Reservoirs are manmade structures that are widely used in water resource management, and are recognized as some of the most efficient infrastructure components in integrated water resource management and development [1
]. Reservoirs are among the major solutions to water demand and water-related problems, including irrigation, hydropower, urban and industrial water supply, conservation of ecology, and flood control. Nevertheless, there are several factors that affect the performance of the reservoir system, for example, the reservoir sedimentation [2
] and the reservoir operation. In reservoir operation, care is required, especially for multipurpose reservoirs where there may be a number of potentially conflicting objectives. For water supply, operations should keep reservoirs as full as possible, whereas flood control requires reservoirs to be kept as empty as possible to allow the capture of flood water [3
]. Reservoirs should be neither partially empty at the end of the rainy season nor full at the time of a series of peak floods that lead to heavy releases, causing floods in downstream areas [4
]. Due to its complexity, reservoir operation is a challenging problem for water resource planners and managers. To optimize operating rules, many optimization and simulation models have been developed and applied over the past several decades [5
]. However, these operating rules are not easy to implement, as appropriate reservoir operations depend on the accuracy of inflow forecasting and the operating time horizon [10
]. Accurate inflow prediction is not only an important non-engineering measure to ensure flood-control safety and increase water resource use efficiency, but also can provide guidance for reservoir planning and management, because streamflow is the major input into reservoirs [11
Due to its importance, several models and methodologies for reservoir inflow forecasting have been developed and applied in real-world situations [13
]. One method that is widely used to forecast reservoir inflow is the artificial neural network (ANN) model. Although this is a black-box model in which the internal structure of the process involved cannot be understood, it has many advantages from the viewpoint of practical application. First, it is able to recognize the relation between the input and output variables without explicit physical consideration [14
]. Second, it is very convenient to review the model when the data of interest are suspected as having changed. It can be recalculated as soon as new data are available with low cost and time requirements. Third, once the model is developed, it can be adapted very flexibly to other areas or for other purposes. In addition to these advantages, ANN models have been shown to be applicable to hydrology, including reservoir inflow prediction [14
]. There have been several reports of the application of the ANN model for predicting short-term reservoir inflow at hourly and daily time scales [16
]. Most studies have concluded that the ANN model provides satisfactory forecasting results. The ANN model can also be applied to forecast long-term and seasonal reservoir inflow as reported in several studies [18
]. Some studies attempted to improve forecasting results by incorporating sea-surface temperature (SST) and climatic indices as inputs of the ANN model [21
]. Most studies reported the good prediction results and the incorporation of SST provide improved predictions relative to the same model using only reservoir inflows.
Although ANNs have been used successfully in various fields, the precision of the results has still required improvement in many cases. Several hybrid ANN models have been proposed to fulfill this requirement. Kim and Valdés [22
] developed a model for drought forecasting in the Conchos River Basin in Mexico, making use of the ability of neural networks to model and forecast nonlinear and non-stationary time series and the ability of wavelet transforms to provide useful decompositions of an original time series. The results indicated that the conjunction model significantly improved the ability of neural networks to forecast the index regional drought. A similar study which indicated the successful integration of the ANN and wavelet analysis to predict water levels in the Nan River, Thailand, can be found in the work of Amnatsan et al. [23
Another technique that has been widely used in forecasting is the analogue method (AM), which was first introduced by Lorenz in 1969 to predict the evolution of the states of a dynamic system [24
]. This is the simplest statistical technique that can establish nonlinear relationships between variables in a straightforward manner [25
]. The analogue forecasting approach is based on the hypothesis that two relatively similar synoptic situations may produce similar local effects [26
]. This approach has two main advantages and has been commonly used in weather prediction. First, the use of observed weather patterns helps to maintain the local-scale weather in the simulated field. Second, it is easy to construct scenarios for non-normally distributed variables, such as daily precipitation, because the AM does not assume the form of probability distribution of downscaled variables [27
]. There have been many reports of successful implementation of the AM in weather prediction [25
]. However, there have been few reports regarding its application to streamflow forecasting. Bellier et al. [30
