THE BRAHMAN BASN 11 BVARATE ANALYSS OF MORPHOMETRC VARABLES AVERAGE RELEF AND OTHERS. RELATVE RELEF AND OTHERS DSSECTON NDEX AND. OTHERS AVERAGE SLOPE AND OTHERS ROUGHNESS NDEX AND OTHERS DRANAGE DENSTY AND OTHERS STREAM FREQUENCY 8 OTHERS SUPERMPOSED REGRESSON LNES
THE BRAHMAN/ BASN 1 1 BVARATE ANALYSS OF MORPHOMETRC VARABLES Bivariate relationships such as coefficient of correlation (r), coefficient of determination (R 2 ) and linear, regr.ession are used to show the nature and degree of relationship between two variables. t is noted that in any such study, correlation coefficient (r) can show a range from + 1 to- 1. When correlation coefficient is+ l,the degree of relationship between two variables is perfectly positive and when it is -1, the. degree of correlation is considered to be perfectly negative. When the correlation coefficient is zero, there is no relationship between two variables. Thus, higher positive and negative values infer correspondingly higher positive or negative correlations.
w CD TABLE 11.1 B VAR J ATE RELATONSHP. BETWEEN AVERAGE RELEF AND OTHER MORPHO'METRC VARABLES SL No. Relationship between Coefficient o f correlation ( r) Coefficient of Determinati on R2 (in%) Linear Regression Equation (Y = a + bx) 1. Average Relief (X) & Relative Relief (Y) 0.9187 84.3973-17.295881 + 0.456065 X 2. Average Relief (X) & Dissection ndex (Y) 0.7774 60.4371 0.074090 + 0.001099 X 3. Averaae Relief (X) & Drainge Density (Y) 0.6800 46.2405 O. 697876 + 0. 0054 30 X. 4. Average Relief (X) & Drainage Texture (Y) 0.0808 o. 6530 0.998611 + 0. 000361 X 5. Average Relief (X) & Stream Frequency (Y) 0.6983 48.7657 1.052384 + 0. 016910 X 6. Average Relief Average slope (X) & ( y) 0.9249 85.5470 0.988155 + 0. 032630 X 7. Average Relief Roughness ndex (X) & 0.9120 83.1749 -... 1.496165 + 0.047275 X..., _...
[ MA TR/X OF CORRELA T/ON CO-EFFC/ENTi_] l A.R. R.R. D.. R.. A.S. S. F. D. D. D. T. A. R. 9181 7774 9120 9249 6983 6800 0808 R. R. 8942 9764 9890 6303-5954 0229 q D.. 8994 9134 6961-6449 - 0761 j R.. -9853-6563 '. 6133-0156 A.S. 6904 6514-0387 S. F -9545-1415 D. D. - 1897 D.T --. -- A.R. Average Relief A.S Average Slope R.R. Relative Relief S.F Stream Frequency D./. Dissection ndex D.O. Drainage Density R.. Roughness ndex D.T. Drainage Texture FG. 11.1
RELATVE RELEF & OTHERS 386 to other morphometric variables except drainage texture. The high average relief areas are concurred by low drainage density, although there are some small patches where the areas have higher zones of density. The high average relief zones are mainly confined to the upper middle parts of the Basin where dense forests protect the surface from rain drops and a ccount for the drainage density of l ow value. The average relief and drainage texture actually show no rel ationship ( r = 0.0808 ).! The morphometric variables like average slope, roughness index, dissection index,strea m frequency are positively correlated with average relief a nd degree of correlation is very high. 11. 2. RELATONSHP BE''t-'EEN RELATVE RELEF & OTHER VARABLES Like average relief with others shows high positive correlation with relative relief also other. morphometric variables except drainage texture (Fig. 11.1). Table (11.2) gives a vivid picture how the rela tive relief is related to other morphometric v a riables. Correlation coefficient can be kept into two distinct groups according to their nature : (a) variables showing strong correlations and (b) variables which are weakly
