Operation of reservoirs for flood control in areas with limited water resources

Transcription

1 Hydrological forecasting ~~ Prévisions hydrologiques (Proceedings of the Oxford Symposium, April 198; Actes du Colloque d'oxford, avril 198): IAHS-AISH Publ. no Operation of reservoirs for flood control in areas with limited water resources W. V. PITMAN University of the Witwatersrand, Johannesburg, South Africa M. S. BASSON Bruinette, Kruger, Stoffberg Inc., Pretoria, South Africa Abstract. This paper describes a procedure for simulating the response of a drainage basin to storm rainfall and for optimizing reservoir gate operation so as to minimize downstream flood damage. Tests on two different dams indicated that substantial benefits could be derived from flood control without reducing reservoir yield. Exploitation des réservoirs pour le contrôle des crues dans des régions présentant des ressources en eau limitées Résumé. Ce rapport décrit un modèle mathématique pour la simulation de la réponse d'un bassin versant à une pluie d'orage et également une méthode pour optimiser l'exploitation des vannes plongeantes en vue de minimiser les dommages d'une crue à l'aval du barrage. Des tests faits sur deux barrages différents ont indiqué que des avantages importants pourraient être obtenus par le contrôle de la crue sans réduire en même temps le rendement du réservoir. INTRODUCTION South Africa's water demands are met mostly from river sources and, because of the generally erratic nature of the rivers, large volumes of storage are needed to regulate streamflow. The most favourable dam sites have already been exploited and so storage of surface water becomes increasingly expensive. Against this background it has seldom been considered justifiable to allocate storage specifically to flood control. Meanwhile development continues to encroach into the flood plains with the results that flood damages spiral ever higher. The main objective of the research on which this paper is based was to develop procedures, first, for simulating in real time the river response to storm rainfall and, second, for optimizing gate operations so as to minimize downstream flood damage. If forecast computations can be initiated with rainfall instead of streamflow inputs, flood warnings can be appreciably advanced, thus allowing more time to create buffer storage by pre-releasing water from the reservoir. An initial study was undertaken at Vaal dam (Basson, 1978), which is probably South Africa's most important storage unit. It showed that by pre-release alone the peaks of major floods could be attenuated by as much as 26 per cent and that a scheme for real time flood forecasting and gate operation was economically feasible. Hartbeespoort dam and the irrigation area downstream was the scene of a second study (Pitman and Basson, 1979). Here the drainage basin is much smaller than that of Vaal dam, with a response time measured in hours not days. Moreover, the intense thunderstorm activity characteristic of the area cannot always be accurately forecast and, with such a short response time, significant attenuation of the flood peaks solely by pre-release is difficult to achieve. Substantial improvement, can, however, be attained by allocating part of the gatecontrolled storage (according to the season) to the flood control function without diminishing the reservoir yield. A survey of downstream damage caused by the 1978 flood was undertaken and an economic analysis proved the merits of assigning a relatively small proportion of the storage space to flood control. 535

2 536 W. V. Pitman and M.S. Basson THE TWO STUDY AREAS The study was initially concentrated on Vaal dam, the major storage unit of South Africa's most important multipurpose water development scheme, but for which no storage space had been officially allocated to flood control (Fig. 1). Situated at the confluence of the Vaal and Wilge rivers and immediately upstream of an important urban and industrial complex, Vaal dam offered attractive features for a study of this kind. It is a mass gravity structure surmounted by 6 vertical-lift flood gates. The reservoir capacity of 233 x 1 6 m 3 exceeds the mean annual runoff by about 1 per cent. The volume of the 3-year flood is roughly the same as the capacity of the reservoir. FIGURE 1. Study basins: location and physical and hydro meteorological features.

