Optimal reservoir operation for transport timescales using an integrated methodology

Dam construction hinders the transport process of water constituents, resulting in various water quality issues in reservoir areas that impede the sustainable development of hydropower. Conventional reservoir operation optimizations to address these issues face challenges in mathematizing multiple water quality objectives and solving high-dimensional computational problems. Taking a comprehensive perspective, we propose a methodology that incorporates the concept of transport timescales into optimal reservoir operation. Firstly, a specific transport timescale is estimated through numerical tracer experiments using a 3D hydrodynamic model. Subsequently, a surrogate model is developed to approximate the hydrodynamic model for computationally efficient estimation. Finally, we employ a non-dominated ranking genetic algorithm, combined with the surrogate model, to search for a Pareto-optimal solution for multiple objectives. As a case study, we selected flushing time as the representation of transport timescales and applied it to Xiangxi Bay (XXB) in the Three Gorges Reservoir, which has experienced serious water quality problems since dam construction. Our results show that under the optimal operation scheme, the average flushing time for the entire XXB is 23.991 d, which represents a 10.9% reduction compared to the practical operation scheme. The reduction rate of flushing time along XXB shows a monotonically increasing trend towards the reservoir mainstream, with a maximum reduction of 90.9%. The proposed methodology provides a heuristic tool that links optimal reservoir operation and the transport process of holistic water constituents for comprehensive water quality management in reservoirs.


Introduction
The need to support growing global populations, escalating demand for electricity, and the imperative to reduce greenhouse gas emissions have sparked a surge in the construction of hydropower dams worldwide (Opperman et al 2023).Hydropower accounts for 16% of global electricity generation, with a capacity of about 1230 000 MW International Renewable Energy Agency (IRENA 2020).Leading energy agencies, such as the International Energy Agency (IEA) and IRENA, anticipate a twofold increase in global hydropower capacity by 2050 (IEA 2021, IRENA 2021).Hydropower dams are often combined with other uses, such as flood control, irrigation, and navigation (Galizia Tundisi 2018).Unfortunately, the multiple benefits of hydropower dams are accompanied by negative environmental impacts, one of which is water quality issues within the reservoir area, including sedimentation, eutrophication, as well as contamination by pollutants like pesticides, heavy metals, and microplastics (Ma et al 2015, Tang et al 2015, Li et al 2021, Dhivert et al 2022), which challenge sustainable hydropower development.
To alleviate water quality issues while meeting other reservoir objectives to maximize benefits, optimal reservoir operations are widely studied (Yeh 1985, Shaw et al 2017).However, a common limitation is that the objectives being used in optimization techniques must be in a mathematical format, i.e., predictive models (Barbour et al 2016).Consequently, water quality issues need to be translated into clear, specific, and quantifiable objectives to be effectively incorporated into models and to assess their effectiveness.The simulation of flow velocity, water level, and water temperature relies on wellunderstood physical laws and can be simulated accurately, while the complexity of chemical and biological processes require multiple assumptions and simplifications in modeling, which limits the ability to capture these variables well (e.g.nutrients, phytoplankton, microplastic) (Bennett et al 2013).Therefore, conventional studies on optimal reservoir operations often employ a single variable that is comparatively easier to simulate as a proxy for water quality objectives, such as dissolved oxygen, chlorophyll a, and total dissolved solids (Chaves et al 2003, Castelletti et al 2014).Another limitation is including multiple objectives extending reservoir optimization modeling to higher dimensions and higher fidelity increases computational demands exponentially, even in simulated conditions for a single reservoir (Shaw et al 2017).
It is often neglected or avoided in reservoir operation studies that the presence of multiple water quality issues occurs contemporaneously in reservoir areas.River water, consisting of various constituents including pure water, dissolved gases, pollutants, nutrients, sediments, and planktonic cells (Lucas and Deleersnijder 2020), undergoes constant dilution or biochemical reactions as they are transported by river flows (Teurlincx et al 2019).However, the construction of dams weakens the connectivity of river systems, altering natural river regimes and slowing down the transport process (Grill et al 2019).Consequently, a substantial portion of the originally transported constituents downstream gets trapped contemporaneously in the reservoir.For example, the Sulejów Reservoir in Poland retains approximately 30% of nutrients and micropollutants, as well as 45% of suspended sediments (Urbaniak et al 2012).In this regard, it is promising to develop an integrated water quality objective that considers the holistic transportation of water constituents for effective reservoir management.
Transport timescales are such potential objectives that incorporate hydrodynamic and transport processes into simple but holistic metrics (Lucas et al 2009).These metrics (e.g.water age, residence time, and transit time) provide information on how long water or constituents transported with water have spent, will spend, or takes to arrive at a defined water body or its sub-regions (Lucas and Deleersnijder 2020).This facilitates a rigorous quantitative assessment of water exchange characteristics at different scales and perspectives that determine the import and export of water constituents (Duran-Matute and Gerkema 2015).In fact, as early as the Water Framework Directive issued by the European Union in 2000 (WFD 2000), water residence time was defined as one of the indicators to evaluate water quality status.Despite being widely used for water resources management in recent decades (Bárcena et al 2012, Tena et al 2013), to our knowledge, transport timescales have rarely been incorporated into reservoir operation schemes.
This study aims to develop an integrated methodology for incorporating transport timescales into an optimal reservoir operation model to improve water quality issues while meeting other reservoir operation objectives to maximize benefits.First, a 3D hydrodynamic model is applied to determine a specific transport timescale via numerical tracer experiments.Second, a surrogate model based on a back propagation artificial neural network (BP-ANN) is built to establish the relationship between the transport timescale and reservoir operation schemes, while substituting the simulation model for more effective evaluations.Third, the developed surrogate model is linked with a non-dominated sorting genetic algorithm (NSGA-II) to search optimal reservoir operation schemes.We apply the methodology to the Xiangxi Bay (XXB).Being one of the closest tributary bays to the Three Gorges Reservoir (TGR), XXB is highly influenced by the reservoir water level management.Since the impoundment of TGR in 2003, there has been a significant concern regarding the deterioration of water quality in XXB, such as eutrophication and persistent organic pollutants.

