## Abstract

Dynamic flood control rule curves (DFCRCs) that balance the use of conservation space between flood control and conservation purposes are usually necessary for the operation of a multipurpose reservoir. This paper therefore proposes a procedure to apply the DFCRCs of an historically-based actual flood for reservoir operation versus different floods whose hydrograph shapes vary widely. The proposal uses related-size characteristics (e.g. net retention of the DFCRCs and peak discharge of associated outflows) in a stepwise manner from those of the smallest return period to those of the largest one. Illustrative applications of the procedure to the operation of the multipurpose Ubol Ratana Dam (The Nam Pong Basin, Thailand) have indicated that it enables the DFCRCs to ensure the reservoir's operation against various floods. Its operational results for the large and moderate floods in 1990 and 1995 are comparable to those of historically based floods. In addition, impact assessment of climate change on the operational performance has shown that the system could not protect the areas upstream and downstream of the dam from the HadCM3A2 and HadCM3B2 floods at the 80th and 95th percentile levels during the future 2050s period.

## INTRODUCTION

A multipurpose dam is a principal infrastructure for risk management of flood and drought in a watershed area. However, the size of flood control space in the reservoir system is usually limited to handle a project designed flood. Consequently, additional storage shared from its retention capacity (i.e. flood control rule curves, FCRCs) is necessary to accommodate the flow excesses of the limited space (Mariën 1984; Kelman *et al.* 1989; Mariën *et al.* 1994; Lee *et al.* 2009, 2011).

Current practice allocates the retention capacity of the reservoir system for every flood season based on the FCRCs because it thoroughly emphasizes the safety of the dam, and thus expects that each arriving flood may become the design flood (Developments in Water Science 2003). The conservation performance for the multipurpose dam in practice depends generally on the size of an incoming flood. It reasonably satisfies a corresponding purpose of the system for most floods whose magnitudes are adequate to compensate a deficit from a total level of desirable water requirements during successive dry seasons. However, its application frequently yields the limited reservoir storage at the start of the dry period because of the large occurrence probability of a considered small flood. This indicates the necessity of efficiently using the retention capacity of the reservoir between the competitive conservation and flood control objectives (James & Lee 1971).

Chaleeraktrakoon & Chinsomboon (2015) developed an approach to derive dynamic FCRCs (DFCRCs) of a multipurpose reservoir system that balanced the uses of its retention space against different floods. The developed approach, consisting of a combination of a flood prediction model and a storage routing method, determined the DFCRCs with certain observed floods of various return periods. The DFCRCs of the approach allotted the associated reservoir storage for the considered floods to meet the purposes of the dam successfully. This supports the possibility of considering DRCRCs for reservoir operation for the other floods. However, as actual flood is a complex process producing a wide variation in flood hydrograph shapes of a particular return period, it is therefore necessary to develop a procedure to apply the DFCRCs of historically based floods for operating the reservoir versus different ones of the same size.

The present paper proposes a procedure that applies the DFCRCs to multipurpose reservoir operation for various floods. The proposal adopts the total shared retention of the DFCRCs and the peak discharge of associated outflow hydrograph as operational parameters to deal with several different floods. The proposed procedure applies the chosen parameters in a stepwise manner starting from the smallest to the largest so the prediction on the size of an arriving flood is not necessary. Illustrative applications to different actual floods of the Ubol Ratana Dam have shown that the DFCRCs are able to operate the reservoir system against various floods. Further impact assessment of climate change on the operational performances of such dynamic rule curves has indicated that the flood control behavior is acceptable for the medians of the HadCM3A2 and HadCM3B2 floods in the 2020 and 2050 periods but it is unsatisfied for the projected floods at the 80th and 95th percentile levels.

## DYNAMIC FLOOD CONTROL RULE CURVES

DFCRCs are generally a sequence of conservation spaces that effectively accommodate the floods of a particular return period. Chaleeraktrakoon & Chinsomboon (2015) developed an approach for the evaluation of the DFCRCs using the historically based flood of the considered size. The developed approach consisted of a combination of a flood prediction model and a storage routing method as follows:

*τ*of an actual flood considered,

*V*be the volume of

**X**and

*P*be the peak discharge of

**X**. Also, we denote the ratio of cumulative flows as:where

*t*is the date of the maximum slope in rising period of

**X**. Following Linsley

*et al.*(1988), Boonyasirikul (2004) and Sookchom (2004), the flood prediction model adopted the cumulative flow

*Y*as an estimator of the flood volume of

*V*. The model started predicting the flood volume based on the flow ratio

*Y*and later anticipated the peak discharge of

*P*by:where F(.) was either a linear or non-linear regression relationship between the flood volume

*V*and the flow ratio

*Y*estimated using available flood data, and G(.) was a considered regression function between the peak discharge

*P*and the total cumulative flow

*V*that best fitted the observations (Nguyen & Chaleeraktrakoon 1992).

