Optimal operation of a multi-reservoir system for environmental water demand of a river-connected lake

River-connected lakes can be characterized as the inland waters with a direct physical and ecological connection to the main river of a watershed, and hence water can exchange freely between the main river and the lakes. Such lakes play important roles in water resources management (e.g., flood control and drought mitigation) and ecosystem services (e.g., water quality maintenance and biodiversity conservation) of watersheds. It is generally accepted that aquatic ecosystem processes are intrinsically related to hydrological regimes. The ecosystem of a river-connected lake is influenced by both the main river and lake tributaries. In particular, upstream reservoirs can significantly alter the hydrological characteristics of rivers and their connected lakes (Braatne et al. 2008), and thus may profoundly affect the structure and functioning of the ecosystem if sustainable reservoir operation is not performed (Jager & Smith 2008).

Dongting Lake, the second largest freshwater lake in China, is a typical river-connected floodplain lake, which is laterally connected to the middle reaches of the Yangtze River (the longest river in China). The lake is of great ecological importance to fisheries, wildlife and water resources. In recent years, under the influence of climate change and human activities (e.g., reservoir operation, sand mining, etc.), the lake water level during the dry season has decreased drastically (∼2 m), especially after the impoundment of the world's largest water resource project, the Three Gorges Reservoir (TGR), on the upper Yangtze River in 2003 (Xu et al. 2013). Such changes have resulted in or will potentially cause severe environmental degradation and water crises, which has raised concerns for the lake ecology and local water resources management (Li et al. 2012; Ye et al. 2016). To lessen the adverse effects of hydroelectric development and meet the environmental demands of this important lake, the optimization of reservoir operation is therefore clearly necessary.

Optimization methods have been applied to reservoir operation problems since the early 1950s, and operation of multi-reservoir systems has also been extensively reported (e.g., Yeh 1985; Labadie 2004; Xu et al. 2014). According to Goor et al. (2010), optimal multi-reservoir operation is generally used to determine a sequence of release decisions that maximizes the system benefits over a given period while meeting operational and institutional constraints. As the problem is often dynamic, nonlinear, multi-dimensional, multi-objective and uncertain, various optimization methods have been designed and used (e.g., dynamic programing, nonlinear programing, heuristic programing, etc.). In recent years, evolutionary algorithms, such as genetic algorithm (GA) and evolutionary programing, have become popular in engineering applications, due to their success in searching complex nonlinear spaces.

Conventional reservoir operations aim to maximize social and economic benefits. Nevertheless, there is now widespread recognition that water resources management must take account of the vulnerability of aquatic ecosystems. Accordingly, many researchers have attempted to incorporate environmental or ecological needs into reservoir operation problems. There is growing awareness that flow regime is the key driver of the ecology of rivers and associated water bodies. In the late 1990s, the concepts of ‘natural flow regime’ and ‘environmental/ecological flow regime’ were developed to mitigate negative effects of human activities (Poff et al. 1997). A variety of methods have been developed to assess environmental or ecological water requirements: for example, Vogel et al. (2007) designed an ecological flow regime to capture the natural flow variability for maintaining the functional integrity of aquatic ecosystems; more recently in China, increasing attention has been paid to the balance between human interests and ecosystem protection (Cai et al. 2013; Hu et al. 2014). Briefly speaking, relevant environmental water demand (EWD) for a water body refers to the basic or proper water (the quantity and timing) needed by the ecosystem to sustain its integrity and sustainability.

Dongting Lake and the middle reaches of the Yangtze River are now periodically regulated by the upstream reservoirs, including the TGR built on the upper Yangtze River and many reservoirs situated on the lake tributaries. The complexity of such a large-scale river-lake and multi-reservoir system presents considerable challenges for lake managers in determining optimal reservoir operation policies. Most previous research on Dongting Lake focused on the field investigation of the hydrological, hydrodynamic and ecological conditions, as well as the vulnerable river-lake interaction. The effects of reservoir operation have also been investigated, but mainly limited to the subjects of local hydrological and sediment changes, either in the Yangtze River or in Dongting Lake (Lai et al. 2013; Xu et al. 2013). As far as we are aware, the possibility of optimal multi-reservoir operations for environmental demands of the important river-connected lake has hitherto not been fully studied.

The objective of this study is to develop optimal operation policies of the upper major reservoirs to meet the EWD of Dongting Lake, which is an important step for enhancing the ecosystem management in the middle Yangtze River watershed. We develop a site-specific optimization model for the operation of a multi-reservoir system, including 9 key reservoirs on both the upper Yangtze River and the tributaries of Dongting Lake. As a preliminary and exploratory study, the optimal target is to maximize the lake EWD satisfaction, while other reservoir functions such as flood control, hydropower generation and navigation are considered in the constraints of the optimization model. A support vector regression (SVR)-based model is developed to link the response of lake water levels to reservoir operation changes. The effect of the existing operation policy on EWD satisfaction is analyzed, for both normal and dry conditions. Through a comparative study among different scenarios, the optimal joint operation policies are numerically studied. The potential improvement in EWD satisfaction rate, due to the optimal multi-reservoir operation, is finally quantitatively estimated.

