By Lynn E. Johnson
INTRODUCTION
The Global Change and Environmental Quality Program at the University of Colorado has fostered a collaborative program on the process of environmental problem-solving. The focus of a team of researchers representing economic, engineering, legal, public administration, and conflict resolution disciplines has been on the water resources problems of the arid Western United States. A near-term emphasis has been a case study of the performance of environmental problem-solving processes during the California drought. The longer term goal is to apply the knowledge gained to other global change and environmental quality problems.
Water supply systems are characterized as having a variety of physical components (e.g., reservoirs) directed to meeting established and projected demands. Changes in global climatic conditions and the impact on hydrological systems have been studied using a scenario approach wherein projected changes in river runoff are examined. For example, Gleick and Nash (1991) in a study of the Colorado River have suggested that (projected) global temperature increases will result in decreased precipitation and river runoffs on the order of 20% or 30%. Similar magnitude effects were projected for California's Sacramento River basin (Gleick, 1986). Moreover, significant changes in the timing and magnitude of runoff were projected for the Upper Colorado River basin with the peak runoff occurring in May rather than June due to less snowfall and earlier melt periods. The climate change scenario studies also indicate a shift in seasonal flow variability -- summer months having a greater frequency of low flows, while winter months have a greater frequency of high flows (Gleick and Nash, 1991).
Although there is considerable uncertainty associated with the climate change scenarios, there are sure to be significant implications for water supply system developments and operations given any change in the hydrological system. It is the purpose of this paper therefore to examine the nature of water supply systems and the means for adjustment to changed hydrological conditions as well as future demand growth.
WATER SUPPLY SYSTEMS AND DROUGHT RESPONSES
Water Supply Systems
From a physical point of view, water supply systems are comprised of their various components -- primarily surface and ground water reservoirs which permit capture and allocation of water over time. Also included are the conveyance channels, pumping stations, and diversion structures which provide capacity for delivery of water to users.
Reservoirs are primary components of water supply systems because they provide the physical capacity and capability for reallocation of water over time -- from periods of freshet to periods of drought. Ground water reservoirs provide a similar capability for water storage and time reallocation, although the groundwater reservoir is more difficult to replenish and make withdrawals. Conveyances of various types -- open canals where gravity flow allows and closed conduits flowing under pressure -- deliver water from sources and diversion structures to the users who in turn distribute it for beneficial purposes. Supply system feasibility and cost are strongly influenced by the geography of the land -- the topography, watershed location and size, climate, and ecology. The amount of storage capacity developed can sustain demands during periods of drought. System interconnections provide the means for water deliveries from locations having surplus to those having deficits.
Water Supply Systems Objectives and Decisions
A water supply system is designed and operated to meet a wide variety of objectives for which it was designed. Water supply systems can be viewed as underspecified systems in that the exact layout and operation of the system can be obtained in a great many ways. The operation of most multiple reservoir systems reflects the existence of most often conflicting, sometimes complementary, multiple purposes served by reservoir storage capacity and the water stored and released from reservoirs. These purposes can include:
Planning for the operation of multiple reservoir systems is complicated by these many purposes, each reflecting different system operation objectives emphasis. It is a multiobjective planning problem. The challenge for the planner/analyst is to provide a capability for formulation of alternative feasible operating policies designed to achieve the various objectives, and to assist in the process of examining tradeoffs between those alternates.
Water supply situations typically have various competing objectives:
Decisions for system development and operations include more than just the quantities of water involved. The water is used for a variety of purposes, the benefits of which may be quantifiable in monetary terms. Many benefits may not be quantifiable in monetary terms but still have important "values" which people support. They may be related directly or indirectly to water quantities occurring at particular points in space and time. Examples of such nonmonetary project benefits include wildlife habitat, recreational activities of many kinds, and aesthetics. In many respects the water resource is central to enhancement of environmental quality and can be managed for those objectives.
