## Abstract

Thermal pollution is an environmental impact of large dams altering the natural temperature regime of downstream river ecosystems. The present study proposes a simulation–optimization framework to reduce thermal pollution downstream from reservoirs and tests it on a real-world case study. This framework attempts to simultaneously minimize the environmental impacts as well as losses to reservoir objectives for water supply. A hybrid machine-learning model is applied to simulate water temperature downstream of the reservoir under various operation scenarios. This model is shown to be robust and achieves acceptable predictive accuracy. The results of simulation–optimization indicate that the reservoir could be operated in such a way that the natural temperature regime is reasonably preserved to protect downstream habitats. Doing so, however, would result in significant trade-offs for reservoir storage and water supply objectives. Such trade-offs can undermine the benefits of reservoirs and need to be carefully considered in reservoir design and operation.

## HIGHLIGHTS

Mitigating thermal pollution of the reservoirs.

Developing a novel environmental optimization model.

Using a combination of machine-learning model and optimization system for reducing potential impacts of water temperature on the aquatics.

### Graphical Abstract

## INTRODUCTION

Large dams are the most important hydraulic structures in river basins and are important suppliers of water and electricity (Di Baldassarre *et al.* 2021). However, the downstream and upstream environmental impacts of large dams are not negligible (Manouchehri & Mahmoodian 2002). Optimal management of these structures to achieve the desired water supply and environmental benefits is important because the construction of a large dam is expensive (Ahmad *et al.* 2014).

Most reservoir design and operation problems have historically been based on a simple loss function to optimize reservoir operation (Ehteram *et al.* 2018). In this loss function, the difference between the target and release is minimized. Generally, the target is defined as the water demand and the release is the actual water supply at each time step. Different methods have been applied for this optimization, including linear programming (LP), non-linear programming (NLP), dynamic programming (DP), and evolutionary algorithms. LP is one of the simpler methods (Reis *et al.* 2006), and NLP and DP methods have been recommended for non-linear functions (Arunkumar & Jothiprakash 2012). The objective function of reservoir operation is complex and, hence, evolutionary algorithms as an advanced method are more appropriate and have been recommended by many studies (Afshar *et al.* 2007, 2011; Asadzadeh *et al.* 2014; Bozorg-Haddad *et al.* 2015a, 2015b; Asgari *et al.* 2016; Ehteram *et al.* 2018; Yaseen *et al.* 2019; Sharifi *et al.* 2021). Different classifications have been proposed for these algorithms: for example, classic algorithms such as genetic algorithms have widely been used for different optimization problems while new algorithms have been proposed to improve the efficiency of the optimization process (Dokeroglu *et al.* 2019); animal-inspired algorithms generally imitate the social behaviour of animals while non-animal-inspired algorithms follow other natural or physical laws (Jahandideh-Tehrani *et al.* 2019).

The protection of river ecosystems is important for the sustainable management of water resources. Reservoirs affect downstream river ecosystems by changing the natural flow regime (Qicai 2011). Water temperature is a key environmental characteristic that affects the biological activities in a river ecosystem, and many such activities (e.g., searching for food and reproduction) are strongly dependent on the thermal regime (Weber *et al.* 2014). Hence, water temperature modelling is important for assessing the ecological status of a river ecosystem. Thermo-hydrodynamic models such as SSTEMP have been used to simulate water temperature in a single reach or river network (Bartholow 1995); however, such models are inflexible in terms of directly linking to reservoir operation optimization models. Data-driven models have shown great promise to simulate environmental systems (Razavi *et al.* 2022); for example, neural networks have been utilized for water quality modelling (Zhu *et al.* 2019). These models can provide a fast and flexible assessment (Razavi 2021), which is especially applicable in water resources models and can be used when an outcome cannot be easily measured (Sreekanth & Datta 2011). A large number of effective inputs might make a system complex and, hence, using a surrogate model can be beneficial. Different types of methods, including neural networks (Mengistu & Ghaly 2008) and Bayesian networks (Shi *et al.* 2012), can be applied to develop a surrogate model.

