Modelling dependence between observed and simulated wind speed data using copulas

In real applications, associations between variables are often non-linear and data commonly exhibit strong asymmetries and/or heavy tails. Copula models enable to create the joint distribution of vectors of random variables independently of their marginal distributions. This work aims to analyse and characterise the dependence between daily maximum wind speeds, X, observed in Portugal and simulated daily maximum wind speeds, Y, produced by a numerical-physical model. One of the major benefits of using simulated data is their availability at high spatial and temporal resolutions contrarily to observed data, which are commonly scarce. The main problem is that the simulated and the observed winds, in some stations, do not match well and tend to differ mostly in the right tail. Consequently, it is very important to understand the dependence between X and Y. The ultimate purpose is to calibrate the simulated data and bring it in line with observed data. That offers practitioners richer data sources. The results showed that, in the overall, Gamma and Lognormal are the most suitable marginal distributions for our data and Gumbel copula is the most adequate to model the dependence structure. Finally, the classical modelling is compared with a Bayesian approach.