Abstract
We present a novel method to analyze extreme events of flows over manifolds called Peaks Over Manifold (POM). Here we show that under general and realistic hypotheses, the distribution of affectation measures converges to a Generalized Pareto Distribution (GPD). The method is applicable to floods, ice cover extent, extreme rainfall or marine heatwaves. We present an application to a synthetic data set on tide height and to real ice cover data in Antartica.
Highlights
Extreme events such as Tsunamis or floods are crucial for the impact they have in societies and ecosystems human developments as financial markets, industrial methods of production, telecommunication systems, and, at last but not least, on natural phenomena and its relationship with antropogenic factors [1]-[9]
The appropriate characterization of the impact of these events requires novel theoretical developments. Techniques such as the peak over threshold (POT) for univariate time series, which describe the distribution of the excess of a time series with respect to a given threshold are well known from decades ago [10] [11] [12]
We explored ice cover data in Antartica using reanalysis data from the Environmental Modeling Center of the National Centers for Environmental Prediction (NCEP) from the National Oceanic and Atmospheric Administration (NOAA) using the second version [13]
Summary
Extreme events such as Tsunamis or floods are crucial for the impact they have in societies and ecosystems human developments as financial markets, industrial methods of production, telecommunication systems, and, at last but not least, on natural phenomena and its relationship with antropogenic factors [1]-[9]. The change from univariate to n-dimensional data implies substantial additional complexity and in particular an unsolved problem is to characterize the distribution of excesses of the progressive development of mass, physical, biological or chemical properties on affected areas (tides, floods, ice cover, etc.) over surfaces or manifolds. We will introduce two preliminary indexes of impact of a set of data flow, in Theorems 1 and 2, helping to arrive to the main result of this paper, Theorem 3. We consider an impact measure, whose density may be chosen according to subjective valuation of risks. We compute this impact of the flow expansion over the region with an (intrinsic) distance greater than u to the base line of the flow.
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