Modelling dependence between observed and simulated wind speed data using copulas
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ORIGINAL PAPER
Modelling dependence between observed and simulated wind speed data using copulas L. M. Andre´1
•
P. de Zea Bermudez1,2
Accepted: 28 August 2020 / Published online: 29 October 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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 paper 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. Keywords Wind speed data Extreme winds Dependence Copula models Bayesian approach
1 Introduction For several reasons it is crucial to understand and to be able to predict the behaviour of the wind. Extreme winds are particularly important since they can cause destruction of property and may also originate casualties. Very strong winds may produce, namely, disruptions of energy supply, damages to houses, to infrastructures, such as bridges and to public service facilities, e.g. hospitals. All of these events will eventually generate huge economical losses, especially to insurance companies. Consequently, the knowledge of the wind distribution is of utmost importance in order to prevent these events to occur. This awareness is
& P. de Zea Bermudez [email protected] 1
Departamento de Estatı´stica e Investigac¸a˜o Operacional, Faculdade de Cieˆncias, Universidade de Lisboa, Lisbon, Portugal
2
CEAUL - Centro de Estatı´stica e Aplicac¸o˜es, Faculdade de Cieˆncias, Universidade de Lisboa, Lisbon, Portugal
also important for adequately designing engineering structures and buildings. Although Portugal is a relatively small country (approximatelly 92 000 km2 in land including the archipelagos of Azores and Madeira) the way wind behaves along the territory varies quite a lot. To begin with, the total coastline of Portugal is 1793 km long and the mainland is entirely bathed by the North Atlantic Ocean on the west and south and, therefore, prone to strong winds especially during the Winter season.
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