At the northeastern end of its eastern region, Dongting Lake is directly connected with the middle Yangtze River, through a short and narrow channel. Water exchanges frequently between the river and the lake at Chenglingji (the junction): (i) when the water level of the Yangtze River is lower, water flows from the lake into the river, and the lake level tends to decrease (i.e., emptying effect); (ii) in contrast, when the water level of the Yangtze River is higher, it can constrain the drainage of the lake (i.e., blocking effect) (Zhang et al. 2012). During the wet season, Yangtze River's water may flow into the western region via 3 diversion outlets (Songzi, Taiping, and Ouchi), and then drains from the eastern region directly back into the Yangtze River. After the impoundment in June 2003, the TGR was formed at the upper Yangtze River. Covering around 75,098.13 km² drainage area and controlling over 1 million km² (56% of the Yangtze River watershed), the TGR plays the critical roles of flood control, hydropower generation, and navigation improvement (Hayashi et al. 2008). In particular, it has a flood storage capacity of 22.15 × 10⁹ m³, which can lessen the frequency of downstream flooding from once every 10 years to once every 100 years (Mao et al. 2015). It is obvious that TGR operation inevitably alters the natural hydrological regime downstream by regulating outflow discharges. In addition, the Qingjiang River, a large tributary of the Yangtze River, joins the mainstem between the TGR and the Songzi outlet.

Suitable hydrological, geometry and bathymetry conditions are required for this study. Most water level and inflow discharge data are provided by the Bureau of Hydrology (BOH) of Changjiang Water Resources Commission.

Various methods are available for assessing environmental flow required in rivers and lakes to achieve ecological objectives, which could generally be grouped into 4 categories: hydrological methods, hydraulic rating, habitat simulation (rating), and holistic methods (Tharme 2003). Among them, hydrological methods are relatively simple, relying primarily on the use of hydrological data for making environmental flow recommendations. Based on the long-term daily observations in Dongting Lake over the past six decades, it can be straightforward to statistically characterize the lowest acceptable lake levels during the study period concerned: (i) first, the representative hydrological gauging stations are selected for different lake regions, and a long sequence of lake level data is collected for the period concerned; (ii) those extremely low lake levels are then excluded (e.g., using the 3σ rule); (iii) the continuous distribution of EWD may be determined by the lowest historical lake level variations; the results could be further upscaled to larger time scales (e.g., several days or monthly) in accordance with intervals of optimal operation.

The hydrological regime of Dongting Lake is dominated by both the Yangtze River and the lake tributaries. As a linkage between source and target, accurate prediction of the response of EWD satisfaction rate (reflected by lake level fluctuation) to upstream multi-reservoir operation is essential for the development of the optimization model. Lake level changes are traditionally predicted using either process-based or data-driven modeling approaches (Li et al. 2015; Mao et al. 2015). Due to the high complexity of the river-lake interaction and the multi-reservoir system, the practical application of process-based models is often hampered by the lack of detailed geometry, bathymetry, and initial and boundary conditions, as well as the difficulty of model calibration. As an alternative approach, data-driven modeling techniques, such as SVR and artificial neural network, are relatively easy to use to model dynamic and nonlinear data, especially when the underlying physical relationships are not fully understood.

As traditional statistical models are usually unable to capture nonlinearity and nonstationarity correlated with hydrological forecasts, here, SVR is used to develop the relationship model between lake level and inflow (controlled by reservoir release), which is then incorporated in the optimization model to provide real-time analysis and prediction. SVR is an extension of the support vector machine (SVM) method for regression and function approximation. SVM is a relatively novel artificial intelligence-based method developed from statistical learning theory (Vapnik 1998). This type of learning machine employs the structural risk minimization principle to obtain good generalization on a limited number of learning patterns. SVM can be applied to regression problems by the introduction of an alternative loss function that is modified to include a distance measure. The basic idea of SVR is the mapping of the input data onto a higher dimensional feature space via nonlinear mapping. Then, a linear regression problem is obtained and solved in this feature space (Gunn 1998). SVR has been proven to be a robust and competent algorithm for hydrological modeling and forecasting (Yu et al. 2006).

In summary, the development of our SVR-based lake-reservoir relationship model involves 5 main steps, as follows:

1. Normalizing the whole data set to a fixed range from 0 to 1 for river inflow, and then separating it into a training data set and testing data set randomly.

