Keywords: 
• encounter of heavy rain and high tidal level /
• peaks over threshold /
• Copula function /
• second return period /
• a pair of designed values /
• coastal city

Abstract: Instream flood in a coastal city usually occurs under the influence of heavy rain and high tidal level. Thus, modeling and design of joint distribution of precipitation and tide require increased attention. With Xixianghe River basin of Shenzhen city, Southern China, used as a case, 24-hour data of heavy rain and comparative daily high tidal level are used for two sampling methods, namely, annual maximum (AM) and peaks over threshold (POT). The joint distribution model of precipitation and tide is established by using Copula functions. In this model, the difference between the traditional and second return periods of joint distribution of precipitation and tide is analyzed. The pair values of precipitation and tide are investigated according to two optimally designed methods, namely, equalized frequency method and most-likely weight function. Results show that the generalized normal distribution (GNO) is optimally selected to model the marginal distribution of precipitation and tide, but the differences of model parameters in precipitation are remarkable. Although precipitation and tide exhibit a weak positive dependence, Archimedean Copulas can well model their joint distribution, and the Gumbel-Hougaard Copula is selected as the optimal bivariate model. According to the equalized frequency method, the pair values of precipitation and tide designed by the second return period are greater than those designed by the traditional return period, and those designed by the POT series are greater than those designed by the AM series. However, the designed values of tide level are greater when associated with lower precipitation on the basis of the most-likely weight function. Provided that the sampling method, the joint distribution model, and the type of joint return period are confirmed, a reciprocal situation for a pair of designed values of precipitation and tide is manifested for given joint return periods, that is, a greater designed value of precipitation corresponds to a smaller designed value of tide, and vice versa. In ensuring a secure engineering design against flood disasters due to heavy rain and high tidal level in the coastal city, the sampling of POT and the bivariable design of the second return period are safer than those of AM and the traditional return period, respectively.