Linear Regression Equation. (Y = a + bx) c w (J) -...J TABLE 11.2 B VARATE RELAT ONSHP BETWEEN RELATVE RELEF AND OTHER MORPHOMETRC VARABLES Sl. No. t t t : Coefficient of : Coefficient of : Relationship between Correlation. : Determination. ( r) : R 2 ( in %) 1. Relative Relief (X) & Dissection ndex (Y) 0. 8942 79.9575 0.110992 + 0.002546 X 2. Relative Relief (X) & Roughness ndex ( y) 0.9764 95. 3354 0. 355815 + 0.101950 X 3. Relative Relief (X) & Average Slope (Y) 0. 9890 97. 8125 0.292997 + 0.070280 X 4. Relative Relief (X ) & Str eam Freque nc y (Y) 0. 6 303 39.7278 1. 9 15237 + 0. 030743 X 5. Relative Relie f (X ) & Drainage Density ( Y ) o. 5954 35. 4 501 0.985248 + 0. 030743 X 6. Relative Relief (X) & Drainage Texture (Y) 0.0229 0. 0524 1.032778 + 0.000207 X
[MATRX OF CO-EFFCENT OF DETERMNATONS - - A.R. R. R.. D.. R.. A.S. S. F. D.O. D. T. A. R. 84 94 80 44 83 17 85 55 48 77 46 24 6530 R. R. 79 96 95 34 97 81 39 73 35 45 0524 D. /. 80 89 83 43 48 46 q41 59 5791 R.. 97 09 43 07 37-61 0243 i A.S. 47-66 42-43 1499 S. F. 91 12 2 003 D. O. 3 599 D. T. -- - A.R. Average Relief A.S. Average Slope R.R. Relative Relief S. F. Stream Frequency 0. 1. Dissection ndex D.O. Drainage Density R.. Roughness ndex D.T. Drainage Texture F G. 11.2
RELAT VE RELEF & OTHERS 38 8 correla ted. Of t hese var iabl es r o ughness i ndex, average slope and dissection index are highly correlated with relative relief. This type o f correlat i ons i s accepted as all of them are relief properties. On the o ther hand drainage properties such as dra inage densit y, d r a inage texture. a nd stream fre- u ency show a weak pesitive cor rela t i ons with r e lative relief. The weakest among these correlations is that- between relative relie f a nd drainage t exture, the r value being + 0.0229 (Fig. 11.1 ). n cas e o f drainage density and stream frequency, the r val ues are+ 0.5954 a nd+ 0.6303 respectively. 11. 2.1. THE RELATVE REL EF AND DSSECTON NDEX These variabl es show high positive correlation. The high relative relief zones a r e occupi ed by high dissection areas. The 79. 96% v a r iati o n i n dissection index is explained alone by r elative r eli e f (Fig. 11.2).The two maps of relative relief and dissect i on index s how close relationship both visua lly a nd statistically. 11. 2.2. THE RELATVE REL EF AND ROUGHNESS NDEX These a r e also h ighly correlated. The degree of cor r e lation is revealed by r value whi ch is 0. 9764. The
RELATVE RELEF & OTHERS 390 roughness of the Brahmani Basin is controlled by relative relief by 95.34%. The regression coefficient (b) of the analysis shows that \vith increase in relative relief the roughness values do increase. 11.2. 3. THE RELATVE REL EF AND AVERAGE SLOPE Slope is the i nherent property of landscape.t is the major parameter which a c t ually controls the landscape feature. The a verage slope shows a highest correlation of 0. 980 with relative rel i e f in the Brahmani Basin (Fig. 11.1). The coefficien t o f detgrmination reveals that relative relief causes t he v a r iation of 97. 