The probable maximum flood at the Ukai and Lakhwar dam sites in India

The Extremes of lite Extremes: Extraordinaiy Floods (Proceedings of a symposium held at Reykjavik. Iceland. July 2000). I A! IS Publ. no. 271. 2002. 283 The probable maximum flood at the Ukai and Lakhwar dam sites in India P. R. RAKHECHA* & C. CLARK CHRS, Shttte Lane, Bntlon. Somerset, UK e-mail: colin chrs@hotiiiail.com Abstract The design of impounding sfructures where failure would lead to catastrophic loss of life requires an estimate of the probable maximum flood. In India there are over 3000 dams and more are being built and planned to meet the needs for water supply, power, and irrigation. Recently, revised estimates of probable maximum precipitation have been published. These new estimates are used in conjunction with instantaneous unit hydrographs (IUH) to assess the safety of two dam sites: the Lakhwar dam on the Yamuna River, and the Ukai dam on the Tapi River. The results show that at the first site the outflow exceeded the design value of the spillway by a factor of 2.27, while at the second site the ratio was 2.25. The IUH results are supported by flood frequency analyses using a modified Gumbel scale and also results derived from the Rational method. These outcomes illustrate that in India more attention to dam safety is a dire need for the future. Key words dam safely; probable maximum precipitation; flood frequency INTRODUCTION Although it is well known that hydrology is an inexact science, there has not always been nearly enough care taken in the estimation of design floods of dam spillways. This sentiment was echoed by Back (1990) when he wrote: "The criteria governing the design of dams can frequently be very imprecise and designing safety into dams must recognize this". The need for a robust estimate of the probable maximum flood (PMF) is nowhere more acute than in India where several catastrophic dam failures have taken place (Rakhecha & Mandai, 1983; CBIP, 1993). In India there are over 3000 dams and more are being constructed to develop water resources for the growing population. In the past, estimates of the PMF have been made by using estimates of probable maximum precipitation (PMP) via statistical methods (HTM, 1989). The reliance of spillway design upon one or perhaps two closely related techniques, coupled with a lack of a big data set has led to many revisions of the design floods at dam sites, e.g. Purohit et al. (1993). Indeed, Lemperiere (1993) showed on a global scale that about 40% of all dam failures are due to inadequate spillway capacity. Recently, attempts have been made to revise existing estimates of PMP in the tropics in general (Collier & Hardaker, 1995) and in India in particular (Rakhecha & Clark, 1999a, 2000), and an atlas showing 1-, 2-, and 3-day PMP has been published (Rakhecha & Clark, 1999b). By using these new estimates of PMP, the PMF of selected drainage basins, which included a dam, were estimated. All of the estimates were in "Now at: Indian Institute of Tropical Meteorology, Pune, India; e-mail: p rakhecha@hotmail.com

284 P. R. Rakhecha & C. Clark Fig. 1 Location of the Lakhwar and Ukai dam sites. excess of existing values (Rakhecha & Clark, 2000). This paper applies the revised estimates of PMP to estimate the PMF at two dam sites (Fig. 1). The first site, which is currently under construction, is the Lakhwar dam on the Yamuna River in Uttar Pradesh. The Yamuna River at the Lakhwar dam drains an area of 2080 km" in the mountainous region of Uttar Pradesh, and the design capacity of its spillway is 8000 m J s" 1. The second is the Ukai dam, which is located on the Tapi River in Gujarat and was completed in 1972. The Tapi River basin is mainly located in Maharashtra State and enters Gujarat State in its lower reaches; it drains an area of 62 224 km" above the Ukai dam. ESTIMATION OF THE PMF AT THE DAM SITES Three basic methods are used in this study. The first three methods involve estimating the PMP and then converting this into the PMF by means of equation (1) the unit hydrograph method, and equation (2) the Rational method, respectively. Estimation of the PMP was achieved by using the transposition and in situ maximization of historic storms over the period 1880-1982 (WMO, 1986). The storm rainfall was maximized according to the following method: Mr ain = (Mpw/Spw) R ( 1 ) where R = storm rainfall, Mpw = maximum precipitable water at the time of the storm, Spw = precipitable water ofthe storm and Mr ain = maximized rain. The third method estimates the PMF from the annual maximum flood series by using the modified Gumbel scale and probability weighted regression (Rakhecha & Clark, 1999a). In this scale the relationship: log Y = a log T+c (2) where T = the return period, Y = reduced variate is linear throughout the return period ranging from 1.1 to 1 000 000 years (Rakhecha & Clark, 1999a, p.346). In using these methods consistency in the result is important, but where consistency is not as high as is desired, reasons for the discrepancies should be determined if a single design figure is to be credible. Furthermore, due regard should be given to future changes in land use and climatic variability which may not have been adequately sampled in the data set on severe storms.

