Development and Application of Reservoir Operation Method Based on Pre-Release Index for Control of Exceedance Floods

Abstract

The pre-release operation has the potential to enhance the ability of a reservoir to manage exceedance floods. However, the mechanisms for the initiation and termination of such operations are unclear, and a clear method for calculating the pre-release water amount at each time step of the scheduling phase is lacking. To address this, the framework and mathematical expression for a pre-release index are proposed herein, and a refined pre-release scheduling model is developed based on the pre-release indices and their thresholds. Then, the proposed pre-release operation model is applied to the Shuifumiao Reservoir in the Lianshui River Basin in Hunan Province, China. The simulation results demonstrate that the refined pre-release scheduling model can effectively prevent exceedance floods, ensuring the safety of flood control without compromising the effectiveness of water supply safety. The proposed model provides a valuable framework and tool for enhancing the ability of reservoir operators to manage flood events and improve overall flood control safety.

1. Introduction

In recent years, the severity and frequency of floods caused by heavy rainfall have increased due to climate change and human activities [1,2,3,4,5]. According to Our World in Data’s annual disaster statistics report [6], floods caused the second greatest damage to global GDP in 2020. In China, for instance, the flood season of 2020 was characterized by multiple episodes of heavy rainfall [7], resulting in severe flooding in Sichuan, Chongqing, and other provinces. The Three Gorges Reservoir, one of the largest in the world, recorded its largest inflow since its construction, reaching as high as 75,000 m³/s. In July 2021, floods hit many regions in the Northern Hemisphere, claiming numerous lives and causing significant economic damage. The western region of Germany experienced the most severe floods in a thousand years, resulting in over one hundred deaths and extensive damage to infrastructure. Zhengzhou in Henan Province, China was hit by floods with a maximum hourly rainfall of 201.9 mm, causing more than 300 deaths. In April 2022, South Africa experienced its largest flood in 60 years, causing a total of 448 deaths and rendering more than 6000 people homeless.

The increasingly frequent occurrence of extreme rainfall-induced floods that exceed control standards has engendered an urgent need to determine effective methods to prevent and mitigate their impacts. Reservoirs play a crucial role in preventing flood disasters in river basins by storing excess water and releasing it in a controlled manner to reduce downstream flood hazards [8,9]. However, floods that exceed the check flood frequency of a reservoir can lead to high water levels in the reservoir, threatening the safety of its flood control function. The management of Japan’s reservoirs for floods exceeding the flood control plan showed an increasing trend from 1960 to 2019 [10]. In China, a coordinated flood control management system among multiple reservoirs in several river basins has been established through the successive construction and operation of large-scale control reservoirs in various river basins. Nonetheless, most reservoirs were established between 1970 and 2010 [11], and the established flood protection standards have not been revised in accordance with changes in meteorological and other hydrological factors. The unpredictability of natural floods and widespread occurrence of extreme hydrological events engenders the possibility that flood prevention standards set according to certain criteria will be exceeded by large floods [12]. Thus, the exceedance of standard floods is a source of risk that cannot be avoided and, so, improving reservoir flood control scheduling technology and measures has gained academic attention.

Current research on reservoir flood control operations has primarily focused on developing two main strategies for deriving optimal operation schemes. The first strategy leverages data-driven approaches, which utilize historical reservoir operation datasets to identify patterns and formulate operating rules through methods such as SVM [13], decision tree [14], and deep learning models [15,16,17,18,19]. These models excel in capturing complex temporal and non-linear dependencies, providing valuable insights into reservoir dispatch under various scenarios. However, their inherent limitation lies in the opacity of the resulting parameters, which makes the decision-making process less interpretable for reservoir operators and challenging to adjust dynamically in real-time contexts [20]. In contrast, the second strategy employs rule-based methods, such as pre-defined flood control charts [21] and stage–discharge relationships [22], which are traditionally designed based on standard flood scenarios under assumed hydrological conditions. These conventional methods, while straightforward and easy to implement, lack adaptability to real-time hydrological fluctuations and extreme flood events. As a result, they often fall short in fully exploiting the flood storage potential of reservoirs, leading to sub-optimal flood control performance during atypical or extreme events. Therefore, recent research has sought to enhance these rule-based strategies by incorporating real-time hydrological forecasts and adaptive control mechanisms to improve their operational flexibility and response to flood events that exceed design standards.

