## ABSTRACT

Bridging the research gap between reservoir operations and inundation risks under the future climate, this study integrates a hydrologic reservoir management model with a 2D hydrodynamic model, comparing the conventional regulations and the optimized reservoir operations based on the particle swarm optimization (PSO) algorithm. Results reveal that optimized operations using the PSO algorithm consistently outperform conventional strategies by better-managing peak discharges and controlling downstream inundation. The study further differentiates between PSO-optimized plans: PSO_{1}, which focuses on minimizing inundation areas, and PSO_{2}, which prioritizes peak reduction at the flood control point. Interestingly, PSO_{2} proves superior for single-point peak reduction, typically the primary objective in current practices, whereas PSO_{1}, despite lesser peak reduction, achieves a smaller inundation area, enhancing basin-scale flood resilience. This discrepancy reveals the need to consider downstream inundation risks as critical evaluation metrics in reservoir optimization, a factor often overlooked in existing studies. The research underscores the importance of updating operational frameworks to incorporate 2D inundation risks and adapt to increased flood risks under changing climate conditions. Despite optimization, future climate scenarios predict increased flood exposure, indicating that the current safety discharge rates and flow regulations at control points are outdated and require revision**.**

## HIGHLIGHTS

A hydrologic reservoir management model was integrated with a 2D hydrodynamic model.

Optimizations by the PSO algorithm outperformed the conventional regulations.

Aiming to reduce the peak flow and the inundation area would lead to different optimized plans.

The critical gap in the current practice that neglects the inundation risk is highlighted.

Current safety drainage standards might be outdated and need revisions.

## INTRODUCTION

Optimizing reservoir operations and schedules is critical for disaster prevention and water resources management. Downstream flood resilience can be maximized by identifying and implementing the optimized reservoir strategies (Serra-Llobet *et al.* 2022), which requires considering the potential hazard of inundation by floodwaters (Cea & Costabile 2022). The analysis of flood propagation could usually be carried out by the 2D hydrodynamic models, which are useful in forecasting the inundation conditions for residential areas (Bhandari *et al.* 2018), developing flood risk zones (Farhadi & Najafzadeh 2021; Erima *et al.* 2022), and assessing the floodplain adaptive measures (Kalra *et al.* 2020). However, hydrodynamic models are usually intrinsically complex and computationally expensive, so existing reservoir operational optimization often relies on simplified routing methods (Dang *et al.* 2020; Wei *et al.* 2022; Ding *et al.* 2023) or neglects downstream routing (Dahmani & Yebdri 2020; Nourani *et al.* 2020).

Flood disasters fall within the realm of hydroclimatic calamities, often intricately linked with climate change (Rahman *et al.* 2021; Munawar *et al.* 2022). The climate drivers affect the flood risk mostly through the altered peak discharge, while reservoir buildup and operations also have an influence on flood risk (Tang *et al.* 2021). So, reservoir management needs to be framed in variable future climates (Nourani *et al.* 2020; Sun *et al.* 2023), though such studies often mainly focus on inflow availability instead of downstream flood risk.

Given multiple variables to consider for determining the reservoir releases, various algorithms have been developed to optimize the reservoir discharge curve, such as the linear and dynamic programming (DP) (Little 1955), genetic algorithm (GA) (Anand *et al.* 2018), or neural networks (Zhang *et al.* 2018). The particle swarm optimization (PSO) algorithm, as an intelligent algorithm that mimics a flock of birds foraging for food, was first proposed by Kennedy & Eberhart (1995) and has become widely accepted as an optimization method in hydrologic models ever since. Kennedy (1997) studied the components and parameters of the PSO algorithm and gave the theoretical significance and reasonable range of each parameter. Clerc (1999) introduced the convergence parameters to improve the convergence speed of the algorithm. Spiliotis *et al.* (2016) used the PSO algorithm combined with the water supply modeling system to optimize reservoir regulations that effectively reduced the deficits of water supply demands during droughts. Al-Aqeeli & Mahmood Agha (2020) developed a PSO model for individual reservoirs to maximize the annual hydropower generation using the annual reservoir generation as an objective function. Diao *et al.* (2022) proposed a simulated annealing particle swarm optimization (SAPSO) algorithm to treat the cascading reservoir system with the objective of maximum peak reduction.

