A neural network based general reservoir operation scheme
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DOI: 10.1007/s0047701511479
 Cite this article as:
 Ehsani, N., Fekete, B.M., Vörösmarty, C.J. et al. Stoch Environ Res Risk Assess (2016) 30: 1151. doi:10.1007/s0047701511479
Abstract
Construction of dams and the resulting water impoundments are one of the most common engineering procedures implemented on river systems globally; yet simulating reservoir operation at the regional and global scales remains a challenge in human–earth system interactions studies. Developing a general reservoir operating scheme suitable for use in largescale hydrological models can improve our understanding of the broad impacts of dams operation. Here we present a novel use of artificial neural networks to map the general input/output relationships in actual operating rules of real world dams. We developed a new general reservoir operation scheme (GROS) which may be added to daily hydrologic routing models for simulating the releases from dams, in regional and globalscale studies. We show the advantage of our model in distinguishing between dams with various storage capacities by demonstrating how it modifies the reservoir operation in respond to changes in capacity of dams. Embedding GROS in a water balance model, we analyze the hydrological impact of dam size as well as their distribution pattern within a drainage basin and conclude that for largescale studies it is generally acceptable to aggregate the capacity of smaller dams and instead model a hypothetical larger dam with the same total storage capacity; however we suggest limiting the aggregation area to HUC 8 subbasins (approximately equal to the area of a 60 km or a 30 arc minute grid cell) to avoid exaggerated results.
Keywords
Dams Reservoir operation Neural network Hydrological alteration Hydrological models1 Introduction
Construction of dams and the resulting water impoundments are one of the most common engineering procedures implemented on river systems. Half of the major global river systems are affected by dams (Dynesius and Nilsson 1994). There are over 45,000 operational large dams globally with an estimated aggregate storage capacity of over 6000 km^{3} (Vörösmarty et al. 1997; WCD 2000; ICOLD 2011; Lehner et al. 2011) trapping over 17 % of global annual runoff (Nilsson et al. 2005; Piao et al. 2007). Dams increase the storage of water in river systems by 700 % and triple the mean residence time of water in the rivers (Vörösmarty et al. 1997). Dams impact ecosystems by flow regulation, upstream flooding, change in sedimentation patterns, draining floodplain wetlands and altering water temperature patterns (Vörösmarty and Sahagian 2000; Kingsford 2000; Syvitski et al. 2005). Overlooking those impacts may significantly affect modelling results and influence decisions addressing water management issues.
In the context of this paper, reservoir or dam operation refers to alteration of the outgoing flow regime via accumulation of the incoming flow and delayed release of water over time. One major problem in dams’ impact studies is the lack of reliable methods for simulating reservoir operation. In reality, dams are regulated in different ways and virtually each dam has a unique operating rule (Simonovic 1992; Wurbs 1993). Actual reservoir operating rules are not available to the public, thus their direct use in models is infeasible, especially for macroscale applications where hundreds or thousands of dams exist in the study domain.
To address this problem, metrics have been proposed to assess the aggregate hydrologic behavior of dam regulated rivers. For example, Graf (1999) used the total reservoir storage in a watershed as a measure of changes in flow regimes and associated downstream effects. Nilsson et al. (2005) used the percentage of the annual discharge of a river system that can be contained by the reservoirs within that system as a measure to quantify flow regulation by dams (Dynesius and Nilsson 1994). Vörösmarty et al. (1997) used the ratio of aggregated reservoir storage along river networks and the mean annual river discharge to calculate the mean local aging of water and showed how large dams might change the residency time in rivers. They used a similar approach to study the impact of reservoir construction on sediment transport to the ocean (Vörösmarty et al. 2003).
