Bydmbgy of Natural and Manmade Lakes (Proceedings of the Vienna Symposium, August 1991). IAHS Publ. no. 206,1991.

Coping with changing objectives in managing an existing multipurpose reservoir

S. P. SMONOVIC Department of Civil Engineering, University of , , MB, Canada, R3T 2N2

ABSTRACT The methodology for formulating, comparing, and evaluating operational rules for a multipurpose reservoir with changing purposes is presented. The issues investigated are examined through the use of the Shellmouth Reservoir and Dam in Manitoba. The methodology is based on combined use of simulation and multiobjective analysis to modify the existing operating rules of the Shellmouth Reservoir. Flood control and water supply objectives are confronted with the use of reservoir water for dilution of the heated effluent from thermal generating plant and improvement of water quality in the river.

INTRODUCTION In 1969 work began on the construction of the Shellmouth Dam near the town of Russell, Manitoba. It began its first full year of operations in 1971. In conjunction with the Project and the Dykes, the purpose of the Shellmouth reservoir was to prevent flooding of the city of Winnipeg and agricultural land along the Assiniboine River. Additional functions of the reservoir included providing public recreational facilities on the newly created Lake of the Prairies, assuring a source of water for the communities of Brandon and , and providing adequate downstream flow for cooling at the Brandon thermal electric plant. Operational procedures were established to meet the demands on the reservoir and these standards are still in use today. The guidelines are based on reaching target reservoir levels to maintain the integrity of the system. Before spring runoff begins water storage volumes of 196.8*106 m? is to be reached by March 31. On November 1, measurement of winter flow begins, and the discharge is adjusted based on projections of these inflows so that the desired spring reservoir level is reached. During the summer months a volume of 369.0* 106 m3 is preferred for recreational purposes. Again adjustments are made to the discharge rate to achieve this desired storage value. Throughout the time period in which the Shellmouth has been in operation the basic outlines for operation procedures have been followed in the hope of preventing a flood situation. Yet in the year 1976 flooding did occur along the Assiniboine River. This failure to provide the promised flood protection has lead to questions about the functioning of the reservoir. An examination of the present operational rules under which the Shellmouth is operating was considered necessary. Through an investigation into how the reservoir would operate under existing conditions using different downstream demand criteria, insights into the ways in which the reservoir could be improved can be achieved. It was for this purpose that the experiments described here were undertaken.

181 S. P. Simonovic 182

DATA In order to undertake an examination of the Shellmouth Reservoir, certain data needed to be collected. The information used during the investigation came from a wide variety of sources including previous reservoir studies and up-to-date streamflow and demands statistics. . Of equal importance to what information was gathered, and where it originated from, is how this knowledge was compiled. Shellmouth Reservoir data were based on existing operational method presented by Kelln (1978). Reservoir volume of 396.0* 106 m3 was indicated as the goal during the summer months under present operational rules, the volumes for the rest of the year varied according to the inflow amounts. Water was released or conserved in order to meet operational standards. For analysis purposes a straight line was assumed between volumes in the months of November and April, and May and June, in order to reach the required spring and summertime levels respectfully. The top of the inactive pool was placed at 12.3*106 m3, the conduit invert elevation. The demands data include the maximum permissible release, the minimum permissible release, the maximum permissible downstream flow, the minimum permissible downstream flow, withdrawal requirements, and downstream water rights. The maximum permissible release is determined by the smaller of the outlet capacity and the downstream channel capacity (US Army Corps of Engineers, 1976). In the case of the Shellmouth reservoir, the channel capacity of 42.5 m3/s was the lower of the two. The minimum permissible release is equated to the leakage value of the system. Due to the unavailability of these data the minimum was taken to be zero. Furthermore, the withdrawal requirements were also left at zero due to the lack of any withdrawal occurring directly from the reservoir. Downstream water rights figures were taken from both a condensed Estimate of Withdrawal from the Shellmouth to Brandon, and a listing of all Assiniboine River Licenses as of December 1989 (Parry and Simonovic, 1990). Finally, a maximum permissible downstream flow of 42.5 m3/s was used (Mudry et al, 1981). The minimum downstream flow was used as a variable in analyzing the reservoir to assess its present operational methods. For the Shellmouth reservoir, the initial month of information to be assessed was indicated to be January of 1971. This date was the beginning of the first year of full operation for the reservoir. The number of years investigated was seventeen, or until the year 1987. Flow data were available only up to this year. Beginning storage was set at 276.75*106 m3, which corresponds to the top of the conservation pool level for the month of January. For the purpose of the analysis flow data are divided into two parts: reservoir inflow and local flow. Reservoir inflow includes all water entering the reservoir, while local flow results from water entering into the channel between the reservoir and the downstream demand point. In the case of the Shellmouth reservoir, information from several streamflow gauging stations was used (Minister of Supply and Services Canada, 1988, 1988a). Three stations were used to record the reservoir inflows; 05MD004 (Assiniboine River near Kamsack), 05MD005 (Shell River near Inglis), and 05MD010 (Stoney Creek near Kamsack). For the local flow, only two stations were used. Each of these stations are found between the Shellmouth reservoir and Russell, Manitoba. The station on the Assiniboine River near Russell, 05ME001, was used as a base from which to judge the differences between the actual releases from the Shellmouth during past years, and the simulation information. Thus it is appropriate that only those local flows up to Russell be used. Data were available for the following stations; 05ME005 (Conjuring Creek near Russell) and 05ME007 (Smith Creek near Marchwell). For 05ME007 no figures were available for the years 1971 to 1975. Also, two smaller tributaries and Thunder Creek enter into the Assiniboine River near Russell. There is no gauging station on these streams. Thus the data used for the analysis is not as exact as possible. Given the low levels of flow recorded, however, the overall effect of these imprecise recordings is minimal. All the input data are available in Parry and 183 Changing objectives in managing a multipurpose reservoir