8 1% in average slope (Fig. 11.2). The regression coef ficient b shows very significant increase in average slope with i ncrease in relative relief. 11.2.4. THE RELATVE REL EF AND STREAM FREQUENCY The relative relief and stream frequency maps show that appa rently high relative relief zones are. covered by high stream f r equency. Though high stream frequency values f all in the high relative relief zones, these values lie at the periphery of the high relative relief boundary.the probab l e cause is the existence of ephemeral rills which develop on the high relative relief zones and integrate into streams at the base of these slopes. The correlation between them is
RELATVE RELEF & OTHERS 391 however weak ( 0.6303) and relative relief does contribute only 39.73% in the variation of stream frequency (Fig. 11.1 & 11.2). So, we are to incorporate other factors for the analysis of the stream frequency in the Brahmani Basin like lithology, soil, slope and vegetation cover, etc. 11.2. 5. THE RELATVE RELEF AND DRANAGE DENSTY The relative relief and drainage density maps in general show a relationship, which is expressed by r value of 0.5954 (Fig. 11.1). t is observed that high relative relief areas are not always followed by high drainage density zones. For this reason the coefficient of determination has been implied to identify the percentage contribution of relative relief on the variation of drainage density in the Brahmani Basin. The relative relief does alone only cause 35.45% variation in drainage density (Fig. 11.2). The regression coefficient b does show positive increase, but it does not necessarily imply a significant one for the drainage density. 11.2.6. THE RELATVE RELEF AND DRANAGE TEXTURE The relative relief and drainage texture maps show a correspondence in some cases and in rrost cases they do not. This is evident from the r value which is ve ry weak(0.0229}. so, the contribution of relative relief on the variation of
D SSECTON NDEX & OTHERS 92 ' drainage texture is onli 0.05%. The drainage texture, therefore, doe s not depend on relative relief as revealed from the analysis of r, R 2 and b. 11. 3. RELAT ONSHP BETWEEN DSSECTON NDEX & OTHER VARABLES The dissection ind ex is also considered as an independent variable likel y t o h ave a fair degree of cor relation with other variables. The correl a tion coefficient, coefficient of determina t i on a nd regress ion have been calculated from the data extracted from topographical sheet (1:50,000) of the Brahmani Basin a nd are tabulated (Table 11.3). t is v isualized f rom the table that dissection index i s strongly c or re l aed with relief properties, average slope (+ 0. 9134) a nd r oughness index (+ 0.8994).There exists s t r ong positive corr ela tion between dissection index average slope and dissection index and rou9hness index. and This is because relativ e rel ief is a common element for dissection index, a verage s lope and r oughness index. Again if the amplitude of relie f tends to i ncr ease with a consta nt distance the values o f aver age slope a nd roughness index will a lso increase. Thus lt may be i nfe rred t hat all these v a r iabl e s are closely linked up with each o ther i n a concealed t ie of relative relief. So i t is commonly found that i n t h e highly dissected parts o f the Basin, all t hese variab les are higher.
