Chapter 5 Morphometric Control on Food Key Words: Morphometry, Linear Morphometry, Areal Morphometry, Relief Morphometry, Morphometric Control and Flood 5.1 Morphometric Aspects Drainage basin or basins should be the study area for the better understanding of the hydrologic system. The optimal and sustainable development of the resource is prerequisite so that it is assessed rationally to avoid any future problems regarding its qualitative and quantitative availability. Morphometry can be defined as Measurement of the shape, or geometry, of any natural form be it plant, animal or relief features (A.N. Strahler, 1969). In geomorphology morphometry may be defined as the measurement and mathematical analysis of the configuration of the earth s surface and of the shape and dimensions of its landforms (J.I. Clarke, 1966). Morphometry includes quantitative study of the area, altitude, volume, slope, profiles of land and drainage basin characteristics of the concerned area (S. Singh, 1972a). Morphometry is the evident expression of integrated structure, process and morphological shape. Its pattern expresses the underlying structure, rock resistance, exogenetic processes, morphological process-form its spatial distribution, hydrological actions and processes etc. Fluvial morphometry incorporates a long range of quantitatively definable aspects like linear or one dimensional aspect, areal or two dimensional aspects and relief or three dimensional aspects of fluvially originated landforms. Each parameter has credit to express the topographical and hydrological features. While studying flood character of a basin it is also essential to analyze the morphometric pattern of the basin because morphometric properties control the flood character in multifarious ways. Shape of the basin, channel sinuosity, drainage density, slope, hypsometric behaviour etc. control
flood routing, flood magnitude and spread. Therefore, this chapter will first analyze the morphometric pattern of basin and attempt to assess the determining role on flood behaviour. Table 5.1 Methods for the Calculation of Different Morphometric Parameters (River basin) Aspect Parameter Formula Reference Stream Order Hierarchical Rank Strahler, 1964 Stream Length Length of the Stream Horton, 1945 (Lµ) Mean Stream Lsm = (Lµ/Nµ) Nµ = Number of stream Strahler, 1964 L Length (Lsm) Length Ratio (Rl) Rl= Lµ/ Lµ- 1 Lµ = The total stream Horton, 1945 I length of µ; Lµ- 1 = Length in next lower N Law of Stream L = L1R L ( 1) L1 = Length of the 1 st Horton, 1945 Length (L ) Order E Bifurcation Ratio N Schumm, 1956 Rb Nµ = Number of stream; (Rb) N 1 A Nµ+1 = Number of stream in next higher R Mean Bifurcation Rb1 n1 Rb2 n2 Rbn nn Rbw Ratio (Rbw) n n n Strahler, 1957 A Law of Stream Number (N ) Channel Sinuosity Indices (CI) Law of Junction Angle (A ) Length of Over Land Flow (Lof) Constant Channel Maintenance (CCM) Form Factor (F) Compactness Coefficient (Cc) 86 1 2 n N = Rb(K ) k = highest of the basin; Horton, 1945 µ = basin CL Muller, 1968 CI = AL CL = Channel length; AL = Air length A = A1R A ( 1) RA = Junction ratio; A1 Schumm, 1956 =Angle of the 1 st (Lof) = ½ Dd Horton, 1945 CCM = 1/Dd Schumm, 1956 A F L 2 A= Basin area; L= Basin length Cc = P b / 2ПA P b = Perimeter of the basin Horton, 1932 Horton, 1932
R E A L R E L I E F Circularity Ratio 4 A C = basin perimeter (C) 2 Elongation Ratio 2 F R 4 R =Diameter of an equivalent circular area Drainage Density L (Dd) Dd A L = Length of the rivers; A= Area Stream Frequency N (Df) Df N = Number of river segments A Drainage Texture Dt = Nµ/P Nµ = Total number of stream in (Dt) all segments; P = Basin perimeter Areal symmetry Ar Aa (Aa) Al Ar = Area of the low area of the stream Al = Area of the more area of the stream Hypsometric Ls HI Integral Lus HI = Hipsometric Integral; Ls = Proportion of un eroded part; Lus = Proportion of eroded part Erosional Integral Ls EI 1 Lus EI = Erosional Integral Percentage h/h/a/a h & a = height & area between hypsometric two contours; H & A = Total Height and Area curve of the entire basin Average slope N I tan 636.6 N = number of contour cuttings per miles or km., I = contour interval, 636.6 = constant Mean and Median Z b = a1z1/ a1 Z b = mean elevation of Analysis the drainage basin, a1, a2 = area between two successive contours of the basin, z1, z2= mean elevation between two successive contours Relative relief Rr = (Rma Rmi) Rma= Relief maximum; Rmi= Relief minimum 87 Miller, 1953 Schumm, 1956 Horton, 1932 Horton, 1932 Horton, 1945 Pal, S. 2010 Strahler (1952) Strahler (1952) Strahler (1952) Wentworth (1930) - Smith (1935)
