Chapter 4 Morphometric Analysis -...

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Chapter 4 : Morphometric Analysis

4.1 Introduction

Geology, geomorphology, structure and drainage patterns especially in hard

rock terrains are the primary determinants of river ecosystem functioning at the

basin scale (Lotspeich and Plats; Frissel et al., 1986). Morphometric descriptions

represent relatively simple approach to describe basin processes and to compare

basin characteristics. Anthropogenic changes have led to widespread modifications

in physical structure of rivers, biotic communities and ecological functioning of

aquatic ecosystems around the world (Thomson et al., 2001).

Understanding the drainage pattern of an area gives a perspective view of the

topography of the area which helps in the planning and development of water sheds

and also provides an indication of the potential zones for obtaining ground water.

Morphometric techniques are applied for interpretation of salient features of

drainage networks. It incorporates a quantitative study of the area, its altitude,

volume, slope, profiles of land and the drainage basin characteristics of the

concerned area (Singh, 1977).

It was the year 1932 when drainage basin attracted the attention of Horton,

an American engineer, who first of all presented an elaborate account of drainage

basin characteristics and in 1945 he acknowledged the drainage basin as a

morphometric system wherein he applied morphometric techniques vigorously for

interpretation of silent features of drainage network. In fact after the classical work

of Horton in 1945, drainage basin attracted attention of a large number of

geomorphologists, engineers and hydrologists, who accepted the drainage network

and the basin as a dynamic rather than static unit. Consequently significant

contribution in the field of drainage basin study came from Miller (1953); Schumm

(1956); Chorley (1967); Strahler (1957); Melton (1959); Morgon (1962); Gregory and

Walling (1973).

59

The morphometric analysis using remote sensing and GIS techniques has

been well attempted by Srivastava and Mitra (1995); Srivastava (1997); Singh and

Singh (1997); Nag (1998); Srinivasa Vittala et al.; (2004) and Nilufer Arshad and G.S.

Gopalakrishna (2008) and all have arrived to the conclusion that remote sensing

technique and GIS have emerged as a powerful tools in the recent years. Satellite

remote sensing has the ability of obtaining synoptic view of large area at a time and

very useful in analyzing the drainage morphometry.

4.2 Data used and Methodology

For carrying out morphometric analysis, hydrological boundary is taken into

consideration rather than the geographical boundary of the study area. Hence, the

Lakshmantirtha River basin was chosen for the present work and not the Hunsur

Taluk. The map showing the drainage pattern of the entire Lakshmantirtha river

basin has been prepared based on the Survey of India (SOI) toposheets and the

drainage pattern has been updated by using the satellite imageries of LISS plus PAN

merged data of 2001. The satellite images used for this study have been taken from

Karnataka State Remote sensing Application Centre. These satellite images and the

SOI toposheets have been geo‐referenced and merged using Image Processing

software ERDAS IMAGINE (V 9.1), (ERDAS, 2001).

The drainages have been delineated using merged satellite data of Geocoded

FCC of bands ‐ 2 3 4 on 1:50,000 scale and SOI toposheets bearing number 57D/3,

57D/4, 57D/7, 57D/8, 48P/15, 48P/16 and 58A/1 have been used as a reference.

Ground truth checks have been made during the field visits (Fig. 4.1). AutoDesk

software like Auto CAD Map 2000 and ArcGIS softwares like Arcmap (v.9.1) and

ArcView (v.3.2a) have been used for digitization and computational purpose and also

for output generation (ESRI ArcGIS, 2001). The morphometric analysis can be

achieved through measurement of linear, aerial and relief aspects of basin and slope

contributions (Nag and Chakraborty, 2003). Factor analysis also has been applied on

the morphometric parameters and has grouped them into different factors and their

association with one another has been discussed in detail in the following sections.

60

Figure 4.1: Drainage pattern of Lakshmantirtha basin

61

4.3 Morphometric Analysis

Following the digitization of the drainage pattern of the Lakshmantirtha

basin, morphometric analysis was carried out for the whole basin and subsequently

for the 26 watersheds which were demarcated according to the water divider (Fig.

4.2). The linear, relief and aerial aspects of the each watershed has been described

and interpreted. The linear aspect treats with unidimensional, while relief and aerial

aspects describes two dimensional and three dimensional characteristics

respectively. The new drainages updated from the satellite Imagery have also been

taken into consideration for measurement of these aspects of the study area. In this

study the linear, aerial and relief aspects have been grouped into five categories: 1)

basic parameters, 2) derived parameters, 3) shape parameters 4) dissection intensity

parameters and 5) relief parameters. All the parameters have been discussed in

detail.

4.3.1 Basic Parameters

4.3.1.1 Area (A)

This is one of the most important physical characteristics, because it directly

affects the size of the hydrographs and magnitude of runoff. The total drainage area

of the Lakshmantirtha basin is 1582 sq.km, and the area of each of the watersheds

are shown in the Table 4.1. Watershed 12 is the smallest (A < 8.683 sq.km) and

watershed 18 is the biggest (A> 346.9 sq.km), (Table 4.1).

4.3.1.2 Perimeter (B)

The perimeter is the total length of the drainage basin boundary. It is the

total length along the water divide of the basin. The perimeter (P) is a linear measure

of the size of the basin and it is largely dependent on the texture of the topography.

The perimeter of the basin is 249 km, and the perimeter of the 26 watersheds is

shown in Table 4.1. Watershed 12 has the smallest perimeter (P< 14.28) and the

watershed 18 has the largest perimeter (P> 81.8) and coincides with highest value of

A in the same watersheds, (Table 4.1).

62

Figure 4.2: Watershed boundary of Lakshmantirtha sub‐basin

63

4.3.1.3 Basin Length (L)

Basin length has been given different meanings by different workers

(Schumm 1956; Gregory and Walling 1973; Gardiner 1975 and Cannon 1976).

According to Gregory and Walling (1973), the L is the longest length of the basin,

from the catchment to the point of confluence. The basin length also corresponds to

the maximum length of the basin and watershed measured parallel to the main

drainage line. The length of the Lakshmantirtha basin is 72 km and the values of L for

the 26 watersheds are shown in the Table 4.1. Watershed 18 is the longest

watershed (L> 28.5 km) while watershed 26 has the minimum value of L (L< 2.78 km),

(Table 4.1).

4.3.1.4 Stream Order (Nu):

The designation of stream orders is the first step in drainage basin analysis

and is based on a hierarchic ranking of streams. There are different methods to

indicate the order of a stream network. Horton (1945) designated a stream without

any tributaries as the first order stream. However, each second order stream is

considered to extend headwords to the tip of the longest tributary. The third order

receives second and first order channels as its tributaries and so on. Strahler (1952)

gave a modified definition and considered each fingertip channel as of first order.

The second order stream commences from the point where two first order channels

meet and continues down to the intersection of two second order streams for which

point a third order stream commences and so on. The modified method proposed by

Strahler (1964) is widely accepted and is the most popular system in classifying the

channels into orders.

In the present study, ranking of streams has been carried out based on the

method proposed by Strahler (1964) which is popularly known as Stream Segment

Method. The order wise stream numbers for all 26 watersheds are given in Table 4.1.

Out of these watersheds, watersheds 25 and 26 belong 20 second order, watershed

6,7,10, 12, 14, 15, 16, 17 and 20 belong to the third order streams, watersheds 1, 4,

64

7, 9, 11, 13, 21, 22, 23 and 24 are of fourth order streams and the remaining

watersheds( 2, 3, 5, 18 and 19) are of fifth order streams.

