Energy Sources, Part A: Recovery, Utilization, and Environmental Effects
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Integration of time series forecasting in a dynamic decision support system for multiple reservoir management to conserve water sources Hamed Zamani Sabzi, Shalamu Abudu, Reza Alizadeh, Leili Soltanisehat, Naci Dilekli & James Phillip King To cite this article: Hamed Zamani Sabzi, Shalamu Abudu, Reza Alizadeh, Leili Soltanisehat, Naci Dilekli & James Phillip King (2018): Integration of time series forecasting in a dynamic decision support system for multiple reservoir management to conserve water sources, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, DOI: 10.1080/15567036.2018.1476934 To link to this article: https://doi.org/10.1080/15567036.2018.1476934
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ENERGY SOURCES, PART A: RECOVERY, UTILIZATION, AND ENVIRONMENTAL EFFECTS https://doi.org/10.1080/15567036.2018.1476934
Integration of time series forecasting in a dynamic decision support system for multiple reservoir management to conserve water sources Hamed Zamani Sabzi a, Shalamu Abudub, Reza Alizadehc, Leili Soltanisehatd, Naci Dileklia, and James Phillip Kinge a
Department of Geography and Environmental Sustainability, University of Oklahoma, Norman, USA; bNew Mexico Interstate Stream Commission, Albuquerque, USA; cThe Systems Realization Laboratory, University of Oklahoma; d Department of Engineering Management and Systems Engineering, Old Dominion University; eDepartment of Civil Engineering, New Mexico State University ABSTRACT
In most of arid and semi-arid regions, there are limited sources of available fresh water for different domestic and environmental demands. Strategic and parsimonious fresh water-use in water-scarce areas such as Southern New Mexico is crucially important. Elephant Butte and Caballo reservoirs are two integrated reservoirs in this region that provide water supply for many water users in downstream areas. Since Elephant Butte Reservoir is in a semi-arid region, it would be rational to utilize other energy sources such as wind energy to produce electricity and use the water supply to other critical demands in terms of time and availability. This study develops a strategy of optimal management of two integrated reservoirs to quantify the savable volume of water sources through optimal operation management. To optimize operations for the Elephant Butte and Caballo reservoirs as an integrated reservoir operation in New Mexico, the authors in this case study utilized two autoregressive integrated moving average models, one non-seasonal (daily, ARIMA model) and one seasonal (monthly, SARIMA model), to predict daily and monthly inflows to the Elephant Butte Reservoir. The coefficient of determination between predicted and observed daily values and the normalized mean of absolute error (NMAE) were 0.97 and 0.09, respectively, indicating that the daily ARIMA prediction model was significantly reliable and accurate for a univariate based streamflow forecast model. The developed time series prediction models were incorporated in a decision support system, which utilizes the predicted values for a day and a month ahead and leads to save significant amount of water volume by providing the optimal release schedule from Elephant Butte into the Caballo Reservoir. The predicted daily and monthly values from the developed ARIMA prediction models were integrated successfully with the dynamic operation model, which provides the optimal operation plans. The optimal operation plan significantly minimizes the total evaporation loss from both reservoirs by providing the optimal storage levels in both reservoirs. The saved volume of the water would be considered as a significant water supply for environmental conservation actions in downstream of the Caballo Reservoir. Providing an integrated optimal management plan for two reservoirs led to save significant water sources in a region that water shortage has led to significant environmental consequences. Finally, since the models are univariate, they demonstrate an approach for reliable inflow prediction when information is limited to only streamflow values. We find that hydroelectric power generation forces the region to lose significant amount of water to evaporation and therefore hinder the optimal use of freshwater. Based on these findings, we conclude that a water scarce region like Southern New Mexico should gain independence from hydroelectric power and save the freshwater for supporting ecosystem services and environmental purposes.