Capacity Expansion
Development of a water supply system occurs over time in response to projected and realized demands and involves considerable expense in monetary, environmental and social terms. Water resources planners and systems analysts generally refer to this system development situation as the capacity expansion problem because it involves estimation of capacity requirements sufficient to meet future projected demands. Decisions in this context concern the magnitude and type of future demands, the sources of supply, their size, and the timing of bringing the supply sources on line. There may be considerable uncertainty associated with the demand projections, thus making more difficult the exercise of balancing the costs of expansion (usually under conditions of decreasing unit costs with increased capacity) against some notion of the costs of shortages to be expected in the absence of expansion.
Figure 1. Capacity expansion involves a continuing process of demand estimation and capacity additions.
The graphic (Figure 1) illustrates the classical form of the capacity expansion process over time. Demand, the aggregate result of water user decisions, generally increases over time, reflecting both a growing population and increases in per capita water demand. Conservation practices of various kinds can be effected to reduce per capita water demand and its growth. Water supplies must be targeted to equal or exceed demands at all times, or have an acceptable frequency and magnitude of failure. Supply additions occur in relatively large discrete steps resulting in the periodic introduction of excess capacity, and the progressive reduction of the surplus due to continued growth. In the diagram the built capacity is defined in terms of the "safe yield," a risk-based concept defined below.
System Operations
Reservoir operating procedures are used to guide operations when there are departures from ideal conditions. These operations guides include establishment of target storage levels, downstream releases and/or diversions to be sought during times of need. Given the large number and variety of water use beneficiaries, it seems that ideal conditions seldom, if ever, occur. Thus, operating procedures are used at all times to obtain some mix of performance on various objectives' performance scales. It is typically during periods of drought that non-ideal conditions occur. Low storage and inflow supplies require that decisions be made in the short term for allocation of available supplies. Adjustments to the amounts of water delivered and to whom would be determined by deliberations in the political, legal, and economic arenas and these decisions would be embodied in the operations rules of the system.
Operating rules are the policy instrument used to define operating conditions and procedures to implement when conditions are not ideal. Operating rules are defined, either separately or in combination, as planned or target storage volumes or pool levels, and associate reservoir releases and diversion quantities, usually as a function of the time year. These storage level and release quantity criteria are based on the assumption that the systems' environment and objectives will not change in the immediate future. The purpose of the operating rules is to provide guidance for distributing deviations from target conditions in a manner that minimizes the aggregate perceived hardship to all water using interest groups.
A number of methods have been used to define target conditions and operating policies for nonideal conditions. The simplest type of rules are those that define each reservoir's target storage level for each season of a year. If the reservoir pool level is above the target or desired level, the release rate is increased. Conversely, if the reservoir pool level is below that desired, the release rate is decreased and shortages of deliveries are assigned to water users. By itself, this type of rule provides little or no guidance on what to do if maintaining the target levels becomes impractical. The reservoir operator thus has considerable flexibility when determining the trade-off among storage volumes and discharge deviations from target conditions, and when deciding on which of the multiple reservoirs from which to withdraw water to meet downstream demands.
Of more interest are those rules which define precisely how much water to release at any time of the year from each reservoir, given specific storage volume and inflow conditions. A "multiple zoning" approach has evolved by which the operating rules are defined to include not only storage target levels, but also various storage allocation zones. As illustrated, five general zones can be defined:
Typical storage allocation zones, or operating rules, may vary in magnitude throughout the year and are illustrated in Figure 2. The flood control zone is above curve B. If the stored volume is (projected to be) in the flood control zone, the rule may provide for the maximum possible release if the volume is above curve A, and the maximum possible without causing flood damage when between curves A and B. Reservoir volumes would be kept at below curve B whenever possible for flood control purposes.
Figure 2.a. Multiple zoning is used to guide reservoir operators in making release flow allocations.
Figure 2.b. Example of seasonally varying storage zone boundaries for a multiple-purpose reservoir.
