 Open Access
 Total Downloads : 140
 Authors : Shriniwas. S. Valunjkar
 Paper ID : IJERTV3IS10375
 Volume & Issue : Volume 03, Issue 01 (January 2014)
 Published (First Online): 16012014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Reappraisal of Hydrological Studies for Computation of Dependable Flows
Shriniwas. S. Valunjkar
Professor, Department of Civil Engineering, Government College of Engineering, Karad, Distt: Satara (Maharashtra), India,
Abstract
The revision of hydrological data and precisely arriving at the availability of water resources will definitely indicate the change required in working system of the scheme. Accordingly, the monitoring operation of reservoirs can be safely and suitably modified. Generally, the hydrological data available is of short duration. Using more advanced methodologies it is possible to design the hydro electric and irrigation schemes successfully. This paper attempts to verify the provisions made in earlier planning and also to examine the effect of record length of rainfalloverland flow (runoff) data on the availability estimates of a basin. Polynomial regression model relationship between two variables
i.e. rainfall and runoff was established for 46, 66 and 80 years data series for computation of reliable flows.
Keywords: Rainfall runoff relationship, Polynomial regression

Introduction
Assessment of correct water resources is a pre requisite for the successful planning, execution and operation of project. Water is one of the essential commodities, which is available cheaply as a natural resource. This resource is random in nature, rare and become costly sometimes. It is necessary that, availability of water resources for the schemes be reviewed from time to time, as more and more historical hydrological data becomes available. The appraisal of hydrological data and precisely arriving at the availability of water resources is a science, at the same time; its utilization for proper planning is an art. Generally, the hydrological data available is of short duration. Using more advanced methodologies it is possible to design the hydroelectric and irrigation schemes successfully. Reappraisal of the project will
definitely indicate the change required in working system of the scheme. Accordingly, the monitoring operation of reservoirs could be safely and suitably modified.
Pench river project complex is selected herein as a case study. The project [1] [2] comprises of (1) Pench hydroelectric project at Totladoh; and (2) Pench Irrigation Project [3], which is 23 km downstream from Totladoh at NavegaonKhairy. Pench River is the largest tributary of Kanhan River, which joins the Wainganga in Godavari basin. It rises from Satpuda hills in Chhindwada district of Madhya Pradesh. It drains a total area of about 4921 km2 up to its confluence with the Kanhan River. It is a subsystem of Godavari basin and the total length is about 274 km. The main tributaries of Pench River are namely, (i) Mandhan; (ii) Suki; (iii) Gatmali; (iv) Gunar; (v) Kajri; and (vi) Kulbhera.

Earlier Planning of the Project
Pench hydroelectric project includes a storage dam that impounds water of 1241 Million m3 (Mm3) gross storage at Totladoh across Pench river just near the interstate border between Maharashtra and Madhya Pradesh. The project consists of masonry dam, intake structure, pressure shafts, and underground powerhouse with an installed capacity of 160 MW and tail race tunnel, 8 km long, through which water is released, after power generation, for irrigation at downstream. The drainage area up to Pench hydroelectric project site is 4273 km2 out of which only 34 km2 is in Maharashtra state and the rest lies in the state of Madhya Pradesh. The drainage area between hydroelectric project and Pench irrigation project is 388 km2 and lies in Maharashtra state. The reliable yield at 75 percent is 1835 M.m3, based on weighted annual rainfall of influencing raingauge stations, and the use of Stranges coefficients. The catchment area is hilly and was classified as Stranges good for the purpose of yield calculations. Four
raingauge stations were only considered and 42 year rainfall data from 1914 to 1955 were used for finding out annual yield. Subsequently, in 1969, project report
[3] for Pench hydroelectric scheme was prepared. In this planning, seven raingauge stations in the vicinity of drainage area were considered and annual rainfall data of 46 years, from 1914 to 1959 were used in the analysis for finding out the annual yield. Raingauge stations are located at Tamia, Amarwada, Seoni, Deolapar, Junnardeo, Mokhed and Chhindwada which are shown in Figure 1.Figure 1 Pench River Project Complex
A seconddegree equation, with correlation coefficient of 0.772 was obtained to work out annual yield for 46 years from 1914 to 1959. The adopted equation was,
y 21.0773 1.1087x 0.02003×2
where, y = annual surface runoff in thousand million cubic feet (TMC) and = weighted rainfall in inches.
storage, 1088 M.m3 as live storage were fixed at Pench hydroelectric project. The annual reliable flow values (or reliable flows) as per project provisions at 50, 75 and 90 percent are 2435 M.m3, 1835 M.m3 and
1532 M.m3 respectively.

Revision of Hydrological Studies
The project is considered to verify the provisions made in earlier planning and also examine the overall performance of the project, as per the available data at present. Overland runoff and corresponding rainfall data (weighted) are used in the analytical studies. Generally more than 90 percent of annual rainfall occurs in the monsoon period from June to October. Rainfall series of 46 years is considered from the data available from seven raingauge stations.

