Flood Modulation

Flood Modulation

Details a rational method of handling floods through dam reservoirs.

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Flood Modulation

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0.1 This article will attempt to explain a suggested procedure for ‘calculating’ and taking the ‘risks’ in dealing with mutually conflicting goals of multi-purpose dams and reservoirs. The Ukai reservoir is used as an example only to make the discussion easily comprehensible and less abstract. It is not the intention to find faults with any person, organization, government or civic body with respect to any past events. The only purpose here is to see if this writer can be of some help for future events.

0.2 Dams are designed and built for different purposes. Some are single-purpose dams whereas others are multi-purpose dams. The multi-purpose dams would be more difficult to operate than the single-purpose ones if they have mutually conflicting purposes. Some multi-purpose dams, although originally designed for compatible purposes, need to be operated to satisfy some non-compatible purpose also. An example of the last type is the Ukai Dam, Gujarat.

0.3 Ukai Dam Project as originally conceived, planned and completed was intended to conserve water for irrigation and hydropower generation. It did not envisage flood control. However, the fact that there is a mega-city Surat only about 60 miles downstream from it requires that the Ukai reservoir be operated so as not to cause excessive damage there. This introduces the non-compatible purpose of flood modulation to the purposes of the dam. The original purposes of irrigation and power generation require that as much water is stored in the reservoir as possible not exceeding the Full Reservoir Level 345.00 (FRL) for which the dam is designed and built although it can structurally withstand water levels up to High Flood Level 351.00 (HFL). On the other hand, flood modulation requires that the reservoir be kept sufficiently unfilled to be able to absorb a probable flood that may or may not bring in enough water to fill the reservoir back to the level we started with. In such a situation, we need to take a ‘calculated risk’. An attempt is made here to suggest a way to ‘calculate’ that ‘risk’ for taking prompt and sound decisions during a flood event in future.

0.4 It is extremely important to realize that one cannot err on the ‘safe side’ while operating such a multi-cross-purpose reservoir because there is none. What is safe from one point of view (say flood modulation) is equally unsafe from the other points of view (such as irrigation, power generation etc.) and vice versa. We must strike and maintain a balance between the conflicting needs.

For a non-technical primary introduction, please see

Flood Analogy.

For a non-technical Gujarati discussion, please see

ઉકાઈ જળાશયની ભયજનક સપાટી

પૂર સંચાલન

ખતરનાક રૂલલેવલ

1.0 Flood Control vs Flood Modulation:

1.1 We need to understand the difference between controlling and modulating a flood. ‘Flood control’ implies that we control a flood such that it causes none or negligible damage to the areas likely to be affected. Very few dams can accomplish this.

1.2 Most of the time, all we can do is ‘modulate’ the flood, which means that we can reduce the peak flow rate to minimize the damages to the affected areas and prevent loss of life. This can be done in two phases. First, we try to delay the arrival of the flood at the target area so that warnings can be issued to the population and people evacuated to safe places. Second, we try to extend the duration of the flood. The same quantity of water is allowed to flow but over a much longer period. The slow release lowers the flow rate in turn resulting in lower water levels, smaller flooded areas and less damages. Not being a ‘flood control dam’, Ukai can only modulate the floods. Some damages are therefore unavoidable in cases of major floods.

1.3 The fact that only flood modulation is possible means that the people who live in the areas likely to be affected by the ‘modulated’ floods must always be vigilant. We must remain prepared all the time for any situation and must not do anything that would worsen it.

2.0 The Basics:

2.1 The basic concept is misleadingly easy. When we come to know that a flood is arriving or developing, we release water from the reservoir to make space. This is called advance depletion. When the flood does arrive at the reservoir, we allow a smaller outflow rate than the inflow rate. The difference gets stored in the space behind the dam. Once the inflow rate starts decreasing, we maintain higher outflow rates to bring the reservoir level down back to the original one at the start of the event.

2.2 The reality is not this simple. In deciding to release water in anticipation of a flood, the concern is the probability that the flood may not bring enough water to fill the reservoir back to the original level or may bring in much more water to make the modulation ineffective. Advance depletion can be hazardous not only when it is excessive but also when it is inadequate. So, how to make sure that it is about the right size? We need to take a ‘calculated risk’. One method to do so is presented below.

