TITLE:
Peaks over Manifold (POM): A Novel Technique to Analyze Extreme Events over Surfaces
AUTHORS:
Gonzalo Perera, Angel M. Segura
KEYWORDS:
Peaks Over Thresholds (POT), Generalized Pareto Distribution, Extreme Events
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.1,
January
27,
2022
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.