Polynomial Regression Model
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A polynomial curve for two variables (i.e. rainfall and runoff) is fitted by correlation and regression method. Polynomial Regression [4] an algorithm is developed to derive the first and higher order equations using leastsquare criterion. A strategy for fitting a best curve of mth degree through the data is to minimize the sum of the square of residual errors.
0 1 2 3 m
Annual rainfall and surface runoff values were converted in SI units and equation was further
y a
a x a x 2 a x3 ………………..a
Pm e
(2)
modified as:
y 596.901 31.398x 0.56×2
(1)
where = residual or error between the model and
observation.
For this case; the sum of the square of the residuals
where, y = annual surface runoff in million cubic metre (M.m3) and = weighted rainfall in cm.
(Sr) is:
n
S ( y a
a x a x 2 a x 3……….. a x m ) 2
(3)
r i
i1
0 1 i 2 i 3 i m i
Annual runoff data were used to estimate reliable yield values at different rainfall conditions. As per the Inter state agreement upstream reservation of 991 M.m3 in normal year, i.e.75 percent reliable yield and 991/1700th of available yield in other years, limited to
566 M.m3 minimum was made in the project
Taking the derivative of Equation (3) with respect to each unknown coefficient of the polynomial and equating these set of derivatives to zero, the set of normal equations is generalized as:
a x m a x m 1 a x m2 a x m3 ……….. a x 2m x m y
planning. Accordingly storge computations were carried out and capacities of 1241 M.m3 as gross
0 i 1 i
(4)
2 i 3 3
m i i i i
where, all summations are from
i 1
to n. These
Table1 shows the generated polynomial equations for
generalized set of equations are linear and are in the order of m, m+1, m+2, m+3..2m with corresponding unknowns ao, a1, a2, a3am. The unknown coefficients of first degree equation are generated from the observed data, and for generating the coefficients of polynomial of higher order, the set of simultaneous equations are solved using Gauss elimination method. Thus, a firstdegree equation is established as:
computation of runoffs along with coefficients of correlation.
Table 1 Generated polynomial equations
y 338.392 20.486x
(5)
A graphical representation through a plot of actual rainfall and runoff points, firstdegree regression line and seconddegree curve developed by Valunjkar [5] based on Equation (1) and (5) are shown in Figure 2.
Figure 2 Plot of actual rainfall and runoff points, first and second degree
At later stage, with the availability of additional data, the analysis was carried for the series of 66 and 80 years [6]. The least square procedure can be extended to fit the data to an mth degree polynomial. A problem associated with implementing polynomial regression while computation was that the normal equations were found sometimes ill conditioned. This was true for regression of higher orders. In such cases, the computed coefficients were found to be highly susceptible to roundoff error, and consequently the results could be inaccurate. Among other things, this problem was related to the structure of the normal equations and to the fact that for higherorder polynomials the normal equations could have very large and very small coefficients augmented matrix. The problem occurred for fourth and higher order polynomials. Hence the scope of the polynomial regression was restricted to second and third order polynomial equations.
Degree of the equation
Polynomial equation
Correlati on coefficie nt
Determina tion coefficient
Record length 46 years
First
y 338.392 20.486x
0.925
0.856
Second
y 596.901 31.398x 0.56×2
0.772
0.596
Third
y 790.78 10.877x 0.276×2 0.0008×3
0.816
0.727
Record length 66 years
First
y 456.35 21.50x
0.931
0.867
Second
y 970.32 30.124x 0.0345×2
0.822
0.789
Third
y 915.880 17.038x 0.3446×2 0.001×3
0.833
0.751
Record length 80 years
First
y 497.857 21.736x
0.934
0.872
Second
y 903.621 28.535x 0.0273×2
0.874
0.874
Third
y 1380.346 28.504x 0.431×2 0.0011×3
0.866
0.867

