Chapter 4 : Morphometric Analysis

Transcription

1 Chapter : Morphometric Analysis. 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., 98). 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., ). 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, 9). It was the year 9 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 9 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 9, 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 (9); Schumm (9); Chorley (9); Strahler (9); Melton (99); Morgon (9); Gregory and Walling (9). 8

2 The morphometric analysis using remote sensing and GIS techniques has been well attempted by Srivastava and Mitra (99); Srivastava (99); Singh and Singh (99); Nag (998); Srinivasa Vittala et al.; () and Nilufer Arshad and G.S. Gopalakrishna (8) 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.. 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. 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.), (ERDAS, ). The drainages have been delineated using merged satellite data of Geocoded FCC of bands on :, scale and SOI toposheets bearing number D/, D/, D/, D/8, 8P/, 8P/ and 8A/ have been used as a reference. Ground truth checks have been made during the field visits (Fig..). AutoDesk software like Auto CAD Map and ArcGIS softwares like Arcmap (v.9.) and ArcView (v..a) have been used for digitization and computational purpose and also for output generation (ESRI ArcGIS, ). The morphometric analysis can be achieved through measurement of linear, aerial and relief aspects of basin and slope contributions (Nag and Chakraborty, ). 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. 9

3 Figure.: Drainage pattern of Lakshmantirtha basin

4 . 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 watersheds which were demarcated according to the water divider (Fig..). 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: ) basic parameters, ) derived parameters, ) shape parameters ) dissection intensity parameters and ) relief parameters. All the parameters have been discussed in detail... Basic Parameters... 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 8 sq.km, and the area of each of the watersheds are shown in the Table.. Watershed is the smallest (A < 8.8 sq.km) and watershed 8 is the biggest (A>.9 sq.km), (Table.).... 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 9 km, and the perimeter of the watersheds is shown in Table.. Watershed has the smallest perimeter (P<.8) and the watershed 8 has the largest perimeter (P> 8.8) and coincides with highest value of A in the same watersheds, (Table.).

5 Figure.: Watershed boundary of Lakshmantirtha sub basin

6 ... Basin Length (L) Basin length has been given different meanings by different workers (Schumm 9; Gregory and Walling 9; Gardiner 9 and Cannon 9). According to Gregory and Walling (9), 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 km and the values of L for the watersheds are shown in the Table.. Watershed 8 is the longest watershed (L> 8. km) while watershed has the minimum value of L (L<.8 km), (Table.).... 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 (9) 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 (9) 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 (9) 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 (9) which is popularly known as Stream Segment Method. The order wise stream numbers for all watersheds are given in Table.. Out of these watersheds, watersheds and belong second order, watershed,,,,,,, and belong to the third order streams, watersheds,,

7 , 9,,,,, and are of fourth order streams and the remaining watersheds(,,, 8 and 9) 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 (9) 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..).... 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 (9) for all the watersheds and presented (Table.). Generally, the total length of stream segments is in maximum in first order streams and decreases as the stream order increases. In Fig.. 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 (9) which has received verification by accumulated data from many localities (Strahler 9; Schumm 9; Smith 98; Melton 98). However there is a sudden increase in length of streams of order III in (watersheds and ), order IV ( watersheds,,, and ) and stream order V (in watershed 8), 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 (99). Mostly all streams rise from the hilly terrains. It is noticed that stream segments up to the rd order traverse the high altitudes zones, which are mainly characterized by steep slopes, while the th, th and th order stream segments occur in comparatively plain land.