Large dams alter downstream thermal conditions, which is defined as a type of thermal pollution (Ling *et al.* 2017). Sedighkia *et al.* (2019) reviewed the importance of thermal conditions to biological habitats, confirming that the consideration of thermal regimes is fundamental with respect to maintaining the integrity of freshwater ecosystems (Olden & Naiman 2010). For example, the impacts of large dams on salmon due to changing thermal regimes demonstrate the importance of thermal regime modelling (Angilletta *et al.* 2008). However, thermal models have not yet been integrated into reservoir operation models, which is a significant research gap. The present study proposes a novel framework to optimize the thermal regime downstream of a reservoir. The proposed method links a thermal model to predict the downstream water temperature with a reservoir operation optimization with the aim to reduce downstream thermal pollution while maximizing water supply. This study could lead to new methods of advanced environmental management of reservoirs in which complex computational frameworks are integrated into water resource management models.

## APPLICATION AND METHODOLOGY

### Study area and methodological overview

*et al.*2019). Ideally, the water temperature regime downstream of the reservoir should be as close as possible to the natural thermal regime (in the absence of the reservoir). Hence, new operational optimization is required to balance environmental needs and demands for water supply. We simulated the downstream water temperature regime and optimized dam operation in this region as a case study. Due to the low available flow in the simulated period, simultaneous satisfaction of environmental and water supply requirements was challenging. Figure 1 shows an overview of the methodology in which the simulation of the downstream water temperature and optimization of the reservoir operation are linked. Figure 2 shows the location of the Latian Dam in the Jajrood River Basin. The capacity of the reservoir is 95 million cubic metres (MCM), with minimum operation storage of 15 MCM and optimal or strategic storage of 70 MCM based on recommendations by the regional water authority.

### Water temperature regime modelling

We utilized the coupled particle swarm optimization-adaptive neuro-fuzzy inference system (PSO-ANFIS) to simulate water temperature in the river downstream of the reservoir. We selected a river reach with a length of 10 km and simulated the downstream water temperature in different cross-sections (intervals between cross-sections were 100–1,000 m). The simulated average water temperature throughout the downstream river reach was then used in each time step of the optimization model. In other words, data from many cross-sections were considered to simulate the downstream water temperature, with the arithmetic mean of these values used as an overall estimation.

*et al.*2022). Table 1 displays the main characteristics of the ANFIS-based water temperature model. The water temperature depends on several factors and, hence, data-driven models are a good option to achieve a reasonable simulation of the thermal regime. This data-driven model can be directly applied to reservoir operation optimization. Two known indices – the Nash–Sutcliffe efficiency (NSE) index and root means square error (RMSE) – were applied to evaluate the goodness-of-fit of the hybrid machine-learning model (see Gupta

*et al.*(2009) for more details).

Inputs . | Number of MFs (inputs) . | Type of MFs (inputs) . | Outputs . | Number of MFs (output) . | Type of MFs (output) . | Clustering method . |
---|---|---|---|---|---|---|

Flow rate (m^{3}/s); Wetted perimeter (m); Distance from the reservoir (m); Elevation from sea level (m); Water temperature at distance = 0 m (°C); Air temperature (°C) | 10 | Gaussian | Water temperature at each cross-section | 10 | Linear | Subtractive clustering |

Inputs . | Number of MFs (inputs) . | Type of MFs (inputs) . | Outputs . | Number of MFs (output) . | Type of MFs (output) . | Clustering method . |
---|---|---|---|---|---|---|

Flow rate (m^{3}/s); Wetted perimeter (m); Distance from the reservoir (m); Elevation from sea level (m); Water temperature at distance = 0 m (°C); Air temperature (°C) | 10 | Gaussian | Water temperature at each cross-section | 10 | Linear | Subtractive clustering |

MFs, membership functions.

### Optimization model

*D*is the maximum water demand at time step

_{t}*t*, RD

*is the water released from the reservoir at time step*

_{t}*t*, and

*P*1 −

*P*4 are penalty functions.

