Joint-probability Methods for Precipitation and Flood Frequencies Analysis

Flooding in irrigation district is often caused by the encounter of flood from the upstream and the precipitation jacking. Archimedean copulas were applied to evaluate the encounter probability of precipitation and flood. The problem of obtaining the joint distribution was reduced to determine the appropriate copula. Four different Archimedean copulas were applied to simulate the joint probability of annual maximum precipitation flood level on two neighboring hydrological stations located at the Pearl River delta, China. Goodness-of-fit tests were introduced to determine the best copula by RMSE and AIC criterion. The joint distribution and condition distribution were obtained based on the best copula. Results show that the joint probability curves were significantly influenced by the marginal distributions. The bivariate precipitation and flood frequency distributions were determined using the copula method without assuming the same form of the marginal distributions. Comparison of the copula-based distributions with bivariate probability distribution showed that the copula-based distribution fit the observed precipitation and flood data better.