Vine copula selection using mutual information for hydrological dependence modeling.

Hydrological risk analysis and management entails multivariate modeling which requires modeling the structure of dependence among different variables. Vine copulas have been increasing applied in multivariate modeling wherein the selection of vine copula structure plays a critical role. Inspired by the relationship between Mutual information (MI) and copula entropy (CE), this study discussed the connection between conditional mutual information (CMI) and CE and developed a mutual information-based sequential approach to select a vine structure which was based on original observations, and model-independent. Then, to reduce the complexity of R-vine copulas, a statistical method-based truncation procedure was applied. Finally, an MI-based approach for hydrological dependence modeling was developed. Two types of hydrological processes with different dependence structures were utilized to show the performance of the proposed approach: (i) drought characterization: showing a D-vine structure; and (ii) multi-site streamflow dependence: showing a C-vine structure. Results indicated that the MI-based approach satisfactorily modeled different kinds of dependence structure and yielded more information on variables in comparison with traditional tau-based approach.

Developing a dual entropy-transinformation criterion for hydrometric network optimization based on information theory and copulas.

Hydrometric information collected by monitoring networks is fundamental for effective management of water resources. In recent years, entropy-based multi-objective criterions have been developed for the evaluation and optimization of hydrometric networks, and copula functions have been frequently used in hydrological frequency analysis to model multivariate dependence structures. This study developed a dual entropy-transinformation criterion (DETC) to identify and prioritize significant stations and generate candidate network optimization solutions. The criterion integrated an entropy index computed with mathematical floor function and a transinformation index computed with copula entropy through a tradeoff weight. The best fitted copula models were selected from three Archimedean copula families, i.e., Gumbel, Frank and Clayton. DETC was applied to a streamflow monitoring network in the Fenhe River basin and two rainfall monitoring networks in the Beijing Municipality and the Taihu Lake basin, which covers different network classification, network scale, and climate type. DETC was assessed by the commonly used dual entropy-multiobjective optimization (DEMO) criterion and was compared with a minimum transinformation (MinT) based criterion for network optimization. Results showed that DETC could effectively prioritize stations according to their significance and incorporate decision preference on information content and information redundancy. Comparison of the isohyet maps of two rainstorm events between DETC and MinT showed that DETC had advantage of restoring the spatial distribution of precipitation.

Improved comprehensive ecological risk assessment method and sensitivity analysis of polycyclic aromatic hydrocarbons (PAHs).

Based on the existing comprehensive ecological risk assessment methods of PAHs, this paper proposed an improved hierarchical Archimedean copula integral assessment (HACIA) model with the optimization in the model selection mechanism and accelerating the calculation speed, and according to which performed the sensitivity analysis of the integrated risk relative to the underlying grouped risk probability. Taihu Lake in China and the Bay of Santander in Spain were taken as study areas, whose samples were obtained and extracted concentrations of 16 priority polycyclic aromatic hydrocarbons (PAHs). After briefly analyzing their concentration characteristics and source, their comprehensive ecological risks were evaluated by the improve HACIA model and their sensitivity was also analyzed. The results proved that, for Taihu Lake, pyrogenic sources occupied the dominance, especially grass, coal and wood combustion, while the risk proportion of 5-rings PAHs was the lowest indeed based on the improved HAICA model. For the Bay of Santander, source apportionment indicated both petrogenic and pyrogenic sources, mainly from vehicle emissions including gasoline and diesel engines, and 4-ring PAHs were urgently needed to be managed. However, the sensitivity analysis results of two study areas showed that the most effective control target for reducing integral risk has no obvious relationship with the maximum grouped risk. And a clear linear relationship between the maximum sensitivity range and the logarithm of the initial overall risk only presented in one of study areas, which required further research to clarify. In brief, the improved HACIA model is helpful to evaluate the comprehensive ecological risk of 16 PAHs, and formulate risk management strategies based on grouped risk assessment and sensitivity analysis, with the former points out the admonitory risk and the latter helps to find the most effective mitigation measures.

Evaluation of information transfer and data transfer models of rain-gauge network design based on information entropy.

Rainfall is one of the most fundamental components of the water cycle and is one of the fundamental inputs of hydrological models. A well-designed network can not only depict the regional precipitation characteristics, but also economically yield maximum needed rainfall information. In regions where either there is limited data or data is not available, it is a common challenge to add stations. The entropy theory-based information transfer model and geostatistical interpolation techniques are two solutions to meet the challenge. In this study, we used a representative rain gauge network to do the network design. Two models, based on information transfer and data transfer, were compared for network design. Other rain gauges in the study area were used as reference ("true values") for assessing the model. Results showed that the information transfer model estimated transinformation between station pairs better than did the data transfer model. Different representative gauges were evaluated separately by the directional information transfer index (DIT). The candidate gauges selected with least information redundancy were similar for both information transfer and data transfer models. Though both models captured some least information-redundant areas, other areas may be bypassed because of model errors or estimation errors.