The rapid development of meteorological and hydrological coupled forecasting [23] as well as ensemble forecasting and operation technology [24,25,26,27] in recent years has resulted in an improvement in the accuracy and reliability of flood forecasting and reservoir operations which have, in turn, increased the robustness of technical support for basin flood control operations. Effectively combining flood forecast information, conducting basin reservoir forecasting and pre-release operations, and fully exploiting the storage potential of reservoirs have become critical technical methods for preventing and controlling flood disasters in various basins. Pre-release operations involve the utilization of flood forecasting results to pre-release a portion of a reservoir’s capacity before the main flood peak arrives, thereby increasing the flood control capacity of the reservoir and ensuring the safety of the reservoir and downstream area. This method has tremendous potential for the systematic control of floods that exceed flood control standards. Chou and Wu [28] proposed a pre-release strategy based on the risk rate of reservoirs failing to reach their target capacity during the flood season. They simulated scheduling for multiple historical floods in the Tsengwen Reservoir in Taiwan and proved that the pre-release strategy can effectively enhance flood control benefits without increasing the risk of water shortages. Nguyen et al. [29] simulated the use of a pre-release strategy for the 2009 flood events in the Vu Gia Thu Bon River basin reservoir system. Based on forecast information, downstream control point water levels were calculated and part of the reservoir’s capacity was pre-released when the inflow exceeded the start threshold but was less than the end threshold. The results showed that the pre-release strategy reduced the maximum downstream water level more effectively than conventional operations. Delaney et al. [30] used the predicted risk of the reservoir’s capacity exceeding the storage threshold as a criterion for initiating the pre-release operation and used the risk-taking curve to calculate the pre-release volume. The pooled forecast operation was simulated using Lake Mendoza Reservoir, with results indicating that the maximum operating level during dispatch could be reduced and the flood control capacity of the reservoir could be improved, when compared to the current dispatch method of the reservoir. However, the calibration of the risk-taking curve was extremely complex. Wei et al. [31] studied the Nierji Reservoir in Northeast China and developed a pre-release strategy that was initiated when the forecast inflow was above the start threshold but below the end threshold. When the forecast inflow exceeded the end threshold, the pre-release operation was terminated. They showed that using pre-release scheduling could reduce the peak flow at downstream protection points and improve the downstream flood control capacity.

Although numerous pre-release operation plans have been developed using different criteria and successfully applied to reservoir flood control, there is a lack of standardized criteria for determining the start and end timing of pre-release operations. Additionally, the methods for calculating the real-time pre-release water volume are not well-defined and the responses to real-time changes in hydrological factors are not sufficiently sensitive, impeding precise and dynamic control. In the present study, reservoir storage, forecast flood volume, forecast flood peak, and peak occurrence time were combined to construct pre-release indices. Then, heuristic algorithms were used to calibrate the thresholds for the pre-release indices in order to determine the start and end of pre-release operations, as well as to calculate the real-time pre-release water volume. A standardized and simplified pre-release operation plan was developed, thus offering technical guidance for the scheduling practice of reservoirs for flood control in each river basin.

In this work, a novel framework and mathematical expression for a pre-release index designed to improve reservoir flood control operations are proposed. The framework clarifies the mechanisms for initiating and terminating pre-release operations and provides a method for calculating real-time pre-release water volumes based on flood forecast information. Based on this pre-release index, a refined model is established for reservoir flood control, enhancing adaptability to exceedance flood conditions. This standardized approach offers technical guidance that can be applied to reservoirs across various river basins, supporting improved flood management practices. The theoretical pre-release index for reservoirs and its threshold identification method are presented in Section 2, followed by the establishment of a refined pre-release operation model for reservoirs based on the pre-release index. The study area is introduced in Section 3, for which the heuristic algorithm is applied to determine the pre-release index threshold. Subsequently, a refined pre-release operation model for the Shuifumiao reservoir is established based on the identified threshold. The results obtained after applying the proposed pre-release operation model to the target reservoir are described in Section 4, and the main conclusions obtained in this work are summarized in Section 5.

