# A Parametric Flood Control Method for Dams with Gate-Controlled Spillways

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. VEM

- Outflows are lower than or equal to the maximum antecedent inflows.
- Outflows increase when inflows increase.
- The higher the reservoir level, the higher the percentage of outflow increase.
- If the reservoir is at maximum capacity, outflows are equal to inflows while gates are partially opened.

_{TCP}) is the maximum reservoir level allowed under ordinary operation conditions in the absence of floods and the flood control level (FCL, the corresponding volume is S

_{FCL}) corresponds to the maximum water level allowed in the reservoir under ordinary operation conditions considering the flood operation [43]. The available flood control capacity at time i $\left({\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}\right)$ is defined by Equation (1):

_{i}is the volume in the reservoir at time i.

_{i−1}is the outflow at time i − 1 and Δt represents the operation time step. In this study, we adopted a time step of one hour. Considering that outflows must be equal to inflows when ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}$ = 0 and that outflows increase linearly until equaling the inflows at time $\u2206\mathrm{t}\xb7\mathrm{n},$ and by assuming a constant inflow in the future, the increment of outflows ($\u2206{\mathrm{O}}_{\mathrm{i}}={\mathrm{O}}_{\mathrm{i}}-{\mathrm{O}}_{\mathrm{i}-1})$ at each time step is $\frac{\left({\mathrm{I}}_{\mathrm{i}}-{\mathrm{O}}_{\mathrm{i}-1}\right)}{\mathrm{n}}$, and can be expressed by Equation (3) (replacing n by Equation (2)):

_{p}) is determined, taking into account S

_{i}and whether the reservoir volume is increasing (ΔS

_{i}= S

_{i}− S

_{i−1}≥ 0) or decreasing (ΔS

_{i}< 0) (Figure 2). The different outflows are proposed as follows:

- If S
_{i}$\le $ S_{TCP}, the method aims to increase the reservoir level to reach the maximum normal operative level (TCP):$${\mathrm{Q}}_{\mathrm{p}}=0.$$ - When S
_{i}> S_{TCP}, the outflow proposed depends on ΔS_{i}:

_{i}≥ 0, the method releases outflows according to the ΔO previously defined by VEM, as follows:

- ○
- If ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}\le \u2206{\mathrm{S}}_{\mathrm{i}}$, the time intervals (n) until the reservoir runs out of flood control capacity are equal to or lower than one, and the method aims to balance the outflows and inflows:$${\mathrm{Q}}_{\mathrm{p}}={\mathrm{O}}_{\mathrm{i}-1}+\frac{\u2206{\mathrm{S}}_{\mathrm{i}}}{\u2206\mathrm{t}}.$$
- ○
- On the other hand, if ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}>\u2206{\mathrm{S}}_{\mathrm{i}}$, the VEM progressively manages the available ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}$, increasing the outflows as the ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}$ decreases:$${\mathrm{Q}}_{\mathrm{p}}={\mathrm{O}}_{\mathrm{i}-1}+\frac{\u2206{\mathrm{S}}_{\mathrm{i}}{}^{2}}{{\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}\xb7\u2206\mathrm{t}}.$$

_{i}< 0 (and S

_{i}> S

_{TCP}), the VEM aims to continue decreasing the reservoir level until reaching the TCP:

_{p}is obtained, it is compared to the maximum discharge capacity at the current reservoir level (O

_{max.disch.}(S

_{i})) and the maximum of the antecedent inflows (I

_{1}, I

_{2}, …, I

_{i}), and the minimum of the three values is the flow selected to be released through the gates (O

_{i}).

#### 2.2. The Proposed K-Method

_{ALT}) as the maximum admissible flow for avoiding downstream damage; and (3) a maximum gate opening/closing gradient (O

_{max.Gr}). Figure 3 shows the general scheme of the K-Method implementation.

_{AL}). The activation level is the reservoir level in which the rules of operation change, increasing the outflows. The aforementioned characteristic levels determine four zones: 1, 2, 3, and 4 (Figure 3). The proposed outflow (Q

_{p}) is determined as a function of S

_{i}, the corresponding zone (1, 2, 3, or 4), and whether the reservoir storage is increasing (ΔS

_{i}= S

_{i}− S

_{i−1}≥ 0) or decreasing (ΔS

_{i}< 0).

#### 2.2.1. Proposed Outflow in Zone 1

#### 2.2.2. Proposed Outflow in Zone 2

_{i}≥ 0), the method gradually starts to release flow, avoiding abrupt changes of outflows that could be dangerous downstream of the dam. The proposed outflow is as follows:

- If ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}>\u2206{\mathrm{S}}_{\mathrm{i}}$, releases increase linearly from 0 m
^{3}/s (when the reservoir level is equal to TCP) to the proposed outflow in Zone 3 at AL:$${\mathrm{Q}}_{\mathrm{p}}=\left({\mathrm{O}}_{\mathrm{i}-1}+\mathrm{K}\xb7\frac{\u2206{\mathrm{S}}_{\mathrm{i}}{}^{2}}{{\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}\xb7\u2206\mathrm{t}}\right)\xb7\frac{{\mathrm{S}}_{\mathrm{i}}-{\mathrm{S}}_{\mathrm{TCP}}}{{\mathrm{S}}_{\mathrm{AL}}-{\mathrm{S}}_{\mathrm{TCP}}}.$$ - If ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}\le \u2206{\mathrm{S}}_{\mathrm{i}}$, the method aims to balance the outflows and inflows:$${\mathrm{Q}}_{\mathrm{p}}={\mathrm{O}}_{\mathrm{i}-1}+\frac{\u2206{\mathrm{S}}_{\mathrm{i}}}{\u2206\mathrm{t}}.$$