Lakshmantirtha basin is designated as a sixth order stream. The details of

stream characteristics confirm with Horton’s first law (1945) of stream numbers,

which states that the numbers of different orders in a given drainage basin tends

closely to approximate an inverse geometric ratio. This means that there is a

negative correlation between the stream order and stream number. This can be seen

clearly in the linear regression graph where an almost straight line is formed when

log values of stream numbers are plotted against stream order (Fig. 4.3).

4.3.1.5 Stream length (Lu)

The number of streams of various orders in the basin and watersheds are

counted and their lengths from mouth to drainage divide are measured with the help

of GIS softwares. In the present study, stream length (Lu) has been computed based

on the law proposed by Horton (1945) for all the 26 watersheds and presented

(Table 4.1). Generally, the total length of stream segments is in maximum in first

order streams and decreases as the stream order increases. In Fig. 4.3 it can be seen

that there is a negative correlation between the stream lenght and stream order

when regression line is fitted. This observation is on the basis of Horton's law of

stream numbers (1932) which has received verification by accumulated data from

many localities (Strahler 1952; Schumm 1956; Smith 1958; Melton 1958). However

there is a sudden increase in length of streams of order III in (watersheds 13 and 4),

order IV ( watersheds 1, 5, 6, 7 and 11) and stream order V (in watershed 18), which

could be due to variation in relief over which the segments occur. This change may

indicate flowing of streams from high altitude, lithological variation and moderately

steep slopes as proposed by Singh and Singh (1997). Mostly all streams rise from the

hilly terrains. It is noticed that stream segments up to the 3rd order traverse the high

altitudes zones, which are mainly characterized by steep slopes, while the 4th, 5th and

6th order stream segments occur in comparatively plain land.

65

Watershed/ Stream Stream Order Stream LengthPerimeter Area

Basin

I II III IV V VI I II III IV V

1 IV 93 24 5 1 0 0 58.32 31.711 12.09 10.75 0 43.36 69.71 14.8

2 V 165 43 8 2 1 0 113.10 40.78 21.27 21.84 18.86 73.7 139.5 20.78

3 V 165 34 10 3 1 0 109.02 38.8 23.37 9.54 12.86 61.91 116.4 22.5

4 IV 45 14 2 1 0 0 26.87 19.33 7.62 2.04 0 37.42 42.25 8

5 V 119 31 7 2 1 0 88.95 36.19 11.39 19.78 9.94 53.71 120.6 18.1

6 III 11 4 1 0 0 0 10.34 3.816 4 0 0 23.72 17.21 6.4

7 IV 69 17 2 1 0 0 59.05 21.8 8.3 15.81 0 44.15 70.95 18.41

8 III 28 6 2 0 0 0 20.09 5.38 3.12 33.94 26.13 5.7

9 IV 53 12 3 1 0 0 42.50 34.93 9.49 9.5 0 44.5 70.75 15

10 III 18 5 1 0 0 11.59 9.65 1 34.16 23.84 10.4

11 IV 24 8 2 1 0 0 14.25 5.46 1.03 7.18 20.03 18.27 7.74

12 III 14 4 1 0 0 0 8.54 4.99 0.56 0 0 14.28 8.683 4.24

13 IV 28 6 3 1 0 0 17.95 4.72 7.89 2.09 0 19.43 20.53 5.56

14 III 23 6 1 0 0 0 15.39 4.23 4.1 0 0 14.63 10.53 5.27

15 III 22 5 1 0 0 0 12.35 5.25 4.62 0 0 14.55 11.31 4.84

16 III 17 4 1 0 0 0 12.28 8.08 3.69 0 0 18.56 15.83 4.5

17 III 26 7 1 0 0 0 17.51 6.16 2.25 0 0 37.97 28.47 9.15

18 V 239 59 19 5 1 0 162.77 91.14 38.05 16.74 25.74 81.8 346.9 28.5

19 V 196 41 11 3 1 0 122.62 45.36 19.65 13.42 10.12 66.44 163.9 24.2

20 III 25 6 1 0 0 0 17.21 6.59 3.40 0 0 20.18 20.13 5.2

21 IV 48 11 3 1 0 0 31.91 18.81 10.51 1.79 0 26.37 43.27 9.6

22 IV 77 15 4 1 0 0 52.95 17.98 12.27 1.67 0 43.47 54.05 7.11

23 IV 55 12 5 1 0 0 35.53 12.96 10.72 0.66 0 53.11 53 6

24 IV 54 10 4 1 0 0 42.71 9.34 12.43 2.33 0 45.61 52.07 10.5

25 II 13 5 0 0 0 0 9.08 1.1 0 0 0 22.67 11.20 3.3

26 II 6 2 0 0 0 0 4.32 2.46 0 0 0 24.28 13.08 2.78

Basin VI 1642 393 94 25 5 1 1112 460.407 222.14 133.898 77.54 249 1582 72 Table 4.1: Basic parameters

66

y = ‐0.638x + 3.8747R² = 0.9989

y = ‐0.218x + 3.108R² = 0.8796

0

0.5

1

1.5

2

2.5

3

3.5

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Lakshmantirtha Basin

Stream Number Stream Length

y = ‐0.5317x + 2.4047R² = 0.945

y = ‐0.4001x + 2.2766R² = 0.8815

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 1

Stream Number Stream Lenght

y = ‐0.5767x + 2.7412R² = 0.9839

y = ‐0.1827x + 2.0695R² = 0.7909

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 2


y = ‐0.5489x + 2.692R² = 0.9952

y = ‐0.2465x + 2.1564R² = 0.865

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 3


y = ‐0.436x + 1.9158R² = 0.8967

y = ‐0.3773x + 1.9062R² = 0.9668

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 4


67

y = ‐0.5341x + 2.545R² = 0.9858

y = ‐0.2166x + 2.0214R² = 0.7647

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 5


y = ‐0.2685x + 1.1341R² = 0.7949

y = ‐0.2611x + 1.2231R² = 0.8926

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 6


y = ‐0.4908x + 2.1465R² = 0.8876

y = ‐0.3682x + 2.1501R² = 0.7769

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 7


y = ‐0.3672x + 1.607R² = 0.8909

y = ‐0.3337x + 1.5071R² = 0.9295

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 8


y = ‐0.4528x + 2.0144R² = 0.9264

y = ‐0.3822x + 2.1721R² = 0.8657

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 9


y = ‐0.321x + 1.3537R² = 0.7921

y = ‐0.3113x + 1.3438R² = 0.7676

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 10


68

y = ‐0.3664x + 1.6159R² = 0.9097

y = ‐0.2189x + 1.2091R² = 0.4425

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 11


y = ‐0.2894x + 1.2179R² = 0.7867

y = ‐0.2561x + 1.0944R² = 0.7961

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 12


y = ‐0.3672x + 1.6422R² = 0.9195

y = ‐0.2863x + 1.4881R² = 0.8574

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 13


y = ‐0.3502x + 1.4785R² = 0.7941

y = ‐0.3002x + 1.386R² = 0.9009

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 14


y = ‐0.3384x + 1.4234R² = 0.7858

y = ‐0.2904x + 1.3667R² = 0.9106

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 15


y = ‐0.3063x + 1.2854R² = 0.7787

y = ‐0.3087x + 1.4388R² = 0.9365

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 16


69

y = ‐0.3675x + 1.5545R² = 0.7969

y = ‐0.3276x + 1.4601R² = 0.929

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 17


y = ‐0.5829x + 2.974R² = 0.9967

y = ‐0.2338x + 2.3786R² = 0.8391

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 18


y = ‐0.572x + 2.8008R² = 0.9962

y = ‐0.2695x + 2.2429R² = 0.937

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 19


y = ‐0.3574x + 1.5074R² = 0.7921

y = ‐0.3291x + 1.5047R² = 0.9476

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 20


y = ‐0.4404x + 1.9611R² = 0.9275

y = ‐0.4029x + 2.0194R² = 0.9504

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 21


y = ‐0.4949x + 2.2177R² = 0.9354

y = ‐0.448x + 2.2021R² = 0.9555

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 22


70

Figure 4.3: Geometric relationship between stream order, stream number and stream length

4.3.2 Derived parameters

4.3.2.1 Stream length ratio

Stream length ratio (RL) may be defined as the ratio of the mean length of the

one order to the next lower order of stream segment.

