Chapter-Ill Analysis of River Longitudinal Profiles 121

120

Chapter-Ill Analysis of river longitudinal profiles 121

Chapter III ANALYSIS OF RIVER LONGITUDINAL PROFILES

3.1. Introduction: Rivers are the most sensitive and dynamic elements of the landscape. The shape of the longitudinal profile of a river is result of the complex interplay between lithology, structure, tectonics, climate and catchment hydrology. In a large number of studies, the river longitudinal profiles have been investigated in order to identify the areas experiencing tectonic deformation and uplift (Begin, 1975; Seeber and Gornitz, 1983; Rice and Church, 2001; Chen et al., 2006; Lee and Tsai, 2009; Whittaker, 2012 and the references therein). In addition to this, the influence of climate and hydrological processes on the longitudinal profiles of the rivers has been investigated (Roe et al., 2002; Zaprowski et al., 2005). Other studies concerned with the long profile analysis include understanding of the role of lithology (Begin, 1975; Bishop et al., 1985; Goldrick and Bishop, 1995), distribution of stream power (Sklar and Dietrich, 1998; Snyder et al., 2000), identification of knick zones (Perez-Pena et al., 2009; Pederson and Tressler, 2012) and description of long profile shape (Shepherd, 1985; Rice and Church, 2001). In this chapter, the characteristics of the longitudinal profiles of the rivers of the Kaveri, Palar and Ponnaiyar Basins and their tributaries are described and an attempt is made to understand whether there is any effect of tectonics on their long profiles as suggested by Valdiya (2001).

3.2. Methodology: In all, the longitudinal profiles of 21 major tributaries of the Kaveri River, 8 tributaries of the Palar and 6 tributaries of the Ponnaiyar River, as well as the profiles of the main channels of the Kaveri, Palar and Ponnaiyar Rivers were extracted and analysed in ArcGIS. For extracting the longitudinal profiles of these streams, the SRTM-DEM data have been processed in an ArcGIS environment. To generate the long profiles of the rivers from SRTM-DEM data, the following procedure was adopted: 122

Streams were identified using the ‘Hydrology’ Routine in the ArcGIS software. These streams were divided into segments of 100 m length. This is in accordance with the resolution of SRTM data (90-m) so as to ensure that the same cell was not extracted for two points. These stream segments were converted into points and only the end points of each segment were extracted to the newly created point file. The elevation of each point along with its x-y coordinates were extracted by the “Feature to DEM” routine of ArcGIS. The data obtained were exported to the Microsoft Excel for fiirther analysis. Using the distance formula (Eq. 3.1), the distances of the extracted points ft'om one another was computed.

= + (^2 ~yif Eq. 3.1 where, d = distance between points X| and X2, xi = x-coordinate (in meters) of point Xi, yi = y-coordinate (in meters) of point yi, X2 = x-coordinate of point xi, y: = y-coordinate of point y2. The distances were then cumulated taking the source as origin (zero) and then the distances of all the points fi-om the source of the river were obtained. Due to stepping in the adjacent elevations and the effect of water bodies (dams), the long profiles derived ft-om DEM are not as smooth and accurate as those produced ft'om other techniques (Snyder et al., 2000), especially for low-gradient reaches. In the present study, first the artificial spikes were deleted and smoothing of the long profiles using a 11-elevation points moving average (5 points upstream and 5 points downstream), was carried out. The distance and the elevation data were used for calculating the Hack’s stream gradient index (SL), stream profile concavity and profile steepness. In addition, the variations in the long profile form were evaluated by curve fitting. The normalized stream profiles and normalized SL were also considered for understanding the long profile characteristics of the stream under review.

3.3. Description of the long profile forms: The longitudinal profiles of the rivers reflect the combined effect of present and past geomorphic processes in the basin. Steady-state systems are characterized by a state of equilibrium between the rates of uplift and denudation. Thus, abrupt changes in slope along 123

river profiles may indicate disequilibrium conditions associated with lithology (Hack. 1973) or active faults that cross these rivers (Seeber and Gomitz, 1983). In the case of the tributaries of the Kaveri, Palar and Ponnaiyar Rivers, although the longitudinal profiles are broadly concave-upward, linearity, convexity and breaks in slope are quite evident (Figs. 3.1, 3.2 and 3.3). This clearly indicates that the rivers of this ancient landscape are not graded, as expected.

H e m a v a t h i Lakatiam ahantirtha

E E §

1 ()0 2iK) 3(X) D istance fr(»m the s<»urce(kiii) D istance from the source(km )

K a b b i n i Suvarnavati 8 0 0 -I lO (X ) - B 8(X ) - 7 0 0 - 6CX) -

4(X ) 50 lOO 150 2(K) O 20 40 60 80 lOO D istance from the s«»urce(km) D istance from the source(kxn)

S h i m s h a A r k a v a t h i

lOO 200 3(X) 5 0 lO O 1 5 0 200 D istance from the source(km ) D istance from source (km)

Dodda Halla

1 .S 'SS

D istance from the source(km ) D istance fr<»m the source(km )

Fig. 3.1. A. Longitudinal profiles of the major tributaries of the Kaveri River. 124

Chinnar Palar

E co .S £

Distance from the source(lun) Distance from the source(km)

Nagavathi B E

Distance from the source(km) Distance from the source(km)

Bhavani

'S •S

Distance from the source(icm) Distance from the source(km)

Am ravati

E g > u

Distance from the source(lun) Distance from the source (km) Fig. 3.1. B. Longitudinal profiles of the major tributaries of the Kaveri River 125

Distance from the source(km) Distance from the source(km)

E E

>es

Distance from the source(km) Distance from the source(km)

E e

Distance from the source(km)

Distance from the source(km) Fig. 3.1. C. Longitudinal profiles of the major tributaries and the main channel of the Kaveri River 126

Distance from the source(km)

Distance from the source(km) Distance from the source(m)

Poini Cheyyar

Distance from the source (km) Distance from the source (km)

Tenneri Palar Channel

Distance from the source (km) Distance from the source (km)

Fig. 3.2. Longitudinal profiles of the major rivers of the Palar Basin 127

E c i

Distance from the source(km) Distance from the sourcedtm)