_{i}< 0), the method aims to continue gradually decreasing the reservoir level, avoiding abrupt changes of outflows and minimizing downstream floods:

- If ${\mathrm{I}}_{\mathrm{i}}<{\mathrm{O}}_{\mathrm{ALT}}$, the method releases the maximum precedent outflow limited by the alert outflow:$${\mathrm{Q}}_{\mathrm{p}}=\mathrm{min}\left({\mathrm{O}}_{\mathrm{ALT}}\text{},\mathrm{max}\left({\mathrm{O}}_{1},{\mathrm{O}}_{2},\dots ,{\mathrm{O}}_{\mathrm{i}-1}\right)\right).$$
- Otherwise, the method maintains the reservoir level, avoiding an increment of downstream floods:$${\mathrm{Q}}_{\mathrm{p}}={\mathrm{I}}_{\mathrm{i}}.$$

#### 2.2.3. Proposed Outflow in Zone 3

_{i}≥ 0):

- If ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}>\u2206{\mathrm{S}}_{\mathrm{i}}$, the method progressively manages the available ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}$, increasing the outflows as the ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}$ decreases:$${\mathrm{Q}}_{\mathrm{p}}={\mathrm{O}}_{\mathrm{i}-1}+\mathrm{K}\xb7\frac{\u2206{\mathrm{S}}_{\mathrm{i}}{}^{2}}{{\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}\xb7\u2206\mathrm{t}}.$$
- Otherwise, if ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{F}}\le \u2206{\mathrm{S}}_{\mathrm{i}}$, the method aims to balance the outflows and inflows:$${\mathrm{Q}}_{\mathrm{p}}={\mathrm{O}}_{\mathrm{i}-1}+\frac{\u2206{\mathrm{S}}_{\mathrm{i}}}{\u2206\mathrm{t}}.$$

_{i}< 0), the K-Method decreases the reservoir level at a linear rate, from the maximum antecedent outflow to the outflow proposed at AL (limit of Zones 2 and 3):

- If ${\mathrm{I}}_{\mathrm{i}}<{\mathrm{O}}_{\mathrm{ALT}}$, the method releases more than the maximum precedent outflow limited by the alert outflow:$${\mathrm{Q}}_{\mathrm{p}}={\mathrm{Q}}_{\mathrm{Eq}.\left(12\right)}+\left(\mathrm{max}\left({\mathrm{O}}_{1},{\mathrm{O}}_{2},\dots ,{\mathrm{O}}_{\mathrm{i}-1}\right)-{\mathrm{Q}}_{\mathrm{Eq}.\left(12\right)}\right)\xb7\frac{\left({\mathrm{S}}_{\mathrm{i}}-{\mathrm{S}}_{\mathrm{AL}}\right)}{\left(\mathrm{max}\left({\mathrm{S}}_{1},{\mathrm{S}}_{2},\dots ,{\mathrm{S}}_{\mathrm{i}-1}\right)\right)-{\mathrm{S}}_{\mathrm{AL}})}\text{},$$${\mathrm{Q}}_{\mathrm{Eq}.\left(12\right)}$ is the proposed outflow in Equation (12).
- Otherwise, the method decreases the reservoir level, minimizing downstream floods:$${\mathrm{Q}}_{\mathrm{p}}={\mathrm{I}}_{\mathrm{i}}+\left(\mathrm{max}\left({\mathrm{O}}_{1},{\mathrm{O}}_{2},\dots ,{\mathrm{O}}_{\mathrm{i}-1}\right)-{\mathrm{I}}_{\mathrm{i}}\right)\xb7\frac{\left({\mathrm{S}}_{\mathrm{i}}-{\mathrm{S}}_{\mathrm{AL}}\right)}{\left(\mathrm{max}\left({\mathrm{S}}_{1},{\mathrm{S}}_{2},\dots ,{\mathrm{S}}_{\mathrm{i}-1}\right)\right)-{\mathrm{S}}_{\mathrm{AL}})}.$$

#### 2.2.4. Proposed Outflow in Zone 4

_{i}≥ 0), the gates are operated, maintaining the reservoir level at FCL until they are fully open:

_{i}< 0), the K-Method aims to decrease the reservoir level as soon as possible. The proposed outflow is the one defined during the last interval:

#### 2.2.5. Determination of the Released Outflow at Each Time Step

_{p}is obtained, it is compared to the maximum discharge capacity at the current reservoir level (O

_{max.disch.}(S

_{i})), the maximum of the previous inflows (I

_{1}, I

_{2}, …, I

_{i}), and the maximum gate opening/closing gradient (O

_{max.Gr.}(Si)), and the minimum of the four values is selected as the flow to be released through the gates (O

_{i}).

#### 2.3. I-O and MILP

_{s}associated with the reservoir volumes (and affecting the dam safety) and the P

_{o}associated with the outflows (and affecting the downstream safety), as shown in Equation (20):

_{o}and w

_{s}represent the weight associated with P

_{o}and P

_{s}respectively. The reader may refer to Bianucci et al. [18] for a detailed description of the MILP model. It should be stressed that, unlike the three other methods, the MILP method requires knowledge in advance of the entire inflow hydrographs, and therefore, it corresponds to an unrealistic situation.

