TABLES 

Table 1 Mean Lnd Extreme Temperatures 

2 Earth Temperatures At Four Inches 
And Three Feet 

3 Number r.f Days Of Ground Frost 

4 Rainfall In Inches 

5 Wind Force 

6 Wind Frequency And Force 

7 Drainage Density (Mi/Mi 2 ) 

8 Constant Of Channel Maintenance 
(Mi2/Mi) 

9 Elongation Ratio 

10 Average Total Relief (Feet) 

11 Relief Ratio 

12 Observed Average Values Of Relief 
Ratio, Drainage Density And 
Length Of Overland Flow 

13 Expected Average Values Of Drainage 
Density And Length Of Overland Flow 
Derived From Tµe Observed Relief Ratio 

14 Average Chann~l Gradient 

15 Percentage Frequency Distributions Of 
Hypsometric I~tegral Of First And 
Second Order Basins, Alton And Bolton 
C~eeks 

page 

8 

8 

8 

9 

9 

9 

28 

29 

31 

40 

41 

44 

44 

45 

48 

16 Average Hypsometric Integrals 49 

17 Table Of Correlation Coefficients 53 

·v 



vi 

LIST OF FIGURES 

following 
page 

Figure 1 Location Of The Study Area 
2 Topographic Map of Alton An~ 

Bolton Basins 
3 Mean Temperatures (°F) 
4 Monthly Rainfall (Inches) 
5 Mean Annual Percentage Frequency 

And Force Of Wind Directions 
6 Palmerston North Area : Geology 
7 Northwest-Southeast Cross Section 

Of The Tiritea Formation 
8 Cross Profile Of The Cliff Stream 

Terraces 
9 Relation Of Stream Order And Number 

10 Relation Of Stream Order And Average 
Length 

11 Relation Of Stream Order And Average 
Area 

12 Histograms Showing Log Distributions 
Of Channel Lengths 

13 Histograms Showing Log Distributions 
Of Basin Areas 

14 Relation Of Channel Length To Basin 
Area, Alton First Order 

15 Relation Of Channel Length To Basin 
Area, Alton Second Order 

16 Relation Of Channel Length To Basin 
Area, Bolton First Order 

17 Relation Of Channel Length To Basin 
Area, Bolton Second Order 

18 Frequency Distribution Histograms 
Of Elongation Ratio 

1 

1 

7 
7 

7 

10 

14 

15 

18 

21 

22 

23 

24 

26 

26 

26 

26 

31 



vii 

following 
page 

Figure 19 Relation Of Basin Order And 
Average Total Relief 

20 Relation Of Basin Order And 
Relief Ratio 

21 Relation Of Drainage Density To 
Relief Ratio, Alton Creek, First 
Order 

22 Relation Of Drainage Density To 
Relief Ratio, Alton Creek, Second 
Order 

23 Relation Of Drainage Density To 
Relief Ratio, Bolton Creek, First 
Order 

24 Relation Of Drainage Density To 
Relief Ratio, Bolton Creek, Second 
Order 

25 Relation Of Basin Order And Channel 
Gradient 

26 Frequency Distribution Histograms 
Of Channel Gradient 

27 Frequency Distribution Histograms 
Of Maximum Slope Angle 

28 Selected First-Order Hypsometric 
Curves 

29 Selected Second-Order Hypsometric 
Curves 

30 Third-Order Hypsometric Curves 

31 Fourth-Order Hypsometric Curves 

40 

41 

43 

43 

43 

43 

45 

45 

47 

49 

51 

51 
52 



LIST OF PLATES 

Plate 1 Cliff Stream Terrace 

2 Headwater Drainage Areas 

3 The Middle Reaches Of Alton Creek 

4 Slope Break Between The Interfluve 
Surface And Valley Side Slope 

viii 

following 
page 

15 

29 

39 

50 



CHAPTER I INTRODUCTION 

I.1 Location Of The Study Area The location of the 

study area is shown 

in Fieure 1. It cor.i.prises part of the terrace to the 

south-east of the Manawatu River just opposite Palmerston 

North City centre. Aloo st all the area of the two 

drainage basins studied is wi thin the boundary of 

Palmerston North City which has been expanded since 1967 

to include land on this side of the river. This suburb 

is generally known as Aokautere. 

Both streams selected for study are secondary tri­

butaries to the Manawatu River (Figure 2). They are 

here designated as Alton Cre ek , on the left, and Bolton 

Creek on the right, and the trunk strea::1 they join 

before entering the Manawatu H.ive r is named Cliff Stream. 

The exact location of the study area can be found on 

NZMS 1 N149, the 11 Palnerston North" sheet, between grids 

E130 and E150, and N290 and N330 . The township of 

Aokautere is about one mile northeast of the study area. 

I.2 Aim The prinary ain of the study was to investi::-;ate 

the characteristics of the fluvial landforms of 

these two basins which are believed to represent the 

overall characteristics of all drainage basins in the 

Aokautere area, and to seek explanation of the charac­

teristics in terms of existine; knowledge and ideas of 



0 40 IO 
I 

mil•• 

NORTH 

c' 
__ , / 

0 
I 

,, ,, 
, 

,.­,, 

mile 

1 
I 

?:::-.: \•::: L•1ul Our 1000 PHt 

'· ·· ...... ltuliy Ar•• 

~M :::::::::: ... ., UftlY•rtlty 

N 

+ 

Fig. J 

Location Of The Study Area 

I 
\ 

\ ,, 
"" ' "\ .. , 

\ .. 
~' 

~­,, \ .( ....... .., 
.... .1 \ 

'. ,1 •••• , ,• 
:~~ .· .··::. 
',',I,•,': I 1,'1' 
I I 1t 1

1 t ,1 

! :•.'.'I::•• 
I 1' ti', I.:·. II: If 
ti I I 1 • 1 I . ' ..... . .. . .. ..·.········ '•'•. •' 

I I 1, I ·.· ... 

I I I I I I I 
1 

~ I I : I I 1

1 
I I I I I 

' '' 



•OO 
I 

Contour. 20 Feet Inter val 

First Order Channel 

··-----. Second Order Channel 

·, , , Third Order Channel 

Fourth Order Channel 

Water Divide 

Fig. 2 . M Of A lton Tnpugraph1 c ap And Bolto n Ras ins 

_ ...... ~ -- -- ---
-~ -------- .... , 



the geomorphological history of the area. 

The study was based upon several hynotheses. The 

first was that these dr~inage systems are generally in 

the state of disequilibrium but are evolving ra~idly. 

2 

The second was that the hi story of the formation of the 

present day relief in the Aokautere drainage basins is 

r elated to the denudation chron ology of the main Mana­

watu River. The types of processes which developed the 

Aokautere basins may have been di fferent from those 

operating in the Manawatu River, however, because the 

deposition of loess from the Manawatu River bed during 

periglacial climatic conditions might have interrupted 

the development of an already established drainage sys­

tem on the original terrace surface. The third hypo­

thesis was that within a single drainage basin are fea­

tures of differing age, the age increasing with increasing 

order. The corollary is that morphometric properties tend 

to be similar among basins of same order. 

I . 3 Data A set of photogrammetric maps with scales of 

1 inc~ to 2 chains and 1 inch to 6 chains 

with contours of five feet intervals was the primary 

source of quantitative landform data . Two missions of 

aerial photographs taken in 1950 and 1g65 were also used. 

Geological informa t ion was derived from published and 

unpublished studies , and field work. 

I . 4 Techniques Most data were measured directly from 

maps and aerial photographs or derived 



3 

through arplications of formulae . From the maps, linear 

values were measured with a chartometer or strings, and 

areal values by pola r planimeter. Aerial photographs 

were studied stereoscopically by pocket and mirror-

type stereoscopes. 

Drainage basins were defined on the photogrammetric 

maps using the contours and aerial photographs. Streams 

were identified by contour indentation in the first 

instance , and then checked on the aerial phot ographs 

and in the field. Conve rsely, all streams id entified 

in the field and on the photographs were located on the 

contour map. The method of ordering followed is as 

outlined by Strahler (1952:1120) in which all finger tip 

streams without tributari es are fj_rst order streams and 

every junction of two streams of the same order forms 

a segment of higher order. 

I.5 Previous Research The most detailed and compre-

hensive studies on the geomor­

phology and geology of this area are those of Rich (1959) 

and Fair (1968). Rich studi ed the geological structure 

of the region, including faulting and stratigraphy. The 

formation on which the Aokautere streams are developed, 

called by him the Tiritea Formation, was described in 

detail. Fair gave a comprehensive account of the denu­

dation chronology of the lower Manawatu River, especially 

the effects of the Pleistocene climatic fluctuations upon 

the formation of the Manawatu River terraces. She came 

to the conclusion that although the Manawatu Region is 



tectonically unstable, thP. fluvial landforms of the 

Manawatu River valley have been mainly shaped by the 

effects of the past climatic fluctuations rather than 

by tectonic factors. 

However, interest in the area goes back to 1910 

4 

when Adkin first described the "raised beach formationn 

of the Horowhenua plain. He considered the terrace 

bounding the Tararua foothills as a "raised beach forma­

tion11 which was deposited under the Pleistocene sea. He 

distinguished the two significant layers of conglomerates 

as beach gravels deposited first when the sea was 

advancing and second when the sea was retreating. 

Cotton (1918) named this same formation the Otaki 

Series. He postulated that the formation was old dune 

sand deposits whose material is similar to that of the 

present beach and the associated dunes. He described 

the gently undulating surface of the formation as a 

surface of erosion due to the effects of peneplanation. 

In 1948, Oliver studied in detail the structure 

and history of the Ot&ki Series. Otaki Sandstones, as 

he named the formation, were identified as of marine 

origin, probably deposited-under very shallow sea con­

ditions. His study area came only to t~e southern bank 

of the Kahuterawa Stream. The equivalent formation to 

the north of the stream is Rich's Tiritea Formation. 

Cowie (1961 ,1964) stuaied the origin and distribu­

tion of the loess and Aokautere Ash in the Manawatu 



5 

region. He contended that the loess was deposit ed from 

the Manawatu river bed during the late Pleistocene. The 

Aokautere Ash was erupted during a late stage of the last 

glaciation, having been dated as 21,000 ± 500 years B. P. 



CHAPTER II CLIMATE AND GEOLOGY 

II .I. CLIMATE The major climatic elements that 

affect r unoff and erosion are t empe­

rature, rainfall, and wind . These three elements are 

here taken to describe t he climate of the study area and 

they are summarised in Tables 1 to 6 . The data are based 

upon records of the ~eriod from 1947 to 1966 for Pal ­

merston North D.S.I.R. weather station wh i ch is located 

about two miles west of +.he study area . Its altitude 

of 110 feet above sea- level is approximatel y at the 

l evel of the basin mouth of the Alton and Bolton Creeks . 

II.I.1 Temperature Table 1 shows a summary of records 

of mean te~perature, mean daily 

tcr.:perature, and mean daily maximum and minimum tempe -

ratures, over the twenty year period . The temperature 

in general is mild, with an annual average temperature 

of 55.4°F, averaging just over 60°F i n summer and not 

l ower than 45°F in winter . The ave r age range between 

warmest and coldest months is 18°F , which is only a 

little larger than the mean diurnal range . Mean daily 

maximum could reach 74°F in summer whi le a mean daily 

minimum of around 40°F during winter i s common ( Fi gure 

3) . 

Temperature readings at f our ~D~hep and three feet 

u~~:1grouna ~~e shown i n ~able 2. These temperatures, 



7 

though warmer than that of the air in summer , and colder 

i n winter, are of very small variation compared to the 

air temperature . 

Table 3 shows the average number of days of ground 

frost. The occurrence of ground frost takes place 

mainly during winter months of June, July and August. 