A new method for wind speed forecasting based on copula theory.

How to determine representative wind speed is crucial in wind resource assessment. Accurate wind resource assessments are important to wind farms development. Linear regressions are usually used to obtain the representative wind speed. However, terrain flexibility of wind farm and long distance between wind speed sites often lead to low correlation. In this study, copula method is used to determine the representative year's wind speed in wind farm by interpreting the interaction of the local wind farm and the meteorological station. The result shows that the method proposed here can not only determine the relationship between the local anemometric tower and nearby meteorological station through Kendall's tau, but also determine the joint distribution without assuming the variables to be independent. Moreover, the representative wind data can be obtained by the conditional distribution much more reasonably. We hope this study could provide scientific reference for accurate wind resource assessments.

A hybrid wavelet de-noising and Rank-Set Pair Analysis approach for forecasting hydro-meteorological time series.

Accurate, fast forecasting of hydro-meteorological time series is presently a major challenge in drought and flood mitigation. This paper proposes a hybrid approach, wavelet de-noising (WD) and Rank-Set Pair Analysis (RSPA), that takes full advantage of a combination of the two approaches to improve forecasts of hydro-meteorological time series. WD allows decomposition and reconstruction of a time series by the wavelet transform, and hence separation of the noise from the original series. RSPA, a more reliable and efficient version of Set Pair Analysis, is integrated with WD to form the hybrid WD-RSPA approach. Two types of hydro-meteorological data sets with different characteristics and different levels of human influences at some representative stations are used to illustrate the WD-RSPA approach. The approach is also compared to three other generic methods: the conventional Auto Regressive Integrated Moving Average (ARIMA) method, Artificial Neural Networks (ANNs) (BP-error Back Propagation, MLP-Multilayer Perceptron and RBF-Radial Basis Function), and RSPA alone. Nine error metrics are used to evaluate the model performance. Compared to three other generic methods, the results generated by WD-REPA model presented invariably smaller error measures which means the forecasting capability of the WD-REPA model is better than other models. The results show that WD-RSPA is accurate, feasible, and effective. In particular, WD-RSPA is found to be the best among the various generic methods compared in this paper, even when the extreme events are included within a time series.

A kriging and entropy-based approach to raingauge network design.

Hydrological data, such as precipitation, is fundamental for planning, designing, developing, and managing water resource projects as well as for hydrologic research. An optimal raingauge network leads to more accurate estimates of mean or point precipitation at any site over the watershed. Some studies in the past have suggested increasing gauge network density for reducing the estimation error. However, more stations mean more cost of installation and monitoring. This study proposes an approach on the basis of kriging and entropy theory to determine an optimal network design in the city of Shanghai, China. Unlike the past studies using kriging interpolation and entropy theory for network design, the approach developed in the current study not only used the kriging method as an interpolator to determine rainfall data at ungauged locations but also incorporated the minimum kriging standard error (KSE) and maximum net information (NI) content. The approach would thus lead to an optimal network and would enable the reduction of kriging standard error of precipitation estimates throughout the watershed and achieve an optimum rainfall information. This study also proposed an NI-KSE-based criterion which is dependent on a single-objective optimization. To evaluate the final optimal gauge network, areal average rainfall was estimated and its accuracy was compared with that obtained with the existing rain gauge network.

[China's Reuse Water Development and Utilization Potential Based on the RDA-REM Model].

To promote the efficient utilization of China's reuse water resources and optimize the allocation of water resources, an analysis of factors influencing the development and utilization of reuse water resources was conducted. The uniqueness and competitiveness of reuse water resources were analyzed, and the driving and constraint mechanisms were revealed. A potential indicator system for the bilateral coordination of the supply and demand of reuse water was also established. Based on redundancy analysis (RDA), key indicators for the prediction of reuse water development and utilization potential were screened. On this basis, a national-scale reuse water development and utilization potential prediction model was constructed (the random effects model, REM). Given some uncertainty in the parameters of the REM model, the confidence interval ranges of the parameters at the 10%-90% quartile levels were identified. The results show that four indicators (ecological water consumption, density of water supply pipelines in built-up areas, fixed asset investment in the construction of reuse water treatment facilities, and total wastewater treatment) are closely related to the development and utilization of reuse water and, hence, are key indicators. The REM for the potential prediction has a high fitting accuracy, which can effectively reflect the fluctuations in the observed values with a maximum fitting error of -8.5%. China's reuse water development and utilization will continue to maintain rapid growth long into the future, reaching 12.9 billion m3 by 2025. This will help optimize national urban water supply structures and improve the reuse rate of regional water resources.