A new rainfall model based on the Neyman-Scott process using cubic copulas

A classical way to model rainfall is to use a Poisson process. Authors generally employed cluster of rectangular pulses to reproduce the hierarchical structure of rainfall storms. Although independence between cell intensity and duration turned out to be a nonrealistic assumption, only a few models link these variables. In this paper, a Neyman-Scott cluster process considering dependence between cell depth and duration is developed. We introduce this link with a cubic copula. Copulas are multivariate distributions modeling the dependence structure between variables, preserving the marginal distributions. Thanks to this flexibility, we are able to introduce a global concept of dependence between cell depth and duration. We derive the aggregated moments (first-, second-, and third-order moments) from the new model for several families of polynomial copulas and perform an application on Belgium and American data.