*V*and the corresponding discharge of

*P*with Equation (2) to those of design flood would yield the return period

*K*of

**X**by:in which was the recurrence interval of the flood volume

*V*taken from the equality of the estimate and the design estimate , and was that of the discharge

*P*obtained from the agreement between the flood peak with the matched estimate . The model then referred to a set of design floods, , and expected the arriving flood of

**X**as:

*K*-yr return period based on the referred design flood . The method routed the flood through the reservoir system by establishing an outflow hydrograph of in triangular shape (Ashkar & Rousselle 1981). It defined the locus of maximum outflow of along the recession limb of because the storage of this routing type depended solely on the outflow hydrograph (Linsley

*et al.*1988). In addition to the routing characteristic, it simultaneously considered the physical characteristics and the objectives (i.e. flood control and conservation purposes) of the reservoir system to evaluate the triangular outflows and associated DFCRCs as:in which was the amount of daily water demand, was the safety discharge of a river downstream of the reservoir,

*D*was the total amount of water demand in successive dry seasons, was the initial storage at the start of the flood

**X**, and was the retention capacity of the reservoir.

## PROPOSED OPERATIONAL PROCEDURE

*K*-yr flood varies widely. It is therefore necessary to propose a procedure that applies the DFCRCs for the reservoir operation versus different floods. A brief description of an operational proposal is as follows: consider the net DFCRC volume , i.e. in which = occurrence date of – of , and the maximum outflow of as fundamental related-size characteristics (Chaleeraktrakoon & Chinsomboon 2015). These properties and are hence adopted as operational parameters of the reservoir system for dealing with various actual floods. At the start of the flood season, the proposal uses the DFCRC volume of , in which is a project design flood of the

*K**-yr return period, to separate the total retention capacity into two portions: a based storage for desirable water-use activities, and the empty volume for the management on the flood . However, the storage at the end of the preceding dry period is usually below the level . To gain the conservation space , the proposed procedure entirely retains the remaining inflow after discharging its outflow to meet the water demand by:

The reservoir spaces and are then maintained until the arrival of an incoming flood **X**.

**X**arrives, prediction of its return period

*K*is usually necessary for choosing the selected characteristics and appropriately. However, it is quite difficult to estimate the recurrence interval

*K*of

**X**accurately because the observed flood data at the location of the dam are usually limited in practice. Hence, the proposal does not expect the flood size

*K*but simply applies the operational parameters and in a stepwise manner from those and of the smallest return period

*K*1 to those and of the largest one

*K**. That is, the proposed procedure initially considers the

*K*1-yr peak discharge as a maximum outflow level in deciding the reservoir release of

**Q**based on effective use of the conservation capacity shared for flood management as:

If the storage of the reservoir is greater than the bound, , in Equation (8), it will increase the cutoff levels and in Equations (7) and (8) to those and of the next larger size , and further apply them to the reservoir operation. Its reservoir operation continues repeating until the flood flow of **X** recedes to be equal to the release of **Q**.

The decision on subsequent release of the procedure depends on the amount of the corresponding storage . If this space, , is greater than or equal to the total amount *D* of water requirements in consecutive dry periods, the proposal will withdraw the storage step-by-step to approach the desirable level *D*. Otherwise, it will keep the inflow to satisfy the water demand *D* as much as possible.

## ILLUSTRATIVE APPLICATIONS

This section considers the proposed procedure to demonstrate the application of the DFCRCs to operate the multipurpose Ubol Ratana Dam for different floods. The location of the reservoir system is 50 km northwest of Khon Kaen Province in the Nam Pong River Basin, Thailand (see Figure 1). The watershed area of the dam is 12,104 km^{2}. The capacity of normal retention storage is 2,263.6 × 10^{6}m^{3}. The main reservoir space for flood control is higher than the level of normal retention to that (3,000 × 10^{6} m^{3}) of the Non Sung Dike. The extra storage for flood surcharge between the dike and the maximum capacity (4,640.4 × 10^{6} m^{3}) of the reservoir is provided to secure the dam against probable maximum flood. The peak discharge of appurtenant spillway is 302.4 × 10^{6} m^{3}/d while the safety discharge of the Nam Pong River downstream of the reservoir is 34.6 × 10^{6} m^{3}/d. The total amount of desirable water requirements in the dry season is 1,500 × 10^{6} m^{3}. Table 1 presents the net DFCRC volume of and the maximum outflow of for the *K*-yr return period ranging from 3 to >10,000 years (Chaleeraktrakoon & Chinsomboon 2015).