] evaluated probabilistic flood forecasting on the Rhone River using ensemble- and analogue-based precipitation forecasts. They reported that forecasting performance of the two methods for the peak amplitude and peak timing of floods was very similar. Svensson [31
] performed flow forecasting based on flow persistence and historical flow analogues. The river flows at one and three months in the future at 93 individual river flow stations across the United Kingdom were forecast using two historical AMs, i.e., the weighted mean method and the shifted weighted mean method. The results indicated that forecasts based on persistence of the previous month’s flow generally outperformed the analogue approach, particularly for slowly responding catchments with large underground water storage in aquifers. For the weighted-mean AM, the forecasting performance was increased with the length of historical flow records. The considerable success used of the weighted-mean in an interlayer forward validated scheme was reported in Panagoulia [32
In this study, the wavelet artificial neural network (WANN) and the weighted mean AM (WMAM) were used to forecast the monthly reservoir inflows of the Sirikit Dam in Thailand. Monthly and seasonal inflow forecasting are very important for proper management of this multipurpose dam, which has a large catchment area of 13,130 km2
and maximum storage of 10.64 km3
. This is one of four major dams that supply water to 22 provinces in the Chao Phraya Basin, covering an irrigation area of 1,513,465 hectares. Difficulty in the operation of this dam occurs mainly in the monsoon season, especially in July to September, the months which account for about 50% of the annual inflow. During this period, the dam managers have to decide whether to keep or release water. They have to retain sufficient water to supply demand in the next dry season, but for downstream flood control they must not keep too much water. As the capacity of the downstream river is limited, large amounts of water cannot be released in too short a time. An incorrect decision due to lack of an accurate and timely inflow forecast will lead to excessive release in a short time, resulting in flooding in downstream areas. On the other hand, a long forecast lead time will allow dam managers to release water gradually. Therefore, monthly or seasonal weather and reservoir inflow forecasting are crucial for proper management of this dam [33
In addition to the WANN and WMAM methods, a forecasting method designated as the variation analogue method (VAM) was developed and employed to forecast the reservoir inflow of this dam. This study was performed to evaluate the performance of different forecasting methods in predicting the reservoir inflow, especially with regard to predicting extreme flow. Many researchers have reported that ANN-based models cannot predict extreme values in river flow [34
]. The WMAM, which was found to show good predictive performance for a low-response watershed [31
], may not be able to forecast the peak flow for the high-response catchment of the Sirikit Dam.
Several previous studies have indicated that SSTs and ocean indices are associated with the seasonal and interannual climate of Thailand [36
], and therefore the variability of rainfall and reservoir inflows may be associated with SST anomalies. Manusthiparom [40
] reported that adding SSTs as ANN inputs significantly improved the results of monthly rainfall and runoff forecasting for the Chao Phraya River Basin. In this study, we incorporated SSTs and ocean indices into the WANN and the VAM to improve the performance of inflow forecasting. Their forecasting performance was compared using four indicators: the root mean square error (RMSE), the correlation (R), the Nash–Sutcliffe efficiency index (EI), and the coefficient of determination (CD).
The forecasting using the WANN model in this study was begun by finding the input parameters of the ANN model that produced the best forecast. After several trials, the best forecasting results were obtained from a model with 22 input parameters, as shown in Table 2
. The activation function of this model in both the hidden and output layers was a hyperbolic function. The number of hidden neurons, learning rate, and momentum that provided the best results were 10, 0.0001, and −0.5, respectively. After obtaining the best forecast from the ANN model, all input parameters were decomposed into their detailed (high frequency) and approximated (low frequency) components. Then, all decomposed components were fed into the neural network model. The performance indicators of the WANN model in each model period are shown in Table 3
For the forecasting using the WMAM and VAM methods, reservoir inflow data from 1974 to 2004 were used to forecast the inflow of the years 2005 to 2014. Therefore, there were at least 31 years of monthly records for use as historical analogues. For the WMAM method, the selection of potential historical analogues was based on calculation of the RMSE as described in the Methodology section. Figure 3
shows an example of reservoir inflow forecasting for March 2013. Five historical analogues gave the minimum root mean square values selected for the forecast. After selection, the weights for each analogue were calculated, and these weights were then used to calculate the forecast standardized value and converted to obtain the forecast inflow for March 2013. The yellow broken line and the yellow solid line are the forecast and observed standardized inflows in March 2013, respectively. The forecast standardized inflows were converted to inflows in a normal form and used to calculate the performance indicators.