Conceptual or empirical relationships have also been used to model reservoir operation. Meigh et al. (1999) and Döll et al. (2003) used an empirical relationship to simulate the monthly release from dams based on reservoir water storage (\( Q_{out} \sim S^{b} \)). Coe (2000) modelled dam operation by assuming that a reservoir is full in the month of average maximum inflow and is at its minimum storage for the month of average minimum inflow. He calculated the storage for other months assuming a linear relation between those upper and lower limits. Wisser et al. (2010a) used a relationship between daily inflow and average longterm inflow to calculate the daily release from a reservoir. Haddeland et al. (2006) calculated reservoir storage and release to meet monthly irrigation and hydropower demand. Hanasaki et al. (2006) predicted monthly release based on reservoir characteristics, river discharge and water use information. Their model tries to meet the industrial, domestic and irrigation water demand (Yoshikawa et al. 2013). Recent studies have applied remote sensing applications to model dam characteristics like storage, surface area and water level (Coe and Birkett 2004; Peng et al. 2006; Gao et al. 2012).
1.1 Artificial neural networks in hydrology
Artificial neural networks (ANN) have been successfully used in various water resources studies (Hsu et al. 1995; Maier and Dandy 2000; Govindaraju 2000a, b) notably in river flow forecasting (Karunanithi et al. 1994; Zealand et al. 1999; Coulibaly et al. 2000; Coulibaly and Baldwin 2008) and also to solve reservoir operation optimization problems through dynamic programming (Raman and Chandramouli 1996; Fontane et al. 1997; Jain et al. 1999; Rani and Moreira 2010). It has been demonstrated that performances of ANNbased models are similar or superior over conventional statistical and stochastic models for prediction of river flows (Abrahart and See 2000; Cigizoglu 2003; Rani and Moreira 2010).
Here for the first time we use ANN to map the general input/output relationships in actual operating rules of real world reservoirs. Our goal is to parameterize actual dam operation data by using ANN and develop a general reservoir operation scheme (GROS) that is suitable for use in largescale hydrological models and is sufficiently accurate in simulating the operation of existing reservoirs. GROS enables us to collectively investigate the impact of dams and reservoirs operation on hydrological systems. We seek to limit the input requirements to essential and conveniently calculable data. For regional and global studies, accurate water demand data with applicable resolution is rarely available; therefore, we do not use water demand as an input to GROS. We compare the performance of GROS with a monthly reservoir model developed by Hanasaki et al. (2006) and a daily reservoir model developed by Wisser et al. (2010a).
1.2 Assessment of hydrologic alteration caused by dams
Dams alter the frequency, duration and timing of annual flooding and drought events. While this has beneficiary effects on human water security, aquatic biota is distressed by these changes as they rely on the natural hydrologic cycle for food and reproduction (Pringle et al. 2000; Kingsford 2000). Earlier works have analyzed the impact of dams on natural hydrology by comparing pre and postdam flow regime from gage station data (Thoms and Sheldon 2000; Magilligan and Nislow 2005). This approach is only valid if no substantial change exists in other factors affecting the hydrologic regime between two periods. Impacts of climate variability and other anthropogenic disturbances such as water use, land cover change, and water transfer projects between the two periods should be accounted for (Yang et al. 2008; Chen et al. 2010). Moreover when comparing data from two periods, it is impossible to see how a different damming strategy could have affected the hydrology of that region.
2 Development of GROS
Inflow, release and storage data are each handled by a separate input layer. The three elements of the inflow vector [I_{t}, I_{t−1}, I_{t−2}] are connected to a hidden layer with six nodes. The two elements of the release vector [R_{t−1}, R_{t−2}] are connected to a hidden layer with four nodes, and the storage [S_{t−1}] is connected to a hidden layer with two nodes. Outputs from these layers are connected to the fourth layer with six nodes which are connected to the fifth layer with one node. The sigmoid hyperbolic tangent was selected as the transfer function for all the hidden layers since it provides better accuracy and faster learning speed compared to other sigmoid transfer functions (Adeloye and De Munari 2006; Taormina et al. 2012). The Logsigmoid transfer function was used in the output layer to ensure that the output is always between 0 and 1. Testing with multiple learning algorithms, the Levenberg–Marquardt algorithm had the best performance (Maier and Dandy 2000; Kişi 2007).