2.3 Similarly, in the later stage, how much smaller should the outflow rate be than the inflow rate? If the difference between inflow and outflow is too small, we may cause avoidable flooding and damages to the areas to be protected and also run the risk of losing precious water. On the other hand, if it were too large, it may cause the reservoir levels to rise too high thereby endangering the safety of the dam. So, this is also a matter that requires taking a ‘calculated risk’. In almost all cases, it is important not to let the dam break because that would cause several times more damages and loss of life than letting the flood pass through without modulation.

3.0 Preparatory work:

3.0.1 We cannot start handling a flood event properly unless we have done our ‘homework’ and made preparatory analysis of the past data before the flood season.

3.0.2 A river is a flow system in which the flow rate (cusecs i.e. cubic feet per second) is the key parameter. A reservoir formed behind a dam is a storage system in which the volume of water is the key parameter. The input to the reservoir is in the form of variable flow rates at different instants of time. It gets converted to volume of water stored. The outflow rate also results in volume of water un-stored. Therefore, it is important that our decisions to store or release water be based in terms of volumes of water rather than flow rates, reservoir levels or dates.

3.1.0 Flood Stages:

3.1.1 It is useful to divide a flood in four stages. Please see the Figure 1. If we plot the flow rate against time, the resulting graph is called a hydrograph.

Stage 1: The flood is minor or medium. The flood flow rate is increasing but is less than the ‘Critical Flow Rate’ Oc that would cause water level at a target point to exceed the ‘danger level’. For example, in 1968, Tapi could carry 8½ lakh cusecs at ‘danger level’ of 98.00 at the Hope Bridge, Surat, when Ukai dam was completed.

T1-2 is the time at which the flood enters Stage 2.

Stage 2: The flood flow exceeds Oc and keeps increasing. The flood is now a major one.

Tp is the time at which the flood reaches its maximum i.e. the peak flow rate Ip.

Stage 3: The flood flow is decreasing but still exceeds Oc. The flood is still a major one.

T3-4 is the time at which the flood passes from Stage 3 to Stage 4. The duration from T1-2 to T3-4 is Tc, the Critical Time Duration (CTD for short).

Stage 4: The flood flow has reduced to less than Oc and keeps decreasing. Now the flood is a medium one tending to become a minor one.

Stages 1 and 2 together make the ‘Rising Limb’ and Stages 3 and 4 are called the ‘Recession Limb’ of the flood. During recession, generally flood flows decrease at a rate that can be approximated by an exponential decay curve as assumed in deriving the US ACE equation below.

Although the minor and medium sized floods do not have Stages 2 and 3, their study can be surprisingly useful in our endeavor because any meaningful advance depletion can be achieved only when the flood is minor or medium.

3.2 Estimating Flood Volume

3.2.1 Taking ‘calculated risk’ means we need to make some calculations. Here, it means being able to calculate the quantity of water that a flood of a given size would bring in and comparing it with what we need to either keep the reservoir partially filled or to its FRL

3.2.2 A very useful tool for such calculations is available in United States Army Corps of Engineers, Engineering Manual No. 1100-2-3600 dated 30 November 1987. On its pages 4-17 and 4-18, there is a derivation leading to Eq. No. 4-4:

S_A = 2T_s [Q₁ – Q₂ (1+log_e(Q₁/Q₂))] (4-4)  {US ACE Equation}

For convenience, let us rewrite it as

Sa = 2Ts[Q1-Q2 {1+ln(Q1/Q2)}] = 2Ts[Ip-Q2{1+ln(Ip/Q2)}] (Eq. 1)

Where

S_A = Sa = volume to be stored (i.e. likely to be brought in by the flood if it peaks at Q1)

(CFt. i.e. cubic feet)

Q₁ = Q1 = Ip = the inflow (peak rate in cusecs)

Q₂ = Q2 = constant outflow (cusecs)

T_s = Ts = recession constant. (Hours)

log_e = ln is the natural logarithm to the base e.

3.2.3 This equation is based on the observation that most of the time a flood recedes following approximately an exponential decay function. It enables us to estimate the quantity of water likely to be available ‘to be stored’ if the maximum flood flow rate is Q1 (= Ip) and if we are withdrawing water for irrigation, hydropower, losses etc. at a constant rate of Q2. We need to know the value of Ts. Let us proceed as follows:

1. Collect all the flood data of the past. Include all floods larger than Q2.

2. Plot the flood hydrographs.

3. Draw a horizontal line at the ordinate Q2.

4. Measure the area under the hydrograph to the right of the ordinate at Tp and above the Q2 line. Convert this area to the appropriate volume unit. This is the Sa corresponding to the Q1 (= Ip) for this particular flood.

