Multivariate hydrologic design under stationary conditions is traditionally performed through the use of the design criterion of the return period, which is theoretically equal to the average inter-arrival time of flood events divided by the exceedance probability of the design flood event. Under nonstationary conditions, the exceedance probability of a given multivariate flood event varies over time. This suggests that the traditional return-period concept cannot apply to engineering practice under nonstationary conditions, since by such a definition, a given multivariate flood event would correspond to a time-varying return period. In this paper, average annual reliability (AAR) was employed as the criterion for multivariate design rather than the return period to ensure that a given multivariate flood event corresponded to a unique design level under nonstationary conditions. The multivariate hydrologic design conditioned on the given AAR was estimated from the nonstationary multivariate flood distribution constructed by a dynamic C-vine copula, allowing for time-varying marginal distributions and a time-varying dependence structure. Both the most-likely design event and confidence interval for the multivariate hydrologic design conditioned on the given AAR were identified to provide supporting information for designers. The multivariate flood series from the Xijiang River, China, were chosen as a case study. The results indicated that both the marginal distributions and dependence structure of the multivariate flood series were nonstationary due to the driving forces of urbanization and reservoir regulation. The nonstationarities of both the marginal distributions and dependence structure were found to affect the outcome of the multivariate hydrologic design.

It is a challenge to describe the hydrogeological characteristics of karst aquifers due to the complex structure with extremely high heterogeneity. As the response of karst aquifers to rainfall events, spring discharge variations after precipitation can be used to identify the internal structure of karst systems. In this study, responses of spring discharge to different kinds of precipitations are investigated by continuously monitoring precipitation and karst spring flow at a single-conduit karst aquifer in western Hunan province, China. Recession curves were used to analyze hydrodynamic behaviors and separate recession stages. The results show that the shape of the recession curve was changed under different rainfall conditions. Recession processes can be divided in to three recession stages under heavy rain conditions due to water drainage mainly from conduits, fracture, and matrix at each stage, but only one recession stage representing drainage mainly from matrix in the case of light rain. With the change in amount and intensity of precipitation, the calculated recession coefficient at each stage changes in an order of magnitude. The influence of precipitation on the recharge coefficient and the discharge composition at each recession are discussed, and then the conceptual model diagram of water filling and releasing in the single-conduit karst aquifers is concluded. The findings provide more insight understand on hydraulic behaviors of karst spring under different types of rainfall events and provide support for water resource management in karst regions.

The fundamental assumption of flood frequency analysis is that flood samples are generated by the same flood generation mechanism (FGM). However, flood events are usually triggered by the interaction of meteorological factors and watershed properties, which results in different FMGs. To solve this problem, researchers have put forward traditional two-component mixture distributions (TCMD-T) without clearly linking each component distribution to an explicit FGM. In order to improve the physical meaning of mixture distributions in seasonal snow-covered areas, the ratio of rainfall to flood volume (referred to as rainfall–flood ratio, RF) method was used to classify distinct FGMs. Thus, the weighting coefficient of each component distribution was determined in advance in the rainfall–flood ratio based TCMD (TCMD-RF). TCMD-RF model was applied to 34 basins in Norway. The results showed that flood types can be clearly divided into rain-on-snow-induced flood, snowmelt-induced flood and rainfall-induced flood. Moreover, the design flood and associated uncertainties were also estimated. It is found that TCMD-RF model can reduce the uncertainties of design flood by 20% compared with TCMD-T. The superiority of TCMD-RF is attributed to its clear classification of FGMs, thus determining the weighting coefficients without optimization and simplifying the parameter estimation procedure of mixture distributions.