1. Introduction
Water stress and scarcity, population growth, ongoing economic development, and climate change are considered to be the major challenges faced by water resource planners and managers. This is because the water resources available in a particular catchment remain essentially unchanged while the water demand continually increases and can also follow different temporal patterns. In most cases, the total water resources, in terms of quantity, could meet the water demand, but the availability of those resources can differ temporally with respect to the water needs. Therefore, the available water resources must be managed to match the temporal patterns of water demand. In this context, water resource planners and decision-makers have suggested that dams be constructed to control river stream flows and create storage reservoirs upstream from dams. By doing so, water resource planners could adjust the volumes of water released from reservoirs, according to the actual water demands associated with temporal patterns. However, challenges remain due to the continual changes in these temporal patterns and the amount of water needed. To ensure the sustainable operation of water released from the dams and reservoirs of a water system, the operation rules must be updated and the water release policy optimized with respect to the water demand patterns.
Hydrologists and water engineers face a number of difficulties in determining the relationship between reservoir parameters due to their nonlinearity. Strong growth in the economy and population bring with them a corresponding increase in the demand for flood regulation mechanisms and water supply. Accordingly, researchers have focused on identifying effective modes of management. The successful operation of reservoirs is one of the challenges inherent in the management and administration of water resources. The optimization of operational procedures is necessary for the effective management and planning of complex water resources systems [
1]. Although water losses are a critical parameter that must be considered in the design of water distribution systems, little attention has been given to the consideration of these losses, which can affect the design accuracy [
2]. Optimization and numerical simulation are the most powerful methods available for analyzing reservoir systems. Decisions about the water released from a reservoir can be guided by operational policies regarding target storage levels at different times. Some researchers have developed numerical simulation and optimization methods for applying to the operation of reservoirs [
3,
4,
5,
6]. The majority of these methods are primarily utilized for planning purposes because there are uncertainties between actual practice and theoretical models with respect to the lake in a physical system. Labadie [
5] reported that decision-making is difficult regarding operational policies, mainly due to the range of unconfirmed scenarios and the randomness of natural phenomena. Consequently, designing optimal policies for water resources management in the operation of reservoirs has become a major concern of researchers [
7,
8,
9,
10]. The surface area of the water stored in a reservoir is utilized to calculate the losses that occur in a dam lake. Mahdouh et al. [
11] used autoregression (AR) analysis techniques to define the relationship between parameters. In the past, the storage and surface area parameters were used to evaluate and determine the relationships in a reservoir system. However, the models obtained by these analyses have not been proven accurate and their simulations have been unreliable. Thus, researchers have become increasingly interested in identifying a new simulation tool that can yield more accurate, better results. In this study, the artificial neural network (ANN) technique is considered for the simulation of a reservoir system [
12] in which the results are applicable to various reservoir systems. We use the stochastic dynamic programming (SDP) technique as a multistage framework that enlarges the dynamic program by combining stochastic data in the system context. This dynamic approach is useful for handling difficulties that arise in reservoir operations. In this work, we created an SDP and an ANN to identify the optimal operation strategies for the Sg. Langat Reservoir in Malaysia. We compare the performance of this model with that of the SDP-AR (Stochastic Dynamic Programming-Auto Regression) model using the same inflow length data and objective function. To evaluate the derived model performances, we utilized detailed performance signals, including resilience, reliability, cumulative penalty, and vulnerability. We determined the reservoir inflow utilizing the Gamma distribution function. The objective of the stochastic model is to develop the optimal strategy for water release from a reservoir and minimize the penalty function by considering the degree of inflow uncertainty.
An efficient and successful reservoir operation depends heavily on the simulation of the reservoir system. As such, special attention must be given for developing the simulation. Various techniques are available for developing simulations, which use statistical analysis. However, reservoir phenomena are nonlinear so statistical methods cannot accurately capture reservoir processes. This problem necessitates that a new technique be identified that can be used to realize more accurate reservoir simulation results. Reservoir simulation models are based on a mass balance equation that characterizes the reservoir’s hydrological behavior based on its inflow and any other operational conditions. Consequently, a model with higher accuracy will produce an optimal result with an optimum release policy. In this work, we used different simulation methods to determine the one with the greatest accuracy for specified parameters. An ANN is used to simulate a reservoir system to realize a more robust and reliable model that can obtain more accurate results.