But the number of occurrences on the whole is so few 

that its effect on the weathering of rocks is insigni-

ficant. Snow has never been recorded as having fallen 

in the area for the past twenty years . 

II.I .2 Rainfall Rainfall of the area is moderate but 

reliable. Although there is no marked 

dry season , rainfall minima occur in March and September. 

Monthly maxima occur in early summer and early winter . 

Winter has a comparatively large amount of rain while 

summer has higher frequencies of maximum daily fall . 

However, over the twenty year period, not a single daily 

fall has ever exceeded three inches. Table 4 shows 

mean annual rainfall and number of rair: days. Figure 4 

shows the average monthly rainfall distributions. 

II. I. 3 Wind As compared to other places under the 

Middle New Zealand Zone climate( 1), 

Palmerston North is relatively calm. Table 6 and 

Figure 5 show that the average percentage of calm days 

on the Beaufort Scale is 13.5 per cent a year. Besides, 

the winds are not strong . The average wind force 

ranges f rom 1. 8 to 2.7 on the Beaufort Scale (Table 5). 



OF 

80 

70 

60 

50 

40 

30 

20 

10 

0 

Fig. 3 Mean Temperatures 

· 11.~ 
&' Q 

---, ,,..~ ~9· , - ...... .. ... •.. ,,... ' ~ , 
......... "'~ .. · 

'" 0<"14,; ,, ' ~ ,, \)~ 
,, f;~ / · ~'~ 

' ~e ,, ~' ,, ,, ,,_ , 
~ --'--~-

~ ~ Mean Daily Ran;: 

J F M A M J J A s 0 N D 

Fi.g.4 Monthly Rainfall 

Inches 

5 

4 

3 

2 

0 -----------
JFMAMJJASOND 



Fig. 5 Mean Annual Percentage Frequency And Force Of Wind Directions 

10 f. Frequency 

• 
1 Force 

D SI R , Palmerston North 

(1947-1966) 



....... •· . .. . .~ 

". 

Mean Temp. -.... ... ... 
Mean Daily Max. 

Mean Daily Min. 

Mean Daily Range 

At Four Inches 

At Three Feet 

Days 

Table 1 Mean and Extreme Temperatures (°F) 

Jan Feb Mar Ap~ May Jun Jul Aug Sep O~t Nov Dec Annual 

63.3 64 •. 3 61._4 56.7 52.1 47 .. 9 46.5 48.1 51 .. 5 54.8 57.8 61.2 55 .. 5 

72.1 73.3 70.0 64 .9 59.8 55.2 54.,0 55.7 59 •. 4 62'!8 65.9 69.6 63.6 

54.5 55.3 52.7 48~5 44~3 40.6 39.0 40~5 43~7 46.? 49.7 52.8 47.4 

17.5 17.9 17.3 16 •. 3 15.4 14.6 15 •. 0 15 •. 2 15 •. 6 16.0 16.2 16.8 1'6 •. 2 

D.S. I.R. ,Palmerston No'r:'th (1947-1966) 

Table 2 Earth Temperatures at Four · Inches and Three Feet 

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual 

65.9 65.5 61.6 55 • .7 50.3 46.1 41.f.0· 45.4 49~6 54.8 59~8 63.8 55 .• 2 

66 •. o 67.1 65 •. 6 61._7 · 5?;;. .1 52 .. 8 49.8 49. 8 52.1 _55.6 59 •. 7 63·.!f 58 •. 4 

Massey University; Palmerston North 
( 1 94 7 -1 966 ) . 

Table 3 Number of Days of Ground Frost .: 

Jan Feb Mar Apr May Jun Jul Aug S&p Oct Nov Dec Total 

0.1 o.4 o.~ 3.p 6.5 10.7 13.6 11.0 5.9 2.6 o.B 0.1 52.8 

Massey University - .. (194·7-1960) 
D.S.J.R .~ Palmerston North - (1961-1966) 

CX> 



Table 4 Rainfall in Inches 

Jan Feb Mar Apr M~y Jun J~l Aug S~p Oct - Nov· D~c Total 

Rainfall 3.44 2.78 2.63 3.95 3.~1 4.03 3.86 3.15 2.~1 3.41 3.38 4.17 39.72 

No. of Raindays 11.5 9.5 12,0 13.5 15.0 17.0 17.0 15.5 13.5 15 . 5 15.0 14.o 169.0 

D. S.I .R.,Palmerston North (1947-1966) 

Table 5 Wind Force 

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Mean 

Wind Force 2.5 2.3 . 2.2 1. 9 ·. 1.8 1.8 1. 8 2.0 2.4 2.7 2. 8 2.7 2.2 (Beaufort Scale) 

D.S.I.R. ,Palmerston North (1947-1966) 

Table 6 Wind Frequency and ·Force 

N NE E SE s SW w NW Calm 
-· 

Wind Days 22 18 62 32 22 15 97 47 50 

Ave. Force 1.9 2.1 3. 0 3.2 2.7 2.2 3.2 2. 7 (Beaufort Scale) 

D.S.I.R.,Palmerston North (1947-1966) \() 



10 

Gales are not commo~; o?e~ the twenty year period of 

observation 1 there we~c only 15 galeo recorded. 

The dominant wi nd is from the west. The wester-

lie s are most pre7a:cnt in the winter months end is in 

general_ strcnger t~12.:1 other winds. Other prevail ing 

winds a re castcrlieG and n0rt h- -we aterli es. 

II. II. G"fi'C;~OGY The terrace on which the Ao~autere 
. -· -···--~ 

Jtreams a~e developed is kn own as 

the Tokomaru Terrace (C owi e, 1961:12), and itc formation 

was described by Rich (~ ~~9: 77) as th~ Tiritea Formation. 

_II. II. _1_S_!ratigrap_l.!l It has been generally believed 

that t he Tiritea Formation is 

an emerged mar ine terrace which was laid down during 

the Hawera Transgression and is a similar formation to 

the Otaki Sandstones south of Kahuterawa Stream (Oliver , 

1948). The unit furt~1~r ncr~'." ~-i-: ----~~r::w.ter~ , "the Tua 

Paka :F'ormatic11, i s also sj.mil ar i n many r espec t s to the 

Tirit ea Formation (Rich,1959:77). I n Figure 6 all the 

three un its a r e col:cctively grouped under marine de­

posits, despite the age . that decreases south~ards. 

The Tiritea Formation consists mainly of fine 

~-~~ A s~v~cc 1 qiltstones, and conglomerates. At the 

river bluff near Anzac ::?ark on ·the southeaD-'-: bank of 

the Manawa t u River ·,1Lerv ~he marine "'J _, :crace comes right 

to the edg e of the river without being bounded by an) 

river t erraces , a very cleAr exposure of the succession 



Fig.6 

.+ .. .... .. 
+ + + 

.... + 
~ 

0 
~ .t ... .. .. .t ... 

+ .. .+ .. 
+ "~ ... ..+ .. _,,. -+ ... .. 

+"' ... 0 2 i 

.... + -+ "' II• ' 

Greywacke 

Marine Deposits 

FI u.v i 8 + Deposits 

Recent Alluvium 

Pohangina Anticline 



of strata in the Tiritea Formation is observed. There 

are five major strata in the formation, which from 

below are silt, conglomerates (12 feet), fine sand 

(12 to 15 feet), conglomerates (15 to 20 feet), and 

sand-silt (75 feet)(Rich,1959:89-90). Overlying the 

surface of the marine deposited terrace are masses of 

airfall materials with thicknesses ranging from two to 

twenty feet. These airfall masses consist mainly of 

fine silt and some pumice ash. Cowie (1961:24,1964) 

identified the fine silt as loess and suggested that 

it had originated from the local aggradational river 

sediments of the late Pleistocene epoch. These fine 

particles were deflated by the then prevailing north-

11 

westerly winds and deposited to the southeastern re­

gions of the river beds( 2 ). About half way through the 

thickness of the loess deposits is a band, two to five 

inches thick, of pumice ash called Aokautere Ash 

(Cowie,1961:21 ,1964a). The ash band is not observed 

in Alton and Bolton basins, either because it i s 

heavily masked by the enclosing loess or because it 

has been eroded away. 

The two strata of conglomerates separated by a 

layer of fine, loose sand are significant members 

of the Tiritea Formation. Both conglomerates are 

poorly consolidated with a sandy matrix and contain 

sub-angular to rounded greywacke pebbles averaging 

between one and two inches in their longest dimension. 

Lenses of very fine sands are found in both bands of 



12 

conglomerates but the upper stratum is relatively more 

sandy and less well sorted. A slight change of facies 

is observed in both strata between the bluff and several 

exposures towards the southeast. As far as the study 

area is concerned, the major strata observed on the 

bluff extend very continuously towards the southeast, 

that is, into the headwater areas of the Alton and 

Bolton Creeks. The general direction of flow of drai­

nage systems on the terrace is from southeast to north­

west, while Alton and Bolton Creeks flow almost at 

right angles to this direction. 

II.II.2 Relief And Geomorphological History 

The relief 

of the study area is dominated by the broad flat Toko­

maru Terrace which forms the extension of the foothill 

region of the Tararua Range. The surface of the terrace 

is about 200 feet above the Manawatu River at the Anzac 

Park location and rises to about 500 feet where uncon­

formi ties are found between the terrace formation and 

the greywacke of the Tararua Range . The actual Tararua 

foothill is overlain by the marine terrace thus resulting 

in an unsually broad and flat foothill extending for 

about thTee miles between the Manawatu River and Tararua 

Range. Alton and Bolton Creeks are developed on this 

terrace foothill. The entire drainage systems are 

within the terrace boundary with none of the tributaries 

being extended into the Tararua Range. 



13 

The retreat of the Hawera Sea and the emergence of 

the Tokomaru Terrace can be conveniently taken as the 

beginning of the geomorphological history of the area. 

Fair (1968:83) suggested 45,000 years E.P. as the date 

of the complete emergence of the Tokomaru Terrace. The 

emergence brought an end to the marine depositional 

process and at the same time the commencement of sub­

aerial erosion on the surfaces of the marine terrace. 

The interval between the exposure of the marine 

surfaces and the fall of the loess was about 8,000 

years (Fair,1968:83). Within this 8,000 year period? 

sub-aerial erosion could have been vigorous. At many 

localities in the area there is a gap in the strati­

graphic sequence between the air fall materials and 

the underlying upper conglomerates. The absence of 

the uppermost sand-silt stratum of the Tiri tea Format.:l ,.. ~, 

in these localities suggests that this soft stratum was 

completely eroded away by processes of sub-aerial 

erosion within this 8,000 year interval. The Aokautere 

Streams were probably initiated as consequent streams 

flowing on slopes of initial surfaces when the marine 

terrace was first exposed. As the sand-silt stratum 

was soft and easily eroded, the drainage patterns could 

have been well established when the loess first began 

to fall. However, the upp~r conglomerates which underly 

the uppermost sand-silt str,atum comprise a very much 

more resistant layer 7 which eventually might have 

slowed down the rate of erosion to a considerable extent. 



The fall of the loess interrupted the development of 

the streams and it was in this period that the incep­

tion of the present day pinnate drainage pattern 

occurred. 

14 

Figure 7 illustrates the present northwest-southwest 

cross section of the Tokomaru Terrace. The diagram is 

bounded by the Manawatu River at the left where the 

marine terrac e ends as a cliff at the bluff. To the 

right the profile runs across the middle reaches of 

Alton and Bolton Creeks. The strata of the Tiritea 

Formation are continuous near the river bluff, but 

become less continuous inland. Furthermore, in many 

localities the uppermost layer of sand and silt has 

been eroded away and its contact with the uµper conglo­

merates has been replaced by airfall materials. Highest 

order segments of both Alton and Bolton Creeks have 

developed to the level of the lower conglomerates which 

offer rather strong resistance to downcutting. The 

lower conglomerates, as have been described, are less 

sandy and better sorted than their upper counterpart 

and so the resistance met at this layer naturally is 

greater than that encountered when the streams first 

reached the upper layer. However, most of the lower 

order streams in the catchments are still on the loess 

and sand~silt strata. At the mouth of both streams 

where they join the Cliff Stream, the stream levels 

have cut through the conglom~rates and have reached . 
the lowest stratum of the Tiritea Formation observed 



Manawatu 

River 

Fig . 7 
Northwest-Southeast Cross Section Of The Tiritea Formation 

Anzac Park 

... . ... ·· :.:: .:._·:· ... :·.·· ···::·-:.::· .... :. ~ ·:·:··:.· .. ·.:·:·: ... . 