*P*1 and

*P*2 are related to the downstream water temperature regime in the optimization model; these penalty functions were developed based on a predetermined target for the water temperature regime. Ideally, the water temperature resulting from the optimal release scenario should mimic resulting from the natural flow. Equation (2) outlines the thermal pollution penalty functions applied in the optimization model as follows:where NTW is the natural temperature regime, OTW is the optimal temperature regime, RE is the release for the environment, and minenv is the minimum environmental flow requirement. In the case study, minenv was defined as 10% of the mean annual flow based on previous environmental flow studies. An initial ecological survey of the study area indicated a 10% change in temperature might impact river habitats; thus, we considered 10% as the tolerance of the change in downstream water temperature in the penalty function. A minimum environmental flow was also considered. The following equation considers a minimum operational storage penalty function, maximum storage penalty function, and water demand function, i.e., storage in the reservoir should not be less than the minimum operational storage or more than the maximum storage or capacity of the reservoir, and water supply should not exceed water demand:where

*S*is the storage at time step

_{t}*t*, and

*S*

_{max}and

*S*

_{min}are the maximum and minimum storage, respectively.

*c*1–

*c*6 are constant coefficients determined based on the sensitivity analysis. The storage of the reservoir must be updated for each time step using the following equation:where

*I*is the inflow,

_{t}*F*is the overflow,

_{t}*E*is evaporation, RE is the downstream release for the environment, and

_{t}*A*is the surface area of the reservoir. The overflow of the reservoir was calculated using the following equation:

_{t}Note that release for water demand is directly pumped from the reservoir and, hence, two releases are defined in the optimization model.

*et al.*(2018) for more details):

The NSE measures the difference between observations and the simulation (values > 0.5 demonstrate the predictive skills of the model are robust), and can be used to measure the performance of hydrologic models (Gupta *et al.* 2009); it can also be applied to water quality parameters.

## RESULTS AND DISCUSSION

^{3}/s in the case study). Notably, previous reservoir operation studies have added environmental flow to the model considering simple hydrological or physical habitat methods (Sedighkia & Abdoli 2022); however, an optimal downstream water temperature regime might require more than the basic environmental flow. We utilized a thermal penalty function in this regard, and therefore the optimal environmental flow is more than the minimum environmental flow for many time steps. At the same time, the water supply is considerably less than the demand for some time steps due to the need to satisfy environmental flows. Thus, environmental considerations might reduce the potential water supply from reservoirs and storage loss might also occur. The results demonstrate how mitigating thermal pollution markedly affects the water supply benefits of the reservoir.

Model factor . | Performance index . | Value . |
---|---|---|

Water supply | 10.1% | |

Storage loss | VI | 82% |

RMSE | 39.9 MCM | |

Downstream water temperature regime | NSE | 0.971 |

RMSE | 1.1 °C |

Model factor . | Performance index . | Value . |
---|---|---|

Water supply | 10.1% | |

Storage loss | VI | 82% |

RMSE | 39.9 MCM | |

Downstream water temperature regime | NSE | 0.971 |

RMSE | 1.1 °C |

The model is not without limitations. High computational complexity reduces the efficiency of optimization models but is inevitable when simulating a long time period or conducting numerous simulations in practical projects. We applied an ANFIS-based water temperature model, which was good in terms of addressing technical issues but resulted in high computational complexity. This is the main limitation of the proposed method, and future studies should aim to address this aspect to improve the applicability of the model. We utilized BBO in the optimization process, yet many other algorithms available in the literature could be applied to improve the model. The main weakness of all evolutionary methods is the inability to guarantee global optimization for the problem; hence, using a wide range of algorithms to find the best solution is recommended. Ranking the algorithms can be done using a decision-making system. Moreover, a multi-objective model is also an appropriate approach. For example, the use of a multi-objective genetic algorithm or multi-objective PSO has been recommended by some studies (Mansouri *et al.* 2022). However, we applied a single-objective algorithm to reduce the computational complexity. Multi-objective models are inherently more complex but might be able to achieve the objectives by Pareto front visualization. Any such approaches must consider any significant resulting decrease in model efficiency.