Dissection index Rr DI 100 Hx Hx =Maximum relief; Rr = Relative relief Ruggedness Rr Dd Rn Index K K = a conversion constant and is 1000; Rr = Relative relief; Dd= Drainage relief Relief ratio Rh=H /H +1 H = mean relief in a given basin; H +1 = mean relief of the next higher basin. Law of Basin H = H1RH 1 H1 = empirically Relief determined constant Slope Ratio Law of Channel Slope Rs = S /S +1 Rs = Slope Ratio, Sµ=Slope of given, S +1=Slope of next higher Dov Nir (1957) /Miller(1945) - - - Horton (1945) Horton (1945) 5.2. Linear Aspects Linear aspects includes stream ing, bifurcation ratio, length of stream, over land flow etc. These aspects help to explain the evolution of drainage basin, hydrological potentialities, chance of hydrological extremities or flood behavior, shifting course of river etc. Entire Basin as a Whole: Morphometric measurement for entire basin gives a generalize picture at a glance. Table 5.2: Linear aspects of drainage network of Mayurakshi River Basin River Stream Number of Total length Log Nu Log lu Basin u streams Nu of streams Lu Mayurakshi 1 st 3957 2365.5 3.5974 3.3739 2 nd 875 1340.5 2.9420 3.1273 3 rd 194 995.5 2.2878 2.9980 4 th 35 650.5 1.5440 2.8132 5 th 10 425 1 2.6284 6 th 2 195.5 0.3010 2.2911 7 th 1 214.5 0 2.3314 88
Bifurcation ratio Rb Mean bifurcation ratio Rbw 1 st /2 nd 2 nd /3 rd 3 rd /4 th 4 th /5 th 5 th /6 th 6 th /7 th 4.522 4.510 5.543 3.500 5.000 2.000 4.179 Length ratio Lb Mean 1 st 2 nd 3 rd /4 th 4 th /5 th 5 th 6 th length ratio /2 nd /3 rd /6 th /7 th Lbw 1.765 1.347 1.530 1.531 2.174 0.911 1.543 Table 5.3: Some Other Morphometric Aspects Length of Over Land Constant of Channel Channel Sinuosity Length of Trunk river Flow (Lof) Maintenance (CCM) Indices (CI) 0.609 0.821 1.715 288 KM The total number of the stream in Mayurakshi River basin is 5074 and total length of all segments of stream is 6487 km. The bifurcation ratio (4.179) for entire basin indicates high rate of stream integration. Bifurcation ratio is 4.179 means four smaller stream segments have merged to form one larger segment. High channel sinuosity index (1.715) refers relatively less resistance of the rocks and structures, greater chance of flood (table 5.3). 5.2.1 Stream Order (Nu) In the drainage basin analysis the first step is to determine the stream s. In the present study, the channel segment of the drainage basin has been ranked according to Strahler s stream ing system. According to Strahler (1964), the smallest fingertip tributaries are designated as 1. Where two first channels join, a channel segment of 2 is formed; Where two of 2 joins, a segment of 3 is formed; and so forth. The trunk stream through which all discharge of water and sediment passes is therefore the stream segment of highest. The study area is a 7 th drainage basin (Table 5.2). The total number of 5074 streams were identified of which 3957 are 1 st streams, 875 are 2 nd, 194 are 3 rd, 35 in 4 th, 10 in fifth, 2 in sixth and one is indicating 7 th streams. Drainage patterns of stream 89
network from the basin have been observed as mainly dendritic type which indicates the homogeneity in texture and lack of structural control. This pattern is characterized by a tree like or fernlike pattern with branches that intersect primarily at acute angles. The properties of the stream networks are very important to study the landform making process (Strahler and Strahler, 2002). Order wise total number of stream segment is known as the stream number. Horton s (1945) laws of stream numbers states that the number of stream segments of each forms an inverse geometric sequence with plotted against, most drainage networks show a linear relationship, with small deviation from a straight line. The plotting of logarithm of number of streams against stream is given in Figure 5.1, according to the law proposed by Horton gives a straight line. This means that the number of streams usually decreases in geometric progression as the stream increases. 