Models and Realities of Reservoir Operation

Social preferences for uses of water invariably change with time, and the purposes and priorities for which existing reservoirs are operated may likewise change. Moreover, because new reservoir construction in the United States has not kept pace with growing demands on water and storage, the need for improved operational efficiency has never been greater. Operational models have a long history of success both in planning and real-time decision support applications, disclosing opportunities for conjunctive use of reservoirs and efficient allocations of water and storage. Since the late 1950s, for example, the Streamflow Synthesis and Reservoir Regulation (SSARR) model has provided invaluable decision support for planning and real-time control of the Columbia River Basin. For nearly three decades the Corps of Engineers HEC-5 model was the most widely applied in the world for all-purpose reservoir system operational planning, its success spawning a new generation of integrated tools designed for shared-vision applications.

Occasionally, performance and efficiency gains promised by models used for operational planning may fail to materialize in practice, with consequences ranging from missed opportunities for water management policy consensus to public water supplies placed at risk, as happened in Atlanta in 2007. Models are here to stay, but their practical utility is best assured by appreciation of their intrinsic limitations, care in preparation of their input data, and circumspection in interpretation of their results.

The proposition that all models at some level simplify reality predates computer models, a by-product of the fall of mathematical formalism beginning in 1931 with Czech logician Kurt Gödel’s incompleteness theorems. To paraphrase the eminent statistician George Box, “Essentially, all models are wrong, but some are useful.” For models to be useful, however, users must understand their limitations and temper expectations accordingly—take them with a grain of salt, so to speak. This can present a challenge with complex models of complex systems.

Numerical models of complex physical phenomena, such as flow of water or forces on structures, approximate solutions to differential equations for which no analytical solutions presently exist. Unknown, unmeasured, and uncertain quantities are often lumped into empirical coefficients, which may be adjusted to ensure the solution is “conservative” relative to its intended use or to provide an added margin of safety in design. For models that simulate interdependent hydraulic, hydrologic, and human decision-making aspects of reservoir operation, however, conservatism may be a slippery concept to define, and instances of clear-cut operational “failure” too infrequent for reliable estimation of appropriate factors of safety. It is easy to imagine, for example, why sound flood management practice, seeking to minimize water in storage for protection against future floods, would not be conservative when applied to drought management strategies seeking to maximize water in storage to augment reliable water supply.

Continuity is normally the most easily satisfied requirement of reservoir system models. Even so, seepage, leakage, inaccurate reservoir outlet works and river rating curves, evapotranspiration, and unaccounted water diversions and returns can introduce significant errors to hydrologic time-series inputs to reservoir models. Analysis of model sensitivity to these uncertainties may be complicated by extraneous factors, and the potential for bias depends upon how errors accumulate in simulated utilization of system storage. Operational models are also called upon to replicate patterns and timing of reservoir release decisions realistically enough for design, operational planning, and/or real-time water control decision support. This is a much more difficult proposition than mere mass balance, given that reservoir operators (unlike models) know that they do not have perfect information and consequently temper release decisions using estimates, forecasts, hedging, and plain intuition. In economics, imperfect information and uncertainty increase transaction costs and thus tend to prevent optimal outcomes (Williamson 2006); the same applies to reservoir operation.

Operational models simulate “perfect” rule-compliant releases given well-defined rules and accurate information on the current state of the system. Models may even accommodate uncertainty with probabilistic inputs, but bias is another matter. Sequential simulation may fail to disclose, for example, the range of possible outcomes when hydroclimatic trends and variability are not adequately represented in time-series inputs. Climate change considerations aside, periods of record of historical system inflows may not be sufficient to capture hydrologic extremes (high and low flows) of long-run cycles, a phenomenon known as trend-dependent autocorrelation. In such cases, models may understate conservation or flood storage required to reliably meet operational objectives. Inadequate period of hydrologic record was identified as a contributing factor in contemporary findings of overallocated water and conservation storage in the Colorado River Basin, and in predictions of probable future water shortages (NRC 2007).

