Introduction
Reservoir storage is necessary to regulate highly variable water flows for more constant uses such as municipal and industrial water supply, irrigation, hydroelectric power generation, and navigation. Typically, the water drawn from a reservoir is used at a much slower (and constant) rate than the rate and consistency of the water flowing into the reservoir (see Figure 1). Reservoir modeling has typically been employed to help size reservoir storage capacities, establishing operating policies, evaluating operating plans, administering water allocations, developing management strategies, and real-time operations.
Figure 1 - Inflow and Outflow Hydrograph
The basic requirement for adequate representation of a reservoir is employment of the continuity equation, or conservation of volume over a period of time. This is a function that interacts dynamically with the current state of the reservoir. The foundational equation for conservation of volume is:
The term “Reservoir System Operations” refers to the practice of maintaining and managing a reservoir for multiple purposes, under dynamic conditions. The word “system” is used because of the complexity inherent in the operations of a typical reservoir or network of reservoirs. The state of the reservoir system is constantly in flux, requiring dynamic methods of simulation to evaluate and model them. The term “Reservoir System Operations Model” refers to a computer program used for simulating and optimizing changes in storage, water deliveries, and flood control for one or multiple reservoirs.
Often times, the objective of the reservoir operation is to balance the control of flood storage and maintain reliable water supply. Operational procedures are different for flood events than what are employed under water scarce conditions and therefore, the model must be adapted for these changing conditions.
To better manage potential changes to reservoir operations given uncertainties or changes in circumstances, it is helpful to develop a calibrated simulation model of the reservoir. Some key topics related to reservoir system operations modeling are presented in this paper.
Single pool operations
The main purpose of a reservoir is to control a determined amount of water during some period of time. The amounts that are controlled depend on the properties of the reservoir system, which include components such as the dam, spillway, inflow facility, and outlet works. Figure 2 depicts a simple example of a basic reservoir system. Inflow to a reservoir is typically uncontrolled if the reservoir is on the river. Some dams are built off-stream and water is delivered to the reservoir in a controlled manner. Usually, the controls on inflows to the reservoir are a function of the water level in the reservoir.
Figure 2 - Simple Reservoir Diagram
As the reservoir begins to approach an upper limit, the flow into the reservoir is turned off if the inflows are able to be controlled. For reservoirs that are located on a stream, the inflows cannot be controlled so the reservoir must operate a flood control system that usually includes an outlet works and an uncontrolled spillway. When the outlet works are not able to discharge enough water to lower the reservoir level, then the water will rise above the spillway and water will discharge over the spillway at a flow rate that is dependent on the height of water above the spillway.
Often times the reservoir system operations need to be simulated in a computer model. Typically, a reservoir model must include the major parts of the reservoir system in order to evaluate the reservoir system operations. The fundamental aspect of reservoir modeling is the routing of water. This is done in various ways, depending on the situation and modeling requirements. All routing methods are based on the continuity of volume.
Operation of multiple pools
Typically, reservoirs are operated based on policies that involve multiple pools that are defined to be used for different purposes. An example of a typical multi-pool reservoir is shown in Figure 3, where the reservoir is divided into surcharge, flood control, conservation, and dead pool zones. Often times, the conservation pool is referred to as the multi-use zone because water needs to be conserved in this pool for multiple and often conflicting uses.
The flood control zone is to remain empty except during the times following a flood event upstream of the reservoir. Flood control zones often include a surcharge zone, which is the uncontrolled storage volume above a spillway elevation. Usually, it is not in the interest of reservoir operators to spill water over the spillway because it is uncontrolled and poses a risk to the channel downstream. The flood zone is typically drained in a controlled manner through use of an outlet works with an operated gate or valve.
Figure 3 - Reservoir Pools
The conservation pool is used to store water temporarily for downstream uses such as power generation, recreation, navigation, irrigation, municipal and industrial water supply, and instream flows for habitat. This pool is only drawn down if a request is made in behalf of one of these uses. Often times the top of the conservation pool varies seasonally as shown in the simple example in Figure 4. Typically, the top of the conservation pool rises during the part of year that additional storage is needed to supply water for beneficial use later on. A rise in the conservation pool poses greater risk on the operations of the reservoir because it requires that the flood pool zone is decreased, which gives the reservoir less opportunity to evacuate flood flows before the reservoir level enters the surcharge stage.
Figure 4 - Seasonal Variations in Conservation Pool
Often times, the top of the conservation pool acts as a guide, target, or rule curve for operators. The reservoir is operated in order to try and keep the reservoir level as close as possible to the top of the conservation pool. Obviously, it is critical that the seasonally varying conservation pool limit is first optimized using appropriate methods prior to actual use in the field.