List of the dams used in this study
Name of dam  Location  Capacity (km^{3})  Mean flow (m^{3}/s)  Residence time (day)  Purpose  Data period  Source  Training (%)  Cross training (%)  Validation (%) 

Palisades  Idaho  1.5  193.3  90  F–I–H  1970–2000  a  60  20  20 
American Falls  Idaho  2.1  207.1  117  I–F–H–R  1978–1995  a  60  20  20 
Navajo  New Mexico  2.1  38.5  631  I–H–F–R  1962–2002  b  60  20  20 
Trinity  California  3.0  55.3  628  I–H–F  1970–2000  c  60  20  20 
Falcon  TexasMexico  3.3  110.8  345  I–F–H–R  1958–1995  b  60  20  20 
Hungry Horse  Montana  4.3  100.5  495  H–I–F  1970–2000  d  60  20  20 
Oroville  California  4.4  190  268  H–F–I–S  1995–2004  c  60  20  20 
Flaming Gorge  Utah  4.7  64.4  845  I–F–H–S  1962–2002  a  60  20  20 
Sirikit  Thailand  9.5  166.4  661  I–F–H  1980–1996  e  0  0  100 
Grand Coulee  Washington  11.6  2993.5  45  F–I–H  1978–1990  d  60  20  20 
Bhumibol  Thailand  13.5  143.5  1089  I–F–H  1980–1996  e  0  0  100 
Glen Canyon  Arizona  32.3  453.1  825  I–H–R  1970–2002  a  60  20  20 
Data used in this study comes from 12 dams with different operating rules, spanning several orders of magnitude. If the actual data is used directly, the training process will fail as no significant pattern will be detectable between inputs and outputs. To avoid this problem, the data were rescaled to be dimensionless, ranging from 0 to 1. For each dam, flow (m^{3}/s) was converted to daily volume (m^{3}) to be comparable to storage (m^{3}); then all the data for each dam were divided by the maximum capacity of that dam. To use outputs of ANN in a hydrological model, the scaling procedure should be reversed (Appendix 1) by multiplying it by the maximum capacity of the dam to get the daily volume of released water (m^{3}) and then converting it to flow rate (m^{3}/s).
This trained ANN is the core of our GROS. Appendix 1 contains a simplified algorithm that explains how GROS simulates the daily reservoir release. Using GROS in a water balance model (WBM_{plus}) (Wisser et al. 2010b), we isolated reservoir effects from other disturbances (i.e. water withdrawal, flow diversions and climate variability) and studied the impact of dams with various storage sizes and distribution patterns on river system dynamics. We calculated Colwell’s parameters (Colwell 1974) and used the Indicators of hydrological alteration (Richter 1996) and Range of Variability Approach (Richter et al. 1997) to show how dams impact rivers hydrology under different scenarios (Mathews and Richter 2007).
2.1 Significance of ANN inputs
We used an Improved Stepwise method (Gevrey et al. 2003) to identify the importance of inputs used in developing GROS. The change in the sum of square errors (SSE) is calculated when that input and its corresponding weights are removed from the Neural Network. The most important variables are those which cause the largest change in SSE.
