Because they strongly disturb the ionosphere properties,the extreme magnetic storms are feared events for integrityand continuity of navigation applications such as WAAS(Wide Area Augmentation System) or EGNOS (EuropeanGeostationary Navigation Overlay Service), the EuropeanSBAS (Satellite-Based Augmentation System) complementingGPS. An accurate modeling of the intensity of occurrenceof severe ionospheric storms is necessary. The aim ofthe present paper is to give an estimation of the frequencyof such extrememagnetic storms per time unit (year) throughouta solar cycle.An innovative approach based on a proportional hazardmodel is developed. Inspired by the Cox model, thismethod allows including non-stationarity and covariate influence.As in Extreme Value Theory (EVT) and especiallyin Peaks over Threshold modeling, all the high level eventsare used to make estimation and the results are extrapolatedto the extreme level events. The model presented in this paperassumes that the number of storms during a cycle is anon-homogeneous Poisson process. The intensity of thisprocess can then be expressed as the product of a baselinerisk and a risk factor. Contrary to what is done in the Coxmodel, the baseline risk is one parameter of interest (andnot a nuisance one), it is the intensity to estimate.The main data set used in this paper is the ap index,the aa index is also utilized for comparison. After a precisedescription of data pretreatments, the innovative model ispresented. The estimation results are given as well as severalextensions. A prediction for the current solar cycle(24th) is also proposed.
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