Joint distribution of design precipitation and tide and impact of sampling in a coastal area
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2017 Royal Meteorological Society Instream flooding in coastal areas becomes more severe when heavy precipitation and high tide occur simultaneously. Flood modelling under such conditions requires the joint design of precipitation and tide. Data of 24-h heavy precipitation and the corresponding daily high tidal level in the Xixiang basin, south China were used. Annual maxima and peaks over threshold sampling methods were applied to construct the precipitation and tidal level series. The joint distribution of precipitation and tide was derived by Archimedean copulas and their joint return period was calculated by the Kendall measure function. Then, equalized frequency and most likely weight function methods were employed for the joint design of precipitation and tide. Results showed that for the peaks over threshold sampling heavy precipitation coincided with more and greater high tidal levels. The general normal distribution was found to fit the marginals of precipitation and tide well, but the location, scale and shape parameters of two sampling methods differed markedly for heavy precipitation and slightly for high tidal level. Although the dependence of heavy precipitation and high tidal level was quite small and positive, Archimedean copulas effectively modelled the joint distribution of precipitation and tide. Based on the equalized frequency method, the joint design precipitation and tide using GumbelHougaard copula for the peaks over threshold sampling was safer than that for the annual maxima sampling. However, for the most likely weight method design pairs remarkably tended to the lower heavy precipitation and the higher high tidal level. If the sampling method and the joint distribution were determined, a reciprocal situation for the design pairs of precipitation and tide occurred for a given joint return period, that is, a greater design value of heavy precipitation corresponded to a smaller design value of high tidal level, and vice versa. Therefore, which design method was safer was underdetermined.