Simonovic (1990).

METHODOLOGY FOR ANALYSIS Using the available data for the Shellmouth Reservoir, a series of experiments were under taken to determine if the reservoir is operating in the manner in which it was intended, or if improvements should be made. Experiments were conducted using simulation program known as RESQ (Ford, 1990). Six simulation experiments were conducted, each of which concentrated on the variable of demand, and are listed below:

Experiment Demand 1 0.0 2 Monthly Water Rights 3 Monthly Water Rights + Minimum Downstream Flow of 3.0 m3/s 4 Monthly Water Rights + Minimum Downstream Flow of 5.7 mVs 5 6 Monthly Water Rights + Minimum Downstream Flow of 8.5 m3/s Monthly Water Rights + Minimum Downstream Flow of 10.0 m3/s

First experiment was selected to investigate the reservoir capability without any demand downstream. This situation was considered not to be of practical importance. Experiment 2 corresponds to present reservoir use. Manitoba Department of Natural Resources, who is responsible for reservoir management, has contractual obligation to satisfy set of requirements corresponding to this experiment. Experiment 3 has been created to incorporate increasing interest of the City of Winnipeg in obtaining sufficient flow in the Assiniboine River for dilution of industrial waste effluent from various facilities during the low flow period. Experiment 4 corresponds to increased concern of Manitoba Hydro related to dilution of the heated effluent from thermal generating plant located in Brandon. With the requirements in experiment 5 effort has been made to expose Shellmouth Reservoir to joint requirements of the City of Winnipeg and Manitoba Hydro. Final experiment (number 6) has been created to expose the reservoir to the maximum possible demand, combining the requirements of the City of Winnipeg, Manitoba Hydro and potential modification of present water rights. Simulation results has been evaluated using multiobjective analysis method known as Compromise Programming (Duckstein and Opricovic, 1980; Simonovic, 1989). Compomise Programming is an approach which identifies solutions closest to the ideal solution minimizing the distance from the goal point to the set of efficient solutions. The distance measure used in compromise programming is the family of Lp metrics given as:

N f j-fi(x) 1/P Lp(x) = Z Wip i=l f*.-f1 i i -i,w (1) in which Lp(x) is the distance metric; Wj are the weights; f*; is the optimal value of the ith criterion; fjjW is the worst value obtainable for criteria i; fj(x) is the result of implementing decision x with respect to the ith criterion; and p is the parameter, 1 < p <

Six discrete alternatives are ranked according to seven criteria. Four quantitative risk- based criteria have been selected to assess the simulation results along with three qualitative criteria expressing preferences of the Department for Natural Resources, City of Winnipeg and Manitoba Hydro. Risk based criteria used in the analysis are: (i) reliability; (ii) resiliency; (iii)storage vulnerability; and (iv) release vulnerability. S. P. Simonovic 184

Reliability

Reliability is the term given to that aspect of the analysis which shows the probability of a reservoir being in a satisfactory state of operation. Mathematically it is defined as

Reliability= Sumzt/Nglob (2)

where: Sumzt is defined as the sum of all satisfactory states, and Nglob as the length of time analyzed.

