the brahmani basin 11 -...

THE BRAHMANI BASIN

11

BIVARIATE ANALYSIS OF MORPHOMETRIC VARIABLES

• AVERAGE RELIEF AND OTHERS .

• ~ RELATIVE RELIEF AND OTHERS

• DISSECTION INDEX AND .· OTHERS

• AVERAGE SLOPE AND OTHERS

• ROUGHNESS INDEX AND OTHERS

• DRAINAGE DENSITY AND OTHERS

• STREAM FREQUENCY 8 OTHERS

• SUPERIMPOSED REGRESSION LINES

THE BRAHMAN/ BASIN

1 1 BIVARIATE ANALYSIS OF

MORPHOMETRIC VARIABLES

Bivariate relationships such as coefficient of correla-

tion (r), coefficient of determination (R 2 ) and linear,

regr.ession are used to show the nature and degree of relation

ship between two variables. It is noted that in any such study

correlation coefficient (r) can show a range from + 1 to- 1.

When correlation coefficient is+ l,the degree of relationship

between two variables is perfectly positive and when it is -1,

the . degree of correlation is considered to be perfectly nega

tive . When the correl ation coefficient is zero, there is no

relationship between two variables. Thus, higher positive and

negative values infer correspondingly higher positive or nega

tive correlations.

,

TA

BL

E

11

.1

B IV

AR

J A

TE

RE

LA

TIO

NS

HIP

. B

ETW

EEN

A

VER

AG

E R

EL

IEF

AN

D

OTH

ER

MO

RPH

O'M

ET

RIC

V

AR

IAB

LE

S

SL

N

o.

1.

2.

3.

4.

5.

6.

7.

Rela

tio

nsh

ip

betw

een

Av

era

ge R

eli

ef

(X)

&

Rela

tiv

e R

eli

ef

(Y)

Av

era

ge R

eli

ef

(X)

&

Dis

secti

on

In

dex

(Y

)

Av

era

ae R

eli

ef

(X)

&

Drai

n~ge

Den

sit

y

(Y)

Av

erag

e R

eli

ef

(X)

&

Dra

inag

e T

ex

ture

(Y

)

Ave

rag

e R

eli

ef

(X)

&

Str

eam

Fre

qu

en

cy

(Y

)

Av

era

ge R

eli

ef

Av

era

ge s

lop

e

Av

era

ge R

eli

ef

Ro

ug

hn

ess

In

dex

(X)

&

( y)

(X)

&

Co

eff

icie

nt

of

co

rrela

tio

n

( r)

0.9

18

7

0.7

77

4

0.6

80

0

0.0

80

8

0.6

98

3

0.9

24

9

0.9

12

0

Co

eff

icie

nt

of

Dete

rmin

ati

on

R

2 (i

n%

)

84

.39

73

60

.43

71

46

.24

05

o. 6

53

0

48

.76

57

85

.54

70

83

.17

49

Lin

ear

Reg

ressio

n

Eq

uati

on

(Y

=

a

+

bX

)

-1

7.2

95

88

1

+

0.4

56

06

5

X

0.0

74

09

0 +

0

.00

10

99

X

O. 6

97

87

6 +

0

. 00

54

30

X

.

0.9

98

61

1

+

0.0

00

36

1

X

1.0

52

38

4 +

0

.01

69

10

X

0.9

88

15

5 +

0

.03

26

30

X

-... 1

.49

61

65

+

0.0

47

27

5

X

...,_

...

w

CD ~

[ MA TR/X OF CORRELA T/ON CO-EFFIC/ENTi_]

l I

A.R. R.R. D. I. R.I. A.S. S . F . D. D. D. T.

A. R . ·9181 ·7774 ·9120 ·9249 ·6983 ·6800 ·0808

R. R. ·8942 ·9764 ·9890 ·6303 -5954 ·0229 q

D. I. ·8994 ·9134 ·6961 -6449 -·0761 I

j R . I. I -9853 -6563 '. 6133 -0156

A.S. ·6904 ·6514 -0387

S. F -9545 - ·1415

D. D. I -·1897

D .T -- .~ --

A .R . Average Relief A.S Average Slope

R.R. Relative Relief S.F Stream Frequency

D./ . Dissection Index D.O. Drainage Density

R . I. Roughness Index D.T. Drainage Texture

FIG . 11.1

RELATIVE RELIEF & OTHERS 386

to other morphometric variables except drainage texture. The

high average relief areas are concurred by low drainage den-

sity, although there are some small patches where the areas

have higher zones of density. The high average relief zones

are mainly confined to the upper middle parts of the Basin

where dense forests protec t the surface from rain drops and

a ccount for the drainage density of l ow value.