5. Plot this information on a separate graph of Ip on x-axis and Sa on the y-axis.

6. Repeat steps 2 through 5 for all the floods.

7. Develop a correlation (regression) between Ip and Sa. This can be done graphically or better statistically.

8. For each flood, calculate the value of Ts by rewriting Eq. 1 as

Ts = Sa/2[Ip -Q2{1+ln(Ip /Q2)}]

9. On a separate graph, plot Ts against Ip. Check to verify if any statistically significant correlation (regression) exists between the two parameters.

10. Compare the strengths of correlations (r values) developed in steps 7 and 9. Select the stronger of the two for future use. Let us call it the ‘Recession Storage Estimator’, RSE for short.

Every year, this analysis must be updated to include the most recent flood data.

3.3 Volume Excess Analysis:

3.3.1 Volume Excess (Ve) is the term this writer uses for the quantity of water brought in by the flood in excess of the Critical Flow Rate (Oc) during the CTD. If we draw a horizontal line representing Oc, the area under the inflow hydrograph but above the Oc line represents the Volume Excess. We proceed as follows:

1. Collect all hydrographs of major floods with peak (maximum) inflow rates (Ip) exceeding Oc.

2. Draw a horizontal line representing Oc.

3. Measure the area under the hydrograph but above the Oc line. This area, converted to appropriate volume units is the Volume Excess (Ve).

4. Also measure the length of the Oc line between the two points where it crosses the hydrograph i.e. ‘Critical Time Duration’ (CTD = Tc).

5. Plot all the points on a graph of Ip against Ve.

6. Draw a curve through all the uppermost points so that all the plotted points are under it. Let us call it the ‘Volume Excess Envelope Curve’ VEEC for short.

7. Plot a graph of the Ip against Tc. Draw a curve through all the uppermost points so that all the plotted points are under it. Let us call it the CTD Envelope, CTDE for short.

Every year, this analysis must be updated to include the most recent flood data.

3.4 Develop Discharge Schedule:

3.4.1 In consultation with the local authorities of the target area to be protected, develop a schedule of the fastest rate at which the outflows from the dam can be increased in case of need. This should consider all relevant factors such as the topography, the flood carrying capacity of the river at different levels, the minimum time needed for temporary relocation of people to higher safer places etc. This schedule must not be too restrictive because the safety of the target area depends very much on our ability to achieve advance depletion. Too slow a schedule would result in inadequate advance depletion thereby jeopardizing effective flood modulation and hurt the very people we intend to protect. The schedule must also be reviewed every year and updated or revised in light of recent experiences and new information that become available from time to time.

4.0 Suggested Procedure:

The procedure has two phases, Advance Depletion and Flood Modulation.

4.1 Phase 1: Advance Depletion:

4.1.1 Advance depletion does not mean keeping the reservoir under filled for fear of a flood that has not even begun yet. It means depleting the reservoir as soon after, but only after, the flood has started arriving or developing. Driving slower than the speed limit does not necessarily prevent an accident unless one slows down as soon as the traffic light turns yellow and stops at red light. Similarly, keeping the reservoir unfilled does not provide effective flood modulation, if proper decisions are not made when the flood does actually arrive.

4.1.2 Reservoirs are normally designed for 75 percent dependable yields. It is therefore expected that it may remain incompletely filled in one out of four years on an average. Therefore, it is not quite necessary to be absolutely certain that a flood would be able to fill the reservoir back to the initial level if we decide to release water for advance depletion.

4.1.3 The floods occur for only a few days during even the flood season. Let us suppose there has been a dry spell. The river flow is slowly but certainly dwindling causing the reservoir level to keep dropping. Let us suppose that the reservoir is somewhat short of its FRL. The volume of water currently stored is less than the target Full Supply Volume (S). Let us call the difference ‘Storage Deficit’ and denote it by ‘Sd’. We keep getting flood information from upstream stations every Dt hours (three hours in our case study).

4.1.4 After dwindling flows for a few days, there may be a reading larger than the previous one indicating that a flood may or may not be developing. Rather than lose precious time waiting to make sure that it does develop further we need to check immediately whether there is any need to right now release water from the spillway in addition to the constant withdrawal of Q2. This is where the US ACE Equation can provide very valuable help.