#### 2.4. Rainfall Generation, Hydrometeorological Model and Comparison of Methods

_{MAX}) and the maximum outflow downstream (O

_{MAX}) as representative variables for a comparison of the methods’ performance. We implemented a comparative analysis by means of two different approaches (Figure 4). On the one hand, we applied a comparative scheme organized in quadrants, which showed the increasing (or decreasing) of the maximum reservoir level and maximum outflow compared to the VEM (Figure 4a). The points located in the upper right quadrant (Q

_{I}) represent events where the maximum level reached in the reservoir and the maximum outflow were higher than by applying the VEM. The points located in the upper left quadrant (Q

_{II}) show an intermediate situation, with lower maximum levels but higher outflows. The lower left quadrant (Q

_{III}) represents cases for which both the maximum level and maximum outflow were lower than by applying the VEM (i.e., the best situation). The lower right quadrant (Q

_{IV}) represents intermediate situations with higher maximum levels and lower maximum outflows. On the other hand, we implemented the global risk index (I

_{R}) analysis (Figure 4b) proposed by Bianucci et al. [18]. This method accounts for a single indicator of the global risk associated for the Z

_{MAX}and O

_{MAX}, by applying the concept of expected annual damage [53]. First, the damage cost curves (D

_{Z}and D

_{O}) and the cumulative distribution functions (CDF) related to Z

_{MAX}and O

_{MAX}were obtained, based on the information included in the Dam Master Plan and the Dam Emergency Plan. The global risk index is obtained by multiplying the probability of the reference variable (Z

_{MAX}or O

_{MAX}) in the given interval by the damages associated with that variable’s value. In the case of O

_{MAX}, the damages are calculated through floodplain analysis. In the case of Z

_{MAX}, the damages are estimated as the product of the probability of reaching during the flood, provided that the reservoir has already reached Z

_{MAX}, multiplied by the damages linked to dam failure. It is important to point out that there was no expected damage below FCL and O

_{ALT}(Figure 4b). Afterwards, we obtained the partial risk indexes I

_{Z}(Equation (21)) and I

_{O}(Equation (22)) associated with Z

_{MAX}and O

_{MAX}, respectively:

_{Z}and D

_{O}are the damage functions for Z

_{MAX}and O

_{MAX}, respectively, and $\mathsf{\delta}$ represents the incremental non-exceedance probability between two consecutive elements in the sample (either O

_{MAX}or Z

_{MAX}(Figure 4b)), being constant and equal to the inverse of the size of the generated sample (100,000 in the current study). The index j represents the position of the sorted series (ascending order) of maximum outflows and maximum reservoir levels. Once I

_{O}and I

_{Z}were obtained, we used the weighted sum aggregation to obtain the global risk index (I

_{R}). Due to the lack of information, we designated equal levels of priority to both partial indexes (Equation (23)):

_{MAX}and Z

_{MAX.}

#### 2.5. Case Study

^{2}. The climate of the region is Mediterranean (mean annual precipitation of 557 mm). The main purposes of the reservoir are flood regulation, hydropower generation, and water supply for the Region of Murcia.

## 3. Results and Discussion

_{II}and Q

_{III}. Following this, we focused the analysis of the K-Method on K-values higher or equal to one. When analysing the variations of the maximum reservoir level compared to VEM (ΔZ), a higher K-value resulted in a lower Z

_{MAX}, regardless of the range of inflow Trs studied, reaching up to −0.15 m for K = 2 and −0.64 m for K = 50 (Figure 6). However, when analysing the variations of the maximum outflows compared to VEM (ΔO), different behaviours were found, depending on the Trs analysed. Figure 7 shows, for different ranges of Trs, the percentage of cases located in Q

_{III}(the best situation), Figure 8(a1–a6) shows the median and quartiles associated with the maximum reservoir levels (Z

_{MAX}), and Figure 8(b1–b6) shows the variations of the median and quartiles associated with the maximum outflows (O

_{MAX}).

_{II}, regardless of the analysed K-value (Figure 7(a1,a2)), decreasing the maximum levels but increasing the maximum outflows when compared with VEM (Figure 6 and Figure 8(a1,a2,b1,b2). Even though the maximum outflows increased, the O

_{MAX}values did not jeopardize the downstream safety for K-values lower than ten, because O

_{ALT}was not exceeded (O

_{MAX}= 97.2 m

^{3}/s for K = 10).

_{III}, decreasing from 73% for K = 1.25, to 4% for K = 10. For K-values higher than 20, all events were located in Q

_{II}(Figure 7(a3)). Higher K-values achieved lower Z

_{MAX}values, but the opposite occurred for O

_{MAX}. For example, the Z

_{MAX}median decreased from 509.8 to 509.5 m and the O

_{MAX}median increased from 111 to 118 m

^{3}/s for K = 1 (VEM) and K = 10, respectively (Figure 8(a3–b3)). For K-values higher than ten, the median of Z

_{MAX}decreased to 509.3 m for K = 50, while the O

_{MAX}median increased to 124 m

^{3}/s for K = 50.

_{III}for K-values from 1.25 to 6.5, more than 92% for K-values lower than ten, and this decreased down to 17% for K = 50 (Figure 7(a4)). The median of Z

_{MAX}decreased from 509.9 m for K = 1 (VEM), to 509.5 m for K = 10 and 509.3 m for K = 50. (Figure 8(a4)). The median of O

_{MAX}decreased from 177 m

^{3}/s to 170 m

^{3}/s with K ranging from one (VEM) to three, but increased for K-values higher than three, up to 180 m

^{3}/s for K = 50 (Figure 8(b4)).

