International Journal of Civil, Structural, Environmental and Infrastructure Engineering Research and Development (IJCSEIERD) ISSN 22496866 Vol. 3, Issue 4, Oct 2013, 18 © TJPRC Pvt. Ltd.
DEVELOPING AN EQUATION FOR COMPUTATION OF RUNOFF FOR JILLEDUBANDERU MINOR BASIN R. BHAVANI Assistant Professor, Civil Engineering Department, JNTUA College of Engineering, Anantapuram, Andhra Pradesh, India
ABSTRACT For design of any water resources project, it is necessary to have the information about the runoff data which may not be readily available. In general, empirical methods are being used to compute the runoff. In this paper, an attempt has been made to develop an equation for computation of runoff. For this purpose, Jilledubanderu minor basin has been selected as study area. Jilledubanderu is a minor basin of Chitravathi which is a subbasin of Pennar basin. To develop the equation for computation of runoff, regression analysis has been used. For regression analysis, ‘Statistical Package for Social Sciences (SPSS) 17.0’ software is used and an equation has been developed using the coefficients obtained from the regression analysis. Various parameters like basin area, rainfall, bifurcation ratio, elongation ratio, relief ratio and runoff are the inputs for regression analysis. Out of these, basin area, bifurcation ratio, elongation ratio, relief ratio are computed based on topo sheets of scale 1:50,000. Runoff has been calculated using Strange’s table since, runoff data is not readily available. Required rainfall data has been collected from the Chief planning office, Anantapuram. For regression analysis, runoff has been taken as the dependent variable and the remaining parameters have been taken as independent variables. Validity of the equation has been checked and found satisfactory. ABBREVIATIONS Basin area  ‘A’; Rainfall  ‘RF’; Bifurcation ratio  ‘Rb’; Elongation ratio  ‘Re’; Relief ratio  ‘Rr’; Runoff  ‘Q’; Millimetres – ‘mm’; Metres – ‘m’; Kilometres – ‘km’; Square Kilometres – ‘Sq.km’; and m3Cum.
KEYWORDS: Basin Area, Rainfall, Bifurcation Ratio, Elongation Ratio, Relief Ratio , Runoff, Strange’s Table and Statistical Package for Social Sciences (SPSS) 17.0’ Software
INTRODUCTION Water is the most precious resource which is some times scarce, some times abundant and is always very unevenly distributed both in space and time. Water resources play a major role in agriculture, hydropower generation, livestock production, industrial activities etc. The demand for water is increasing with the rapid increase in population and industries. It is essential to estimate probable runoff so that it can be utilized effectively for various purposes. In this connection an attempt has been made to develop an equation for estimating the runoff in Jilledubanderu minor basin. Reimers, W., has estimated hydrological parameters from basin characteristics for large semiarid catchments. Ferreira. R.F has estimated mean annual stream flow using regression for selected drainage basins in the coal area of Southeastern Montana, U.S.
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R. Bhavani
STUDY AREA Jilledubanderu minor basin situated in Anantapuram district has been selected for the present study. The hierarchy of the river system related to the study area is shown below. Jilledubanderu

A tributary of Maddileru
Maddileru

A tributary of Chitravathi river
Chitravathi

A tributary of river Pennar
Jilledubanderu originates in Kothakota reserved forest in the eastern part of the Puttaparthi mandal, Anantapuram distrit, Andhra Pradesh state. It joins Maddileru a little upstream of Kodavandlapalli (v) at 77 0 58’ 11” East longitude and 140 26’ 45” North latitude. Corresponding schematic diagram is shown in figure 1.
Figure 1: Schematic Diagram Jilledubanderu Minor basin has an area of 438 km2. The minor basin is located between 77048’34” E longitude to 78002’30” E longitude and 14005’35” N latitude to 14026’45” N latitude. Jilledubanderu minor basin has been divided into seven number of segments namely Cherlopalli tank group, Upper Jilledubanderu (Left), Upper Jilledubanderu (Right), Middle Jilledubanderu, Chinnacheruvu tank group, Ramasagaram tank group and Lower Jilledubanderu. The details of location, drainage and segments are presented in figure 2 which has been prepared using the topo sheets.
Developing an Equation for Computation of Runoff for Jilledubanderu Minor Basin
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Figure 2: Location, Drainage and Segments Map of Jilledubanderu Minor Basin
DATA Basin area, bifurcation ratio, elongation ratio and relief ratio are computed based on figure 2. Stranges table has been used for calculation of runoff based on rainfall data for the influencing rain gauge stations viz., Nallamada, Puttaparthi, Bukkapatnam and Mudigubba. Rainfall (RF) Rainfall data for the years, 2011 and 2012 for Puttaparthi, Bukkapatnam, Mudigubba and Nallamada rain gauge stations which are influencing the study area has been collected from the Chief Planning Office, Anantapuram. The details of influencing rain gauge stations and corresponding average monsoon (June to November) rainfall for all the segments in the study area for the year, 2011 are shown in table 1.
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R. Bhavani
Table 1: Details of Influencing Rain Gauge Stations and Corresponding Average Monsoon Rainfalls for the Study Area S. No
Name of the Segment
1 2
Cherlopalli tank group Upper Jilledubanderu (Left) Upper Jilledubanderu (Right) Middle Jilledubanderu Chinnacheruvu tank group Ramasagaram tank group Lower Jilledubanderu
3 4 5 6 7
Monsoon Rain Fall for the Influencing Rain Gauge Stations (mm) Nallamada Puttaparthi Bukkapatnam Mudigubba 497.20 498.00 497.2 498.00 434.60 
Average Monsoon Rain Fall (mm) 497.60 476.60
497.2
498.00
434.60