8 Watershed/ Stream Stream Order Stream Length Basin Perimeter Area I II III IV V VI I II III IV V IV V V IV V III IV III IV III IV III IV III III III III V V III IV IV IV IV II II Basin VI Table.: Basic parameters

9 Stream number... Lakshmantirtha Basin y =.8x +.8 R² =.9989 y =.8x +.8 R² = Stream Number Stream Length. Watershed.. Watershed. Stream number.. y =.x +. R² =.88. y =.x +. R² =.9. Stream number.. y =.8x +.9 R² =.99 y =.x +. R² = Stream Number Stream Lenght Stream Number Stream Lenght. Watershed.. Watershed. Stream number.. y =.x +. R² =.8 y =.89x +.9 R² =.99.. Stream number.. y =.x +.98 R² =.89 y =.x +.9 R² =.98.. Stream Number Stream Lenght Stream Number Stream Lenght

10 Stream number... y =.x +. R² =.988 Watershed y =.x +. R² =.... Stream number... Watershed y =.x +. R² =.89.. y =.8x +.. R² =.99 Stream Number Stream Lenght Stream Number Stream Lenght. Watershed.. Watershed 8. Stream number.. y =.98x +. R² =.88 y =.8x +. R² =.9.. Stream number.. y =.x +. R² =.899 y =.x +. R² =.99.. Stream Number Stream Lenght Stream Number Stream Lenght Stream number.. y =.8x +.. R² =.9 Watershed 9 y =.8x +. R² =.8 Stream Number Stream Lenght... Stream number.. y =.x +.8 R² =.. y =.x +. R² =.9 Watershed Stream Number Stream Lenght...

11 Stream number... Watershed y =.x +.9 R² =.99 y =.89x +.9 R² =.... Stream number... y =.89x +.9 R² =.8 Watershed y =.x +.9 R² =.9... Stream Number Stream Lenght Stream Number Stream Lenght Stream number.. Watershed. y =.x +. R² =.99 y =.8x +.88 R² =.8... Stream number.. Watershed y =.x +.8 R² =.99. y =.x +.8 R² =.9... Stream Number Stream Lenght Stream Number Stream Lenght Stream number... y =.8x +. R² =.88 y =.9x +. R² =.9 Stream Number Watershed Stream Lenght... Stream number... y =.x +.8 R² =.8 Watershed y =.8x +.88 R² =.9 Stream Number Stream Lenght... 8

12 Stream number.. Watershed. y =.x +. R² =.99 y =.x +. R² = Stream number... y =.89x +.9 R² =.99 Watershed 8 y =.8x +.8 R² = Stream Number Stream Lenght Stream Number Stream Lenght. Watershed 9.. Watershed. Stream number.. y =.x +.88 R² =.99 y =.9x +.9 R² =.9.. Stream number.. y =.x +. R² =.9 y =.9x +. R² =.9.. Stream Number Stream Lenght Stream Number Stream Lenght Stream number... Watershed y =.x +.9 R² =.9 y =.9x +.9 R² =.9... Stream number... Watershed y =.8x +. R² =.9 y =.99x +. R² =.9... Stream Number Stream Lenght Stream Number Stream Lenght 9

13 Stream number... Watershed y =.x +. R² =.9 y =.x +.9 R² = Stream number... Watershed y =.x +. R² =.9 y =.8x +.9 R² = Stream Number Stream Lenght Stream Number Stream Lenght Stream number... Watershed y =.9x +.98 R² =. y =.9x +. R² = Stream number... Watershed y =.x +. R² =.98 y =.8x +. R² =.... Stream Number Stream Lenght Stream Number Stream Lenght Figure.: Geometric relationship between stream order, stream number and stream length.. Derived parameters... 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'

14 Lu = Total stream length of its next lower order to the next lower order of stream segment. Horton's law (9) 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.). 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. to.. 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., ). 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, 9).... Stream Frequency (Fs) Horton (9) 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. 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)

15 ... 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, 9). Horton (9) considered the bifurcation ratio as an index of relief and dissections. Strahler (9) 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+ Where, Rb = Bifurcation Ratio Nu = Total number of stream segments of order 'u' Nu + = Number of segments of the next higher order It is observed from Table. that the Rb is not same from one order to its next higher order. According to Strahler, 9 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. and the values of all the watersheds vary from... The lower values of Rb are characteristics of the watersheds which have suffered less structural disturbances (Strahler, 9 and Nag, 998).... RHO coefficient (RHO) Horton (9) 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