The average relie f and drainage texture actually show

no re l ationship ( r = 0.0808 ). ! I

The morphometric variables like average slope, rough-

ness index, dissection index ,strea m frequency are positively

correlated with average relief a nd degree of correlation is

very high.

11. 2. RELATIONSHIP BE'I't-'IEEN RELATIVE RELIEF & OTHER VARIABLES

Like average relief with others

shows high positive correlation with

relative relief also I

other . ~

morphometric

variables except drainage texture (Fig. 11.1). Table (11.2)

gives a vivid picture how the rel a tive relief is related to

other morphometric v a riables.

Correlation coeffic ient can be kept into two distinct

groups according to their nature : (a) variables showing

strong correlations and (b) variables which are weakly

TA

BL

E

11.2

BIV

AR

IAT

E

REL

AT

ION

SH

IP

BET

WEE

N

REL

AT

IVE

R

EL

IEF

A

ND

O

THER

M

OR

PHO

MET

RIC

VA

RIA

BL

ES

Sl.

N

o.

1.

2.

3.

4.

5.

6.

t I

t t

: Co

eff

icie

nt

of

: C

oeff

icie

nt

of

: R

ela

tio

nsh

ip

betw

een

C

orr

ela

tio

n.

: D

ete

rmin

ati

on

. ( r)

:

R 2

( in

%

) I

I

Rela

tiv

e R

eli

ef

(X)

&

0.8

94

2

79

.95

75

D

issecti

on

Ind

ex

(Y

)

Rela

ti

ve R

eli

ef

(X)

&

0.9

76

4

95

.3

35

4

Ro

ug

hn

ess

In

dex

( y)

Rela

tiv

e R

eli

ef

(X)

&

0.9

89

0

97

.81

25

A

vera

ge S

lop

e

(Y)

Rela

tiv

e R

eli

ef

(X)

&

0.6

303

3

9.7

27

8

Str

eam

F

req

ue

nc

y (Y

)

Rela

tiv

e R

eli

ef

(X)

&

o. 5

95

4

35

.45

01

D

rain

ag

e

Den

sity

(Y

)

Rela

tiv

e

Rel

ief

(X)

&

0.0

22

9

0.0

52

4 D

rain

ag

e T

ex

ture

(Y

)

Lin

ear

Reg

ress

ion

E

qu

ati

on

. (Y

=

a

+

bX

)

0.1

10

99

2

+

0.0

02

54

6

X

0.

35

58

15

+

0

.10

19

50

X

0.2

92

99

7

+

0.0

70

28

0

X

1.9

15

23

7 +

0

.0

30

74

3

X

0.9

85

24

8

+

0.

03

07

43

X

1.0

327

78

+

0

.00

02

07

X

c

w

(J)

-....J

[MATRIX OF CO-EFFICIENT OF DETERMINATIONS I - -

A.R . R. R. . D. I. R.I. A.S. S . F. D.O . D. T.

I I A . R . 84·94 80·44 83·17 85·55 48·77 46·24 ·6530

R. R. 79·96 95·34 97·81 39·73 35·45 ·0524

D. /. 80·89 83·43 48·46 q41·59 ·5791

R.I. I I 97·09 43·07 37-61 ·0243 i

I I I

A.S . 47-66 42-43 ·1499

S . F . 91· 12 2·003

D. O. I 3·599

D. T. -- -

A.R . Average Relief A .S. Average Slope

R.R. Relative Relief S. F. Stream Frequency

0 . 1. Dissection Index D.O. Drainage Density

R . I . Roughness Index D.T. Drainage Texture

F IG. 11.2

RELAT I VE RELIE F & OTHERS 38 8

correl a ted.

Of t hese var iabl es r o ughness i ndex, average slope and

dissection index are highly correlated with relative relief.

