Statistical modelling of extreme rainfall in Madeira Island

Extreme rainfall events have triggered a significant number of flash floods in Madeira Island along its past and recent history. Madeira is a volcanic island where the spatial rainfall distribution is strongly affected by its rugged topography. In this thesis, annual maximum of daily rainfall data from 25 rain gauge stations located in Madeira Island were modelled by the generalised extreme value distribution. Also, the hypothesis of a Gumbel distribution was tested by two methods and the existence of a linear trend in both distributions parameters was analysed. Estimates for the 50– and 100–year return levels were also obtained. Still in an univariate context, the assumption that a distribution function belongs to the domain of attraction of an extreme value distribution for monthly maximum rainfall data was tested for the rainy season. The available data was then analysed in order to find the most suitable domain of attraction for the sampled distribution. In a different approach, a search for thresholds was also performed for daily rainfall values through a graphical analysis. In a multivariate context, a study was made on the dependence between extreme rainfall values from the considered stations based on Kendall’s τ measure. This study suggests the influence of factors such as altitude, slope orientation, distance between stations and their proximity of the sea on the spatial distribution of extreme rainfall. Groups of three pairwise associated stations were also obtained and an adjustment was made to a family of extreme value copulas involving the Marshall–Olkin family, whose parameters can be written as a function of Kendall’s τ association measures of the obtained pairs.

Transport modelling: macro and micro simulation for the studied case of Funchal

The work done in this thesis attempts to demonstrate the importance of using models that can predict and represent the mobility of our society. To answer the proposed challenges two models were examined, the first corresponds to macro simulation with the intention of finding a solution to the frequency of the bus company Horários do Funchal, responsible for transport in the city of Funchal, and some surrounding areas. Where based on a simplified model of the city it was possible to increase the frequency of journeys getting an overall reduction in costs. The second model concerns the micro simulation of Avenida do Mar, where currently is being built a new roundabout (Praça da Autonomia), which connects with this avenue. Therefore it was proposed to study the impact on local traffic, and the implementation of new traffic lights for this purpose. Four possible situations in which was seen the possibility of increasing the number of lanes on the roundabout or the insertion of a bus lane were created. The results showed that having a roundabout with three lanes running is the best option because the waiting queues are minimal, and at environmental level this model will project fewer pollutants. Thus, this thesis presents two possible methods of urban planning. Transport modelling is an area that is under constant development, the global goal is to encourage more and more the use of these models, and as such it is important to have more people to devote themselves to studying new ways of addressing current problems, so that we can have more accurate models and increasing their credibility.