Where, RL = Stream Length Ratio

Lu = Total stream length of the order 'u'

y = ‐0.456x + 2.0717R² = 0.9425

y = ‐0.4214x + 2.0029R² = 0.8989

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 23


y = ‐0.4465x + 2.0063R² = 0.9315

y = ‐0.3863x + 1.9717R² = 0.9149

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 24


y = ‐0.2927x + 1.2406R² = 0.799

y = ‐0.2239x + 0.9278R² = 0.722

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 25


y = ‐0.1857x + 0.773R² = 0.7447

y = ‐0.1664x + 0.705R² = 0.7985

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7

Stream

lenght

Stream

number

Stream order

Watershed 26


71

Lu – 1 = Total stream length of its next lower order to the next lower order of

stream segment.

Horton's law (1945) of stream length states that mean stream length

segments of each successive orders of a basin tends to approximate a direct

geometric series with streams length increasing towards higher order of streams.

The RL between streams of different order in the study area reveals that there is a

variation in RL in each watershed (Table 4.2). This variation might be due to changes

in slope and topography. The stream length ratio of the sub‐basin reveals that the

values are different for different watersheds and are changing haphazardly from 1.70

to 6.322. The RL variation can be attributed to differences in slope and topographic

conditions and has a relationship with surface flow discharge and erosional stage of

basin (Sreedevi et al., 2004). The same kind of condition too was observed in the

study area. This change could also be attributed to the late youth or medium stage of

geomorphic development (Singh and Singh, 1977).

4.3.2.2 Stream Frequency (Fs)

Horton (1932) introduced stream frequency (Fs) or channel frequency which

is the total number of stream segments of all orders per unit area. Hypothetically, it

is possible to have the basin of same drainage density differing in stream frequency

and basins of same stream frequency differing in drainage density. Table 4.2 shows

Fs for all the watersheds of the study area.

Fs = Nu / A.

Where, Fs = Stream Frequency

Nu = Total number of streams of all orders

A = Area of the Basin (Sq.Km)

72

4.3.2.3 Bifurcation ratio (Rb)

The term bifurcation ratio (Rb) may be defined as the ratio of the number of

the stream segments of given order to the number of segments of the next higher

order (Schumn, 1956). Horton (1945) considered the bifurcation ratio as an index of

relief and dissections. Strahler (1957) demonstrated that bifurcation ratio shows a

small range of variation for different regions or for different environment except

where the powerful geological control dominates.

Rb = Nu/Nu+1

Where, Rb = Bifurcation Ratio

Nu = Total number of stream segments of order 'u'

Nu + 1 = Number of segments of the next higher order

It is observed from Table 4.2 that the Rb is not same from one order to its next

higher order. According to Strahler, 1964 these irregularities are dependent upon the

geological and lithological development of the drainage basin.

Bifurcation ratio is a dimensional parameter indication of branching pattern

of a drainage network. The Rb for the basin is 4.42 and the values of all the

watersheds vary from 2.60‐5.0. The lower values of Rb are characteristics of the

watersheds which have suffered less structural disturbances (Strahler, 1964 and Nag,

1998).

4.3.2.4 RHO coefficient (RHO)

Horton (1945) defined this parameter as the ratio between the stream length

ratio and bifurcation ratio. It can be calculated from the following formula:

Where, RI: Mean Stream Length Ratio

73

Rb: Mean Bifurcation Ratio

Horton (1945) stated that by calculating this value one could estimate how

much water will be lost as runoff during flood period and also determine the amount

of water which could be stored in a basin showing the drainage capacity of a basin.

RHO is influenced by many external parameters like climate, anthropogenic factors

and also by the geologic and geomorphologic conditions of the terrain. The value of

RHO for the Lakshmantirtha basin is 0.38 and for the watersheds it varies from 0.370‐

1.686 (Table 4.2). Watershed 10, 11, 12 AND 23 show higher values than the other

watersheds and there is a possibility that that they have higher hydric storage during

flood period and attenuate the erosion effects during elevated discharge.

4.3.3 Shape parameters

4.3.3.1 Elongation ratio

Elongation ratio (Re) is the ratio between diameters of a circle of the same

area to the basin length (L) (Schumm, 1956).

1.128√ / ,

Where, Re = Elongation Ratio


Pi = 'Pi' value i.e., 3.14

Lb = Basin length

A circular basin is more efficient in the discharge of run‐off than an elongated

basin (Singh and Singh, 1997). The values of Re generally vary from 0.6 to 1.0 over a

wide variety of climatic and geologic types. Values close to 1.0 are typical of regions

of very low relief, whereas values in the range 0.6 ‐ 0.8 are usually associated with

high relief and steep ground slope (Strahler, 1964).

The Re of watersheds of the study area varies from 0.51–1.46 (Table 4.3). The

low values of Re in case of watersheds which their values are between 0.6‐0.8, reveal

74

an elongated shape and indicate higher relief and steep slope. The Value of Re for

the whole basin too is 0.62 which indicates an elongated shape. While very high Re

values 0.8 ‐1.0 and greater than 1, indicates that plain land with low relief and low

slope which are seen more on eastern part of the basin which the terrain is more or

less flat.

4.3.3.2 Circularity index (Rc)

According to (Miller, 1953 and Strahler 1964,) the circularity index is defined

as the ratio of basin area (A) and the area of a circle with the same parameter as that

of the basin. It is calculated from the following formula:

Rc = 4 * ∏ * A / P²

Where, Rc = Circularity Ratio

∏ = 'Pi' value i.e., 3.14


P² = Square of the Perimeter (Km)

The circularity ratio (Rc) is influenced by the length and frequency of streams,

geological structures, land use/land cover, climate, relief and slope of the basin.

The Rc of Lakshmantirtha basin is 0.32 while the Rc calculated for its 26

watersheds are shown in Table 4.3. The value of Rc of Lakshmantirtha basin clearly

shows lack of circularity in shape. This is because the value is less than 0.5. Almost all

the watersheds are showing values less than 0.5, which indicates an elongated

shape, while the watersheds 12, 13, 14, 20 and 21 are more or less circular in shape.