Interaction with groundwater in bank storage
Since the permeability of the bottom of a reservoir tends to decrease over time due to sedimentation, seepage from the reservoir into the surrounding groundwater aquifer is usually ignored. This said, it is possible for groundwater seepage to be a significant factor in overall reservoir losses for some sites and an appropriate method of seepage simulation should be considered. Some reservoirs are intentionally sited in locations were permeability is high as a way to inject water into the ground. This is referred to as aquifer storage recovery and it is becoming more popular as many groundwater aquifers are being mined of their water supply due to increased groundwater pumping.
One of the simplest ways to estimate seepage to groundwater is to develop a function related to reservoir depth. This usually requires the assumption that seepage flows are always a net loss from the reservoir, which is likely case for most sites. However, there are times when you might need to consider bi-directional flux due to seepage outflows and inflows, depending on the elevation of the reservoir pool compared to the surrounding groundwater levels.
Water Supply Allocation
Before discussing allocations of water to multiple users from a reservoir or reservoir system, it is necessary to first introduce the term “firm yield”. This is an important concept used in reservoir system operations. Firm yield is the amount of water that can be continuously delivered from a reservoir with 100% reliability over a historical period-of-record or hypothetical repetition of hydrology. Reliability is usually defined as the ratio of total water supplied by the reservoir (n) to the total amount of water requested (V). The equation looks something like this:
There are other reservoir yields (i.e. secondary yield, etc) that can also be provided for beneficial use but are not 100% reliable. Often times, water from a reservoir is allocated based on various levels of reliability, with the highest priority water demand being given the 100% reliable yield. This is how multiple water users are allocated their supplies: Each successive priority is given an incrementally less reliable reservoir yield.
Another important aspect of water supply allocation is the implementation of a permit system and adjudication of water rights. Usually, priorities are assigned to the various permit/water right holders as a way to simulate the allocation of water supplied to the user. Due to the complexity, a numerical methods formula such as linear programming (LP) might be necessary to solve for the overall firm yield given multiple users with varying priorities. The LP algorithm might also be useful for solving a priority based water allocation for a reservoir and water demand network. A good reference for this type of programming for reservoir operations is the book entitled, “Modeing and Analysis of Reservoir System Operations” by Ralph A. Wurbs, 1996 Prentice Hall PTR.
Network flow programming might also be appropriate as this is an efficient form of LP which can be used to represent a network of nodes and links similar to a reservoir/water demand network. This type of algorithm has been used many times for complex models that require prioritization of water supplies to multiple and conflicting water demands. Other methods include dynamic programming (DP), various non-linear programming techniques, and univariate gradient search.
Multiple reservoirs in series
When evaluating the operations of multiple reservoirs in series, special considerations need to be made. The decision of which reservoir to release water from will affect overall operations of the system. Typically, it is best practice to minimize spills from the upstream reservoirs so that capacity in the downstream reservoirs is preserved and will be able to catch uncontrolled spills from the upper reservoirs and thus protect the downstream river channel. It is also helpful to maximize conservation pool water in the upper reservoirs so that the most users will benefit at any given time. It is easy to release water from an upstream reservoir to a downstream reservoir but not the other way around. Figure 5 shows a simple example reservoir network with two reservoirs in series (Reservoir A and Reservoir B).
Figure 5 - Simple Reservoir Network Example
The objective for reservoirs in parallel should be to balance storage depletions between the two (see Reservoir B and Reservoir C). Under such a reservoir system setup, you might end up with control points to operate Reservoir A located at diversions 1-4 and the other two reservoirs. As discussed in the previous section, more complex systems like this may require an LP or optimization solver approach.
Thank you!
Thank you for reading! I hope you found this information useful. Please feel free to comment. I welcome criticism and suggestions.
References:
Wurbs, Ralph A. "Modeling and Analysis of Reservoir System Operations". 1996 Prentice Hall.
Wurbs, Ralph A. Modeling river/reservoir system management, water allocation, and supply reliability. Journal of Hydrology, Volume 300, Issues 1-4, 10 January 2005, Pages 100-113
Wurbs, Ralph A, Reservoir-System Simulation and Optimization Models. Journal of Water Resources Planning and Management, Vol. 119, No. 4, July/August 1993, pp. 455-472
Yazicigil, Hasan; Houck, Mark H.; Toebes, Gerrit H. Daily operation of a multipurpose reservoir system. WATER RESOURCES RESEARCH, VOL. 19, NO. 1, PP. 1-13, 1983
Yeh, William W-G. Reservoir Management and Operations Models: A State-of-the-Art Review. WATER RESOURCES RESEARCH, VOL. 21, NO. 12, PP. 1797-1818, 1985
Reservoir storage is necessary to regulate highly variable water flows for more constant uses such as municipal and industrial water supply, irrigation, hydroelectric power generation, and navigation. Typically, the water drawn from a reservoir is used at a much slower (and constant) rate than the rate and consistency of the water flowing into the reservoir (see Figure 1). Reservoir modeling has typically been employed to help size reservoir storage capacities, establishing operating policies, evaluating operating plans, administering water allocations, developing management strategies, and real-time operations.