When compared to the GA, evolutionary planning, and other algorithms, the PSO algorithm was proved as an effective global optimization method (Parsopoulos & Vrahatis 2002). Mirza *et al.* (2020) combined DP with the PSO to propose a DP-PSO algorithm, which outperformed the DP-GA algorithm in terms of search space and computational efficiency. Zarei *et al.* (2019) combined the PSO with the Bat Algorithm to improve the convergence speed of the algorithm by over 20%. Jahandideh-Tehrani *et al.* (2020) summarized 22 existing algorithms that evolved from PSO algorithms and compared them with evolutionary algorithms and mathematical optimization algorithms, showing that most of the PSO algorithms outperformed GA, mainly in terms of faster convergence. Ma *et al.* (2021) proposed spark-based parallel dynamic programming and spark-based parallel particle swarm optimization (SPPSO) methods based on cloud computing and found that SPPSO algorithms converged fast and could jump out of the local optima. The PSO has also been applied to optimize reservoir operations for multi-objectives such as water supply, flood storage, and hydroelectric power production and was proved to achieve comparable effects as the non-dominated sorting genetic algorithm II (Afshar & Hajiabadi 2018; Hojjati *et al.* 2018).

Collectively, the reservoir optimization and downstream inundation prediction were often vaguely considered together but conducted separately, which led to great uncertainty to flood risk management at the watershed scale. If any downstream fluvial flooding is considered, most current practices relied on the 1D channel routing model to predict the hydrograph at the critical cross-section, which hardly predicts the spatial inundation areas and potential consequences, especially to the critical infrastructures at the riparian. Furthermore, current studies rarely associated the climate variations with the reservoir management for the watershed scale, other than their effects on increasing the reservoir storage and overflowing risk (Beiranvand & Rajaee 2023).

Therefore, this work delves into the correlation between reservoir optimization scheduling and downstream inundation while evaluating solutions to the challenges posed by future climate change on reservoir optimization. For this purpose, the reservoir operational model, essentially a hydrologic model, was integrated with the 2D hydrodynamic model accordingly. The effects of the conventional and optimized reservoir operations were compared during four typical historic flood events. The reservoir releases through different operations drove a hydrodynamic model to simulate the effect of reservoir management on the channel safety at critical cross-sections and the downstream inundation risk in different climate scenarios. By comprehensively considering the 2D flood inundation levels at downstream, this work transcends traditional 1D channel model-based scheduling strategies. Through the comparison of two different release plans optimized by the PSO algorithm, this work provides a new finding that points out the necessity of considering the downstream inundation during the optimization of reservoir operations. This finding not only provides water resource managers with a more effective strategy for flood risk control but also aids in enhancing the efficiency of reservoir management to confront the increasingly severe impacts of climate change.

## METHODS

### Study site

Completed in 2015, the Nierji Reservoir was the largest water conservancy project in the Nenjiang River basin. It is located 189 km upstream of Qiqihar, which is the downstream flood control point that the Nierji reservoir protects. The upper river basin above the reservoir covers 22.35% (66,400 km^{2}) of the entire Nenjiang River basin area, with an annual inflow of 104.7 × 10^{8} m^{3}, accounting for 45.7% of annual runoff in the Nenjiang River basin. As an earth–rockfill reservoir made of asphalt concrete, it was designed for the 1,000-yr flood control standard. The characteristic water levels and the corresponding storage capacity of the Nierji Reservoir were listed (Liang *et al.* 2021) (Table 1).