Distance from the source (km) Distance from the source (km)

.S I s

Distance from the source (km) Distance from the source (km)

Fig. 3.3. Longitudinal profiles of the major rivers of the Ponnaiyar Basin 128

Tributaries in the middle domain of the Kaveri Basin notably the Arkavathi, Shimsha and Chinnar as well as the Nagavathi River in the lower domain, particularly show deviation from the normal concave steady-state profile. Furthermore, the long profiles of the Amaravati and Bhavani Rivers in the lower domain of the Kaveri Basin are characterized by remarkably steep upper segments (Fig. 3. IB). This implies a rapid decline in channel slope and associated unit stream power in the headwaters of these tributaries. The main channel of the Kaveri River shows noteworthy absence of steeper upper segment. It has been stated earlier that the Kaveri originates over the Mysore Plateau and descends to the Tamil Nadu Plains before being deeply entrenched into bedrock in its middle course between Shivasamudram and Hogenakkal Falls. The long profiles of most of the tributaries of the Palar and Ponnaiyar Rivers as well as the tributaries in the lower domain of the Kaveri Basin also do not exhibit the typical concave-up profile, one would expect in the case of the rivers draining areas characterized by tectonic stability or uniform lithology or an ancient landscape.

3.4. Normalized Longitudinal Profiles: It is likely that the slight to noteworthy differences in the long profile shapes (Figs. 3.1, 3.2 and 3.3) may be also due to the differences in basin relief and size (surrogate for power and discharge). Therefore, the long profile length and relief were normalized to minimize the effects of these two variables and highlight the effects of tectonics and/or lithology. The elevations and distances were divided by the head (i.e. maximum basin relief) and the total stream length, respectively to normalize the long profiles (Seidl et al., 1994; Lee and Tsai, 2009) (Fig. 3.4). The normalized longitudinal profiles of the streams (Hemavathi, Kabbini, Suvarnavati and Lakahamahantirtha) in the upper domain of the Kaveri Basin (Fig. 3.4 A), display slight change in channel-bed elevation with distance. This is the typical property of the rivers originating over plateaux characterized by nearly flat terrain. These rivers originate on the Mysore Plateau and meet the Kaveri while on plateau without descending onto the plains. Hence, steep segments and knick points are absent. 129

The middle domain of the Kaveri Basin is characterized by tributaries meeting the Kaveri within the gorge section between Shivasamudram to Hogenakkal Falls (e.g. Shimsha, Arkavathi, Chinnar, Dodda Halla and Thattai Halla). Hence, these rivers exhibit knick points or breaks in their longitudinal profiles (Fig. 3.4 B). This is due to the fact that most of these rivers flow through an area which is controlled by the structural fabric. Presence of active faults in this zone (Valdiya, 2001) further adds to the irregular characteristics of the river profiles. In the lower domain of the Kaveri Basin (Fig. 3.4 C), most of the tributaries display the concave-up profile indicating gradual decline of channel slope downstream. However, two rivers namely the Amaravati and the Bhavani show some sort of deviation from the rest. These rivers are characterized by the steep upper segments. The loss of elevation with distance is rapid. Within 10-20% of their distance from source nearly 80-90% of their elevation is lost suggesting intense erosion in the headwaters of these streams. It is pertinent to mention here that the Bhavani and the Amaravati originate from the high-elevation Nilgiri and Anaimalai Ranges, respectively and comprise the highest portions of the Kaveri Basin. In case of the Palar and Ponnaiyar Basins (Fig. 3.5 and 3.6), most of the tributaries exhibit the typical characteristics of rivers underlain by uniform lithology. An interesting observation from the figures is that the long profiles of the Cheyyar and Vaniar, tributaries of the Palar and Ponnaiyar, respectively are characterized by the presence of steep upper segments, suggestive of intense erosion in the headwaters of these streams. It is worthwhile to mention here that the Vaniar River originates in the Biligirirangan Ranges, which comprise the headwaters of many of the middle domain tributaries in the Kaveri Basin. 130

- P a l a r

“ N ag av o th i

■*Sarabhanga * B h a v a n i

- N o y y ll

- Tirumanniuttar -A m r a v a ti - A iy ar - Koraiyar “ U p p o r

N orm alized DiKtnnce - N a n d y a r

Fig. 3.4 Normalized longitudinal profiles of the major tributaries of the Kaveri River. (A) Upper Domain, (B) = Middle Domain, (C) = Lower Domain

-D innckerc Hal la

“ M alattar

-Agaram Aru

-Kaundinya Nadi

•P oini

“ Cheyyar

“ Tenneri

-Palar Channel

Normalized Distance Fig. 3.5 Normalized longitudinal profiles of the major tributaries of the Palar River. 131

■S - Nuchikuppum

- P um bar

“ Semmandakuppam

-Turinjular

“ V an iar

•Ponnaiyar Channel

Normalized Distance Fig. 3.6 Normalized longitudinal profiles of the major tributaries in the Ponnaiyar River Basin.

3.5. Variations in Profile Form: Curve Fitting

Another approach that was adopted to describe the form of the long profiles is to fit simple linear, logarithmic, exponential and power-law regression models to the elevation versus distance data.

• The linear function y = ax + b

• The exponential function y = ae’’*

• The logarithmic function y = a In x + b

• The power regression model y = ax'*

where, y is the elevation, x is the length or distance from source, a and b are the coefficients derived independently from each profile. The r‘ or the explained variance of the relationship determines the best fit (Lee and Tsai, 2009). 132

The best fit model is one which minimizes the sum of squares of residuals and which also gives the minimum standard deviation of residuals (Snow and Slingerland, 1987). Lee and Tsai (2009) have indicated that when the channel bed grain size is greater than the capacity of the river for transportation, the long profile shows a low degree of concavity and hence a better linear function fit. As the transportation and deposition of channel sediment approaches dynamic equilibrium, the long profile better fits the exponential function. As the system approaches the graded profile, the channel sediment grain size will decrease downstream and hence the long profile fits more suitably for the logarithmic function. With further increase in the profile concavity, the power function becomes more appropriate. Thus, the evolution sequence should be linear exponential logarithmic power (Lee and

Tsai, 2009). The exercise of fitting the best fit regression models was undertaken for all the tributaries in the Kaveri, Palar and Ponnaiyar Basins (Table 3.1 and 3.2).