The efficiency and successful operation of a reservoir depends largely on the effectiveness of the reservoir simulation system on which it is based. The determination of a reservoir simulation must, therefore, be given special attention. Various methods are used for developing simulations. Most of these methods rely on statistical analysis. However, the problem with most of these methods is that they cannot handle the nonlinear processes that occur in reservoirs. This has necessitated the consideration of other reservoir simulation methods to obtain more accurate results. Simulation models associated with reservoir operations are usually based on a mass balance equation, which represents the hydrological behavior of the reservoir systems based on their inflows and other operating conditions. Therefore, a more accurate model will produce better results in terms of optimal release. Consequently, in this study, we consider various simulation processes to obtain more accurate values for the specified parameters. Specifically, in this work, we use an ANN model to simulate a reservoir system, and find this model to be more reliable and robust since it provides a more accurate simulation and, thus, more accurate results.
The objective of this study was to simulate the operation of a reservoir, based on a specific case study, using both the ANN and SDP techniques to, thereby, obtain an optimal reservoir policy. The effectiveness of SDP is compared with other models. The findings of this reservoir simulation study are specific for identifying the model that exhibits more accurate performance, which can then be applied to enhance the reservoir release strategy and distribution system.
2. Case Study—Sg. Langat Dam
For our case study, we considered the Sg. Langat dam (
Figure 1), which is located in Malaysia at a latitude of 3°12′43.07 north of the Equator and a longitude at 101°53′39.28″ east of the prime meridian in Kuala Lumpur. An upstream forest surrounds the dam of the Sg. Langat River at Batu 24, Hulu Langat, which was built and completed for the water supply in 1979. The maximum height of the dam is 61 m with a 223.72-m crest elevation and 2.5 million cubic meters (MCM) of earth embankment. The dam has a primary gated spillway with a 220.96-m crest elevation. The catchment area of the reservoir is 41 km
2, as shown in
Figure 1. The stated purpose of the dam is to regulate and control the water released into the Sg. Langat River during the dry season to ensure adequate water for the Sg. Langat water treatment plant at Batu 10, which is located 14 miles from the dam. The majority of the drinking water for the towns of Bangi and Kajang is supplied from the dam’s reservoir, which has a capacity of 37,480.0 million liters. As such, this dam is extremely important to these residents. As shown in
Figure 2, the fundamental aspects of the reservoir are the relationships between the storage volume, water surface area, and elevation, which must be determined for the model in this study. The information provided in
Figure 2 can be used to obtain the water level associated with each representative storage volume.
The volumes of evaporation are a function of both the evaporation rate and the water surface area. Evaporation computations usually depend on the relationship between elevation and surface area.
Table 1 shows a statistical analysis of historical data for the Sg. Langat reservoir over a period of 15 years from June 1996 to December 2010. In the table, it is apparent that the average minimum inflow occurs during the month of June, whereas the average maximum inflow occurs during September, with the average annual inflow being 46.78 × 10
6 m
3. The water intake demand must be determined to estimate the water demand for the Sg. Langat reservoir. We note that the water intake at the station is kept constant at 13.620 MCM per month.
4. Results and Discussion
In this work, we utilized the ANN technique to simulate the reservoir system. We selected this approach based on the experience of previous studies that had used regression models to simulate the storage and surface area values of reservoirs. However, we also took into consideration the shortfalls of the ANN in comparison to regression models regarding the storage–surface area relationship. The first stage in the ANN is training, since this stage reduces the error by finding the best connection set and threshold value that enables the ANN model to generate a result that is close or equal to the targets. We adjusted the expected mean square error (MSE) obtained in the training phase to 10−4, based on the principle that considers the best model performance will have the lowest MSE value during the training phase.
4.1. Storage–Surface-Area Relationship
The performances of the simulation methods were compared using various indicators including the MAPE, RRMES, RMSE, and CE.