3 Operation of reservoirs for flood control 537 The drainage basin measures 38 5 km 2 and extends 22 km eastwards to the Drakensberg range, a dominant topographical feature forming the southeastern boundary (Fig. 1). Except in the steep upper reaches of its southeastern sector, the basin is rather flat. Typical rise times of major flood hydrographs are of the order of five days. The second study focussed on Hartbeespoort dam, which is situated at the confluence of the Crocodile and Magalies rivers about 4 km west of Pretoria (Fig. 1). The original capacity, 152 x 1 6 m 3, was increased in 1968 to 193 x 1 6 m 3 when 1 vertical-lift flood gates were erected on the original spillway crest. The drainage basin measures 4 km 2 and is roughly semi-circular in shape with the dam at the centre of circle (Fig. 1). The main tributaries are fairly steep and converge radially towards the dam a drainage configuration that makes for a comparatively rapid runoff response. A typical rise-time of the flood hydrograph is of the order of loh. Both the Vaal dam and Hartbeespoort basins lie in the sub-humid zone of South Africa. In both cases mean annual rainfall is about 75 mm and gross mean annual evaporation roughly double this figure. Rain occurs mostly as summer thunderstorms. RESERVOIR OPERATION PHILOSOPHY However good the forecasting technique, prediction of complete sequences of future events can seldom be consistently accurate. It follows that, in real time, forecasts must be continuously repeated as fresh transmitted observations come to hand. The simulated flood hydrographs will therefore as a rule grow incrementally as new forecasts are made. Decision-making based on these forecast hydrographs will also follow step by step; in other words, there must be a continuous stream of decisions rather than one based on a single forecast which can hardly ever be correct. There are many different strategies for controlling a flood by means of a single reservoir (Plate and Schultz, 1973). Investigations into flood damages sustained below Vaal and Hartbeespoort dams indicated that by far the most important factor relating to flood damage was the height to which the water rose; duration of inundation was only of minor significance. Inflow hydrograph Release hydrograph FIGURE 2. Illustration of basic flood release strategy for a single reservoir. Figure 2 illustrates a control measure aimed at minimizing the peak discharge and therefore the extent of downstream land subjected to inundation without too much concern for the duration of flooding. For each flood event, the storage available and the size and shape of the incoming hydrograph are fixed, as is also the volume of storage associated with the permissible degree of overfilling of the reservoir. Therefore, in the relevant mass balance equation, B=A+C+S (1)

4 538 W. V. Pitman and M, S. Basson the sole item that can be manipulated to lower the level of the release plateau is the pre-release volume A. In equation (1), S is the initial storage available, B is the volume by which the damaging part of the hydrograph can be modified by gate manipulation and C the volume of surcharge. To maximize the pre-release volume^, it is essential to start pre-release at the earliest possible moment. The maximum permissible rate of pre-release is determined by the acceptable risk of flood damage and the magnitude of the forecast hydrograph. The procedure was programmed for the computer with the following built-in constraints: (1) to conserve water supplies the reservoir must be 1 per cent full after the flood has passed; (2) the maximum rate of increase in discharge should not exceed the maximum rate of natural rise of the river; (3) to minimize sloughing of the river banks the rate of decrease in releases should not exceed the rate of recession of the typical flood hydrograph; (4) surcharge storage may be utilized only when the release plateau would otherwise exceed the level of damaging discharge in the river. To meet the set objective of minimizing downstream stage, optimum release rates must be repeatedly re-calculated from the mass balance equation as fresh data become available. The basic equation is: f te I t ât = Ç e O t àt + Si + S 2 (2) Jtf Jtf where I t is the rate of inflow at time t, O t the rate of release at time t, S\ the storage available at the time of forecast, S 2 the maximum permissible surcharge storage, tf the time of forecast and t e the time at end of flood. Subject to the set of constraints, the optimum plateau release rate is determined by an iterative procedure. This 'optimized' release rate is again updated as soon as fresh rainfall data become available with which to forecast a revised inflow hydrograph. Included in the program is a comparison of the simulated with the observed hydrograph (up to the time of forecast) and consequent adjustment of the forecast hydrograph. This adjustment is made only after the flood peak has been reached because on the rising stage it is difficult to establish whether departures constitute errors of timing or of magnitude. FLOOD FORECASTING River flow responses to storm rainfall were simulated by the models developed by Pitman (1976, 1977). The daily input version was employed for initial calibration and warm-up, and the hourly input version for simulation of the actual flood. As these models are of the lumped parameter type they cannot make provision for spatial variations of conditions within the basin. Furthermore, account cannot be taken of the differences in time lag associated with movement of the flood waters from the various parts of a basin. Accordingly, each basin was sub-divided into a number of sub-areas, thus converting the lumped models to distributed models on the macro scale. Antecedent conditions, particularly the state of wetness or dryness of various parts of the basin, strongly influence the shape and magnitude of the hydrograph associated with a given storm rainfall. It follows that the model must be operated with inputs covering a reasonably long period prior to the flood event of interest, to ensure that