Likewise, operating rules, as defined by the storage zoning approach, may dictate curtailing or reducing the allocation to lower priority uses when storage volume falls below a specified level. Curve C shows the pool elevation below which allocations to only critical or high priority uses would be maintained. Even further restrictions would be required if the pool level were to fall below curve D. For multiple reservoir systems, similar rules defining different release zones are used to assist operators in meeting various water use needs with minimum disruption. Multiple subzones or levels within the conservation zone are established as a means for balancing the operation of a group of reservoirs. Storage levels would be kept within the same subzone in each reservoir and increasing degrees of curtailment of withdrawals would be effected as storage levels drop into the lower zones. These subzone storage volumes can each be associated (explicitly or implicitly) with a failure probability or risk level.
The terms "firm," "safe," "surplus," and "secondary" are categorical references to the reliability of supplies delivered from storage. For example, firm yields would be those which are delivered with highest reliability such as no failures of water deliveries over the historical inflow record. If defined more rigorously, the reliability of firm yields may be 98 percent. Surplus yields may have lesser reliabilities of 95 percent or 90 percent.
Other types of components of operating rules include those which establish flow ranges for the channels downstream as a function of upstream storage. Conditional rules define reservoir releases not only as a function of existing storage and season of year, but also as a function of expected natural inflows into the reservoir. Such inflow forecasts may be based on the winter snow pack and/or the recent and expected precipitation.
Adjustments of System Capacity and Operating Policies
It seems that none of these adjustments -- short or long term -- are without conflict. The problem is fundamentally one of relative scarcity and the allocation of scarce supplies -- all in the face of considerable uncertainty. Many aspects of these short and long-term supply-side drought adjustment actions can be aided by the use of various technical metrics and systems analysis methods. Over the past several decades, increasing attention has been directed to the use of mathematical simulation and optimization models for articulating development scheduling and release policies of multiple reservoir systems. In some cases, with only small improvements in systems operation, increased yields and millions of dollars of additional annual benefits can be realized. This appreciation has been coupled with a substantial research effort and has led to continuing developments in the conceptual thinking and mathematical formulations of a variety of models.
However, in spite of these research efforts, there remains no generally accepted method by which to derive acceptable water supply system development schedules and operating policies for multi-purpose, multiple reservoir systems. The problem is two-fold, involving:
DROUGHT TECHNICAL METRICS AND ANALYSES
Drought Statistics
Technical information on hydrologic conditions relates to both the natural and manageable components of the supply system. Metrics for the natural hydrologic conditions derive from historical measurements and statistical analyses of these (see for example, Haan, 1986). Probabilistic characterizations of precipitation and runoff provide a fundamental metric of water supply reliabilities. It is the variability of hydrologic inputs, their stochastic nature that drives the risk element in water resources systems. Examples of common statistical hydrologic metrics include: mean annual flow, seven day-ten year low flow, and the ninety-five percent duration low flow. It is also common that risk-related metrics be derived directly from the historical record (e.g., the "drought of record").
It is of obvious benefit that the historical records be as long as possible in order to better appreciate the magnitude and frequency of hydrologic extremes. Here the use of tree ring data has proven valuable in extending the length of hydrologic record (Gleick and Nash, 1991). Drawbacks of testing designs against only the historical flows have been emphasized (Loucks, 1981), particularly for systems with large amounts of overyear storage. Synthesis of streamflows statistically equivalent to observed hydrologic records has been used by hydrologists for many years (Bras and Rodriguez-Iturbe, 1985). Although theoretically attractive and proven useful in many instances, stochastic hydrology has found limited applications in central decision contexts because of parameter uncertainty and credibility issues. For these reasons the historical record is most often used for testing designs and operating rules.
Drought statistics of the sort noted can be valid indicators of the amounts of water available in the future provided the climate remains stable. That is, if the climatic conditions which gave rise to the historical flows were to change, then the statistics would become "nonstationary" and their value as indicators of future conditions would become less reliable.
