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:
be a series of observed inflow 
during day 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:
of V. The model started predicting the flood volume 
based on the flow ratio Y and later anticipated the peak discharge 
of P by:
of V and the corresponding discharge 
of P with Equation (2) to those 
of design flood 
would yield the return period K of X by:
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:
of the 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:
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
, 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.
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 K1 to those 
and 
of the largest one K*. That is, the proposed procedure initially considers the K1-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:
. The procedure later assesses the amount 
of the resulting space using a maximum net-storage limit 
by:
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 km2. The capacity of normal retention storage is 2,263.6 × 106m3. The main reservoir space for flood control is higher than the level of normal retention to that (3,000 × 106 m3) of the Non Sung Dike. The extra storage for flood surcharge between the dike and the maximum capacity (4,640.4 × 106 m3) of the reservoir is provided to secure the dam against probable maximum flood. The peak discharge of appurtenant spillway is 302.4 × 106 m3/d while the safety discharge of the Nam Pong River downstream of the reservoir is 34.6 × 106 m3/d. The total amount of desirable water requirements in the dry season is 1,500 × 106 m3. 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).
Net DFCRC volume 
of 
and maximum outflow 
of 
for 
return period ranging from 
| 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 |
Location of the Ubol Ratana Dam and Khon Kaen rainfall station.
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.
Outflows and storages of the proposed DFCRC and existing FCRC operational procedures against actual flood in 1990.
Outflows and storages of the proposed DFCRC and existing FCRC operational procedures against actual flood in 1990.
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.
Outflows and storages of the proposed DFCRC and existing FCRC operational procedures against actual flood in 1995.
Outflows and storages of the proposed DFCRC and existing FCRC operational procedures against actual flood in 1995.
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 R2 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.
Outflows and storages of the DFCRC operational procedure against the HadCM3A2 and HadCM3B2 floods in the 2030s period.
Outflows and storages of the DFCRC operational procedure against the HadCM3A2 and HadCM3B2 floods in the 2030s period.
Outflows and storages of the DFCRC operational procedure against the HadCM3A2 and HadCM3B2 floods in the 2050s period.
Outflows and storages of the DFCRC operational procedure against the HadCM3A2 and HadCM3B2 floods in the 2050s period.
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.
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