_{III}for K-values ranging from one to ten (Figure 6 and Figure 7(a5)) and more than 93% for K-values higher than ten (Figure 7(a5) and Figure 8(a5,b5)). The Z

_{MAX}and O

_{MAX}median values decreased from 510.0 m and 270 m

^{3}/s for K = 1 (VEM), to 509.6 m and 252 m

^{3}/s for K = 10, respectively. For K-values higher than ten, the Z

_{MAX}and O

_{MAX}median values remained almost constant.

_{III}(Figure 6 and Figure 7(a6)). The Z

_{MAX}and O

_{MAX}median values ranged from 511.0 m and 375 m

^{3}/s for K = 1 (VEM), to 510.8 m and 360 m

^{3}/s for K = 10, respectively (Figure 8(a6,b6)). For K-values higher than ten, the Z

_{MAX}and O

_{MAX}median values remained almost constant. We also compared I-O and MILP with VEM. As expected, the I-O behaviour was similar to the K-Method for higher K-values (Figure 6). By comparing MILP and VEM, the results showed that all events with a Tr higher than 25 years were located in Q

_{III}, and those with a Tr lower than 25 years located in Q

_{II}presented outflows that did not jeopardize the downstream safety (Figure 6).

_{MAX}and O

_{MAX}for the different methods (Figure 9). For the K-values analysed (and for K-values greater than one), they showed an intermediate behaviour between VEM and I-O. For the Z

_{MAX}frequency curves, the higher the K-value, the lower Z

_{MAX}obtained for the same return period (Figure 9a). However, when analysing the O

_{MAX}frequency curves, they intersected the VEM maximum outflow frequency curve (Figure 9b). For Tr values higher than one, and until the intersection of the O

_{MAX}frequency curves, the greater the K-value, the greater the O

_{MAX}was for the same Tr. Moreover, the intersection with VEM occurred at higher Trs, corresponding to a Tr of 31, 50, 86, and 102 years for K = 2, 10, 50, and I-O, respectively. Once the O

_{MAX}frequency curves intersected, the behaviour was the opposite.

_{MAX}and avoided damages associated with the released outflows. As mentioned, for this case study, it was K = 10.

_{III}or the entity of the decrease of Z

_{MAX}and O

_{MAX}was prioritized. In the case study, K = 1.25 maximized the number of events improved for 25 < Tr < 50 years and K = 10 for 50 < Tr < 500 years. The reservoir levels reached Zones 3 (in all events with Tr values higher than 50 years) and 4. The influence of the K-value on Equation (10) implied an increase of the released outflows at the beginning of the operation (Zone 2), increasing the available flood control capacity with respect to VEM for the next time steps. Therefore, Zones 3 and 4 were reached later, for which the O

_{MAX}was reduced (Figure 3).

_{p}was higher than the maximum discharge capacity when the gates were fully opened and the outflow responded to an un-controlled fixed-crested spillway (Figure 3). This explains why Z

_{MAX}and O

_{MAX}tended to be constant when analysing K-values higher than ten for Tr values higher than 500 years (Figure 8(b6) and Figure 9). This also explains the shape of the half loop of the comparative scheme between the K-Method and VEM (Figure 6).

_{MAX}and O

_{MAX}frequency curves, and regardless of the analyzed operation rule. For small and medium floods, the outflows are governed by the operation of the partially opened gates. Once the FCL is exceeded and gates become fully open, the spillways work as un-controlled fixed-crested spillways, justifying the behavior of the frequency curves.

_{Z}), the peak released flow index (I

_{O}), and the global risk index (I

_{R}) for the Talave dam (Figure 12c).

_{R}value for the Talave dam with respect to the VEM. There is also a range of K-values for which the I

_{R}is even lower than for the I-O, which is a very conservative flood management strategy. This global reduction is due to the effect of management strategies on the I

_{O}. If I

_{O}is analysed, I-O is found to be the worst strategy, since it implies no peak attenuation during the controlled phase of the flood. The K-Method outperforms the VEM for K-values smaller than 20. For the case of the I

_{Z}, the minimum values are obtained for the I-O strategy, which emphasizes controlling the reservoir level. This strategy is even better than MILP optimization. In the case of the K-Method, it always outperforms VEM, and I

_{Z}tends to be the value obtained for I-O for large values of K. MILP represented the minimum expected value for I

_{R}. For this case study, the K-value that optimized I

_{R}is 5.25, reducing the annual expected damage by 8.4%, when compared to VEM. The reduction represented 17.3% of the maximum possible reduction determined by MILP. Even though this may seem like a small reduction, it should be taken into account that the application of the K-Method has no associated construction costs and the improvement would be applied annually, during the whole dam life (according to the Dam Master Plan, Talave Dam’s expected life is 167 years).