16 Rb: Mean Bifurcation Ratio Horton (9) 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.8 and for the watersheds it varies from..8 (Table.). Watershed,, AND 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... Shape parameters... Elongation ratio Elongation ratio (Re) is the ratio between diameters of a circle of the same area to the basin length (L) (Schumm, 9)..8 /, Where, Re = Elongation Ratio A = Area of the Basin (Sq.Km) Pi = 'Pi' value i.e.,. Lb = Basin length A circular basin is more efficient in the discharge of run off than an elongated basin (Singh and Singh, 99). The values of Re generally vary from. to. over a wide variety of climatic and geologic types. Values close to. are typical of regions of very low relief, whereas values in the range..8 are usually associated with high relief and steep ground slope (Strahler, 9). The Re of watersheds of the study area varies from.. (Table.). The low values of Re in case of watersheds which their values are between..8, reveal

17 an elongated shape and indicate higher relief and steep slope. The Value of Re for the whole basin too is. which indicates an elongated shape. While very high Re values.8. and greater than, 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.... Circularity index (Rc) According to (Miller, 9 and Strahler 9,) 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 = * * A / P² Where, Rc = Circularity Ratio = 'Pi' value i.e.,. A = Area of the Basin (Sq.Km) 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. while the Rc calculated for its watersheds are shown in Table.. The value of Rc of Lakshmantirtha basin clearly shows lack of circularity in shape. This is because the value is less than.. Almost all the watersheds are showing values less than., which indicates an elongated shape, while the watersheds,,, and are more or less circular in shape.

18 Watersheds Elongation ratio Circularity Ratio Form factor W... W... w..8. w.8.. W.8.. w..8. w... w w9... w... w... w.8..8 w.9.8. w.9..8 w.8..8 w..8.8 w... w8..8. w9...8 w.9.. w..8. w... w... w.8.. W... W... basin... Table.: Shape parameters

19 Watershed/ Elongation ratio Stream Length Ratio Mean Stream FS RHO Basin Rb Rb Rb Rb Rb Mean Rb I II III IV V Length ratio W W W W W W W W W W W W W W W W W W W W W W W W W W Basin Table.: Derived parameters

20 ... Form Factor According to Horton (9), 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 A = Area of the Basin (Sq.Km) Lb² = Square of Basin length Rf value of the basin is. and the value for all the watersheds are shown in Table..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, 9). From the shape parameter analysis, one thing which is very clear is that all the 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, 9). The relationship among form factor, circularity ratio, elongation ratio and length of overland flow in each sub watershed has been presented in Fig water shed Form factor Circularit y ratio Elongati o ratio Figure.: The relationship among form factor, circularity ratio and elongation ratio

21 .. Parameters for Dissection Intensity... Drainage density (Dd) Horton (9) 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 A = Area of the Basin (Sq.Km) Dd is an indicator of basin dissection. Langbein (9) recognized the significance of Dd as a factor determining the time of travel by water and he also suggested a drainage density varying between. and.9 km/sq.km in humid region with an average density of. 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 (998), 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. 8

22 follows: Smith (9) has classified drainage density into different textures as Drainage Density (km/ sq.km) Texture < Very coarse Coarse Moderate 8 Fine >8 Very fine Table.: Classification of drainage density (after Smith, 9) The parameters like resistance to erosion of rocks, infiltration capacity of land and climate conditions influence the drainage density (Vestappan 98). Drainage density of the Lakshmantirtha basin as a whole is. and those of the watersheds are shown in Table.. According to the classification given by Smith (9), The Dd of the watersheds and the basin are all less than 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 (.8) with Fs values of the watersheds and the basin (Fig.). This was estimated by using the SPSS (V.) statistical software. According to Melton (98), 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, 998). 9