Study area
The TGR spans a total area of 1084 km 2 and has a storage capacity of 393 million m 3 (figure 1).The backwater extends for approximately 600 km, forming 38 large backwater zones within its tributaries.The reduced flow velocity in these areas poses hindrances to the transport and biogeochemical transformation of water constituents, ultimately leading to water quality deterioration.Notable changes include increased levels of nutrient substances and potassium permanganate, as well as decreased pH values and dissolved oxygen concentrations.Furthermore, algal blooms have been reported in the tributary bays annually.Among these bays, XXB is particularly noteworthy.Located 35 km upstream of the dam, the intrusion of density currents impacts the temperature and hydrodynamic conditions within XXB, which are widely recognized as primary factors influencing water quality in this bay (Yang et al 2018).

Selection of transport timescales
Given the various definitions and estimation methods for transport timescales, the first step is to determine the most appropriate metric for addressing water quality problems in a given water body or condition.Extensive research has been conducted, comparing different transport timescales and providing detailed discussions on their assumptions and applicability (Andutta et al 2014, Lemagie and Lerczak 2015, Lucas and Deleersnijder 2020).For instance, residence time, which denotes the duration for a water particle to exit the water body from its current position (Takeoka 1984), is commonly employed to assess changes in hydrodynamic conditions in the reservoir area before and after dam construction (Rueda et al 2006).Water age represents the time taken for a water particle to travel from the water body entrance to its current location, and can be used to estimate the migration time of exogenous pollution to protected water sources.Similarly, flushing time is defined as the time required for the initial material concentration in a water body decreasing to a certain level.In the case study, we choose flushing time as it represents the physical self-purification capability of the water body via exchange with outer water bodies (Monsen et al 2002).

Integrated modeling methodology
To incorporate transport timescales into reservoir operation, we propose an integrated modeling methodology consisting of a hydrodynamic and transport model, a surrogate model, and a multiobjective optimization model (figure 2).In this section, we utilize flushing time as a representative of transport timescales and apply it to XXB to demonstrate the procedure.Our focus lies on the impoundment period (September to October) of TGR operational mode, during which water is impounded from 145 to 175 meters.This impoundment period holds great significance in terms of water resource security, sediment retention, and water quality management (Xiang et al 2021).