Significance of ANN inputs using the improved stepwise method
Experiment  Input variables  SSE  R^{2} 

Control  ANN (I_{t}, I_{t−1,}I_{t−2}, R_{t−1,}R_{t−2}, S_{t−1})  0.102  0.976 
Exclude inflow at t−2  ANN (I_{t}, I_{t−1,}R_{t−1,}R_{t−2}, S_{t−1})  0.106  0.975 
Exclude inflow at t−1  ANN (I_{t}, I_{t−2}, R_{t−1,}R_{t−2}, S_{t−1})  0.114  0.973 
Exclude inflow at t  ANN (I_{t−1,}I_{t−2}, R_{t−1,}R_{t−2}, S_{t−1})  0.119  0.972 
Exclude inflow at t−2 and t−1  ANN (I_{t}, R_{t−1,}R_{t−2}, S_{t−1})  0.126  0.971 
Exclude release at t−2  ANN (I_{t}, I_{t−1,}I_{t−2}, R_{t−1,}S_{t−1})  0.173  0.960 
Exclude release at t−1  ANN (I_{t}, I_{t−1,}I_{t−2}, R_{t−2}, S_{t−1})  0.181  0.959 
Exclude storage  ANN (I_{t}, I_{t−1,}I_{t−2}, R_{t−1,}R_{t−2})  0.188  0.958 
Exclude release  ANN (I_{t}, I_{t−1,}I_{t−2}, S_{t−1})  0.818  0.808 
Exclude inflow  ANN (R_{t−1,}R_{t−2}, S_{t−1})  2.844  0.351 
2.2 Model performance
Simulation results from GROS are significantly more accurate than the outputs from the other two models. On average, GROS reduces the NRMSE (and RMSE) for simulated daily release by 72 % compared to Wisser et al. (2010a) method. For monthly simulated release, the average NRMSE (and RMSE) for Wisser et al. (2010a) and Hanasaki et al. (2006) models are comparable to each other at around 0.65 but the average NRMSE (and RMSE) for GROS is 0.11, nearly 80 % smaller. The average daily Nash efficiency coefficient is 0.86, and Rsquared is 0.85 using GROS.
Accuracy of GROS outputs for simulated release from Bhumibol and Sirikit dams which were excluded from the development of ANN to be used as independent validation datasets, confirms that the ANN used in GROS is not overfitted to its training datasets.
3 Methods for assessing alteration of flow regimes by dams
We used Colwell’s parameters (Colwell 1974), a suite of indicators of hydrological alteration (Richter 1996) and range of variability approach (Richter et al. 1997) to demonstrate how changes in storage size and distribution pattern of dams in a drainage basin alter their hydrological impacts.
Colwell (1974) proposed three parameters of predictability, constancy and contingency to describe patterns of temporal fluctuation in physical and biological phenomena. Predictability is a measure of temporal uncertainty across successive time domains spanning a periodic phenomenon. Maximum predictability occurs when the state of a phenomenon is known with absolute certainty in time. Maximum constancy happens when the state of a phenomenon is always constant. Contingency shows to what degree state of the phenomena depends on time. Values of these parameters range from 0 to 1 (Colwell 1974; Poff and Ward 1989).
Summery of IHA hydrological parameters
IHA statistics group  Parameter number  Hydrological parameters 

Group 1: magnitude of monthly water conditions  1–12  Mean value for each calendar month 
Group 2: magnitude and duration of annual extreme water conditions  13–23  Annual min 1day means 
Annual min 3day means  
Annual min 7day means  
Annual min 30day means  
Annual min 90day means  
Annual max 1day means  
Annual max 3day means  
Annual max 7day means  
Annual max 30day means  
Annual max 90day means  
Base flow index: 7day min flow/mean flow for year  
Group 3: timing of annual extreme water conditions  24 & 25  Julian date of each annual 1day max 
Julian date of each annual 1day min  
Group 4: frequency and duration of high/low pulses  26–29  No. of high pulses each year 
No. of low pulses each year  
Mean duration of high pulses in each year (days)  
Mean duration of low pulses in each year (days)  
Group 5: rate/frequency of water condition changes  30–32  Rise rates: means of all positive differences between consecutive daily values 
Fall rates: means of all negative differences between consecutive daily values  
Number of hydrologic reversals 
We implemented GROS in WBM_{plus} and used various scenarios to understand how variation in size and location of dams in a drainage basin changes their hydrological impact. Size and location of dams in each scenario is allocated based on analysis of national inventory of dams (NID) database (USACE 2013) to be representative of realworld conditions (Appendix 4).