2. Materials and Methods

Figure 1 shows a simplified schematic diagram of the operation method based on the pre-release index. The pre-release index refers to a collection of parameters that guide the real-time pre-release operations of a reservoir. These parameters include the real-time pre-release index (r_t), real-time pre-release depth (V_t-pre), and a set of thresholds, consisting of the pre-release start threshold (r_st), pre-release end threshold (r_nd), and pre-release depth threshold (V_pre). Pre-release operations are mainly affected by the reservoir’s storage volume, flood flow, flood peak, and the timing of peak arrival. The mathematical expression for the pre-release index theory is based on the interdependence between these factors and is expressed as follows:

$$r_t={\alpha }_1\sqrt{(1-{\displaystyle \frac{V_{obj}-V_t}{V_{obj}}}}{)}^2+{\alpha }_2{\displaystyle \frac{Q_k}{(1+k)Q_p}}+{\alpha }_3{\displaystyle \frac{W_k}{W_p}}$$

(1)

where t is the time period, h; rt is the pre-release index of the reservoir in period t; V_obj is the target storage capacity of the reservoir in period t; V_t is the storage capacity at the beginning of period t; k is the number of periods between the forecast peak occurrence time and the present time; Q_k is the forecast peak flow rate; Q_p is the designed flood peak flow rate of the reservoir; W_k is the flood volume of the forecast flood; W_p is the flood volume of the designed flood of the reservoir; and α₁, α₂, and α₃ are weighting coefficients, where α₁ + α₂ + α₃ = 1.

The pre-release depth of a reservoir refers to the vertical distance between the flood control level and the target water level [32]. This parameter determines the volume of water that needs to be pre-released at each time step during the reservoir’s operation. The pre-release depth is a function of r_t, r_st, r_nd, and V_pre, and is calculated as follows:

$$V_{t-pre}={\displaystyle \frac{r_t-r_{nd}}{r_{st}-r_{nd}}}{V}_{pre}$$

(2)

where V_t-pre is the pre-release depth in time period t.

2.1. Identification of Thresholds for Pre-Release Indices

The “optimization-simulation” technique was used to determine reasonable thresholds for the pre-release indices [33,34]. The optimal scheduling model of reservoir flood control operation was established with the objectives of reservoir water storage safety and downstream flood control safety, with constraints such as water balance and reservoir capacity. The thresholds for pre-release indices were determined based on the results of this model.

2.1.1. Optimal Scheduling Model of Reservoir Flood Control Operation

(1)

Objective functions

The safety objectives of a reservoir encompass two main aspects: reservoir storage safety and downstream flood safety [35,36]. The former aims to maintain the water level as close as possible to the flood limit water level (FLWL), in order to prevent the downstream discharge from exceeding the safe discharge capacity in downstream flood control sections.

a.

Reservoir storage safety:

$$\min f_1(V)={\displaystyle \frac{1}{T}}{{\displaystyle \sum _t^T(\Delta V_t/V_{obj})}}^2$$

(3)

$$\Delta V_t=\left\{\begin{array}{c}{V}_{obj}-V_t\\ V_t-V_{obj}\\ (V_t-V_{obj})+\beta (V_t-V_{\max })\end{array}\right.\begin{array}{c}{V}_t\le V_{obj}\\ V_{obj}<V_t\le V_{che}\\ V_t>V_{che}\end{array}$$

(4)

where f₁(V) is a dimensionless number for the reservoir storage safety objective, which aims to maintain the water level close to the flood limit to ensure flood safety and maximize the benefits; T is the total number of time periods; ΔV_t is the difference between the actual storage and the target storage in period t; V_obj is the target storage in period t; V_t is the initial storage in period t; V_che is the reservoir capacity corresponding to the check flood level; V_max is the maximum reservoir capacity; and β is the penalty coefficient when the water level exceeds the design flood level (β > 10).

b.