Forecasts of unregulated flows are typically seasonal in nature. Although there is active research on climatic predictors of hydrologic conditions, it cannot be said that methods are operationally useful beyond a period of a few months. Within the few month period, observed snow pack and snow moisture data coupled with knowledge of expected precipitation amounts can provide operationally useful forecasts. The forecast methods include various types of conceptual mathematical simulation models (e.g., NWS, 1987) or regression models based on basin conditions (e.g., Schaake and Peck, 1987; Stedinger, 1990). Remote sensing of snow pack, soil moisture, and other hydrologic data and GIS-type data management and analysis techniques are becoming increasingly useful for forecasts modeling. These methods provide capability for estimating the probability of filling a reservoir given initial storage conditions.
Regulation of natural flows through reservoir storage provides the means to deliver water in periods of low inflows. Depending on the magnitude of storage relative to inflows, water of constant quantity can be delivered through all periods. The so-called "safe" or "firm" yield is that amount which can be delivered during the "design drought" condition. Deliveries in excess of the firm yield are termed "secondary" or "surplus" yields. Distinct levels of risk may be associated with the terms "firm" and "secondary." Depending on how the drought condition is defined, a firm yield would have a high reliability level, on the order of 98 percent. That is, the firm yield would be deliverable on average in 98 percent of the years. Secondary yields would be deliverable a lesser percentage of time and have a lower reliability level, say 90 percent or less.
These reliability levels are decisionable metrics. They are also specific information items which can become part of the operation rules and water delivery contracts these rules serve. Although traditionally, the reliability levels have been implicit in the planning and design process, perhaps assigned under the aegis of engineering judgment, more recently it has become recognized that the reliability levels associated with water deliveries ought to be determined more explicitly, and that tradeoffs between yield and reliability be accounted for.
A common metric for assessing the overall reliability of a water supply system is the ratio of system capacity to demand (existing and projected). This was the approach taken by Russell, Arey and Kates (1970) and has proven useful in assessing the requirements and staging of drought adjustment actions.
Simulation and Optimization Models
Various analytical methods, or modeling approaches, have been developed to identify the magnitude and reliability of yields obtainable from alternate system configuration, capacity and operational schemes. Two basic categories of modeling approaches are simulation and optimization. A simulation model consists essentially of a sequence of mathematical and logical statements describing operation of the river basin system over time using a given sequence of streamflows. By trial and error or possibly some search procedure, a system size, configuration, or set of operating rules is found that best achieves the desired objectives. The simulation approach has traditionally been used and continues to be the primary method to investigate alternatives, but the large number of simulation runs required can be time consuming and expensive.
While simulation methods are effective methods for evaluating and refining alternative reservoir system configurations and operating procedures, they are not a very effective means for choosing or defining the "best" policies. For this purpose, optimization models have proven effective, if not for finding the best solution, at least for eliminating the worst solutions from further consideration. The analysis of a complex water resources system may involve thousands of decision variables and constraints. Once the objectives and constraints have been (mathematically) determined, most problems lend themselves to solution techniques developed in the fields of operations research and management. The choice of methods depends on the characteristics of the reservoir system being considered, on the availability of data, and on the objectives and constraints specified. In general, the available methods can be classified as follows (Yeh, 1985):
It has become common to have optimization schemes embedded in the simulation model to perform certain degrees of optimization. It is desirable for the simulation model to have some capability for self-optimization to reduce the amount of computations. Further strategies for combined use of optimization and simulation have been developed (e.g., Johnson, 1980). Here, the optimization performs a screening function on the range of alternates, the reduced set which can then be examined using more detailed simulation models. Thus, the distinction between simulation and optimization can be obscured.
Multiobjective programming methods which involve the exploration of the non-dominated set of policy alternatives have been the subject of considerable research over the past two decades (e.g., Cohon and Marks, 1975; Cohon, 1978). However, as a practical tool the value of the optimization process is rather limited. This is because specification of a community welfare function presupposes complete information concerning all possible combinations of actions, the relative tradeoffs between all actions, and all constraints prevailing in the decision-making context. Further consideration of the multiple objective problem is presented below in the discussion of strategies for model use.