This type o f correla t i ons i s accepted as all of them are ~

rel ief properties. On the o ther hand drainage properties

such as dra inage densi t y , d r a inage texture . a nd stream fre-

~uency show a weak pesitive cor rel a t i ons with r e lative relief .

The weakest among these correlations is that - between relative

relie f a nd drainage t exture , the r value being + 0.0229

(Fig. 11 .1 ) . I n cas e o f drainage density and stream frequency,

the r val ues are+ 0 .5954 a nd+ 0.6303 respectively.

11 . 2 .1 . THE RELATIVE REL IEF AND DISSECTION INDEX

These variabl es show h igh positive correlation. The

high relative relief zones a r e occupi ed by high dissection

areas. The 79 . 96% v a r iati o n i n dissection index is explained

alone by r elative r el i e f (Fig. 11.2).The two maps of relative

rel ie f and dissec t i on index s how close relationship both

visua lly a nd statis tically .

11 . 2.2 . THE RELATIVE REL IE F AND ROUGHNESS INDEX

These a r e also h ighly correlated. The degree of

co r r e latio n is revea led by r value whi ch is 0 . 9764 . The


roughness of the Brahmani Basin is controlled by relative

relief by 95.34%. The regression coefficient (b) of the ana-

lysis shows that \vith increase in relative relief the rough-

ness v alues do increase.

11.2. 3. THE RELATIVE REL I EF AND AVERAGE SLOPE

Slope is the i nherent property of landscape.It is the

major parameter which a c t ual ly controls the landscape fea-

ture~ . The a verage slope shows a highest correlation of

0 . 98~0 with relative rel i e f in the Brahmani Basin (Fig. 11.1).

The coefficien t o f detGrmina tion reveals that relative relief

causes t he v a r iation of 97 . 8 1% in average slope (Fig. 11.2).

The regression coef fici e nt b shows very significant increase

in average slope with i ncrease in relative relief.

11.2 .4. THE RELATIVE REL I EF AND STREAM FREQUENCY

The relative relief and stream frequency maps show

tha t appa rently high relative relief zones are . covered by

high stream f r equency. Though high stream frequency values

f all in the high relative relief zones, these values lie at

the periphery of the h igh relative relief boundary.The proba-

b l e cause is the existence of ephemeral rills which develop

on the high relative relief zones and integrate into streams

at the base of these slopes. The correlation between them is


however weak ( 0 .6 303) and relative relief does contribute

only 39.73% in the variation of stream frequency (Fig. 11.1

& 11.2). So, we are to incorporate other factors for the

analys is of the stream frequency in the Brahmani Basin like

lithology, soil, slope and vegetation cover, etc.

11.2 . 5 . THE RELATIVE RELIEF AND DRAINAGE DENSITY

The relative relief and drainage density maps in gene-

ral show a relationship, which is expressed by r value of

0.5954 (Fig. 11.1). It is observed that high relative relief

areas are not always foll owed by high drainage density zones.

For this reason the coefficient of determination has been ~

implied to identify the percentage contribution of relative

relief on the variation of drainage density in the Brahmani

Basin . The relative relief does alone only cause 35.45%

variation in drainage density (Fig . 11.2). The regression

coefficient b does show positive increase, but it does not

necessarily imply a significant one for the drainage density.

11.2.6 . THE RELATIVE RELIEF AND DRAINAGE TEXTURE

The relative relief and drainage texture maps show a

correspondence in some cases and in rrost cases they do not.

This is evident from the r value which is ve~ry weak(0.0229}.

so, the contribution of relative relief on the variation of

DI SSECTION INDEX & OTHERS ~92 •'

drainage texture is onli 0.05%. The drainage texture, there-

fore , doe s not depend on relative relief as revealed from the

analys is of r, R2 and b .

11 . 3 . RELATI ONSHIP BETWEEN DISSECTION INDEX & OTHER VARIABLES

The dissection ind ex is also considered as an indepen-

dent v ariable likel y t o h a ve a fair degree of cor relation with

other v ariables. The c orrel a tion coefficient, coefficient of

determina t i on a nd regress ion have been calculated from the

da ta extracted from topographical sheet (1:50,000) of the

Brahmani Basin a nd are tabulated (Table 11.3).

