In this study, a robust two-step method (RTSM) is developed to solve the interval linear programming (ILP) problem. It improved upon the two-step method (TSM) proposed by Huang et al. (1992) through incorporating additional constraints into solution procedures to avoid absolute violation. RTSM was applied to a simple case related to environmental management. The results demonstrated its applicability of the developed methodology. Compare with the modified interval linear programming (MILP) method proposed by Zhou et al., (2008) and the three-step method (ThSM) developed by Cao and Huang (2011), RTSM can generate a relatively larger solution space and thus avoid significant loss of decision-related information. Besides, RTSM has simpler solution procedures than ThSM, and will not lead to great computational requirement.

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ABSTRACT:In this study, different interpolation techniques in a geographical information system (GIS) environment are analysed and compared for estimating the spatial distribution of precipitation in the province of Ontario, Canada. A high-resolution regional climate modelling system [Providing Regional Climates for Impacts Studies (PRECIS)] is used to simulate the present and future (2071-2100) precipitation events for 12 meteorological stations over Ontario. The results verify that for the present case PRECIS simulates well the precipitation events when compared with observed data. The future precipitation events can be projected after the validation of PRECIS. Six interpolation methods are then used to generate spatial distribution of precipitation based on the projections of future precipitation of 12 meteorological stations; they include inverse distance weighting (IDW), global polynomial interpolation (GPI), local polynomial interpolation (LPI), radial basis functions (RBF), ordinary kriging (OK), and universal kriging (UK). Cross-validation is applied to evaluate the accuracy of interpolation methods in terms of the root mean square error (RMSE). The results indicate that LPI is the optimal method with the least RMSE for interpolating the PRECIS precipitation. LPI is then used to analyse spatial variations of the average annual precipitation for the period of 2071-2100 over Ontario.

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 volumeduration 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 m 3 /s. Moreover, a flood in the Xiangxi River may last at least 5 days without significant decrease of the bivariate risk for flood peak-duration.

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Drought is one of the most widespread and destructive hazards over the Loess Plateau (LP) of China. Due to climate change, extremely high temperature accompanied with drought (expressed as hot drought) may lead to intensive losses of both properties and human deaths in future. A hot drought probabilistic recognition system is developed to investigate how potential future climate changes will impact the simultaneous occurrence of drought and hot extremes (hot days exceeding certain values) on the LP. Two regional climate models, coupled with multiple bias‐correction techniques and multivariate probabilistic inference, are innovative integrated into the hot drought probabilistic recognition system to reveal the concurrence risk of droughts and hot extremes under different Representative Concentration Pathway (RCP) scenarios. The hot‐day index, TX90p, indicating the number of days with daily maximum temperature (Tmax) exceeding the 90th percentile threshold, and the Standardized Precipitation Index are applied to identify the joint risks on the LP using copula‐based methods. The results show that precipitation will increase throughout most of the LP under both RCP4.5 and RCP8.5 scenarios of 2036–2095, while Tmax may increase significantly all over the LP (1.8–2.7 °C for RCP4.5 and 2.7–3.6 °C for RCP8.5). The joint return periods of Standardized Precipitation Index and TX90p show that fewer stations will experience severe drought with long‐term hot extremes in two future scenarios. However, some stations may experience hot droughts that are more frequent and extreme, particularly certain stations in the southwest and south‐central regions of the LP with recurrence period less than 10 years.

In this study, bivariate hydrologic risk analysis was conducted based on the daily streamflow discharge at the Xianyang station on the Wei River. This bivariate hydrologic risk analysis was conducted based on copula methods, in which the bivariate hydrologic frequency was firstly quantified through copulas, and the bivariate hydrologic risk analysis was then characterized based on the joint return period of flood pairs. The maximum likelihood estimation (MLE) and the method-of-moments-like (MOM) estimator were compared in estimating the unknown parameters in copula. The results showed that the GumbelHougaard copula was most appropriate for modelling the dependence for all three flood pairs, in which the parameter of the copula for flood peak-volume was estimated by MLE and the parameters of the copulas for flood peak-duration and volume-duration were needed to be obtained by MOM. The bivariate hydrologic risk values are then obtained based on the AND-joint return period. The results show that the bivariate hydrologic values will not decrease until the corresponding volume for a flood is larger than 1.0 9 10 4 m 3 /s. For the bivariate hydrologic risk for flood peak-duration, the value will decrease quickly when the duration is longer than 5 days. Such bivariate hydrologic risk analysis can provide decision support for hydraulic facility design as well as actual flood control and mitigation.