Characteristic water levels . | Level (m) . | Storage capacity (10^{8} m^{3})
. |
---|---|---|

Flood-limited water level | 213.37 | 52.2 |

Normal water level | 216 | 64.56 |

Flood control high water level | 218.15 | 75.88 |

Characteristic water levels . | Level (m) . | Storage capacity (10^{8} m^{3})
. |
---|---|---|

Flood-limited water level | 213.37 | 52.2 |

Normal water level | 216 | 64.56 |

Flood control high water level | 218.15 | 75.88 |

The study selected four significant historical events as design floods that occurred in the Nierji-Qiqihar reach: Type 1969 (Gao *et al.* 2008), Type 1988 (Gao *et al.* 2007), Type 1998.6 (Liu *et al.* 2020), and Type 1998.8 (Guan *et al.* 2021); the first three represent the floods coming from the reservoir point, while the last one incorporates the influence of the lateral inflows from the intermediate basins within the reach (Ding *et al.* 2023). Type 1998.8 represents a historical extreme case, which caused 14,800 m^{3}/s peak flow and exceeded the safety capacity of the flood control infrastructures at Qiqihar. These pivotal design floods served as benchmarks for assessing the flood simulation tools and reservoir operations before implementation (Lu & Zhang 1999).

The performance of the Nierji Reservoir in terms of flood storage, peak reduction, and postponing the flood arrival has far-reaching implications for the normal functioning of the downstream cities such as Qiqihar with a population of 1,237,300. The suburban levee is 136 km long and is distributed along the city which is designed for a 50-yr event with a peak flow of 8,850 m^{3}/s. The urban levee of Qiqihar is 47 km long, which is designed for a 100-yr event with a peak flow of 12,000 m^{3}/s (Ding *et al.* 2023).

### Particle swarm optimization

*et al.*2011). Each particle in the algorithm ‘flies’, i.e. seeks, based on its own and other particles' flight experience. The PSO algorithm has the advantages of a concise principle, simple implementation, fast convergence, and fewer parameters, which is suitable for solving multi-objective and non-linear optimization problems. To optimize the daily discharge flows within the studied period,

*N*particles with

*D*variables were selected and their initial values were randomly assigned. During each iteration, each particle calculated its fitness value by the objective function. Various criteria could usually be considered as the objectives for flood control such as the maximum peak reduction, the shortest flood duration, or the minimum flood volume. In this work, the maximum peak reduction was determined to be the objective:where

*q*

_{m}is the maximum discharge flow at the downstream flood control point,

*t*is time,

*q*(

*t*) is the reservoir discharge at time

*t*,

*Q*

_{q}(

*t*) is the observed lateral inflows, and

*f*represents the channel routing function. Based on the objective, the local optimal and the global optimal solutions of the reservoir discharge were stochastically determined through the following iterative process, and each particle could be updated as follows:where is the velocity of the (

*k*+ 1)th iteration in the

*d*th dimension of the

*i*th particle, is the velocity of the

*k*th iteration in the

*d*th dimension of the

*i*th particle, is the individual optimal solution for the

*k*th iteration in the

*d*th dimension of the

*i*th particle, is the global optimal solution of the

*d*th dimension, is the particle value of the

*k*th iteration in the

*d*th dimension of the

*i*th particle,

*N*is the number of particles set as 150,

*D*is the dimensionality of the solution vector set as 34,

*c*1 and

*c*2 are learning rates both set as 0.7,

*r*1 and

*r*2 are two independent numbers randomly selected in the range [0,1], and is the inertia weight controlling the strength of the search capability.

*k*is the current time step,

*k*

_{max}is the allowed maximum time step,

*ω*

_{ini}is the initial inertia weight set as 0.9, and

*ω*

_{end}is the last inertia weight when evolving to the maximum number of iterations set as 0.4. This strategy of using adaptive inertia weight is exhibited through the tests of this study, and it is showed an improved searching effect on approaching convergence compared to the traditional means of using a constant inertia weight.

*Z*is the current reservoir level,

*Z*

_{min}is the flood-limited water level, and

*Z*

_{max}is the flood prevention level. Second, the downstream discharge must not exceed the maximum allowable streamflow:where

*Q*

_{downstream}is the downstream streamflow at Qiqihar, and

*Q*

_{safety}is the maximum safety discharge allowed at Qiqihar (8,850 m³/s for 50-yr flood and 12,000 m³/s for 100-yr flood). Third, the discharge released from the reservoir should meet the minimum demand for power generation, irrigation, and environmental baseflow, and the maximum discharge should not exceed the maximum allowed discharge rate:where

*q*

_{min}is the minimum discharge required for power generation, irrigation, and downstream environmental baseflow,

*q*is the current reservoir discharge, and

_{t}*q*

_{t}_{max}is the maximum allowed reservoir discharge. Lastly, the change of discharge between time steps is subject to the flow capacity of the spillway gates and operational convenience:where

*q*

_{t}_{+1}is the reservoir discharge flow at

*t*+ 1 time step and Δ

*Q*

_{max}is the maximum allowable change of the reservoir discharge between adjacent time steps.