X X X X w \0 w TABLE 11.3 BVARATE RELATONSHP BETWEEN DSSECTON NDEX AND OTHER MORPHOMETRC VARABLES Sl. No. Relationship between Coefficj.ent of Correl a tion (r) Coefficient of Determination R2 (in%) Linear Regression Equation ( Y = a + bx) 1. Dissection ndex (X) & Roughness ndex ( y) 0.8994 80.8920-2.6762 + 32.981481 2. Dissect i on ndex (X) & Average Slope o. 9134 83.4299-1.809259 + 22. 796296 3. Dissection ndex (X) & Stream Frequency (Y) 0.6961 48.4555 0.604815 + 11.925925 4. Dissection ndex (X) & Drainage Density (Y) 0.6449 41.5896 0.586667 + 03.666666 5. Dissection ndex (X) & Drainage Texture - 0.0761 oo. 5791 1.088148 + (-.240741) X i:: ' '------
ROUGHNESS NDEX & ohers 394 From the Table ( 11.3) it i s a lso v i sua lised that the correl ation bet ween dissection index and other drainage properties like s t ream f req uency, drainage density and drainage textur e i s r e l a t i v e l y weak. This is because of the fact that drainage properti es are not solely determined by the nature of rel ief properties of a n a rea. Rather it is the cumulative effect of several other var iables such as structure a nd lithology, rainfall dnd rat e o f evapotranspirati on, etc Dissection index a nd drai nage texture present negative correlation of only- 0.0761, which is poor in relationship. so the coefficient of determination is na1u trally poor,which is only 0.58%. This analysis may suggest us that drainage texture in the Basin is not due t o the dissection of the Basin. The regression coefficient b (-0.2407) a lso recommends this idea. 11.4. ROUGHNESS NDEX AND OTHER MORPHOMETRC VARABLES The roughness index a nd other variables of morphometry show the correlation which are noted in the Table 11.4. From the Table 11. 4 it is clear that the degree o f correlation coefficient betwe e n r oughness, j_ndex and ave r age slope is highest of the lot (the val ue is +0.9853)indicating that there lies a better positi v e correlation between thee two vaziables. t i ndic a t es that roughness index increases
w 1.0 lj1 TABLE 11. 4 BVARATE RELATONSHP BETWEEN ROUGHNESS NDEX AND OTHER VARABLES Sl. No. Relationship between Correla t i on o f Coeffi cient ( r) Coefficient of Dete rmina 1:.ion R2 (in%) Linear Re gression Eq uation ( Y = a + bx) 1. Roughness ndex ( X) & Average Slope ( Y) 0.9853 97. 0856 0. 1 2 1 319 + 0.670582 X 2. Roughness ndex (X} & Stream Frequency (Y ) 0.6563 4 3. 07 30-1.788291 + 0. 306574 X 3. Roughness ndex ( X } & Drainage Density (Y) 0. 6133 37.6137 0.949710 + 0. 094462 X 4. Roughness ndex (X) & Dra inage Texture 0. 01 56 0 0.024 3 1.034710 + 0.001349 X e
AVERAGE SLOPE & OTHERS 396 degree of slope. The coefficient of determination for the case is obviously high (97.09%). The table also reveals that the correlation between roughness index a nd drainage properties such as drainage density and stream frequency is medium. They are + 0.6563 and + o. 6193 respectively. But roughness inde>: and drainage text ure are ve ry weakly corre l ated. These two variables present correl ation of only + 0. 1 56 which is very poor in relationship. so the coefficient o f determination (0.0243%) is also very :weak. 11.5. AVERAGE SLOPE AND OTHER MORPHOMETRC VARABLES Coefficient of correlation {r), determination (R 2 ) and r egression coefficient values between average slope and other morphometric variables have been calculated and furnished in t h e Table 11.5. Among the variables the relationship between averae slope and stream frequency is highest denoting + 0.6904 and the de.termination is 47.67% for the variation of stream frequency accounted by average slope. There is weak positive correlation (+0.0387) between average slope and drainage texture. correlation coefficient of the variables average s l ope and drainage density is medium (+0.6514). The average slope contributes 42. 43% for the variation of drainage density.
t,-- TABLE 11.5 BVARATE RELATONSHP BETWEEN AVERAGE SLOPE AND OTHER VARABLES Sl. No. Relationship between Correlation of Coefficient ( r) Coefficient of Determination R2 (in%) Linear Regression Equation (Y = a + bx) 1. Average Slope (X) & Stream Frequency (Y) 0.6904 47.6652 1.686822 + 0.473883 X 2. Average Slope (X) & Drainage Density 0.6514 42.4322 0.914576 + 0.147427 X 3. Average Slope (X) & DYainage Texture (Y) 0.0387 00.1499 1.026510 + 0.004905 X <".:--
STREAM FREQUENCY & OTHERS 398 11.6. DRANAGE DENSTY AND OTHER MORPHOMETRC VARABLES Following the same procedure the correlation between drainage density and otter variables have been calculated (Table 11.6). From the Table 11.6 it is visualised tha t the correlation between drainage density a nd roughness index is strongest (+0.8978). The variation i n roughness index(80.68%)is accounted for drainage density. The relationship with drainage texture is lowest denoting - 0.1897 and the determination is 3.5 for the Vdriation of drainage texture accounted by density. drainage 11.7. STREAM FREQUENCY AND OTHER MORPHOMETRC VARES Stream frequency has been correlated with two different variables drainage density and drainage texture (Table 11.7). Among the variables drainage density is highly correlated (+0.9545) and determination is 91.12% for the variation of drainage density accounted ny stream frequency. On the other hand drainage texture is weakly correlated (-0.1415) and the stream frequency contributes 2.0027% for the variation of drainage texture.