5.2.2 Stream Length (Lu) Stream length is one of the most significant hydrological features of the basin as it reveals surface runoff characteristics streams of relatively smaller lengths are characteristics of areas with larger slopes and finer textures. Longer lengths of streams are generally indicative of flatter gradients. Generally, the total length of stream segments is maximum in first streams and decreases as the stream increases. The number of streams of various s in the basin is counted and their lengths from mouth to drainage divide are measured with the help of GIS software. Plot of the logarithm of stream length versus stream (Figure 5.2) showed the linear pattern which indicates the homogenous rock material subjected to weathering erosion characteristics of the basin. 90
Log of Stream Number Log of Stream Length Chapter -5, Morphometric Control on Flood Regression of logarithm of number of stream vs. stream 4 3.5 3 2.5 2 1.5 1 0.5 0 1 2 3 4 5 6 7 Stream Order u Regression of logarithm of stream length vs. stream 4 3.5 3 2.5 2 1.5 1 0.5 0 1 2 3 4 5 6 7 Stream Order u Fig 5.1 Fig 5.2 5.2.3 Bifurcation Ratio The term bifurcation ratio (Rb) is used to express the ratio of the number of streams of any given to the number of streams in next higher (Schumn, 1956). Bifurcation ratios characteristically range between 3.0 and 5.0 for basins in which the geologic structures do not distort the drainage pattern (Strahler, 1964). Strahler (1957) demonstrated that bifurcation ratio shows a small range of variation for different regions or for different environment dominates. The spatial variation of morphometric behaviour is very high all over the basin area. Bifurcation ratio is very high along 40 m. contour which indicates sudden break of slope. As large number of stream segments suddenly coalesce to each other, the formation of wider river channel, formation of micro fluvial deposits along topographical bent (40 m. contour), raising of hydrological potentialities of the down slope rivers, increasing rate of river bed deposition etc. have happened. The chance of flood extremities is also high. Very high degree of positive relationship between stream number and stream length indicates a fair degree of allometric growth of these two morphometric items. 5.3 Areal Aspects Area of a basin (A) and perimeter (P) are the important parameters in quantitative morphology. The area of the basin is defined as the total area projected upon a horizontal plane contributing to cumulate of all of basins. Perimeter is the length of the boundary of the basin which can be 91
drawn from topographical maps. Basin area is hydrologically important because it directly affects the size of the storm hydrograph and the magnitudes of peak and mean runoff. It is interesting that the maximum flood discharge per unit area is inversely related to size (Chorley, et al., 1957). The aerial aspects of the drainage basin such as drainage density (Dd), stream frequency (Fs), texture ratio (T), elongation ratio (Re), circularity ratio (C) and form factor ratio (Rf) were calculated and results have been given in Table 5.4. Table 5.4: Areal parameters Morphometric parameters Symbol/Formula Result Area (Sq. Km.) A 5325.00 Basin perimeter (Km.) P 488.00 Drainage density (Km./Sq. Km.) Stream frequency (No./ Sq. Km.) D = Lu/A 1.218 Fs = Nu/A 0.971 Texture ratio Dt = Nµ/P 10.397 Basin length (km.) Lb 166.55 Elongation ratio 2 F R 4 0.494 Circularity ratio 4 A C 2 0.281 Form factor ratio F A L 2 0.192 Compactness co-efficient Cc = P b / 2ПA 2.267 Basin (area) symmetry Aa Ar Al 0.448 92
