دانلود رایگان مقاله مدل چند متغیره آماری حوادث شدید

Abstract

Wave extreme events can be understood as the combination of Storm-intensity, Directionality and Intra-time distribution. However, the dependence structure among these factors is still unclear. A methodology has been developed to model wave-storms whose components are linked together. The model is composed by three parts: an intensity module, a wave directionality module, and an intra-time distribution module. In the Storm-intensity sub-model, generalized Pareto distributions and hierarchical Archimedean copulas have been used to characterize the storm energy, unitary energy, peak wave-period and duration. In the Directionality and Intra-time sub-models, the wave direction (at the peak of the storm) and the storm growth–decay rates are linked to the variables from the intensity model, respectively. The model is applied to the Catalan coast (NW Mediterranean). The outcomes denote spatial patterns that coincide with the state of knowledge. The proposed methodology is able to provide boundary conditions for wave and near-shore studies, saving computational time and establishing the dependence of the proposed variables. Such synthetic storms reproduce the inter-variable co-dependence of the original data.

7. Conclusions

The statistical wave-storm model proposed is composed by three sub-modules: a) Storm-intensity, b) Wave-directionality and c) Intra-time distribution. In these sub-modules, waves have been defined by a set of storm-components (E, Eu,p, Tp, D, h∗ p and growth– decay rates), representing their nature in a more accurate manner. Our model is well validated by buoy records, whereas main sources of residuals are related to growth–decay rates. Storms have been defined with a threshold of Hm0 = 2.2 m, which has been obtained after testing on D∗ , plus Hm0 excess-overthreshold plots. In the Intensity sub-model, the marginal distributions of each variable are characterized by GPDs, whereas dependences among the variables are represented by HACs. The best fitting HAC type is Gumbel. It is observed that the strongest dependence may be between E and D. Two HAC structures are observed along the Catalan coast: type A and type B, depending on the degree of semi-dependence between Eu,p and (E,D). The semi-dependence parameter t(E,D) increases northward. Therefore, northern E and D present more correlation. Wave-directions are described via movM. The movM distribution is selected using a statistic from the Watson test as convergence criteria. The principal peak-wave incoming-direction, h∗ p, at N1 to N6 are, by decreasing order of importance, North and East; whereas eastern and southern directions are predominant from N7 to S7. The most appropriate model for wave-height evolution is the irregular-trapezoidal model. On the other hand, the growth–decay rates are related to the rest of the storm components through a polynomial relationship with D. A mean behavior of D for D < 100 h is reproduced by the model, although for greater D the model tends to predict higher growth rates and lower decay rates. One feature of our model is its ability to generate synthetic storm conditions and to classify them by Tr; these storms are evaluated in the form of pie-charts. In general, for a Tr of 5 years, storms at the northern Catalan coast have greater E, D, and Hm0; while Tp are similar to central or southern Catalan coasts. Also, the principal h∗ p is eastern and the growth and decay rates approximate 0.55 and 0.35, respectively.