STRATEGIES FOR MODEL USE
It has been observed that the full benefits of mathematical modeling have not been realized. Eichert (1979) pointed out that from a practitioner's point of view mathematical programming techniques have thus far not proven to be widely useful because of the complexities of water resources systems and noncommensurable objectives in water resources management. Yeh (1985) observed that reservoir operators are reluctant to use optimization models for various reasons: (1) the reservoir operations decision makers have not been involved in development of the computer model and thus are not comfortable in using it; and (2) there are institutional constraints that impede user interactions. Rogers and Fiering (1986) echo this view noting that institutional factors (e.g., single function planning agency) limit the applicability of models and inclusion of the spectrum of objectives and interest groups.
This planning strategy aspect relates to the manner in which the analysis instruments (i.e., the computer models) are manipulated to facilitate bargaining among decision makers. Policy objectives can be operationalized as fixed targets to be strived for or as arguments of some community welfare function to be optimized. The optimizing approach is based on the assumption that different objectives can be expressed in a common denominator by means of tradeoffs (or marginal rates of substitution along indifference curves) so that the loss in one objective can be evaluated against the gain in another. This idea of compensatory changes underlies both the classical economic utility theory (Henderson and Quandt, 1971) and the traditional benefit-cost analysis (Howe, 1971).
Various approaches for addressing multiobjective planning problems were summarized by Cohon (1978) and include: (1) generating methods; (2) preference-oriented methods; and (3) conflict resolution methods. The first two methods do not explicitly consider the political dynamics of the problem.
Generating techniques emphasize the development of information and presentation to a decision maker in a manner that allows the range of choice and tradeoffs among objectives to be understood. The information flow is bottom-up, and preferences need not be articulated prior to development of the noninferior set, which can be obtained using various optimization techniques. Preferences are implicitly applied in choosing a "best compromise" solution.
Preference-oriented methods require that decision makers articulate their preferences in advance of analysis. Various iterative or noniterative techniques are used to solicit and capsulize preference statements, including multiattribute utility functions (Keeney and Raiffa, 1976), goal programming, and the so-called step method (Johnson and Loucks, 1980). Mathematical definition of preference functions are required for use in analytical optimization models. However, as a practical matter the shape of the preference curves are difficult, if not impossible, to define. Moreover, they differ for each individual, and for a group of people having multiple interests there would be no single preference curve.
As noted above, planning for water supply system capacity expansions and operations is a situation involving multiple purposes and multiple objectives, many of which are conflicting. Evaluating reservoir operating policies necessarily involves the computer because it permits simulation of reservoir performance per alternate water management plans -- plans which are complex and could not be evaluated otherwise. These planning efforts can become quite complex given that a variety of groups have an interest in the outcome. Furthermore, planning efforts which involve the use of computer models are often hampered by a lack of communication between the various groups of technical and nontechnical individuals involved in planning and decision making.
To identify an acceptable balance between objectives, the planning and decision process for defining reservoir operating policies should inform concerned interest groups and individuals of the physical limits and opportunities which exist as well as provide opportunity for incorporating their judgements and preference statements. The problem is made more difficult by the fact that measures of reservoir benefits vis-a-vis one objective versus another are often expressed in noncommensurate terms and cannot be directly compared. For example, the value of reservoir water for irrigation uses can be quantitized in monetary terms, whereas other recreation and environmental quality objectives are difficult to express in terms of money. Sometimes, individual judgements by involved decision makers -- perhaps skewed by their understanding of the reservoir system and personal preferences -- are the way a selection is made.
Model Forums and Institutional Contexts
Modeling of water resource systems occurs in some institutional context, and the degree of integration of model-generated information into decisions is considered to be in part a function of that context. The most straightforward instance of model integration is that of the reservoir operations agency. Here, staff are developed to generate and apply systems analysis techniques to the water system at hand. These models are used by the staff and through their interpretation, results are prepared and reported by means of the administrative hierarchy.