Resiliency

Resiliency, the measure of how quickly a reservoir system is able to recover from a failure state, may be equated to the following formula:

Resiliency= l/((Maxtimes/Nglob)*Numfail) (3)

where: Nglob is the length of time analyzed; Maxtimes is the maximum number of consecutive failure states; and Numfail is the number of failure states.

Vulnerability

When a failure state occurs, it is useful to have some method by which to measure the degree of failure which has occurred. The term designated to describe this facet of an investigation is vulnerability. The equation used to determine the degree of failure which occurred in the reservoir simulation was

Vulnerability= Maximum [P*f] (4)

where: P*fisthe maximum penalty for a time of failure. The penalty for failure was determined by the difference between the desired operational method and the actual, unsatisfactory, operational method. An unsuccessful state of operation occurred whenever there was water in the flood-control pool, due to the run storage exceeding the level set by the rule curve. The case in which the actual downstream flow was less than the downstream demands was also considered inadequate. The occurrence of either or both of these events within a given month of examination constituted a failure of the reservoir.

RESULTS

When assessing the results generated by the analysis activities described previously, special attention was paid to the four quantitative risk-based criteria. Through the information found in these data an accurate picture of the events which took place during the Shellmouth reservoir simulation was painted. Individual examination of each of these factors and the changes which occurred in each over the six experiments are recorded below.

Reliability

As expected, as the total downstream demand increased the net reliability of the system decreased (column 2 of Table 1). Beginning with a reliability of 0.89 in experiment 1, there was a significant drop in the system's predictability between the first and the 185 Changing objectives in managing a multipurpose reservoir second experiments. For the second, third, and fourth experiments the reliability of the reservoir remained fairly much static, with values of 0.71, 0.68, and 0.65 respectfully. Decreases in reliability, though less significant than that between experiment 1 and 2, occurred in experiments 5 and 6. Reliability can also be assessed over the time period examined. Here too it is possible to see that the reliability of the system decreases over the six runs. It is also possible, however, to see other aspects of the output. As seen in Figure 1, during the first seven years examined, from 1971 to 1976, there is not a tremendous degree of difference in reliability between the six experiments. They all fall within a range between 1.00 and 0.68, excluding values for 1972. Run 6 results in this time period are, however, somewhat different from what might normally have been assumed. In 1972 the reliability of experiment 6 is greater than that of both experiments 4 and 5. This trend again appears in 1974 and 1975, but more extreme. Here experiment 6 is greater in its reliability that all of the other experiments, a reverse of the anticipated outcome.

1971 Year 1987 FIG. 1 Shellmouth Reservoir reliability.

From 1977 to 1983, the results generally follow the expected pattern for the reliability of the reservoir. Experiment 1 has the greatest reliability while experiment 6 has the least. The difference between these two experiments is extreme. Experiment 1 maintains a mean reliability of 0.94. Experiments 2 to 4 fall within the general range of 0.4 to 0.6 reliability. There is a profound decrease in reliability between the first and the second experiment at this time. Though both maintain a reliability of 1.00 in 1977, until 1983 there is a difference in reliability between these two trials of 0.42. For the final two experiments, the degree of change is great. There is a rapid decrease in the reservoir's reliability during both experiment 5 and 6, culminating in 1981 when their reliability bottoms out at 0.08. The degree of change in reservoir reliability in 1981 is tremendous, beginning at full reliability (1.00) in experiment 1 and ending with almost no reliability by experiment 5. For the years 1984 to 1987 reliability again returns to within the range of 1.00 to 0.67, except for experiment 6. The final experiment continues in its erratic behaviour, surpassing the reliability of other experiments in one year only to then fall to a noticeably lower level of reliability than the other experiments the next year. While the overall picture which emerges from the reliability data is consistent with what may be expected when the downstream demands on the reservoir are increased, a comparison of the individual years of data reveals a picture which is not as straightforward. S. P. Simonovic 186

Resiliency In regards to the resiliency of the Shellmouth reservoir over the six experiments, here too there was a general decrease. Most profound is the decline from experiment 1 to experiment 2. The net resiliency in experiment 1 is 2.22 while the experiment 2 value is 0.86. The ability of the reservoir to recover from failure situations continues to decrease over the next experiment to 0.52. Experiment 4 linearly decreases to 0.35. This trend towards declining resiliency of the system continue with the net resiliency of the system dropping to 0.14 in experiment 5, and a slight decrease to 0.13 in experiment 6. Column 3 in Table 1 shows the net resiliency of the examination. When looking at the resiliency on a year by year basis over the six experiments a slightly different impression emerges. From experiment 1 to experiment 5 for 1971 to 1977 there is a decrease in the resiliency value. In all years though the experiment 6 resiliency is slightly higher than the experiment 5 net resiliency. From 1978 to 1984 the pattern changes to conform more to the anticipated steady decrease over the six experiments each year. In 1985 though there is yet another change in trend. Both in 1985 and 1987 experiment 4 increases its resiliency over that of experiment 3. During 1986 both experiment 3 and experiment 4 have the same resiliency, but experiment 5 and experiment 6 increase theirs. Despite these bumps in the road towards a linear decrease in resiliency over the six experiments, the net resiliency generally follows this pattern.