KEYWORDS
ARIMA; Decision support systems; dynamic systems; reservoir management; sarima; time series analysis
CONTACT Hamed Zamani Sabzi
[email protected] Dept. of Geography and Environmental Sustainability, University of Oklahoma Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ueso. © 2018 Taylor & Francis Group, LLC
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Introduction Elephant Butte is a multi-purpose reservoir that has a 27,945-kilowatt hydroelectric power plant (Bureau of Reclamation, 2006), in which reservoir management plans simultaneously affect the energy production by utilizing significant amount of water. Basically, hydroelectric power plants utilize significant source of water to produce energy. American wind energy association reports that by the end of 2016, state of New Mexico had 1112 megawatts (MW) of wind-powered electricity generating capacity, in which counts for 11% of electricity produced in the same year (American Wind Energy Association., 2017). In addition, the evaluations show that wind power in State of New Mexico has a potential ofgenerating more electricity than the consumed electrical energy statewide. Therefore, it is highly recommended to save more water in these two reservoirs and rely on other renewable and clean energy sources in semi-arid regions such as New Mexico. With the shortage of freshwater and ongoing increases in domestic and agricultural water demands, the optimal management of freshwater is crucially important. In multi-objective integrated reservoir systems, optimal management involves balancing the need for a reliable water supply with the minimization of evaporation losses. Under deterministic conditions for inflows to and outflows from the reservoir system, it is simple to develop optimal decision plans. However, real conditions are uncertain and dynamic, so any optimal operating plan should consider this inherent uncertainty. In the past several decades, widely used optimization techniques for the operation of single-purpose and multi-purpose reservoirs have included evolutionary algorithms, such as genetic algorithms (GAs) and particle swarm optimization (PSO); several dynamic programming methods; several linear and nonlinear mathematical models; and several intelligent systems, such as Bayesian networks (BNs), and artificial neural networks (ANNs). The following material summarizes previous studies on inflow prediction and optimal reservoir operation systems. From 1974 to 2010, multiple review studies were done on optimizing the operation of singlepurpose and multi-purpose reservoirs (Becker and Yeh 1974; Labadie 2004; Rani and Moreira 2010; Simonovic 1992; Wurbs 1993). Becker and Yeh (1974) used dynamic programming to optimize the real-time operation of the Shasta-Trinity multiple reservoir in California. Forecasting the inflow to the reservoirs has been a critical step in developing the optimal operation plans for reservoirs in last several decades. Stedinger, Sule, and Loucks (1984) applied the best forecast of inflow amount in a stochastic dynamic programming model to maximize the expected benefits from release policies. Stedinger, Sule, and Loucks (1984) also reviewed previous studies on reservoir operation optimization and showed that the Markov chain concept was utilized by several researchers as a useful method to optimize single purpose reservoir operation; additionally, Stedinger, Sule, and Loucks (1984) showed that, in stochastic dynamic programming models, operation policies generally are dependent on the reliability constraints. Their studies showed that predictions based on long periods of historical inflow data derive more accurate predicted inflow values, and additionally, utilizing the snowpack information improved the prediction accuracy. Rani and Moreira (2010) thoroughly discussed the importance of simulation, optimization, and simulation-optimization of reservoir operations, and they showed the powerful capability of evolutionary algorithms for dealing with the nonlinear models of reservoir operation optimizations. In addition, they studied the capability of intelligent control systems in combination with simulation models on reservoir operation. They showed that, in most of the simulation-optimization systems, linear programming and dynamic programming are widely used; however, there is still a need to develop simulation-optimization systems that use computational intelligence systems. Furthermore, in the optimal operation of multi-objective reservoirs, the application of the modeling tools is critically important, as is the applied data and related information. Most of the modeling tools try to address the operational strategies (“what if?” questions) in facing any specific scenario of reservoir conditions. According to Labadie’s review study (Labadie 2004), researchers in most previous studies tried to develop flexible systems to deal with the various potential scenarios resulting from the uncertainty in the true state of nature.