3D hydrodynamic and transport model
We used the 3D hydrodynamic model developed in our previous studies to calculate the spatial characteristics of flushing time in XXB (Mao et al 2015, Zhao et al 2019).The general boundary information of the numerical model is shown in figure 1.Briefly, flushing times for XXB were calculated using the numerical tracer method, which is based on the idea of calculating the time required for a conservative tracer introduced uniformly into the study area at the initial condition of the model run to reduce to a certain level (i.e.1/e).For investigations into long-term reservoir operation strategies, we recommend employing the adjoint method for transport timescales assessments of both spatial and temporal aspects within a single model run (Delhez 2004).

Surrogate model
Surrogate models, typically developed using statistical or artificial intelligence techniques, aim to approximate complex simulation models using a limited number of data points (Razavi et al 2012).Machine learning algorithms have been widely demonstrated to be superior in such tasks (Xu et al 2021).Artificial neural networks (ANNs), in particular, have highly generic model structures, enabling them to automatically extract valuable information from raw inputs.In the case study, we developed a BP-ANN model to effectively estimate flushing time.

Multi-objective optimization model
NSGA-II is a widely used algorithm for solving multiobjective optimization problems (Chang and Chang 2009).The initial water level, daily water level rise, daily water level fall, water level fluctuations (WLFs) duration, and daily water level rise in October were considered as decision variables to capture the range, frequency, and duration of the TGR's WLF.The multi-objective reservoir operation in our case study consists of two objective functions: (1) maximizing total hydropower generation (TPG); (2) minimizing flushing time in XXB.
(1) The objective function of economic benefit (1) where E is the TPG; N t is the capacity of hydropower plant outlets in period t (MW); ∆t is the time length of each period (s); α is the output factor; Q t is the water release in period t (m 3 s −1 ); H t is the water head in period t (m).
(2) The objective function of environmental benefit where FT is the average flushing time; f (x) is the sigmoid function; ω 1 is the weight matrix from the input layer to hidden layers; ω 2 is the weight matrix from hidden layers to the output layer; x(j) is the decision variables; b 1 is the threshold from the input layer to hidden layers; b 2 is the threshold from hidden layers to the output layer.
In accordance with the operational guidelines of TGR, we imposed the following constraint conditions.
(1) Water balance where V t+1 and V t are the water storage volumes of a reservoir at period t + 1 and t (m 3 ), respectively; I t is the inflow of the reservoir at period t (m 3 s −1 ).( 2) Hydropower plant discharge rate: where Q t,min and Q t,max denote the lower and upper water discharge in period t.
(3) Reservoir storage volume limits: where V t,min and V t,max denote the minimum and maximum reservoir storage volume in period t. (4) Capacity of hydropower plant outlets where N min is the minimal capacity of hydropower plant outlets (MW); N max is the maximal capacity of hydropower plant outlets (MW).(5) Flood control discharge limits where Q f is the maximal applied capacity of flood control.(6) Shipping discharge limits: where Q s is the minimum shipping required discharge.(7) Variables of WLF limits:

Training and validation of the BP-ANN model
The five decision variables were considered as input variables, and the flushing time as output variables.
The BP-ANN model in our case study consisted of five input neurons and one output neuron.Figure 3 shows the performance of the BP-ANN model in predicting the average flushing time values for the entire XXB during the training and testing phases with relative errors of less than 0.50% and 4.55%, respectively.These results indicate that the developed BP-ANN surrogate model is accurate and can be used as a proxy for the hydrodynamic and transport model to calculate flushing time.

Pareto optimal front solutions
The NSGA-II algorithm was run for 600 sequential generations to obtain the Pareto front solutions between the values of the two objective functions (figure 4 If the water quality objective is improved more, the hydropower generation decreases more rapidly.Thus, the point of transition (point B) is selected as the optimal operation scheme to reflect the effectiveness of the proposed methodology when we consider the economic and environmental needs relatively equally (FT = 22.991 d and TPG = 150.73 billion MWh).

WLF under the optimal operation
Figure 5 shows the detailed WLF process under the selected optimal trade-off operation scheme (point B).Compared with a gradually increasing trend of the water level in the practical operation scheme, the trend of the water level in the optimal operation scheme fluctuates over four stages.