The basic requirement for adequate representation of a reservoir is employment of the continuity equation, or conservation of volume over a period of time. This is a function that interacts dynamically with the current state of the reservoir. The foundational equation for conservation of volume is:
The term “Reservoir System Operations” refers to the practice of maintaining and managing a reservoir for multiple purposes, under dynamic conditions. The word “system” is used because of the complexity inherent in the operations of a typical reservoir or network of reservoirs. The state of the reservoir system is constantly in flux, requiring dynamic methods of simulation to evaluate and model them. The term “Reservoir System Operations Model” refers to a computer program used for simulating and optimizing changes in storage, water deliveries, and flood control for one or multiple reservoirs.
Often times, the objective of the reservoir operation is to balance the control of flood storage and maintain reliable water supply. Operational procedures are different for flood events than what are employed under water scarce conditions and therefore, the model must be adapted for these changing conditions.
To better manage potential changes to reservoir operations given uncertainties or changes in circumstances, it is helpful to develop a calibrated simulation model of the reservoir. Some key topics related to reservoir system operations modeling are presented in this paper.
Single pool operations
The main purpose of a reservoir is to control a determined amount of water during some period of time. The amounts that are controlled depend on the properties of the reservoir system, which include components such as the dam, spillway, inflow facility, and outlet works. Figure 2 depicts a simple example of a basic reservoir system. Inflow to a reservoir is typically uncontrolled if the reservoir is on the river. Some dams are built off-stream and water is delivered to the reservoir in a controlled manner. Usually, the controls on inflows to the reservoir are a function of the water level in the reservoir.
As the reservoir begins to approach an upper limit, the flow into the reservoir is turned off if the inflows are able to be controlled. For reservoirs that are located on a stream, the inflows cannot be controlled so the reservoir must operate a flood control system that usually includes an outlet works and an uncontrolled spillway. When the outlet works are not able to discharge enough water to lower the reservoir level, then the water will rise above the spillway and water will discharge over the spillway at a flow rate that is dependent on the height of water above the spillway.
Often times the reservoir system operations need to be simulated in a computer model. Typically, a reservoir model must include the major parts of the reservoir system in order to evaluate the reservoir system operations. The fundamental aspect of reservoir modeling is the routing of water. This is done in various ways, depending on the situation and modeling requirements. All routing methods are based on the continuity of volume.
Operation of multiple pools
Typically, reservoirs are operated based on policies that involve multiple pools that are defined to be used for different purposes. An example of a typical multi-pool reservoir is shown in Figure 3, where the reservoir is divided into surcharge, flood control, conservation, and dead pool zones. Often times, the conservation pool is referred to as the multi-use zone because water needs to be conserved in this pool for multiple and often conflicting uses.
The flood control zone is to remain empty except during the times following a flood event upstream of the reservoir. Flood control zones often include a surcharge zone, which is the uncontrolled storage volume above a spillway elevation. Usually, it is not in the interest of reservoir operators to spill water over the spillway because it is uncontrolled and poses a risk to the channel downstream. The flood zone is typically drained in a controlled manner through use of an outlet works with an operated gate or valve.
The conservation pool is used to store water temporarily for downstream uses such as power generation, recreation, navigation, irrigation, municipal and industrial water supply, and instream flows for habitat. This pool is only drawn down if a request is made in behalf of one of these uses. Often times the top of the conservation pool varies seasonally as shown in the simple example in Figure 4. Typically, the top of the conservation pool rises during the part of year that additional storage is needed to supply water for beneficial use later on. A rise in the conservation pool poses greater risk on the operations of the reservoir because it requires that the flood pool zone is decreased, which gives the reservoir less opportunity to evacuate flood flows before the reservoir level enters the surcharge stage.
Often times, the top of the conservation pool acts as a guide, target, or rule curve for operators. The reservoir is operated in order to try and keep the reservoir level as close as possible to the top of the conservation pool. Obviously, it is critical that the seasonally varying conservation pool limit is first optimized using appropriate methods prior to actual use in the field.