476.60
497.2 

434.60 434.60 
390.40 390.40 390.40 390.40
443.80 412.50 412.50 390.40
Basin Area (A) Entire geographical area drained by a river and its tributaries is Basin area. It can also be defined as the area characterized by runoff being conveyed to the same outlet. Basin area for Jilledubanderu minor basin has been estimated as 438 km2 using the topo sheets, 57 F/15, 57 F/16, 57 J/3 and 57 J/4 of scale 1:50,000. The areas of all the segments are shown in table 3. Bifurcation Ratio (Rb) Bifurcation Ratio is a ratio of the number of streams of any given order to the number in the next higher order. For a drainage basin of Nth order there will be (N1) number of bifurcation ratios. For each basin, single bifurcation ratio is obtained as the simple arithmetic mean of the ‘Rb’s of the different orders of the basin. To identify the order of the stream, Strahler method has been adopted. ‘Strahler’ defined order1 stream as one receiving no tributaries. When two first order streams join, a stream of order2 is formed. When two streams of order2 join a stream of order3 is formed and so on. The details are shown in table 2. Table 2: Stream Segments and Bifurcation Ratios S. No
Name of the Segment
1
Cherlopalli tank group Number of streams Bifurcation ratios Upper Jilledubanderu (Left) Number of streams Bifurcation ratios Upper Jilledubanderu (Right) Number of streams Bifurcation ratios Middle Jilledubanderu Number of streams Bifurcation ratios Chinnacheruvu tank group Number of streams Bifurcation ratios Ramasagaram tank group Number of streams Bifurcation ratios Lower Jilledubanderu Number of streams Bifurcation ratios
2
3
4
5
6
7
1
Order of Streams 2 3 4
5
63 3.94
16 3.2
5 5
1
181 4.21
43 3.91
11 5.5
2 2
1
192 4.68
41 4.56
9 4.5
2 2
1
137 3.43
40 5
8 4
2 2
1
161 3.83
42 4.2
10 2.5
4 4
1
143 4.33
33 4.13
8 4
2 2
1
127 3.97
32 6.4
5 2.5
2 2
1
Average Bifurcation Ratios
4.05
3.91
3.94
3.61
3.63
3.62
3.72
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Developing an Equation for Computation of Runoff for Jilledubanderu Minor Basin
Elongation Ratio (Re) Elongation Ratio can be defined as the ratio of diameter of a circle of same area as that of the basin to the maximum basin length. Elongation Ratio (Re) =1.13√A/L Where, A = Area of the Basin and L = Longest axis of the basin from the mouth (observed from topo sheets). The details are shown in table 3. 3.5 Relief Ratio (Rr) Relief ratio is the ratio between the relative relief and the longest axis (L) of the basin. Relative relief is the difference between the maximum and minimum elevations of the basin. The details are shown in table 3. Table 3: Details of Areas, Elongation Ratios and Relief Ratios S. No
Name of the Segment
1 2 3 4 5 6 7
Cherlopalli tank group Upper Jilledubanderu (Left) Upper Jilledubanderu (Right) Middle Jilledubanderu Chinnacheruvu tank group Ramasagaram tank group Lower Jilledubanderu
Area in Sq.km 31 56 68 86 65 57 75
Longest Axis (L) in km 8.22 15.27 15.52 14.52 13.68 15.71 15.99
Re 0.77 0.55 0.60 0.72 0.67 0.54 0.61
Maximum Elevation in m 733 943 971 771 745 780 678
Minimum Elevation in m 550 459 459 390 440 390 315
Difference in Elevation in m 183 484 512 381 305 390 363
Rr in m/km 22.263 31.696 32.990 26.240 22.295 24.825 22.702
METHODOLOGY Runoff (Q) has been estimated based on rainfall data and Stranges table. For the purpose of runoff calculations, the type of the catchment for the first three segments have been considered as ‘Good’ and for the remaining four segments, 50% of the basin has been considered as ‘Average’ and 50% as ‘Good’ based on the topography. Runoff values computed based on Stranges table for average monsoon rainfall for the year 2011 are shown in table 4. Table 4: Runoff Calculations Using Strange’s Table S. No 1 2 3 4 5 6 7
Name of the Segment Cherlopalli tank group Upper Jilledubanderu (Left) Upper Jilledubanderu (Right) Middle Jilledubanderu Chinnacheruvu tank group Ramasagaram tank group Lower Jilledubanderu
Catchment Area in Sq.km
Average Rainfall in mm