### Muskingum routing

*et al.*2017), which was proposed for studying flood control in the Muskingum watershed in Ohio, U.S. (McCarthy 1939) and then improved by Cunge (1969). The Muskingum method was adopted in this study as the channel routing function for optimizing the reservoir operations as follows:where

*C*

_{0},

*C*

_{1}, and

*C*

_{2}are the Muskingum routing coefficients, respectively,

*Q*

_{1}and

*Q*

_{2}are the outflows of every reach at the current and next time steps,

*I*

_{1}and

*I*

_{2}are the inflows of every reach at the current and next time steps,

*K*is the storage constant set as 4,

*x*is the specific gravity factor set as 0.2, and Δ

*t*is the time step.

*L*could be further divided into

*n*segments, and each segment would be modeled in a consecutive way downstream with the same set of parameters (

*K*and

_{l}*x*):where

_{l}*n*is the number of river segments,

*K*is the segmented storage constant set as 1,

_{l}*L*is the total river length,

*L*is the segmented river length, and

_{l}*x*is the segmented flow-specific gravity coefficient.

_{l}### Operational strategies

#### Conventional operation

According to the preliminary design plan to minimize the flood peak at Qiqihar, a conventional operating model was established to represent the current operations that met the downstream flood control standard as follows (Liang *et al.* 2021):

(a) During a flood event with a less than 50-yr return period, the peak flow at Qiqihar should be less than 8,850 m³/s.

(b) During a flood event of the 50–100-yr return period, the peak flow at Qiqihar should be less than 12,000 m³/s.

(c) The operational water level of the reservoir should not exceed 216 m.

(d) The maximum water level of the reservoir shall be less than 218.15 m.

#### Optimized operation

The maximum peak reduction downstream at Qiqihar was chosen as the optimization objective. The reservoir discharge was optimized through the PSO algorithm, which should meet the safety requirements of the reservoir and, at the same time, provide storage for the beneficial use of flood water. The water level of the reservoir was updated based on a simple water balance considering the inflow and discharge.

### Flood inundation risk

Based on the Type 1969 design flood as an example, the HEC-RAS software was used to simulate the 2D flood inundation in three scenarios (flood, conventional operation, and optimized operation) to analyze the flood control effects of conventional and optimized operations. In the flood scenario, the pre-dam discharge at Qiqihar was estimated by applying the flow time series of the corresponding return periods, e.g. 50 yr, as the boundary condition at the location of the reservoir to drive the 2D inundation simulation as if the dam was unbuilt. This serves as a baseline to evaluate the effects of reservoir operations.

Most of the relevant studies targeted the hydrograph of a downstream river cross-section during reservoir optimization, which failed to take account of the spatial information such as the flood inundation. Due to the stochastic diversity of the optimization method, two PSO-based optimized operations were compared for different flood scenarios. For the PSO_{1} plan, the peak flow at Qiqihar tended to be higher and the flood discharge dropped quickly during the receding stage. For the PSO_{2} plan, the peak flow at Qiqihar was relatively lower and the flood discharge was maintained at a high level during the receding stage. Both plans met all other necessary constraints. In this way, PSO_{2} was characterized by the lower flood peak as the common optimization objective that mainly focused on the hydrograph at the critical downstream cross-section, while PSO_{1} was characterized by less flood discharge during the receding stage which led to lower total volume and inundation. So, the influence of the different optimization strategies focusing on the peak reduction and inundation extents could be closely compared.

### Climate scenarios

The global average precipitation was projected, based on the SSP1-2.6 scenario, to increase by approximately 2.9% (1.0–5.2%) in the phase of 2081–2100 compared to the phase of 1995–2014. In the SSP3-7.0 scenario, the global average precipitation was projected to increase by about 4.7% (2.3–8.2%) in the period of 2081–2100 compared to the period of 1995–2014 (Lee *et al.* 2021). Based on the simulation of the above two climate scenarios, distributed projection data were obtained on the percentage increase in winter and summer precipitation in Northeast China for the period 2081–2100 compared with the period 1995–2014.