A closely prescribed modeling situation generally occurs with legal forums associated with water rights adjudications. Here, the procedures of disclosure are applied to all aspects of the modeling -- the data, methods, and results. This occurs through expert testimony and is characterized as being an adversarial process. Some (e.g., King, 1991) would characterize the legal forums as being a "battle of the models" where competing interest groups present their particular modeled views of reality.
Computer-Aided Planning
In recent years there has been a steady increase in awareness that modeling activities must be conducted in an iterative, open, and understandable environment to promote credibility and trust. Johnson (1986) described the structure of a decision-support system and the process for its use by water managers as an aid for making implementation and operational decisions. Visual interactive methods which give the user an appropriate role in controlling prescriptive inputs, the model database, calibration, application, and output display changes the role of modeling from a product-oriented function to a process-oriented function. With the process-oriented approach, modeling and model use are the important elements of a learning process which in turn facilitates policy formulation and decision-making.
Conflict resolution modeling methods find application because these methods facilitate understanding of the physical limits of the system, provide opportunity for incorporation of decision maker preference information, communication of feedback on system response to be expected with a particular reservoir operating policy, and negotiation amongst interest groups. Examples of conflict resolution modeling methods include the CAP (computer-aided planning) approach described by Johnson (1990) and the CAN (computer-aided negotiation) approach described by Sheer, et al. (1989) and Randall, et al. (1990).
Johnson (1990) described the process of CAP and how these interactive systems analysis and display tools could be integrated with the public involvement program. CAP is directed to allowing incorporation of people's judgement into the planning and analysis process. Because the computer and the analyst have no special capacity for judging preference for one performance outcome versus another, a public involvement program linked closely with the computer modeling activity is appropriate. Various forums for public involvement are involved, such as workshops and public meetings, during which interactive computing can occur with computer graphic displays of reservoir performance. An important outcome of the public involvement activities is statements of objectives (or desires) and identification of assessment criteria by participating individuals. Assessment criteria are the factors against which performance is measured. Solicitation of the criteria, and incorporation and display of "their" criteria in the valuation module of the computer model demonstrates that the modeling activity is responsive to the needs and opinions of the participants.
Interactive computation of specified operating policies can be conducted quickly in response to questions at policy exploration work sessions and public meetings. The concept of visual interactive modeling (e.g., Bell, 1985) implies an ease of model validation by the decision maker -- thus engendering confidence in the model. Testing of the model in an interactive way, and obtaining rapid feedback allows for learning and exploration, as well as validation. A person who can question the computer analysis, and obtain appropriate responses will develop a sense of control and ownership. The computer mystique is replaced by a useful tool responsive to the perceptions and needs of the planning participant.
Perhaps the most noteworthy example was the Potomac River Basin studies during the late 1970s (Palmer, et al., 1980). The Potomac does not have adequate unregulated minimum flows for the water supply of the Washington area. Development of a computer-based model which related anticipated flows served as the basis for development of a consensus among water users to modify reservoir operations for the common good. As a result the minimum flow was enhanced 30 percent without any additional dam construction. The political nature of the problem posed additional engineering challenges. Not only was it necessary to develop new solutions, techniques had to be developed to demonstrate, beyond question, the feasibility of coordinated regional operations and the impact they would have on each utility, the environment, and the regional economy. This was accomplished using simulation and gaming techniques, the process of which identified objectives and constraints not articulated prior to the exercises. The Potomac River case study is held up as an example of the benefits obtainable from an objective, open process which leads to education of all parties, improved management, and institutional reforms.
CASE STUDY - CALIFORNIA DROUGHT RESEARCH PROJECT
California, selected as a case study, has a rich array of computer models developed to represent various components of their complex water supply system. The primary water systems include the State Water Project (SWP) and the Central Valley Project (CVP). The SWP is a state project and the CVP is a federal project. An overview of the computer models developed for these systems is presented with a review of the models' use following.