23 Watershed/basin Drainage Density Drainage Texture Length of over land flow W..8. W... w... w... W.8.8. w..98. w.8.8. w8.9.. w9... w.9.9. w..9. w... w.9.9. w..8. w.9.8. w... w.9.9. w w w... w... w..8. w... w.8..8 w.99.. w...9 basin..9. Table.: Dissection intensity parameters Drainage Density Fs Drainage Density Pearson Correlation.8 ** Sig. (-tailed). N Fs Pearson Correlation.8 ** Sig. (-tailed). N **. Correlation is significant at the. level (-tailed). Table.: Correlation table between stream frequency and drainage density variable 8

24 Figure.: Scatter plot matrix shows the correlation between Fs and Dd... Drainage texture (T) An important geomorphic concept is drainage texture which defines the relative capacity of drainage line (Smith, 9). 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 9), (Table.). 8

25 T Value Drainage Texture < Coarse Intermediate Fine > Ultra f Table.: Classification of drainage texture (after Smith, 9) The T of the Lakshmantirtha basin as whole is.9 while that of the watersheds are shown in Table.. The T values of all the watersheds are below and belong to the coarse texture.... 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, 9). 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 = / Dd *, Where, Lg = Length of Overland flow Dd = Drainage Density Table. reveals that the Lg is more in watershed as drainage density is the least in this watershed when compared to remaining watersheds. The computed value of Lg for all watersheds varies from. to.9. A high negative correlation (r=.888) is seen between the drainage density and length of over land flow and by plotting a correlation matrix, using SPSS software (v.), this can be clearly seen in Fig... 8

26 Figure.: : Scatter plot shows the correlation between Dd and Lg.. Relief aspects... 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.... 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. 8

27 ... 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 9). In the present study the basin relief of the basin is 8 m and for the watersheds the values vary from m to 8 m (Table.8).... Relief Ratio: According to Schumm (9), the relief ratio is the dimensionless heightlength 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 8

28 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 subwatersheds of a given drainage basin (Gottschalk, 9). In the present study, the values of Rh are given in Table.8. The relief ratio of the whole basin is. and the values for the watersheds range from. to.). It is noticed that the high values of Rh indicate steep slope and high basin relief (8 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, 98).... Relative relief (Rr) Melton (98) 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 (98) has been adopted for the present study and represented in Table.8. It can be seen from table that the maximum value of Rr observed in watershed (.) and the minimum in watershed (.8). 8

29 ... 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.9 and the values for the watersheds are presented in Table.8 and range between.., showing low to moderate gradient.... 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, 98).By using the following formula ruggedness number is calculated. Nr = Dd * H / 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 8

30 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.8. High value of Nr for the basin (.) indicates that lower order streams which extend very close to the water divide. Sharma (98); Prasad (98); Balasubramanian (98) and Venugopal (988) have also observed same type of results in the river basins of hard rock areas of South India.. 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.). Using the contour reading values the relief map was prepared by the help of Arcview (.a) software (Fig.. and.8). The topographic map of the study area also was prepared using Global Mapper software (v.) (Fig..9). In the Fig..9 the profile of the terrain is shown from the southwest (SW) to northeast (SE). In both the figures Fig..8 and Fig..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. 8

31 Figure.: map of the drainage basin of Lakshmantirtha 88

32 Figure.8: map of the drainage basin of Lakshmantirtha 89

33 Figure.9: Profile of the drainage basin of Lakshmantirtha. 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, 9) 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., 998). Hypsometric curves (HC) and hypsometric integrals are important indicators of watershed conditions (Ritter et al. ). 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., 99). In the present study Hypsometric curve is obtained by plotting the relative area along the abscissa and relative elevation along the ordinate. 9