To accommodate the phases of 2081–2100 and 1995–2014 in the climate scenarios, the Type 1998.6, 50-yr design flood, falling within the current phase, was used as the baseline. During the flooding season in the summer, the reservoir inflow was predicted to be enhanced by 0–10% in the SSP1-2.6 scenario and by 10–20% in the SSP3-7.0 scenario for the study region. For these two climate scenarios, the inflow was designed to increase by 10% and 20% correspondingly to provide indications to compare the conventional and optimized reservoir operations in the future climate. The flood inundation was simulated for those two climate scenarios, and the inundation risk was analyzed to serve as a reference for developing future flood control measures.

## RESULTS AND DISCUSSION

### Comparison of the single-point operational strategies

*et al.*2023).

The conventional regulation model, based on the established rules, describes a critical state of flood control, which just meets the downstream safety discharge rate at Qiqihar. The optimization model fully utilizes the reservoir storage and reduces the downstream discharge at Qiqihar (Table 2). Consistently, the optimization of the reservoir operations for the 50-yr design floods was relatively more effective than that for the 100-yr design floods, and the ratio of the peak reduction in the former turned out to be 3–5% higher than the latter.

Operating method . | Return period . | Flood type . | After-dam peak flow at Qiqihar (m^{3}/s)
. | Pre-dam peak flow at Qiqihar (m^{3}/s)
. | Peak reduction rate (%) . |
---|---|---|---|---|---|

Conventional operation | 50a | 1,969 | 8,850 | 12,371.2 | 28.46 |

1,988 | 8,850 | 12,123.8 | 27.00 | ||

1,998.6 | 8,850 | 12,062.9 | 26.63 | ||

1,998.8 | 8,850 | 12,213.2 | 27.54 | ||

100a | 1,969 | 12,000 | 15,100 | 20.53 | |

1,988 | 12,000 | 14,637.8 | 18.02 | ||

1,998.6 | 12,000 | 14,342 | 16.33 | ||

1,998.8 | 12,000 | 14,748.1 | 18.63 | ||

Optimized operation | 50a | 1,969 | 8,326.81 | 12,371.2 | 32.69 |

1,988 | 7,766.92 | 12,123.8 | 35.94 | ||

1,998.6 | 7,578.36 | 12,062.9 | 37.18 | ||

1,998.8 | 8,197.24 | 12,213.2 | 32.88 | ||

100a | 1,969 | 10,677.8 | 15,100 | 29.29 | |

1,988 | 9,937.59 | 14,637.8 | 32.11 | ||

1,998.6 | 9,709.24 | 14,342 | 32.30 | ||

1,998.8 | 10,424.3 | 14,748.1 | 29.32 |

Operating method . | Return period . | Flood type . | After-dam peak flow at Qiqihar (m^{3}/s)
. | Pre-dam peak flow at Qiqihar (m^{3}/s)
. | Peak reduction rate (%) . |
---|---|---|---|---|---|

Conventional operation | 50a | 1,969 | 8,850 | 12,371.2 | 28.46 |

1,988 | 8,850 | 12,123.8 | 27.00 | ||

1,998.6 | 8,850 | 12,062.9 | 26.63 | ||

1,998.8 | 8,850 | 12,213.2 | 27.54 | ||

100a | 1,969 | 12,000 | 15,100 | 20.53 | |

1,988 | 12,000 | 14,637.8 | 18.02 | ||

1,998.6 | 12,000 | 14,342 | 16.33 | ||

1,998.8 | 12,000 | 14,748.1 | 18.63 | ||

Optimized operation | 50a | 1,969 | 8,326.81 | 12,371.2 | 32.69 |

1,988 | 7,766.92 | 12,123.8 | 35.94 | ||

1,998.6 | 7,578.36 | 12,062.9 | 37.18 | ||

1,998.8 | 8,197.24 | 12,213.2 | 32.88 | ||

100a | 1,969 | 10,677.8 | 15,100 | 29.29 | |

1,988 | 9,937.59 | 14,637.8 | 32.11 | ||

1,998.6 | 9,709.24 | 14,342 | 32.30 | ||

1,998.8 | 10,424.3 | 14,748.1 | 29.32 |

### Inundation factor

Scenario . | Inundation area (km^{2})
. | Average depth (m) . | |
---|---|---|---|