Downstream flood safety:

$$\min f_2(Q)={\displaystyle \frac{1}{T}}{{\displaystyle \sum _t^T(\Delta Q_t/Q_{safe})}}^2$$

(5)

$$\Delta Q_t=\left\{\begin{array}{cc}{Q}_{out,t}-Q_{safe}& Q_{out,t}>Q_{safe}\\ 0& Q_{out,t}\le Q_{safe}\end{array}\right\}$$

(6)

where f₂(Q) is a dimensionless number representing the downstream flood control section safe discharge objective, ΔQ_t is the portion of the outflow from the reservoir in period t over the downstream safe discharge, Q_safe is the downstream safe discharge of the reservoir, and Q_out,t is the average outflow of the reservoir during period t.

c.

General objective:

$$\min F={\gamma }_1{f}_1(V)+{\gamma }_2{f}_2(Q)$$

(7)

where F is the general objective of reservoir flood safety, and ${\gamma }_1$ and ${\gamma }_2$ are weighting factors (${\gamma }_1+{\gamma }_2$ = 1).

(2)

Constraints

The optimal scheduling model is subject to the following constraints:

a.

Water balance equation:

$$V_{t+1}=V_t+(Q_t-Q_{out,t})\Delta t$$

(8)

where Vt is the reservoir capacity at the beginning of period t, Qt is the average inflow to the reservoir during the period t, and Δt is the length of the period t.

b.

Reservoir capacity constraints:

$$V_{dead}\le V_t\le V_{\max }$$

(9)

where V_dead is the dead storage capacity of the reservoir.

c.

Outflow constraints:

$$out{Q}_t<f(V_t)$$

(10)

where f(V_t) is the maximum outflow corresponding to the reservoir capacity during the period t.

2.1.2. Threshold Identification Steps

The flood control optimization scheduling model utilizes multiple historical flood events of varying frequencies (p ∈ [check flood frequency, 1)) as inputs, and heuristic algorithms are employed to obtain the optimal scheduling process for each flood event [37,38,39]. Based on the model results, threshold values for the pre-release indices (r_st, r_nd, and V_pre) are identified. The steps to identify the pre-release index threshold value are as follows:

(1)

Consider the kth flood event as an example (where k = 1, 2, 3, …, K); see the schematic diagram shown in Figure 2. The time k_t_s when the reservoir water level first drops below the FLWL before the flood arrives is identified as the start time of the pre-release operation. At this moment, the reservoir starts to vacate its capacity to alleviate flood control pressure, which is equivalent to the starting point of the pre-release operation. Therefore, the rt value at this moment is recorded as k_r_st.

(2)

The time k_t_p when the reservoir water level first drops to the FLWL after the flood peak is identified as the end point of optimization scheduling. Therefore, the end point of the pre-release operation occurs in the stage from k_t_s to k_t_p. The pre-release index termination threshold is set to be lower than the lowest r_t value in the stage from k_t_s to k_t_p, in order to ensure flood control safety. Therefore, the pre-release index k_r_t (where t = t_s, t_s+1,…, t_p) is calculated for each time period, and the moment when k_r_t achieves the minimum value is set as the kth flood pre-release termination moment; the k_r_t at this moment is recorded as k-r_nd.

(3)

The difference in storage volume between the minimum reservoir level and the FLWL in the stage between k_t_s and k_t_p is recorded as k_V_pre.

(4)

The characteristic values of k-r_st, k-r_nd, and k_V_pre for the K flood events are calculated, and appropriate characteristic values are selected as the r_st, r_nd, and V_pre thresholds.