Computer Models and Programs
The California State Water Project (Figure 3a) consists of a series of reservoirs linked by rivers, pumping plants, canals, tunnels, and generating plants and is operated by the California Department of Water Resources. The Department provides water to municipal and agricultural users, and manages its electrical loads and resources. A large-scale simulation/optimization model provides schedules for the operation of water and power for the California State Water Project (SWP) (Sabet and Coe, 1986; Coe and Rankin, 1988). The model performs hydraulic and electrical computations leading to optimal operation of the entire system given the defined constraints. It consists of hydraulic network programming components to meet the storage objectives at all of the reservoirs, a linear programming component to determine the schedules at pumping and generating plants, an electrical network programming component to balance electrical loads and resources, and a number of other simulation components. It operates on yearly, weekly, and daily bases. It is primarily used for real-time operation of the SWP and can provide hourly detailed schedules which are implemented by the SWP staff using the computer system. The model is also used to assess the effectiveness of possible expansion to the system.
Figure 3a. California State Water Project.
Figure 3b. California Central Valley Project.
The Central Valley Project (CVP) was authorized by Congress in the mid-1930s, and initial operation started with the closure of Shasta Dam in 1944 (Coleman, 1981; Crowther, et al., 1988). A schematic of the system is shown in Figure 3b. By the mid-1960s nearly 5 million acre feet (MAF) was being delivered annually and two-thirds of the project was considered complete. Specific Standard Operating Procedures (SOPs) and Design Operators' Criteria (DOCs) have been prepared for each facility, and numerous contracts and agreements have been developed with water and power users as well as with the California Fish and Game Department and the National Park Service. Although initially not well documented due to generally surplus runoff, a large number of agreements have been established and renegotiated in the intervening years.
These policies have become integral to the many computer models developed for the CVP. Six models have been developed to provide CVP operators with tools to improve the managerial decision-making process.
There has been continued development and evolution of these models so the above summary may be outdated at present.
Model Uses for Decision Support
The California water supply system computer models are used continuously to generate information relevant to short-term operations and long-term capacity expansion. For the State Water Project model development and use is centered in two departments for planning and system operations. Considerable staffing and continued development work are applied to the models and interpretation of the results. It seems that the models are a primary means for generating decision-relevant information for a wide variety of system operations.
Simulation models are used to conduct storage-yield frequency analyses. For example, Figure 4a shows results of California State Water Project supply capability obtained with existing facilities and planned facilities (California DWR, undated). These results obtain from a simulation model using the historical unregulated inflows. The next figure (Figure 4b) presents these same results in a statistical format relevant to reliability assessment. For example, from Figure 4b, one can deduce that the 90 percent reliable yield is increased from 2 MAF to 2.6 MAF with the planned system additions.
Figure 4a. Computer simulation results of existing and planned supply.
Figure 4b. Frequency representation of computer simulation results.
The bulletins of the California Department of Water Resources provide annual and special reports on water resource conditions (existing and projected) (California DWR, 1990). For example, the primary measure of the SWP's delivery capability is founded on the concept of "firm yield" operation and this concept is obtained through the computer model. Defined in the water supply contract as "minimum project yield," firm yield is the dependable annual water supply that can be made available without exceeding allowable reductions in agricultural deliveries during extended drought periods. The firm yield of existing is about 2.4 MAF per year, based on the historical dry period from 1928 through 1934.
The concept of firm yield based on the historic worst drought conditions has been criticized in recent years (e.g., Meyer-Zangri, Inc., 1982). The contention is that the natural flows obtained during the 1928-34 period have a return frequency in excess of once in 400 years. Thus, the firm yields based on this criteria are effectively higher than 99 percent reliable. In response to these criticisms and through negotiation with water users, the DWR and the SWP contractors have been examining alternative operational strategies to improve the existing facilities average annual delivery capabilities. Particular attention has been directed to methods outside the conventional firm yield procedures, involving a calculated risk of reduced deliveries in some years.