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In most of the previous studies, several stationary and nonstationary dynamic programming models have been utilized. In the majority of those stationary and nonstationary models, the reservoir operation policies are optimized for the next T periods based on all available information at the beginning of the operation period, except for nonstationary dynamic programming models, in which observed values can be fed to the prediction models to update the prediction models and provide more accurate values than the preceding prediction model could with previously available information. The prediction period, depending on the model accuracy, can be defined as a shortterm or long-term period. In nonstationary models, the available information is updated in each step of the prediction period, and because of the adaptation process on prediction models, the nonstationary models are more time-consuming and costly than the stationary dynamic models. One of the sources of uncertainty in a reservoir system is river inflow, and multiple approaches have been developed to predict this factor and optimize reservoir operation. Karamouz, Houck, and Delleur (1992) studied stochastic dynamic programming (SDP), where the nature of the inflows is considered stochastic. They developed synthetic inflows to incorporate in a simulation model. Lund and Ferreira (1996) utilized implicit stochastic optimization to find the optimal operating rules on a multi-purpose reservoir system on the Missouri River. Papamichail and Georgiou (2001) used a stochastic autoregressive integrated moving average (ARIMA) model to generate the historical monthly inflow series for the Almopeos River in Greece. They utilized their stochastic ARIMA model to predict monthly inflows for one month and several months ahead. The inflow prediction helped them to optimally design and operate the reservoir in real time. The main concern in using ARIMA and seasonal ARIMA (SARIMA) is the accuracy of the prediction model: In some ARIMA and SARIMA models, although the regression correlation coefficient is high, the sum of squared error (error is defined as the difference between observed and simulated values) is a significant amount. Significant error values can cause significant impacts on the design and operation policies; therefore, considering the error amount is as critical as regression coefficient value. De Oliveira and Ludermir (2014) developed a hybrid evolutionary algorithm for time series forecasting. They mainly used several single and hybrid forecasting methods of ARIMA, ANN, and ANN-ARIMA to map linear and non-linear patterns in time series. Then, they utilized a PSO algorithm to find the near-optimal values of parameters in their developed forecast models. Their numerical results showed the power and significantly high accuracy of hybrid models in time series forecasting. Alizadeh et al. (2016a) used an integrated scenario-based robust planning approach for foresight and strategic management to manage uncertainty in water resource management. They also studied the predicted the implications of energy consumption on water reservoirs (Alizadeh et al. 2016b, 2015). Raje and Mujumdar (2010) investigated optimal reservoir operation under uncertainty. They considered the impact of climate change on the operation of the multi-purpose Hirakud reservoir in India. They projected and downscaled outputs from three global circulation models to predict the inflow of the Mahanadi River going to the Hirakud reservoir. Considering the predicted potential scenarios and by utilizing the stochastic dynamic programming, Raje and Mujumdar were able to define the optimal reservoir operation plans to satisfy multiple objectives of hydropower, flood control, and irrigation. Despite the last several decades of intensive research on the optimal operation of reservoirs and dealing with uncertainty in water management, there is still a significant gap between the theoretical models and the real-world application of those models. In this study, the authors consider two reservoirs, Elephant Butte and Caballo reservoirs in New Mexico, as an integrated operation system and simultaneously investigate the operation optimization of two reservoirs. A dynamic optimal operation model was developed to simultaneously utilize an accurate prediction model to find the inflow values, and the model uses a dynamic system to integrate ongoing daily values and update the decision support system to make optimal decisions. Based on the Bayes’ theorem, the authors combine recent data with historical data and update previous beliefs. Therefore, based on the historical belief and the predicted inflow, the optimal operation plan (release schedule) for one month is developed; then, in the operation period of one-month, daily data are combined with
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historical data, and then the prediction model’s indices are calculated. If those indices have changed, the prediction model is updated, and by changing the indices, the inflow for the rest of the operation period is predicted; otherwise, the previous indices of the prediction model are utilized. The optimal operation policy utilizes the developed ARIMA prediction models and defines the optimal operation policies for one month ahead; then, the observed values are incorporated with historical data to update the prediction model and predict the inflow value for the next day. Finally, the optimal operation values are determined, and the reservoir with minimum evaporation loss is selected to store the inflow to the system.
Materials and methods First, we describe the study area (Figure 1) and utilized data. Then, we describe the procedure of developing the time series models and integrating into the reservoir operation policies.
Study area Elephant Butte Reservoir, a multi-objective reservoir, provides electrical power and water for southcentral New Mexico and west Texas, including irrigation water for 68,708.25 ha (169,650 acres) of farmland. Caballo Reservoir, located 40.25 km (25 miles) downstream of Elephant Butte Reservoir, is fed primarily by water released from Elephant Butte Reservoir and provides direct release to downstream lands through the Rio Grande Project in cropping season. Consequently, the two reservoirs can be represented as an integrated control volume, whose inflows, outflows, and storage volume can be simulated. A reliable release plan from Caballo Reservoir to meet existing demands downstream in the Rio Grande Project directly depends on the Caballo Reservoir’s storage level, whose optimal operation plan must be developed under uncertain conditions. Required input data include the historical inflow to Elephant Butte Reservoir, agricultural water demands downstream of Caballo Reservoir, evaporation loss from reservoir storage (which is related to the surface area of the water volumes stored behind both reservoirs), and agricultural demands downstream of Caballo Reservoir. Constraints include physical limits of the reservoirs, Rio Grande Compact requirements, and required flood control pools in both reservoirs. Stage-storage and stagesurface area relationships from the Bureau of Reclamation’s 2007 bathymetry studies were used to characterize the storage in the reservoirs. Rio Grande inflow to Elephant Butte Reservoir was based on historical inflows measured at the San Marcial gauges, a USGS metering station with historical inflows going back to 1952. Direct precipitation on the reservoir surfaces was estimated based on the rainfall gauges maintained by the U.S. Bureau of Reclamation at both reservoirs. Outflow from Caballo was, for the model development stage, determined from the historical record of flow in the Rio Grande below Caballo Reservoir. Surface water demand from Caballo Reservoir was estimated from full supply years. Evaporation was estimated based on historical pan evaporation measured at the same points as the rainfall. There are sometimes significant ungauged inflows to both reservoirs from arroyos. There is also an inflow and outflow effect from groundwater interaction with the reservoirs’ storages, with storage loss to groundwater when the reservoir level is rising and a gain as it is dropping. The historical inflow data from 1952 to 2015 were utilized to develop both monthly and daily inflow prediction ARIMA models to the Elephant Butte Reservoir. The methodology used in this research contains the following steps: 1) develop daily and monthly time step time series forecasting models for Elephant Butte reservoir using the traditional ARIMA model, and 2) develop a reservoir release plan considering minimum evaporation loss by adjusting the storage levels on the reservoirs based on the predicted daily and monthly reservoir inflow.