It is evident that linear regression or exponential regression relationships are the best statistical models for describing the relationship between elevation and distance for the rivers under consideration (Table 3.1 and 3.2). This implies low concavity of the long profiles of the rivers under examination, and confirms earlier observations. The linear model fits well for the tributaries of the Kaveri River in the middle domain of the basin, namely Arkavathi,

Chinnar, Shimsha and Thattai Halla as well as the Lakahamahantirtha in the upper domain. 133

Table 3.1. Long profile derivatives of different tributaries in the Kaveri Basin

SI. No. Sub-basin Mathematical Modelling SL a e K.„

Best Fit Regression Model 1 Hemavathi Linear 0.9 7 26 0 .9 6 0.12 10.3

2 Lakahamahantirtha Linear 0.9 8 13 0 .5 6 0.55 40.2

3 Kabbini Exponential 0.98 16 0.36 -0.24 5.0

4 Suvamavati Exponential 0.93 62 0 .35 0 .64 32.5

5 Shimsha Linear 0.88 55 6.03 -0.13 19.7

6 Arkavathi Linear 0.95 71 8.75 -0.94 35.4

7 Thattai Halla Linear 0 .9 9 133 14.16 -0.24 18.7

8 Dodda Halla Exponential 0.99 161 8.45 0.16 59.9

9 Chinnar Linear 0.98 120 3.98 0.03 44 .9

10 Palar Exponential 0.99 114 3.44 0 .8 9 16.9

11 Nagavathi Exponential 0.98 46 1.49 2.4 9 6.3

12 Sarabhanga Exponential 0 .9 9 35 1.58 0 .5 4 5.6

13 Bhavani Logarithmic 0.95 239 -0.59 0.91 52.5

14 Noyyil Linear 0.99 66 1.89 0.05 7.5

15 Tirumanmuttar Exponential 0.99 46 1.29 0.15 26.6

16 Amaravati Logarithmic 0.89 161 -0.15 1.03 25.5

17 Aiyar Exponential 0.99 34 0.59 0.72 12.6

18 Koraiyar Exponential 0.99 38 0.63 0 .6 6 15.4

19 Uppar Exponential 0 .98 13 0.25 0.89 3.3

20 Nandyar Exponential 0.98 11 0.36 0 .7 9 27.3

21 Marudaiyar Exponential 0.9 9 15 0.63 0.58 19.5

22 Kaveri River Linear 0.93 192 -0.12 0.58 26.2

SL = Stream Gradient Index, b = Rate of change of SL Index with distance from the source, 0 = Long profile concavity, Ksn = Reference steepness, r^ * = Regression model with highest explained variance. 134

Table 3.2. Long profile derivatives of diRierent tributaries in the Palar and Ponnaiyar Basins River Basin Sub-basin Mathematical Modelling SL e K,„ Best Fit Regression Model Dinnekere Halla Linear 0.86 100 -6.48 0.84 3.9 Malattar Exponential 0.96 62 -1.3 0.70 5.7 Agaram Aru Exponential 0.96 27 -2.5 0.45 Kaundinya Nadi Exponential 0.97 12 -0.4 0.85 18 Palar Poini Exponential 0.99 54 -2.2 0.25 Cheyyar Exponential 0.98 68 -0.5 0.39 3.4 Tenneri Exponential 0.99 10 -0.9 1.23 7.8 Palar Linear 0.94 130 -0.6 0.13 9.8 Nachikuppam Nadi Linear 0.95 57 0.4 0.46 10 Senimandakuppam Exponential 0.98 24 -0.6 0.76 12 Pambar Exponential 0.99 36 -0.8 0.34 7.6 Ponnaiyar Vaniar Exponential 0.93 70 1.4 0.1 23.8 Turinjalar Exponential 0.99 -2.7 0.67 16.8 Ponnaiyar Exponential 0.94 128 -2.9 0.1 9.2 For notations, refer Table 3.1

3.6. Stream Gradient Index (SL): Generally, the long profiles of the rivers are plotted on a semi-logarithmic paper in order to neutralize the exponential increase in the distance from the headwaters (Seeber and Gomitz, 1983; Bishop et al, 1985; etc.). A river under graded condition is expected to be in a state of balance between uplift and erosion rate and hence the long profiles of such rivers would plot as a straight line on a semi-logarithmic paper. Such linear plots are generally observed for areas of uniform lithologies or under relative tectonic stability (Hack, 1973; Bishop et al., 1985) The long profile of a graded stream in static equilibrium can be ideally described as a straight line on a semi-logarithmic graph paper (Goldrick and Bishop, 1995). On the other hand, if a river flows through a tectonically active area characterized by uphft exceeding denudation, or over erosion-resistant rocks, its long profile displays convexity (Lee and Tsai, 2009). 135

A river is referred to as “graded” when the gradient, width and depth of its channel are in equilibrium with discharge and load imposed from upstream. The gradient of a graded river usually decreases downstream as the discharge increases, and the longitudinal profile of this river can be often approximated by a straight line on a semi logarithmic plot (Hack,

1973):

H = C-K InL Eq. 3.2

where, H = channel bed elevation, L = distance from the source, and C and K are constants.

K, the slope of this idealized profile, is called the stream gradient index (Hack, 1973) and can be evaluated by:

K=Hi-Hj/lnLi-InLj Eq. 3.3

where, i and j refer to two points along the river profile.

The SL Index can be used to characterize a relatively short reach (segment) of the river as well as the entire profile. By comparing the river long profiles to the ideal semi- logarithmic profiles, the significance of anomalous gradients can be evaluated in the context of the discharge increasing downstream.