Channel . | Overland . | ||

Design flood | 1,443.26 | 5.89 | 1.15 |

Conventional operation | 1,190.25 | 5.87 | 1.22 |

Optimized operation | 1,024.01 | 5.58 | 1.12 |

Scenario . | Inundation area (km^{2})
. | Average depth (m) . | |
---|---|---|---|

Channel . | Overland . | ||

Design flood | 1,443.26 | 5.89 | 1.15 |

Conventional operation | 1,190.25 | 5.87 | 1.22 |

Optimized operation | 1,024.01 | 5.58 | 1.12 |

Criteria . | Reduction (%) . | |
---|---|---|

Conventional . | Optimized . | |

Inundation area | 17.53 | 29.05 |

Channel depth | 0.28 | 5.22 |

Overland depth | −5.66 | 3.29 |

Criteria . | Reduction (%) . | |
---|---|---|

Conventional . | Optimized . | |

Inundation area | 17.53 | 29.05 |

Channel depth | 0.28 | 5.22 |

Overland depth | −5.66 | 3.29 |

^{2}, accounting for 29.05% of the total affected area, and reduced the total affected area by 116.24 km

^{2}(9.77%) compared to the conventional regulation. In addition, the optimized operation also reduced the average flood depth in the channel by nearly 30 cm and reduced the average flood depth in the inundated overland by 3 cm. Given the large area affected by inundation, the optimized operation makes a considerable difference in the flood volume and the inundation consequence. The difference between the three flooding scenarios could be further illustrated by subtracting the depth distribution of the baseline from that of the two flooding scenarios (Figure 5). Compared with the conventional operation, the optimized operation significantly reduced the flood depth downstream, i.e. the reduction in the inundated depths by the optimized operation was larger than that in the conventional operation.

_{1}operation, the peak flow at Qiqihar was 8,263.71 m

^{3}/s, and the flood discharge in the receding stage was lower; for the PSO

_{2}operation, the peak flow at Qiqihar was 8,251.58 m

^{3}/s, while the flood discharge in the receding stage was higher (Figure 6). Although PSO

_{2}had a better optimization effect judged from the peak reduction, its higher discharge in the receding stage resulted in a larger inundation area (Figure 7).

Therefore, the effect of the optimized reservoir management could be graded differently with and without considering the inundation process. If the single-point peak discharge was used as the optimization objective as a common practice, the PSO_{2} optimized operation, which achieved 12.13 m^{3}/s lower peak flow than the PSO_{1} operation, should be regarded as a better strategy. However, the comparison of the inundation areas indicates that the PSO_{1} operation, achieving the lower inundated area, could be regarded as a better strategy for reducing flood exposure (Table 5). Such conflict indicates the necessity of adding the downstream inundation risk as an additional optimization objective or an evaluation metric, which, however, was neglected by most current studies.

Scenario . | Peak flow at Qiqihar (m^{3}/s)
. | Inundation area (km^{2})
. | Average depth (m) . | |
---|---|---|---|---|

Channel . | Overland . | |||

PSO_{1} | 8,263.71 | 1,055.54 | 5.658 | 1.150 |

PSO_{2} | 8,251.58 | 1,084.49 | 5.648 | 1.132 |

Scenario . | Peak flow at Qiqihar (m^{3}/s)
. | Inundation area (km^{2})
. | Average depth (m) . | |
---|---|---|---|---|

Channel . | Overland . | |||

PSO_{1} | 8,263.71 | 1,055.54 | 5.658 | 1.150 |

PSO_{2} | 8,251.58 | 1,084.49 | 5.648 | 1.132 |

### Climate factor

*et al.*2023).