4.1.5 Using the RSE, we can now use the equation to estimate the ‘Recession Storage’, the volume of water this ‘flood’ is likely to bring in even if it starts receding immediately i.e. turns out to be just a ‘micro-flood’. At this stage we use a value that is low enough to be highly reliable in favor of conservation. In fact we can use statistical formula to compute a 95 percent reliable value. Let us denote it by Sr.

4.1.6 If Sr is smaller than Sd, we do nothing.

4.1.7 If it is larger, then we can release the difference. Let the ‘Outflow Volume’ be denoted by ‘Vo’. Then,

Vo = Sr - Sd (Eq. 2)

The outflow rate O is then,

O = Vo/(3600*Dt) = (Sr – Sd)/(3600*Dt) (Eq. 3)

4.1.8 We compare this rate with the rate permissible by the Discharge Schedule and select the smaller of the two as the outflow rate for the next Dt hours. The actual volume Va to be released may be less than Vo and needs to be calculated.

4.1.9 The reservoir storage would be reduced by Va. We compute the new storage and estimate the corresponding water level at the end of Dt hours by referring to the reservoir capacity curve or table. Dt hours later, or earlier if possible or necessary, we review the situation. If the flood has fizzled out, the reservoir would drop down to the estimated level sooner. We stop releasing the water immediately. Even then, there will be a high probability that the reservoir will fill back to the target level. More important is the fact that we have gainfully used the time should the flood become a major one. It may happen, as in 1968 Tapi flood, that the rising limb is so steep that we may not have too much time for advance depletion. Therefore, it is imperative not to waste time.

4.1.10 If the flood flow rate has increased, we repeat the process and increase the outflow rate based on similar calculations with updated appropriate values of the parameters. We keep doing this every Dt hours or sooner until the outflow flood rate (release rate) reaches Oc. As the flood changes from micro to mini to medium one, we may use values that have progressively lower statistical confidence levels in favor of conservation. Thus we gradually shift our emphasis from conservation to flood modulation.

4.1.11 By this time, a medium incoming flood has almost become a major outflow flood due to our actions. This is not so objectionable as it might appear to be. In fact such escalation of the outflow flood enables us to create adequate space behind the dam for detaining much larger inflow rates should it become necessary and yet it can be filled back if the inflow flood subsides. This should be treated as the insurance premium we have to pay for protection against major floods. Also, this will alert the population and the authorities in the target area to be prepared for the flood. An incidental advantage may be that the ‘old’ water released from the reservoir is laden with less silt load and may erode the downstream riverbed thereby temporarily increasing the flood flow capacity of the river.

4.1.12 Spillway Capacity Limitation

4.1.12.1 The spillway of the dam may not be able to discharge the outflow rate selected as above. In that case all we can do is to release as much as possible but only until the reservoir level has risen high enough to discharge the required outflow rate. This limitation is an additional justification for treating even a micro-flood as if it were the seed of a catastrophic one without wasting any time in achieving advance depletion.

4.2 Phase II: Flood Modulation:

4.2.1 Once the outflow rate has reached the Critical Flow Rate, we need to follow a different strategy. Now we need not worry about conservation and must focus on flood modulation.

4.2.2 As of now, the inflow flood rate may still be less than Oc and flood is still a medium one. But it has now a much greater potential of becoming a major or a disastrous one. Therefore we cannot be complacent. However, by now much better hydro-meteorological forecasts or warnings may be available for our guidance.

4.2.3 A simple logical criterion can be used to devise and test the scheme for handling the flood now on. If the space that has become available due to the advance depletion is utilized efficiently, then the reservoir will touch the permitted HFL (High Flood Level) just at the instant T3-4. If the reservoir level does not go up to HFL at all, it means that the outflows were larger than necessary. If the reservoir reaches the HFL earlier than T3-4, it would mean that the releases were smaller than necessary which may then necessitate much larger outflows to prevent the reservoir from crossing the HFL and endangering the dam. Neither situation is acceptable. This criterion may be replaced by another one under special circumstances for valid reasons by a properly authorized person after thorough evaluation of the pros and cons of such replacement.

4.2.4 There can be several ways in which the above goal of making the reservoir just touch the HFL at T3-4 can be achieved. The choice would depend upon the availability of reliable forecast data at this point of time.