5.3.1 Basin Symmetry Areal symmetry means the proportion of area in two sides of the trunk river. Noteworthy to mention that weighted basin asymmetry can be calculated as the ratio between two sides of the trunk river including areal extent, cumulative number of rivers, cumulative length of river etc. Here calculation has been done in regard to side having small areal extent: side having large areal extent (in case of Mayurakshi river it is left side 1648 sq. Km., right side 3677 sq. Km.). The basin asymmetry value (0.448) indicates that out of total basin area 30.94% area is at the left side and 69.06% area is found at the right side. Basin symmetry value = 1 means there is no disparity of areal extent between two sides of the basin and value more toward 0 means increasing trend of areal asymmetry. So, it can be said that the basin is asymmetric in terms of areal distribution. From this point another important conclusion can be drawn that the basin is to some extent tilted rightward. As a result of this flood tendency and magnitude are also more in the right hand side of the basin. 5.3.2 Form Factor Form factor value ranges from 0-1; if the value is toward 1 means circular basin geometry and 0 indicates absolutely elongated basin. F= 1 also signifies that the basin is characterized by nearly homogeneous structural pattern, morphogenetic characteristics and morphological process. But highly elongated basin signifies greater structure-topographical control over the river pattern. In Mayurakshi river basin the form factor value is only 0.192 which indicates fairly elongated river basin, so structure-topographical control is obvious fact. In general principle there is positive relation between form factor value and flood propensity. In Mayurakshi river basin although the basin is elongated and form factor value is very low but flood condition is grave. So, the presence of other factors is vital. 5.3.2.1 Elongation Ratio Schumm (1956) used an elongation ratio (Re) defined as the ratio of diameter of a circle of the same area as the basin to the maximum basin length. It is a very significant index in the analysis of basin shape which helps to give an idea about the hydrological character of a drainage basin. Values near to 1.0 are typical of regions of very low relief (Strahler, 1964). The value Re of the study area is 0.494 indicates that the low relief of the terrain and elongated in shape. 93
5.3.2.2 Circularity Ratio Miller (1953) defined a dimensionless circularity ratio (C) as the ratio of basin area to the area of circle having the same perimeter as the basin. He described the basin of the circularity ratios range 0.4 to 0.5 which indicates strongly elongated and highly permeable homogenous geologic materials. The circularity ratio value (0.281) of the basin corroborates the Miller s range which indicating that the basin is elongated in shape, low discharge of runoff and highly permeability of the subsoil condition. 5.4 Spatial Pattern of Basin Morphometry 5.4.1 Drainage Density Drainage density is the length of river per unit area. It is affected by the factors which control the characteristic length like resistance of weathering, permeability of rock formation, climate, vegetation etc. In general low value of Dd is observed in the region underlained by highly resistance permeable material with vegetative cover and low relief. High drainage density is noticed in the regions of weak and impermeable surface material and sparse vegetation and mountain relief. The mean value of Dd in Mayurakshi river basin is 1.218 km. /sq.km. which indicates the resistance permeable material with fairly vegetative cover and low relief. But as the spatial variation is concerned, the upper Mayurakshi basin indicates very high Dd value (5 to 8 km. per sq. km.). Therefore, the basin is weak and impermeable surface material and relatively greater topographical relief. But in the Lower Mayurakshi river the condition is completely opposite to the Upper Mayurakshi river basin. 5.4.2 Stream Frequency The average stream frequency is 0.971/sq.km. (table 5.4). The stream frequency is very high (5-8/sq.km.) in the Upper Mayurakshi river basin while it is low (1 or <1/sq.km.) in the lower basin. Greater stream frequency in the Upper basin indicates relatively steeper slope, greater relief variation and multifaceted slope directions. Very low stream frequency in the Lower segment of the basin says the monotonous flat slope with marginal relief variations. 94