Ideally, the downstream water temperature during the optimal operation of the dam should be the same as the natural flow condition. Water temperature in a river is dependent on key factors used in the model, one of which is river flow or release from the reservoir. The release will not be necessarily the same as the natural flow due to the simultaneous impact of different factors. Due to the impacts of a reservoir on water temperature and stratification, simulating water temperature is complex (Table 1). In the proposed simulation–optimization, release is used as the main factor used to adjust the water temperature based on ecological requirements. Stratification was only indirectly taken into account in the model (i.e., selected input parameters were able to cover the possible impact of stratification on the downstream thermal regime). Moreover, many cross-sections were considered to simulate the downstream water temperature. Deviations from suitable temperatures were noted for some cross-sections but, due to the use of average values in the case study, these deviations were not considered in the assessment of the model. Revisiting this issue in future studies is recommended.

The case study used a daily time scale, as a monthly time scale is not appropriate for managing the thermal regime and a time scale of less than a day is not practical with respect to dam operation. Water temperature might be influenced by many environmental factors and we tested different combinations of inputs. Our initial simulations in the case study indicated that the proposed combination of inputs in Table 1 generated the most accurate results. Adding more inputs to the data-driven model increased the computational complexity and reduced model accuracy. However, all case studies are different, and thermal model development should be carried out based on the relevant considerations. For example, here we considered a 10% deviation in temperature as the maximum tolerable change. A fixed temperature could also be selected but might reduce the water supply benefits of the reservoir due to reduced flexibility for managing release. However, a large amount of tolerance (e.g., 10 °C) would certainly be detrimental to aquatic species. Notably, in some cases, reservoir operations that do not consider environmental requirements can be in place for long periods of time. The consequent effect on the downstream water temperature regime can result in irreversible impacts on the river ecosystem akin to the extinction of species.

Despite the limitations noted, the proposed approach could be successfully applied to reservoir operation. The optimization model simultaneously considers the requirements of a successful water supply operation and environmental considerations. Using two appropriate penalty functions for thermal pollution could improve reservoir operation models in terms of environmental concerns. However, the low-reliability index for the water supply demonstrates that considering environmental impacts might markedly reduce the water supply benefits of the reservoir. The results suggest that using secondary storage is necessary for the management of the water supply. For example, if release is used for irrigating lands, storage tanks on farms might be necessary to regulate irrigation supply.

Most studies to date have not included an environmental modelling component in reservoir operation optimization. In recent years, an environmental component has been added but these have typically been superficial and lacked the ability to properly integrate environmental complexities into water resources management. For example, many studies have applied hydrological methods in the optimization of environmental flow but did not consider other effects on habitat degradation (Shaeri Karimi *et al.* 2012). Some studies highlight the need to mitigate downstream water quality challenges but fail to consider thermal pollution (Dhar & Datta 2008). In other words, the ecological component in these models is not sufficiently robust to minimize the difference between natural flow and the altered flow regime. Several methods are available for estimating the natural thermal regime but are beyond the scope of the present study. In the case study, the change of elevation before and after dam construction was not considerable, and historical data demonstrated that the natural thermal regime upstream of the dam could be used to estimate the natural regime downstream.

## SUMMARY AND CONCLUSIONS

The present study developed a novel framework of reservoir operation in which changes in downstream temperature regimes, water supply loss, and storage loss were minimized in a simulated period. A hybrid machine-learning model was used to simulate the downstream water temperature. The values of two indices, the NSE and RMSE, indicate that the data-driven model was robust with respect to simulating the downstream water temperature. BBO was used to optimize reservoir operation in which the thermal pollution is minimized while the supply benefits are maximized. Indices used to measure the performance of the optimization model included the reliability index, vulnerability index, RMSE, and NSE. The model was not fully able to satisfy water demand (only 10% could be supplied) in the simulated period due to the downstream environmental requirements. However, the temperature regime proposed by the optimization model is close to the natural temperature regime, which indicates the method can minimize environmental impacts but at the expense of water supply and storage. Notably, the storage loss was considerable during the simulation due to a challenging period for the reservoir in terms of inflow.

## FUNDING

This research work was not supported by any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

## 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.

## REFERENCES

*Journal of Irrigation and Drainage Engineering*

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Journal of Water Resources Planning and Management141(8), 04014097.