Spatial variations of flushing time
Overall, the average flushing time in the whole XXB is 23.991 d under the optimal operation scheme, which decreases by 10.9% more than it is under the practical operation scheme (figure 6).We also examine the corresponding flushing time in the surface, middle, and bottom layer along the XXB, respectively.Generally, the flushing time under the two operation schemes    Interestingly, the decreasing rate of flushing time at vertical layers all shows clearly monotonic longitudinal characteristics.The rate generally remains at a relatively low level in the upper reach, while it shows an increasing trend towards the mouth and eventually reaches a higher level in the lower reach.However, the flushing time of the surface layer shows a more significant decrease than other layers, especially in the lower reach.The average flushing time under the optimal operation scheme is decreased by 13.9%, 10.1%, and 9.6% in the surface, middle, and bottom layers, respectively.Specifically, the maximum change rate of flushing time in the XXB occurs in the confluence with the TGR mainstream, with values of 90.9%, 88.8%, and 59.1% for the surface, middle, and bottom layers, respectively.

Discussion
In practical reservoir management, the trade-off between maximizing hydropower generation and improving water quality issues is one of the many conflicting benefits of reservoirs (Al-Jawad et al 2019).To solve the complex problems of reservoir management, optimization is a commonly used and powerful mathematical tool, although its application is limited by computational efficiency, challenges related to high dimensionality, and the complexity of the aquatic ecosystem (Maier et al 2014).In this context, more general and holistic objectives assist decision-makers and stakeholders in engagement and adoption.However, to translate these objectives into quantitative goals that can be modeled and optimized, certain assumptions must be made (Nicholson and Possingham 2006).

Advantages of the developed methodology
To address the computational challenges associated with multiple water quality objectives, a common approach is to treat water quality issues as constraints in reservoir operation models.Hu et al (2014) developed statistical models for water quality parameters and incorporated them as constraints within a multi-objective reservoir operation model.Similarly, Haghighat et al (2021) employed various water quality parameters to estimate a water quality index, which was then used as a constraint.However, it is important to acknowledge that treating water quality as a constraint has limitations in terms of model accuracy and precision (Ferreira and Teegavarapu 2012).In contrast, we propose a comprehensive water quality objective, namely transport timescale, which helps decision-makers overcome the trade-offs among multiple water quality indicators while avoiding dimensionality issues.Our previous studies have also demonstrated that by reducing the flushing time in the operation of TGR, it is possible to contemporaneously reduce the concentration of total nitrogen, dissolved silica, and algal cells in XXB (Zhao et al 2023).This is because water flow plays a crucial role in transporting various constituents, and changes in the transport timescale can contemporaneously impact the transport processes of multiple constituents (Teurlincx et al 2019, Lucas and Deleersnijder 2020).
Another advantage of the developed methodology is that it uses a data-driven model as a proxy for the hydrodynamic and transport model, enabling more efficient estimation of transport timescales (Razavi et al 2012).Coupling a 3D hydrodynamic and transport model with a search-based optimization algorithm would be computationally expensive and require a high number of function evaluations to meet termination criteria (Johnson and Rogers 2000).Consequently, this computational burden hinders the use of transport timescale as an objective for optimal reservoir operation.In this context, our study is consistent with previous studies showing that the predictive performance of ANNs as surrogate models is quite consistent with process-based hydrodynamic models, while largely speeding up the simulation process (Yaseen et al 2015, Saadatpour et al 2017, Bermúdez et al 2018).

Trade-off between TPG and transport timescales
Consistent with the trade-off relationship commonly observed between water quality objectives and hydropower generation, our results illustrate that enhancing flushing time entails a trade-off with TPG.This trade-off arises from WLFs, particularly rapid and prolonged declines, which enhance water exchange, weaken stratification, and reduce the average water head, consequently diminishing hydropower generation (Wang et al 2020, Song et al 2023).
Interestingly, our results exhibit a piecewiselinear Pareto shape instead of a smooth curve or straight line, indicating the existence of critical points in the decision space where the operating mechanisms or strategies undergoes substantial changes.One potential explanation is that the optimization model's multiple constraints introduce step changes or discontinuities in the decision space.To meet the water storage and geological safety requirements of TGR, we impose strict limitations on the variables of WLFs.
An intriguing area for future investigation involves examining the impact of optimization parameters or varying constraints on the shape of the Pareto front (Luo et al 2018, Unal et al 2018).By introducing such sensitivity analysis, it becomes possible to attain a more desirable shape of the Pareto front or enhance the trade-off relationship.Notably, the shape of Pareto front solutions is also influenced by various other factors, including non-linear correlations between objective functions, the discreteness of model-driven data, and the performance of optimization algorithms (Hua et al 2021).