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Figure 1. Study area showing the locations of Elephant Butte and Caballo reservoirs, the watershed area above Elephant Butte Reservoir, and the Rio Grande above Caballo Reservoir.
ARIMA model The main concern in developing the optimal storage levels in both reservoirs is accurately estimating inflow volume to the reservoir, considering the control volume elements in both reservoirs. By reliably predicting the inflow to the Elephant Butte Reservoir, the storage levels for two reservoirs are optimally planned for the operation period. The stochastic univariate time series forecasting approach, particularly the ARIMA modeling method, was utilized in this study. The ARIMA models originally were developed by Box and Jenkins (1976). The ARIMA model is a generalized version of the autoregressive moving average (ARMA) model. The ARIMAðp; d; qÞ represents the non-seasonal model, in which the parameters p; d; andq are the number of autoregressive lags, the order of differencing, and the number of moving average lags in the ARIMA model. For both developed monthly and daily models in this paper, Box and Jenkins’ three defined stages of
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identification, estimation, and diagnostic check were followed and examined. Evaluation of the autocorrelation function (ACF) and partial autocorrelation function (PACF) leads to exploring the system behavior through time dependency and selecting the most appropriate parameters (p and q) for the time series model (Abudu et al. 2010; Abudu, King, and Bawazir 2011; Sabzi 2016; Sabzi, King, and Abudu 2017). In the present work, ARIMA and SARIMA models were developed in two daily and monthly time scales, respectively, where in monthly scales it utilizes the complete set of data from 1952–2015. Statistical Analysis Software (SAS) was used to develop ARIMA model using proper data preprocessing procedures. Generally, a non-seasonal ARIMA model is defined through equations 1 to 8 as follows: φðBÞyt ¼ θðBÞat
(1)
yt ¼ 1 Bd Yt as stationary series after differencing;
(2)
φðBÞ ¼ 1 φ1 B φ2 B2 . . . φp Bp ; as nonseasonal autoregressive polynomial;
(3)
θðBÞ ¼ 1 θ1 θ2 B2 . . . θq Bq ; as nonseasonal moving average polynomial
(4)
where,
where at is defined as white noise process; Yt is defined as a dependent variable; and B is defined as backward shift operator (lag operator), which is calculated through Equation 5 as follows: BXt ¼ Xt1
(5)
The general form of SARIMA model has been defined by Vandaele (1983) as follows: φðBÞΦðBs Þxt ¼ θðBÞΘðBs Þat d
(6)
s D
where xt ¼ ð1 BÞ ð1 B Þ Xt ., D is the number of seasonal differencing, ΦðBÞ is the seasonal autoregressive polynomial, s is the order of seasonal differencing, P is the order of seasonal autoregressive polynomial, ΘðBÞ is the seasonal moving average polynomial, and Q is the order of seasonal moving average. The seasonal autoregressive polynomial and seasonal moving average polynomial are calculated through equations 7 and 8 as follows: ΦðBÞ ¼ 1 Φ1 Bs Φ2 B2s . . . ΦP BPs ΘðBÞ ¼ 1 Θ1 Bs Θ2 B2s . . . ΘQ BQs
(7) (8)
Dynamic operation model In this study, the initial operation plan is defined for one month ahead based on the predicted values for inflow to the Elephant Butte Reservoir and related parameters of the control volume, including evaporation volumes from both Elephant Butte and Caballo Reservoir, tributary inflows to the reservoirs, and seepage volume from both reservoirs. By considering the evaporation loss as the main objective and deciding on the storage levels in both reservoirs, the daily-based operation is optimized. Considering the existing agricultural downstream demands and predicted inflows to the Elephant Butte Reservoir through the operation period, different optimization methods can be utilized to find the optimal decision on storage levels in both reservoirs. Based on the geometric characteristics of both Elephant Butte and Caballo Reservoirs, in different storage levels, storing a specific amount of water volume will increase the surface area in each reservoir by a different amount; therefore, selecting the appropriate reservoir to store the specific amounts of water volumes in operational periods is a critical decision to take. A dynamic hydrologic model of the Elephant Butte-Caballo reservoir system was developed using Excel on a daily time step to minimize the