.. :: ':. ~ ·_:. : : . . ·::: ·. . .. " ..... : .. : ... ... .. : :. ~ ._-; : .: ... ' ... : ·: ........ ': : ·:: .... . 

~ 
GI 
GI ... 
u 
c: 
0 ... 

. :·:-:.:. ·~ -.::..:·:·:./_:' ;' ;·: .... : : .. .... 

2 00 feet 

~ 
GI 
GI ... 
u 
c: 
0 ... 

.. · .. ·. · .. : · .. ·.: .·. 

lOESS 

SAND-SILT 

CONGLOMERATES 
SAND 
CONGLOMERATES 

FINE SAND 



on the bluff, the stratum of silt and clay. 

At the lower Cliff Stream valley a well-marked 

river terrace has been formed (Plate 1). The height 

of this terrace is ten to twenty feet higher than the 

Ashurst Terrace nearby in the Manawatu Valley. The 

15 

Ashurst Terrace, according to Fair, was deposited in 

the Kumara-2 second interstadial period (1968:83). The 

evidence obtained in the Cliff Stream terrace, however, 

suggests that it is a degradational terrace cutting 

through the various strata of the Tiritea Formation 

(Figure 8). Though the height difference and nature 

of the formation distinguish them as different terraces, 

they are of very similar age. First, the absence of 

Aokautere Ash on both the Ashurst and Cliff Stream 

terraces suggests that they were formed only after the 

fall of the Aokautere Ash; second, the thickness of 

loess that covers both terraces is almost the same. 

Cliff Stream terrace has an average thickness of three 

feet while Ashurst Terrace two and a half feet. This 

difference in the nature of the formation of the 

terraces formed at almost the same time suggests the 

possibility that processes in the Manawatu River were 

different to those in its tributaries during the 

Pleistocene epoch. The small tributaries widened 

their valley floors by lat eral corrasion while the 

trunk stream was transporting large quantities of .. 
debris. 



Fig.8 Cross Profile Of The Cliff Stream Terraces 

Marine Terrace -Tread& 

1 River Terrace 

I . . . . 

LOE SS 

CONGLOMERATES 

SAND- SIU 

FINE SAND 



Plate 1 Cliff Stream Terrace. The tread is 

predominantly flat a:nd is well marked 

at the edges. The marine terrace 

riser, masked with loess and fine-sand, 

is dominated by terracettes. 



NOTES 

(1) Garnier (1958) classified climates of Taranaki, 

Manawatu, Wellington-Hutt, and Nelson areas under 

the Middle New Zealand ~one type. 

(2) The deposition of loess could have begun as early 

16 

as the Kumara-2 first advance in the Otiran Glaciation 

(Fair , 1968:83), and en ded at least earlier than 

3,000 years B.P.(Cowie , 1964 :392). The thickness 

of the deposits is greate~ near the river banks 

than those further i nlan d. · 



CHAPTER III BASIN CHARACTERISTICS 
AREAL AND LINEAR 

· The recent recognition of geometrical relationships 

among various properties of drainage basins has led to 

the formulation of morphometric laws. The explanation 

of drainage basin characteristics by subsumption under 

laws has achieved the aims of classifying various types 

and forms of drainage basins and of describing drainage 

basin characteristics. This chapter and chapter IV 

analyse the morphometric properties of Alton and Bolton 

basins with the aim of assessing the degree of conformity 

of their compositions to the existing morphometric laws. 

The analysis explains the extent to which the components 

of the studied drainage basins conform to or depart from 

the characteristics predicted by the morphometric laws. 

Not all the aspects of the laws are conformed to; in 

many cases, additional explanation is needed. 

Both the areas of Alton and Bolton drainage basins 

are small (Figure 2). Alton Creek drains an area of 

8,752,362 square feet with a total channel length of 

26,182 feet, and Bolton Creek has an area of 8,867,544 

~~1are feet and 29,668 feet of channel. Despite their 

small sizes, the streams are fourth order in rank, with 

drainage densities of 13.1 for Alton and 13.4 for Bolton. 

These c2nsities are considered as moderate for basins 

in this type of climate under which drainage densities 



18 

normally range between 5 and 20 (Schumm,1956:602). 

Both the Alton and Bolton Creeks are intermittent 

streams. For most of the year the channels are dry. 

Even channels of highest order dry up during the summer 

months leaving only small pools of water scattered along 

deeper sections of the lower reaches. In the winter 

months, the lower sections of the fourth order streams 

normally contain an average depth of water of between 

eight and ten inches and have an average channel width 

of two and half feet. The estimated discharge under 

such conditions is about 2.5 cusecs( 1 ). The beds of 

these fourth order sections are floored by greywacke 

pebbles transported from the upper reaches of the 

streams or being scoured from the local channel banks; 

along the valleys, miniature floodplains are formed. 

Channels of first and second orders are mostly incipient 

valleys which contain water only immediately after 

intense rainfalls. 

III.1 Stream Numbers Horton (1945:291) stated the 

Law of Stream Numbers( 2 ) as : 

"The numbers of streams of different orders in a given 

drainage basin tend closely to approximate an inverse 

geometric series in which the first term _i ·s unity and 

the ratio is the bifurcation ratio." The relationship 

is expressed exponentially in Figure 9 for Alton and 

Bolton Creeks. Although the g~aphs of first to third 

orders are reasonably straight, especially tqat of the 



NUMBER 

300 

100 

50 

10 

5 

Fig. 9 Relation Of Stream Order And Number 

. 
\ 
' ' ' ' \ 

\ 
\ 
\ 
\ 
\ 

' ' ' ' ' \ 
' \ 
' ' \ 
\ . 
\ 
\ 

' ' ' . \ 
\ 
\ 

' \ \ 
\ 
\ 
' ' \ 
' \ 
\ . 
' \ 

2 3 

ALTON 

\ 
\ 

\ 
' \ 
\ 
\ 
\ 
\ 

4 ORDER 

• 
' 
' ' ' ' ' ' \ 

\ 

' \ 
' ' \ 

\ 
\ 

' ' \ 
\ 
\ 

' ' \ 
\ 
• 
' ' ' ' \ 
' \ 
' 

• 

' ' \ 
' ' ' ' ' ' \ 
' ' ' ' ' ' \ 
' \ 
~ 

' ' ' ' ' \ 
\ 

' ' ' \ 
\ 
\ 
\ 

' . ' 

2 3 

BOLTON 

' \ 
' ' ' ' . 
' ' ' 



Bol ton Creek, both graphs display slight concavities 

at the lowest ends . This indicates that the observed 

~umbers of first, second and third order channels are 

proportional to each other but not to the highest or 

fourth order number . 

19 

Assuming that both creeks continue to develop so 

as to maintain their rresent weighted mean bifurcation 

ratio(3), and also the fourth order status, the geome-

trical regressions of both creeks would appear as the 

dotted regressions in Figure 9. At this theoretical 

stage, regressions of both creeks would be straight . 

A comparison of the observed regressions with the 

theoretical regressions indicates that the developments 

of the stream systems, although near parallel to the 

theoretical pattern of development, according to Horton ' s 

law of stream numbers, are still at some stage away from 

the described theoretical stage. 

The distribution of stream numbers is connected 

with the pattern of the drainage system itself. The 

drainage pattern of the Alton and Bolton Creeks resembles 

the pinnate drainage pattern described by Parvis (1949), 

where the lower order channels join the main stream in 

a parallel manner. Von Bandat (1962) described such a 

pattern as dendritic-pectinate and associated it with 

loess formation . In A:ton and Bo1ton basins, many of 

~~n f irst and s e c ond or der streams join the trunk orders 

directly without passing through orders in between. ~~i~ 



20 

has resulted in the high bifurcation ratio , especially 

that between s econd and third order streams, because a 

large proportion of second order channels join the fourth 

order segment without passing through the third order 

channels . 

It could be suggested that the uppermost layer of 

loess and its underlying layer of siltstone and fine ­

snndstone strata of the Tiritea Formation have contributed 

to the formation of such a drainage pattern . Almost all 

the first and second order streams flow on these easily 

eroded strata and the development of channels is rapid. 

On the other hand , part of the third and fourth order 

segments of both creeks have developed into the lower 

strata of the Tiritea Formation which are more resistant 

than the two uppermost layers . The development of 

channels thus is more pronounced at the lower orders 

than at higher orders. 

III.2 Stream Lengths The length component used in 

this study is the accumulated 

length(4) rather than the segment length. This reduces 

the effect of the drainage pattern to a minimum. 

The Law of the Stream Lengths(S) was stated by 

Horton (1945:29 1) as : "The average l engths of streams 

of each of the different orders in a drainage basin 

tend closely to approximate a direct geometric series 

i n which the first term is the average l ength of streams 

of the firs~order and the ratio is the stream length 



ratio". Figure 10 illustrateq the 'JXponenti a l rela­

tionships between the average accumulated lengths and 

orders. The dotted regressions are the theoretical 

regressions of both creeks obtained according to the 

law. 

The weighted mean stream length ratio of Alton 

Creek is 3.6 and that of Bolton Creek is 5. 0 . As 

stream length ratio is obtained by dividing stream 

length of the order by stream length of the next lower 

order, and as the basic stream lengths (first order 

stream lengths) are near:J the same fo£ both cre 2ks, 

21 

it could be deduced that thG ratio between higher and 

lower order stream lengths in Alton Creek is lower than 

that in the Bolton Creek. This has resul ted in the 

considerably shorter lengths in the theoretical regres­

sion of the Alton Creek than that of the Bolton's. 

A comparison betv1een the obc:·y·.· ::d and theoretical 

regressions shows that at the first and second order 

basins, the lengths of observed and theoretical stage 

are the same, but the difference in~reases with increasing 

order, especially for Alton Creek. This indicates a 

stage of inequilibrium relationships between the lengths 

of lower and higher orders , and is espec i ally obvious in 

the Alton Creek. 

III . 3 Basin Areas Schumm ( 1956:606) proposed the Law 

of Basin Areas( 6 ) as : "The mean 

drainage basin areas of streams of each order tend to 



Fig. 10 Relation Of Stream Order And Average Length 

30,000 

• • 

• 
I 
I 
I 
I 

10.000 
I 

I 
I 
I 
I 
I , 

• I I I I 

5,000 
I I 

I • I I I 

I I 
I 

I I I • • I I 

I I 

I I 
I I ... I I c 

I I Cl) 

u.. I I 
I 

I I 
I I .c 
I I ... 

I C) I c 
I I 

Gl I ~ 
1,000 I I 

I I 

Gl I I 
C) I ~ ... I c 

I • > 
ct 

500 • 

• • 

100 

2 3 ORDER 2 3 

ALTON BOLTON · 



22 

approximate closely a direct geometric series in which 

the first term is the mean area of the first order 

basins and the ratio is the basin area ratio11 • Figure 

11 shows both observed and theoretical regressions for 

both creeks. These areal regressions show a similar 

regression pattern as that of the length regressions. 

The Alton Creek's graph resembles that of Figure 10 

showing average lengths where the expected basin areas 

of the higher orders are considerably lower than those 

of the Bolton Creek. The observed and theoretical re­

gressions of Bolton Creek are very close together except 

in second and third orders which is caused by the pre­

sence of two anomalous second order tributaries in the 

headwater area of Bolton Creek. 

