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Colorado State University (2008)

Stochastic characterization of droughts in stationary and periodic series

Cancelliere, Antonino

Titre : Stochastic characterization of droughts in stationary and periodic series

Auteur : Cancelliere, Antonino

Université de soutenance : Colorado State University

Résumé : Doctor of Philosophy (PhD) 2008

The research described in this dissertation includes the stochastic modelling of drought characteristics, in cases where the underlying series is either periodic or with non-negligible autocorrelation. In addition, extension of the derived models to the regional case has been explored. Moments of drought characteristics, probability distribution functions and return period have been developed in all cases, thus providing tools to characterize droughts in a broad set of situations that may occur in practice. Drought length, accumulated deficit and intensity in stationary dependent processes are investigated jointly by assuming an autoregressive model for the underlying hydrological series. Analysis of accumulated deficit indicates that although the underlying process is stationary, the sequence of deficits is not and thus a truncated multivariate distribution is proposed to model the deficits. Approximate expressions of the joint distribution of the characteristics are derived and employed to estimate analytically the return period of droughts. Drought length in periodic stochastic hydrological series is analyzed by modelling the dependence structure of the underlying hydrological series through a periodic lag 1 Markov chain. Moments and probability mass function of drought length are derived analytically as well as return period of droughts with length greater or equal to a fixed value. Accumulated deficit and intensity in periodic series are investigated either marginally or jointly with drought length by deriving approximate expressions for the corresponding moments, pdf’s and return period with reference to droughts starting either in a given season or in any season. Probabilistic features of characteristics of regional droughts are analyzed and analytical expressions are derived for the moments, pdf’s and return period of areal coverage of deficit, of areal deficit and of accumulated deficit making use of copulas concepts. The overall conclusion of the research is that exact and/or approximate analytical expressions of probability distributions of drought characteristics derived from the statistics of the underlying hydrological series enables one a more reliable probabilistic characterization than employing the inferential approach. The examples using several water supply series and climatologic and hydrological drought indices illustrate and confirm the applicability of the analytical derivations obtained for drought characteristics and associated return periods.

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Page publiée le 16 mai 2011, mise à jour le 18 novembre 2018