Vulnerability As the vulnerability of the reservoir was divided into two types, storage vulnerability and flow vulnerability, it is necessary to describe each individually. The storage vulnerability of the reservoir, as seen in column 4 of Table 1, remained the same (241.46*106 m') for the first four experiments. There then followed a fairly rapid decrease in storage vulnerability due to the necessity to release more water to meet the increasing downstream demands. While the decline in vulnerability from experiment 4 to experiment 5 was moderate, ending with a storage vulnerability for the fifth experiment equal to 233.57*106 m3, there then followed a swift decline in storage vulnerability in experiment 6. The final storage vulnerability was 197.41*106 m3. In all six experiments the net storage vulnerability, the maximum amount from all seventeen years examined, was taken from the year 1976. When broken down on a year by year basis, the storage vulnerability of the Shellmouth reservoir experiments follows a predictable pattern. As the downstream demands increase, the storage vulnerability each year decreases. This outcome is plainly seen in Figure 2. The storage vulnerability also accurately reflects the years which experienced high inflow levels, and those with low levels. High storage vulnerability was experienced in 1976, a year of heavy inflows, while the storage vulnerability for 1977, 1978, 1981, 1982, and 1984 for all of the experiments was 0.00 m3, times of drought. Thus both on an individual year basis and overall, the storage vulnerability results are as may be predicted. The downstream flow vulnerability operates in the opposite manner to the storage vulnerability. As the downstream demands increased, so did the flow vulnerability. Viewing column 5 in Table 1 it can be seen that the increase was moderate between experiment 1 and experiment 2, while remaining at 0.97 m3/s for both experiment 2 and experiment 3. There is a significant increase in flow vulnerability between experiment 3 and experiment 4, followed by a continuous, tapered increase for experiments 5 and 6. Over the course of the experiment flow vulnerability increases from 0.00 m3/s to 10.97 m3/s. Examined yearly, it is also possible to clearly see the increase in flow vulnerability which takes place in the fourth, fifth, and sixth experiments. The experiment 1 results 187 Changing objectives in managing a multipurpose reservoir

1971 Year 198? FIG. 1 Shellmouth Reservoir storage vulnerability. show a constant flow vulnerability of 0.00 m3/s over the entire period of examination. Experiment 2 and experiment 3 follow more or less an identical path across the graph, with output within the 0.00 mVs to 0.97 m3/s range. When downstream demand is equal to the sum of monthly water rights plus a minimum downstream flow of 5.7 mVs for experiment 4, initially there is little difference from its flow vulnerability than from previous experiments. However, from the years 1978 to 1984 there is a dramatic increase in the flow vulnerability before returning to the low levels of former experiments during the final years examined. For the last two trials there was a sudden jump in flow vulnerability during the early years of the experiment. For example, the recorded flow vulnerability in 1974 increased from 0.27 m3/s in experiment 4 to 8.77 m3/s and 10.27 m3/s in experiments 5 and 6 respectfully. During the latter part of the time period investigated the flow vulnerability remained high for both trials, except for recovery periods in 1980 and 1986. Experiment 5 was able to undergo a period of recuperation in 1984 as well. The only year in which a recording of 0.00 m3/s flow vulnerability was made for all of the experiments was 1975. Slight amounts of vulnerability were recorded in 1976, a year of historical flood conditions, for both experiment 5 and experiment 6.

Multiobiective analysis Multiobjective evaluation of the simulation results has been expanded to include qualitative criteria representing preferences of the Department of Natural Resources (column 6, Table 1), City of Winnipeg (column 7, Table 1), and Manitoba Hydro (column 8, Table 1). In order to rank alternatives, Compromise Programming requires set of weights, usually to be provided by the decision maker. Introduction of wj allows the expression of the decision makers feelings concerning the relative importance of the various criteria. Thus, the Compromise Programming is providing a double- weighting scheme. The parameter p (equation 1) reflects the importance of the maximal deviation from the ideal point and the weight Wj reflects the relative importance of the ith criterion. Procedure provides the best compromise expressed in the form of optimal rank of alternatives. In this study the search for optimal rank has been replaced with the search for the most robust alternative. As suggested by Simonovic (1989) this task can be successfully accomplished by generating wide range of weights simulating S. P. Simonovic 188

decision maker's preferences. Comparing obtained ranks, the alternative which is the most of the time found between the first three is recommended as the most robust one. Table 2 lists 13 different weighting schemes used in this study, and Table 3 lists the first three ranked alternatives for each of 13 weighting schemes.