5 Operation of reservoirs for flood control 539 antecedent conditions have been correctly simulated. This interval, referred to as the warm-up period, was found to be of the order of six months. To effect economies in both computer time and input data, the daily model was used for simulations during the warm-up period. As the daily and hourly models are structurally similar, the internal variables in warmed-up status can be transferred from the daily to the hourly model a few days (modelling time) prior to the flood event to be monitored. GATE OPERATION TESTS Any flood forecasting and gate operation system would need to be thoroughly tested on historical data before being accepted to operate in a real time situation. Such was the case for this system. Autographic records of rainfall in the basin of Vaal dam are virtually non-existent. Hourly rainfalls were therefore synthesized from daily falls (of which there were plenty of records) by a simple disaggregation procedure. Tests of sensitivity of the simulated flood flows to the number of raingauges used in estimating basin rainfall indicated that of the total of 192 gauges used in the study, 54 were needed for acceptable accuracy. One of the main reasons for selecting Hartbeespoort dam for the second study was that there were eight autographic raingauges operating in the area. Nevertheless, these were still insufficient for proper forecasting and additional data from 34 daily-read gauges were used to improve the estimates of hourly sub-basin rainfalls. The three largest Vaal dam floods on record were selected for initial testing of the flood forecasting and gate operation model. To re-enact these past events as realistically as possible observed data were fed into the computer at hourly intervals of historic time. To avoid all possible bias by virtue of the fact that what had happened was actually known, the release rates calculated by the program were accepted without question. In the normal course of operation, one would have the option of making manual adjustments based on data additional to that used by the program, e.g. weather forecasts. The result of automatic routing of one of the floods is given in Fig. 3, where programmed releases are compared with actual releases. In both cases 3.87 per cent surcharge was allowed. From these routings it is evident that damaging flood levels can be substantially lowered. Real time flood routings supplemented by frequently updated rainfaë based on a telemetry network, or radar, or both, with human intervention where necessary, could of course yield improved results. The eight most severe floods that have occurred since the raising of Hartbeespoort spillway were selected for further testing of the forecasting and operating model. In the automatic routings of these eight floods several different operational strategies were tested, covering a range of allowable surcharge volumes up to a maximum of 27 per cent of full supply capacity (i.e. maximum safe level) and initial flood storages up to a maximum of 23 per cent (i.e. to spillway crest). The free spillway option, which does not require any forecasting or gate operation, was also tested. Figure 4 displays the results achieved by the computerized forecasting and operation model operating under the various strategies, for one of the major Hartbeespoort flood events. Noteworthy here is the extremely steep rise and fall of this double peaked hydrograph, compared with those of a typical Vaal flood (Fig. 3). The rapid runoff response at Hartbeespoort virtually eliminates the prospect of relying solely on pre-release. Uncertainties in the forecast inflow hydrograph can also cancel out the benefits of pre-release. On the other hand, as the hydrographs are generally slender, the provision of modest volumes of buffer storage can help appreciably to reduce peak outflow rates as shown in Fig. 4.

6 54 W. V. Pitman and M. S. Basson Observed inflow (average daily) Observed inflow (6 hourly means) Simulated inflow Actual release Programmed release ! I February 1975 March FIGURE 3. Vaal dam gate operation during the flood of February Observed inflow BankfuM discharge Releases S3,2%surcharge 1 allowed) FIGURE 4. Jan 1977 Feb 1977 Jan S977 Feb 1977 Comparison of different flood control strategies at Hartbeespoort dam. ANALYSIS OF RESULTS The economics of flood damage prevention and the benefits of flood warning are discussed in some detail by Kuiper (1971) and Day (1973) respectively. The total annual cost of flood forecasting and gate operation package for Vaal dam, based on a

7 Operation of reservoirs for flood control Flood/Surcharge storage (% full supply capacity) FIGURE 5. Relationship between flood/surcharge storage and average flood peak attenuation for Hartbeespoort dam, telemetry network, would be of the order of 2. The annual flood damage likely to be suffered in the urban and industrial complex immediately downstream of Vaal dam is estimated at about 9. Without doubt distinct economic advantages would follow from a system for the control of flood releases from Vaal dam". Figure 5 was derived from an analysis of many automatic routings of each Hartbeespoort flood controlled according to differing strategies. Since every flood will respond differently to a given strategy, because of differences in forecasting accuracy, the graph merely represents an average attenuation possible for the given strategies. A survey of downstream damage resulting from the major flood of January 1978 provided data against which to assess the economic benefits of providing varying volumes of buffer storage. Outflow hydrographs resulting from various control strategies were routed through the downstream flood plain. With the aid of a backwater model (Weiss, 1976) it was possible to relate peak discharge to inundated area and, in turn, to damage cost. In this way the reduction in mean annual flood damage associated with each strategy could be established. The annual cost of a forecasting and gate operation package for Hartbeespoort dam is estimated at 15. The cost of surcharge storage was related to the cost of expropriating properties around the periphery of the lake. The cost of storage allocated to flood control was assessed on the basis of a corresponding reduction in firm yield and therefore a loss of irrigation water converted to monetary terms. A summary of the cost benefit analysis is shown in Table 1. Because expropriation costs are relatively low the most attractive solution appears to lie in the