5.4.3 Drainage Texture It is the total number of stream segment of all s per perimeter of that area (Horton, 1945). He considered that infiltration factor is the single important factor which influences drainage texture and considered drainage texture to include drainage density and drainage frequency. Smith (1950) has classified drainage texture into different coarseness zones. As per his classification, Mayurakshi river basin is included under fine drainage texture (Dt = 10.397) (table 5.4). Like drainage density and frequency, drainage texture is also very high (fine) in the Upper river basin and low (coarse) in the Lower segment of the basin. Textural fineness in the Upper catchment means diversity in landscape and opposite in the Lower catchment. Fig: 5.3 95
5.5 Relief Aspects Fig.5.4 Relief aspects or three dimensional features of a drainage basin involve area, volume and altitude. Some important aspect of relief properties includes hypsometric analysis, clinographic analysis, average ground slope, relative relief, relief ratio, dissection index, profile analysis of river basin and river channel etc. (S.Mukhopadhyay, M. Mukhopadhyay, S. Pal, 2010). In my present study, here I have included hypsometric analysis, relative relief, ruggedness index, dissection index etc. because these features are very important for any kind of watershed management. Table: 5.5 Relief parameters Morphometri Symbol/Formula Result c parameters Relative relief Rr = (Rma Rmi) Rma= Relief maximum; Rmi= Relief minimum (419 m 24 m) =395 m. Dissection Rr 94.27 index DI 100 Hx Hx =Maximum relief; Rr = Relative relief 96
Ruggedness Index Rr Dd Rn K K = a conversion constant and is 1000; Rr = Relative relief; Dd= Drainage density 0.481 Fig. 5.5 5.5.1 Hypsometric Analysis Hypsometry analysis deals with measurement of relationship between basin area and altitude of and thereby its stage of evolution, erosion potentiality etc. can be assessed. Hypsometric integral (HI) shows the how much portion of the total basin area are to erode. The hypsometric integral has been accepted as an important morphometric indicator for the stage of drainage development. A.N. Strahler (1952) suggested the relationship between HI and stage of drainage development in the following way. HI >0.6 or > 60% = Youthful stage HI = 0.6-0.35 or 60%-35% = Mature stage HI = <0.35 or <35% = old stage. In Mayurakshi river basin it is only 0.38 which means 38% area of the total land still to be eroded and river basin is at the old stage of the cycle of erosion. 97
>400 360-400 320-360 280-320 240-280 200-240 160-200 120-160 80-120 40-80 0-40 Cumulative h/h in % Chapter -5, Morphometric Control on Flood Table 5.6 Hypsometric Pattern of Mayurakshi River Basin Height Area in % of % of Cumulative Cumulative Cumulative Cumulative in m. sq.km. Height area % of height % of height % of Area % of Area 0-40 1842.63 0.83 34.60 0.83 100 34.60 100 40-80 753.21 2.54 14.14 3.37 99.18 48.74 65.39 80-120 1074.36 4.12 20.18 7.49 96.64 68.92 51.25 120-160 960.14 5.78 18.03 13.27 92.52 86.95 31.07 160-200 490.78 7.43 9.22 20.7 86.74 96.17 13.04 200-240 132.16 9.09 2.48 29.71 79.31 98.65 3.82 240-280 17.75 10.74 0.33 40.45 70.22 98.98 1.34 280-320 16.43 12.39 0.31 52.84 59.48 99.29 1.01 320-360 12.45 14.04 0.23 66.88 47.09 99.52 0.70 360-400 14.84 15.70 0.28 82.58 33.05 99.80 0.47 >400 10.25 17.35 0.19 100 17.35 100 0.19 2420 5325 100 100 HYPSOMETRIC CURVE 100 90 80 70 60 50 40 30 20 10 0 HEIGHT IN METER Fig. 5.6 98
% of area Chapter -5, Morphometric Control on Flood 40 Area Height Relation Mayurakshi River Basin 30 20 10 0 Ranges of height in M. % of Fig. 5.7 5.5.2 Relative Relief Relative relief or amplitude of relief is defined as differences between maximum height and minimum height. M.A. Melton (1958a & 1958b) assumed to calculate relative relief by dividing the difference between highest and lowest points of basin and basin perimeter. Here I calculate block wise relative relief within the basin area and formulate relation between flood height or flood stagnation with relative relief. From the calculation it is clear that there is a relation between relative relief and flood height and also flood stagnation period as coefficient of determination value (R 2 ) are 0.691 and 0.682 (vide table no.5.8 and 5.9). 