75

Watersheds Elongation ratio Circularity Ratio Form factor

W1 0.64 0.47 0.32

W2 0.64 0.32 0.32

w3 0.54 0.38 0.23

w4 0.86 0.44 0.72

W5 0.68 0.45 0.75

w6 0.73 0.38 0.42

w7 0.52 0.46 0.21

w8 1.01 0.28 0.80

w9 0.63 0.45 0.31

w10 0.53 0.26 0.22

w11 0.62 0.57 0.30

w12 0.78 0.53 0.48

w13 0.92 0.68 0.66

w14 0.69 0.62 0.38

w15 0.78 0.42 0.83

w16 1.00 0.48 0.78

w17 0.66 0.25 0.34

w18 0.74 0.48 0.43

w19 0.60 0.47 0.28

w20 0.97 0.62 0.74

w21 0.77 0.78 0.47

w22 1.17 0.36 0.37

w23 1.37 0.25 0.43

w24 0.78 0.31 0.47

W25 0.62 0.32 0.30

W26 0.64 0.47 0.32

basin 0.64 0.32 0.32

Table 4.2: Shape parameters

76

Watershed/ Elongation ratio Stream Length Ratio Mean Stream Length ratio

FS RHOBasin Rb1 Rb2 Rb3 Rb4 Rb5 Mean Rb I II III IV VW1 3.88 4.80 5.00 ‐ ‐ 4.56 1.84 2.62 1.12 ‐ ‐ 1.86 1.76 0.41

W2 3.84 5.38 4.00 2.00 ‐ 3.80 2.77 1.92 0.97 1.16 ‐ 1.70 1.57 0.45

W3 4.85 3.40 3.33 3.00 ‐ 3.65 2.81 1.92 2.45 0.74 ‐ 1.98 1.83 0.54

W4 3.23 6.50 2.00 ‐ ‐ 3.91 1.36 2.45 3.72 ‐ ‐ 2.51 1.55 0.64

W5 3.84 4.43 3.50 2.00 ‐ 3.44 2.46 3.18 0.58 1.99 ‐ 2.05 1.33 0.60

W6 2.75 4.00 ‐ ‐ ‐ 3.38 2.71 0.95 ‐ ‐ ‐ 1.83 0.93 0.54

W7 4.06 8.50 2.00 ‐ ‐ 4.85 2.71 2.63 0.52 ‐ ‐ 1.95 1.25 0.40

W8 4.67 3.00 ‐ ‐ ‐ 3.83 3.73 1.72 ‐ ‐ ‐ 2.73 1.38 0.71

W9 4.42 4.00 3.00 ‐ ‐ 3.81 1.22 3.68 1.00 ‐ ‐ 1.97 0.98 0.52

W10 3.60 5.00 ‐ ‐ ‐ 4.30 1.20 9.66 ‐ ‐ 5.43 1.01 1.26

W11 3.00 4.00 1.00 ‐ ‐ 2.66 2.61 5.29 0.14 ‐ ‐ 2.68 1.92 1.01

W12 3.50 4.00 ‐ ‐ ‐ 3.75 3.80 8.85 ‐ ‐ ‐ 6.32 2.19 1.69

W13 4.67 2.00 3.00 ‐ ‐ 3.22 3.80 0.60 3.78 ‐ ‐ 2.72 1.85 0.85

W14 3.83 6.00 ‐ ‐ 4.90 3.63 1.03 ‐ ‐ ‐ 2.33 2.85 0.48

W15 4.40 5.00 ‐ ‐ ‐ 4.70 2.35 1.13 ‐ ‐ ‐ 1.74 2.48 0.37

W16 4.25 4.00 4.13 ‐ ‐ 4.13 1.52 2.19 1.86 ‐ ‐ 1.86 1.39 0.45

W17 3.14 7.00 ‐ ‐ ‐ 5.00 2.84 2.74 ‐ ‐ 2.79 1.19 0.52

W18 4.05 3.11 3.80 5.00 ‐ 3.98 1.79 2.40 2.27 0.65 ‐ 1.78 0.93 0.45

W19 4.78 3.73 3.00 ‐ ‐‐ 3.84 2.70 2.31 1.46 1.33 ‐ 1.95 1.54 0.51

W20 4.17 6.00 ‐ ‐ ‐ 5.08 2.61 1.94 ‐ ‐ ‐ 2.27 1.59 0.45

W21 4.36 3.67 3.00 ‐ ‐ 3.67 1.70 1.79 5.86 ‐ ‐ 3.11 1.46 0.85

W22 5.13 3.75 4.00 ‐ ‐ 4.29 2.94 1.47 7.35 ‐ ‐ 3.91 1.79 0.91

W23 4.58 2.40 5.00 ‐ ‐ 3.99 2.74 1.21 16.25 ‐ ‐ 6.73 1.38 1.69

W24 5.40 2.50 4.00 ‐ ‐ 3.96 4.57 0.75 5.32 ‐ ‐ 3.55 1.33 0.90

W25 2.60 ‐ ‐ ‐ ‐ 2.60 4.33 ‐ ‐ ‐ ‐ 4.33 1.61 1.56

W26 3.00 ‐ ‐ ‐ ‐ 3.00 1.75 ‐ ‐ ‐ ‐ 1.75 0.61 1.70

Basin 4.17 4.18 3.76 5.00 5.00 4.42 2.42 2.07 1.66 1.73 1.73 1.72 1.35 0.38

Table 4.3: Derived parameters

77

4.3.3.3 Form Factor

According to Horton (1932), form factor (Rf) may be defined, as the ratio of

basin area to square of the basin length.

Rf = A / Lb²,

Where, Rf = Form Factor


Lb² = Square of Basin length

Rf value of the basin is 0.30 and the value for all the watersheds are shown in

Table 4.3.The low values of Rf for the basin and most of the watersheds once again

confirms an elongated shape. The index of Rf shows the inverse relationship with

square of axial length and a direct relationship with peak discharge (Gregory and

Walling, 1973). From the shape parameter analysis, one thing which is very clear is

that all the 3 above mentioned factors indicate an elongated shape of the basin

which in turn has an effect on the discharge characteristic of the basin. Floods take a

longer time to travel in an elongated basin when compared to a circular basin

(Gregory and Walling, 1973).

The relationship among form factor, circularity ratio, elongation ratio and

length of overland flow in each sub‐watershed has been presented in Fig. 4.4.

Figure 4.4: The relationship among form factor, circularity ratio and elongation ratio

0

0.5

1

1.5

2

2.5

1 3 5 7 9 11 13 15 17 19 21 23 25water shed

Form factor

Circularity ratio

Elongatio ratio

78

4.3.4 Parameters for Dissection Intensity

4.3.4.1 Drainage density (Dd)

Horton (1945) defined the drainage density as the ratio of total length of all

stream segments in a given drainage basin to the total area of that basin.

,

Where, D = Drainage Density

Lu = Total stream length of all orders


Dd is an indicator of basin dissection. Langbein (1947) recognized the

significance of Dd as a factor determining the time of travel by water and he also

suggested a drainage density varying between 0.55 and 2.09 km/sq.km in humid

region with an average density of 1.03 km/sq.km. Density factor is related to climate,

type of rocks, relief, infiltration capacity, vegetation cover, surface roughness and

run‐off intensity index. Of these only surface roughness has no significant correlation

with drainage density. The amount and type of precipitation influences directly the

quantity and character of surface run‐off. An area with high precipitation such as

thundershowers loses greater percentage of rainfall as run‐off resulting in more

surface drainage lines. Amount of vegetation and rainfall absorption capacity of soils,

which influences the rate of surface run off affects the drainage texture of an area.

The similar condition of lithology and geologic structures, semi‐arid regions have

finer drainage density texture than humid regions.

According to Nag (1998), low drainage density generally results in the areas of

highly resistant or permeable subsoil material, dense vegetation and low relief. High

drainage density is the result of weak or impermeable subsurface material, sparse

vegetation and mountainous relief. Low drainage density leads to coarse drainage

texture while high drainage density leads to fine drainage texture.

79

Smith (1950) has classified drainage density into 5 different textures as

follows:

Drainage Density (km/ sq.km) Texture

<2 Very coarse

2‐4 Coarse

4‐6 Moderate

6‐8 Fine

>8 Very fine

Table 4.4: Classification of drainage density (after Smith, 1950)

The parameters like resistance to erosion of rocks, infiltration capacity of land

and climate conditions influence the drainage density (Vestappan 1983). Drainage

density of the Lakshmantirtha basin as a whole is 1.33 and those of the 26

watersheds are shown in Table 4.5. According to the classification given by Smith

(1950), The Dd of the watersheds and the basin are all less than 2 which is a

characteristic feature of course drainage system and reveals to some extent the

permeable nature of the sub strata. It is noted that drainage density exhibits positive

and high correlation (0.871) with Fs values of the watersheds and the basin (Fig 4.6).

