# Risks Analysis and Response of Forecast-Based Operation for Ankang Reservoir Flood Control

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Contrast of Risk Factors for Two Operation Modes

- The flood inflow is actually an instantaneous value, which changes from time to time, thus it is difficult to measure along with the rise and the drop of the flood wave. Even if it can be calculated as the average inflow in a certain period of time, there are still deviations. In practice, the flood inflow is usually estimated according to the observation of the adjacent upstream hydrometric station, or the change of water level in the period by back calculation. Therefore, the so-called “observed inflow” is actually an estimated value, which largely based on the upstream river flow and the experience of dispatcher; the value, in fact, has a large deviation sometimes from “the true inflow”.
- What is “inflow”? Where is the cross section once the stream flow passes? Can it be thought of as in the reservoir? All these concepts are actually vague. In view of dynamic change of the water surface curve under different storage conditions of reservoirs and the impact of different flood waves, there is no a constant cross section to define “inflow” and the inflow itself is a concept with fuzzy characteristics, which cannot be accurately determined.
- The flood wave and real-time inflow are under the effects of boundary conditions. Even if the dynamic change of storage capacity is considered, it is not possible to fully describe the inflow process and its effects. Although they theoretically comply with the Saint-Venant equations for the unsteady flow, they are difficult to solve due to various complicated conditions. Conversely, even if the flood flow is the same, for different water levels or different operation stages of the reservoir, the evolution and the hydraulic effects of the flood wave in the reservoir are different.

#### 2.2. The Main Risk Sources and Factors

#### 2.3. Forecasted Accuracy and Flood Regulation Risk

#### 2.3.1. The Distribution and Evaluation of Forecast Error

_{1}, X

_{2}, ..., X

_{n}be the given sample, assuming:

_{1}< t

_{2}< ... <t

_{k−1}on the real axis and divide the real axis into k intervals $(-\infty ,{t}_{1}]$, $({t}_{1},{t}_{2}]$…$({t}_{k-1},+\infty )$.

_{0}.

_{0}is true, the statistics always approximately obey the ${\chi}^{2}$ distribution, and the degree of freedom is k−r−1, r is the number of parameters to be estimated.

_{0}is rejected, otherwise H

_{0}is accepted.

#### 2.3.2. Flood Regulation Risk Based on Monte-Carlo

## 3. Case Study

#### 3.1. Overview of Ankang Reservoir

^{2}. Ankang Reservoir is a large-scale water project with multiple purposes such as electricity generation, flood control, water supply, shipping and other comprehensive utilization. The reservoir is an incomplete annual regulation reservoir with a total capacity of 3.2 billion m

^{3}and a maximum flood storage capacity of 980 million m

^{3}. The dead water level of the reservoir is 305 m, the normal water level is 330 m, the limit water level in flood season is 325 m, the design flood level is 333 m and the maximum flood level is 337.33 m. The climate in the upper reaches of the Han River is a subtropical humid climate with relatively abundant water resources. The rainfall in the flood season, i.e., July, August and September, accounts for about 50% of the yearly total in the basin. The average annual runoff is approximately 26 billion m

^{3}. The annual runoff distribution is 75–80% in summer and autumn, 10–15% in spring and only about 5% in winter. The largest flood peak usually appears in July or September.

#### 3.2. The Formulated FBO Rules for Ankang Reservoir

#### 3.3. Error Analysis on Forecasted Net Rainfall

^{2}. Letting the random variable of the net rainfall forecast error be $X$, the absolute error-frequency histogram and the corresponding normal function curve were drawn (Figure 4).

_{0}: the population X obeys normal distribution $N(0.019,{0.188}^{2})$, the distribution function is:

_{0}is accepted, the forecast error of the net rainfall obeys $N(\mu ,{\sigma}^{2})$, where $\mu =\overline{X}=0.019$, $\sigma ={S}^{*}=0.188$.

#### 3.4. Risk Analysis of Ankang Reservoir Forecast-Based Operation

^{3}/s, the distribution of the error was estimated and complied with the normal distribution: $Y~N(189.32,{775.81}^{2})$.

_{a-max}and the maximum discharge Q

_{a-max}in the simulations, if any of them went beyond the corresponding permissible value Z

_{a-max}and Q

_{a-max}as shown in Table 4, then the risk events were triggered.

^{3}/s, respectively, according to flood control requirements. Figure 5 shows that, for maximum discharges in the 10,000 simulations for five-year flood, 46 points in the graph exceed the permissible value 12,000 m

^{3}/s, and eight overtop the permissible water level Z

_{a_max}, totaling 54 risk events out of 10,000 simulations, as shown in Table 4.

_{a_max}and Q

_{a_max}, were the same as CO while conducting simulations for floods with different return periods. The results are listed in Table 5.

_{a_max}at all, and in only 22 out of 10,000 does the maximum discharge overtop the permissible value of 12,000 m

^{3}/s, as shown in Figure 6.

#### 3.5. Preliminary Probing on the Remedies of Significant Forecast Error

## 4. Conclusions

- (1)
- Qualitative analysis showed that, among different types of uncertainties, the hydrological uncertainty should be considered as the significant risk source in reservoir flood control. Therefore, the forecast factor accuracy and its availability are crucial to determine the feasibility of FBO. As an illustration, the distribution of forecasted net rainfall errors for the Ankang hydrological monitoring and forecasting system obeyed approximately normal distribution $N(0.019,{0.188}^{2})$ based on the hypothesis test.
- (2)
- The Monte Carlo simulation is more appropriate for risk evaluation of FBO in view of its multiple factors and complexity. In contrast to CO, there are obvious advantages for FBO in risk control during real time flood regulation: for 20-year floods, the possible risk rate was reduced to approximately a quarter of CO. For five-year floods, the possible risk rate was reduced by more than half of CO.
- (3)
- The risk remedial measures for FBO were discussed conceptually. The basic assumption on remedies of significant forecast bias in FBO was put forward according to the different classifications of the forecast errors, false-negative and false-positive. Theoretically, there are two types of risk reduction techniques: single-step operation and multi-step operation. Taking the single-step risk reduction as an example, the main idea of the technique is presented with a schematic diagram, while, in view of the complexity of this problem, especially the intrinsic uncertainties in hydrologic process and forecast products, we believe that it is hard to find a quantitative and fixed model for various situations. All of these issues are subject to further study.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**Schematic diagram of flood regulation risk reduction for significant forecast error in FBO.

