Y.P. Li

Maximum entropy-Gumbel-Hougaard copula method for simulation of monthly streamflow in Xiangxi river, China

A maximum entropy-Gumbel-Hougaard copula (MEGHC) method has been proposed for monthly streamflow simulation. The marginal distributions of monthly streamflows are estimated through the maximum entropy (ME) method with the first four non-central moments (i.e. mean, standard deviation, skewness and kurtosis) being the constraints. The Lagrange multipliers in ME-based marginal distributions are determined using the conjugate gradient (CG) method which is of superlinear convergence, simple recurrence formula and less calculation. Then the joint distributions of two adjacent monthly streamflows are constructed using the Gumbel-Hougaard copula (GHC) method. The developed MEGHC method has been applied for monthly streamflow simulation in Xiangxi river, China. The goodness-of-fit statistical tests, consisting of K–S test, A–D test, RMSE and Rosenblatt transformation with Cramér von Mises statistic, show that the MEGHC method can reflect dependence structure in adjacent monthly streamflows of Xiangxi river, China. Comparison between simulated streamflow generated by MEGHC and observations indicates the satisfactory performance of MEGHC with small relative errors.

A robust risk analysis method for water resources allocation under uncertainty

A robust risk analysis method (RRAM) is developed for water resource decision making under uncertainty. This method incorporates interval-parameter programming and robust optimization within a stochastic programming framework. In the RRAM formulation, penalties are exercised with the recourse against any infeasibility, and robustness measures are introduced to examine the variability of the second stage costs which are above the expected levels. In this study, a number of weighting levels are considered which correspond to the robustness levels of risk control. Generally, a plan with a higher robust level would better resist from system risk. Thus, decision with a lower robust level can correspond to a higher risk of system failure. There is a tradeoff between system cost and system reliability. The RRAM is applied to a case of water resource management. The modeling results can help generate desired decision alternatives that will be particularly useful for risk-aversive decision makers in handling high-variability conditions. The results provide opportunities to managers to make decisions based on their own preferences on system stability and economy, and ensure that the management policies and plans be made with reasonable consideration of both system cost and risk.

Robust interval linear programming for environmental decision making under uncertainty

In this study, a robust interval linear programming (RILP) method is developed for dealing with uncertainties expressed as intervals with deterministic boundaries. An enhanced two-step method (ETSM) is also advanced to solve the RILP model. The developed RILP improves upon the conventional interval linear programming (ILP) method since it can generate solution intervals within a larger feasible zone. The decision space based on ETSM contains all feasible solutions, such that no useful information is neglected. Moreover, the RILP can guarantee the stability of the optimization model due to no violation for the best-case constraints. The results also suggest that the RILP is effective for practical environmental and engineering problems that involve uncertainties.

Bivariate hydrologic risk analysis based on a coupled entropy-copula method for the Xiangxi River in the Three Gorges Reservoir area, China

In this study, a bivariate hydrologic risk framework is proposed based on a coupled entropy-copula method. In the proposed risk analysis framework, bivariate flood frequency would be analyzed for different flood variable pairs (i.e., flood peak-volume, flood peak-duration, flood volume-duration). The marginal distributions of flood peak, volume, and duration are quantified through both parametric (i.e., gamma, general extreme value (GEV), and lognormal distributions) and nonparametric (i.e., entropy) approaches. The joint probabilities of flood peak-volume, peak-duration, and volume-duration are established through copulas. The bivariate hydrologic risk is then derived based on the joint return period to reflect the interactive effects of flood variables on the final hydrologic risk values. The proposed method is applied to the risk analysis for the Xiangxi River in the Three Gorges Reservoir area, China. The results indicate the entropy method performs best in quantifying the distribution of flood duration. Bivariate hydrologic risk would then be generated to characterize the impacts of flood volume and duration on the occurrence of a flood. The results suggest that the bivariate risk for flood peak-volume would not decrease significantly for the flood volume less than 1000 m3/s. Moreover, a flood in the Xiangxi River may last at least 5xa0days without significant decrease of the bivariate risk for flood peak-duration.

A fuzzy-Markov-chain-based analysis method for reservoir operation

In this study, a fuzzy-Markov-chain-based stochastic dynamic programming (FM-SDP) method is developed for tackling uncertainties expressed as fuzzy sets and distributions with fuzzy probability (DFPs) in reservoir operation. The concept of DFPs used in Markov chain is presented as an extended form for expressing uncertainties including both stochastic and fuzzy characteristics. A fuzzy dominance index analysis approach is proposed for solving multiple fuzzy sets and DPFs in the proposed FM-SDP model. Solutions under a set of α-cut levels and fuzzy dominance indices can be generated by solving a series of deterministic submodels. The developed method is applied to a case study of a reservoir operation system. Solutions from FM-SDP provide a range of desired water-release policies under various system conditions for reservoir operation decision makers, reflecting dynamic and dual uncertain features of water availability simultaneously. The results indicate that the FM-SDP method could be applicable to practical problems for decision makers to obtain insight regarding the tradeoffs between economic and system reliability criteria. Willingness to obtain a lower benefit may guarantee meeting system-constraint demands; conversely, a desire to acquire a higher benefit could run into a higher risk of violating system constraints.

