A simulation–optimization framework for reducing thermal pollution downstream of reservoirs

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.

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.

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

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.

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.

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.

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

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

The authors declare there is no conflict.