In this study, as zero cannot be plotted on the logarithmic scale, the source of all the rivers has been taken as 0.05 km (50 m). The convex nature of the semi-logarithmic profiles

(Figs. 3.7, 3.8 and 3.9) indicates that all the tributaries of the Kaveri, Palar and Ponnaiyar

Rivers are in the above-grade condition which may be ascribed to lithologic, structural and/or tectonic control. 136

Hemavathi Lakahamahantirtha

900 -

U S L = 2 6 S L = 13 6(X) 700 1 ICX) HKKX) KXXXKX) I 100 KKKK) KXHKXX) Distance from the source(m) Distance from the source(m)

K abbini Suvarnavati 10(X)

E 8(X) .£e I 6«) S L = 61 4(X) 1 100 UKK)0 lOOOO(X) Distance from the source(m) Distance from the source(m)

Shimsha Arkavathi 1(X)0

.1 I U 400

200 1 100 HX)00 10(X)(KX) Distance from the source(m) Distance from the source(m)

Fig. 3.7. A. Semi-logarithmic profiles of the tributaries in the Kaveri Basin. The straight line represents the theoretical graded profde 137

Thattai Halla Dodda Halla

Distance from the source(ni) Distance from the source(m)

Chinnar Palar

1 100 10000 10(KK)00 Distance from the source(m) Distance from the source(m)

Nagavathi Sarabhanga

Distance from the source(m) Distance from the source(m)

Fig. 3.7. B. Semi-logarithmic profiles of the tributaries in the Kaveri Basin. The straight line represents the theoretical graded profile 138

B havani Noyyil

Distance from the source(m) Distance from the source(in)

Tirumanmuttar Amravati 400

I> 200 U S L = 4 6

1 100 10000 1000000 Distance from the source(m) Distance from the source(m)

Aiyar Koraiyar 400

200

100 10000 1000000

Distance from the source(m) Distance from the source(m) Fig. 3.7. C. Semi-logarithmic profiles of the tributaries in the Kaveri Basin. The straight line represents the theoretical graded profile 139

Distance from the source(m) Distance from tiie source(m)

Distance from tiie source(m)

Kaveri

Distance from tiie source(m)

Fig. 3.7. D. Semi-logarithmic profiles of the tributaries and the main channel of the Kaveri River. The straight line represents the theoretical graded profile. 140

Dinnekere Halla

.2 «00 a S L = 12 700 1 100 KXKX) IO(X)000 100 10000 10(KXXX) Distance from the source(in) Distance from the source(m)

Distance from the source(m) Distance from the source(m)

Poini

Distance from the source(m) Distance from the source(m)

100 Tenneri

■2 50

s S L = 10 0 1 100 10000 lOOO(XM) Distance from the source(m) Distance from the source(m)

Fig. 3.8. Semi-logarithmic profiles of the tributaries and the main channel of the Palar River. The straight line represents the theoretical graded profile. 141

Semmandakuppam 6(X)

E B C 4(X)

SL = 24 2(K) 1 100 10000 lOOO(XX) Distance from the source(m) Distance from tlie source(m)

Pambar Vaniar

10 100 10(X) 10000 100(KK) Distance from tlie source(m) Distance from tlie source(m)

l\irinjalar Ponnaiyar Channel 1 5 0

100

S L = 9 50 100 UXXX) 100 10000 lOOO(KK) Distance from tlie source(m) Distance from tiie source(m) Fig. 3.9. Semi-logarithmic profiles of the tributaries and the main channel of the Ponnaiyar River. The straight line represents the theoretical graded profile. 142

76°E 80“E __ I__

Fig. 3.10. kaveri Basin: Variations in the average SL Index values across different tributaries. For stream numbers, refer Table 3.1 1%'^E 79°E 80°E ■ __ I______I___

—I-- --1-- 79“E 80*E Fig. 3.11. Palar and Ponnaiyar Basins: Variations in the average SL Index values across different tributaries. For stream numbers, refer Table 3.2 143

The spatial distribution of the average SL Index values across different tributaries in the Kaveri Basin is depicted in Fig. 3.10. The correspMjnding map for the Palar and Ponnaiyar Basins is shown in Fig. 3.11. From the figures and Table 3.1 it is evident that the average stream gradient index values for the tributaries in the Kaveri Basin range from 11 (for Nandyar) to 239 (for Bhavani). The arithmetic mean of the SL indices of all the tributaries of the Kaveri River is 69. It is clear from the Fig. 3.10 that high SL indices are concentrated in the middle domain of the Kaveri Basin comprising the tributaries such as the Dodda Halla (161), Thattai Halla (133), Chinnar (120) and Arkavathi (71). The upper and lower domains of the Kaveri Basin are characterized by relatively lower values of SL Index with the tributaries such as the Bhavani (239), Amaravati (161) and Palar (114) being the notable exceptions. It is pertinent to niention here that the Bhavani and Amaravati Rivers originate in the Nilgiri and Anaimalai Ranges at elevations of 1216 m and 1852 m, respectively. But their mouths are located on the Tamil Nadu Plains at elevations below 200 m ASL. The rapid decline in elevations along a length of about 200 km accounts for high SL Index values for these tributaries. The Palar River, although included in the lower domain of the Kaveri Basin, originates in the Biligirirangan Ranges, similar to many tributaries in the middle domain of the Kaveri Basin. Furthermore, this tributary shows remarkable similarity in its morphometric attributes to the tributaries in the middle domain of the Kaveri Basin. The mean stream gradient index values for all the tributaries in the Palar and Ponnaiyar Basins are 57 and 54, respectively. The SL indices in the Palar Basin range from 12 (for Kaundinya Nadi) to 130 (for Palar main channel), whereas the corresponding range in the Ponnaiyar Basin is 9 - 128. Needless to mention the average SL Index values for the tributaries of the Palar and Ponnaiyar are comparatively lower than their counterparts in the Kaveri Basin.