A scenario-based modeling approach for emergency evacuation management and risk analysis under multiple uncertainties

Nuclear emergency evacuation is important to prevent radioactive harms by hazardous materials and to limit the accidents consequences; however, uncertainties are involved in the components and processes of such a management system. In the study, an interval-parameter joint-probabilistic integer programming (IJIP) method is developed for emergency evacuation management under uncertainties. Optimization techniques of interval-parameter programming (IPP) and joint-probabilistic constrained (JPC) programming are incorporated into an integer linear programming framework, so that the approach can deal with uncertainties expressed as joint probability and interval values. The IJIP method can schedule the optimal routes to guarantee the maximum population evacuated away from the effected zone during a finite time. Furthermore, it can also facilitate post optimization analysis to enhance robustness in controlling system violation risk imposed on the joint-probabilistic constraints. The developed method has been applied to a case study of nuclear emergency management; meanwhile, a number of scenarios under different system conditions have been analyzed. It is indicated that the solutions are useful for evacuation management practices. The result of the IJIP method can not only help to raise the capability of disaster responses in a systematic manner, but also provide an insight into complex relationships among evacuation planning, resources utilizations, policy requirements and system risks.

A robust simulation-optimization modeling system for effluent trading—a case study of nonpoint source pollution control

In this study, a robust simulation–optimization modeling system (RSOMS) is developed for supporting agricultural nonpoint source (NPS) effluent trading planning. The RSOMS can enhance effluent trading through incorporation of a distributed simulation model and an optimization model within its framework. The modeling system not only can handle uncertainties expressed as probability density functions and interval values but also deal with the variability of the second-stage costs that are above the expected level as well as capture the notion of risk under high-variability situations. A case study is conducted for mitigating agricultural NPS pollution with an effluent trading program in Xiangxi watershed. Compared with non-trading policy, trading scheme can successfully mitigate agricultural NPS pollution with an increased system benefit. Through trading scheme, [213.7, 288.8]u2009×u2009103xa0kg of TN and [11.8, 30.2]u2009×u2009103xa0kg of TP emissions from cropped area can be cut down during the planning horizon. The results can help identify desired effluent trading schemes for water quality management with the tradeoff between the system benefit and reliability being balanced and risk aversion being considered.

A stepwise-cluster forecasting approach for monthly streamflows based on climate teleconnections

In this study, a stepwise cluster forecasting (SCF) framework is proposed for monthly streamflow prediction in Xiangxi River, China. The developed SCF method can capture discrete and nonlinear relationships between explanatory and response variables. Cluster trees are generated through the SCF method to reflect complex relationships between independent (i.e. explanatory) and dependent (i.e. response) variables in the hydrologic system without determining specific linear/nonlinear functions. The developed SCF method is applied for monthly streamflow prediction in Xiangxi River based on the local meteorological records as well as some climate index. Comparison among SCF, multiple linear regression, generalized regression neural network, and least square support vector machine methods would be conducted. The results indicate that the SCF method would produce good predictions in both training and testing periods. Besides, the inherent probabilistic characteristics of the SCF predictions are further analyzed. The results obtained by SCF can presented as intervals, formulated by the minimum and maximum predictions as well as the 5 and 95xa0% percentile values of the predictions, which can reflect the variations in streamflow forecasts. Therefore, the developed SCF method can be applied for monthly streamflow prediction in various watersheds with complicated hydrologic processes.

A Factorial-based Dynamic Analysis Method for Reservoir Operation Under Fuzzy-stochastic Uncertainties

In this study, a factorial-based fuzzy-stochastic dynamic programming (FFS-DP) method is developed for tackling multiple uncertainties including fuzziness, randomness and their interaction in reservoir operation management (ROM). FFS-DP is framed on the integration of stochastic dynamic programming, fuzzy-Markov chain, vertex analysis and factorial analysis techniques. It can not only deal with the conventional optimization problem for reflecting dynamic and uncertain features in ROM, but also obtain detailed effects of uncertain parameters and their interactions on the system performance. The developed method is applied to a case study of a reservoir operation system, where the local authority is in charge of allocating relative scant water to the downstream municipality. The results obtained can help the local authority identify desired water release policies under uncertain system conditions. Besides, the results simultaneously indicate that significant factors and their interactions can be identified in ROM. Moreover, the results can be further analyzed for generating optimal parameter inputs to obtain maximized system benefits.

Risk assessment of agricultural irrigation water under interval functions

In recent years, water shortages and unreliable water supplies have been considered as major barriers to agricultural irrigation water management in China, which are threatening human health, impairing prospects for agriculture and jeopardizing survival of ecosystems. Therefore, effective and efficient risk assessment of agricultural irrigation water management is desired. In this study, an inexact full-infinite two-stage stochastic programming (IFTSP) method is developed. It incorporates the concepts of interval-parameter programming and full-infinite programming within a two-stage stochastic programming framework. IFTSP can explicitly address uncertainties presented as crisp intervals, probability distributions and functional intervals. The developed model is then applied to Zhangweinan river basin for demonstrating its applicability. Results from the case study indicate that compromise solutions have been obtained. They provide the desired agricultural irrigation water-supply schemes, which are related to a variety of tradeoffs between conflicting economic benefits and associated penalties attributed to the violation of predefined policies. The solutions can be used for generating decision alternatives and thus help decision makers to identify desired agricultural irrigation targets with maximized system benefit and minimized system-failure risk. Decision makers can adjust the existing agricultural irrigation patterns, and coordinate the conflict interactions among economic benefit, system efficiency, and agricultural irrigation under uncertainty.