This was estimated by using the SPSS (V.16) statistical software.

According to Melton (1958), these are characteristics of moderately well

drained streams, having a higher runoff when compared to their infiltration rate

indicative of a medium dissected topography. It is suggested that low drainage

density indicates the region has highly permeable subsoil, dense vegetative cover

and low relief as suggested for similar watershed elsewhere (Nag, 1998).

80

Watershed/basin Drainage Density

Drainage Texture

Length of over land

flow

W1 1.62 2.86 0.30

W2 1.55 2.43 0.32

w3 1.66 3.04 0.30

w4 1.44 2.23 0.34

W5 1.38 1.83 0.36

w6 1.06 0.98 0.47

w7 1.48 1.86 0.33

w8 1.09 1.51 0.45

w9 1.36 1.33 0.36

w10 0.93 0.94 0.53

w11 1.53 2.93 0.32

w12 1.62 3.55 0.30

w13 1.59 2.95 0.31

w14 2.25 4.38 0.22

w15 1.97 4.87 0.25

w16 1.52 2.11 0.32

w17 0.91 1.09 0.54

w18 0.96 0.90 0.51

w19 1.29 1.98 0.38

w20 1.35 2.15 0.36

w21 1.46 2.12 0.34

w22 1.57 2.82 0.31

w23 1.13 1.56 0.44

w24 1.28 1.70 0.38

w25 0.99 1.60 0.50

w26 0.51 0.31 0.96

basin 1.33 1.79 0.37

Table 4.5: Dissection intensity parameters

Drainage Density Fs

Drainage Density Pearson Correlation 1 0.87**

Sig. (2-tailed) 0.00

N 27 27

Fs Pearson Correlation 0.87** 1

Sig. (2-tailed) 0.00

N 27 27

**. Correlation is significant at the 0.01 level (2-tailed).

Table 4.6: Correlation table between stream frequency and drainage density variable

81

Figure 4.5: Scatter plot matrix shows the correlation between Fs and Dd

4.3.4.2 Drainage texture (T)

An important geomorphic concept is drainage texture which defines the

relative capacity of drainage line (Smith, 1950). Drainage texture (T) is one of the

important concepts of geomorphology which means that the relative spacing of

drainage lines. Drainage lines are numerous over impermeable areas than permeable

areas.

Drainage texture can be calculated from the following formula:

T = Dd * Fs

Where, Dd = Drainage density

Fs= Stream Frequency

According to Smith many parameters like soil type, infiltration capacity have a

bearing on drainage texture. Based on value of T, the drainage texture can be

classified in the following categories (Smith 1950), (Table 4.7).

82

The T of the Lakshmantirtha basin as whole is 1.79 while that of the 26

watersheds are shown in Table 4.7. The T values of all the watersheds are below 4

and belong to the coarse texture.

4.3.4.3 Length of overland flow (Lg)

The Length of overland flow is described as the average length of flow of

water over the surface before it become concentrated in definite stream channel

(Horton, 1945). He defined Lg as the length of flow path, projected to the horizontal

of the non‐channel flow, from a point on the drainage divide to an overland flow as

one of the most important variable, affecting both hydrologic physiographic

development of drainage basin. The Lg is approximately equal to half of the

reciprocal of the drainage density. It is calculated from the following formula:

Lg = 1 / Dd * 2,

Where, Lg = Length of Overland flow

Dd = Drainage Density

Table 4.5 reveals that the Lg is more in watershed 26 as drainage density is

the least in this watershed when compared to remaining watersheds. The computed

value of Lg for all watersheds varies from 0.232 to 0.96. A high negative correlation

(r= ‐0.888) is seen between the drainage density and length of over land flow and by

plotting a correlation matrix, using SPSS software (v.16), this can be clearly seen in

Fig. 3.6.

T Value Drainage Texture

<4 Coarse

4‐10 Intermediate

10‐15 Fine

>15 Ultra f

Table 4.7: Classification of drainage texture (after Smith, 1950)

83

Figure 4.6: : Scatter plot shows the correlation between Dd and Lg

4.3.5 Relief aspects

4.3.5.1 Relief aspects

Vertical inequalities of an area play an important role not only in controlling

the distribution of precipitation, formation of surface water features like streams,

tanks etc., but also in the availability and circulation of ground water. Relief aspects

are the function of the elevation or elevation difference at various points in a basin

or along the channels. It includes relief measures, ruggedness number and

hypsometric analysis.

4.3.5.2 Relief measures

Relief measures are indicative of potential energy of a drainage basin by

virtue of elevation above a given datum line. Different relief characteristics viz.,

maximum basin relief (H), Minimum basin relief (h), relief ratio (Rh) and relative

relief are measured.

84

4.3.5.3 Basin relief

The basin relief is an important factor in understanding the extent of

denudational characteristics (the denudational landforms are formed as a result of

active processes of weathering, mass wasting and erosion caused by different

exogenesis geomorphic agents such as water, glaciers, wind etc., the landforms

formed by agents of dedudation are identified as pediments, pediplains etc., ) of the

basin. Relief is the difference between maximum and minimum elevations in the

basin.

Basin Relief= H‐h

where, H=Maximum height of basin

h=Minimum height of basin

Basin relief has an influence on the channel slope which controls the flood

pattern and the amount of sediments which get transported (Hedley and Schumm

1961). In the present study the basin relief of the basin is 840 m and for the

watersheds the values vary from 20 m to 780 m (Table 4.8).

4.3.5.4 Relief Ratio:

According to Schumm (1963), the relief ratio is the dimensionless height‐

length ratio equal to the tangent of the angle formed by two planes intersecting at

the mouth of the basin, one representing the horizontal, the other passing through

the highest point of the basin. The relief ratio is calculated by using the following

formula:

Relief ratio = H‐h/L

Where, H= highest elevation in the basin

h= lowest elevation in the basin

L= longest axis of the basin

85

Dimensionless relief ratio measures the overall steepness of a drainage basin

and also is an indicator of the intensity of erosion process operating on the slopes of

the basin and is closely related to peak discharge and runoff intensity. Relief ratio is

directly proportional to fluvial erosion material and drainage density. There is also a

correlation between hydrological characteristics and the relief ratio of a drainage

basin. The Rh normally increases with decreasing drainage area and size of sub‐

watersheds of a given drainage basin (Gottschalk, 1964).

In the present study, the values of Rh are given in Table 4.8. The relief ratio of

the whole basin is 0.011 and the values for the watersheds range from 0.004 to

0.037). It is noticed that the high values of Rh indicate steep slope and high basin

relief (780 m ), while the lower values may indicate the presence of basement rocks

that are exposed in the form of small ridges and mounds with lower degree of slope

(GSI, 1981).

4.3.5.5 Relative relief (Rr)

Melton (1958) suggested the relative relief as ratio of maximum basin relief

(H) to basin perimeter (P).

Rr = basin relief / P

Where, Rr = Relative Ratio

Basin relief= H‐h

P = Perimeter (km)

For calculating the relative relief, the method proposed by Melton (1958) has

been adopted for the present study and represented in Table 4.8. It can be seen from

table that the maximum value of Rr observed in watershed 2 (0.0105) and the

minimum in watershed 24 (0.0008).

86

4.3.5.6 Gradient ratio

Gradient ratio is an indication of channel slope from which and assessment

of the runoff volume could be elevated. Gradient ratio is calculated by using the

following formula:

Gradient ratio = (a‐b)/L

Where, a = Elevation at source of the basin

b= Elevation at Mouth of the basin

L= Length of the main stream

The basin has a gradient ratio of 0.0097 and the values for the 26 watersheds

are presented in Table 4.8 and range between 0.01 ‐ 0.003, showing low to moderate

gradient.

