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INTRODUCTION
Surface water has a significant impact on life in the arid west. According to Loucks (1976), surface water is the only source of hydroelectric power, water-based recreation, and flow for maintaining fisheries. Surface water also accounts for the majority of the arid west's irrigation and flood damage. Therefore, the first efforts to use mathematical models for water resource planning focused on surface water. This has resulted in the existence of many of methods for mathematically modeling all aspects of surface water.RESERVOIR MODELING
The majority of surface water models deal with some aspect of reservoir operation. These models simulate reservoir operation, provide for real time operation of a reservoir system, and optimize reservoir operation, hydropower output, and flood control. Many programming techniques were also used to create these models. Yeh (1985) provides an excellent review of the various models and modeling techniques used to simulate reservoir operations. A significant amount of research has occurred in the field of reservoir modeling since Yeh (1985) did his review. This later research focused on applying expert systems to real-time reservoir operations (Anibal, et al. 1990), optimization of a system involving multiple reservoirs (Changchit and Terrell 1989; Kuo, et al. 1990), methods to incorporate social objectives into the reservoir models (Flug and Ahmed 1990; Flug, et al. 1990), optimizing hydropower output from a system of reservoirs (Diaz and Fontane 1989; Tejada- Guibert, et al. 1990), and integrating multi-objective planning into reservoir operation (Loganathan and Bhattacharya 1990). There has also been a tendency to adapt large models for use on personal computers (Rockwood, et al. 1988; Eichert and Franke 1988; Mohammadi 1988) and to create models with interactive graphic user interfaces for easier model operation (Ford 1990). This is not a complete list of all the articles that have been written about reservoir system modeling, but indicates the types of articles available.Of the numerous models that represent reservoir operation, two models warrant further discussion. These models represent major advances in the area of reservoir operation modeling.
CVP MODEL
The first model is the California Central Valley Project Power (CVPOWER) program for optimizing hydropower output from the Central Valley Project (CVP). The program optimizes the output from nine reservoirs and ten power plants on three rivers, subject to the water available in the system (Tejada- Guibert, et al. 1990). Other work includes efforts to integrate CVPOWER's optimization with the peak power demands of the local utility Pacific Power and Gas (Crower, et al. 1988; Staschus, et al. 1988). It is believed that the next step with the CVPOWER model will be to make it real-time operational. Real-time operation refers to the ability to model and operate a system at the same time, so that the results from the model change system operation.TVA MODEL
The second program to be discussed is the Tennessee Valley Authority (TVA) reservoir operations model. This model provides a weekly schedule of releases from 40 major dams with hydropower capabilities in two river basins (Shane, et al. 1988). The model tries to optimize flood control and hydropower generation while meeting multiobjective uses at twenty-one of the reservoirs. This is accomplished by performing reservoir operation optimization at 19 of the reservoirs. The optimizations are based on past reservoir operations. Flows into the system are selected by the system operator from 52 years of historical flow data. In addition, the model uses climatic data, current river flow, and current reservoir levels to predict flows into the reservoirs for periods up to one week (Shane and Gilbert 1982). Courtney and Whitlock (1988) describe how remote sensors and micro-computers have replaced the old system of observers and main-frame computers for gathering and processing climatic and flow data. This eliminates the need to manually input the large amounts of data required for model operation which reduces the amount of time needed to run a simulation. Using these remote sensors and micro-computers, the model is currently able to simulate real-time-operation of the system of reservoirs. This model is unique in the large number of reservoirs modeled and the ability to model such a large system on a real time basis.RIVER BASIN MODELING
There are very few models that attempt to represent a complete river system. Wurbs (1991) provides an excellent review of programs for modeling, analyzing, and optimizing reservoir system operations. This review covers many of the water planning models discussed in this chapter.Currently there are five techniques used to model a complete river system: Graphic Information Systems (GIS), water balancing, mass-balancing of inflows and outflows, network analysis, and water accounting. Examples of these types of models are presented and discussed in this chapter. Besides the models presented, numerous models were found that have been developed specifically for a single river or a single river basin. The models discussed either demonstrate one of the five techniques listed above, or a model that is directly related to this project or the state of Wyoming. In addition, a number of California models are described as an example of how a model evolves with the development of new programming techniques.