4.2.5 If the forecast indicates that the flood is likely to subside, we just maintain the outflow at Oc or start gradually reducing it to the expected Ip. Once it becomes fairly certain that the flood will not increase any more, we can stop the outflow and start conserving the water from the recession limb of the flood with a fairly good chance of recouping our ‘losses’.

4.2.6 If the forecast is for a larger flood, we may be able to get at least an estimate of Ip. Then we proceed as follow:

1. Refer to the VEEC developed prior to the flood season to read off the Ve for the Ip value from the forecast.

2. Calculate the Sf value, the Flood Space available behind the dam between the current water level and the HFL (or a lower level only if necessary due to compelling reasons).

3. If Ve is smaller than Sf, all of it will be absorbed behind the dam. The outflow can be maintained at Oc until T3-4 and then made to match the inflow rate. This is illustrated by the 12-lakh cusecs flood in the case study discussed later. Please see Fig. 2.

4. If Ve is larger than Sf, the excess volume must be released. Let us call this the ‘Outflow Volume Excess’. Now the outflow must exceed Oc, but by how much? The shape of the outflow hydrograph should be such that the area between itself and the inflow hydrograph becomes equal to Sf. The outflow ordinates can be made proportionate to the volumes using the equation

O = Oc + (Ve – Sf)(I-Oc)/Ve Eq. 4

4.2.7 We must keep reviewing the developing situation and adjusting the outflows based on updated values of these parameters from time to time. The new values of Ve as well as Sf must be reduced by the quantities that are already experienced/utilized after T1-2. This approach was used in the routing studies for 16-lakh and 20-lakh cusecs floods reported in the case study and depicted in Fig. 3a through 4.

4.2.8 If at all a reliable forecast is available for the entire CTD, it may be possible to adjust the outflow hydrograph to insure a sustained but lower peak outflow rate using the equation

Op = Oc + (Ve – Sf)/(3600 x 0.65 x Tc ) Eq. 5

4.2.9 In this case, increase the outflow gradually from Oc to Op as calculated above within the first 35% of CTD, maintain at Op for the next 30% of the CTD and then gradually reduce it to Oc during the last 35% of CTD as shown in Fig. 4. This will not always give a lower Op than Eq. 4. This is illustrated by the results for different combinations of flood peak, Oc and PMS of the case study entered in the last row of Table 1. It is always better to compare different alternatives to select the best that meets our needs.

4.2.10 During Stage 3 of the flood, we can use Eq. 1 by replacing Q2 with Oc to estimate the remaining Ve. Then we can use that estimate of Ve in Eq. 4 to compute outflows.

4.2.11 Once the reservoir level reaches HFL, the outflow must equal the inflow to prevent further rise otherwise the dam would be endangered. After the inflow drops down to Oc, the outflow should be maintained at Oc until the reservoir level drops back to FRL. There can be a second peak to the flood which would be extremely difficult to handle if the reservoir is still above the FRL.

Fig. 3a ROUTING OF 16 LAKH CUSECS FLOOD WITH NORMAL CONSTRAINTS

Trial routing calculations using this approach indicate that its success is sensitive to the Ts value selected in computing the Vp component. The Ts value for this purpose need not be the same as the one used for advance depletion. Numerous paper trials on historical and hypothetical floods should be run by the damtender during off-season using a range of Ts values to develop a feel for what is likely to work best for the dam in question.

4.2.16 The above approach tends to cause smaller releases during Stage 2 in some cases thereby necessitating larger ones in Stage 3. One way to counter this is to release, during Stage 2, an average of the observed inflow rate and the Oc value. This should also be subjected to trial paper studies.

5.0 River Capacity Preservation

5.1 Any method for handling a flood can accomplish good results only if the downstream river channel is maintained in such a way to preserve its original Critical Capacity Oc. If, through any mistaken steps, we allow the Oc to go down to a lower value, then the ability of the reservoir to provide effective flood modulation will be severely impaired because then the advance depletion time and quantity will be smaller, the CTD will be longer and Ve values will be much larger necessitating higher Op values. This can be seen in Fig. 3 charting the result of routing the 16-lakh cusec flood with a lower value of Oc. It will also cause higher water levels in the target area for the same flow rates that were safely handled in the past. We must therefore take all necessary steps including dredging etc. to make sure that the flood flow capacity of the river channel in the target area is preserved at what it was when the dam in question was built.