3.7. Identification of knickpoints/knick zones: A landform that is commonly found in tectonically active landscapes is the knickpoint (Kale et al., 2014). These transient forms are often described as breaks in the longitudinal profiles and represent an abrupt change in the river gradient. The prominent 144

breaks or knickpoints in the long profile of a river are identified by estimating the segment- wise SL index. The stream gradient index was proposed by Hack (1957) and in recent years a large number of workers have used the segment-wise SL Index in order to detect the control of lithology, structure and tectonics on the long profiles of the rivers (Seeber and Gornitz, 1983; Bishop et al., 1985; Goldrick and Bishop, 1995; Goldrick and Bishop, 2007; Lee and Tsai, 2009). A segment of the river with anomalously high SL Index has high stream energy corresponding to resistant rock area (control of lithology) or differential uplift zone (control of tectonics) (Bishop et al., 1985; Lee and Tsai, 2009). In the present study, the SL Index was obtained for all the segments in each river by applying the Eq.3.3. The segment-wise variations in SL index for each tributary was then plotted against distance from the source. Fig. 3.12, 3.13 and 3.14 show the downstream variations in the SL index for all the tributaries of the Kaveri, Palar and Ponnaiyar Basins, respectively. It is expected that the SL Index of most of the streams generally decreases downstream (Chen et al., 2006). This is due to the fact that the channel slope declines as one move away fi-om the source. From Fig. 3.12C, it is clear that in the case of the Kaveri River, the SL Index values are remarkably higher in its middle reach, especially in the gorge section between Shivasamudram and Hogenakkal Falls. In the vicinity of these falls, the SL index gets increased considerably and hence these are the two prominent knickpoints on the Kaveri River. The river in its reach between these two knickpoints has developed an entrenched course where it is deeply incised into bedrock. It has been stated earlier that the tributaries which meet the Kaveri in its entrenched reach between Shivasamudram and Hogenakkal Falls comprise the middle domain of the Kaveri Basin. Furthermore, the tributaries which meet the Kaveri in this domain such as the Shimsha, Arkavathi and Chinnar are marked by downstream segments where the SL Index values are elevated significantly (Fig. 3.12 A and B). 145

Distance from the source (km) Distance from the source (km)

eooo Shimsha 6000 Ariiavathi

2000

~a A-A.

50 100 150 200 250 50 100 150 200 Distance fo m the source (km) Distance from the source (km)

Dodda Halla 4000 Ihattai Halla

= 2000 _) c/2

10 20 30 40 50 60 70 Distance from the source (km) Distance from the source (km)

Fig. 3.12.A. Plots showing the downstream variations in the SL Index for tributaries in the Kaveri Basin. 146

Distance from the source (km) Distance from the source (km)

2000 X u T3 C '1000 -J C/3

Distance from the source (km) Distance from the source (km)

Fig. 3.12. B Plots showing the downstream variations in the SL Index for the tributaries in the Kaveri Basin. 147

Aivar Koraivar

Distance from the source (km) Distance from the source (km)

Distance from the source (km)

Kaveri

Distance from the source (km) Fig. 3.12. C Plots showing the downstream variations in the SL Index for the tributaries and the main channel of the Kaveri River. Prominent knickpoints on the Kaveri River with abnormally high values of SL Index at S: Shivasamudram and H: Hogenakkal Falls 148

Distance from the source (km) Distance from the source (km)

A garam Aru Kaundinya Nadi 100 - 300 200 - c 50 ■ 100 - 0 - 20 40 60 10 20 30 40 50 Distance from the source (km) Distance from the source (km)

C heyyar

Distance from the source (km) Distance from the source (km)

Tenner! Palar Main Channel

300 £ 200 ■ B

10 20 30 40 50 Distance from the source (km) Distance from the source (km)

Fig. 3.13. Plots showing the downstream variations in the SL Index for the tributaries and the main channel of the Palar River. 149

Nachikuppam Semmandakuppam

g "O *o c C/3

Distance from the source (km) Distance from the source (km)

Pambar Vaniar

..J W3•iJ C/3

Distance from the source (km) Distance from the source (km)

X £ -o C/3

Distance from the source (km) Distance from the source (km)

Fig. 3.14. Plots showing the downstream variations in the SL Index for the tributaries and the main channel of the Ponnaiyar River. 150

In addition to the plots (Fig. 3.12, 3.13 and 3.14), the rate of change (b-coefficient) in SL index was computed from the scatter plot by fitting a linear trend line. The slope (b- coefficient) of the regression line represents the rate of change of SL index. The slope of the linear trend line fitted to the scatter plot between SL Index and distance (Table 3.1). Negative values of b-coefficient imply that the stream gradient index (SL) decreases downstream. This is the typical characteristic associated with areas underlain by homogeneous lithologies. On the other hand, positive values of b-coefficient mean that the SL index increases downstream. This is an anomaly usually found in areas undergoing uplift or having differential erosional characteristics, due to variations in rock resistance or stream power. Most of the rivers in the Kaveri Basin exhibit positive rate of change in stream gradient index, which implies, downstream increase in the SL Index. The pattern for the Palar Basin is different. The major tributaries of the Palar and Ponnaiyar depict negative values of b-coefficient, that is, the SL Index decreases downstream. This may be due to the fact that the lower reaches of these rivers are alluvial and not affected by lithological variations.

1 2 3 4 5 Fig. 3.15. Box plots showing inter-basin and intra-basin variations in the rates of change of SL Index across different tributaries of the Kaveri, Palar and Ponnaiyar Rivers, I = Upper domain of Kaveri Basin, 2 = Middle domain of Kaveri Basin, 3 = Lower domain of Kaveri Basin, 4 = Palar Basin, and 5 = Ponnaiyar Basin. The dotted lines represent the median values, whereas the whiskers represent the maximum and the minimum values. The circles represent the outliers. 151

From Fig. 3.15 it is clear that the tributaries in the middle domain of the Kaveri Basin are characterized by high positive rates of change in SL Index, whereas those of the upper and lower domains display lower values of b-coefficient. It is evident from the figure as well as Table 3.3 that high values of b-coefficient are observed in case of Thattai Halla (14.15), Arkavathi (8.74), Dodda Halla (8.515), Shimsha (6.03) and Chinnar (3.985). All these tributaries belong to the middle domain of the Kaveri Basin. Furthermore, it is observed that almost all the tributaries in the Palar and Ponnaiyar Basins are characterized by negative values of b-coefficient suggesting no abnormality. This once again points out to the fact that the influence of lithology, structure and tectonics on the Palar and Ponnaiyar Rivers and its tributaries is modest. Another noteworthy point is that the upper reach of the Kaveri River channel is associated with high positive value of the rate of change in SL Index (3.47). This is because, in the downstream part, the river is on the verge of entering the gorge which leads to abrupt increase in channel gradient and hence the SL Index. The middle reach of the Kaveri River, specifically the stretch between Shivasamudram and Hogenakkal Falls (along the gorge), is characterized by high negative rate of variation in the SL index (-8.54). It is pertinent to mention here that the Kaveri River in this reach has developed an entrenched course where it crosses the Biligirirangan-Mahadeswaramalai (BR-MM) Ranges. The BR-MM Ranges are regarded to be horst mountains that were uplifted during the Quaternary (Valdiya, 2(X)1). This accounts for extremely high channel gradient in the upper part of the gorge and therefore, the SL Index is also higher. Downstream, the river is on the verge of leaving the gorge before flowing over the nearly flat Tamil Nadu Plains to debouch into the Bay of Bengal. Therefore, the channel gradient decreases and hence the rate of change in SL Index of the middle reach of the Kaveri River is negative.