Number | Inflow (m^{3}/s) | Water Level Z (m) | Release (m^{3}/s) | Notes |
---|---|---|---|---|

1 | $12,000<{Q}_{in}\le 15,100$ | $Z\le 326$ | ${Q}_{out}=12,000$ | Q_{in} and Q_{out} represent flood inflow and discharge |

$Z>326$ | ${Q}_{out}={Q}_{in}$ | |||

2 | $15,100<{Q}_{in}\le 17,000$ | $Z>326$ | ${Q}_{out}={Q}_{in}$ | $P=10\%$, flood rising |

3 | $17,000<{Q}_{in}\le 21,500$ | $326<Z\le 328$ | ${Q}_{out}=17,000$ | |

$Z>328$ | ${Q}_{out}={Q}_{in}$ | |||

4 | $21,500<{Q}_{in}\le 24,200$ | $Z>328$ | ${Q}_{out}={Q}_{in}$ | $P=1\%$ |

5 | ${Q}_{in}>24,200$ | Free overflow |

No. | Cumulative Net Rainfall (mm) | Water Level Z (m) | Release (m^{3}/s) | Remarks |
---|---|---|---|---|

1 | $\sum R}\le 43$ | ${Q}_{out}={Q}_{in}$ | Q_{in} and Q_{out} represent flood inflow and discharge | |

2 | $43<{\displaystyle \sum R}\le 55$ | $Z\le 326$ | ${Q}_{out}=\mathrm{12,000}$ | |

$Z>326$ | ${Q}_{out}={Q}_{in}$ | |||

3 | $55<{\displaystyle \sum R}\le 62$ | $Z\le 326$ | ${Q}_{out}=\mathrm{15,100}$ | |

$Z>326$ | ${Q}_{out}={Q}_{in}$ | |||

4 | $62<{\displaystyle \sum R}\le 79$ | $Z\le 326$ | ${Q}_{out}=\mathrm{15,100}$ | |

$326<Z\le 328$ | ${Q}_{out}=\mathrm{17,000}$ | |||

$Z>328$ | ${Q}_{out}={Q}_{in}$ | |||

5 | $79<{\displaystyle \sum R}\le 90$ | $Z\le 328$ | ${Q}_{out}={Q}_{c}$ | |

$Z>328$ | ${Q}_{out}={Q}_{in}$ | |||

6 | $\sum R}>90$ | Free overflow |

Frequency$\mathit{P}$(%) | 0.01 | 0.1 | 1 | 5 | 10 | 20 |

The Absolute Error of the Net Rain$\Delta \mathit{R}$(mm) | 0.7182 | 0.6 | 0.4564 | 0.3282 | 0.2599 | 0.1772 |

Return Period (year) | Z_{a_max}(m) | Q_{a_max} (m^{3}/s) | Simulation Times | Counts (Z > Z_{a_max} or Q > Q_{a_max}) | Frequency P (%) | Risk Rate Ψ (%) |
---|---|---|---|---|---|---|

10,000 | 337.05 | —— | 10,000 | 0 | 0 | 0 |

1000 | 333.1 | —— | 10,000 | 0 | 0 | 0 |

100 | 330.0 | —— | 10,000 | 0 | 0 | 0 |

20 | 328.6 | 17,000 | 10,000 | 5 | 0.05 | 0.0025 |

5 | 326.7 | 12,000 | 10,000 | 54 | 0.54 | 0.108 |

Return Period (year) | Z_{a_max}(m) | Q_{a_max} (m^{3}/s) | Simulation Times | Counts (Z > Z_{a_max} or Q > Q_{a_max}) | Frequency P (%) | Risk Rate Ψ (%) |
---|---|---|---|---|---|---|

10,000 | 337.05 | —— | 10,000 | 0 | 0 | 0 |

1000 | 333.1 | —— | 10,000 | 0 | 0 | 0 |

100 | 330.0 | —— | 10,000 | 0 | 0 | 0 |

20 | 328.6 | 17,000 | 10,000 | 1 | 0.01 | 0.0005 |

5 | 326.7 | 12,000 | 10,000 | 22 | 0.22 | 0.044 |

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**MDPI and ACS Style**

Liu, Z.; Lyu, J.; Jia, Z.; Wang, L.; Xu, B.
Risks Analysis and Response of Forecast-Based Operation for Ankang Reservoir Flood Control. *Water* **2019**, *11*, 1134.
https://doi.org/10.3390/w11061134

**AMA Style**

Liu Z, Lyu J, Jia Z, Wang L, Xu B.
Risks Analysis and Response of Forecast-Based Operation for Ankang Reservoir Flood Control. *Water*. 2019; 11(6):1134.
https://doi.org/10.3390/w11061134

**Chicago/Turabian Style**

Liu, Zhao, Jiawei Lyu, Zhifeng Jia, Lixia Wang, and Bin Xu.
2019. "Risks Analysis and Response of Forecast-Based Operation for Ankang Reservoir Flood Control" *Water* 11, no. 6: 1134.
https://doi.org/10.3390/w11061134