Strategic Project - UI 6 - 2011-2012

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Organizational Unit

Publications

Statistical modelling of extreme rainfall in Madeira Island

Publication . Réis, Délia Canha Gouveia; Lopes, Luiz Carlos Guerreiro; Mendonça, Sandra Maria Freitas

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.

2014-08Doctoral thesis

Open access

A parametric cure model with covariates

Publication . Abreu, Ana M.

Cure models were developed to deal with situations where it is plausible to assume that there are non-susceptible (or cured) individuals within the study population.Usually,inacuremodel,theaimistoestimatetheproportionofnonsusceptible individuals, the survival function of the susceptible individuals and the effect of the covariates, if they have been included in the model. Therefore, researchers are interested in knowing if the event will occur (which is called incidence) and when it will occur, given that it can occur (which is called latency). For each covariate there are two parameters: one that describes how the covariateaffects incidence andthe otherthat describes howit affects latency. In this context, the population under study is heterogeneous not only because thereare susceptibleandnon-susceptibleindividualsbut also dueto the different values of their covariates. This chapter follows another one Abreu and Rocha [Um novo modelo de cura param´etrico. In: Castro, L.C., Martins, E.G., Rocha, C., Oliveira, M.F., Leal, M.M., Rosado, F. (eds.) Ciˆencia Estat´ıstica, pp. 151– 162.Edic ¸˜ oesSPE,Lisboa(2006)],whereweproposedacuremodelbasedonthe Chendistribution[Chen,A newtwo-parameterlifetimedistributionwith bathtub shapeorincreasingfailureratefunction.Stat.Probab.Lett.49,155–161(2000)]. The good results obtained with this new model when ﬁtted to real data was a motivationfor includingcovariates into the model.

2013Conference object

Restricted access

A spatial extremes characterization of the annual maxima precipitation in Madeira Island

Publication . Reis, Délia Gouveia; Lopes, Luiz Guerreiro; Mendonça, Sandra

A variety of statistical tools such as copulas and spatial max-stable processes have been used in the most recent decades for modelling spatial extreme data. Our aim is to give a spatial extremes characterization of Madeira Island’s annual maxima precipitation using annual maximum daily precipitation data from 17 rain gauge stations throughout the island.

2013Conference object

Open access

Modelling annual maxima of daily rainfall in Madeira Island

Publication . Réis, Délia Gouveia; Lopes, Luiz; Mendonça, Sandra

Madeira Island is located in the Atlantic Ocean off the coast of Northwest Africa, between latitudes 32º30'N–33º30'N and longitudes 16º30'W–17º30'W. Extreme rainfall events have triggered a significant number of flash floods, landslides and debris flows in this volcanic island along its past and recent history. One of the most significant events was the one that happened on the 20th of February 2010, which caused 45 casualties, six missed people and extensive damage to properties and infrastructures. Madeira Island is therefore a natural laboratory for the study of extreme precipitation events and its consequences. In this study, tests based on the likelihood ratio statistic and the probability-weighted moments were used to test the hypothesis of a Gumbel distribution for the annual 1-day maximum rainfall data, from 19 rain gauge stations, provided by the Department of Hydraulics and Energy Technologies of the Madeira Regional Laboratory of Civil Engineering. The rainfall records, with 22, 23 and 31 years of extension, were drawn from rain gauge stations located in the northern and southern hillsides of the island. The estimates for the generalised extreme value distribution (GEV) obtained by the methods of maximum likelihood and probability-weighted moments revealed the influence of the proximity to the sea and altitude on the spatial distribution of extreme rainfall, in addition to the natural differences observed on the windward and lee sides of any mountainous island. Estimates for 50- and 100-year return levels were also obtained. The existence of trends in the parameters’ values was also analysed, revealing a significant evidence of a linear trend, both in location and scale parameters, for one location in the north side of the island.

2013Conference object

Open access

A dependence modelling study of extreme rainfall in Madeira Island

Publication . Gouveia-Reis, Délia; Lopes, Luiz Guerreiro; Mendonça, Sandra

The dependence between variables plays a central role in multivariate extremes. In this paper, spatial dependence of Madeira Island's rainfall data is addressed within an extreme value copula approach through an analysis of maximum annual data. The impact of altitude, slope orientation, distance between rain gauge stations and distance from the stations to the sea are investigated for two different periods of time. The results obtained highlight the influence of the island's complex topography on the spatial distribution of extreme rainfall in Madeira Island.

2016Journal article

Open access