Figure 6 and
Figure 7 show the test results as percentage errors for the reservoir simulations of the elevation-surface-storage relationship. The authors of Reference [
34] reported that percentage error values provide a basis for determining model accuracy. In the figure, we can see that the percentage error of the predicted surface area continually decreases with respect to elevation (the height from the bottom of the reservoir) up to 199.63 m. In addition, we can see a sudden fluctuation in the percentage error pattern in the predicted surface area when the altitude is between 184.4 m and 196.59 m. This is due to the fact that, upstream of the reservoir, a dam had formed naturally without any human interference to re-shape it and sediment had accumulated over the years of operation since completion of the dam. As such, the vertical, horizontal, and longitudinal cross-sections of the reservoir are completely irregular. As a result, there can be sudden, abrupt, or rapid changes in the horizontal cross-section at this range of elevation due to the unexpected changes in the surface area, which may cause fluctuation in the accuracy of the predicted surface area. Furthermore, the same observation is noted in the FBNN and RBF results, which confirms that the relationship between the elevation and surface area within this particular elevation range is highly nonlinear, as illustrated in
Figure 7.
Table 2 lists the FBNN, RBF network, and regression model analyses with regard to the surface area and its relationship to water storage at Sg. Langat reservoir. In addition, the table lists the CE values of the models. The results reveal that the RBF model has a higher accuracy and productivity during the testing phase, with a CE value of 0.9993. This result confirms that the RBF has higher reliability and accuracy for simulating the surface area and storage relationship. To be considered a very accurate model, the MAPE values for the Sg. Langat reservoir model simulation should be less than 1%. The result presented in
Table 2 indicates that the RBF has a MAPE value of 0.982%, and can, thus, be considered to be very accurate. However, the AR and FBNN models have MAPE values of 10.2% and 3.879%, respectively, which reveal that the RBF model performed better than the AR and FBNN models. Moreover, when the RRMSE and RMSE values are close to zero, there is a smaller degree of error in the simulation phase. In the table, the RBF model has an RRMSE value of 0.011 and an RMSE of 0.009 km
2, which are nearly zero and are about half those of the AR and FBNN models. This further confirms that the RBF system yields greater simulation accuracy. From these simulation results and the rigorous confirmation procedures applied, it is clear that the RBF application performs better with regard to the relationship between surface area and storage of Sg. Langat reservoir than the AR and FBNN models. In summary, the AR and FBNN models generated greater errors than the RBF model, which obtained higher CE values and lower RRMSE and RMSE values.
Regarding the errors associated with different models that use different methods for simulating the surface area, as shown in
Figure 6;
Figure 7, the RBF method has an error with a respective minimum and maximum of −2 and 2. The error of the FBNN is higher, with a minimum error of −5 and a maximum error of less than 7, as shown in
Figure 7. The AR method error exceeded those of the other two methods, and its error value range differs in nature. Its results are presented in
Figure 6. Moreover, we identified a linear relationship between the surface area and storage in the AR model results, which indicates that the model has a higher error than the ANN models, whose error values are close to the axis. When the models were evaluated, the RBF showed the best performance. From the tables and figures obtained from the testing set, the RBF model also yielded better results in terms of accuracy, as compared to the AR and FBNN models, with constant values of RRMSE and RMSE. We also proved that the AR method is able to handle the nonlinear relationship of the reservoir. It is, thus, certain that flexible models can yield the lowest MAPE, RRMSE, and RMSE errors, with the AR results revealing that the AR model has the necessary flexibility for modeling the relationship between the storage and surface area.
The ANN modeling method is convenient for modeling hydrological processes. The ANN is a powerful and useful tool that has been utilized for mapping complicated relationships and achieving better performance than conventional methods. The results obtained from the simulation analysis proved that the reliability and accuracy of the ANN is greater than those of the other methods, and the storage-surface-area relationship was accurately determined by the ANN modeling method in this study. The ANN outputs confirmed the superiority of ANN over traditional simulation methods used for solving hydrological problems. The ANN model developed in this study provides an accurate and beneficial means for resolving problems related to water storage.
4.2. ANN or AR with Stochastic Dynamic Programming as a Simulation Model
SDP models with either an ANN or AR were established to develop effective policies for the reservoir operation.