It is v is ua lized f rom the table that dissection index

i s stro ngly corre l a~ed with relief properties,~·· average

slope (+ 0 . 9134) a nd r oughness index (+ 0.8994).There exists

s t r ong positive corr el a tion between dissection index and

average slope and dissection index and rou9hness index. This

is because relativ e re l ie f is a common element for dissection

index , a verage s lope an d r oughness index. Again if the ampli-

tude of relie f tends to i nc r ease with a consta nt distance the

values o f aver age slope a nd roughness ind ex wil l a lso increase. I

Thus lt may be i nfe rred t hat all these v a r iabl e s a re closely

linked up with each o ther i n a concealed t ie of relative

relief . So i t is commonly found that i n t h e highly dissected

parts o f the Basin, a ll t hese variab les are higher.

' I '------

TA

BL

E

11

.3

BIV

AR

IAT

E

RE

LA

TIO

NS

HIP

B

ETW

EEN

D

ISS

EC

TIO

N

IND

EX

A

ND

O

THER

M

OR

PHO

MET

RIC

V

AR

IAB

LE

S

Sl.

N

o.

1.

2.

3.

4.

5.

Rela

tio

nsh

ip

betw

een

Dis

secti

on

In

dex

(X

) &

R

ou

gh

ness

In

dex

( y)

Dis

sec

tio

n

Ind

ex

(X

) &

A

vera

ge

Slo

pe

Dis

secti

on

In

dex

(X

) &

S

tream

F

req

uen

cy

(Y

)

Dis

secti

on

In

dex

(X

) &

D

rain

ag

e D

en

sit

y

(Y)

Dis

secti

on

In

dex

(X

) &

D

rain

ag

e T

ex

ture

Co

eff

icj.en

t o

f C

orr

ela

tio

n

(r

)

0.8

99

4

o. 9

13

4

0.6

96

1

0.6

44

9

-0

.07

61

Co

eff

icie

nt

of

Dete

rmin

ati

on

R

2 (i

n%

)

80

.89

20

83

.42

99

48

.45

55

41

.58

96

oo. 5

79

1

i::

Lin

ear

Reg

ress

ion

Eq

uati

on

(

Y

= a

+

bX

)

-2

.67

62

+

32

.98

14

81

-1

.80

92

59

+

2

2.7

96

29

6

0.6

04

81

5

+

11.9

25

92

5

0.5

86

66

7

+

03

.66

66

66

X

X

X

X

1.0

88

14

8 +

(-

.24

07

41

) X

w

\0

w

~

ROUGHNESS INDEX & o~HERS 394

From the Table ( 11 .3) it i s a lso v i sua lised that the

correl ation bet ween d issection index and other drainage pro

perties like s t ream f req uency, drainage density and drainage

textur e i s r e l a t i v e l y weak. This is because of the fact that

drainage properti es are not solely determined by the nature

of rel ief properties of a n a rea. Rather it is the cumulative

effect of several other var iables such as structure a nd

lithology, rainfall dnd ra t e o f evapotranspirati on, etc ••

Dissection index a nd drai nage texture present negative

correlation of o nly- 0 .0761, which is poor in relationship.

so the coefficient of determination is na1~utrally poor ,which

is only 0 .58%. This analysis may suggest us that drainage

texture in the Basin is not due t o the dissection of the

Basin . The regression coefficient b (-0 .2 407) a lso recommends

this ·idea.

11.4 . ROUGHNESS INDEX AND OTHER MORPHOMETRIC VARIABLES

The roughness index a nd other variables of morphometry

show the correlation which are noted in the Table 11.4.

From the Table 11 . 4 it is clear that the degree o f

correlation coefficient betwe e n r oughness ,, j_ndex and ave r age

slope is highest of the lot (the val ue is +0 .9853)indicating

that · there lies a better positi v e correlation between the~e

two vaziables . It i ndic a t es that roughness index increases

TA

BL

E

11

.4

BIV

AR

IAT

E

RE

LA

TIO

NS

HIP

B

ETW

EE

N R

OU

GH

NES

S IN

DE

X A

ND

O

THER

V

AR

IAB

LE

S

Sl

. N

o.

1.

