Time-varying copula and average annual reliability-based nonstationary hazard assessment of extreme rainfall events

• Complete preprocessed tests are implemented to detect different forms of nonstationarity. • Various kinds of marginal and copula models with time-varying patterns are considered as candidate nonstationary models. • Dependence structure nonstationarity impact more on design value than nonstationary margins. Due to global climate change and urbanization, more attention has been paid to decipher the nonstationary multivariate risk analysis from the perspective of probability distribution establishment. In this study, a multivariate nonstationary hazard assessment of annual extreme rainfall events, extracted from daily precipitation data observed at eight meteorological stations in Haihe River basin, China, was done in three phases: (1) Several statistical tests, such as nonparametric trend tests, log likelihood ratio ( LR ) tests and Change-point (CP) tests were applied to both the marginal distributions and the dependence structures to decipher different forms of nonstationarity; (2) estimation of the time-varying parameter for the marginal and joint probability distributions by maximum likelihood method; and (3) calculation of hydrologic design quantiles at different average annual reliability levels (ARR) during a certain design life period in terms of hazard assessment. According to the results, the attributes and their dependence structure belonging to several stations show nonstationarity because of existed trend in model parameter or change point. In the process of hazard assessment, the nonstationarity of dependence structure would produce less impact on ARR-based designed quantile estimation than the nonstationarity of marginal distribution on the one hand. On the other hand, it would add more uncertainty of quantile estimation for hydrologic design.