2.2. Refined Pre-Release Operation Model

The rolling-horizon approach is used to calculate the reservoir discharge flow at each time step. The forecast horizon is the flood forecast period and the decision horizon is the time when the calculated target outflow should be executed [40,41]. The specific steps are as follows:

a.

At the beginning of the operation, the reservoir is assumed to be in its existing operation state, based on the current flood control regulations.

b.

The reservoir forecast information is obtained and the real-time rt is calculated for the current time step by combining it with the current reservoir storage status.

c.

When rt is less than the preset r_st, the reservoir carries out the existing operation and calculates the target outflow.

When rt is greater than or equal to r_st, the reservoir begins the pre-release operation. The pre-release depth V_t-pre is calculated using Equation (2) and the target outflow is calculated using the following equation:

$${\mathrm{q}}_{\mathrm{t}}={\displaystyle \frac{V_t-(V_{obj}-V_{t-pre})}{3600}}$$

(11)

d.

The next time step is entered and steps a-c are repeated. When rt is less than or equal to r_nd, the reservoir terminates the pre-release operation and implements the existing operation.

3. Case Study

3.1. Shuifumiao Reservoir

The Shuifumiao Reservoir controls a catchment area of 3160 km² and occupies 44% of the area of the Lianshui River Basin in Hunan Province, China (Figure 3). With a total capacity of 560 million m³, it is the largest reservoir in the basin. Its characteristic water levels, corresponding capacity, and outflow capacity are listed in

Table 1. Characteristic water levels and corresponding storage capacities of Shuifumiao Reservoir.

Characteristic Water Level	Water Level (m)	Storage Capacity (108 m3)	Outflow Capacity (m3/s)
Dead water level	85.50	1.100	0
FLWL	93.00	3.225	2258
Normal storage water level	94.00	3.700	3141
Flood control high water level	94.00	3.700	3141
Design flood level	95.72	4.556	4905
Check flood level	97.11	5.600	6450

. The frequency of check floods for this reservoir is 0.1%, while the frequency of design floods is 1%.

Table 2. Inflow flood characteristics.

Frequency (%)	Peak Flow Rate (m3/s)	One-Day Flood Volume (108 m3)	Three-Day Flood Volume (108 m3)	Seven-Day Flood Volume (108 m3)
0.05	9524	5.81	10.53	12.88
0.10	8710	5.30	9.72	11.86
1.00	6270	3.77	6.92	9.73
3.33	4940	2.97	5.45	7.73
5.00	4490	2.68	4.92	6.97
0.05	9524	5.81	10.53	12.88

lists the inflow flood characteristics of the reservoir. To ensure downstream safety, the allowable outflow from the Shuifumiao Reservoir is limited to 3000 m³/s and the minimum outflow during the flood season is 45 m³/s, considering the downstream ecological and irrigation requirements.

Initially, the Shuifumiao Reservoir was designed without any flood control capacity below the normal water storage level of 94 m, and the FLWL was set at this level. However, based on operational experience, the FLWL was later revised to 93 m. When an incoming flood is anticipated, the water in the reservoir is pre-released to a safe level of 92.5 m based on short-term flood forecasting and current reservoir water levels. During flood control operations, the outflow is maintained within a safe limit of 3000 m³/s when the water level is below the normal storage level. However, when the water level exceeds the normal storage level, the discharge flow is set to its maximum capacity.

3.2. Identification of Pre-Release Index Thresholds

The optimal flood control dispatch model described in Section 2.1.1 was established with a total time period T of 168 h (7 days) and a target storage capacity of 322.5 million m³ during the flood season, corresponding to the storage capacity at the FLWL of the Shuifumiao Reservoir. The target weights γ1 and γ2 were determined using the interactive Chebyshev method [42] based on a random discrete weight space, with values of 0.7 and 0.3, respectively [43]. Historical floods were selected and amplified to different frequencies, resulting in a total of 160 flood events, including 60 floods with a return period frequency p of 0.1%, 60 floods with a p value in the range of (0.1%, 1%], and 40 floods with a p value greater than 1%. The optimal dispatching process for the reservoir was then determined.