Scenario . | Inundation area (km^{2})
. | Average depth (m) . | |
---|---|---|---|

Channel . | Overland . | ||

1998.6 flood | 1,583.40 | 6.050 | 1.202 |

10% enhanced | 1,767.03 | 6.161 | 1.253 |

20% enhanced | 1,913.58 | 6.264 | 1.270 |

Scenario . | Inundation area (km^{2})
. | Average depth (m) . | |
---|---|---|---|

Channel . | Overland . | ||

1998.6 flood | 1,583.40 | 6.050 | 1.202 |

10% enhanced | 1,767.03 | 6.161 | 1.253 |

20% enhanced | 1,913.58 | 6.264 | 1.270 |

Criteria . | Increase (%) . | |
---|---|---|

10% water enhancement . | 20% water enhancement . | |

Inundation area | 11.60 | 20.85 |

Chanel depth | 1.83 | 3.53 |

Overland depth | 4.21 | 5.59 |

Criteria . | Increase (%) . | |
---|---|---|

10% water enhancement . | 20% water enhancement . | |

Inundation area | 11.60 | 20.85 |

Chanel depth | 1.83 | 3.53 |

Overland depth | 4.21 | 5.59 |

^{3}/s after optimization, while in the 20% water enhancement scenario, the peak flow at Qiqihar even reached 10,700.82 m

^{3}/s after optimization, both of which were above the safety drainage rate of 8,850 m

^{3}/s.

The discrepancy from the current safety standard indicates that the new drainage threshold as well as more rigorous adaptive measures, such as consolidating river embankment, should be proposed for the future climate. This also agrees with the previous finding that reservoir operations cannot completely eliminate the increasing risks of future floods for this region (Sun *et al.* 2023). Although climatic factors are rarely considered in practical reservoir operations due to their long-term effects and uncertainty, it is found in this study that neither the conventional nor optimized reservoir operations may guarantee a safe release schedule, because the requirement of the maximum allowed flow at the downstream flood control point becomes outdated.

## CONCLUSIONS

Targeting the current research gap between the reservoir operations and the inundation risk compounded with climate variations, this work integrated a hydrologic reservoir management model with a 2D hydrodynamic model. The scheduling of the reservoir release was controlled by a conventional regulation model and an optimized model based on the PSO algorithm. Through the comparison, it was found that the optimized operation was always better than the conventional operation in terms of effectively managing the peak discharge at the downstream flood control cross-section and controlling the downstream inundation.

Two reservoir operations optimized by the PSO algorithm were developed with the PSO_{1} plan focusing on a smaller inundation area and the PSO_{2} plan focusing on the peak reduction at the flood control point. The comparison indicates that the PSO_{2} plan was more effective when the single-point peak reduction was the only objective as the common practice, while the PSO_{1}, regarded as the worse choice due to the lower single-point peak reduction, achieved a smaller inundation area that is more favorable for the basin-scale flood resilience. Such conflict indicates the necessity of considering the downstream inundation risk as an additional objective or an evaluation metric during reservoir optimization, which, however, was neglected by most current studies.

This work highlights the need to incorporate 2D downstream inundation risk into reservoir operational optimization frameworks. This imperative becomes particularly urgent, given the projected rise in flood risk due to changing climate patterns. Despite the apparent efficiency of the PSO algorithm in optimizing reservoir operations for the current climate, our analysis proves its inability to address the future climate. Even after the optimization, the downstream area could still expect increased flood exposure due to the increased inundation area and the exceeded safety discharge rate at the flood control cross-section. This indicates that the current maximum allowable flow rate at the flood control point has become outdated and needs to be updated for the future climate.

This work reveals the complex relationship between the reservoir operation and downstream inundation, when dealing with the immense challenges posed by the upcoming climate change. The discrepancy between associating the reservoir operation with and without inundation risk highlights the need to establish the dynamic feedback between the inundation risk and reservoir operations. Jointly addressing this human–natural process could enhance our preparedness for flood risks under future climate conditions.

## FUNDING

This work was kindly supported by the Scientific Research Program of The Education Department of Jilin Province (JJKH20231179KJ).

## DATA AVAILABILITY STATEMENT

Data cannot be made publicly available; readers should contact the corresponding author for details.

## CONFLICT OF INTEREST

The authors declare there is no conflict.