Interaction with groundwater in bank storage
Since the permeability of the bottom of a reservoir tends to decrease over time due to sedimentation, seepage from the reservoir into the surrounding groundwater aquifer is usually ignored. This said, it is possible for groundwater seepage to be a significant factor in overall reservoir losses for some sites and an appropriate method of seepage simulation should be considered. Some reservoirs are intentionally sited in locations were permeability is high as a way to inject water into the ground. This is referred to as aquifer storage recovery and it is becoming more popular as many groundwater aquifers are being mined of their water supply due to increased groundwater pumping.
One of the simplest ways to estimate seepage to groundwater is to develop a function related to reservoir depth. This usually requires the assumption that seepage flows are always a net loss from the reservoir, which is likely case for most sites. However, there are times when you might need to consider bi-directional flux due to seepage outflows and inflows, depending on the elevation of the reservoir pool compared to the surrounding groundwater levels.
Water Supply Allocation
Before discussing allocations of water to multiple users from a reservoir or reservoir system, it is necessary to first introduce the term “firm yield”. This is an important concept used in reservoir system operations. Firm yield is the amount of water that can be continuously delivered from a reservoir with 100% reliability over a historical period-of-record or hypothetical repetition of hydrology. Reliability is usually defined as the ratio of total water supplied by the reservoir (n) to the total amount of water requested (V). The equation looks something like this:
There are other reservoir yields (i.e. secondary yield, etc) that can also be provided for beneficial use but are not 100% reliable. Often times, water from a reservoir is allocated based on various levels of reliability, with the highest priority water demand being given the 100% reliable yield. This is how multiple water users are allocated their supplies: Each successive priority is given an incrementally less reliable reservoir yield.
Another important aspect of water supply allocation is the implementation of a permit system and adjudication of water rights. Usually, priorities are assigned to the various permit/water right holders as a way to simulate the allocation of water supplied to the user. Due to the complexity, a numerical methods formula such as linear programming (LP) might be necessary to solve for the overall firm yield given multiple users with varying priorities. The LP algorithm might also be useful for solving a priority based water allocation for a reservoir and water demand network. A good reference for this type of programming for reservoir operations is the book entitled, “Modeing and Analysis of Reservoir System Operations” by Ralph A. Wurbs, 1996 Prentice Hall PTR.
Network flow programming might also be appropriate as this is an efficient form of LP which can be used to represent a network of nodes and links similar to a reservoir/water demand network. This type of algorithm has been used many times for complex models that require prioritization of water supplies to multiple and conflicting water demands. Other methods include dynamic programming (DP), various non-linear programming techniques, and univariate gradient search.
Multiple reservoirs in series
When evaluating the operations of multiple reservoirs in series, special considerations need to be made. The decision of which reservoir to release water from will affect overall operations of the system. Typically, it is best practice to minimize spills from the upstream reservoirs so that capacity in the downstream reservoirs is preserved and will be able to catch uncontrolled spills from the upper reservoirs and thus protect the downstream river channel. It is also helpful to maximize conservation pool water in the upper reservoirs so that the most users will benefit at any given time. It is easy to release water from an upstream reservoir to a downstream reservoir but not the other way around. Figure 5 shows a simple example reservoir network with two reservoirs in series (Reservoir A and Reservoir B).
The objective for reservoirs in parallel should be to balance storage depletions between the two (see Reservoir B and Reservoir C). Under such a reservoir system setup, you might end up with control points to operate Reservoir A located at diversions 1-4 and the other two reservoirs. As discussed in the previous section, more complex systems like this may require an LP or optimization solver approach.
Thank you!
Thank you for reading! I hope you found this information useful. Please feel free to comment. I welcome criticism and suggestions.
References:
Wurbs, Ralph A. "Modeling and Analysis of Reservoir System Operations". 1996 Prentice Hall.
Wurbs, Ralph A. Modeling river/reservoir system management, water allocation, and supply reliability. Journal of Hydrology, Volume 300, Issues 1-4, 10 January 2005, Pages 100-113
Wurbs, Ralph A, Reservoir-System Simulation and Optimization Models. Journal of Water Resources Planning and Management, Vol. 119, No. 4, July/August 1993, pp. 455-472
Yazicigil, Hasan; Houck, Mark H.; Toebes, Gerrit H. Daily operation of a multipurpose reservoir system. WATER RESOURCES RESEARCH, VOL. 19, NO. 1, PP. 1-13, 1983
Yeh, William W-G. Reservoir Management and Operations Models: A State-of-the-Art Review. WATER RESOURCES RESEARCH, VOL. 21, NO. 12, PP. 1797-1818, 1985