## 4. Conclusions

_{R}, by 8.4% compared to VEM, and represented 17.3% of the maximum possible reduction determined by MILP.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

δ | Incremental of non-exceedance probability between two consecutive elements in the sample |

ΔO | Variation of maximum outflows of the tested method respect to the reference model |

ΔO_{i} | Variation of outflows at a time i |

ΔS_{i} | Variation of the storage in the reservoir at a time i |

Δt | Time step |

ΔZ | Variation of maximum reservoir levels of the tested method respect to the reference model |

AL | Activation level |

CDF | Cumulative distribution functions |

COD | Crest of dam |

DFL | Design flood level |

D_{O} | Function of damage costs associated to the maximum outflows |

D_{Z} | Function of damage costs associated to the maximum reservoir levels |

FCL | Flood control level |

I-O | Inflow-Outflow rule of operation method |

IDF | Intensity-Duration-Frequency curves |

I_{i} | Inflow at a time i |

I_{O} | Peak released flow index |

I_{R} | Global risk index |

I_{Z} | Storage risk index |

K | It is also mentioned as K-value, represent a parameter used in the K-Method |

MILP | Mixed Integer Linear Programming rule of operation method |

n | number of time intervals until the reservoir runs out of flood control capacity |

O_{ALT} | Alert outflow |

O_{max.disch.}(S_{i}) | Maximum outflow that can be discharged at the current reservoir level |

O_{EMER} | Emergency outflow |

O_{i} | Outflow at a time i |

O_{max.Gr} | Maximum gate opening/closing gradient |

O_{MAX} | Maximum released outflows |

O_{WARN} | Warning outflow |

P | Objective penalty function applied in MILP |

P_{o} | Penalty function of released outflows |

P_{s} | Penalty function of storage volume |

Q_{I}, Q_{II}, Q_{III}, Q_{IV} | Quadrants of the comparative scheme: first, second, third and fourth respectively |