5.5.3 Dissection Index Dissection index can be calculated as a ratio of maximum relative relief to maximum or absolute relief. It is an important indicator of the nature and magnitude of the terrain (S. Mukhopadhyay, M. Mukhopadhyay, S. Pal, 2010). Here, Dissection index of different blocks within the basin correlate with flood height and flood stagnation period of the basin (vide table no. 5.8 & 5.9). 5.5.4 Ruggedness Number Ruggedness generally means degree of corrugation of topography. Relative relief on the one hand gives altimetric differences in topography and on the other hand drainage density also intensifies the level of dissection.. Here, ruggedness index of different blocks within the basin correlate with flood height and flood stagnation period of the basin (vide table no. 5.8 & 5.9). 99
Flood Height in M. No. of Days Chapter -5, Morphometric Control on Flood 5.6 Relation between Morphometric Parameters and Flood Occurrences How morphometric parameters are related with flood parameters has been described in the following tables. Most of the morphometric parameters are negatively influencing on flood height and flood stagnation irrespective of linear, areal and relief aspects. It seems to be quite reverse that there is negative relationship between stream frequency, stream density and flood. It is true that in upper catchment area, the number of stream segments is more but these are small in length, less water potential and have good draining capacity. Relative Relief Vs Flood Height 2.5 Mayurakshi River Basin 2 1.5 1 0.5 0 Fig.5.8 y = -0.020x + 1.687 R² = 0.691 0 20 40 60 80 Relative Relief in M. 20 15 10 5 0 Disection Index vs. Flood Stagnation Mayurakshi River Basin Fig.5.9 y = -0.198x + 13.92 R² = 0.691 0 20 40 60 D.I. Value Table 5.7: Coefficient of Correlation and Co-efficient of Determination between Morphometry and Flood Height Correlation Coefficient of Variables Coefficient (r) determination Regression equation (R 2 ) Relative relief vs. Flood height -.645(**) 0.691 y = -0.020x + 1.687 Dissection index vs. Flood height -.746(**) 0.592 y = -0.022x + 1.882 Ruggedness index vs. Flood -.426(**) height 0.004 y = -0.047x + 1.212 Stream frequency vs. Flood height -.626(**) 0.003 y = -0.005x + 1.212 Drainage density vs. Flood height -.257(*) 0.002 y = -0.001x + 1.208 Drainage texture vs. Flood height -.614(**) 0.643 y = -1.814x + 1.885 100
Table 5.8: Coefficient of Correlation and Co-efficient of Determination between Morphometry and Flood Stagnation Variables Correlation Coefficient (r) -.589(**) 101 Coefficient of determination (R 2 ) Regression equation Relative relief vs. Flood stagnation 0.682 y = -0.166x + 11.84 Dissection index vs. Flood -.783(**) stagnation 0.691 y = -0.198x + 13.92 Ruggedness index vs. Flood -.446(**) stagnation 0.052 y = -1.279x + 8.221 Stream frequency vs. Flood -.669(**) stagnation 0.040 y = -0.145x + 8.224 Drainage density vs. Flood -.375(**) stagnation 0.040 y = -0.045x + 8.198 Drainage texture vs. Flood -.512(**) stagnation 0.499 y = -13.11x + 12.82 ** Correlation is significant at the 0.01 level (2-tailed). * Correlation is significant at the 0.05 level (2-tailed). Major Focusing Points: 1. Total number of the stream in Mayurakshi River basin is 5074 and total length of all segments of stream is 6487 km. 2. Bifurcation ratio is 4.179 means four smaller stream segments have merged to form one larger segment. 3. Channel sinuosity index (1.715) refers relatively less resistance of the rocks and structures, greater chances of flood 4. The form factor value is only 0.064 indicating fairly elongated river basin and greater structure-topographical control over the river pattern. 5. Drainage textural fineness in the upper catchment of Mayurakshi means diversity in landscape and opposite in the Lower catchment. 6. Area height relationship denotes that maximum area is covered by the river below 40 m. height which is the flood prone area. 7. There is a strong relationship between relative relief and flood height; relative relief and flood stagnation period; drainage texture and flood height etc.