Abstract:Based on the hourly precipitation data from 122 national meteorological stations in Shandong Province from 1966 to 2023, the frequency variations of heavy precipitation are analyzed. Different marginal distribution functions are used to fit the duration and amount of precipitation, and the change patterns of the return periods of heavy precipitation with different durations are investigated based on Copula function. The results are as follows. There exists a significant dependence relation between the duration and amount of heavy precipitation, which can be fitted well using generalized extreme values and logarithmic normal distribution functions. The Gumbel Copula and Clayton Copula functions are suitable for portraying the dependence structure of the binary variables of the short-time heavy precipitation in Shandong. However, the Clayton Copula function is more appropriate when the precipitation lasts for more than 8 h. The return period estimated by daily precipitation may seriously underestimate the hazard of short-time heavy precipitation. For a short-time heavy precipitation event under the same hazard-bearing condition, the shorter the duration, the longer the joint return period. The high-value areas of joint return period estimated by the Copula function gradually narrow down from the east and the south of Shandong to the east of Shandong, along with the increase of precipitation duration. Especially, the hazard of heavy precipitation that comes along once every 60 years is higher in the east and the south of Shandong. This method can more scientifically describe the disaster risks of heavy precipitation in different scenarios, especially in the short-time heavy precipitation scenario, so it can provide a scientific reference for disaster prevention and mitigation planning as well as disaster risk managing in Shandong.