| Summary: | Tese de doutoramento, Física, Universidade de Lisboa, Faculdade de Ciências, 2010. This thesis addresses pertinent challenges underneath the estimation of the state of the system at a set of circumstances B given a set of conditions A. In particular, two main problems are considered: on one hand, that of atmospheric downscaling; on the other hand, that of atmospheric predictability. For that purpose, novel methods in nonlinear statistics and dynamics are developed and implemented in the aforementioned contexts. As far as the atmospheric downscaling is concerned, nonlinear statistical features are assessed within the statistical response of the monthly winter precipitation to the North Atlantic Oscillation (NAO) over the North Atlantic European Region. For that purpose, two major methodologies are developed and implemented. On one hand, a diagnostic measure is built in order to measure the asymmetric part of an estimated variable’s response to its predictor, a measure undetected by linear correlation. As a practical application, that variable is chosen to be the precipitation and its predictor the NAO regime (NAO+ and NAO-). The asymmetric features are then used to define an asymmetry-based measure of non-Gaussianity. On the other hand, an information-theoretical assessment on non- Gaussianity is performed and a corresponding measure of informationtheoretical correlation − also transcending the limited scope of linear correlation − defined and applied to the aforementioned downscaling application. As main results, the proposed estimators for asymmetry and non- Gaussianity are proven to be consistent in their domain of validity. The statistical response of monthly precipitation to NAO is seen to be asymmetric and non-Gaussian. New relevant features are brought out as a result of the application of the proposed nonlinear statistical methods. As far as atmospheric predictability is concerned, a systematic formalism is derived for the dynamics of prediction errors under the combined influence of initial-condition ...
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