2. Deriving the dual problem to avoid explicitly computing the mapping ϕ and reduce the computing complexity, in which the Gaussian kernel function is used here.

3. Using a GA to find the best error threshold ɛ, regularization parameter C and kernel parameter γ, during which the 3-fold cross-validation is applied to prevent the overfitting problem.

4. Training the SVR model based on the training data set to obtain the final approximate function.

5. Validating the model based on the independent testing data set.

Additionally, a well validated hydrodynamic model, including Dongting Lake and the river network in the middle Yangtze River, is used to evaluate the spatial-temporal effects of existing and potential optimal operation schemes (given by the optimization model) on lake levels. The type of process-based model is based on a generally accepted framework of hydrodynamics, in which numerical methods are used to solve continuity and momentum equations. The hydrodynamic model has been calibrated and validated against a series of observations, and more details are provided in Dai et al. (2013). The 1D-2D coupled hydrodynamic model is suitable for simulating the hydrodynamics of complex river-lake systems, in which the lake is modeled as a two-dimensional water body while the river network is described by the one-dimensional governing equations.

The study concentrates on high-risk periods of low lake levels caused by existing reservoir operation policies. The flood period of the Yangtze River is from early June to mid-September, of which the main flood period begins in early July. The flood season of Dongting Lake is from April to September. According to the existing rule curves, the storage period of the TGR is from late September to late October, and the storage periods of most major tributary reservoirs also end in October (Table 1). In recent years, low lake levels are often observed during the storage periods of upper reservoirs; that is, the lake EWD satisfaction rate might show a decreasing trend due to inflow reduction after the flood period. It is reasonable to only consider the EWDs from late September to late October. In this study, we select the period from early July to mid-November as the optimization period for the multi-reservoir system, covering the main flood season, the storage period, and part of the after-storage period.

The above model employs the GA technique to obtain optimal solutions. GA is an adaptation procedure based on the mechanics of natural genetics and natural selection (Darwin's evolutionary principle) (Goldberg 1989). Its principal advantage is to intelligently explore the solution space from many different points simultaneously enabling higher probability for locating a global optimum. This optimization algorithm has been widely used in water resources optimization models, including the multi-reservoir optimization problem (e.g., Oliveira & Loucks 1997; Sharif & Wardlaw 2000). In the study, the population size is 2000 and the iteration is set to be 200 generations. The method proceeds generation by generation until it is terminated when the maximum number of allowed generations is reached, or a solution to the problem is found, namely, the difference of successive iterates is less than an extremely small number specified.

The SVR-based lake-reservoir relationship models are developed based on historical data for typical normal and dry years, and conducted at 5 representative lake gauging stations respectively: Lujiao (the eastern); Yangliutan and Yingtian (the southern); Xiaohezui and Nanzui (the western). For each station, lake level is treated as the output variable (y), and the discharges from the Yangtze River and the main tributaries are treated as the input variables (x). As demonstrated previously, although there are 9 reservoirs to be optimized in the system, to avoid the curse of dimensionality problem, the reservoirs on the same lake tributary have been grouped as one aggregate reservoir in the optimization solution. As such, in the optimization model, there are actually 5 solo and aggregate reservoirs to be optimized. Accordingly, the effects of the Yangtze River and the 4 main tributaries in the relationship models (Figure 4) are expressed by 6 input variables: the discharges of TGR (x₁), Qingjiang River (x₂), Xiangjiang River (x₃), Zishui River (x₄), Yuanjiang River (x₅) and Lishui River (x₆). These input variables are closely related to upper reservoir operations.

For the present study, it is found that wet conditions may meet the necessary lake EWDs (i.e., lake EWD satisfaction rates >100%); therefore, we demonstrate the optimization model results for two representative hydrological conditions: Case I, a normal condition; and Case II, a dry condition. These cases represent an average flow year (1974) and a low flow year (1978) based on BOH hydrological records on Yangtze River and Dongting Lake tributaries from 1953–2012. During the high-risk period (September-October), the normal condition has a mean discharge approximately 1.5 times the dry condition: 20,183.5 m³/s (Case I) and 14,422 m³/s (Case II) for the Yangtze River, and 3,063 m³/s and 1,926.5 m³/s for the lake tributaries. In each case, the modeling study is carried out for 5 scenarios:

• Scenario 0: without reservoirs in the study area;

• Scenario 1: with the existing operation schemes for all reservoirs;

• Scenario 2: with the optimal operation scheme for the TGR, but with the existing operation schemes for tributary reservoirs of Dongting Lake;

• Scenario 3: with the existing operation scheme for the TGR, but with the optimal operation schemes for tributary reservoirs of Dongting Lake;

• Scenario 4: with the optimal joint operation schemes for all reservoirs.