2.

3.

4.

Rela

tio

nsh

ip

betw

een

Ro

ugh

ness

In

dex

(X

) &

A

vera

ge S

lop

e (

Y)

Ro

ug

hn

ess

In

dex

(X

} &

S

tream

Fre

qu

en

cy

(Y)

Ro

ug

hn

ess

In

dex

(

X}

&

Dra

inag

e D

en

sity

(Y

)

Ro

ug

hn

ess

Ind

ex

(X

) &

D

rain

ag

e T

extu

re

Co

rrela

tio

n

of

Co

eff

icie

nt

( r)

0.9

85

3

0.6

56

3

0.6

13

3

0.0

15

6

Co

eff

icie

nt

of

Dete

rmin

a 1:

.io

n

R2

(in

%)

97

.08

56

4 3

. 07

30

37

.61

37

00

.02

43

Lin

ear

Re

gre

ss

ion

E

qu

atio

n

( Y

=

a

+

bX

)

0.

12

13

19

+

0

.67

05

82

X

-1.7

88

29

1

+

0.

30

65

74

X

0.9

49

71

0

+

0.0

94

46

2

X

1.0

34

71

0 +

0

.00

13

49

X

e

w

1.0

lJ1

AVERAGE SLOPE & OTHERS 396

degree of slope . The coefficient of determination for the

case is obviously high (97.09%).

The table also reveals that the correlation between

roughness index a nd drainage properties such as drainage den

sity and stream frequency is medium. They are + 0.6563 and

+ o. 6193 respectively. But roughness inde>: and drainage tex-

t ure are ve ry weakly corre l ated. These two variables present

corre l at ion of only + 0 . ~1 56 which is very poor in relation-

ship. so the coeff icien t o f determination (0.0243%) is also

very :weak . I

11.5. AVERAGE SLOPE AND OTHER MORPHOMETRIC VARIABLES

Coefficient of correlation {r), determination (R 2 ) and

r egression coefficient values between average slope and other

mo rphometric variables have been calculated and furnished in

t h e Table 11.5.

Among the variables the I relationship between avera~e

slope and stream frequency is highest denoting + 0.6904 and

the de.termination is 47.67% for the variation of stream fre-

quency accounted by average slope. There is weak positive

correlation (+0.0387) between average slope and drainage

texture . correlation coefficient of the variables average

s l ope and drainage density is medium (+0.6514). The average

slope contributes 42 . 43% for the variation of drainage density.

TA

BL

E

11

.5

BIV

AR

IAT

E

RE

LA

TIO

NS

HIP

B

ETW

EEN

A

VE

RA

GE

S

LO

PE

A

ND

O

THER

V

AR

IAB

LE

S

Sl.

N

o.

1.

2.

3.

Rela

tio

nsh

ip

betw

ee

n

Av

era

ge S

lop

e

(X)

&

Str

eam

F

req

uen

cy

(Y

)

Av

era

ge

Slo

pe

(X)

&

Dra

inag

e D

en

sity

Av

era

ge

Slo

pe

(X)

&

DY

ain

ag

e T

ex

ture

(Y

)

Co

rrela

tio

n o

f C

oeff

icie

nt

( r)

0.6

90

4

0.6

51

4

0.0

38

7

Co

eff

icie

nt

of

Dete

rmin

ati

on

R

2 (in

%)

47

.66

52

42

.43

22

00

.14

99

Lin

ear

Reg

ressio

n

Eq

uati

on

(Y

=

a

+

bX

)

1.6

86

82

2

+

0.4

73

88

3 X

0.9

14

57

6

+

0.1

47

42

7

X

1.0

26

51

0 +

0

.00

49

05

X

<".

:--

t,--

STREAM FREQUENCY & OTHERS 398

11.6. DRAINAGE DENSITY AND OTHER MORPHOMETRIC VARIABLES

Following the same procedure the correlation between

drainage density and otter variables have been calculated

(Table 11.6). I

From the Table 11.6 it is visualised tha t the correla-

tion between drainage density a nd roughness index is strongest

(+0.8978) . The variation i n roughness index(80.68%)is accoun-

ted for drainage density. The relationship with drainage tex-

ture is lowest denoting - 0 .1897 and the determination is 3.5~~

for the Vdriation of drainage texture accounted by drainage

density .