8 542 W. V. Pitman and M.S. Basson TABLE 1. Cost-benefit analysis Flood control strategy Cost [ p a-1 Forecastir ig Other Total Benefit [ p.a.] Net benefit [ p.a.] Current strategy No surcharge 3.2% surcharge 5.2% surcharge 1.7% surcharge 16.3% surcharge 27% surcharge 1% flood storage 23% flood storage Free spillway provision of surcharge storage; in this case a volume of about 16 per cent of the full supply capacity. The foregoing analysis was based on the assumption that the flood control policy would be held constant throughout the year. However, because of the strongly seasonal distribution of rainfall, flood expectancy varies considerably from month to month. The period of highest flood expectancy is mid-summer, December February and the lowest, June August. The highly seasonal character of the rainfall also gives rise to a pronounced variability in the expected replenishment and therefore in the yield at different times of the year. It follows that without reducing the yield it would be permissible to draw down the reservoir level at the start of the wet season to create buffer storage for flood control. The rule curve presented in Fig. 6 was derived by methods developed by Midgley and Pitman (1969). The curve gives the storage at each month of the year required to maintain the same draft as that of a full reservoir at the critical time of the year, viz. May, the start of the dry season. By operating according to this rule curve one could achieve flood alleviation benefits similar to those attained by provision of a seasonally invariant flood storage of 1 per cent but without the costs associated with the loss of production. The resulting net benefit of 33 a year is competitive with that of optimum surcharge. A combination of the two strategies would yield an annual net benefit of the order of 5. o C 5 top of spillway crest ~i r-rule curve based on equal risk of supply failure 1. FIGURE 6. -estimated rule curve based solely on considerations of flood ottenuaflon J I L_J L Dec Jan Feb. Mar. Apr. May. Jun. Jul. Aug. Sep. Oct. Nov. Dec. Time of year Rule curves for Hartbeespoort dam.

9 CONCLUSIONS Operation of reservoirs for flood control 543 A procedure for simulating the response of a river to storm rainfall and for optimizing gate operation so as to minimize downstream flood damage has been tested on two different drainage basins. In the first study, at Vaal dam, with a large basin which responds relatively slowly to storm rainfall, sufficient time is available to create substantial buffer storage by prereleasing water from storage. Major floods could be attenuated by as much as 26 per cent, with potential benefits far outweighing the cost of implementing the flood warning and gate operation package. The second study concentrated on the relatively small, steep basin of Hartbeespoort dam which is subject to intense thunderstorm activity and therefore generates flash floods. The result is that the floods cannot always be accurately forecast, and as the response time is so short, pre-release alone seldom achieves satisfactory attenuation. By analysing the performance of the gate operation model over a range of flood storages it was possible to derive a relationship between buffer storage and average attenuation. Benefit -cost analyses showed that reduction of yield could not be economically justified. However, operation with a seasonally varying volume of flood storage was shown to bring about substantial savings in flood damage without reducing the yield. By operating the reservoir according to a rule curve and allowing reasonable surcharge, net benefits from flood control can be maximized. REFERENCES Basson, M. S. (1978) Flood forecasting for reservoir operation by deterministic hydrological modelling. Report no. 1 /78, Hydrological Research Unit, University of the Witwatersrand, South Africa. Day, H. J. (1973) Benefit and cost analysis of hydrological forecasts. WMO Report no. 314, Geneva, Switzerland. Kuiper, E. (1971) Water Resources Project Economics: Butterworth, London, UK. Midgley, D. C. and Pitman, W. V. (1969) Surface water resources of South Africa. Report no. 2/69, Hydrological Research Unit, University of the Witwatersrand, South Africa. Pitman, W. V. (1976) A mathematical model for generating daily flows from meteorological data in South Africa. Report no. 2/76, Hydrological Research Unit, University of the Witwatersrand, South Africa. Pitman, W. V. (1977) Flow generation by catchment models of differing complexity - a comparison of performance. Report no. 1/77, Hydrological Research Unit, University of the Witwatersrand, South Africa. Pitman, W. V. and Basson, M. S. (1979) Flood forecasting for reservoir operation with specific reference to Hartbeespoortdam. Report no. 1/79, Hydrological Research Unit, University of the Witwatersrand, South Africa. Plate, E. J. and Schultz, G. A. (1973) Flood control policies developed by simulation. In Proceedings of 2nd International Symposium on Hydrology (Fort Collins, Colorado, USA). Weiss, H. W. (1976) An integrated approach to mathematical flood plain modelling. Report no. 5/76, Hydrological Research Unit, University of the Witwatersrand, South Africa.

10