K, yrs
. | 3 . | 30 . | 200 . | > 10,000 . |
---|---|---|---|---|

419.4 | 995.2 | 1,236.1 | 1,939.9 | |

13.4 | 15.8 | 18.7 | 34.3 |

K, yrs
. | 3 . | 30 . | 200 . | > 10,000 . |
---|---|---|---|---|

419.4 | 995.2 | 1,236.1 | 1,939.9 | |

13.4 | 15.8 | 18.7 | 34.3 |

The DFCRC operational proposal was tested using large and moderate floods in 1990 and 1995 respectively that were not considered in the development of the DFCRCs. Figure 2 presents sequences of the great flood flows in 1990, and the series of outflow and corresponding storage of the proposed procedure, as compared with those of the FCRC approach. It is apparent that the maximum outflows of the candidates do not exceed the river safety discharge and their largest cumulative storages are approximately close to the normal retention. These operation performances are similar to those of the large flood considered for the DFCRC development in the referred paper.

Figure 3 further displays the outflows and storages of the procedures for the moderate flood in 1995. The figure shows that the DFCRCs yield greater storage for the next dry period than the FCRC approach. The advantage in gaining more storage is the same as that found in the development of the DFCRCs. This consequently indicates that the proposal enables the application of the DFCRCs to the reservoir operation against various floods.

Moreover, the impact of climate change generally affects the performance of the operational proposals. Hence, we assessed the climate change impact by first developing an accepted hydrodynamic model, MIKE 11, with observed daily rainfall at Khon Kaen Province and actual flood at the Ubol Ratana Dam. The development on the MIKE 11 model used the observed flood and rainfall in 2006 for model calibration and applied the data in 2011 for model validation. The coefficient of determination *R*^{2} was 0.7 for both calibration and validation. In addition to this developed MIKE 11 model, we considered the HadCM3A2 and HadCM3B2 scenarios of the daily rainfall process at Khon Kaen Province (Artlert *et al.* 2013) to project corresponding flood hydrographs during the 2030s and 2050s periods. Results of the impact assessment of these projected floods on the operational performances are given below.

Figure 4 presents the outflows and storages of the DFCRC operational procedure against the HadCM3A2 and HadCM3B2 floods at the 50th, 80th and 95th percentile levels in the 2030s period. It is evident that the procedure operates the reservoir for the 50th and 80th percentile floods of both scenarios successfully. The maximum outflows are below the safety discharge and the maximum storages do not exceed the level of the main flood-control space (i.e. there is no inundation in the area upstream of the dam). However, when dealing with the 95th percentile floods, the current river capacity is insufficient, and the extra flood-control space is necessary for flood management. The impact of climate change is more severe for the reservoir operation versus the flood scenarios in the 2050s period (see Figure 5). Enlargement of the river capacity is imperative for the flood whose size is greater than or equal to the 80th percentile level.

## CONCLUSIONS

Effective allocation of retention capacity of a multipurpose dam is often essential for the operation of its reservoir system. Such an allocation is a basis for development of the DFCRCs of the system with a certain observed flood. However, we should consider that only this actual flood in the DFCRC development has raised a problem in the application of the rule curves to the reservoir operation for the other floods whose hydrograph shapes vary widely.

The present paper therefore proposes a procedure that enables the DFCRCs to operate a multipurpose reservoir system for different floods. The proposed procedure adopts relative-size characteristics, such as net retention of the DFCRCs and peak discharge of associated outflows, to deal with various floods. The proposal applies the chosen properties step-by-step from those of the smallest return period to those of the largest recurrence interval, regardless of the prediction on magnitude of the considered flood.

The procedure applied the DFCRCs of the Ubol Ratana Dam, the Nam Pong Basin, Thailand to operate the reservoir system for a large flood in 1990 and the moderate flood 1995 that were different from those considered in the DFCRC development. The results have indicated that the operational performances of the proposal for these floods are similar to those of actual floods found in Chaleeraktrakoon & Chinsomboon (2015). In particular, the results are equal to traditional rule curves when managing the large flood. However, they have the advantage of enabling more dry-season storage for management of the moderate flood. The comparable results indicate that the proposal improves the ability of the DFCRCs to ensure the reservoir operation for different floods. Further applications of the procedure to assess the impact of climate change on the operational performances have shown that they are satisfactory for the medians of the projected HadCM3A2 and HadCM3B2 floods in the 2030s and 2050s periods but fail to meet the flood control purpose for the floods at the higher 80th and 95th percentile levels.

## ACKNOWLEDGEMENTS

Financial support from Research Fund, Faculty of Engineering, Thammasat University is acknowledged. The authors would like to thank anonymous reviewers for their valuable comments and suggestions regarding this paper.