The above optimal operation schemes would be determined for the individual scenarios through the optimization model. Table 6 compares the predictions of EWD satisfaction rates in different scenarios of Case I. Assuming no effect of reservoirs (Scenario 0), the SVR-based model results show that the EWD satisfaction rates for all lake regions are moderately larger than 100% during the high-risk period, implying that the ‘natural’ river regimes in the normal condition can meet the environmental water requirements of the lake. However, the presence of upper reservoirs causes a marked decrease in EWD satisfaction rates. With the existing reservoir operation schemes (Scenario 1), it is estimated that all lake regions' EWD satisfaction rates would fall within the range of 80–90%. In particular, the value for the western region significantly decreases from 139.47% to 87.14% because of the dual effects of the TGR and 4 tributary reservoirs.

The primary benefit of the optimal joint operation, compared with the existing schemes, is that the specific releases could be increased (e.g., by around 2,377 m³/s on average from the TGR) during the original storage period. As the storage capacity of the TGR (39.3 × 10⁹ m³) is much greater, it has more impact than the tributary reservoirs do on the entire lake. The TGR exerts influence in two ways: (i) increasing the inflow into Dongting Lake from the 3 diversion outlets (∼0.909 × 10⁹ m³); and (ii) raising the water levels in the middle reaches of the Yangtze River (∼0.3 m at Station Chenglingji), which helps to enhance the ‘blocking effect’ of the Yangtze River. Therefore, as shown in Table 6, the eastern and the western lake regions are more sensitive to the operation of the TGR, while the southern region is more sensitive to the operation of the tributary reservoirs.

In conclusion, the existing operation policies cause significant hydrologic alteration. The optimal joint operation may improve the lake EWD satisfaction rates in the normal condition, approximately satisfying the environmental water requirements, while it has a limited role in the dry condition. The improvement of EWD satisfaction in the normal condition is mainly affected by the TGR; in the dry condition, however, the southern and western lake regions are more sensitive to the tributaries' reservoirs.

The foregoing demonstrations show that, the optimal operation policies may be reasonably determined by the optimization model, and the SVR-based model correctly reproduces the rapid changes of lake level. Nevertheless, those modeling results are limited to several representative stations located in different lake regions. To further illustrate the performance of the proposed optimal operation schemes, the corresponding spatial patterns of hydrodynamic change are numerically investigated using a process-based hydrodynamic model. In this 1D-2D coupled model, the lake domain is discretized using unstructured triangular grids (9,424 points and 14,289 cells). By changing the boundary conditions, the well validated model may make projections of the detailed lake level response (in time and space) to reservoir operation changes.

Our results show that, both for Case I and Case II, the overall spatial patterns (lake level increase) from the hydrodynamic model are generally in agreement with the relative differences (EWD satisfaction rate) at representative stations given by the SVR-based models. Although the hydrodynamic model cannot be directly applied to describe the spatial distribution of the EWD satisfaction rate, it may be used to forecast the spatial influence of the reservoir release on the propagation of lake level changes, thus introducing a feedback mechanism into the multi-reservoir optimization model.

This work presents a multi-reservoir optimization system for EWD of a river-connected lake. The elements of the ecologically oriented reservoir operation optimization are outlined. The optimal target index of EWD satisfaction rate is defined, of which EWD is estimated at representative stations in different lake regions of Dongting Lake. Station-specific SVR-based models are developed to quantitatively relate the lake and reservoirs, which are incorporated in the optimization model to provide a real-time forecast of lake level response to reservoir operations. To meet the lake EWD, an optimization model is further developed for the operation of this multi-reservoir system; the optimal operation policies for the TGR and 8 major tributary reservoirs of Dongting Lake can be determined by reference to the optimal target index and SVR-based model results.

This study unravels the cause of abnormally low lake level periods, due to the existing operation schemes, in both normal and dry conditions. The multi-reservoir optimization system leads to valuable insights into lake EWD satisfaction changes caused by optimal operation schemes. For example, in the normal condition, the proposed optimal joint operation policy could aid greatly in risk mitigation, increasing the lake EWD satisfaction rate from 85.4% to 95.7%. On the other hand, the results show that the spatial patterns of EWD satisfaction rate and lake level fluctuation in the lake are definitely dependent on the operation schemes. The success of the multi-reservoir optimization system paves the way for the development of more comprehensive aquatic ecosystem management in Dongting Lake. It is recognized that some important factors such as hydropower generation, navigation and irrigation have not been considered in the optimal target, which might be addressed in more refined modeling in the future.

This research is funded by the National Basic Research Program of China (973 Program) (2012CB417006), the National Natural Science Foundation of China (51379059, 51279047), the Program for Changjiang Scholars and Innovative Research Team in University (IRT1233), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).