Bivariate rainfall frequency distributions using Archimedean copulas

Joint distributions of rainfall intensity and depth, rainfall intensity and duration, or rainfall depth and duration are important in hydrologic design and floodplain management. Multivariate rainfall frequency distributions have usually been derived using one of three fundamental assumptions: (1) Either rainfall variables (e.g., intensity, depth, and duration) have each the same type of the marginal probability distribution, (2) the variables have been assumed to have joint normal distribution or have been transformed and assumed to have joint normal distribution, or (3) they have been assumed independent-a trivial case. In reality, however, rainfall variables are dependent, do not follow, in general, the normal distribution, and do not have the same type of marginal distributions. This study aims at deriving bivariate rainfall frequency distributions using the copula method in which four Archimedean copulas were examined and compared. The advantage of the copula method is that no assumption is needed for the rainfall variables to be independent or normal or have the same type of marginal distributions. The bivariate distributions are then employed to determine joint and conditional return periods, and are tested using rainfall data from the Amite River basin in Louisiana, United States.