3.1 The significance of water storage capacity of a single dam
Analysis of the NID database (USACE 2013) reveals that real world dams, with different purposes and significantly different storage capacities, may be built on rivers with statistically similar flow conditions (Appendix 4). Therefore, storage capacity is a critical input to reservoir models and models that do not use storage values for simulation of release cannot reliably capture the impact of dam operation. For example Wisser et al. (2010a) reservoir operation model (Eq. 1) does not use water storage in its calculations thus simulated release will be identical for dams with significantly different storage capacities. Hanasaki et al. (2006) use ratio of storage capacity to mean total annual inflow (Eq. 4); but the way it is formulated does not enable the model to respond to change in storage capacity properly.
We assumed five scenarios to show the advantage of GROS compared to other models and to quantify how variation in the size of a dam changes its hydrological impact. In the first scenario, flow was simulated without any dams. For the other scenarios, operation of a dam with 5, 10, 15 and 20 km^{3} storage volume was simulated at the mouth of the drainage basin (Fig. 6, S4).
Dams decrease the range of fluctuations in the magnitude of monthly flows (IHA parameter 1–12). Magnitude, frequency and duration of extreme water conditions were considerably affected by dams operation (IHA parameter 13–23). Dams shifted the date of the occurrence of the minimum and maximum flows by up to 2 months (IHA parameter 24–25). There were no low pulses and the number of high pulses was reduced (IHA parameter 26–29). Because of the flow regulation by dams, the frequency and rate of daily flow change were also significantly reduced (IHA parameter 30–32).
Colwell’s parameters for dams with different storage sizes
Parameters  0 km^{3}  5 km^{3}  10 km^{3}  15 km^{3}  20 km^{3} 

No dam  GROS  
Annual C. V.  0.87  0.82  0.77  0.71  0.63 
Predictability  0.5  0.54  0.58  0.62  0.72 
Constancy  0.36  0.40  0.46  0.51  0.64 
Contingency  0.14  0.13  0.12  0.11  0.08 
3.2 The significance of distribution patterns of water storage capacity of multiple dams in a basin
Working with incomplete reservoir databases that do not list relatively small reservoirs is a concern in reservoirs impacts studies (ICOLD 2011; Lehner et al. 2011). This is especially important as most of the world’s dams are relatively small structures (Rosenberg et al. 2000). Hydrological impacts of individual small dams may be relatively small, but the aggregate effects of numerous small dams may be substantial.
In regional and global studies it is challenging to match reservoirs with the correct rivers in the model due to inaccurate or missing georeferencing information in many databases. To address these issues, it is customary to aggregate the storage capacity of multiple reservoirs in a watershed (Graf 1999; Nilsson et al. 2005) or a grid cell (Vörösmarty et al. 1997; Hanasaki et al. 2010) and assume only one larger reservoir exists on the main river of that watershed or grid cell.
By studying the hydrological impact of different distribution patterns of dams in a drainage basin, we show how the hydrological impact of numerous, dispersed, small dams compares to the impact of a few larger ones. We also investigate if this is a valid approach to aggregate the capacity of smaller dams and instead model a hypothetical larger dam with the same total storage capacity.
Five scenarios to study the impact of dams’ distribution patterns
Scenario  Description 

S0  The base scenario to model flow conditions without dams 
S1  475 Dams with average capacity of 0.04 km^{3} and total capacity of 20 km^{3} 
S2  Storage volume of S1 dams aggregated to HUC 12 subwatersheds. 217 dams with average capacity of 0.09 km^{3} and total capacity of 20 km^{3} 
S3  Storage volume of S1 (or S2) dams aggregated to HUC 8 subbasins. 9 dams with average capacity of 2.2 km^{3} and total capacity of 20 km^{3} 
S4  One large dam with 20 km^{3} capacity located at the mouth of the drainage basin 
Colwell’s parameters for different dam distribution patterns
Parameters  S0  S1  S2  S3  S4 

Annual C. V.  0.87  0.70  0.70  0.65  0.63 
Predictability  0.50  0.60  0.59  0.63  0.72 
Constancy  0.36  0.49  0.48  0.52  0.64 
Contingency  0.14  0.11  0.11  0.11  0.08 
Magnitudes of monthly flows (IHA parameter 1–12) are very similar for scenarios S1–S3. From scenario S1–S4, as the number of dams decreases and their capacity increases, they have a larger impact on magnitude, frequency and duration of extreme water conditions (IHA parameter 13–23). Date of the minimum and maximum flows (IHA parameter 24–25) is approximately the same for scenarios S1–S4 and is not sensitive to the distribution pattern of dams. The same is true for low and high pulses (IHA parameter 26–29). The frequency and rate of flow changes (IHA parameter 30–32) do not show a significant difference between different scenarios.