Fig. 3b ROUTING OF 16 LAKH CUSECS FLOOD WITH SMALLER O_C

6.0 Case Study

(One lakh equals 100,000. Thus a 1.2 Million cusecs flood is a 12-lakh cusec flood and vice-versa.)

6.1 The above approach has been tested by flood routing calculations. In absence of actual data, three hypothetical floods with peaks of 12 lakh, 16 lakh and 20 lakh cusecs respectively were studied using a computer program developed for the purpose by this writer. It is assumed that the flood occurs at the very end of the season so that the reservoir is full to its FRL. All the floods have identical rising limbs in Stage 1 to insure proper comparison. A Ts value of 18 hours, the smallest observed for Tapi at Ukai, is used for computing Recession Storage. The Discharge Schedule is not available. Therefore it is assumed that the outflow rate can safely be one and a half times as large as the current inflow rate but not more than Oc.

6.1.1 The computer program used for the case study is an MSExcel spread sheet. It can read the storage capacity table and also the spillway capacity table. It uses a slightly different approach in Stage 3 of the flood. It has detailed explanation of each step of the computing process. Any interested reader can obtain a copy of the program by sending an e-mail to tatoodi@gmail.com. This writer will willingly share it with the reader.

6.2 The results are presented as the computer-generated hydrographs in Fig. 2, 3a, 3b, 3c, 3d and 4. They are also summarized in Table 1. The High Flood Levels permitted for each case is depicted as the reservoir storage capacity at that level because they truly represent the effects of lowering or raising the HFL rather than the nominal values. For example, a one foot rise at lower elevations does not add to S_f as much as the same one foot increase at higher elevations.

6.3 The 12-lakh flood is the easiest to handle as shown in Fig.2. There is no need to exceed Oc the Critical Outflow Rate because the Volume Excess is less than the Advance Depletion. The 16-lakh flood is also studied for variations in the values of the Critical Outflow Rate and Maximum Permissible Storage (MPS) between the FRL and the HFL.

6.4 Fig. 3a shows the inflow hydrograph for the 16-lakh flood and the outflow hydrograph as a result of the same parameters as those for Fig. 2 and 4.

6.5 The outflow hydrograph in Fig. 3b results from the Critical Outflow Rate reduced from 8,50,000 to 6,00,000 cusecs.

6.6 In Fig. 3c, the situation is worsened by lowering the permissible maximum storage from 4,00,000 CFt. to 2,00,000 CFt. i.e. by lowering the HFL.

6.7 In Fig. 3d, the Critical Outflow Rate is restored to 8,50,000 Cusecs but not the permissible maximum storage.

6.8 Fig 4 shows that the 20-lakh flood is evidently the worst to handle.

6.9 It is noteworthy that in all cases the curve of storage volumes just touches, but does not cross, the maximum permissible storage line at about T3-4 proving that the criterion discussed in paragraph 4.2.3 above is satisfied.

Fig. 3c ROUTING OF 16 LAKH CUSECS FLOOD WITH SMALLER O_C AND SMALLER MPS

6.10 All outflow hydrographs show a downward dip at about T3-4. This only indicates that the outflow should be made equal to the inflow before the end of that routing period to prevent slight depletion of the reservoir below the initial level. The computer program does not yet have the ability to plot intermediate points. (In a later revision of the computer program, this could be corrected.) It could not be made to write the numbers in Indian style.

6.11 With the same parameters, the 16-lakh and 20-lakh floods need outflows exceeding Oc because Ve is larger than Sf the total Space Available i.e. the sum of Advance Depletion and the space between FRL and HFL.

Fig. 3d ROUTING OF 16 LAKH CUSECS FLOOD WITH SMALLER MPS

6.12 The effects of changing the parameters Oc and HFL can be readily seen in Figures 3a through 3d and Table No.1. Reducing Oc ends Stage 1 earlier. The time to achieve Advance Depletion is shortened. Naturally its size is curtailed. Stage 3 ends later. CTD is much longer. All these result in a much larger Ve. The need for larger outflows becomes inescapable.

6.13 If the HFL is lowered, then Sf becomes smaller necessitating larger outflows to prevent exceeding HFL. If both these constraints are imposed together, much worse situation is created.

