Laura Read

Reliability, return periods, and risk under nonstationarity

Water resources design has widely used the average return period as a concept to inform management and communication of the risk of experiencing an exceedance event within a planning horizon. Even though nonstationarity is often apparent, in practice hydrologic design often mistakenly assumes that the probability of exceedance, p, is constant from year to year which leads to an average return period To equal to 1/p; this expression is far more complex under nonstationarity. Even for stationary processes, the common application of an average return period is problematic: it does not account for planning horizon, is an average value that may not be representative of the time to the next flood, and is generally not applied in other areas of water planning. We combine existing theoretical and empirical results from the literature to provide the first general, comprehensive description of the probabilistic behavior of the return period and reliability under nonstationarity. We show that under nonstationarity, the underlying distribution of the return period exhibits a more complex shape than the exponential distribution under stationary conditions. Using a nonstationary lognormal model, we document the increased complexity and challenges associated with planning for future flood events over a planning horizon. We compare application of the average return period with the more common concept of reliability and recommend replacing the average return period with reliability as a more practical way to communicate event likelihood in both stationary and nonstationary contexts.

Optimality versus stability in water resource allocation

Water allocation is a growing concern in a developing world where limited resources like fresh water are in greater demand by more parties. Negotiations over allocations often involve multiple groups with disparate social, economic, and political status and needs, who are seeking a management solution for a wide range of demands. Optimization techniques for identifying the Pareto-optimal (social planner solution) to multi-criteria multi-participant problems are commonly implemented, although often reaching agreement for this solution is difficult. In negotiations with multiple-decision makers, parties who base decisions on individual rationality may find the social planner solution to be unfair, thus creating a need to evaluate the willingness to cooperate and practicality of a cooperative allocation solution, i.e., the solutions stability. This paper suggests seeking solutions for multi-participant resource allocation problems through an economics-based power index allocation method. This method can inform on allocation schemes that quantify a partys willingness to participate in a negotiation rather than opt for no agreement. Through comparison of the suggested method with a range of distance-based multi-criteria decision making rules, namely, least squares, MAXIMIN, MINIMAX, and compromise programming, this paper shows that optimality and stability can produce different allocation solutions. The mismatch between the socially-optimal alternative and the most stable alternative can potentially result in parties leaving the negotiation as they may be too dissatisfied with their resource share. This finding has important policy implications as it justifies why stakeholders may not accept the socially optimal solution in practice, and underlies the necessity of considering stability where it may be more appropriate to give up an unstable Pareto-optimal solution for an inferior stable one. Authors suggest assessing the stability of an allocation solution as an additional component to an analysis that seeks to distribute water in a negotiated process.

Voting Under Uncertainty: A Stochastic Framework for Analyzing Group Decision Making Problems

Water resources policy making often involves consideration of a broader scope of environmental, economic, and social issues. This inevitably complicates policy making since consensus among multiple stakeholders with different interests is needed to implement decisions. This work employs several practical and popular voting methods to solve a multi-stakeholder hydro-environmental management problem. Conventionally, voting methods or social choice rules have been applied for consensus development in small groups and elections. This work combines voting methods with a Monte-Carlo selection, in order to help with social choice making under uncertainty. This process is intended to aid decision-makers with understanding of the risks associated with potential decision alternatives. The Sacramento-San Joaquin Delta’s water export conflict is solved here as a benchmark problem to illustrate the proposed framework for social decision making and analysis under uncertainty.

Hazard function analysis for flood planning under nonstationarity

The field of hazard function analysis (HFA) involves a probabilistic assessment of the “time to failure” or “return period,” T, of an event of interest. HFA is used in epidemiology, manufacturing, medicine, actuarial statistics, reliability engineering, economics, and elsewhere. For a stationary process, the probability distribution function (pdf) of the return period always follows an exponential distribution, the same is not true for nonstationary processes. When the process of interest, X, exhibits nonstationary behavior, HFA can provide a complementary approach to risk analysis with analytical tools particularly useful for hydrological applications. After a general introduction to HFA, we describe a new mathematical linkage between the magnitude of the flood event, X, and its return period, T, for nonstationary processes. We derive the probabilistic properties of T for a nonstationary one-parameter exponential model of X, and then use both Monte-Carlo simulation and HFA to generalize the behavior of T when X arises from a nonstationary two-parameter lognormal distribution. For this case, our findings suggest that a two-parameter Weibull distribution provides a reasonable approximation for the pdf of T. We document how HFA can provide an alternative approach to characterize the probabilistic properties of both nonstationary flood series and the resulting pdf of T.

A Multi-Participant, Multi-Criteria Analysis of Energy Supply Sources for Fairbanks, Alaska

The selection of a future energy source for Fairbanks, Alaska, is a multi-criteria, multi-decision maker (MCMDM) problem as it involves a range of stakeholders who must consider economic, sociopolitical, and environmental criteria in deciding the best project. The primary motivation for the new energy project is to provide an additional affordable heating and electric source to local residents. Proposed projects range from liquid-natural gas pipelines to hydropower and differ greatly in development costs, environmental impacts, and political support. Stakeholder interests vary from local and state government officials, to local and international business developers, and to residents and environmentalists. Traditionally, water and resource MCMDM problems have been simplified to analyze a single decision maker (DM) for multiple criteria; this work defines model criteria at different levels based on input from stakeholder representatives through a collaborative process. Model inputs can be ordinal when cardinal information is unavailable, thereby increasing the models flexibility for a wide range of source data. The model employs a range of social choice, fall back bargaining, and MCDM to solve the problem. Uncertainty in the model is characterized by a Monte Carlo analysis, which measures sensitivity of the solution from the range of inputs provided by stakeholder data. Given the economic and social components included in this MCMDM analysis, characterizing the uncertainty associated with each outcome is crucial for policy interpretation. This work provides a new application for MCMDM problems combining a range of social choice and game theoretic methods with a rigorous sensitivity analysis to inform decision makers about the most feasible and stable alternatives.

Assessing the Stability of Social Planner Solutions in Multi-Participant Water Conflicts

The use of optimization techniques to identify socially optimal solutions to allocation problems is widely accepted in the water resources literature. For cases with multiple criteria and multiple decision makers (MC-MDM), techniques traditionally lump the decision makers (DM) into a single user and evaluate the criteria, thus not capturing the influence of power dynamics that occur between DMs. Through application of stability methods such as the power index, an alternative method for solving allocation problems, one can assess whether a decision rule is likely to be accepted based on the parties’ relative power. This work presents a method for applying the power index to MCMDM problems to determine the most stable decision rule. Since stability is concerned with minimizing the dissatisfaction of the most powerful party, stability can produce different outcomes from the conventional system-level optimization. This work presents this comparative analysis through a case study of the Caspian Sea resource allocation negotiation between five littoral states (Iran, Russia, Kazakhstan, Turkmenistan, and Azerbaijan). Goal programming, compromise programming, and power index methods are employed to evaluate the best scheme for allocation of the Caspian Sea resources. Results show that optimal solutions, analyzed by social planner methods, may not be stable in practice, as certain parties may be too dissatisfied with their allocation to enter into an agreement. This finding has important policy implications as it justifies why stakeholders may not accept the socially optimal solution in practice, and underlies the necessity of considering solution stability in social planning and decision making.