31 56 68 86 65 57 75
497.60 476.60 476.60 443.80 412.50 412.50 390.40
Runoff for Good Catchment in Cum 2440000 3750000 4550000 2390000 1480000 1300000 1440000
Runoff for Average Catchment in Cum 1790000 1110000 970000 1100000
Total Runoff in Cum 2440000 3750000 4550000 4180000 2590000 2270000 2540000
Considering the estimated runoff as dependent variable and parameters like basin area, rainfall, bifurcation ratio, elongation ratio and relief ratio as independent variables, regression analysis has been carried out. For this purpose, ‘SPSS 17.0’ software has been used to get the coefficients for developing the equation. ‘Weight estimation’ option under ‘Regression’ has been selected in the process of regression.
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R. Bhavani
ANALYSIS AND RESULTS Logarithmic values of the variables basin area, rainfall, bifurcation ratio, elongation ratio, relief ratio and runoff have been taken to make them more symmetrically distributed and are shown in table 5. Table 5: Log Values of Variables S.No 1 2 3 4 5 6 7
Name of the Segment Cherlopalli tank group Upper Jilledubanderu (Left) Upper Jilledubanderu (Right) Middle Jilledubanderu Chinnacheruvu tank group Ramasagaram tank group Lower Jilledubanderu
A 1.4914 1.7482 1.8325 1.9345 1.8129 1.7559 1.8751
RF 2.6969 2.6782 2.6782 2.6472 2.6154 2.6154 2.5915
Rb 0.6075 0.5922 0.5955 0.5575 0.5599 0.5587 0.5705
Re 0.1135 0.2596 0.2218 0.1427 0.1739 0.2676 0.2147
Rr 1.3476 1.5010 1.5184 1.4190 1.3482 1.3949 1.3561
Q 6.3874 6.5740 6.6580 6.6212 6.4133 6.3560 6.4048
These values have been used as input for ‘SPSS 17.0’ software to carry out regressions analysis. The coefficients obtained from output file for different variables have been used to develop the runoff equation and the equation is shown in Eq.1. Q = 10 3.113 x A 0.899 x RF 2.75 x Rb 0.783 x Re 0.101 x Rr 0.207
...
(Eq.1)
Validation of the Equation Using the above regression equation (Eq.1), the runoff is computed for each segment considering rainfall for the year, 2012. Also, the runoff is computed using the Strange’s table for comparision and all these are tabulated in Table 6. Table 6: Rainfall and Runoff Values for the Year, 2012 Segment No.
Name of the Segment
1 2 3 4 5 6 7
Cherlopalli tank group Upper Jilledubanderu (Left) Upper Jilledubanderu (Right) Middle Jilledubanderu Chinnacheruvu tank group Ramasagaram tank group Lower Jilledubanderu
Average Monsoon Rain Fall for the Year 2012 486.30 504.40 504.40 478.60 525.50 525.50 510.40
Runoff in Cum Computed as Computed Per Strange's Using Table Equation 2240000 2287869 4520000 4362009 5490000 5306777 5100000 5143283 4800000 4983221 4220000 4424450 5280000 5303994
% Variation 2.14 3.50 3.34 0.85 3.82 4.84 0.45
The comparision between the values of runoff computed as per Strange’s table and as per the regression equation are represented in figure 3.
Figure 3: Comparision of Runoff Obtained by Strange’s Table and the Equation
Developing an Equation for Computation of Runoff for Jilledubanderu Minor Basin
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CONCLUSIONS As per the above comparison, it is observed that the variation between the runoff values obtained by regression analysis and Strange’s table is meager and it can be concluded that the obtained equation may be acceptable.
REFERENCES 1.
Ferreira, R.F., (1981), “Mean annual stream flow of selected drainage basins in the coal area of Southeastern Montana, U.S”, Geological Survey Water Resources investigations 8161, p 21.
2.
Hann, C.T., (1995), “Statistical methods in Hydrology”, Affiliated East west press pvt. Ltd. New Delhi.
3.
Reimers, W., (1990), Estimating hydrological parameters from basin characteristics for large semiarid catchments, Regionalization in Hydrology (Proceedings of the Ljubljana Symposium, April 1990). IAHS Publ. no. 191.
4.
Strahler,A.N., (1964), “Quantitative Geomorphology of drainage basins and channel networks”, Handbook of Applied Hydrology, Section4II, Mc.Graw Hill Book Company, New York.