4.3.5.7 Ruggedness number (Nr)

To combine the qualities of slope steepness and length, a dimensionless

ruggedness number is formed of the product of basin relief (“H‐h”) and drainage

density “Dd” where both terms are in same units (Strahler, 1958).By using the

following formula ruggedness number is calculated.

Nr = Dd * H / 1000

Where, Nr = Ruggedness Number

Dd = Drainage Density

H (H‐h) = Total relief of the basin in Kilometres

If “Dd” increases while “H‐h” remains constant, the average horizontal

distance from divides to adjacent channels is reduced, with an accompanying

increase in slope steepness. If “H‐h” increases while “Dd” remains constant, the

elevation difference between divides and adjacent channels also increases, so that

87

slope steepness increases. Extremely high values of the ruggedness number occur

when both variables are large, this is when slopes are not only steep but long as well.

In the present study, the Nr for the basin and all watersheds have been

calculated and given in Table 4.8. High value of Nr for the basin (1.11) indicates that

lower order streams which extend very close to the water divide. Sharma (1982);

Prasad (1984); Balasubramanian (1986) and Venugopal (1988) have also observed

same type of results in the river basins of hard rock areas of South India.

4.4 Topography of the area

Topography maps are the most important source for a detailed study of

landforms and characteristic features of the surface area, which provide more

information about shape, size and relief of the area. Topographic map provides

details about shape, relief and size in three dimensional view of the area.

The contours of the study area were digitized using Auto CAD (V.2000). Using

the contour reading values the relief map was prepared by the help of Arcview (3.2a)

software (Fig. 4.7 and 4.8). The topographic map of the study area also was prepared

using Global Mapper software (v.10) (Fig. 4.9). In the Fig. 4.9 the profile of the terrain

is shown from the southwest (SW) to northeast (SE). In both the figures Fig. 4.8 and

Fig. 4.9 it can be clearly seen that the SW of the basin shows more undulation when

compared to the NE which is comparatively a flat terrain.

88

Figure 4.7: map of the drainage basin of Lakshmantirtha

89

Figure 4.8: map of the drainage basin of Lakshmantirtha

90

Figure 4.9: Profile of the drainage basin of Lakshmantirtha

4.5 Hypsometric analysis (Area altitude analysis)

Hypsometry involves the measurement and analysis of relationships between

altitude and basin area to understand the degree of dissection and stage of cycle

erosion. Here the hypsometric curve is used to show the relationship between the

altitude and area of a basin.

Hyposmetric Curve (HC) is generally used to show the proportion of area of

surface at various elevations above or below a datum (Morkhousa and Wilkinson,

1967) and thus the values of area are plotted as ratios of total area of the basin

against the corresponding height of the contours. Hypsometric analysis is appealing

because of its dimensionless parameter that permits comparison of watersheds

irrespective of scale issues (Dowling et al., 1998). Hypsometric curves (HC) and

hypsometric integrals are important indicators of watershed conditions (Ritter et al.

2002). Differences in the shape of the curve and the hypsometric integral value are

related to the degree of disequilibria in the balance of erosive and tectonic forces

(Weissel et al., 1994).

In the present study Hypsometric curve is obtained by plotting the relative

area along the abscissa and relative elevation along the ordinate.

91

Basin / Watershed

Relief Elevation in 'm"

basin relief

Longest Axis L

Relative Relief

Relief ratio (H‐h)/L

Gradient Elevation Height (a‐b)

Longest axis L

Ratio (a‐b)/L

Ruggedness No. (Nr)

Max H Min H Source a mouth b

1 1020 820 200 14.8 0.004 0.013 1000 820 180 14.8 0.0121 0.324 2 1600 820 780 20.78 0.010 0.037 1480 820 660 20.78 0.0317 1.207 3 1040 820 220 22.5 0.003 0.011 1000 820 180 22.5 0.01 0.366 4 880 800 80 8 0.002 0.01 880 800 80 8 0.01 0.115 5 1000 800 200 18.1 0.003 0.011 940 800 140 18.1 0.007 0.276 6 880 800 80 6.4 0.003 0.0125 860 800 60 6.4 0.009 0.084 7 1220 820 400 18.41 0.009 0.021 1000 820 180 18.41 0.009 0.592 8 840 800 40 5.7 0.001 0.007 840 800 40 5.7 0.007 0.044 9 980 800 180 15 0.004 0.012 940 800 140 15 0.009 0.245 10 840 800 40 10.4 0.001 0.0038 840 800 40 10.4 0.0038 0.037 11 880 800 80 7.74 0.003 0.01 880 800 80 7.74 0.01 0.122 12 860 800 60 4.24 0.004 0.014 860 800 60 4.24 0.014 0.097 13 880 800 80 5.56 0.004 0.015 860 800 60 5.56 0.01 0.127 14 880 800 80 5.27 0.005 0.015 860 800 60 5.27 0.011 0.180 15 840 800 40 4.84 0.002 0.008 840 800 40 4.84 0.008 0.079 16 840 800 40 4.5 0.002 0.008 840 800 40 4.5 0.008 0.061 17 840 780 60 9.15 0.001 0.0065 840 800 40 9.15 0.004 0.055 18 980 780 200 28.5 0.002 0.007 980 780 200 28.5 0.0108 0.193 19 900 780 120 24.2 0.001 0.004 900 780 120 24.2 0.0049 0.155 20 900 780 120 5.2 0.005 0.023 820 780 40 5.2 0.007 0.162 21 900 780 120 9.6 0.004 0.0125 860 780 80 9.6 0.008 0.175 22 840 760 80 7.11 0.001 0.011 820 760 60 7.11 0.008 0.126 23 800 780 20 6 0.001 0.0004 800 780 20 6 0.0004 0.023 24 820 780 40 10.5 0.0008 0.003 820 780 40 10.5 0.003 0.051 25 800 780 20 3.3 0.0001 0.0060 800 780 20 3.3 0.0060 0.020 26 860 800 60 2.78 0.002 0.0215 860 800 60 2.78 0.0215 0.031

Basin 1600 760 840 72 0.003 0.01101 1460 760 700 72 0.0087 1.117 Table 4.5: Relief parameters

92

The relative area is obtained as a ratio of the area above a particular contour to the

total area of the watershed encompassing the outlet (a/A) and the relative elevation is

calculated as the ratio of the height of the given contour (h) from the base plane to the

maximum basin elevation (H), (up to the remote point of the watershed from the

outlet), (Sarangi et al., 2001 and Ritter et al., 2002). The resulting curve called the

hypsometric curve starts at the top left hand corner at 1.00 and ends at the bottom

right hand corner at 1.00 (Fig. 4.10). For computing the relative area of the basins and

the watersheds, with the help of the of the surface analysis tool in the Arcview software

the area above each contour was computed. Another important parameter in

hypsometric analysis is the hypsometric integral (HI). The hypsometric integral is

obtained from the hypsometric curve and is equivalent to the ratio of the area under

the curve to the area of the entire square formed by covering it. It is expressed in

percentage units and is obtained from the percentage hypsometric curve by measuring

the area under the curve. This provided a measure of the distribution of landmass

volume remaining beneath or above a basal reference plane. According to Strahler

(1952), the entire period of cycle of an erosion of a basin can be grouped in to three

stages viz., monadnock (old) (Hsi≤0.3), in which the watershed is fully stabilized;

equilibrium or mature stage (0.3≤Hsi≤0.6); and inequilibrium or young stage (Hsi≥0.6),

in which the watershed is highly susceptible to erosion (Strahler 1952; Sarangi et al.,

2001), (Fig. 4.10).