It can be concluded that the numbers, lengths and 

areas of Alton and Bolton Creeks do not conform exactly 

to the laws of morphometry . This indicates that the 

relationships between the variables and orders are still 

in an unbalanced stage where further development will 

be needed before the relationships in the systems re­

flect the stage of equilibrium as stated in the laws. 

Alton Creek shows a greater deviation in regression 

patterns of lengths and areas. The cause could be 

attributed to the loss of its headwater areas to the 

Tiritea Stream. It is believed that at a stage in the 

late Pleistocene epoch, the Tiritea Stream, which was 

then at a higher level than its present day level, 



Fig. 11 Relation Of Stream Order And Average Area 

0 ·4 

• • 
I 
I 
I 
I 
I , 

I 
I 

' I , 
0·1 I 

I I I 
I I I I 

I I 
I 

I ' I I 

' I 
I I 

0·05 • ' I 
I I 

I , 
I I N I 

I I 

J , I 
I I 
I I 
I I • / . I e I I .. I c I , 

' I I 
I) I I 
OI I I • I I .. I e I 

I 
> I c I , 

I , 
I , 

0·01 I 
I 

I 
• • I 

I 
I 

' 0-005 I 
I , 
I 

~ , , 
1 

• 
• 

0·001 

2 3 OADEA 2 3 

ALTON BOLTON 



23 

eroded part of the Tokomaru Terrace where Alton 

headwater areas used to be . The loss of length and 

area is difficult to replace or readjust . Therefore 

the adjustments of the relationships of length and 

area with order after the interruption have been slow. 

Stream numbers, on the other hand, can adjust to such 

an interruption more quickly than lengths and areas 

of the basins; and considering the length of time 

since the interruption occurred, the adjustments of 

the stream numbers in Alton Creek have been rapid. 

III . 4 Freguency Distributions Of Lengths And Areas 

Because of 

the small number of streams in higher orders, only 

first and second order streams are t aken for study; 

and for convenience of interpretation of summary sta­

tistical measures , the values of length (feet) and 

area (square feet) are transformed into log values and 

are shown diagrammatically in Figures 12 and 13 . 

Frequency distributions of lengths of both creeks 

are very similar (Figure 12). Both creeks show slight 

positive skewness with higher frequencies occuring at 

lower values. They have very similar means and modes 

at first order, but those of the second orders differ 

considerably. The Alton second order shows a sharp 

drop at the class centred on 2. 85 immediately after the 

modal cl~FR , while the corresponding order of Bolton 



... 
c 
Q) 

u 

... 
Q) 

Q. 

... 
c 
Q) 

u 

Fig.12 Histograms Showing Log Oistribut ion Of Channel Lengths 

50 

" 0 

30 

20 

10 

0 

40 

30 

20 

1 o-...-~ 

0 

It') 
co 

It') 

co 

First Order 

Second Order 

r---., 
: : (a) Alton Creek 
I I x1= 2·140 : : x2=2 ·701 
I I 
I I 
I I 

~--- ____ _, . 
I I 

' I 
--- I 

It') 

0 
N 

Mid-Value 

I 
I 
I r-- --, 
I I I 
I I I ._ ___ _, I 

It') 
co 
c'.t 

(Log Ft.) 

X2= 2 ·803 

It') 

0 
M 

I 

------- -, 
• 

(b) Bolton Creek 

... --- ------- ----------. 

It') 

0 
c'4 

Mid-Value (Log Ft.) 

I 
I 

It') 

'° M 



Creek has its modal class centred on 2,25. Frequencies 

decrease slowly and extend into a higher range of values, 

producing a higher degree of skewness than for Alton 

Creek. Though their mean values are similar, Bolton 

has a wi de r range of values. However, the transition 

range between first and second orders of both creeks 

are similar. Alton ran~es from 2.16 to 2.75 and Bol ton 

ranges from 1.96 to 2.95. These broad transition zones 

suggest the lack of equilibrium in the systems of the 

basins as an equilibrium system normally has a sharper 

distinction between lengths of higher .and lower orders. 

Frequency distributions of areas vary remarkably 

between the two basins, although their mean values are 

nearly the same. Again, Bolton basin has a wider range 

than Alton basin; and its distributions are more dis­

persed (Figure 13). The first order of Alton Creek 

has a standard deviation of 0.462 and a coefficient of 

variation of 10.6 per cent, while the second order has 

values of 0.479 and 9.6 per c ent respectively. Corres­

pondingly, the Bolton first order has a standard devia­

tion of 0.529 and a coefficient of variation of 12.5 

per cent. As far as areas are concerned, their first 

order basins show similar distributions but the distri­

butions of second order basins vary considerably. The 

transition between first and second orders in Alton 

Creek occurs continuously from 4.16 to 5.55, while that 

of the Bolton Creek occurs mainly from 3. 76 to 5.75. 

Again, these wide transition zones indicate the lack 



40 

... 
c: 3 0 
G> 

(.) 

... 20 
G> 
~ 

1 o-1-----' 

... 
c: 
Q) 

0 

50 

40 

(.) 30 

... 
:. 20 

10 

.,., 
'9 
M 

Fig.13 

.,., 
00 
M 

:g 

"" 

Histograms Show ing Log Distribution Of Basin Areci~ 

- First Order ----- Second Order 

x1= 4 ·656 x2= 5 -282 
(a) A I ton Creek 

r---, 
I I 

r---, : : 
I I I I 

I 1 I 
-------~--.J '----, : : 

I L--------, 

.,., 
~ 

"" 

.,., 
"" ~ 

It) 
-0 
...;, 

Mid-Value 

~ 

"" 

.,., 
0 .,., 

.,., 
~ .,., 

(log Sq. Ft.) 

,---------, 

x1= 4·606 

r-- --

.,., .., .,., 
.,., 
'9 
It) 

x2= 5 ·580 

.,., 
~ .,., 

I 

.,., 
0 
-0 

(b ) Bolton 

:-------, 
o....L.~-----==:;::::::'.:.......,_;_-r....i..--r----r--'-~--r----,-1:::: --J 

I 

I I I I I I 
It) 

0 
M 

It) 
N 
M 

It) 

"" <"'> 

.,., 
-0 
<"'> 

.,., 
00 
M 

It) 

0 ... 
Mid-Value 

.,., .,., 
N ~ 

"' "" 
(Log Sq. Ft.) 

.,., .,., It) .,., It) .,., It) .,., 
'<? 00 9 N "'!' '9 00 0 
~ ..;, .,., It) It) .,., .,., .,() 

Creek 

r--------, 
.,., It) .,., 
N ~ 00 
-0 -0 .(;, 



25 

of equilibrium of the basin developments. Due to the 

wide range of transition zones between the two orders, 

it is difficult to draw · a lower limit for the second 

order basin areas, or an upper limit for the first 

order areas. It could only be deduced that first order 

basins with areas l arger than 112,200 square feet are 

likely to be developed into second order basins . 

A few points about the frequency distributions of 

length and area of the two creeks can be observed. First, 

dispersions in Bolton Cre ek, both in length and area, 

are greater than for Alton Creek. This indicates that 

the lengths and areas of Bolton Creek are more varied 

than in Alton Creek. Second, the distributions are 

skewed, mainly positively, with Bolton's second order 

length distributions being most strongly skewed. Channel 

lengths are short and basin areas are small. Over 70 

per cent of the first order channels of each basin are 

shorter than 180 feet, and about 30 per cent shorter 

than 80 feet . Second order channels have a wider range 

of lengths and the two creeks vary considerably. The 

minimum channel lengths of first order channels in both 

basins are between 40 and 50 feet, while the lower 

limits of second orders range between 100 and 150 feet. 

However, short second order channels are plentiful in 

both the creeks. The minimum first order basin area 

is 3,000 square feet; and over half of the number of 

first order basins of both creeks fall into the class 

of between 3,000 and 30,000 square feet. The transition 



26 

limits between the two orders, especially for area , are 

difficult to decide. Th~ upper limit of the first order 

basin a r eas can be as high as 278,000 square feet, 

while some second order basins have areas as low as 

the lower limit of first order pa sin areas. These 

broad overlappings are identical in the distributions 

of l ength and area of both creeks; and t hese can be 

attributed to the l ack of equilibrium in the systems of 

both creeks. 

III.5 Relation Between Area And Length 

As stream numbers, 

lengths and areas are all related to orders, they should 

therefore be related to each other. 

Figures 14 to 17 show the regressions between areas 

and lengths within each order. Again, due to the small 

number of basins of higher orders, only first and second 

order basins were taken to investigate the degree of 

correlations between the t wo variables. The results 

reveal that high degre e of correlations exists . The 

correlation coef ficient of Alton's first order basins 

is 0.71 and second order basins 0.79; while in Bolton 

Creek, the first order coefficient is 0 . 85 and that of 

the s ec ond order is 0.75. All these relationships are 

positively correlated so that larger basins tend to 

have longer channels . The correlation coefficient 

ma·rks an increasing degree of correlation fr om first 

to s econd order in Alt on Creek, but decreasing in 



Area (Mi2) 

0·010 

0·005 

0 

Fig.14 Relation Of Channel Length To 'Basin Area 

Alton First Order 

II') 
0 
6 

0 -6 

Length 

(Mi) 



0·015 

0·010 

0·005 

0 

Fig-16 Relation Of Channel Length To Basin Area 

. . 

Bolton First Order 

/ 

Ltngth 
(Mil 



Area {Mi2) 

0·020 

0·010 

0 

Fig. IS Relation Of Channel Length To Basin Area 

0 

0 

A I t o n Second Order 

0 
N 
6 

Length 
(Mi) 



Area {Mi2) 

0·1 

0·08 

0·06 

0 ·04 

0·02 

Fig.17 Relation Of Channel Length To Basin Are a 

Bo! ton Second Order 

I 

I 

/ 

Length 

(Mi) 



Bolton Creek. The regression equations show that all 

the expected values of basin areas of the first order 

basins of both creeks, and the second order of the Alton 

Creek, based upon unchanged channel length, are slightly 

higher than the observed basin areas. This indicates 

that a majority of these basins have a slightly loLg 

channel length for the basin area drained . However, 

there is also a considerable number of basins whose 

areas are exceedingly large for the existing channels . 

III.6 Drainage Density And Constant Of Channel Maintenance 

The relationship between channel length and bas i n 

area can also be expressed in terms of drainage density 

and constant of channel maintenance . Drainage density 

is a measure of the degree of dissection while the 

constant of channel maintenance measures the erodibility 

of the land surface. The former is expressed as miles· 

per square mile and the later as square miles per mile . 

It has been suggestet that drainage density is 

independent of order and that the drainage density of 

the total basin tends to approximate the mean drainage 

density of £irst order basins (Morisawa,1962:1035; 

Hack,1957:66). However, this property does not apper:l.l' 

to be present in either creek. First order basin ~ 

densities are highest in the systems and drainage den­

sities decrease towards higher orders until the total 

basin order (Table 7). The total basin density of 



Table 7 Drainage Density 
(Mi/Mi 2 ) 

ORDER ALTON CREEK ·BOLTON CREEK 

First 15.3 17.8 
Second 14.2 9.2 
Third 11. 2 8.6 
Fourth 13. 1 13.4 

Alton Creek is closer to the first order density than 

that of the Bolton Creek. The relationship of drai­

nage density and relief is discussed in Chapter IV. 

28 

The con:,+.ant of channel maintenance expresses the 

basin area in square miles required to maintain a mile 

of channel and is the minimum area required for the 

development of a drainage channel (Schumm,1956:607). 

It is the reciprocal value of drainage density so that 

the higher the drainage density, the lower the constant 

of channel mainten~~ce. 