Models may also be biased if input data errors are one-sided, with potential cumulative effects on storage utilization. Reservoir stage and streamflow recording gages, outlet works rating curves, outdated turbine/generator performance characteristics, and reservoir elevation-area-capacity curves are examples of nonrandom input errors that can cause models to consistently under- or overestimate reservoir releases. Other important sources of bias are the operating rules themselves and the manner in which they are replicated in models. Simplistic representation of complex operating rules may implicitly embody unrealistic assumptions concerning (1) operator capabilities for real-time data acquisition and interpretation; (2) accuracy of hydrologic and hydraulic model inputs; (3) physical capabilities of the system for precise flow regulation; and (4) operator hedging and prioritization of operational objectives.

Simulations that gloss over important details and operational constraints are not likely to provide realistic predictions of reservoir yield and storage utilization. Models applied to evaluation of proposed new operating rules in the Apalachicola-Chattahoochee-Flint (ACF) River Basin draining portions of Georgia, Alabama, and Florida exhibited many of the above-described sources of bias. The models, driven by $63\text{years}$ of historical naturalized inflows and measured consumptive water uses, failed to predict the rapid drawdown of system storage to record lows in 2006 and 2007, despite the fact that drought conditions experienced during these two years did not necessarily redefine the system critical period—the multimonth period when the limitation of system inflow is most critical with respect to demands and usable storage.

The question naturally arises as to which types of models might be inherently better, i.e., more realistic, than others. Unfortunately, there is no standard response, except to say that the more details (hydrologic, physical system, operator performance) considered, the more accurate the simulation. Model utility is not merely a function of realism alone, however, but of how realistically results are interpreted in view of the model’s limitations. Expert modelers may be well equipped to understand and interpret models correctly, but may not effectively communicate this information to nontechnical stakeholders and decisionmakers. Moreover, as planning has become more participatory and models evolved to become more versatile and “user friendly,” their inner workings, inputs, and outputs may paradoxically have become less understandable and accessible—even by experts—than the legacy models they replace (Rovak 2008).

Operational models have been broadly categorized (Wurbs 1996) as descriptive simulation, prescriptive optimization, and hybrid simulation/optimization models involving elements of both. These are briefly described as follows:

An emerging class of models employs evolutionary computation methods, including heuristic searches and genetic algorithms, to find approximate solutions to optimization problems. Such techniques avoid some of the difficulties associated with optimization models, including rigorous mathematical formulation of objectives and constraints, and provide additional capabilities for dynamic adaptation of operating rules to changing state-dependent or externally imposed conditions. However, models of this type may not necessarily incorporate all of the decision variables involved in real-world reservoir system operation.

Each of the previously described model types has strengths and weaknesses with respect to specific operational planning and real-time water control applications. Descriptive simulation models are most useful for detailed analysis and evaluation of predefined operating rules, but less useful in systematic searches for efficient operational alternatives. The practical utility of prescriptive optimization models depends on (1) the degree to which complex real-world operational objectives and constraints can be represented by mathematical equations; and (2) how closely the inferred operating rules mimic the optimal solution when input to more detailed sequential simulation models. Inference of logical operating rules from evolutionary computation models can also be difficult if the “fitness” of the solution does not reflect all decision variables.

The foregoing discussion is not intended to discourage the use of models, but to improve their utility by urging care in preparation of inputs and caution in interpretation of results. Regardless of the type of model employed, the following basic steps can be taken to promote reasonably faithful replication of the most important aspects of real-world reservoir operations:

Models and their capacity for realistic simulation of reservoir operation continue to improve, but their value is maximized by appreciation of the huge uncertainties involved in simulation of interdependent hydrologic, water demand, and human decision-making processes. Besides accurate and complete input data, successful model application requires rational expectations, effective communications between modelers and stakeholders, and avoidance of overreliance on models alone to measure operational performance. The conclusion to be drawn is not that models are imperfect, but that they can be quite useful despite their imperfections when considered in the contexts of data uncertainties, real-world operator experience, social priorities for water management, and externally imposed constraints on actual operational practice.