Figure 4.7: Cycle erosion of a basin (after Strahler, 1952)

93

4.5.1 Estimation of Hypsometric Integral (HI)

The hypsometric integral or the area under the curve can be estimated by four

different methods which are as follow:

1) Integration of Hypsometric Curve

2) Use of the Leaf Area Meter (LAM)

3) Use of the Planimeter Equipment

4) Use of Elevation–Relief Ratio (E)

In the present study the integral values of the basin and the watersheds were

calculated using the mathematical integration value. The plotted hypsometric curves

were fitted with a trend line (polynomial) in excel software to represent an equation of

the curve and the best fitting equation was obtained for highest coefficient of

determination (R2) value. The equation was further integrated within the limits of 0 to 1

(due to the non‐dimensional nature of the graph) for estimating the area under the

curve. Thus the estimated area gives the hypsometric integral value of the hypsometric

curve. The developed polynomial equation by fitting the hypsometric curve of the basin

is shown in Fig. 4.11. The fitted equation was integrated within the desired limits to

estimate the area under the HC. The hypsometric integral values, relative area and

relative heights obtained for the basin and 26 watersheds are presented in Table 4.9.

Figure 4.8: The fitted equation of the hypsometric curves for the basin

y = ‐20.648x5 + 56.269x4 ‐ 58.044x3 + 28.626x2 ‐ 7.1344x + 0.9273

R² = 0.9945

0.00

0.20

0.40

0.60

0.80

1.00

0.00 0.20 0.40 0.60 0.80 1.00

Relative

height (h/H

)

Relative area (a/A)

basin

94

Contour

values

Relative area

(a/A)

Relative

height

Hypsometric

Integral

Basin

760 1 0

0.204

800 0.96 0.047840 0.72 0.095880 0.46 0.14920 0.32 0.19960 0.22 0.231000 0.18 0.281050 0.14 0.341100 0.11 0.401150 0.09 0.461200 0.07 0.521250 0.06 0.581300 0.04 0.641350 0.03 0.701400 0.02 0.761450 0.007 0.821500 0.001 0.881550 0.0005 0.941600 0 1

Watershed 1

820 1 0

0.267

840 0.32 0.11860 0.17 0.22880 0.136512 0.33900 0.108 0.44920 0.06 0.55940 0.03 0.66960 0.01 0.77980 0.008 0.881000 0.0030 0.91020 0 1

Watershed 2

820.00 1.00 0.00

0.287

860.00 0.66 0.05900 0.58 0.10940 0.54 0.15980 0.48 0.211020 0.44 0.261100 0.36 0.361180 0.29 0.461260 0.22 0.561340 0.16 0.671420 0.08 0.771500 0.01 0.871600 0.00 1.00

Watershed 3

820 1.00 0.00

0.245

860 0.69 0.13900 0.41 0.27940 0.13 0.40980 0.04 0.531020 0.02 0.671060 0.01 0.801080 0.00 0.931100 0.00 1.00

Watershed 4

800 1.00 0.00

0.562 820 0.91 0.25840 0.66 0.50860 0.18 0.75880 0.00 1.00

95

Watershed 5

800.00 1.00 0.00

0.253

840.00 0.85 0.11880.00 0.45 0.22920.00 0.22 0.33960.00 0.09 0.441000.00 0.05 0.561040.00 0.03 0.671080.00 0.01 0.781120.00 0.00 0.891140.00 0.00 0.941160.00 0.00 1.00

Watershed 6

800 1.00 0.00

0.385

820 0.79 0.20840 0.46 0.40860 0.15 0.60880 0.03 0.80890 0.01 0.90900 0.00 1.00

Watershed 7

800 1.00 0.00

0.319

840 0.90 0.10880 0.69 0.19920 0.45 0.29960 0.29 0.381000 0.21 0.481020 0.17 0.521060 0.11 0.621100 0.06 0.711120 0.05 0.811160 0.02 0.901200 0.00 0.951220 0.00 1.00

Watershed 8

800 1.00 0.00

0.203

820 0.62 0.14840 0.22 0.29860 0.13 0.43880 0.09 0.57900 0.05 0.71920 0.02 0.86940 0.00 1.00

Watershed 9

800.00 1.00 0.00

0.389 820 0.89 0.11840 0.70 0.22860 0.56 0.33880 0.35 0.44900 0.24 0.56

920 0.14 0.67940 0.04 0.78960 0.01 0.89980 0.00 1.00

Watershed 10

800.00 1.00 0.00

0.382

820 0.89 0.11840 0.70 0.22860 0.56 0.33880 0.35 0.44900 0.24 0.56920 0.14 0.67940 0.04 0.78960 0.01 0.89980 0.00 1.00

Watershed 11 800 1.00 0.00 0.429 820 0.88 0.20

96

840 0.60 0.40860 0.17 0.60880 0.04 0.80900 0.00 1.00

Watershed 12

800 0.00 1.00

0.496 820 20.00 0.69840 40.00 0.30860 60.00 0.00

Watershed 13

800 1.00 0.00

0.407

820 0.87 0.20840 0.51 0.40860 0.13 0.60880 0.06 0.80900 0.00 1.00

Watershed 14

800 1.00 0.00

0.392 820 0.74 0.25840 0.25 0.50860 0.11 0.75880 0.00 1.00

Watershed 15

800 1.00 0.00

0.517 810 0.74 0.25820 0.51 0.50830 0.31 0.75840 0.00 1.00

Watershed 16 800 1.00 0.00

0.601 820 0.68 0.50840 0.00 1.00

Watershed 17

780 1.00 0.00

0.445 800 0.69 0.33820 0.19 0.67840 0.00 1.00

Watershed 18

780 1.00 0.00

0.244

820 0.95 0.10860 0.68 0.19900 0.28 0.29940 0.14 0.38980 0.08 0.481020 0.05 0.571060 0.03 0.671100 0.02 0.761140 0.01 0.861180 0.00 0.951200 0.00 1.00

Watershed 19

780 1.00 0.00

0.476

800 0.88 0.17820 0.70 0.33840 0.44 0.50860 0.24 0.67880 0.09 0.83900 0.00 1.00

Watershed 20

780 1.00 0.00

0.377

800 0.75 0.20820 0.42 0.40840 0.19 0.60860 0.05 0.80880 0.00 1.00

Watershed 21

780 1.00 0.00

0.411 800 0.90 0.17820 0.67 0.33840 0.30 0.50860 0.07 0.67

97

880 0.02 0.83900 0.00 1.00

Watershed 22

760 1.00 0.00

0.477 780 0.79 0.25800 0.48 0.50820 0.15 0.75840 0.00 1.00

Watershed 23

780 1.00 0.00

0.267 800 0.37 0.33820 0.05 0.67840 0.00 1.00

Watershed 24

760 1.00 0.00

0.374 780 0.66 0.25800 0.27 0.50820 0.10 0.75840 0.00 1.00

Watershed 25

780 0.0075 0.00

0.377 785 0.0045 0.25790 0.0023 0.50795 0.0008 0.75800 0.00 1.00

Watershed 26

800 1.00 0.00

0.45 820 0.74 0.33840 0.05 0.67850 0.02 0.83860 0.00 1.00

Table 4.6: Relevance of relative area, relative height and Hypsometric Integral (HI) on Watershed Hydrologic Responses

The HI value of Lakshmantirtha basin (0.204) indicated that 20.4% the original

rock masses still exist in this basin. The estimated HI values reveal that the basin (0.204)

and few watersheds mainly on the western part were in the monadnock stage and the

remaining watersheds were all in the mature stage. The watersheds with mature stages

were located at lower elevations, the reason of which can be mainly attributed to the

human interventions in the form of construction of roads, intensive agricultural

practices and deforestation activities. It is understood that the hydrologic response of

the sub basins attaining the mature stages will have slow rate of erosion (Ritter et al.,

2002) unless there is very high intense storms leading to high runoff peaks. According to

Omvir Singh (2008), the HI values less than 0.5 needs minimum mechanical and

vegetative measures to arrest sediment loss but may require more water harvesting

type structures to conserve water at appropriate locations in the watershed for

conjunctive water use. Whereas watersheds, which are having hypsometric integral

values more than 0.5 (i.e., approaching youthful stage) need construction of both

vegetative and mechanical soil and water conservation structures to arrest sediment

load and conserve water for integrated watershed management.