shows an example of the variation values plotted against standardized inflow values from February to January of the following year. Assuming that the most current month is December 2005, we can forecast the inflow in January 2006. The variation from March to January of previous years is plotted alongside the variation from March to December of 2005. Then, the most similar variation analogue is selected by comparing the variation vectors from November to December. In this example, the most similar analogue is the plot for 1993–1994, as shown in Figure 4
. Thus, the variation in January 2006 is calculated from the variation in December 1993 and January 1994. Then, the forecast standardized value for January 2006 is calculated from this forecast variation value, as shown in Figure 4
. The plot of standardized inflows from October 2005 to January 2006 is very similar to the plot from October 1993 to January 1994. It is evident from the plot that VAM forecasting has the advantage that it allows determination of similar patterns among inflow events even if they occurred in different zones. This is different from the WMAM, in which selection of potential historical dialogues depends on the RMSE between inflows of previous years and the current year. The selection will include all nearby inflow patterns even if they are not similar to the inflow pattern of the current year, while similar patterns in different zones, as in this example, will not be selected.
To improve forecasting results of the VAM, additional processes to assist selection of the most similar analogue were investigated. Consider the predicted inflow of the Sirikit Dam in August 1995, which was the most extreme Sirikit Dam inflow on record, shown in Figure 5
. The plot of the variation in standardized inflow for June–July 1995 is very similar to the plot for the same period in 1992. The forecast variation in standardized inflow in August 1995 should follow the red dotted line. Nevertheless, the actual variation followed the dark red line, which is very far from the forecast result. These observations indicate that the VAM still has some weaknesses and requires further improvement.
Several previous studies have indicated that SSTs and climatic indices are associated with climate and rainfall in Thailand. Moreover, several previous studies have reported that incorporating SSTs and climatic indices into river-flow forecasts can improve results. The incorporation of SSTs and climatic indices as inputs to the WANN in this study confirmed that these data can improve reservoir inflow forecasts, implying that SST and climatic indices are also associated with reservoir inflow. Based on this assumption, years with similar patterns of standardized inflow variation should have similar SST and climatic-index patterns. These similar SST and climatic-index patterns can then act as guidelines in the selection of the most potentially useful historical analogues. Therefore, cross-correlation analysis between SSTs and the climatic indices used as the inputs of the WANN model and standardized inflow was performed. The correlation values between SSTs, climatic indices, and standardized inflow were calculated for each month. The SSTs and climatic indices with correlation values exceeding the threshold for significance (0.304 for 41-year inflow data in this study) [44
] were considered significant SSTs and indices in the selection of historical analogues of the corresponding month. As examples, Appendix A
lists the significant SSTs and climatic indices for the Sirikit Dam inflows in January and August; the number −1 behind a month indicates the month in the previous year compared to the year of inflow. For example, Niño 3 (Jan-1) refers to the Niño 3 index in January of the previous year compared to the year of the inflow to be forecast. These significant SSTs and climatic indices will be used to decide the most useful potential historical analogue for forecasting the inflow of the current year.
An example of forecasting the inflow of the Sirikit Dam in January 2008 is presented. In this case, the most current month is December 2007, and the inflow to forecast is that of January 2008. The steps of forecasting the inflow are as follows.
The variations in standardized inflows for March to December 2007 are plotted along with the variations in standardized inflows for March to January of the available analogues. Potential analogues with variation patterns similar to that of December 2007 are selected. In this case, there are three historical analogue candidates: December 1976, December 1988, and December 1989 (Figure 6
To forecast the inflow for January 2008, the significant SSTs and climatic indices for inflows in January 2008, January 1977, January 1989, and January 1990 are plotted to assist in selection of the best potential analogue (see Appendix B
). In this case, most of the significant climatic indices and SSTs for January 2008 are very similar to those for January 1989, and therefore January 1989 is selected as the best potential analogue.