The probable maximum flood at the Ukai and Lakhwar dam sites in India 285 Lakhwar dam site Rakhecha & Clark (1999b) give the 1-day PMP for this area as 110 cm. A duration of one day is based on the observed time to peak of severe floods in the area (Jain et al., 1986). The storm profile was based on the severe rainstorms which have occurred in the area (CBIP, 1993) and the IUH method was used to estimate the PMF. Table 1 shows the results where a value of 18 700 m 3 s" 1 is given. The same storm data are also used in the Rational equation which gives a slightly lower result. Analysis of the flood flow data show a PMF of 12 000 m J s"' (Fig. 2), which although even lower is still within 50% of the highest value. Bearing in mind the relatively short duration of the flood data of 20 years this result is well within the expected range of values, where the 1% confidence limit at the PMF is 2466 m 3 s" 1. Table 1 Estimates of the PMF (nr s"') at the Lakhwar and Ukai dam sites. Ukai Lakhwar Flood frequency analysis 102 600 12 100 Rational method 105 700 14 000 IUH using storm profile 100 700 18 700 Ukai dam site This drainage basin is over 30 times larger than the Lakhwar dam site. Shenoy et al. (1969) mention historic floods since 1727 but they do not use these data to estimate the PMF, possibly because of the 50-year gap in records after 1876. Hydraulic calculations showed that the response time for the basin is about three days. Figure 3 shows the areal variation of 3-day PMP which when corrected for the areal reduction in rainfall gives a 3-day value of 556 mm. This result is based on daily observations and is increased by a factor of 1.13 (WMO, 1986) to reflect the difference between the 72-h rainfall as compared with the 3-day depth of rainfall. Before the dam was completed in 1972, the largest flood was produced by a 260-mm rainfall event over three days. This event was used to calibrate both the IUH and the Rational method. Table 1 shows the results wherein there is a good degree of consistency. Flood frequency analysis is shown in Fig. 2 which results in a comparable estimate of the PMF. Only discharges with a return period in excess of three years were analysed because of the change in slope of the flood frequency curve due to the large flood-plain storage in the basin. COMPARISON WITH OTHER FLOODS IN INDIA It is vital to compare estimates of the PMF to judge both their consistency with existing data and their credibility for use in design. Figure 4 shows some examples of this approach together with the preferred estimate of the PMF for the two example sites. The new results for both examples are close to previous estimates at other sites and are also comparable with recorded extreme floods. Also included on the diagram

286 P. R. Rakhecha & C Clark RETURN PERIOD (YEARS) 1.01 «2 5 10 20 50 100 10? 10 4 10 1Q 6 P ' ' 1 r-r-i 1 1 r-n 1 1 1 1 1 1 r I 1 0.11 1-1 0 1 2 3 4 5 6 7 8 9 Fig. 2 Flood frequency for the Tapi River and Yamuna River. are the values for the existing spillway design flows at the same two sites. These are considerably lower than recorded floods, partly because of the effects of reservoir routing but mainly because of the low value of PMP. For the Lakhwar site (Jain et al, 1986) gave a value of 6300 m J s 1 for the standard project flood which is nearly 20% higher than their estimate of PMF. 240.-y 160 200 140 V >- * * 130 l.-'j 0 '--'IOO Fig. 3 Spatial variation of 3-day PMP (cm) over the Tapi River basin. km N t

The probable maximum flood at the Ukai and Lakhwar dam sites in India 287 100 opmf ' Recorded flood A PMF this paper»-design flow 4- o 1 '100 1000 10000 100000 * Basin area (km 2 ) Fig. 4 Rates of runoff in relation to drainage basin area. RESERVOIR FLOOD ROUTING AND IMPLICATIONS FOR DAM SAFETY Flood routing through a storage reservoir enables the outflow hydrograph to be estimated, and, as a result, a reliable estimate of the spillway capacity to be produced. The weir equation as used for a high head was applied to the spillway and dam crest cross-section to evaluate the stage or water level for a given discharge. For both sites the PMF rapidly filled the space between the base and top of the spillway. For the Lakhwar dam site there would be significant flow over the dam crest after 12 h from the start of the storm hydrograph and this would be maintained for over 18 h. The maximum depth of flow over the crest would be 4 m which is large enough to cause major if not catastrophic damage to the dam structure. At the Ukai site the duration of flow over the crest is about 100 h with a depth of flow 1.5 m or more lasting for about 80 h. Severe to very severe damage to the dam would be expected. In addition, any large floating debris would add, in the early stages of overflow, to the potential damage to the dam. The ratio of design spillway discharge to the estimate in this paper is 2.27 in the case of the Ukai dam and 2.25 for the Lakhwar dam which is now under construction. CONCLUSIONS The continued rise in demand for water in India will mean that more dams will be built in the future. The present study of the PMF at two sites has shown that the design floods have been seriously underestimated. The consequences for dam safety and the likely loss of life in the event of a major dam breach are serious. Although the estimates of the PMF are open to debate and may be revised in the future, lack of knowledge of the long-term flood frequency means that assumptions have been made in the techniques used. In the future, with increasing intensity of land use, the rate of runoff is likely to increase so that a degree of safety should always be incorporated into the design flood. Acknowledgements The authors would like to thank the conference organizers for financial help to attend the conference. C. Clark would also like to thank the Royal Meteorological Society and the British Hydrological Society for further financial help which made attendance at the conference possible.

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