Reappraisal of Hydrological Studies for Computation of Dependable Flows

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 rainfall-overland 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

1. 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 hydro-electric 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 Navegaon-Khairy. 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 sub-system 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.

2. 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 inter-state 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 hydro-electric 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 second-degree 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.

3. 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.

4. 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 least-square 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 first-degree 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, first-degree regression line and second-degree 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 round-off 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 higher-order 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

5. 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 post-monsoon flow. Accordingly runoffs are estimated adding monsoon runoff and post-monsoon 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

6. 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 log-log 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 log-log 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 first-degree 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.

7. Concluding Remarks

   In the present study, the reappraisal of rainfall-runoff 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.

8. References

1. Project Report. 1966, Pench Hydro-Electric Project Vol-1 Reports, Estimates and Appendices, Irrigation Department, Govt. of Maharashtra, Nagpur circle office, Nagpur.

2. Project Report. 1967, Pench Irrigation Project Vol-1 Reports, Estimates and Appendices, Irrigation Department, Govt. of Maharashtra, Nagpur circle office, Nagpur.

3. Project Report. 1969, Pench Hydro-Electric Project Supplement to Project Report Of 1966, Irrigation Department, Govt. of Maharashtra, Nagpur circle office, Nagpur..

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

5. 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, 27-28 Jan 1996, pp 128-132.

6. 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 117-122.

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

8. 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.

9. 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 663-672.