The pre-release index threshold for the Shuifumiao Reservoir was identified using the process described in Section 2.1.2. Using the interactive Chebyshev method, the values of the weights α₁, α₂, and α₃ in the pre-release index calculation formula were set to 0.2, 0.46, and 0.34, respectively. The calculated values of k_r_st, k_r_nd, and k_V_pre for 160 floods are shown in Figure 4, and the associated characteristic values are presented in

Table 3. Pre-release index thresholds.

Characteristic Values	Maximum Value	Minimum Value	Average Value
rst	0.87	0.54	0.74
rnd	0.71	0.40	0.50
Vpre/(108 m3)	0.65	0.16	0.35

. To ensure safe flood control operations, the pre-release period was appropriately extended, and the pre-release depth was increased. Accordingly, r_st was set to its minimum value, r_nd was set to its minimum value, and V_pre was set to its maximum value. The final r_st, r_nd, and V_pre values for the Shuifumiao Reservoir were taken as 0.54, 0.40, and 0.65 billion m³, respectively.

3.3. Refined Pre-Release Scheduling Model for Shuifumiao Reservoir

After identifying the pre-release index thresholds, a refined pre-release operation model for the Shuifumiao Reservoir was constructed, as described in Section 2.2. The flood forecast lead time in the Lianshui River basin was taken as 7 days, corresponding to a forecast horizon of 168 h. The decision horizon was 1 h, the flood forecast data were updated at intervals of 1 h, and the model performed rolling calculations at hourly intervals.

Considering the downstream flood control safety and flow release capacity limitations, when the reservoir water level was below the flood control high water level (FCHWL), the target outflow would be equal to the downstream flood control safety discharge or the corresponding discharge capacity, whichever was lower. Conversely, when the reservoir water level was equal to or higher than the FCHWL, the outflow would be equal to the discharge capacity if the target downstream discharge was greater than the corresponding discharge capacity.

4. Results and Discussion

To assess the effectiveness of the reservoir flood control model, a number of historical floods were selected and amplified to produce 20 events of 2000-year floods (exceedance floods), 20 events of 1000-year floods (check floods), and 20 events of 100-year floods (design floods). The main objective of reservoir flood control scheduling is to ensure the safety of both the reservoir’s storage and downstream areas. To evaluate their effects on the safety of downstream flood control sections, the pre-release operations, existing operations, and original operations were compared based on two perspectives: reducing peak flow and the duration of downstream safe discharge. The impacts of the three scheduling methods on reservoir storage safety were analyzed and compared based on the highest water level occurring in the reservoir during scheduling and the duration of operating time for which the water level was above the FCHWL.

4.1. Benefit Analysis of Perfect Forecast Cases

Perfect forecast cases simulate actual unimpaired flows for the next 7 days at each simulation time step. These cases involve simulated operations based on perfect forecast skill, representing an ideal but unrealistically perfect scenario that yields the highest attainable benefit of the proposed refined pre-release operation model.

Figure 5 illustrates the simulation and operation processes for the three scheduling methods used for different flood frequencies (one flood was selected for analysis for each frequency). The maximum outflow, peak-cutting rate, and duration of super downstream safe discharge during each flood scheduling process were calculated, as well as the maximum reservoir water level and duration of operations for which the water was above the FCHWL.

Table 4. Simulation results for different operations.