Figure 8 shows the SDP-ANN and SDP-AR cumulative penalty models in which the reservoir system used a penalty function to measure performance and determine the decision-making method that would contribute the most to the reservoir operation [
35]. A decision-making process was developed to improve the water release schedule to meet operational requirements and target demands with reference to the target demand. To keep forces to a minimum, a penalty function was implemented. The use of the choice system was, thus, expected to improve the resiliency and reliability with minimum cumulative and vulnerability penalty values. The existing model (Model 2) integrated the SDP and ANN, and
Figure 8 shows that the obtained cumulative penalty value for Model 1 is 0.39 whereas that for Model 2 is 0.36. The obtained minimum penalty value from the Model 2 SDP-ANN are identical to those of the other models, which reveals that Model 2 performs better by 8.3% than Model 1.
The performance indicators used for water demand of the reservoir downstream section for the 15-year period were limited to resiliency, vulnerability, and reliability. We found the reliability of Model 1 to be 0.66% and of Model 2 to be 0.71%. The water supply reliability is improved by 7.5% by using Model 2. Over the 175 months of the study period, we determined water supply shortages had occurred, and that Model 2 found 51 months to have had unsatisfactory water supply, whereas Model 1 found that 60 months had experienced shortages in water supply. In addition,
Figure 9 shows the reliability, resilience, and vulnerability results. The resilience value obtained for Model 2 is 6.3% better than that of Model 1, which indicates that Model 2 is more suitable than Model 1. The vulnerability values, which are based on the non-supply of expected water, was 0.38 for Model 1 and 0.36 for Model 2, which indicates that the Model 2 value was 5.5% better than Model 1.
Reservoirs are essential facilities that can provide sustainable and reliable sources of water for all water users downstream. For the current case study, it is vital to ensure that the proposed operation rules can provide sustainable functionality for present and future water demands. Several approaches are available for considering the sustainability of dams and reservoir operations. For example, a sustainable evaluation could involve the river ecology, flood and drought control, sediment management, river water quality, and water resources allocation. The main concern of decision-makers in the case study was to ensure the sustainable allocation of water resources for downstream water users. To guarantee that the rules generated for optimal reservoir operation would provide sustainable usage of the available water resources, several evaluation metrics must be considered. In this study, we focused on three performance indices, including reliability, resilience, and vulnerability to determine the performance of the generated operation rules based on a new proposed reservoir simulation model utilizing the RBF model.
5. Conclusions
In this study, we established and applied an SDP-ANN model, and compared its results with those of the SDP-AR model. The accurate simulation of a reservoir is considered to be a vital step in achieving appropriate operational policies regarding water release from the reservoir. In practical terms, the main application of the proposed optimization model is to generate sustainable and reliable operational policies for managing the available water resources to meet and match the temporal water usages downstream from the reservoir. We developed SDP-ANN and SDP-AR models using the same objective function and inflow data. The natural nonlinearity of the physical processes is the main challenge when developing a reservoir system simulation, especially when using linear systems such as the AR method. Therefore, we used a nonlinear computational technique to simulate the system. A comparison of the performances of the AR and ANN models highlights the superiority of the ANN. Moreover, the results reveal that the proposed Model 2 is less vulnerable and more resilient and reliable than Model 1. In summary, the SDP-ANN model performs better than the SDP-AR model for the purposes of developing operational policies for the reservoir system.
Although the proposed model effectively improved the operation rules for the reservoir operation and enabled the generation of a sustainable and reliable water release policy, there are two major disadvantages in this model structure. First, the proposed optimization model (SDP) experienced a slow convergence process, and might become trapped in local minima while searching for the global optimal objective function. Therefore, we recommend that the potential for utilizing a more advanced optimization algorithm be investigated as an alternative, such as the meta-heuristic optimization algorithm. The meta-heuristic optimization algorithm may realize faster convergence than SDP and more efficiently obtain the global optima, which means it is more effective when applied to real-time operation of the dam and reservoir water system. Second, the proposed model has only been examined with respect to water resources allocation. In future research, more sustainable factors should be considered as evaluation metrics, such as sediment management, water quality, and the river ecosystem, to determine the sustainable functionality of the operational policies from multi-objective angles.