Alton's first order average constant of channel 

maintenance is 0.065, but 50 per cent of the basins 

are between 0.011 and 0.039. Correspondingly, 45 per 

cent of Bolton's first order basins fall within this 

range. Of the second order basins, 39 per cent of 

Alton basins have a constant of channel maintenance 

between 0.011 and 0.029 and 41 per cent of Bolton'~ 

are within this range. For both the orders, the 



Table 8 Constant Of Channel Maintenance 
(Mi 2/Mi) 

ORDER ALTON CREEK BOLTON CREEK 

First 0.065 0.056 
Second 0.070 0.108 

Third 0.089 o. 116 

Fourth 0.076 0.074 

highest frequencies occur in the class from 0.021 to 

0.029. This indicates that a greater proportion of 

29 

the basins have a constant of channel maintenance that 

is well below the average value obtained for each order. 

These basins are normally basins which are of smaller 

area or basins which are formed on valley side slopes 

of higher order channels at the lower reaches of the 

streams. The high average values (Table 8) are the re~ 

sult of the presence of basins of very poor drainage 

which are normally situated on the large interfluve 

plateau at the headwater areas (Plate 2). 

III.7 Basin Shapes The shape of basins is relatively 

more stable than other variables. 

Miller (1953,cited in Gray,1961:1220) had suggested that 

the stability could be an expression of universal equi-

librium basin form. 

Two indices, the elongation ratio and roundness 

number, are used to investigate the shapes of the 



Plate 2 

" 

Basins of very poor drainage are 
normally observed at headwater areas 
of both creeks. The channels of these 
basins are not well defined and valley 
side slopes merge gently with the terrace 
surface without obvious break of slope. 
The rushes in this particular basin also 
signify the lack of effective drainage. 



30 

Aokautere basins. The elongation ratio is derived by 

the method described by Schumm (1956:612) which can be 

stated as R
8 

= ~-D~- where Re is thi?. e! •·rigation 

11u 
ratio, D the diameter of a circle with area equal to 

the basin, and Lm is the maximum length of the drainage 

basin parallel to the principal drainage line. 

The roundness number is the ratio between the area 

of the drainage basin and the area of circle whose 

diameter is the Lm used in the elongation ratio. It 

can be stated as N = r 
A , where Nr is the 

roundness number, A the area of drainage basin, and Am 

is the area of a circle whose diam~ter is the maximum 

length of the basin parallel to the principal drainage 

line. 

Both indices describe the shapes of basins in 

terms of the closeness of the actual shape to a circle. 

The nearer the basin shape is to a circle, the greater 

the index becomes. The theoretical maximum value is 

unity. But in reality, no basin shape can achieve unity. 

While Schumm'$ elongation ratio is a ratio between the 

length of the idealised circle's diameter to the actual 

maximum length of the basin, the roundness number 

expresses the areal ratio between the idealised circle 

area drawn around the maximum length and the 2.ctua l 

area of the basin. 



31 

Because of the squares involved in the calcula-

tions, the roundness number generally has a lower value 

than the elongation ratio. The use of areal values in 

the roundness number brings out a greater range between 

basins and also results in greater departures from unity. 

Therefore although the roundness number provides impres-

sive visual distinctions, the values it generates are 

too often over-emphasised. However, the roundness 

number is useful in describing basins with identical 

linear shapes but different areal irregularities. 

Table 9 Elongation Ratio 

ORDER AJ.iTON CREEK BOLTON CREEK 

First 0.476 0.459 
Second 0.609 0.510 
Third 0.651 0.449 
Fourth 0.344 0.326 

Table 9 shows the average elongation ratios of 

all orders of both creeks, and Figure 18 illustrates 

the frequency distributions of first and second order 

basin shapes of both creeks. There is an obvious 

increase of ratio from the first to second order basins, 

but in general, there is no definite association between 

the shape and order of basins. The average ratios, 

except the second and third order basins of Alton Creek, 

are relatively low(?) illustrating the elongated shape 



45 

40 

35 

JO 

~ 25 
Q) 

u 

... ., 
20 

ll. 15 

10 

5 

Fig.18 Frequency-Distribution Histograms Of Elongation Ratio 

-- First Order· ----- Second Order 

r-----, 

(a) Alton Creek 

'----, r---, 
I : I I 
I I I ,-------- -- -..... L---~ ----, 

I I 
I I 
I I 

I 

0 -----------''--------------------.....r.---...a...---&--.....L.-----' 
0 .,, 
<:< 
a ,. 
0 
<:< 
0 

25 

20 

... 
c: ., 15 
u 
... 10 ., 
ll. 

5 

0 
8 
M 
6 
I 

;;:; .... 
6 

8 0 .,, 
M M 

0 6 
I I 
;;; g 
<:< 
0 6 

8 0 8 0 .,, .,, ... ... .,, 
II) 

6 6 6 0 
I I I I ;;; 0 ;;:; 0 

M ... ... .,, 
6 cb 6 6 

Elongation 

X1•0·-4S9_ 
X2aO ·S10 

r---i r---, 
I : I 
I 1 I 
I I ---+, --.,; -_J 
I 
I 
I 

,..---J 
I 
I 
I 
I 

&:li:.::ir.- - ~ - ~ 

0 .,, 
M 
6 

8 0 8 0 0 .,, .,, 0 ... 1' 
.,, .,, '<> 

6 0 6 6 6 
I 

0 
M 
0 

! I .!. I ! .,, 0 .,, 0 .,, 
M ... ... .,, .,, 
6 6 6 6 6 

Elongation Ratio 

8 0 ~ 
0 

~ 
0 .,, .,, 

'<> '<> ..... :g 
0 6 6 6 0 6 
I I I I I I ;;:; 0 ;;:; 5 ~ 0 
"'.' 'Q '<> ~ ., 
0 0 6 0 6 6 

Ratio 

(b) Bolton Creek 

----, 
I 
I 

0 8 0 .,, IQ 
'<> ..... 
6 6 6 
I ,!. I 

0 .,, 0 
'<> '<> ..... 
0 6 6 



32 

of the basins. The histograms show that the overlapp­

ing between first and s econd order ratios are great, 

covering almost the total range. This reflects the 

lack of distinction between shape and order associat ion. 

The first order Alton basins are close to ~ · ~mal while 

those 'of the corresponding order of Bolton Creek are 

skewed sligijtly to the right. However, the similar 

pattern of distributions of the elongation ratio groups 

and average values show that the shape of the first 

order basins Qf both creeks are very similar. Those 

of the second order basins are not so ~imilar. While 

Bolton's second order basin shape increases slightly 

from the first order shapes, Alton's second order ratio 

rises considerably 1 resulting in a high frequency in 

the 0.601 to o.650 class while other low frequencies 

spread over a wide range. 

III.8 Summary The relationships between stream num­

ber, length and area , although depart­

ing from the morphometric laws, show trends similar to 

those described in these laws. Given adequate time 

for development, the relationships should fit the 

criteria prescribed in the laws. 

Frequency distributions of length and area show 

that there are large overlaps between first and second 

order basins reflecting the lack of length and area 

identifications in basins of these two orders. 



The correlations between lengths and areas are 

positive but not very high. There are two extreme 

33 

types of basin. Firstly there are basins with re­

latively long channels for the size of the basins and 

secondly there are basins of large areas wi th relatively 

short channels. This has resulted in the characteris-

tics shown in the drainage density, constant of channel 

maintenance and the shapes of basins. 

NOTES 

(1) The field measurements were obtained during June, 

October and November. Discharge was estimated by 

the equation Q =AV (Morisawa,1968:21), where 

Q is discharge in cubic feet per second, A is 

cross-sectional area of the channel, and V is 

mean velocity. Mean velocity was estimated by 

disposing matchsticks on stream water, and the 

time taken for the first matchstick to travel 10 

feet downstream along the channel was recorded. 

Each process was repeated three times and the 

average speed obtained was the estimated stream 

velocity of the section. 

(2) The Law of Stream Numbers can be expressed as 

N = Rb (u-x) , in which N is the number of 
x w x 



34 

:::tream of the o:Lde::- x, u is the trunk order, and 

Rbw is the weighted mean bifurcation ratio. 

(3) Weighted mean bifurcation ratio (Rbw) was obtained 

by Schumm's method (1956:603) where each rank of 

bifurcation ratio is multiplied by the total 

number of streams of the two or ders involved, and 

the sum of these multiplications divided by the 

total number of streams involved in the multipli-

cation. 

(4) Accumulated length was first suggested by Br~ 0coe 

(1959) to substitute segment length. Under this 

definition, a second order length, for example, 

includes not only the second order segment, but 

also the lengths of all first order channels that 

have joined to form the second order basin. 

(5) The Law of Stream Lengths can be expressed as 

in which Lx is the average length 

of streams of order x, L1 is the average length of 

first order channel, and R1w is the weighted mean 

stream length ratio. Stream length ratio (R1 ) 

= and method of deriving weighted 
tx - 1 

mean stream length ratio is similar to that of 

obtaining weighted mean bifurcation ratio. 

(6) The Law of Basin Areas can be expressed as 

Ax= I 1Raw(x-1) , in which Ax is the average 



35 

area of basins of order x, I 1 is the average area 

of first order basins, and Raw is the weighted 

mean basin area ratio. Basin area ratio (Ra) = 

Ax and method of deriving weighted 

I - 1 x 

mean baGin area ratio is similar to that of ob-

taining weighted mean bifurcation ratio. 

(7) Comparisons of basin shapes of several areas were 

given in Schumm,S.A.,1956:612 where ratios of 

over 0.6 are common. 



CHAPTER IV BASIN CHARACTERISTICS - RELIEF 

IV.1 Drainage Basin Relief Cotton (1949: 149) des -

cribed the vital charac-

teristi cs of mature relief as sharp and uneven crestlines 

formed by the intersection of steep valley side slopes . 

However, the stages of landform and channel evolution, 

though. parallel, are never quite co-existent (C ott on, 

1941:55). In his works of the late fifties and early 

sixties, Cotton (1958,1962,1963) used the term "feral 

relief" for the finely dissected landforms of New Zealand 

particularly common on the greywacke r anges of the North 

Island. Most of the works were on the origin of feral 

relief rather than on quantitative description. How-

ever, an estimate of drainage density was given as around 

100 for the feral relief of Wellington Peninsular (C otton, 

1958:199). 

Selby (1967) studied the relief of the greywacke 

ranges in the south Auckland area and compared its 

geometry with that of Dartmoor and Unaka drainage basins( 1 ), 

He concluded that New Zealand has a finer texture and 

the morphometric properties do generally conform to the 

existing laws (1967: .41) . However, the maps which Selby's 

study was based on were one inch to one mile maps and his 

fourth order channels were obviously not the highest 

order in the system. There fore the values he obtained 



from his study area cannot be validly compared with 

those of the present study . 

37 

Not all parts of New Zea l and are finely dissected . 

In t he southwestern Manawatu area where geology is 

similar t o the Aokautere area, Oliver (1948) found that 

river basins have broad and flat interfluves and box 

shaped river valley with c~eep valley side slopes. The 

streams are small and valleys are large in the lower 

courses while towards the headwater a r ea valley side 

slopes are replaced by amphitheatre valley hr;ads. 

The relief of the Aokautere area i s closer in 

similarity to the type described by Oliver than to the 

11 f eral relief" common in many parts of the country. There 

are two possible reasons for this . First, much of Cotton 1
: 

" feral r elief;' with serrate characteristics refer. s 

to landforms in the stage of maturity or sub-maturi ty 

where dissecti on has ta~en place ove r a considerable 

period of t ime, while forms of the study area suggest a 

younger stage of development from t hose described by 

Cotton. Second, a great number of landfor ms studi ed by 

Cotton are found in the greywacke regions where geology 

is entirely different from the l oess and mari ne sand­

stones of the Aokautere area. Therefor e while the cli­

matic r eg imes that affected the North I sland as a whole 

may be similar , the len~t~s of time available for ero­

sion and the materials on which the drainage systems are 

developed are very different for 11 feral relief" and 

Aokautere relief . 