11.7. STREAM FREQUENCY AND OTHER MORPHOMETRIC VAR~ES

Stream frequency has been correlated with two diffe

rent variables ~· drainage density and drainage texture

(Table 11.7).

I

I ~

Among the variables drainage density is highly correla

ted (+0.9545) and determination is 91.12% for the variation of

drainage density a ccounted ny stream frequency. On the other

hand drainage texture is weakly correlated (-0.1415) and the

stream frequency contributes 2.0027% for the variation of

drainage texture.

SUPERIMPOSED REGRESSION LINES OF


6 5 4 3 2 6 1!5 ·6

>- X w w oc >- u 0 ~ ~ :z: ul 'Z X w ~ (/) ~ a.. - w ><4 :Z:4 oB . oro .. 20 - ~ · 4 w w w .J ~ 0 [ !/)

!/)

w (/)

w w w (!) (!) ~ (!) z <t

~2 ~4 :5 rEI ~2 6 <t <i oc w ~ oc oc f- > 0

0 0 0 !/) <t 0::

0 0 0 0 50 100 150 200 RELATIVE RELIEF (Me t res)

2 8

7 6 5 4 3 2

I· I· 6

>- lL. w >- u X w oc !:: z w :J ~ w 0 w ~ (/)

~ w z oc X/ z, 04 0..4 -4 5 0 7 w w w 0 1- 0 oc ..J

!/) u.. (/) z llJ (/) 0 (!) w w

1-<t ~ (!) z 'Z·5 ~2 <t2 :x:2

u

Ci oc (!) W· l oc w ::> (/)

oc 1- > 0 (/)

0 (/) <t oc 0

0 0 0 0 0 0 100 200

AVERAGE RELIEF (M et res)

FIG . 11.3

SUPURIMPOSED REGRESSION LINES OF

3 r 3.- 12r 12°;:...._----------------:;.,...------::::o""i /

""'~ I 4 w 0::2 :::> IX w I-

3 2 >-

W CL ~8, w :::> 0 0 .J w U)

~I ~I ~4

'

k / / ,......-- 4 _, 7 ::;:> w w I fE z z ~ - :::i w w '

~ ~ ~ I ;; t . I l ol ol o~ ~ 1 ~ 1 ~ 20

ROUGHNESS INDEX

3

-5 4 3 12

>- >-t-2 ~4 U) w w z :::> CL

UJ 0 0 0 w _J

a::

~ I ~ 1.1...

w [w UJ • U)

C!>l ~I ~2 e!>4 ~I ~ z ~ ~ :X:

- <i w a:: (!)

~ a:: a:: UJ :::>

~ 0 1- > 0 U) ~ a::

• 0 0 0 ().I

DISSECTION INDEX

FIG. 11.4


3-

3

w (!)

~, z <i a:: 0

3r 3

2 I 1 I ' w a:: ~2 X w I-

UJ

~ c: 0

~,~!'I/' , 2 q

~ a:: 0

ol oL 0

3

I >-<..> z UJ4 :::> 0 UJ a:: 1.1...

0

I l l I 2 4 6

STREAM FREQUENCY

6

AVERAGE SLOPE

I

SUPERIIMPOSED REGRESSI ON LINES 402

- -----11.8 . SUPER I MPOSED REGRESS I ON L INES

The s uperimposed r eg r e ssio n l ines of morphometr i c

variables of t he Brahmani Basin on average r e lief (Fig. 11.3)

reveal a v e ry i nterestin g f act with increase in average re-

l ief all the variables show increasing trend values except

drainage texture . Th e drainage texture shows almost parallel ·'

t rend with increas e i n a verage relief. Same is the case among

regress ion lines on relative relief, roughness index,average

slope, etc •.

. The superimposed regr e ssion lines of variables on

dissection index and stream f req ue ncy a lso p r esent some inte-

r esting phenomena . With i ncrease in the dissection index and

stream frequenc y , al l t he morphometric variables show increa-

sing tre nd value s excep t drainage texture. The texture shows ,

negativ e trend with inc rea se in dissection index and stream

f requency (Fig . 11.4).

the brahmani basin 11 -...

Documents