Colwell’s parameters for scenarios S1 and S2 are similar. Generally as the number of dams decreases and their size increases and they move from small streams to larger ones, their impact on Colwell’s parameters increases.
4 Summary of results and discussion
By using ANN, we developed a new general reservoir operation scheme (GROS) which may be added to daily hydrologic routing models for simulating the releases from dams, in regional and globalscale studies. GROS is specifically designed to provide a broad perspective of the general behavior of dams and improve our understanding of the largescale hydrological impact of dams operation in a relatively easy and efficient way. Comparisons with two other models using a variety of performance metrics verify that using GROS to model the operation of reservoirs can significantly improve the accuracy of the simulation of daily and monthly reservoir release time series.
Analysis of the NID database shows that dams with significantly different storage capacities may be located on rivers with similar flow characteristics. General reservoir models should be tested for their response to changes in storage capacity of dams before being implemented into hydrological models. One advantage of GROS over other models is that it properly responds to changes in storage capacity of dams and therefore can be reasonably used for simulating reservoir releases in regional and global domains where hundreds and thousands of dams with various storage capacities exist.
Using GROS in WBM_{plus} we investigated the practice of aggregating the storage capacity of multiple reservoirs in a watershed and simulating the operation of a hypothetical larger reservoir with the same total storage capacity. For this purpose we aggregated the storage capacity of dams in three scales, HUC 12 subwatersheds (scenario S2), HUC 8 subbasins (scenario S3) and basin level (scenario S4) and compared their hydrological impact on the water flow that leaves the basin. Based on our analysis results, hydrological impact of the original condition (scenario S1) is almost identical to scenario S2 (HUC 12 level aggregation) and very similar to scenario S3 (HUC 8 level aggregation). We conclude that for largescale studies it is generally acceptable to aggregate the capacity of smaller dams and model a hypothetical larger dam with the same total storage capacity; however we suggest limiting the aggregation area to HUC 8 subbasins (average of 3861 km^{2} in this experiment) or a grid cell of approximately 60 km or 30 arc minute resolution to avoid exaggerated results.
Based on analysis of significance of capacity and distribution pattern of dams in the way they alter water flow out of a basin, hydrological parameters are mostly affected by the total storage capacity in the basin rather than the pattern in which storage is distributed in the basin. However, it should be noted that a few large dams have a greater impact on hydrological parameters compared to numerous smaller dams with the same total storage capacity. In our experiment, hydrologic alteration of the flow leaving the basin caused by a single large dam was greater than the combined impact of 475 relatively smaller dams with the same cumulative storage. This means that a single large reservoir is a more effective structure to regulate water compared to numerous smaller reservoirs with the same cumulative water storage capacity. Having only one large dam on the main stream of a basin decreases the level of river fragmentation as tributary branches are not affected by the dam operation. These points should be considered for both cases of building new dams and restoration of rivers by dam removal.
Acknowledgments
We are grateful to Naota Hanasaki for sharing datasets and giving us access to results from his previously published work. The authors wish to express their gratitude to Reza Khanbilvardi, Eugene Z. Stakhiv, Michael Piasecki and Matthew C. Larsen for providing valuable insights. We extend our gratitude to Katherine M. Jensen and the anonymous reviewers for their valuable comments that shaped the final form of this article. This work was supported by the National Science Foundation, Award No. 1049181.
Funding information
Funder Name  Grant Number  Funding Note 

National Science Foundation (US) 

Copyright information
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