6.14 The above analysis makes it imperative to preserve the Critical Outflow Rate that existed before impounding the reservoir. The river’s capacity to carry the flood flow must not be allowed to be impaired. All necessary means like dredging etc. must be employed to achieve this goal.

6.15 It is also obvious that the HFL should also be kept as high as possible.

Fig. 4 ROUTING OF 20 LAKH CUSECS FLOOD WITH NORMAL CONSTRAINTS

6.16 Even with the best combination of Oc and Sf it is not possible to keep the outflows less than Oc if the flood is a severe one. For example, a 16-lakh flood can be reduced to 13-lakh and a 20-lakh one to 15 ¼ lakh cusecs but not any lower. The people and authorities in the target area must therefore always be prepared to face such situations.

Table 1 Comparison of Results of Routing Floods with Different Parameters

Parameters

Note: - One LCFt. equals 100,000 CFt.

7.0 Conclusion:

7.1 Operation of a reservoir impounded behind a dam during a flood event involves taking a risk. It is better to be able to calculate it than to rely on guesswork. A simple but effective method has been presented above for taking such ‘calculated risk’ based on the analysis of past data for the particular river at the particular dam. One can only hope that it will be put to good use.

7.2 Any interested reader can obtain an electronic copy of the case study sending an e-mail to tatoodi@gmail.com.

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DERIVATION OF THE FORMULA FOR

HIGH FLOOD RECESSION STORAGE FOR UKAI DAM PROJECT

Introduction:

‘High Flood Recession Storage’ is the quantity of water that must be temporarily stored after a flood has peaked but is still above the Critical Outflow rate and would therefore raise the reservoir level above the Full Reservoir Level. It needs to be estimated to adjust the releases so as to prevent the reservoir level from exceeding the permissible High Flood Level.

Ukai Dam is built across river Tapi about 100km east of Surat, Gujarat State, India. For more information on the project, the reader is advised to refer to one of the official publications. This write-up is limited to detailing the derivation of the formula for ‘High Flood Recession Storage’ only.

Arrangements are made to provide the dam operators with forecast information for handling floods. However, it is prudent to be prepared for even an unlikely situation in which, for some reason beyond human control, the information does not reach the dam. Also, if the available forecast were for a partial duration only, one would need to estimate the quantity of water likely to flow in during the remaining period. The procedure would then need to be partially modified.

(4) These data were plotted on a graph. Points representing the average HFRS v/s average Ip values were also plotted on the graph.

(5) Three straight lines were drawn, one each for the three Oc values. These lines must pass through the pairs of points (Oc ,0) and (Ip,average, HFRSaverage) as indicated on the chart below.

Chart No. 1

(6) The slopes of the straight lines for each Oc were computed. Obviously, these slopes vary with Oc. Therefore, we need a relationship between the slope of a line for a given value of Oc and Oc itself.

(7) The slopes vs Oc were plotted as shown below.

Chart No. 2

(8) The average slope of this line was calculated to be -0.0000007109. Its intercept on y-axis was calculated to be 1.0204.

(9) The slope of the straight line for any given Oc value can therefore would be

M = 1.0204 – 0.0000007109 * Oc

(10)This line must pass through the point (Oc, 0). Therefore, the y-axis intercept of the line is given by

C = -M * Oc

(11)This gives us the relationship

HFRS = (1.0204 – 0.0000007109*Oc)*Ip – (1.0204 – 0.0000007109*Oc)*Oc

This relationship must be updated and revised after each event of flood exceeding the Oc value to incorporate the latest information.

Conclusion:

The above derivation is imperfect because the data of floods larger than 4,25,000 cusecs but smaller than 8,37,000 cusecs are not available for inclusion in the analysis. Once these data become available, the whole process shall have to be repeated to include them. For the present this serves to indicate methodology for the review of the reader.

This relationship enables one to estimate the quantity of water that a high flood with inflow rate greater than Oc is likely to bring in if it peaks at the current inflow rate Ip between the current time and the time it recedes down to the Oc value. This enables one to investigate the effects of changing the Oc values on the outcomes of a proposed flood handling policy without having to change the parameters for each Oc value. On the other hand, once it is decided to use a certain value of Oc for all future events, it may be useful make up a table of HFRS for that value of Oc and different values inflow rates for the ready use of the dam operators. Such a table must, however, be updated after each flood exceeding the chosen Oc value.

Flood Analogy

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