3.8. Normalized SL Index: The next exercise was to identify the knickpoints and/or reaches in each of the longitudinal profiles of the tributaries of the Kaveri, Palar and Ponnaiyar Rivers which are characterized by abnormally higher values of SL Index. A segment with anomalously high 152

gradient index (knici

7 6 ”E 7 8 ” K 8 0 " E

concentrated in to the middle reach of the Kaveri River (enclosed by hollow square) 153

According to Seeber and Gornitz (1983), segments having SLA > 2 are regarded as significantly steeper, whereas the reaches with SL/k > 10 are classified as extremely steeper reaches. These attributes are characteristically associated with the areas undergoing uplift. In the present study, the knickpoints characterized by anomalously high SL values were identified using the criterion SL/k > 10 (Fig. 3.16). It is evident that these points are, more or less, concentrated in the middle domain of the Kaveri Basin. An attempt was made to identify whether there is any stretch of the rivers with a series of continuous points with extremely high values of SL Index. If there were two or more closely spaced points having normalized stream gradient indices greater than 10, then the reaches were regarded as steep stretches in the rivers and were mapped (Fig. 3.17). Fieldwork was carried out for actual verification of these steep stretches. Fig. 3.17 further illustrates and reconfirms the earlier observations that the middle domain of the Kaveri Basin is an area of high stream energy and hence strong disequilibrium conditions. Extremely steep stretches of the rivers (NSL > 10) are observed only in this domain of the basin. In the upper and lower domain of the Kaveri Basin as well as in the Palar and Ponnaiyar Basins, such steep segments are absent. The Kaveri exhibits such conditions of disequilibrium in the vicinity of the Shivasamudram Falls (Fig. 3.17 A). In addition, some tributaries of the Kaveri River namely the Shimsha (Fig. 3.17 B), Arkavathi and Thattai Halla are also characterized by the presence of steep lower segments. All these tributaries belong to the middle domain of the Kaveri Basin and display the characteristics of hanging tributaries (Kale, et al., 2014). Therefore, one important finding is that the middle domain of the Kaveri Basin is a region of extremely steep reaches with significantly higher values of SL index and NSL values. 154

Fig. 3.17. Steep stretches o f rivers in the Kaveri Basin. H: Hogenakkal Falls. Field-based photographs A) The majestic Shivasamudram Falls on the Kaveri River B) Incised reach of the Shimsha River, Karnataka.

3.9. Profile Concavity and Steepness: It has been observed in the Sections 3.3 and 3.4 that the majority of the tributaries do not display the typical concave-up long profiles as exhibited by the rivers draining areas underlain by uniform lithology and tectonic stability. Hence, the profile concavities and steepness indices were computed for each river in the Kaveri, Palar and Ponnaiyar River Basins. The two properties were derived from the power logarithmic regression relationship between upstream drainage area and channel slope. The upstream drainage area is considered as a proxy for discharge (Sklar and Dietrich, 1998; Zaprowski, 2005; Lee and Tsai, 2009; Perez-Pena et al., 2009). 155

The relationship that has been used to calculate the long profile concavity and steepness is described below: S = Eq. 3.5 where, S is the channel slope, A is the basin area, 0 is the concavity and K, is the steepness index. Whipple (2004) has classified river profiles on the basis of profile concavity (0) into four types; (a) rivers with low concavities (0 < 0.4) associated either with short steep drainage influenced by the debris flows or with downstream increase in the incision rates, commonly observed in case of areas undergoing uplift and dominated by knick points, (b) rivers with moderate concavities (0 = 0.4-0.7) found in actively uplifting bedrock channels in homogeneous substrates with uniform uplift, (c) rivers with high concavities (0 = 0.7-1.0) are a representative of downstream increase in the discharge along with decline in uplift, and (d) rivers with extreme concavities (0 > 1 or negative ). Concavities greater than 1.0 are the evidence of long-term tectonic stability. Negative values of concavities are typically associated with areas undergoing rapid rate of uplift or the presence of knickpoints. Sometimes, the presence of a large dam in the lower reach of a river also increases its concavity. The channel slopes were calculated from the SRTM-DEM derived elevation and distance data. For calculating the channel slope, the vertical interval was obtained by computing the difference in elevation between the point located at 1 km upstream and the second point situated at 1 km downstream. The distance between the two points measured along the course of the stream was regarded as the horizontal equivalent. The slope (or gradient) was obtained as the ratio between the vertical interval and the horizontal equivalent. The area upstream of the point was derived by the “Calculate Areas” command in the ArcGIS toolbox. Log-log relationship between upstream area and channel slope (Figs. 3.18 156

and 3.19) was derived to estimate the intercept or steepness index and the regression slope or concavity index for the tributaries of the river basins under consideration (Table 3.1).