GIS MODELS
The main application of GIS in water resources has been in representing groundwater quantity and quality (Weghorst, et al. 1991). However, there are instances where GIS has been applied to a surface water system or to an integrated surface water/groundwater system. Weghorst, et al. (1991) describe a GIS model for the Santa Ana River Basin that accounts for the availability of surface water resources for groundwater recharge, but other than that the model's primary purpose is to model groundwater. Johnson (1991) presents a model that graphically represents changes in reservoir levels and the impact of such changes on riparian areas below the reservoir. This, allows the operator to propose different reservoir operating rules and evaluate their impact on environmentally critical reaches of the river downstream form the reservoir. GIS's strong point is its ability to visually display the results of a model run, demonstrating its suitability to information that is spatial in nature.The states of Idaho (Anderson and Shaw 1987) and Oregon (Grainey 1987) have taken the data from their adjudicated water rights and entered it into a GIS system. These databases will allow a water engineer to display water rights and to produce maps of irrigated land.
GIS can not decide who gets water based on a priority date and enormous amounts of data required for GIS. Therefore, it is a good tool for showing the effects of more or less water in a river system and for modeling groundwater quality and quantity. However, it can only assign water on a spatial basis with no value given to priority. This would require taking GIS values and inputting them into a model for a watershed which handles water flow and water rights. Fisher (1989) describes an interface that accepts GIS information and formats the data for input into the Hydrological Simulation Program-Fortran (HSPF) watershed model.
WATER BALANCE MODELS
The Streamflow Synthesis and Reservoir Regulation (SSARR) model developed by the U. S. Corps of Engineers is a water balance model (Rockwood 1982). This is a complete hydrologic model that generates runoff for a drainage basin and predicts streamflow for that basin based on the runoff generated by the model. The runoff is generated from precipitation, humidity, snowmelt, infiltration, soil conditions, groundwater returns, and measured runoff. When combined with an automated data collection system the model is capable of real-time river system simulation (Rockwood, et al. 1988). The model provides for the operational management of reservoirs. A method is also available to account for diversions and irrigation requirements. This model is the first to introduce the concept of assigning flows at the headwaters of rivers and distributing the flow through the system. The model is highly generalized and has been adapted to meet the needs of many of users around the world. However, all inflow and outflows (diversions) are treated as part of the water-balance, and the priority of diversions is not of major interest in the model.MASS BALANCE MODELS
The use of mass-balance for water planning has decreased since mass-balance is not capable of assigning priorities to diversions. Historically, water planning models have relied upon mass-balance to simulate reservoir operation. Two of the earliest reservoir simulation models developed were the HEC-3 and HEC-5 models produced by the U. S. Hydraulic Engineering Center (HEC). The HEC models use mass-balance and flow routing to determine releases from a reservoir or a system of reservoirs. The HEC models are generalized for application to any reservoir system, and have been the prototypes for many models developed for specific river systems.Sigvaldason (1976) describes the development of the ACRES model, (based on HEC-3) for modeling the Trent River basin. The ACRES model has no capacity to account for diversions from the river system. Instead it is used strictly to regulate river operation for hydropower generation and navigation. The model is unique because it was the first to incorporate rule curves and storage zones in the same model.
Most reservoir optimization models only use rule curves to simulate reservoir operations. Rule curves are a set of curves that describe how a reservoir is operated given a measurable reservoir parameter (inflow, demand, current storage, etc... ).
Many simulation models find it easier to account for reservoir water using zones of storage as developed by the U. S. Corps of Engineers. For storage zones, the reservoir is divided into zones of storage and each storage zone has separate rules for reservoir operation. Each storage zone is also attributed to some function, such as flood storage, conservation storage, and/or a buffer zone. Sigvaldason (1976) defined additional storage zones, such as minimum pool level, inactive storage, a spill zone, multiple conservation zones, and a rule curve zone.
Another model that uses mass balance principles is the Colorado River Simulation Model (CRSM) (Schuster 1989). CRSM models water availability and salt concentrations and tries to satisfy the many decrees and compacts that regulate the Colorado River. Only the major features of the river are modeled since the Colorado river is such a large system that covers a massive area. Major rivers and the large reservoirs are the main model parameters. Smaller rivers are modeled as inflows into the Colorado River System. The Colorado River Basin is divided into 25 reaches with inflow points, diversion points, and reservoirs. Inflows are used to model headwaters, return flows, and gains or losses. Diversions are used to model demands on the system. Eighty-five years of natural flow data and salt contents for 29 inflow points are the hydrologic data supplied. The model is operated on a monthly time basis.