Q_{p} | Outflow proposed by VEM. |

R | Reference model |

S_{AL} | Volume at the activation level |

S_{FCL} | Volume at the flood control level |

S_{i} | Reservoir storage at a time i |

S_{i-1} | Reservoir storage at time i−1 |

S_{i}^{F} | Available flood control capacity at a time i |

S_{TCP} | Volume at the top of conservation pool |

T | Tested model |

TCP | Top of control pool |

Tr | Return period |

VEM | Volumetric Evaluation Method |

w_{o} | weight associated to the penalty function of released outflows |

w_{s} | weight associated to the penalty function of storage volume |

Z_{MAX} | Maximum reservoir levels |

## References

- Wurbs, R. Comparative Evaluation of Generalized River/Reservoir System Models; Texas Water Resources Institute: College Station, TX, USA, 2005. [Google Scholar]
- Wang, L.; Nyunt, C.T.; Koike, T.; Saavedra, O.; Nguyen, L.C.; Van Sapt, T. Development of an integrated modelling system for improved multi-objective reservoir operation. Front. Archit. Civ. Eng. China
**2010**, 4, 47–55. [Google Scholar] [CrossRef] - Hossain, M.S.; El-Shafie, A. Intelligent systems in optimizing reservoir operation policy: A review. Water Resour. Manag.
**2013**, 27, 3387–3407. [Google Scholar] [CrossRef] - Feng, M.; Liu, P. Spillways scheduling for flood control of Three Gorges Reservoir using mixed integer linear programming model. Math. Probl. Eng.
**2014**, 2014, 1–9. [Google Scholar] [CrossRef] - Pan, L.; Housh, M.; Liu, P.; Cai, X.; Chen, X. Robust stochastic optimization for reservoir operation. Water Resour. Res.
**2015**, 51, 409–429. [Google Scholar] [CrossRef] - International Commission on Large Dams (ICOLD). World Register of Dams; International Commission on Large Dams: Paris, France, 2003. [Google Scholar]
- Sordo-Ward, A.; Garrote, L.; Bejarano, M.D.; Castillo, L.G. Extreme flood abatement in large dams with gate-controlled spillways. J. Hydrol.
**2013**, 498, 113–123. [Google Scholar] [CrossRef] - Afshar, A.; Salehi, A. Gated spillways operation rules considering water surface elevation and flood peak: Application to Karkheh Dam. In Proceedings of the World Environmental and Water Resources Congress 2011: Bearing Knowledge for Sustainability, Palm Springs, CA, USA, 22–26 May 2011; Beighley, R.E., Killgore, R.W., Eds.; American Society of Civil Engineers: Reston, VA, USA, 2011; pp. 3007–3015. [Google Scholar]
- Molina, M.; Fuentetaja, R.; Garrote, L. Hydrologic models for emergency decision support using bayesian networks. In Symbolic and Quantitative Approaches to Reasoning with Uncertainty, Proceedings of the 8th European Conference, ECSQARU 2005, Barcelona, Spain, 6–8 July 2005; Godo, L., Ed.; Springer: Berlin/Heidelberg, Germany, 2005; pp. 88–99. [Google Scholar]
- Li, Y.; Guo, S.; Quo, J.; Wang, Y.; Li, T.; Chen, J. Deriving the optimal refill rule for multi-purpose reservoir considering flood control risk. J. Hydro-Environ. Res.
**2014**, 8, 248–259. [Google Scholar] [CrossRef] - Girón, F. The evacuation of floods during the operation of reservoirs. In Transactions Sixteenth International Congress on Large Dams; Report 75; International Commission on Large Dams (ICOLD): San Francisco, CA, USA, 1988; Volume 4, pp. 1261–1283. [Google Scholar]
- Loucks, D.; Sigvaldason, O. Multiple-reservoir operation in North America. In The Operation of Multiple Reservoir System; Kaczmarek, Z., Kindler, J., Eds.; International Institute for Applied System Analysis: Laxenburg, Austria, 1982. [Google Scholar]
- Needham, J.T.; Watkins, D.W.; Lund, J.R.; Nanda, S.K. Linear programming for flood control in the Iowa and Des Moines rivers. J. Water Resour. Plan. Manag.
**2000**, 126, 118–127. [Google Scholar] [CrossRef] - Raman, H.; Chandramouli, V. Deriving a general operating policy for reservoirs using neural network. J. Water Resour. Plan. Manag.
**1996**, 122, 342–347. [Google Scholar] [CrossRef] - Chang, L.C. Guiding rational reservoir flood operation using penalty-type genetic algorithm. J. Hydrol.
**2008**, 354, 65–74. [Google Scholar] [CrossRef] - Le Ngo, L.; Madsen, H.; Rosbjerg, D. Simulation and optimisation modelling approach for operation of the Hoa Binh reservoir, Vietnam. J. Hydrol.
**2007**, 336, 269–281. [Google Scholar] [CrossRef] - Oliveira, R.; Loucks, D. Operating rules for multireservoir systems. Water Resour. Res.
**1997**, 33, 839–852. [Google Scholar] [CrossRef] - Bianucci, P.; Sordo-Ward, A.; Perez, J.I.; Garcia-Palacios, J.; Mediero, L.; Garrote, L. Risk-based methodology for parameter calibration of a reservoir flood control model. Nat. Hazards Earth Syst. Sci.
**2013**, 13, 965–981. [Google Scholar] [CrossRef] - Chang, F.-J.; Chang, Y.-T. Adaptive neuro-fuzzy inference system for prediction of water level in reservoir. Adv. Water Res.
**2006**, 29, 1–10. [Google Scholar] [CrossRef] - Chang, L.C.; Chang, F.J.; Hsu, H.C. Real-time reservoir operation for flood control using artificial intelligent techniques. Int. J. Nonlinear Sci. Numer. Simul.
**2010**, 11, 887–902. [Google Scholar] [CrossRef] - Ishak, W.W.; Ku-Mahamud, K.-R.; Norwawi, N.M. Mining temporal reservoir data using sliding window technique. CiiT Int. J. Data Min. Knowl. Eng.
**2011**, 3, 473–478. [Google Scholar] - Khalil, A.; McKee, M.; Kemblowski, M.; Asefa, T. Sparse bayesian learning machine for real-time management of reservoir releases. Water Resour. Res.
**2005**, 41. [Google Scholar] [CrossRef] - Mediero, L.; Garrote, L.; Martin-Carrasco, F. A probabilistic model to support reservoir operation decisions during flash floods. Hydrol. Sci. J.
**2007**, 52, 523–537. [Google Scholar] [CrossRef] - Cuevas Velasquez, V. Modelo de Gestión de un Embalse en Tiempo Real Durante Avenidas Basado en Redes Bayesianas Entrenadas con el Método de Optimización PLEM. Ph.D. Thesis, Technical University of Madrid, Madrid, Spain, 2015. (In Spanish). [Google Scholar]
- Klipsch, J.; Hurst, M. HEC-ResSim Reservoir System Simulation User's Manual Version 3.0; USACE: Davis, CA, USA, 2007; p. 512.