38 

IV.2 Erosional Surfaces Most of the surfaces of the 

study area are under good 

pasture. Only a small percentage of the total area is 

under scrub and secondary trees, and bare ground is 

negligible. The surfaces can be gen erally considered 

as free from a dense cover of vegetation and are uni­

formly exposed. The top three to four inches of surface 

soil on the marine terrace c omprises a black humus­

enriched layer underlain by yellow brown subsoil derived 

from loess. Lower level surfaces have mixtures of loess 

and recent alluvium. Grcywacke pebbles derived from the 

terrace conglomerates are commonly found on inclined 

surfaces and valley floors. 

All surfaces of the study area are erosional sur­

faces, including the miniature flood plains developed in 

the highest order valleys. Fi eld observations suggest 

that colluvium derived from valley side slopes, rather 

than stream alluvium 1 is dominant in the formation of 

the miniature floodplains. The colluvium transported 

onto the valley floors as a result of mass movement and 

slope failure is normally not entirely washed away un­

less there is a prolonged period of flood water. How­

ever 9 the colluvium is norma lly smoothed by flood water 

before the establishment of grass. Some debris has had 

grass developed on it before being smoothed by flood -

water and this has resulted in bumps which form irregu­

lar debris deposits along the valley floors. 



39 

The interfluve hills of the area are broad and 

flat, resembling the original surfaces of the marine 

terrace. However, such features were described by 

Horton (1945:361) . as "residual hills'' because they are 

in fact remnan ts of original surfaces. The orig inal 

surfaces have been removed throug~ overland flow and 

surface wash. 

Between t h e valley floors an d the flat-~op~ed 

interfluves the valley side slope s are domina ted by 

mass movement features, predominantly t err ace ttes. 

Terracettes are most common in middle an d lower reaches • 
of the main valley (Plate 3), but a re als o f ound in 

large lower order valleys. Minor slumps are normally 

ass ociated with the terracettes. In a few ~ac alit ies 

where slopes are steep, scree creep is present where 

conglomerates are exposed. 

IV.3 T-0tal Relief The net elevation between t he 

lowest and highest points of a 

basin Ls an important factor in considering the 

erosional power within a basin. The greater the ele­

vation range, the greater the potential energy, and the 

conversion to kinetic energy of streamflow results in 

the development of more complicated landforms( 2 ). 

Table 10 shows the average total reli e f of all 

orders of Alton and Bolton Creeks. The variable is 

measured i n f ee t and is rounded to the n~arest half foot. 



Plate 3 The mi ddJ ~ reach b.J of .hl toll Oreek. 
Mass movement features dominate the 
valley side slopes whose breaks with 

the flat topped interfluve hills are 

obvious. In the background is the 

Tararua Range . 



40 

Table 10 Average Total Relief (Feet) 

ORDER ALTON CREEK BOL'.I:·ON CREEK 

First 74.5 76.5 
Second 95.0 110 . 5 
Third 108.5 190 .5 
:B~ourth 274.0 316.0 

The mean total reli ef of both creeks is very similar 

for first order basins, but it varies with i ncreasing 

order. Alton Creek has ~ generally lo~ar total relief 

than Bolton Creek, especially in the third and fourth 

order basins . 

A log-linear relati_onship normally exists between 

average total relief and order. The derived morphometric 

law states that the average total relief of basins of 

each order forms a d2-rect gr:>om8 t:d.c AP,ries in which the 

first term is the average total relief of the first order 

basin and the ratio is the total relief ratio (Mor isawa , 

1962:1035). The relationship is plotted in Figure 19 

and a regression line is eye-fitted to each group of 

data. A good fit is achieved in Bolton Creek while in 

Alton Creek residuals are larger. The slopes of the 

regression lines are approximate1y equal. 

_±:_v.4___E!3lief Ratio ScL ~::r.m (1 956 : 612 ) devised the re­

lief ratio and defined it as the 

ratio between total relief and longest dimension of the 



Total 

Relief (Feet) 

400 

300 

200 

100 

50 

0 

• 

ALT 0 N BOLTON 

Fig .19 Relation Of Basin Or der And 

Average Total Rel ief 

• 

Basin 
Order 



41 

drainage basin parallel to the principal drainage line. 

It is in fact the result of the combined expression of 

total relief and longest dimension of the drainage 

basin. Table 11 shows the average relief ratio of 

Alton and Bolton Creeks. 

Table 11 Relief Ratio 

ORDER ALTON CREEK B~T@ CREEK 

First 0.198 0.229 

Second 0.172 0.209 

Third 0.054 0.045 

Fourth 0 .02 8 0.030 

No valid law has yet been devised for the relief 

ratio; but the main function of the ratio is to enable 

comparison of the relief of basins regardless of diffe­

rences in scale of topography. Figure 20 shows the 

exponential relationship between the relief ratio and 

order of the two creeks, with relief ratio on the log 

scale and order on the linear scale. The regression 

lines are eye-fitted and both creeks display considerable 

similarity in the relationships of relief ratio among the 

orders . 

Despite the high residual values for the total 

relief regression for Alton Creek, the regression for 

the relief ratio has much smaller residuals and is very 

similar to that of Bolton Creek. As relief ratio is 



0·2 

0·1 

0 
... 0·05 
ta 
a:: 

.... 
Gl 

0·01 

Fig.20 

• 

Relation Of Basin Order And Relief Ratio 

• 

• 
• 

2 3 4 2 3 4 
0 rd er 

A It on Bolton 



42 

the combined expression of total relief and longest 

dimension of basins, it therefore suggests that the 

longest dimensi on of the basins has been adjusted to 

compensate for the abnormal total rel ief relations to 

present consequently a similar relief ratio regression 

pattern to that of the Bolton Creek. 

The residuals in the average total relief of Alton 

Creek in Figure 19 can be explained by the incision of 

the Tiritea Stream discussed in the previous chapter. 

This incision has not only reduced the area and shortened 

the lengths of the tributaries at the headwater of Alton 

Creek, but has also eroded away a great part of the 

higher relief at the headwater areas of Alton Creek. 

Therefore the Alton drainage system has not only been 

reduced in terms of space and length, but also of height. 

From this investigation, it can be concluded that the 

interruption of area, length and height is more diffi­

cult to adjust. The internal variables, such as the 

long dimension which is very much the shape of the 

basins, could react more independently to adjust to the 

interruption. 

IV.5 Relation Between Drainage Density And Relief Ratio 

Within homogeneous areas of similar develop­

ment, Schumm (1956:613) found that drainage density is 

a power function of the relief ratio, and, in mature 

basins, a definite positive correlation exists between 



43 

these two variables. A correlation and regression 

analysis is worked on the fiTst and second order basins 

of Alton and Bolton ireeks and it is concluded that this 

statement is applicable. Due t o the few numbers of 

basins, third and fourth orders are not studied. 

The power form relationships between drainage 

density and relief ratio of first and second order 

basins of both creeks are shown in Figures 21 to 24. 

The correlation coefficients obtained are h i gh. The 

first order correlation coefficient of Alton Creek i~ 

0.87 and that of Bolton Creek is 0 . 65 . The Alton se­

cond order correlation coefficient is 0 .90 and Bolton's 

is 0.93, 

Tables 12 and 13 show the observed and expected 

values of drainage density and length of overland flow, 

and the observed values of relief ratio. The expected 

values are obtained from the T :~gressions in Figures 21 

to 24, holding the observed relief ratio constant. The 

results show that both drainage density and length of 

overland flow at present are very different from the 

expected values. The observed drainage densities are 

l ow for the observed relief ratio, while the length of 

overland flow should reduce to a shorter length. It is 

deduced that the development of the drainage basins in 

the near future would be not so much of t h e lowering of 

the local relief as the increase of drainage density 

and decrease of the length of overland flow. The relief 



200 

100 

50 

> .. 
Cll 
c: 
Cl) 

0 

Cl) 

Cl 
ca 
c: 10 
ca ... 
0 

5 

§ 

Fig.21 Relation Of Drainage Density To Relief Ratio 

in 
0 

8 

Alton Creek, First Order 

'\o~ 

-0 
6 

~~ 

cf' co 
,q 

Relief 

I( 

;.. 
'\o~ 

bq'\. 
c/t> 

Ratio 

in 
0 
6 

·. 

. · . / 
... 

/ / . . 
// .. ·. 

/.
/ ( 

. . .. 

6 

·. 

in 

6 
0 
..:. 



200 

100 

50 

> ... 
Ill 
c: 
Cl) 

c 

Cll f DI 
«I 
c: 10 
«I ... 
c 

5 

0 
0 
6 

Fig. 22 Relation Of Drainage Density To Relief Ratio 

Alton Creek. Second Order 

a 
0 
0 

0 
6 

. ,o'o+/ 
~ cqj 

"' JC / 
!), , 

~<--, 
ri; 'V 

~* 
,c~ 

a 
0 0 

Relief Ratio 

/ 
/ 

W'l 

0 



200 

100 

50 

> ... ·-Ill 
c 
Q) 

0 

Q) 
D> 
al 
c 
l'C 

10 
.... 
0 

5 

6 
0 
6 

Fig.23 Relation Of Drainage Density To Relief Ratio 

Bolton Creek. First Order 

/ 

/ ... 

...., 
0 
0 
6 

~~ 
,oq, 

0 
6 

':'l .. 
~'b 

~o 

"""' ,oQ,, / 
~"'" / 

o·q 

I(') 

0 

0 

Relief Ratio 

/ 
/ · 

.. 
·. 

0 

.. 

I(') 

0 



200 

100 

50 

> ... 
en 
c: 
II> 
0 

II> 
Cl 
IV 10 c: 
IV ... 
0 

s 

5 
0 

0 

Fig. 24 Relation Of Drainage Density To Relief Ratio 

Bolton Creek, Second Order 

a 5 
0 0 
0 

+ 
,c~. 

co' /. 
~ 

-..:' 

* ~ 
,c~ 

'),­
'o'o 

'V'Y 

Relief · Ratio 

II') 
0 

0 
6 

II') 

0 



Table 12 

1st 

Relief Ratio 

Observed Average Values Of 
Relief Ratio, Drainage Density 
A~d Length Of Overland Flow 

Alton Creek Bolton 
Order 2nd Order 1st Order 

0.198 0.172 0.229 

44 

Creek 
2nd Oro 

o. ~ 

Drainage Density 15.3 14.2 12.5 9.2 
Length of Over-
land Flow (Mile) 

Table 13 

1st 

Drainage Density 
Length of Over-
l and Flow (Mile) 

0.033 0.035 0.040 o. 051, 

Expected Average Values Of Drainage 
Density Ahd Length Of Overland Flow 
Derived From The Observed Relief Rat: 

Al tori Creek Bolton Creek 

Order 2nd Order 1st. Order 2nd O:.·l 

23.5 26.3 28. 6 29. 1 

0.021 0.019 0.017 o.c 

ratio will remain unchanged until the drainage density 

has reached the expected values, which could be achieve~ 

through the development of higher bifurcations or in-

crease of channels, reducing the length of overland 

flow and eliminating surfa ce wash and inter-basin areas. 



