Copula-based models for design rainfall

Funded by: FWO (Research Foundation - Flanders)
Researcher: Sander Vandenberghe
Promoters: Niko Verhoest, Bernard De Baets (
Short name: COPRAIN
Begin date: 01/10/2008
End date: 30/9/2012


For the dimensioning of hydraulic structures one often uses design storms, with a certain return period, or long time series of simulated rainfall to make sure the design satisfies all risk-related norms. Until recently, this exercise was usually carried out using extreme value distribution functions (e.g. Gumbel) for the estimation of intensity-duration-frequency (IDF) relations and stochastic rainfall models. However, limiting assumptions regarding the dependence structure between storm variables always had to be made.
Recently, with the introduction of copulas in hydrology as a flexible tool for modelling the dependence structure between different variables, independently of their marginal behaviour, new research opportunities for rainfall modelling are created. Some topics that will be covered in this research project are:

  • The use of copulas for the description and modelling of the internal storm structure.
  • The exploration of copula-based alternatives for existing (point) rainfall models , with a detailed emphasis on the improvement of rectangular pulses models regarding the reproduction of extremes and the clustering of rainfall in time.
  • The incorporation of spatial dependencies with means of copulas in space-time rainfall models, based on radar rainfall images.
    Eventually, an advanced copula-based rainfall model will be constructed that is able to generate synthetic rainfall time series which resemble more the physical rainfall in terms of extremes, internal storm structure (at different aggregation levels), spatial dependencies, etc.

More mathematically involved research questions will also be addressed:

  • The use and evaluation of existing copula parameter estimation methods and goodness-of-fit techniques, aiming at finding the most reliable and practical methods.
  • The construction and use of high dimensional copulas.
  • The use of asymmetric copulas, both in terms of specific tail dependencies and in terms of non-exchangeable random variables.