- Karbowski, A. FC-ROS—Decision Support System for reservoir operators during flood. Environ. Model. Softw.
**1991**, 6, 11–15. [Google Scholar] [CrossRef] - Zhao, T.T.G.; Cai, X.M.; Yang, D.W. Effect of streamflow forecast uncertainty on real-time reservoir operation. Adv. Water Res.
**2011**, 34, 495–504. [Google Scholar] [CrossRef] - Cheng, C.T.; Chau, K.W. Fuzzy iteration methodology for reservoir flood control operation. J. Am. Water Resour. Assoc.
**2001**, 37, 1381–1388. [Google Scholar] [CrossRef] - Liu, P.; Lin, K.R.; Wei, X.J. A two-stage method of quantitative flood risk analysis for reservoir real-time operation using ensemble-based hydrologic forecasts. Stoch. Environ. Res. Risk Assess.
**2015**, 29, 803–813. [Google Scholar] [CrossRef] - Choong, S.M.; El-Shafie, A. State-of-the-art for modelling reservoir inflows and management optimization. Water Resour. Manag.
**2015**, 29, 1267–1282. [Google Scholar] [CrossRef] - El-Shafie, A.; El-Shafie, A.H.; Mukhlisin, M. New approach: Integrated risk-stochastic dynamic model for dam and reservoir optimization. Water Resour. Manag.
**2014**, 28, 2093–2107. [Google Scholar] [CrossRef] - Hosseini-Moghari, S.M.; Morovati, R.; Moghadas, M.; Araghinejad, S. Optimum operation of reservoir using two evolutionary algorithms: Imperialist competitive algorithm (ICA) and cuckoo optimization algorithm (COA). Water Resour. Manag.
**2015**, 29, 3749–3769. [Google Scholar] [CrossRef] - Ahmadi, M.; Bozorg-Haddad, O.; Marino, M.A. Extraction of flexible multi-objective real-time reservoir operation rules. Water Resour. Manag.
**2014**, 28, 131–147. [Google Scholar] [CrossRef] - Ahmed, E.M.S.; Mays, L.W. Model for determining real-time optimal dam releases during flooding conditions. Nat. Hazards
**2013**, 65, 1849–1861. [Google Scholar] [CrossRef] - Jood, M.S.; Dashti, M.; Abrishamchi, A. A system dynamics model for improving flood control operation policies. In Proceedings of the World Environmental and Water Resources Congress 2012, Albuquerque, NM, USA, 20–24 May 2012; Loucks, D., Ed.; American Society of Civil Engineers: Reston, VA, USA, 2012; pp. 962–972. [Google Scholar]
- Gioia, A. Reservoir Routing on Double-Peak Design Flood. Water
**2016**, 8, 553. [Google Scholar] [CrossRef] - García-Marín, A.; Roldán-Cañas, J.; Estévez, J.; Moreno-Pérez, F.; Serrat-Capdevila, A.; González, J.; Francés, F.; Olivera, F.; Castro-Orgaz, O.; Giráldez, J.V. La hidrología y su papel en ingeniería del agua. Ingeniería del Agua
**2014**, 18, 1–14. (In Spanish) [Google Scholar] - Alemu, E.T.; Palmer, R.N.; Polebitski, A.; Meaker, B. Decision support system for optimizing reservoir operations using ensemble streamflow predictions. J. Water Resour. Plan. Manag.
**2011**, 137, 72–82. [Google Scholar] [CrossRef] - Labadie, J.W. Optimal operation of multireservoir systems: State-of-the-art review. J. Water Resour. Plan. Manag.
**2004**, 130, 93–111. [Google Scholar] [CrossRef] - Lund, J.R. Floodplain planning with risk-based optimization. J. Water Resour. Plan. Manag.
**2002**, 128, 202–207. [Google Scholar] [CrossRef] - Jain, S.K.; Yoganarasimhan, G.N.; Seth, S.M. A risk-based approach for flood-control operation of a multipurpose reservoir. Water Resour. Bull.
**1992**, 28, 1037–1043. [Google Scholar] [CrossRef] - Loukas, A.; Vasiliades, L. Streamflow simulation methods for ungauged and poorly gauged watersheds. Nat. Hazards Earth Syst. Sci.
**2014**, 14, 1641–1661. [Google Scholar] [CrossRef] - International Commission on Large Dams (ICOLD). Technical Dictionary on Dams: A Glossary of Words and Phrases Related to Dams; International Commission on Large Dams: Paris, France, 1994. [Google Scholar]
- Loukas, A.; Quick, M.C.; Russell, S.O. A physically based stochastic-deterministic procedure for the estimation of flood frequency. Water Resour. Manag.
**1996**, 10, 415–437. [Google Scholar] [CrossRef] - Loukas, A. Flood frequency estimation by a derived distribution procedure. J. Hydrol.
**2002**, 255, 69–89. [Google Scholar] [CrossRef] - Blazkova, S.; Beven, K. Flood frequency estimation by continuous simulation of subcatchment rainfalls and discharges with the aim of improving dam safety assessment in a large basin in the Czech Republic. J. Hydrol.
**2004**, 292, 153–172. [Google Scholar] [CrossRef] - Sordo-Ward, A.; Garrote, L.; Martin-Carrasco, F.; Bejarano, M.D. Extreme flood abatement in large dams with fixed-crest spillways. J. Hydrol.
**2012**, 466, 60–72. [Google Scholar] [CrossRef] - Etoh, T.; Murota, A.; Nakanishi, M. SQRT-Exponential Type Distribution of Maximum. In Proceedings of the International Symposium on Flood Frequency and Risk Analyses, Louisiana State University, Baton Rouge, LA, USA, 14–17 May 1986; Shing, V.P., Ed.; Reidel Publishing Company: Boston, MA, USA, 1987; pp. 253–264. [Google Scholar]
- Ministerio de Fomento. Máximas Lluvias Diarias en la España Peninsular; Dirección General de Carreteras; Ministerio de Fomento: Madrid, Spain, 1999. (In Spanish)
- Ministerio de Fomento. Instrucción de Carreteras 5.2-IC Drenaje Superficial; Dirección General de Carreteras; Ministerio de Fomento: Madrid, Spain, 2016. (In Spanish)
- USDA Soil Conservation Service (SCS). National Engineering Handbook, Section 4: Hydrology; USA Department of Agriculture: Washington, DC, USA, 1972.
- McCarthy, G.T. The Unit Hydrograph and Flood Routing; US Army Corps of Engineers: Providence, RI, USA, 1939.
- Arnell, N.W. Expected annual damages and uncertainties in flood frequency estimation. J. Water Resour. Plan. Manag.
**1989**, 115, 94–107. [Google Scholar] [CrossRef]