Category	Flood Frequency (%)	Pre-Release Operation			Existing Operations			Original Operations
		Max	Min	Avg	Max	Min	Avg	Max	Min	Avg
Maximum outflow (m3/s)	0.05	6342.5	5417.5	5951.5	6504.9	5727.7	6137.6	6993.4	6054.9	6380.8
	0.10	5758.1	4977.3	5424.1	5880.4	5283.2	5580.5	6236.7	5521.5	5816.2
	1.00	4343.8	3749.0	3971.6	4405.9	3899.5	4085.1	4671.3	4139.2	4400.2
Peak-cutting rate (%)	0.05	43.12	33.41	37.65	39.86	31.70	35.66	36.42	28.51	33.13
	0.10	42.86	33.89	37.75	39.34	32.49	35.96	36.61	28.40	33.25
	1.00	40.55	30.72	36.77	37.81	29.73	34.97	33.99	25.50	29.96
Duration of outflow exceeding 3000 m3/s (h)	0.05	57.00	42.00	47.85	58.00	44.00	49.90	58.00	45.00	52.85
	0.10	49.00	37.00	42.55	52.00	39.00	45.00	53.00	43.00	48.05
	1.00	29.00	19.00	23.95	30.00	21.00	26.00	40.00	28.00	32.55
Maximum reservoir water level (m)	0.05	97.01	96.20	96.68	97.15	96.48	96.84	97.54	96.77	97.04
	0.10	96.51	95.79	96.21	96.62	96.08	96.35	96.92	96.30	96.56
	1.00	95.18	94.61	94.82	95.24	94.76	94.94	95.50	94.99	95.24
Duration of reservoir water level exceeding FCHWL (h)	0.05	51.00	40.00	44.10	53.00	42.00	46.65	58.00	45.00	52.60
	0.10	46.00	35.00	39.30	48.00	37.00	41.55	53.00	42.00	47.90
	1.00	27.00	16.00	20.90	28.00	19.00	23.15	40.00	28.00	32.20

presents the results obtained.

As depicted in Figure 5, pre-release operations begin before the flood arrives; the lower the flood frequency, the earlier the pre-release begins. Due to the increase in inflow, discharge capacity constraints, and pre-release depth constraints, the gradient of the reservoir capacity reduction decreases. Moreover, the smaller the flood frequency, the greater the total pre-release depth. During the flood inflow period, floodwaters occupy the previously vacated reservoir capacity, and the outflow and reservoir level increase slowly. After the main flood peak, pre-release operations are terminated in a timely manner and scheduling is performed according to existing operations, with the reservoir water level dropping to the FLWL.

Figure 6 shows the reservoir level change curves for simulations of the pre-release operations corresponding to 60 flood events. The results demonstrate that, although pre-release operations led to the release of a part of the reservoir capacity, the water level in the reservoir did not fall below the dead water level. Subsequently, the reservoir water level gradually decreased to the FLWL after the peak of the flood, thereby ensuring adequate post-flood water supply security.

Compared to existing and original operations, the pre-release scheduling method resulted in a higher discharge before the flood arrived, but the downstream safe discharge was not exceeded. The results of the over-control standard flood scheduling showed that the maximum outflow using the pre-release operations method was, on average, 2.97% and 6.73% lower than that when using the current and original operations, respectively. The peak-cutting rate increased by an average of 1.99% and 4.52%, respectively, and the maximum reservoir water level was decreased by an average of 0.16 m and 0.36 m, respectively, when compared to the existing and original operations. Moreover, in the 20 different flood scheduling processes, the maximum reservoir water level was below the check flood level, and the duration of the super downstream safe discharge was reduced by an average of 2.05 h and 5 h, respectively, whereas the duration of operations for which the water level was above the FCHWL was reduced by an average of 2.55 h and 8.5 h, respectively. The design flood and check flood scheduling results both indicate that pre-release operations can ensure better downstream flood safety and enhance reservoir storage safety.

4.2. Benefit Analysis of Cases Considering Forecasted Flood Error

The accuracy of hydrological forecasts directly affects the efficiency of reservoir pre-release operations [44]. Thus, this section provides a detailed analysis of the impacts of forecast errors, specifically based on the inflow forecast results for the Shuifumiao Reservoir. To select appropriate probability distributions to fit the flood forecast error series, the relative error of the flood forecast should be calculated first, which can be defined as follows:

$$\mathrm{e}\left(\mathrm{t}\right)={\displaystyle \frac{Q_{in}^{*}(t)-Q_{in}(t)}{Q_{in}(t)}}$$

(12)

where e(t) is the relative prediction error of the flood at time t, $Q_{in}^{*}(t)$ denotes the predicted flow at time t, and $Q_{in}(t)$ denotes the observed flood at time t.

