Frequency analysis of streamflow is critical for water-resources system planning, water conservancy projects and the mitigation of hydrological extremes events. In this study, a maximum entropy-Archimedean copula-based Bayesian network (MECBN) method has been proposed for frequency analysis of monthly streamflow in the Kaidu River Basin, which integrates the maximum entropy-Archimedean copula (MEAC) and Bayesian network methods into a general framework. MECBN is effective for representing the uncertainties that exist in model representation, preserving the distributional characteristics of streamflow records and addressing the correlation structure between streamflow pairs. Application to the Kaidu River Basin shows a good performance of MECBN in describing the historical data of this basin in China. The results indicate that the interactions between two adjacent monthly streamflow pairs are non-linear. There is upper tail dependence between monthly streamflow pairs. The dependence coefficients including Spearman’s rho, Kendall’s tau, and the upper tail dependence coefficient are in inverse proportion of monthly streamflow values in the Kaidu River Basin, due to the fact that other factors (i.e., rainfall, snow melting, evapotranspiration rate and requirement of water use) provide more contributions to the streamflow in the flooding season. These findings can be used for providing vital information in the prevention and control of hydrological extremes and to further water resources planning in Kaidu River Basin.

In this study, an initial water-rights allocation (IWRA) model is proposed for adjusting the traditional initial water-rights empowerment model based on previous water intake permits, with the aim of improving the productivity of water resources under population growth and economic development. A stochastic scenario with Laplace criterion mixed fuzzy programming (SSLF) is developed into an IWRA model to deal with multiple uncertainties and complexities, which includes dynamic water demand, changing water policy, adjusted tradable water rights, the precise risk attitude of policymakers, development of the economy, and their interactions. SSLF not only deals with fuzziness in probability distributions with high satisfaction degrees, but also reflects the risk attitudes of policymakers with the Laplace criterion, which can handle the probability of scenario occurrence under the supposition of no data available. The developed IWRA model with the SSLF method is applied to a practical case in an alpine region of China. The results of adjusted initial water rights, optimal water-right allocation, changed industrial structure, and system benefits under various scenarios associated with risk attitudes and water productivity improvement were obtained and analyzed. It was found that the current initial water-rights allocation scheme based on previous intake water permits is not efficient, and this can be modified by the IWRA model. Based on the strategies of drinking safety and ecological security, the main tradeoff between agricultural and industrial water rights can facilitate optimization of the current initial water-rights allocation. This can assist policymakers in producing an effective plan to promote water productivity and water resource management in a robust and reliable manner.

In this study, an agroforestry ecosystem project (AEP) is developed for confronting the conflict between agricultural development and forest protection. A fuzzy stochastic programming with Laplace scenario analysis (FSL) is proposed for planning water resources in an AEP issue under uncertainties. FSL can not only deal with spatial and temporal variations of hydrologic elements and meteorological conditions; but also handle uncertainties that are expressed in terms of probability, possibility distributions and fuzzy sets; meanwhile, policy scenario analysis with Laplace’s criterion (PSL) is introduced to handle probability of each scenario occurrence under the supposition of no data available. The developed FSL can be applied to an AEP issue in Xixian county, located in north of China. The result of ecological effects, water allocation patterns, pollution mitigation schemes and system benefits under various scenarios are obtained, which can support policymakers adjusting current strategy to improve regional ecological function with cost-effective and sustainable manners. Meanwhile, it can support generating a robust water plan for regional sustainability in an AEP issue under uncertainties.

An interactive two-stage fractile optimization (ITFO) model is applied to a case study of agricultural irrigation systems in Sanjiang Plain. The advantages of ITFO are as follows: (1) ITFO can reflect the uncertainties and complexes of agricultural irrigation systems, and deal with dual uncertainties expressed as interval fuzzy numbers and stochastic distributions; (2) The optimal water-allocation strategies for agricultural irrigation systems under different feasibilities and fractile values can be generated through ITFO in order to reflect the preference to the system cost; (3) ITFO combines objectivity of mathematical programming method and subjectivity of human beings into a framework which can increase the applicability. ITFO could provide feasible schemes for decision makers to support the rational development and utilization for agricultural irrigation systems in Sanjiang Plain.