Hemavathi Lakahamahantirtha 0.01 I 0.001 us ^ 0.0(X)1 y = 0.001 X-"' 2 r>= 0.017 0.00001 10 100 1000 lOOOO 100 1000 10000 Area(sq.km) Area(sq.km)

0.1 Suvarnavati 0.01 Kabbinr

2 0.001 0.0001 u y = 4 E - 0 5 x " ^ ” y = 0.132x-"“ r» = 0 . 0 1 r ’ = 0 . 6 8 0 3.000001 0.00001 100 1000 lOOOO 10 100 1000 10000 Area(sq.km) Area(sq.km)

0.1 Shimsha 0.1

g 0.001 g 0.001 1 E L. y = O.OOOx" '25 o y = 2E-06x«*'2 H = 0 . 0 0 7 * r> = 0 . 2 1 7 0.00001 0.00001 100 10(X) 1 0 0 0 0 100 100 0 10000 Area(sq.kin) Area(sq.km)

Dodda Halla Thattai Halla 0.1 0.1 .1

c 0.01 1 00'

♦♦ y = 0.023X-0 y = 0.002x» r> = 0.022 r » = 0 . 2 4 7 0.(K)1 0.001 10 100 1000 10 100 1000 Area(sq.km) Area(sq.km) Fig. 3.18.A. Power-law relationship between upstream drainage area and channel slope for the tributaries in the Kaveri Basin 157

Chinnar Palar 0.1 1

■o.1 0.01 0.01 £ *^.0001 y = Q .005x°% r» = 0.001 y = 1.012x-"*» r*= 0.244 0.001 0.0(X)(X)1 10 100 1000 lOO(X) 10 100 1000 10000 Area(sq.kin) Area(sq.km)

Nagavathi Sarabhanga 0.01

t g 0.001 ♦ c1 y = 0.062x-°5^ r»= 0.531 0.0001 10 100 1000 10000 10 100 IQOO 10000 Area(sq.km) Area(sq,km)

Noyyil 0.01

B)001 1 u y = 0.002x-«“ r» = 0.011 0.0001 10 100 1000 10000 Area(sq.km) Area(sq.km)

Amaravati 0.1

"O•S S 0.(X)1 u y = 4.337x'“ r» = 0.546 0.0(K)01 100 1000 10000 10 1(X) 1000 10000 Area(sq.km) Area(sq.km) Fig. 3.18.B. Power-law relationship between upstream drainage area and channel slope for the tributaries in the Kaveri Basin 158

Aiyar Koraiyar 0.01 0.01

eu B .Si 'Sa O y = 0.120x-o^ r2 = 0.79 r^ = 0.690

0.0001 0.0001 10 100 1000 10000 10 Area(sqi25f 10000 Area(sq.km)

Nandyar Uppar 0.01 0.01

•D 2 o 0.001 I 0.001

y = 0.227x-««* y = 0.067X-® H = 0.65 r2 = 0.55

0.0001 0.0001 100 1000 10 100 1000 Area(sq.km) Area(sq.kin)

Kaveri Channel Marudaiyar 0.01

I 0.01 £ 0.001 a ,— .•*— « f u09 o y = 0.031x^5'' 0.0001 ♦ * * t * H = 0.39 y = O.OOOxO"-’ ♦ = 0.003 0.0001 0.000001 10 100 1000 100 1000 10000 100000 Area(sq.km) Area(sq.km)

Fig. 3.18.C. Power-law relationship between upstream drainage area and channel slope for the tributaries as well as the main channel of the Kaveri River 159

Dinnekere Halla Malattar

Area (sq. km) Area (sq. km)

0.1 P o i t i i

I 0.01 u O1

0.001 100 1000 100(K) Area (sq. km) Area (sq. km) Palar Channel 0.1 Tenneri

g 0.001 1 0.01 %.00(X)l ■ y = 0.332X-' “ r» = 0 . I 4 5 O.(XXKXX) 0.0001 10 100 1000 UK) 1000 10000 10000 Area (sq. km) Area (sq. km)

Fig. 3.19. Log-log relationship between upstream drainage area and channel slope fo r the tributaries in the Palar Basin. 160

Nachikuppam Nadi Semmandakuppam

0.01

g u a

y = 0.079X r ^ = 0 . 5 6 7 0.001 100 1000 10000 Area (sq. km) Area (sq. km)

Vaniar Pambar

0.1 £ 1 0.01 y = 0.016x-o^ r^ = 0.013 0.001 10 100 1000 Area (sq. km) Area (sq. km)

T\irinjalar Ponnaiyar Main Channel 0.01 0.01

1.001 ■o I 0.001 2 CQ « y = 0.133x-«‘7 y = 0.003x-o'« r2 = 0.266 r» = 0.026 0.0001 0.0001 10 100 1000 10 100 1000 10000 100000 Area (sq. km) Area (sq. km) Fig. 3.20. Power-law relationship between upstream drainage area and channel slope for the tributaries in the Ponnaiyar Basin. 161

Upper Middle Lower 3 Domain D onkin Domain ___ \____ 1 \ r

5 I j i 1 0.

n n

1 2 .1 4 5 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24

River Numbers Fig. 3.21. Kaveri Basin: Variation in the long profile concavity across different tributaries. For names of the tributaries refer Table 3.1.

Palar Basin Ponnaiyar Basin i r

.1^ 1 2 3 4 5 6 7 8 9 10 II 12 13 14

River Numbers Fig. 3.22. Palar and Ponnaiyar Basins: Variation in the long profile concavity across different tributaries. The tributaries have been numbered as per Table 3.2 162

From Fig. 3.21 and Table 3.1, it is clear that most of the rivers in the middle domain of the Kaveri Basin exhibit extremely low concavities (0

3.10. Normalized Channel Steepness Index: Generally, the rivers tend to steepen their longitudinal profile with increasing uplift rate and/or strong lithological control because a high erosion rate is required to attain dynamic equilibrium. The constant in Eq. 3.5 is referred to as the steepness index of the river. It has been recognized that the values of steepness index (KJ give a direct measure of channel steepness. However, due to difference in the catchment area, the comparison on the basis of steepness index is not meaningful (Kirby et al, 2007). Hence, the normalized channel steepness index (Ksn) was calculated by using a reference concavity of 0.45 (Snyder et al., 2(XX); Whipple, 2(X)4) to facilitate corrparison between different rivers. It is pertinent to mention here that the value of reference concavity (0.45) is close to the mean value of concavity (0.47) obtained for the rivers in the Kaveri Basin. A strong correlation between incision rate and the normalized steepness index has been noted by various workers (Kirby et al., 2007; Goswami et al., 2012). Therefore, the normalized steepness indices of all the rivers under consideration were calculated by using the reference concavity of 0.45. Fig. 3.23 shows that the tributaries in the middle domain of the Kaveri Basin such as the Dodda Halla (Ksn = 60) and the Chinnar (Ks„ =45) are steeper than the rest. In the lower domain of the Kaveri Basin, only the Bhavani (Ks„ =53) appears as an outlier. The long profile of this tributary has a much steeper upper segment and the highest average stream gradient index. Furthermore, the highest elevation in the Kaveri Basin is observed in the headwaters of the Bhavani River (Dodda Betta - 2,636 m ASL). This tributary has been included in the lower domain simply because it drains into the Kaveri River downstream of Hogenakkal Falls, but it has all the typical characteristics of the tributaries of the middle domain. In comparison, the normalized steepness indices (Ksn) of the tributaries of the Palar and Ponnaiyar Rivers are much lower (Fig. 3.23) 164