98

Legend: X axis: Relative area (a/A) Y axis: Relative height (h/H)

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101

Figure 4.9 : Hypsometric curve of the basin and its 26 watersheds

4.6 Interrelationship of Different Morphometric Parameters by Using factor Analysis

Statistics methods are applied in a variety of fields in hydrological research.

Factor analysis is useful for interpretation of morphometric parameters and relating the

same to specific hydrological processes. Multivariate analysis is simply a collection of

procedures for analysing the associations between two or more sets of data that have

been collected on each object in one or more samples of objects. By using factor

analysis the less significant variables are eliminated and the remaining is arranged in a

manner which would make interpretation an easy task.

Adopting statistical applications in hydrological studies began with Synder (1962)

who introduced some solutions in hydrological modelling. Later on many other workers

like Wong (1979); Wallis (1965); Shukla and Verma, (1975) and Mishra and

Satyanarayana (1988), also used different statistical methods like cluster analysis and

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102

principal component analysis for developing hydrological prediction equation and to

group the most likely significant groups.

The method of factor analysis and varimax rotation is based on the principles

demonstrated by Davis (1973). A correlation matrix was first computed in the first step

for the given geomorphic parameters (Table 4.10). The eigen values were computed

since these eigen values of each component explains the total variance explained by the

variables on the component. The factor extraction was done with a minimum

acceptable eigen values of > 1. The fourteen variables were reduced to four factors. The

factors account for 82% of the total variability of the data. The factor‐loading matrix is

rotated to varimax rotation which results is maximisation of the variance of the factor

loadings of the variables on the factor matrix (Table 4.11). The factor loading is a

measure of the degree of closeness between variables and the factor.

By observing the correlation matrix on the 12 selected geomorphic parameters,

it is very clear that a good correlation exists among some of the variables and some of

the variables do not show any significant correlations. For this purpose, by the rotation

factor matrix in factor analysis using SPSS software (V16), the variables were further

classified as factors and these factors having one or few variables in each (Table 4.11)

As shown in the Table 4.11, the variables are classified in to 5 factors, which are

discussed as bellow:

Factor 1: This factor includes the area, perimeter and the basin length of the 26 watersheds.

Factor 2: Drainage density and stream frequency

Factor 3: Relative relief and Rugedness number

Factor 4: Elongation ratio, Circularity ratio and form factor

Factor 5: Bifurcation ratio

103

The first factor is mainly loaded on variables i.e., basin perimeter, basin area and

basin length and it reveals that these parameters have the greatest influence on the

form and processes of the drainage basin. The second factor which is termed as run‐off

factor shows a high correlation between the drainage density and stream frequency

(r=0.872) and these geomorphic variables control the run‐off of the basin. Calculating

the run‐off an area is important specially in hydrologic modelling. For example when

one wants to calculate sediment yield silted by this run off in reservoirs of the

watershed and also in management of water resources this factor plays an important

role. Factor 3 is termed as the relief parameter and exhibits a high correlation between

relative relief and Nr (r=0.844). By this it can be said that if the relative relief increases,

the Nr also increases and influences on the slop of the terrain. As it can be seen in the

correlation Table 4.7 of the fourth factor, a moderately negative correlation exists

between the elongation ratio and circularity ratio and a moderately positive correlation

exist between the form factor and elongation ratio. As discussed earlier, all the

mentioned parameters suggest an elongated shape for the whole basin while is some of

the watersheds were circular in shape. A negative loading also is seen on the steam

length ratio in the fourth factor which concludes that this variable does not effect on

the shape parameter. The last factor is seen with a single variable of high loading and it

is the bifurcation ratio.

4.7 Significance

Laskmantirtha basin and its 26 watersheds exhibit a dendritic drainage pattern.

The variation in stream length ratio is due to change in slope and topography. The

higher values of mean bifurcation ratio of watersheds indicate that geological structure

has a stronger control on their drainage pattern compare to the watersheds with lower

values.

104

Correlation Matrix

area Perimeter

Basin

Length

Stream Length

Ratio(mean)

Drainage

Density

Elongation

ratio

Circularity

Ratio

Form

factor Fs

Relative

Relief Nr.

Bifurcation

Ratio(mean)

Correlation

area 1.00 0.86 0.88 -0.28 -0.13 -0.28 -0.007 -0.22 -0.26 0.11 0.36 -0.005

Perimeter 0.86 1.00 0.88 -0.16 -0.20 -0.26 -0.31 -0.37 -.035 0.12 0.50 0.03

Basin Length 0.88 0.88 1.00 -0.37 -0.00 -0.59 -0.008 -0.42 -0.22 0.29 0.55 0.06

Stream Length

Ratio(mean)

-0.28 -0.16 -0.37 1.00 -0.14 0.30 -0.22 -0.11 0.08 -0.34 -0.35 -0.08

Drainage Density -0.13 -0.20 -0.005 -0.14 1.00 -0.36 0.55 0.14 0.87 0.42 0.27 .028

Elongation ratio -028 -0.26 -0.59 0.30 -0.36 1.00 -0.24 0.35 -.015 -0.38 -040 -0.25

Circularity Ratio -.00 -0.31 -0.008 -0.22 0.55 -0.24 1.00 0.19 0.41 0.38 0.026 0.01

Form factor -0.22 -0.37 -0.42 -0.11 0.14 0.35 0.19 1.00 0.18 -0.20 -0.30 0.01

Fs -0.26 -0.35 -0.22 0.08 0.87 -0.15 0.41 0.18 1.00 0.19 0.04 0.19

Relative Relief 0.11 0.12 0.29 -0.34 0.42 -0.38 0.38 -0.20 0.19 1.00 0.84 0.21

Nr. 0.36 0.50 0.55 -0.35 0.27 -0.40 0.02 -0.30 0.04 0.84 1.00 0.09

Bifurcation

Ratio(mean)

-0.00 0.03 0.06 -0.08 0.28 -0.25 0.01 0.01 0.19 0.21 0.09 1.00

Table 4.7: Correlation matrix of morphometric units

105

Component

1 2 3 4 5

area 0.93

Perimeter 0.87

Basin Length 0.95

Stream Length Ratio(mean) -0.71

Drainage Density 0.89

Elongation ratio 0.51

Circularity Ratio 0.73

Form factor 0.72

Fs 0.87

Relative Relief 0.92

Nr. 0.87

Bifurcation Ratio(mean) 0.95

Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.

a. Rotation converged in 6 iterations.

Table 4.8: Rotated Component Matrix

The Dd of the basin as well as those of the watersheds, reveal that the nature

of the subsurface is permeable. This is a characteristic feature of coarse drainage.

The shape parameters also reveal the elongated shape for the basin. Due to this

characteristic, the basin will tend to have lesser flood peaks but longer lasting flood

flows compared to round basins. This particularly is very important while considering

the management and reservoir projects and a progressive land use pressures. The

geomorphic development of the basin also reveals it is in the monadnock stage.

Factor analysis was carried out on morophmetric units and grouped them in to 5

factors.

Chapter 4 Morphometric Analysis -...

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