Assuming e(t) follows a normal distribution [45,46], the probability distribution of the relative error for a 7-day forecast can be obtained, as shown in Figure 7.

As the existing operations were significantly better than the original operations, as discussed in Section 4.1, the original operations were not analyzed. To generate a series of 7-day incoming flow forecasts that accounted for flood forecast errors, the Monte Carlo method [47] was applied at each time step in pre-release operations to randomly generate a series of forecasted flood relative errors e(t). These errors were then used, based on the flood data from Section 4.1, to generate the incoming flow forecast data.

Figure 8 presents a comparison of evaluation indicators for simulations using three operation methods: pre-release operations based on actual unimpaired flow data (perfect forecast), pre-release operations based on forecasted flood data (actual forecast), and existing operations based on actual unimpaired flow data.

For the 60 floods, the pre-release scheduling under the perfect forecast achieved better evaluation indicators than that under existing operations. For most flood events under the actual forecast, the indicators were also better than those under the existing operations. During the pre-release process, pre-release was initiated before the flood arrived and the reservoir water level was lowered to a reasonable height before the flood peak arrived. The pre-release was stopped after the flood peak, and the target water level was restored. This demonstrates the rationality of using the pre-release index threshold to determine the initiation and cessation of pre-release operations and the effectiveness of the real-time calculation method for the pre-release discharge. The pre-release operation model based on the pre-release index theory can be used for reservoir flood control scheduling and can effectively improve flood control safety.

During operations for certain floods, the pre-release operations based on actual forecast data did not achieve the goal of reducing both the maximum reservoir water level and the maximum outflow while also reducing the operating time for which the reservoir water level exceeded the FCHWL and the outflow exceeded 3000 m³/s. This is because the pre-release operation model based on the theoretical pre-release index is limited by the accuracy of flood forecasting. Therefore, improving the accuracy of flood forecasting can further enhance the flood control benefits of pre-release operations.

5. Conclusions

The study proposed a framework and mathematical expression for a pre-release index, which combines reservoir storage, forecasted flood volume, forecasted flood peak, and peak occurrence time. Based on “optimization-simulation” technology, a refined pre-release operation model that identifies pre-release index thresholds for initiating and terminating pre-release operations, as well as the pre-release depth threshold, was developed in this study. The model includes a clear mechanism for determining the start and end points of pre-release operations, and can accurately calculate the real-time pre-release water volume.

The evaluation of the refined pre-release operation model was based on five criteria: the highest reservoir water level during operation, the time spent operating above the flood control level, the maximum outflow, the time spent with outflow greater than the allowable outflow, and the peak-cutting rate. The results demonstrated that the refined pre-release operations under perfect forecasting conditions significantly outperform current and original operations for all evaluation criteria. Although the refined pre-release operations under actual forecasting conditions did not achieve the maximum benefit, due to limitations related to the forecasting accuracy, they demonstrated significant improvements over current operations.

The proposed refined pre-release operation method can enhance the flood control capacity of reservoirs, provide technical support for the resilience of reservoirs to exceedance floods, and ensure the safety of both the reservoir and downstream flood control sections. To improve the efficacy of the method more effectively and broaden its applicability in actual river basin flood control scenarios, the following research prospects should be undertaken in future studies:

(1) Further research is needed on how to use the pre-release index theory to establish a pre-release operation model for a multi-reservoir system in a basin to cope with large-scale floods.

(2) It is necessary to further analyze the adaptability of the pre-release index theory to flood forecasting errors from different perspectives, such as different lead times for flood forecasting.

6. Patents

Cao Huang, Weiqi Li, Sizhong He, Qi Liu, Wan Jiang, Xu Deng (2023). Flood Control Operational Method, System, and Storage Medium Based on Pre-release Index for Reservoirs. Chinese Patent CN202110696147.9.