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evaporation loss from both Elephant Butte and Caballo reservoirs and satisfy the water release to agricultural demand downstream of Caballo Reservoir. The concept of mass balance (control volume) was utilized to find the storage level changes in both Elephant Butte and Caballo reservoirs. In order to find the volumes’ variations in both reservoirs, the mass balance concept was defined in the form of equations 9 and 10 as follows: Inflow ðto Elephant ButteÞt þ Precipitation ðon Elephant ButteÞt Evaporation ðfrom Elephant ButteÞt þ ðStorage ðin Elephant ButteÞt Release ðfrom Elephant ButteÞt ¼ ðStorage ðin Elephant ButteÞtþ1 (9) Release ðfrom Elephant ButteÞt þ Precipitation ðon CaballoÞt Evaporation ðfrom CaballoÞt þ Storage ðin CaballoÞt Seepage ðthrough the path of Elephant Butte to CaballoÞt Release ðfrom CaballoÞt ¼ Storage ðin CaballoÞðtþ1Þ (10) Two regression models were developed to indicate the relationships between the storage levels and surface areas on both reservoirs. Then, considering the water surface increments in both reservoirs and the evaporation rate in terms of depth from both reservoirs, the total volume of evaporation losses was calculated; therefore, the reservoir with the minimum added surface area is selected as the best reservoir for storing a specific amount of water. The predicted inflow and the mass balance concept are fed as input data to the developed dynamic model to find the optimal release plan and select the optimal reservoir for water storage, decisions that simultaneously minimize the net evaporation from both reservoirs and increase the release reliability (of course, the main concern is minimizing total evaporation loss to save water). The optimal selection of the reservoir for storing water and adjusting the storage levels of both reservoirs in each specific period minimizes total surface area and therefore minimizes evaporation loss. The two reservoirs are considered as an integrated control volume for which the inflows and outflows are shown in Figure 2. In addition, it demonstrates the schematic procedure of optimizing the prediction model and the simultaneous operation model for Elephant Butte and Caballo Reservoirs.
Result and discussion Development of daily ARIMA models The ARIMA models were investigated and developed to predict the monthly and daily inflows to the Elephant Butte. When the means and variance of time series data are constant, the time series data are stationary; when the mean and variance of time series data are not constant, the data are nonstationary. The daily inflow to the Elephant Butte Reservoir is not stationary. Therefore, one order of differencing was applied on the squared root values of daily inflow data to stabilize the mean and variance of historical data and reach the stationary condition. To provide a true and appropriate basis for analyzing the time-dependent system behavior, the autocorrelation function (ACF) and partial autocorrelation function (PACF) were developed in order to select the best p and q orders. The parameters of p and q are selected based on the covariance values in PACF and ACF plots, respectively. Figure 3 shows the Time series plot, the ACF, the PACF, and the inverse autocorrelation function (IACF) of the daily inflow time series after square root transformation and differencing with the order of 1. Graphical outputs in Figure 3 demonstrate that longer lags of autoregressive and moving average parameters were needed to model daily data sufficiently.
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Figure 2. Optimization process in the developed dynamic model.
Figure 3. Time series plot, ACF, PACF, and IACF of the daily inflow time series after square root transformation and differencing with order 1.
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Table 1. Parameter estimation Daily Model. Parameter MA1,1 AR1,1 AR1,2 AR1,3 AR1,4 AR1,5 AR1,6
Estimate 0.85063 1.05209 −0.23324 0.02130 −0.02406 0.00835 −0.01832
Standard Error 0.02195 0.02208 0.00670 0.00698 0.00658 0.00340 0.00345
t Value 38.76 47.65 −34.78 3.05 −3.66 2.46 −5.32
Approx Pr > |t|