Riebsame (1988) described the changes in the rule curves resulting from the negotiation process. The 1978 rule curve required maintenance of large carry-over storages to increase the likelihood of meeting subsequent year water requests, but decreases the amount delivered in the current year. Using 1980 facilities, the DWR estimated they could deliver 2.96 billion cubic meters (BCM) 90 percent of the time, and only 1.36 BCM 99 percent of the time (California DWR, 1983). The assessments noted above included examination of capacity expansions to increase the overall and firm supply. The perception emerged (Riebsame, 1988) that unnecessary delivery shortages are worse that than simply running out of water further into a multi-year drought. A new operations policy was developed which sought to maintain full contract deliveries early in the drought by drawing more heavily on stored waters, thus accepting greater risk of failing to meet demands in later years. New SWP rule curves were designed to deliver more water at slightly lower reliability levels.
In 1989, the Rule Curve was retitled the "Water Delivery Risk Analysis" (WDRA) and is used to determine the amount of water deliveries that can be approved each year (California DWR, 1989). The WDRA defines the relationship between forecasted water supply at a certain probability level for the current water year, current carryover storage, target end-of-year carryover storage, and total approvable SWP deliveries for the calendar year. The WDRA objective is to ensure that enough carryover storage will be maintained to meet next year's water quality protection requirements in the Delta and to supply at least an emergency level of deliveries next year, without the need for extraordinary measures. Updating of current conditions and generation of new forecasts are conducted on a monthly basis. Examples of the operational alternates generated for both the CVP and SWP are summarized in the following tables.
As another example of model use, Randall, et al. (1988) conducted computer-aided negotiation (CAN) exercises for the Stanislaus River to help negotiate fishery flow agreements. The conflict over water use involves the fisheries interests (i.e., the state and federal fish and game agencies) in wanting larger reservoir releases to maintain the salmon fishery below the dam, Also, there is concern that too little water is being released into the southern portion of the Delta causing a degradation of water quality. A CAN session with the fisheries and system operations agency staff resulted in identification of alternate operating policies which can sustain the fisheries yet, not negatively impact water users. It seems that the life cycle of the salmon is such that one dry year, or two dry years in succession, would not have disastrous effects on the fishery. The focus of the fishery interests shifted from getting the full allotment every year to getting the full amount every second, third, or even fourth year.
CONCLUSIONS AND RECOMMENDATIONS
This paper has reviewed the nature of technical metrics associated with water supply decision making. Applications of systems analysis techniques for simulation and optimization of reservoir operations to meet competing demands and in the face of climate change scenarios are shown to be widely used and necessary. Only through use of computerized techniques can the complexity and range of choice be represented.
However, the nature of use of computer models is changing due to identified shortcomings in integrating model information into decision making processes. The problem is shown to have two primary aspects relating to: (1) the models themselves and our ability to represent the plethora of physical/chemical/biological components of the systems; and (2) how the models are used, by whom and in what institutional context.
The first aspect on mathematical representations involves continued development of accurate models which represent as much as possible the physical components and processes of the system. It remains a challenge, but successful applications have been demonstrated and this is now considered the state-of-the-art. Beyond the mathematics we are making advances in how data are portrayed (i.e., visualization) so that a wider audience might understand the models and the systems they represent. However, it remains an imposing and perhaps impossible task to capture all aspects of a decision situation in a mathematical model. In real situations the degree of complexity can be humbling to the analyst who must maintain some perspective that there remain aspects of the situation (e.g., non-economic impacts) which cannot readily be captured by the models.
Regarding model use, competing interest groups are seeking full disclosure of technical information and access to models and data so that they can examine model validity and make their own selections of inputs and performance controls. Some experience has been gained in using the models in alternate ways and forums. It is this area where advancements can be sought in order to take maximum advantage of the information which the models do generate. Computer-aided planning, computer-aided negotiation and gaming simulations hold promise for increasing the forums for communication, providing for "defensible" decisions, and perhaps for identification of new "compromise" alternates.
The technical metrics area is one of rich opportunities for applied research, particularly in how the models are and can be used to facilitate more informed decision making. Indeed, the California situation with the drought apparently continuing could be the context in which such research could be accomplished.
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