Limitations and implications for management
Although our study provides an enlightening perspective for integrated reservoir water quality management by treating all water constituents that contribute to water quality problems as a whole, the holistic nature of transport timescales is limited by the performance of 3D hydrodynamic and transport model, i.e.only the processes considered in the hydrodynamic model will be used to derive transport timescales (Choi and Lee 2004).Mechanisms affecting constituent retention may also include other hydrodynamic processes and biogeochemical processes (Vollenweider 1975, Ralston and Geyer 2017, Teurlincx et al 2019, Hong et al 2020).We suggest that the next step could be to combine models describing component-specific cycling processes (e.g.water quality models) with the proposed approach.A comparison of constituent-specific versus pure water transport timescales will help us to quantitatively assess the effectiveness of transport timescales as a proxy for transporting water constituents before applying the optimal operating scenario.
Considering the multiple objectives and constraints of reservoirs, the improvement in transport timescales from the proposed reservoir operation approach may be limited by the longitudinal distance from the dam.As our case study shows, the location with the lowest rate of reduction in flushing time coincides with the location of the tail end of the backwater controlled by the TGR operation, which is also a frequent area for water quality problems such as algal blooms (Li et al 2018).In this regard, the proposed optimized operation could serve as a short-term (and emergency) practical measure to mitigate water quality problems.The practical applicability of the proposed approach would also be effectively enhanced if reservoirs upstream of the interested study area are included to conduct joint operations on transport timescales (Li et al 2012).

Conclusions
Our study proposes a methodology for optimal reservoir operation that addresses water quality issues while considering other reservoir requirements.By utilizing transport timescales as the objective for water quality, we heuristically integrate the overall transport process of water constituents with the optimal operation of the reservoir.Through a case study, we identified a conflict between reducing flushing time and increasing hydropower generation in the reservoir system.However, we found that it is possible to reduce the flushing time in the TGR tributary bay with an acceptable loss of hydropower generation, particularly in the near-dam area.This optimized operation can serve as a practical short-term and emergency measure to mitigate water quality problems.
Our methodology effectively tackles the challenges of objective simulation and dimensionality in multi-objective optimization reservoir operation while improving computational efficiency.By utilizing transport timescale as a comprehensive objective, decision-makers and stakeholders are relieved from the burden of balancing multiple water quality objectives.This facilitates decision-maker acceptance and enables comprehensive water quality management in reservoirs.Nevertheless, we acknowledge that although hydrodynamics is the primary factor influencing water constituent transport, the retention of water constituents is also influenced by other biogeochemical processes.Future work should focus on integrating hydrological, hydrodynamic, and water quality models to quantitatively evaluate the effectiveness of using transport timescales as proxies for water quality management.

Figure 1 .
Figure 1.Map of the study area (a) location of TGR in China; (b) location of XXB in the reservoir; and (c) general information of the hydrodynamic model for XXB.

Figure 2 .
Figure 2. Conceptual framework of the model combination procedure.

Figure 3 .
Figure 3.Comparison of predicted and calculated flushing time for the training phase and testing phase.

Figure 4 .
Figure 4. Pareto front values for FT and TPG under various operating scenarios.FT = average flushing time and TPG = total hydropower generation.Points A, B, and C represent an environmental operation scheme, a balanced operation scheme, and an economic operation scheme, respectively.

Figure 5 .
Figure5.Time series of water level upstream of the TGD in the practical operation scheme and the optimal operation scheme.

Figure 6 .
Figure 6.distribution and change rate of the flushing time along the XXB in the practical operation scheme and the optimal operation scheme (a) in the surface layer, (b) in the middle layer, and (c) in the bottom layer.
).A clear paradoxical relationship between flushing time and TPG can be found, i.e. flushing time decreases as TPG decreases.Notably, when the flushing time increases from 22.930 d to 22.991 d, hydropower generation only decreases from 154.30 billion MWh to 150.73 billion MWh.
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