CALIFORNIA MODELS
There are two main water projects in the state of California, the State Water Project (SWP) and the CVP (Central Valley Project). Both projects remove water from the Sacramento-San Joaquin Delta (DELTA) for use in the southern part of the state, so the projects are worked in cooperation. The SWP is operated by the California Department of Water Resources and the CVP is operated by the USBR. Each has endeavored to model their project separately. This has resulted in numerous models to simulate these two projects.The first attempt to develop a model involved modifying HEC-3 to handle the complex water sharing agreement between the two agencies at the DELTA. The model assumed a constant demand for the CVP and simulated water available to control structures on the SWP (Chung and Helweg 1985). The model used rule curves and storage zones to model reservoir operations. Demands were given and the model satisfied these demands by using mass balance with no consideration of priority. Storage zones were established comparable to the method used by Sigvaldason (1976) in the ACRES model. A special subroutine was written to model the complex DELTA sharing agreement between the two agencies.
In March 1983, the contract that the SWP had for low- cost power expired (Sabet, et al. 1985). This forced the SWP to optimize its power producing capabilities. The operators of the system developed a program to simulate water deliveries made by the SWP. Network Flow Programming (NFP) was then applied to optimize the release of these deliveries for peak power production and to minimize power use.
NFP consists of representing a river as a system of nodes and links, similar to a piping network. Once the system of nodes and links are established, the user assigns a value or cost to each link. The program then tries to minimize the total cost for the system. Several NFP programs were developed by the Texas Water Board during the late 1970's and early 1980's. NFP requires an enormous amount of data preparation before a simulation is ran.
The operation of the SWP and CVP were incorporated into a single model, the California Department of Water Resources Simulation (DWRSIM) model (Barnes and Chung 1986). This model is based on HEC-3 with many changes incorporated into the program to account for the uniqueness of the system. The model is designed to operate the combined SWP-CVP system on a monthly time basis. The model simulates water supply, recreation, instream-flows, and hydroelectric power generation. The system provides a minimum flow to maintain water quality at the DELTA. The model is structured so that any configuration of reservoirs, diversions, power generating plants, pumping plants, and conveyance facilities can be modeled. Changes in the configuration of the system are accomplished by altering the input data files.
Inflows to the system can come from two sources, historic hydrology from 1922-1978, or a stochastic hydrology model which produces synthetic streamflows.
Reservoirs are defined by elevation versus storage, elevation versus surface area, outlet capacity, and power plant characteristics for power generation. In addition, reservoirs operate to satisfy downstream demands at selected control points. Storage zones are established for each reservoir to assist in assigning priorities for releases. Diversion amounts can remain fixed for each month or vary according to the flow in the system and return flows are restored to the system over a twelve month period. Available water and reservoir storage are accounted for by applying mass-balance to the system.
Chung, et al. (1989) describe how NFP was applied to the DWRSIM model, and Bridgeman, et al. (1988) describe how NFP was applied to the ACRES model. NFP results in more efficient models capable of assigning priorities to system operations. Updating a model for NFP consist of representing the systems by a series of nodes and arcs with "costs" assigned to the arcs. The data preparation is enormous for NFP systems.
In addition to the models discussed above, there are models for simulating or optimizing parts of the SWP. These models may try to model one function of the SWP, or try to improve upon one of the models presented. However, the models presented provide a good representation for modeling the complete CVP and SWP projects.
NETWORK FLOW PROGRAMMING MODELS
Another model that uses NFP is the Central Resource Allocation Model developed for the City of Boulder, Colorado (Brendecke, et al. 1989). The water supply system for the City of Boulder receives water from Boulder Creek and two transbasin diversions. The object of the model is to evaluate additions to the system considering two population projections for the year 2040. The model uses historical data for water rights and water use in the Boulder Creek Basin and the hydrology of Boulder Creek for the years 1950-1985. A model of the Colorado River Basin water rights and hydrology estimates the yield from transbasin diversions to the City of Boulder. The final step of the model is to check the ability of the water treatment facilities and the distribution network to handle the estimated flow capacity needed to supply population projections for the year 2040.The modeling of water rights and streamflow section of the program estimates the flow in Boulder Creek by applying a mass- balance to the system. Costs are then assigned to the various water rights based on priority, and storage facilities are assigned costs based on priority and desired operating procedures. The model then minimizes total cost for the system. Streamflows are also computed in the system to assess the possibility of exchanges with other is water right holders. once again, assigning costs to each link is very tedious.
The next example of NFP is MODSIM3 which is based on the NFP models developed by the Texas Water Board (Labadie, Bode, and Pineda 1986). The City of Fort Collins, Colorado was used to demonstrate MODSIM3 as a water supply model. The model provides monthly or weekly management guidelines for the entire water supply system. It considers formal water rights and informal water exchanges to formulate an optimal operation plan. Inputs to the program include unregulated stream flow, reservoirs and evaporation losses, demands and water rights, conveyance and seepage losses, return flows, imported water, and transbasin diversions. The model is operated similar to the other NFP models discussed and has the same problems.