60 n

50-

.40- I C/2 1 30-

'4 20 - zo 10^

0 ------1------1------1------1------1------1 2 3 4 5 Fig. 3.23. Normalized channel steepness index across different tributaries in the Kaveri, Palar and Ponnaiyar Basins, 1 = Upper domain of Kaveri Basin, 2 - Middle domain of Kaveri Basin, 3 = Lower domain of Kaveri Basin, 4 = Palar Basin, 5 = Ponnaiyar Basin. The dotted lines in the box represent the median values, whereas the whiskers represent the maximum and the minimum values. The circle represents the outlier.

3.11. Key Points from this Chapter; The following key and noteworthy findings emerge from the analysis of the SRTM-DEM derived longitudinal profiles of the Kaveri, Palar and Ponnaiyar Rivers and their major tributaries: • Although the longitudinal profiles are, by and large, concave-upward, linearity, convexity and breaks in the profiles are quite evident. 165

The long profile of the main channel of the Kaveri River is marked by a conspicuous absence of the upper steep segment. It is pertinent to mention here that although the river originates in the Western Ghat, in its upper reach the major part of its flow is over the Mysore Plateau. This probably explains the absence of upper steep segment in the longitudinal profile of the Kaveri River. Two prominent knickpoints at Shivasamudram and Hogenakkal are observed in the long profile of the Kaveri River. In the upper domain of the Kaveri Basin, the normalized longitudinal profiles of the tributaries such as Hemavathi, Lakahamahantirtha and Kabbini display little change in altitude with distance suggesting gentler reaches. This is typically the case associated with rivers and streams draining the Mysore Plateau. The tributaries that meet the Kaveri River in its middle domain especially its course between Shivasamudram and Hogenakkal Falls such as the Dodda Halla, Thattai Halla and Chinnar exhibit deviation from the normal. The long profiles of these streams are characterized by the presence of knickpoints and hence disequilibrium conditions. It appears that the middle domain of the Kaveri Basin is controlled by the regional structural fabric and lithology. The long profiles of nx)st of the tributaries in the Palar and Ponnaiyar Rivers as well as those in the lower domain of the Kaveri Basin also do not exhibit the typical concave-up profile one would expect in an area of homogeneous lithology and relative tectonic stability. In the lower domain of the Kaveri Basin two tributaries namely Bhavani and Amaravati display steep upper segments indicating intense erosion in the headwaters of these streams which constitute the Nilgiri Hills. Statistical modelling of the longitudinal profiles of the river basins under examination reveals that all the rivers in the Kaveri, Palar and Ponnaiyar Basins show the best fit for the linear or exponential regression model. The linear model fits well for the middle reaches of the Kaveri Basin which is an indicator of recent disturbances in this region. Semi-logarithmic plots of elevation versus distance reveal that almost all the rivers under examination display profile convexity, a signature of above-grade condition. 166

The average stream gradient (SL) indices of the rivers in the Kaveri Basin range from 11 to 239. High SL indices are concentrated in the middle domain. The upper and lower domains of this basin as well as the Palar and Ponnaiyar Basins are associated with fairly lower values of SL index. Most of the rivers in the Kaveri Basin exhibit positive rate of change in the stream gradient indices which means that the SL index increases downstream. This is an anomaly because the stream gradient index normally decreases downstream as a consequence of downstream flattening of the river profile. However, all the sub basins of the Palar and Ponnaiyar Basins exhibit normal pattern of downstream decrease in SL uidex. Furthermore, the tributaries in the middle domain of the Kaveri Basin such as the Shimsha, Arkavathi, Chinnar and Nagavathi exhibit higher rate of change in SL Index with distance. Extremely steep segments (knickpoints) of the rivers of normalized SL index > 10 are observed ^nly i» middle domain of the Kaveri Basin especially in the vicinity of the Shivasamudram and Hogenakkal Falls. Incised reach of the Kaveri River and many of its tributaries such as the Shimsha are signatures of intense fluvial erosion in these regions. In other parts of the Kaveri Basin as well as in the Palar and Ponnaiyar Basins, such steep segments are absent. ^ Most of the tributaries in the middle domain of the Kaveri Basin exhibit low values of concavity index (0). That is, the channel gradient does not decrease rapidly with catchment area. There are some tributaries in this domain, such as the Shimsha, Arkavathi and Thattai Halla which display negative values of concavity (0). In contrast, the tributaries in the upper and lower domains of the Kaveri Basin as well as in the Palar and Ponnaiyar Basins are characterized by higher values of concavity index. 167

The normalized channel steepness indices of the tributaries in the Kaveri Basin are much higher than their counterparts in the Palar and Ponnaiyar Basins. In the Kaveri Basin, the streams with higher values of normalized channel steepness index are confined to the middle domain, particularly in the entrenched reach between Shivasamudram and Hogenakkal Falls. The main conclusion of this chapter is that the tributaries in the middle domain of the Kaveri Basin are characterized by higher values of SL Index and normalized steepness index as well as lower values of profile concavity (0). Thus, the middle domain of the Kaveri Basin provides a number of signatures of litho-structural and/or tectonic control. In comparison, the upper and the lower domains of the Kaveri Basin as well as the Palar and Ponnaiyar Basins do not provide strong indications of tectonic deformation as well as control of lithology or structure. .