TABLE 1 Compromise programming input data rank.

Experiment Reliability Resiliency Storage Flow Department City of Manitoba Vulnerability Vulnerability Natural Winnipeg Hydro Resources (1) (2) (3) (4) (5) (6) (7) (8)

1 0.89 2.22 241.46 0.00 2 1 1 2 0.71 0.86 241.46 0.97 10 2 2 3 0.68 0.52 241.46 0.97 9 10 8 4 0.65 0.35 241.46 6.67 8 9 10 5 0.56 0.14 233.57 9.47 6 8 9 6 0.51 0.13 197.41 10.97 3 5 6

TABLE 2 Weighting schemes used in multiobjective analysis.

Weighting Scheme Criteria 1 2 3 4 5 6 7

1 1 1 1 1 1 1 1 2 2 2 2 2 5 1 1 3 2 2 2 2 1 1 5 4 2 2 2 2 1 5 1 5 5 1 1 1 3 3 3 6 1 5 1 1 3 3 3 7 1 1 5 1 3 3 3 8 1 1 1 5 3 3 3 9 10 10 10 10 5 1 1 10 10 10 10 10 1 1 5 11 10 10 10 10 1 5 1 12 3 3 5 3 5 2 2 13 3 3 3 5 2 5 5

TABLE 3 Final ranking of alternative solutions (only first three shown).

Rank Wei ghting scheme 1 2 3 4 5 6 7 8 9 10 11 12 13

1 3 2 3 3 3 3 3 3 1 1 1 3 3 2 4 3 4 4 4 4 4 4 2 2 2 2 4 3 2 4 5 5 2 2 5 2 3 3 3 4 5 189 Changing objectives in managing a multipurpose reservoir

CONCLUSIONS From the simulation and multiobjective analysis it was found that present size of the Shellmouth Reservoir allow for possible modification of its operation to include the requirements of the City of Winnipeg in the amount of up to 3 m3/sec. This solution corresponds to the experiment number 3. Table 3 shows that experiment 3 has been ranked 9 times as the first, 1 time as the second and 3 times as the third alternative. Corresponding values for reliability, resiliency, and vulnerabilities are 0.68, 0.52, 241.46 and 0.97 respectively. Consideration of other additional requirements is possible only at the expense of reduced reservoir reliability, resiliency and vulnerability. For any other modification including change of the reservoir storage (by increasing the dam hight) the same analysis should be performed to provide the insight into the reservoir capability to handle additional requirements.

ACKNOWLEDGEMENTS The simulation analysis presented in this paper has been performed by Miss.Jo-Ellen Parry. Her help is greatly appreciated.

REFERENCES Duckstein, L. and S.Opricovic (1980) Multi-objective Optimization in River Basin Development, Water Resources Research 16( 1 ), 14-20 Ford, D.T. (1990) Reservoir Storage Reallocation Analysis with PC. ASCE Journ. of Water Res. Plan, and Mang. (116Y2. 157-173. Kelln, D.E. (1978) Simulation Study to Assess the Flood Peak Reduction Capability of Shellmouth Reservoir. Internal report. Manitoba department of Natural resources. Minister of Supply and Services Canada (1988) Historical Streamflow Summary Manitoba to 1987. Environment Canada. Minister of Supply and Services Canada (1988a) Historical Streamflow Summary to 1987. Environment Canada. Mudry, N., G.H. Mackay and V.M. Austford (1981) Flood Control and Flow Regulation Problems on the Assiniboine River. Canadian Water Resources Journal (6)4, 157-173. Parry, J-E., and S.P.Simonovic (1990) Shellmouth Reservoir Simulation Investigation Using Various Downstream Demands. Water Resources Research Report 17, The University of Manitoba, 235pp. Simonovic, S.P. (1989) Application of Water Resources Systems Concept to the Formulation of a Water Master Plan, Water International 14,37-50. US Army Corps of Engineers (1976) HEC-3 Reservoir System Analysis for Conservation: Programmers Manual. Corps of Engineers, US Army.