The forecast variation for January 2008 is calculated from the variation in January 1989 using Equation (6) and plotted as the red-dotted line in Figure 6
After obtaining the variation for January 2008, the standardized inflow is calculated using Equation (7) and converted to the normal form of inflow. The forecast inflow values calculated from this method and the observed inflow in January 2008 are 138.29 and 136.84 million cubic meters, respectively.
For a greater understanding of forecasting using the VAM with the consideration of SSTs and climatic indices (the VAM-improved), the readers can read the examples of forecasting for the inflow in August 1995 and August 2011, which were the most extreme inflows on record (Appendix C
and Appendix D
Based on the results described above, the improved VAM that considers climatic indices was used to forecast July, August, and September, which are high-flow periods in Sirikit Dam inflow. The forecasting performance of all methods for the whole-year and high-flow periods was evaluated and compared. To compare the performance of the WANN with other methods, the forecasting results of the WANN in the validation and testing periods were combined and the performance indicators were recalculated to match the forecasting period of the WANN with that of the WMAM and VAM. The performance indicators of all methods in predicting the reservoir inflow of the Sirikit Dam from January 2005 to December 2014 are shown in Table 4
. Plots of forecast and observed inflows for the whole-year and high-flow periods are shown for comparison in Figure 7
and Figure 8
For the whole-year forecasting period, which included both low-flow and high-flow patterns, the WANN model provided good forecasting results as all performance indicators were above 0.80. The WMAM provided only satisfactory forecasting results, as the EI and CD values were <0.70 and the RMSE was higher than for the other methods. The forecasting performance of the VAM was superior to that of other methods as all performance indicators were >0.9 and the RMSE had the lowest value. It can also be seen from the comparison plot in Figure 8
that the VAM forecast captured the extreme inflow of the Sirikit Dam reservoir.
For the high-flow period, the forecasting performance of all methods significantly worsened. The WANN method, which produced good results for the overall period, provided only satisfactory results for this period. This was not unexpected; poor performance in predicting peak flow is a common weakness of ANN methods, as noted in several previous reports (e.g., Sudheer [34
]; Yang et al. [35
]). The forecasting performance of the WMAM was markedly lower in the high-flow period compared to the whole year, indicating that this method is not suitable for prediction of inflow in a high-response watershed, especially for the high-flow season, as in this case. This weakness of the WMAM was also noted by Svensson [31
], who reported a high degree of uncertainty in the historical analogue approach, particularly in catchments with a rapid response. The VAM captured flow best in this period comparing to the WANN and the WMAM, especially peak flow. Taking SSTs and climatic indices into consideration significantly improves forecasting results of the VAM. The VAM-improved performance indicators were the best in both the whole-year and high-flow forecasting periods; this model provided very good performance indicators even in high-flow periods, with all indicators having values above 0.85. The improvement can be seen in Figure 8
, where most of the VAM-improved forecast values are closer to the observed values than those of the standard VAM (i.e., the VAM without consideration of SSTs and climatic indices).
Based on the very high reliability and low uncertainty of the improved VAM indicated by the results, this method can be used for management of the Sirikit Dam, especially in high-flow periods. It provides very good forecasting results, with all performance indicators above 0.85, and its uncertainty as defined by RMSE values is less than the reservoir surcharge storage (998,000,000 m3). Moreover, in testing, it predicted extreme flow such as occurred in August 2011, whereas other methods did not. However, in forecasting based on historical analogues, there may be high-return-period events for which no suitable analogues are available. Therefore, scenarios based on forecasts with various uncertainty values should be modeled. The most suitable scenario for the current month can then be selected for dam operation. For example, if the water level in the dam is very low in August, well below the upper curve of the reservoir operation rule, and low inflow is forecast in September, then a scenario with less inflow than that forecast is selected to retain the water for the coming dry season. On the other hand, if the water level in the dam is very high in August, close to the upper curve of the reservoir operation rule, and high inflow is forecast in September, then a scenario with more inflow than that forecast is selected. The dam operator can then decide to release water gradually to make space for the expected inflow. For the low-flow season, the forecasting results of all of the methods examined in this study were acceptable for dam operation, as their uncertainties were close enough to observed values. Moreover, most of the inflow in the low-flow period is kept for water supply, so uncertainty is less important.