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.

Multivariate analysis for the classification and differentiation of Madeira wines according to main grape varieties

In order to differentiate and characterize Madeira wines according to main grape varieties, the volatile composition (higher alcohols, fatty acids, ethyl esters and carbonyl compounds) was determined for 36 monovarietal Madeira wine samples elaborated from Boal, Malvazia, Sercial and Verdelho white grape varieties. The study was carried out by headspace solid-phase microextraction technique (HS-SPME), in dynamic mode, coupled with gas chromatography–mass spectrometry (GC–MS). Corrected peak area data for 42 analytes from the above mentioned chemical groups was used for statistical purposes. Principal component analysis (PCA) was applied in order to determine the main sources of variability present in the data sets and to establish the relation between samples (objects) and volatile compounds (variables). The data obtained by GC–MS shows that the most important contributions to the differentiation of Boal wines are benzyl alcohol and (E)-hex-3-en-1-ol. Ethyl octadecanoate, (Z)-hex-3-en-1-ol and benzoic acid are the major contributions in Malvazia wines and 2-methylpropan-1-ol is associated to Sercial wines. Verdelho wines are most correlated with 5-(ethoxymethyl)-furfural, nonanone and cis-9-ethyldecenoate. A 96.4% of prediction ability was obtained by the application of stepwise linear discriminant analysis (SLDA) using the 19 variables that maximise the variance of the initial data set.