SUPERMPOSED REGRESSON LNES OF 6 5 4 3 2 6 1!5 6 w >- w oc >- u 0 :z: ul 'Z X w (/) a.. - w ><4 :Z:4 ob. oro.. 20-4 w w w.j 0!/) [!/) (/) w w w w (!) (!) MORPHOMETRC X (!) z VARABLES <t 2 6 2 4 :5 re <t <i oc w oc oc f- > 0 0 0!/) <t 0:: 0 0 0 0 0 2 8 50 100 150 200 RELATVE RELEF (Me t res) 7 6 5 4 3 2 6 >- ll. w >- u X w oc!:: z w :J w 0 w (/) w z oc X/ z, 04 0..4-4 5 0 7 w w w 0 1-0 oc..j!/) u.. (/) z (/) 0 llj (!) w w (!) 1- <t z u 'Z 5 2 <t2 :x:2 oc (!) W l (/) Ci oc w ::> (/) oc 1- > 0 0 (/) <t oc 0 FG. 11. 3 0 0 0 0 0 0 100 200 AVERAGE RELEF (M et res)
SUPURMPOSED REGRESSON LNES OF MORPHOMETRC VARABLES 4 w 0::2 :::> X w - 3 r 3.- 12r 12 ;:..._----------------:;.,...------::::o""i / 3 2 >- 8, w W 4 w w fe CL :::> 0 0.J w U) k / /,...-- 4 _, 7 ::;:> ' ""' z z - :::i w w ' ;; t. l ol ol o 1 1 20 ROUGHNESS NDEX 3r 3 2 1 ' w a:: 2 X w - UJ,!'/', 2 q c: 0 a:: 0 ol ol 0 l l 2 4 6 STREAM FREQUENCY 3-5 4 3 12 w [w >- >- t-2 4 U) w w z :::> CL UJ 0 0 0 w _J a:: 1.1... UJ U) C!>l 2 e!>4 z :X: w a:: (!) - <i a:: a:: UJ :::> 1- > 0 0 U) a:: 0 0 0 (). 3 w (!), z <i a:: 0 3-3 >- <..> z UJ4 :::> 0 UJ a:: 1.1... 0 6 DSSECTON NDEX AVERAGE SLOPE FG. 11.4
SUPERMPOSED REGRESS ON LNES 402 - ----- 11.8. SUPER MPOSED REGRESS ON L NES The s uperimposed r egr essio n l ines of morphometri c variables of t he Brahmani Basin on average r e lief (Fig. 11.3) reveal a v ery i nterestin g f act with increase in average rel ief all the variables show increasing trend values except drainage texture. Th e drainage texture shows almost parallel ' t rend with increas e i n average relief. Same is the case among regress ion lines on relative relief, roughness index,average slope, etc.. The superimposed regr ession lines of variables on dissection index and stream f req ue ncy a lso p r esent some inter esting phenomena. With i ncrease in the dissection index and stream frequenc y, al l t he morphometric variables show increasing tre nd value s excep t drainage texture. The texture shows, negativ e trend with inc rease in dissection index and stream f requency (Fig. 11.4).