WATER ACCOUNTING MODELS
The first true water rights model that accounted for the priority of downstream diversions in reservoir operation was the North Platte River Management Model (NPRMM) developed by the USBR (Wei 1977). With the NPRMM, diversions are recognized as having a priority date that must be satisfied. However, the NPRMM is primarily a reservoir simulation model that accounts for water ownership and evaporation at each reservoir. only large diversion projects are considered when determining system demand and priorities are assigned by the user. The model is very specific to the North Platte River since a complex set of reservoir operating rules are programmed into the model. Instead of having inflows to the North Platte, the model assigns reach gains based on return flows and inflows from other streams.In spite of its limitations, the NPRMM introduced some interesting concepts in river management. The NPRMM was the first to store water in the reservoir farthest upstream. The belief is that water can be released from that reservoir to meet any downstream demand. Second, the NPRMM sets an operating range for reservoir storage by declaring a minimum reservoir level and an absolute minimum reservoir level. Finally, water stored in reservoirs is assigned to a project indicating that the project owns the water in stored in the reservoir.
A model that uses many of the concepts introduced by the NPRMM is HYDROSS, also developed by the USBR (1991). HYDROSS could be considered a more improved general version of the NPRMM. HYDROSS is primarily a program for assessing the feasibility of new storage facilities on a river system. Natural stream flows are calculated for each control point on the system, and priorities are assigned to diversions and instream flow rights based on their priority date. Flows to the reservoirs are accomplished after all other rights have been met. The operation of reservoirs are quite complex, considering pool elevation, downstream channel capacity, tailwater elevation, and outlet works capacity to determine releases. Releases can be made for power generation, to meet downstream demands, and to provide flood control. Complex relationships for areacapacity-elevation, flow versus tailwater depth, generator efficiency versus storage and tailwater depth, and seepage versus pool level are possible. Return flows enter the system over a twelve month schedule, and evaporation is removed from the reservoirs. once all the data is input to the model, an accounting of the water available is performed. However, the programs method of calculating a diversion amount is not practical and assigning priorities is very tedious.
The Texas Water Commission has developed a surface water availability model called TAMUWRAP (Texas A&M University Water Resources Allocation Program) (Wurbs and Walls 1989). TAMUWRAP is a generalized computer model for simulating surface water management under a prior appropriation water rights system. Water systems are represented by the following components; control points, basin hydrology, reservoirs, and water rights. Control points are specified to indicate the location of streamflow data, reservoirs, and water rights. The basin hydrology consists of streamflows and reservoir evaporation rates at each control point. A storage capacity versus water surface area relationship is input for each reservoir for use in evaporation computations. Water rights are represented by the following data: control point location, annual diversion amount, reservoir storage capacity, priority number, type of use, and return flow factor (all but the control point location may be set to zero). The model distributes the annual diversion amount over the twelve months of the year, and the priority number is the date that the water right was adjudicated.
From Wurbs and Walls (1986):
The output from the model is used as input into a reservoir optimization model such as HEC-3 or HEC-5.
WIRSOS MODEL
The last model to be discussed is the WIRSOS model (WIRSOS 1985). The WIRSOS model is similar to the TAMUWRAP model. Control points, basin hydrology, reservoirs, and water rights are inputs to the system. However, WIRSOS has a provision for allowing instream flow rights to be modeled and natural water rights are separate from project rights. Project rights are rights that receive all or part of their allocated water from reservoir storage. WIRSOS allows the user to assign inflows to the river system at the headwaters of the river. The model then distributes that water downstream through the system.The WIRSOS model starts by retrieving information from the input data files. The information read is the run data for the simulation, the station data, the delay tables, the reservoir data, and the evaporation data. Next, the model reads in the first two years of runoff data and calculates the non-project releases from the reservoirs. The water accounting is then handled in the main body of the program.
The main body of the model consists of seven functions performed by separate sections of the program. First, the instream flow rights, the reservoir rights, and the diversion rights are read from their data files, and the priority dates for each right is compared. The program is then directed to the proper section to handle the most senior right, then the next most senior right until all rights have been addressed. Six of the sections perform essentially the same function; each section compares the amount of water needed to satisfy the right with the amount of water available. In the case of project rights, the water right is also subject to the availability of water in the reservoir and the flow capacity out of the reservoir. The final section of the main body distributes return flows from diversions back to the river system over a twelve month period. After the main body of the program, evaporation is removed from reservoir storage, and the final reports of water allocation are written.
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