34 Basin / Watershed Relief Elevation in 'm" Max H Min H basin relief Longest Axis L Relative Relief Relief ratio (H h)/l Gradient Elevation Source a mouth b Height (a b) Longest axis L Ratio (a b)/l Ruggedness No. (Nr) Basin Table.: Relief parameters 9

35 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., and Ritter et al., ). The resulting curve called the hypsometric curve starts at the top left hand corner at. and ends at the bottom right hand corner at. (Fig..). 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 (9), the entire period of cycle of an erosion of a basin can be grouped in to three stages viz., monadnock (old) (Hsi.), in which the watershed is fully stabilized; equilibrium or mature stage (. Hsi.); and inequilibrium or young stage (Hsi.), in which the watershed is highly susceptible to erosion (Strahler 9; Sarangi et al., ), (Fig..). Figure.: Cycle erosion of a basin (after Strahler, 9) 9

36 .. 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: ) Integration of Hypsometric Curve ) Use of the Leaf Area Meter (LAM) ) Use of the Planimeter Equipment ) 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 (R ) value. The equation was further integrated within the limits of to (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... 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 watersheds are presented in Table.9. Relative height (h/h) basin y =.8x +.9x 8.x + 8.x.x +.9 R² = Relative area (a/a) Figure.8: The fitted equation of the hypsometric curves for the basin 9

37 Basin Watershed Watershed Watershed Watershed Contour values Relative area (a/a) 9 Relative height Hypsometric Integral...8..

38 Watershed Watershed Watershed Watershed 8 Watershed 9 Watershed Watershed

39 Watershed Watershed Watershed Watershed Watershed Watershed Watershed 8 Watershed 9 Watershed Watershed

40 Watershed Watershed Watershed Watershed Watershed Table.: Relevance of relative area, relative height and Hypsometric Integral (HI) on Watershed Hydrologic Responses The HI value of Lakshmantirtha basin (.) indicated that.% the original rock masses still exist in this basin. The estimated HI values reveal that the basin (.) 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., ) unless there is very high intense storms leading to high runoff peaks. According to Omvir Singh (8), the HI values less than. 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. (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. 9

41 Legend: X axis: Relative area (a/a) Y axis: Relative height (h/h) basin w w w w w w w... 98

42 w w w w w w w w... 99

43 w w w w w w w w...

44 w w w... Figure.9 : Hypsometric curve of the basin and its watersheds. 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 (9) who introduced some solutions in hydrological modelling. Later on many other workers like Wong (99); Wallis (9); Shukla and Verma, (9) and Mishra and Satyanarayana (988), also used different statistical methods like cluster analysis and

45 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 (9). A correlation matrix was first computed in the first step for the given geomorphic parameters (Table.). 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 >. The fourteen variables were reduced to four factors. The factors account for 8% 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.). The factor loading is a measure of the degree of closeness between variables and the factor. By observing the correlation matrix on the 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 (V), the variables were further classified as factors and these factors having one or few variables in each (Table.) As shown in the Table., the variables are classified in to factors, which are discussed as bellow: Factor : This factor includes the area, perimeter and the basin length of the watersheds. Factor : Drainage density and stream frequency Factor : Relative relief and Rugedness number Factor : Elongation ratio, Circularity ratio and form factor Factor : Bifurcation ratio

46 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=.8) 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 is termed as the relief parameter and exhibits a high correlation between relative relief and Nr (r=.8). 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. 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.. Significance Laskmantirtha basin and its 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.

47 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 Perimeter Basin Length Stream Length Ratio(mean) Drainage Density Elongation ratio Circularity Ratio Form factor Fs Relative Relief Nr Bifurcation Ratio(mean) Table.: Correlation matrix of morphometric units

48 area.9 Perimeter.8 Basin Length.9 Component Stream Length Ratio(mean) -. Drainage Density.89 Elongation ratio. Circularity Ratio. Form factor. Fs.8 Relative Relief.9 Nr..8 Bifurcation Ratio(mean).9 Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in iterations. Table.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 factors.