**Figure 2.**General scheme of the Volumetric Evaluation Method based on Girón [11].

**Figure 4.**Comparative analysis of operation rules. (

**a**) Comparative scheme of quadrants. The tested method is called “T”, while the reference method is called “R”. The horizontal axis shows the variations of the maximum reservoir level of T with respect to R ($\Delta \mathrm{Z}$) in m. The vertical axis shows the variations of the maximum outflows of T with respect to R ($\Delta \mathrm{O}$ ) in m

^{3}/s. (

**b**) Global risk index analysis. The storage (I

_{Z}) and peak released flow (I

_{O}) risk indexes were calculated and combined to obtain the global risk index (I

_{R}) for the K-Method, VEM, I-O, and MILP method.

**Figure 5.**Case study scheme. (

**a**) Location of the Talave dam. (

**b**) Scheme of the discharge structures and the elevation of their axis (

**left**). Details of gated spillways (

**right**). Abbreviations are defined in Table 1.

**Figure 6.**Comparison of the K-Method (for different K-values), I-O and MILP with respect to the VEM. The horizontal axis shows the increments of the maximum reservoir level in m (ΔZ). The vertical axis shows the increments of the maximum outflow in m

^{3}/s (ΔO). The red points correspond to events with Tr ranging from one to 10 years, blue points ranging from 10 to 25, green points from 25 to 50, black points from 50 to 100, cyan points from 100 to 500, and magenta points from 500 to 10,000 years.

**Figure 7.**Percentage of cases in Q

_{III}from K = 1.25 to K = 50, for different ranges of Tr of the inflow hydrographs. The red colour corresponds to events with Tr ranging from one to 10 years (

**a1**), blue from 10 to 25 (

**a2**), green from 25 to 50 (

**a3**), black from 50 to 100 (

**a4**), cyan from 100 to 500 (

**a5**), and magenta from 500 to 10,000 years (

**a6**).

**Figure 8.**Comparison of the K-Method (for different K-values) with respect to the VEM (K = 1). The continuous line shows the median and the shaded areas show the range between the 25th and 75th percentile of the maximum reservoir levels (Z

_{MAX}) (

**a**) and the maximum outflows (O

_{MAX}) (

**b**), from K = 1 (VEM) to K = 50. The horizontal axis shows the different values of K. The red colour corresponds to events with Tr ranging from one to 10 years (

**a1**,

**b1**), blue from 10 to 25 (

**a2**,

**b2**), green from 25 to 50 (

**a3**,

**b3**), black from 50 to 100 (

**a4**,

**b4**), cyan from 100 to 500 (

**a5**,

**b5**), and magenta from 500 to 10,000 years (

**a6**,

**b6**). For specific K-values (K = 1, 2, 4, 6, 8, 10, 20, 50), box plots are presented with their corresponding outliers (when existing) represented by red dots.

**Figure 9.**Frequency curves. (

**a**) Maximum reservoir level frequency curves for VEM (blue continuous line), different values of K (black lines of different types, see legend), I-O (dashed-dotted blue line), and MILP (dashed red line). (

**b**) Maximum outflows frequency curves for VEM (blue continuous line), different values of K (black lines of different types, see legend), I-O (dashed-dotted blue line), and MILP (dashed red line).

**Figure 10.**Peak flow attenuation for different return periods and methods of operation of dams. Y axes represent the ratio between the maximum outflow and the maximum inflow for each event with their corresponding Tr (X axes). Blue dots represent the events routed by the dam by applying the VEM, dark grey dots by applying the K-Method with a K-value = 2, grey dots with a K-value = 10, light grey dots with a K-value = 50, cyan dots by applying the I-O method, and red dots by applying the MILP.

**Figure 11.**Comparison of outflow hydrographs (top) and reservoir levels (bottom) resulting from the aplication of different dam operation methods. (

**a**) Hydrograph corresponding to Tr = 20 years and (

**b**) corresponding to Tr = 1000 years. Colored lines represent the application of the different methods: VEM (blue continuous line), different values of K (red lines of different types, see legend), I-O (dashed-dotted blue line), and MILP (magenta continuous line). Coloured shading (bottom) represents the different Zones of application of the K-Method (Zone 1 in green, Zone 2 in yellow, Zone 3 in orange, and Zone 4 in red).

**Figure 12.**Risk-based approach. (

**a**) Expected Talave Dam damage cost vs. released maximum reservoir level. (

**b**) Expected damage cost downstream Talave Dam vs. released maximum outflows. (

**c**) Risk indexes for VEM (dashed lines), I-O (dotted lines), MILP (dashed-dotted lines), and different values of the K-Method (continuous lines). Blue lines show the storage risk index (I

_{Z}), red lines show the released flow risk index (I

_{O}), and black lines show the global risk index (I

_{R}). Horizontal axis shows the different values of K. The optimum K for I

_{R}is 5.25.

Reservoir Levels (m.a.s.l) | Maximum Outflow Capacity at Design Flood Level (DFL) (m^{3}/s) | Characteristic Outflows (m^{3}/s) | |||
---|---|---|---|---|---|

Top of control pool (TCP) | 508.9 | Gated-spillway | 2 × 142.5 | Alert outflow (O_{ALT}) | 100 |

Activation level (AL) | 509.3 | ||||

Flood control level (FCL) | 509.9 | Bottom outlet | 1 × 99.5 | Warning outflow (O_{WARN}) | 150 |

Design flood level (DFL) | 511.3 | Dam body water intakes | 2 × 9.0 | Emergency outflow (O_{EMER}) | 300 |

Crest of dam (COD) | 512.4 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sordo-Ward, A.; Gabriel-Martin, I.; Bianucci, P.; Garrote, L.
A Parametric Flood Control Method for Dams with Gate-Controlled Spillways. *Water* **2017**, *9*, 237.
https://doi.org/10.3390/w9040237

**AMA Style**

Sordo-Ward A, Gabriel-Martin I, Bianucci P, Garrote L.
A Parametric Flood Control Method for Dams with Gate-Controlled Spillways. *Water*. 2017; 9(4):237.
https://doi.org/10.3390/w9040237

**Chicago/Turabian Style**

Sordo-Ward, Alvaro, Ivan Gabriel-Martin, Paola Bianucci, and Luis Garrote.
2017. "A Parametric Flood Control Method for Dams with Gate-Controlled Spillways" *Water* 9, no. 4: 237.
https://doi.org/10.3390/w9040237