45 

I V. 6 Channel Gra dient 

* Table 14 Average Channel Gradient 

ORDER ALTON CREEK BOLTON CREBK 

First 17 . 0 18 . 5 
Second 11. 5 15. 0 
Third 2.5 2.0 
Fourth 1 . 5 1. 5 

* To the nearest half degree 

Morisawa (1 962 :1 044) observed t hat the rel ation-

ships between both relief ratio and s t ream gradient and 

order were not suitably expressed by Horton ' s Law of 

Stream Gradients(3). However , she noted that stream 

gra dient, like relief ratio , decre ases cons i stently with 

increasing order. Study fr om the rel i ef ratio and stream 

gradient of the first and second order basins of Alton 

and Bolton Creeks confirmed Morisawa ' s statement. Fi-

gure 25 shows the plot of average channel gradient 

against orde r on a l i near- log scal e which i llustrates 

similar relationships as exist between the relief ratio 

and order in Figure 20 . 

Figures 26(a) and (b) show the frequency distribu-

tion histograms of the channel gradient of first and 

second or der b~sins of both creeks . The first order 

basins of both creeks show slight left skewnes s wi th 

high frequencies occurring at higher gradients. The 



Fig. 25 Relation Of Basin Order And Channel Gradient 

30 

20 

10 ... 
c: 
4) 

"'Cl 
cu 
I.. 

(.!) 5 

4) 

c: 
c: 
cu 

.J:. 
u 

1 
1 2 3 4 1 2 3 4 

0 rd er 

Al ton Bo It on 



25 

... 
~ 20 
u 
... 
Q) 

Q. 

... 
c: 
G> 
u 

... 
Q) 
Q. 

1 5 

10 

5 

0 

30 

2 5 

20 

1 5 

1 0 

5 

0 

Fig.26 Frequency Distribution Histograms Of Channel Gradient 

~---- .. 
I I 
I I 
I 
I. I 

I... - -- , 
I 

----~ 
I ., 
I 

~ 
It') N 

I I 
It') ... 

It') 

..:. 
I 
":' 
It') 

--- .... 
I 

• . . 
I 

~---

":' It') 
It') " N 

I I I .,., ... ~ 
6 It') 

--- First Order 

It') 

0 r. 
I I 

Cll ~ 
0 

0 It') 

.; 
"j 

Cll It') 

6 

. 

x1= 17· 0 
,----, 

I 
I 
I . . 

'------' 

It') 

I ... 

It') 

I ... 

It') 

r:.. 
I 

":' 
It') 

. r-- _.,. 

It') 

r:.. 
I 
It') 

.;, 

------ Second Order 

---, 

I 

'-----1 
• 

It') 

0 ,:., 
N N 
I I 

Cll It') 

6 
N 

Channel 

x1= 1s-s 

• --- -. 

0 ":' 
N N N 

I I 
Cll It') 

6 
N 

Channel 

It') 
It') r:.. 
N N 
I I ... ~ N 

It') 
N 

Gradient 

It') 

N 
I ... 

N 

,.. ---
I 
I 

It') 

r:.. 
N 

.I 
~ 
N 

Gradient 

(a) Alton Creek 

0 ... 
I 

Cll 
N 

(b) Bolton Creek 

0 
It') 

"" ... ... 
I I 

Cll It') 

N 6 ... 



46 

second order basins show considerable increases of fre­

quencies in lower gradients, but the modes are above 

the mean values. In the Alton second order distribu­

tions, the histogram shows a tendency towards the de­

velopment of a bimodal distribution with a mode at the 

15 . 5 to 17.5 class and the other developing at the 3 

to 5 class. The large overlap between the first and 

second order distributions indica tes that although the 

mean gradient show the difference between first and 

second order gradients, the overlapping is so broad 

that a marked distinction is difficult to distinguish. 

Stream gradient of channels that were developed on 

the terrace surfaces is lower than those developed on 

valley s ide slopes of the main streams. Most of the 

first and s econd orde r channels of the Al ton and Bolton 

Creeks are developed on the valley side slopes of the 

fourth order channelsi resulting in the abrupt break of 

channel gradients fr om the average gradients of the 

third and fourth order channels. This reflects the 

effects of the ground slope on the first and s econd 

order channe l gradients. The dissection of these 

lower order basins has yet to reach the characteristic 

gradient for the geology of the area. 

IV.7 Maximum Slope Angle Strahler (1 950:685) outlined 

the law of constancy of 

slopes which states that within an area of uniform li-

thology, soils, vegetation and climate , and stage of 



47 

development, maximum slope angles tend t o be normally 

distributed with low dispersion about a mean value de· · 

termined by the combined factors of drainage density , 

relief and slope-profile curvature. 

This law is tested on the frequency distributi on s 

of the first and second order basins of both creeks and 

the histograms are shown in Figures 27(a) and (b) . Th~ 

means and modes of both creeks are similar, but the 

standard deviations are considerably different between 

t h e two creeks. The degree of dispersion in both ordc~s 

of Alton Creek are higher than the corresponding ord~ rs 

of Bolton Creek. Distributions in Bolton Creek, espe-· 

cially that of the second order basins, have very low 

dispersi ons approaching very closely to Strahler ' s 

descriptions. 

From Strahler ' s point of view, and since both creeks 

are developed under similar physical conditions, thi s 

variation in the nature of frequency distributions 

suggests the difference i n the stage of development 

between the two creeks. 

IV.8 Hypsometric Integral Hypsometric analysis i s tne 

study of the distribution 

of ground surface area with respect to elevation 

(Strahler,1952:1118). The hypsometric integral, which 

is equivalent to the ratio of area remaining to the 

total original area available for erosion , was obtained 





48 

by the method outlined by Strahler (1952:1120-1121). 

Strahler (1952 :1 130- 1131) envisaged that there 

are two major stages in landform development(4). Ba­

sins with integrals higher than 60 per cent are consi-

dered to be in disequilibrium, while basins with inte-

grals between 35 per cent and 60 per cent are in the 

equilibrium stage. Basins with integrals lower than 

35 per cent are in the monadnock phase where total re-

lief is abnormally large in comparison to the general 

relief features. 

Table 15 Percentage Frequency Distributions of 
Hypsometric Integral Of First And Second 
Order Basins, Alton And Bolton Creeks 

Monadnock Equilibrium Disequilibrium 
Phase Stage Stage 

Basin Order 
0.350 & 0.351- 0 .501- 0 . 601- 0.701- 0 . 801 & 

Below 0 . 500 0 . 600 0 . 700 0 . 800 Above 

First Nil 2.2% 5.6% 31 . 1% 38. 9% 22 . 2% 
ALTON 

Second Nil Nil 11. 1% 16.7% 50 . 0% 22 . 2% 

First Nil 2.8% 18 . 9% 33 . 0% 35 . 8% 9°5% 
BOLTON 

Second Nil 6 . 0% 17 . 6% 17. 6% 29 . 4% 29 . 4% 

This concept of classification is applied to the 

analysis of the hypsometric integrals of the first and 

second orders of Alton and Bolton Creeks, and the per­

centage frequency distributions are shown in Table 15. 



49 

Table 16 Average Hypsometric Integrals 

ORDER ALTON CREEK BOLTON CREEK 

First 0. 7 31 0 . 689 

Second 0.739 0.701 

Third 0.695 0.626 

Fourth o. 649 o. 612 

·----

Of the first order basins 1 92.2 per cent of those 

in Alton Creek and 78.3 per cent of Bolton Creek belong 

to the category of disequilibrium stage. Three sub­

classifications of integrals in disequilibrium stage 

are found to be useful for the description of the study 

area. On the very top of the scale of disequilibrium is 

the above 80 per cent category where most of the sur­

faces in a basin are yet t o be developed into valley 

side slopes . Figure 28(a) shows the common hypsometric 

curves under this category obse rved in the fir£t order 

basins of both creeks. The curves indicate that only 

slight erosion has taken pl ace while most of the land­

mass still remains. The steep lower portion is normally 

caused by the decrease of area at the mouth of the basin 

and by the abrupt break where the lower order basin 

joins a channel of h i gher order 1 which i~ the study area 

could well be a third or fourth orde r stream. 22.2 per 

cent of Alton's f irst order basins belongs to this 

category while the p roportion in Bolton Creek is con -



FIG 2 8. SELE C TED Fl RST-ORDER HYPSOMETRIC CURVES 

ALTON CREEK BOLTON CREEK 

0·9 ···~:.:.:.::.~:.:~:.> •• 
0·8 ···"~-,....,~······ 

0·7 ··-.::·.~---•.• 

0·6 

(c) 0·5 (c) 

0·3 

0 ·2 

O·l 

0 0-+---.--~-~~-~-~-~---,----~~ 

O 0 ·1 0 ·2 0 ·3 0 ·4 0·5 0-6 0·7 0 ·8 0·9 0 

········· ... 

(. b) 

0 -+---~-~-.- - --.---.----,----.---.---r---1 0-4----~-~-~~-~-~---.----,----.----'I 

0 0 

( a ) 

0-+---~-~-~~~~-~---.----,----.---"1 

0 0 



50 

siderably lower . This i s not due to heavy dissection of 

Bolton ' s first order basins but because a great number 

of the basins are developed on valley side slopes of 

higher or der channels; the gener al erosion as related 

to the relief has actually been the re sult of the 

larger higher order channels rather than of the first 

order basins. 

Basins which had 20 to 30 per cent of mass removed 

are more stable than the previ ous cat egory (Fi gure 28b). 

This category contains the highest frequencies of the 

first order basin distributions of both creeks. Altr 

nearly 30 per cent of the total landmass has been re·­

moved , the hypsometric curves display obvious broad in­

terfluve areas with only minor relief features at the 

headwater a reas . However , valley s i de slopes bec ome 

promi nant at this stage of development and the break 

between the se valley side slopes and the flat inter­

fluves is normally marked by format ions of mass movemci1 t 

features (Plate 4) . First order basins of this catego~y 

of i ntegral s are mostly basins that were developed on 

the valley side slopes of higher order channels. 

Of the f i rst order basins, one - third of the total 

of each creek are at the lower interval of the dis­

equilibrium stage where 30 to 40 per cent of the origir 

landmass had been removed. The hypsometric curves shoi, 

a di stinctive r elief where headwater areas had been 

coneideragly eroded and the vert'.i.cal rise at the l ower 



Plate 4 Slope break between the interfluve 

surface and valley side slope. 



end reduced so that a near model S-shape is approached 

(Figure 28c). The landmass removed is normally balance 

at the basin mouth. 

Frequency distributions of second order int egrals 

show a similar range to that of the first order inte­

grals. In Alton Creek, there is a decrease of frequenc~ 

in the 70.1 to 80 per cent group, but slight increases 

in the upper equilibrium and upper disequilibrium cate­

gories. Frequencies in Bolton's equilibrium stage do 

not vary much from the first order integrals but there 

is a slight decrease in lower disequilibrium compensc 

ted for by increases in upper disequilibrium. Figures 

29(a) and (b) show selected hypsometric curves illus­

trating the common forms of curves observed in the se-· 

cond order basins of both creeks. The diagrams show tha~ 

these second order basins also consist of reli ef which i~ 

not extensively dissected, where broad flat int erfluves 

still occupy large proportions of the basins. 

There are only two third order basins in each creek 

Their hypsometric curves are shown in Figure 30. In 

contrast to the first and second order curves, the thi~d 

order curves are appreciably different between Alton and 

Bolton Creeks. The Alton third order basins show a 

remarkable youthful stage of development as compared to 

the third order basins of Bolton Creek where a conside·­

rable amount of landmass bad been eroded. The headwater 

areas of both the basins of Alton Creek are broad and 



h 

H 

0·9 

0-8 

0·7 

0·6 

0·5 

0·4 

0 ·3 

0·2 

0·1 

0 

h 

H 

0 0·1 

0 

Fig.29 Selected Second-Order Hypsometric Curves 

-- .. __ --. 