Computation of Annual Runoff Series
Annual runoff series based on the algorithm [7], are computed for 46, 66 [8] and 80 [9] years. As per the general practice established on actual observation, 10 percent of monsoon runoff was taken as postmonsoon flow. Accordingly runoffs are estimated adding monsoon runoff and postmonsoon flow for each year. Annual reliable flow values in M.m3 at different percent for 46, 66 and 80 years of record length are computed and generated important results are shown in Table 2.
Dependability
in Percent
First degree
equation
Second degree
equation
Third degree
equation
Record length 46 years
50
2070.799
2435.000
1988.389
55
1983.002
2226.000
1918.876
60
1929.614
2141.000
1856.068
65
1826.246
1972.000
1791.546
70
1752.737
1930.000
1767.229
75
1678.618
1835.000
1647.798
80
1529.225
1737.000
1604.757
85
1461.689
1599.000
1581.753
90
1434.128
1532.000
1468.557
Record length 66 years
50
1933.445
1939.048
1921.298
55
1899.787
1869.222
1849.69
60
1827.781
1815.444
1795.359
65
1752.734
1801.253
1781.149
70
1679.617
1775.326
1755.325
75
1662.210
1653.213
1636.401
80
1543.333
1596.734
1583.006
85
1461.686
1506.390
1499.915
90
1235.729
1360.519
1372.289
Record length 90 years
50
1933.446
1922.626
1903.554
55
1899.758
1849.038
1827.751
60
1829.960
1814.301
1792.516
65
1752.738
1781.263
1759.356
70
1679.616
1754.749
1733.006
75
1655.424
1633.370
1615.609
80
1543.302
1577.356
1563.385
85
1447.573
1531.568
1521.675
90
1413.235
1361.804
1375.518
Table 2 Annual dependable flow values

Result and Discussions
it is observed that the results of first degree equation was more consistent than the second degree equation since the second degree curve shows that the runoff values goes on reducing, with the increase in rainfall. Similarly, it was observed that, the rainfall increases runoff decreases in case of second and third degree equations. However in loglog correlation, the trend of runoff values was uncertain with the increase in record length. In case of 46 years of record length, the values of yields in case of first, third degree and loglog correlation values were close to each other at lower rainfall as compared with project provisions. However with the increase in record length i.e. 66 and 80 years this difference was found minimum at lower rainfall values with the subsequent decrease in runoff values. The values obtained from the firstdegree equation were more consistent for 80 years of record length as compaed with the record length of 46 and 66 years.
It could also be observed that the reliable values are decrease with the increase in the record length. However it may not be true for all the cases but it may have certain impact on hydrological studies of the project. It was observed that; the comparative percentage of reliabilities decreases with the increase in record length; however this was not found very correct for higher degree equations at lower side of record length but it may have certain effect over the computation. On the other side this comparative percentage increases with the increase in percentage of reliable yield. Table 2 shows the comparison of different polynomial curves for 46, 66 and 80 years of record lengths.

Concluding Remarks
In the present study, the reappraisal of rainfallrunoff relationship was examined using polynomial regression models. The different record lengths were considered for the estimation of annual reliable flow values. The results of the analysis indicate that for estimation of accurate yields, record should be sufficiently long in order to establish hydrologic phenomenon effectively. It was found possible to establish a relationship between reliable values and the length of data series. In a case study of Pench river project, annual runoff series worked out by first degree equation for the record length of 80 years was found more consistent. In recent years, the nature of rainfall was found scanty due to deforestation in the
vicinity of case study area. This effect leads to decrease in reliable values which results in reduction of flow values from the reservoirs. Considering these aspects there is a need to revise the earlier planning provisions. Hence, the values of 50 percent, 75 percent and 90 percent reliable flow values could be taken as 1933 M.m3 1655 M.m3 and 1413 M.m3 respectively against the values as per project provisions (i.e. 2435 M.m3, 1835M.m3 and 1532M.m3 respectively) for further analysis.

References

Project Report. 1966, Pench HydroElectric Project Vol1 Reports, Estimates and Appendices, Irrigation Department, Govt. of Maharashtra, Nagpur circle office, Nagpur.

Project Report. 1967, Pench Irrigation Project Vol1 Reports, Estimates and Appendices, Irrigation Department, Govt. of Maharashtra, Nagpur circle office, Nagpur.

Project Report. 1969, Pench HydroElectric Project Supplement to Project Report Of 1966, Irrigation Department, Govt. of Maharashtra, Nagpur circle office, Nagpur..

Chapra S.C and Canale R.P., 1989. Numerical Methods for Engineers, McGrawHill Book Co. (International Edition), Singapore

Valunjkar S.S. 1996, Water Planning And Yield Studies for Pench River Projects Complex, Proceedings of All India Seminar on Hydraulic Engineering, Institution of Engineers (India), Nagpur, 2728 Jan 1996, pp 128132.

Mehrotra R. and Singh R.D.Singh, 1999. Impact of Record Length on the Water Availability Estimates, Journal of Institution of Engineers (India), Vol. 80, pp 117122.

Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. 2005, Numerical Recipes The Art of Scientific Computing, Cambridge University Press.

Valunjkar S.S. 2005, Development of fuzzy logic system for optimal water resources and cropping planning in context with sustainable development, R&D Project Report (Unpublished), Submitted to the All India Council for Technical Education, New Delhi., India.

Valunjkar S.S. Reappraisal of rainfall – runoff studies for computation of reliable flows, Proceedings of National Conference on hydraulic and water resources (HYDRO 2012), IIT Bombay, India, 7 & 8 December 2012, pp 663672.