(a) ALTON 

<<·~> .. ... ..:. . ...... 
"·~~' 
"·' ....... \\ 

" \ 

\ \ 
\. \ 
\ \ 
" \ 
\ \ 
',I 

~ \ 

\ \ 
', I 

"' "' ll 

" "' ': I 

" "' " " 
\\' \~ I 

0·2 0 ·3 0 ·4 0·5 0·6 0 ·7 0·8 0·9 
a 
A 

(bl BOLTON 

a 
A 

CREEK 

h 
H 

0 

CREEK 

h 

H 

·· .. ·· ... 
·· ...... 

-....... . ....... . ---.............. _ ··· .. ..... . 
----------~~·~<:-. 

:-~~::·:> 
\ \ 
"·\\ 

\I 
~· 

a 
A 

1-,...,--~~~~~~~~~~~~~~~~~~~---, 

··· ... 

· .... 
"· .. 

0 

· .... 
··· ...... 

······ .... 
·,, 

·· .... 
......... · ..... 

... ---......... . ... --. 

1 !. 
A 



Fig.30 Third - Order Hypsometric Curves 

lt 
H 

0·9 

0-8 

0·7 

0·6 

0 ·5 

0·4 

0·3 

0·2 

0·1 

.... ........... ................ .. _ 
-- ........................ -.. ....... 

Alton 

.... ........... .o.> 
',l<S ...... 

...... , 
', 

',,, 
... , 

' ·'" 

0-+----.r------r-----..---------r--r----ir----1 

0 0· 1 0·2 0·3 0·4 0·5 0·6 0·7 0·8 0·9 
a 
A 

h 
H' 

0·9 

0 ·8 

0 ·7 

0 ·6 

0 ·5 

0 ·4 

0 ·3 

0·2 

0 ·1 

, ... , 

Bolton 

-... .... ... 
..... ............ 

' .............. _ 
..... ...................... _ 

.......... - ............. ..0...:.~62 

0 ------.--"""?----------------.----
0 0 ·1 0·2 0·3 0·4 0·5 0·6 0 ·7 0·8 0·9 1 

a -A 



52 

free of erosion. On the other hand, both basins of 

Bolton Creek show considerable erosion at the headwater 

areas and shorter vertical distances at the lower ends, 

giving a closer approximation to the s-shaped mo del 

curve. 

The hypsometric integrals of the fourth or to*al 

order of both creeks are at the lower end of the inter­

val of the stage of disequilibrium where more than one 

third of the original landmass had been removed by 

erosion. The curves are very close to the typical S­

shape of the model hypsometric curve (Figure 31). Relief 

exists at the headwater areas of both creeks but in ge­

neral the upper and middle reaches of the basins still 

consist of broad basin areas. The lower reaches near 

the mouths of basins consist of small areas where over 

30 per cent of the altitudes enclose about 10 per cent 

of the total areas. Slight differences between the two 

basins at the middle and upper portions above the one 

third total altitude are observed, but below that alti­

tude both basins display very similar features . No 

obvious geological effect is observed on the curves. 

IV.9 Correlation Of Relief Variables Strahler (1950: 

1136) observed 

that in mature basins, the hypsometric integral is nor­

mally negatively correlated with drainage density, total 

relief, stream gradient, and maximum slope. Based upon 

this postulate, an investigation wa s made into the rela­

tionships between hypsometric integral and the above 

mentioned four variables of the first and second order 



Fig. 31 Fourth -Order Hypsometric Curves 

\ 

' \ 
' 0.9 ' 

', "'' ', "o ....... .... ~ 
0.8 

0.7 
' ' ', 

' ' 0.6 0 , ' ' ~,~ ' ' ' h ' 0.5 \ 

H \ 

0.4 

0.3 

0 ·2 

0 ·1 

0 
0 0·1 0·2 0·3 0 ·4 0·5 0·6 01 0·8 0 ·9 

~ 
A 



53 

bas:~~ of both creeks. Th e investigati on, however, shows 

that in the first and sec ond order ba sins of Alton and 

Bolton Creeks, these variables are in many cases only 

weakly correlated and more often than not, the correla­

tion is positive. Table 17 shows the correlation coef­

ficients between hy psometric integral and various va­

riables of each or1er. 

Table 17 Table Of Correlation Coefficient& 

Basin Order Max. Sl. Ch. Sl. T.Re . ])d 

ALTON First 0.18 0.20 0.03 -0.27 
Second 0.39 0.44 0.41 0.03 Hyp.Int . 

BOLTON First 0. 12 0.29 0.02 -0.24 
Second -0. 10 0.58 -0.35 -0.20 

A negative correlation pattern exists in the second 

order basins of Bolton Creek except for channel slopes. 

This general increase of negative correlations from t he 

first order basins to second order basins in Bolton 

Creek, suggests , in Strahler's terms, a higher degree 

of maturity in the second order basins. However, the 

degree of negative correlation is low and so they are 

still to reach full maturity. Basins of other orders 

do not display any obvious pattern of negative corre­

lation between hypsometr~c and t he rest of the varia­

bles. Among ~h..em , patterns of relationships between 



Alton's and Bolton's f irst order basins are similar in­

dicating that the relationships between hypsometric in­

tegral and the rest of the variables occur in the same 

manner in both first order basins . The complication of 

relationships increases with increasing orders. 

The only variable that exists in a negative corre­

lation with hypsometri c integral throughout mo st of the 

first and second order basins is drainage density. It 

is inversely related to the hypsometric integral in 

three of the four groups of data, but is virtually un­

related to the hypsometric integral in Alton's second 

order basins . 

The positive relations between hypsometric inte­

gral and channel slope is noteworthy, especially in the 

second order basins 1 indicating that channel slope not 

only does not increase when hypsometric integral becomes 

lower, as suggested by Strahler, but tends to dec~ · ease 

with decreasing integral. 

The relation between total relief and hypsometric 

integral is low in the first order basins of both creeks. 

However, it becomes more prominant in second order basins 

where it is positive in Alton Creek and negative in Bol­

ton Creek . A similar situation arises for the relation­

ship between maximum slope angle and hypsometric inte­

gral. The positive correlation between these two 

variables in Alton's second order basins is considerably 

~igher than in other cases. 



55 

It can be concluded that among the first order 

basins of the two creeks, the patterns of correlation 

between hypsometric integral and the rest of the varia­

bles are very much the same, and that the relationships 

vary among the second order basins. Bolton Creek re­

sembles very closely Strahler's postulated condition 

while the Alton Creek presents a pattern of relation­

ships remarkably at variance to his description. 

It also suggests that while drainage density ad­

justs readily to changes in the hypsometric integral, 

channel gradient is the slowest among the four variables 

to reach a stable negative relationship. In this case 

study, where a large number of channels are developed 

on valley side slopes of higher order basins, Strahler's 

postulation of the negative trend of development might 

not occur at all. 

IV. 10 Summary Relief features of the study area are 

no where close to Cotton's description 

of "feral relief". The large flat interfluves and gen­

tle slopes are in sharp contrast to the fine texture 

serrate landforms predominant in many parts of the North 

Island. The hypsometric integral, as an index measuring 

the amount of erosion that has taken place, indicates 

that a very high proportion of basins are in the stage 

;;~1ere only a minor poption of the original landmass has 

been removed. Howeve r, the eroded portion increaeee 

with increasing order. 



56 

Relief ratio, which represents the general incli­

nation of a basin, is relatively high for the drainage 

density and length of overland flow. Channel gradient 

and maximum slope angle further demonstr~te this feature 

and emphasises the effect of an antecedent surface slope 

where th e present drainage systems are established. 

Total relief of third and fourth orders of Alt on 

Creek show a marked set back by the stream capture of 

the Tiritea Stream. This, together with the phenomena 

discussed in the previous chapter, demonstrates that 

the loss of length, area, and height is difficult to 

re-adjust. 

The abnormal relationships observed between hypso-~ 

metric integral and total relief, drainage density, 

channel gradient and maximum slope angle reveal the 

unbalanced relationships among these variables. 

NOTES 

(1) Chorley,R.J. and M.A. Mor6an,1962, Comparison of 

morphometric features, Unaka Mountains, Tenessee 

and North Carolina, and Dartmoor, England; 

Geol.Soc.Am.Bull. ,vol.73(1):17-34. 

(2) Leopold,L.B. and W.B. Langbein,1962, The ~oncept 

of entropy in landscape evolution; U.S.Geological 

Survey Professional Paper 500A, 20pp. 



57 

(3) Law of Stream Gradient s (Horton ,1 945: 195 ,cited in 

Morisawa,1962:1034) : The mean channel gradients 

of each order form an inver se geometric seri es 

with order, where the first term i s gr adient of 

the f i rst order segment and the slope of the curve 

is the slope r atio. 

(4) Strahler (1952:1130) : "From the standpoint of 

hypsometric analysis, the development of the dr a i­

nage basin in a normal fluvial cycle seems to 

consist of two major stages only; (i) an in­

equil i brium stage of early development, in which 

slope transformati ons are taking place rapidly as 

the dr ainage system is expanded and ramified, 

(ii) an equilibrium stage in which a stable hyp­

sometric curve is developed and maintained in a 

steady state as relief slowly diminishe~- The 

monadnock phase with abnormally low hypsometric 

integral, when it do es occur, can be regarded as 

transitory , because removal of the monadnock will 

r esult in restoration of the curve to the equili­

brium form ..•...• The hypsometric curve of the 

eguil~ b,.rium sta.J?'e is an expression of the a t tain­

ment of a steady state in the processes of erosion 

and transportation within the fluvial system and 

its contributing slopes . 11 



CHAPTER V CONCLUSIONS 

Thi s study , which has i nvolved only two drainage 

basins, does not claim to have investigated acryects of 

all the drainage systems developed on the Tokomaru 

Terrace . However, it has provi ded some comprehensive 

insight into the forms and features of t he Alton and 

Eolton basins, which could be regarded as a possible 

basis for f uture explanation of t he characteristics of 

the Aokautere dr ainage systems. 

The study of the linear, areal and re l ief charac ­

teristics of t he Alton and Bolton Creek s has pro7en 

that most of the basins of all orders are in the state 

of disequilibrium . However, rapid changes are underw~ 

to achi eve the state of equilibrium by adjustments of 

the internal vari ables. The major factor in causi ng 

this unt~lnnced state is the di fference i n length of 

time available for basin development . Basins of higher 

orders which have had more time available for develop­

ment tend to have achieved char acteristics closer to 

the equilibrium stat e . This has resulted in the exis­

tence of charac t eri stic features of differing ages in 

a single drainage system and so the spatial features of 

diff ering ages in a single drainage system and .. the 

spatial features of different properties are in fact 

the sequence of fac ets of gradual growth of the systems. 



59 

The criteri a of assessing the state of equilibrium 

i n drainage basins were based upon work done overseas 

which obviously was on very di fferent types and sizes 

o.f landforms . Bven the scales of maps used have varied. 

This inevitably has resulted in differences of values of 

a bsolute properties of the systems involved. Therefore 

no absolute comparison of orders has been attempted 

hetwe en the present study area and results of other 

s tu.d.ies. All comparisons have been made on a relative 

ba s is. 

The study has also revealed that detailed morpho-

r;ietric study on very li:irge scale maps may possibly lead 

Lo different types of concl usions from those studies 

A 
largb 

based on small scale maps of extensive areas. ·~ 

s cale study like this has very high chances of discovering 

pf:r::::mnena of minor importance, which may eventually lead 

to inter1retations of different meanings in landform 

Although the small size of the study area has 

prE' cluded the study of l arge scale features of "histo-

rical inheritance", i t has to some extent expressed the 

non - continuous nature of New Zealand landform history 

~ ~d its high tempo of temporal changes a s discussed in 

Chapter II . 

Developments toward equilibrium can also be dis­

rupted by a neighbouring system. Alton Creek, which is 



60 

developed on the same geology and under the same climate 

as Bolton Creek, has remarkably different and more un­

stable morphometric characteristics due to the capture 

of parts of its catchment areas by the neighbouring 

Tiritea Stream. 



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-.- ....