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Crossing properties for geophysical systems forced by Poisson noise
Author(s) -
Tamea S.,
Laio F.,
Ridolfi L.,
RodriguezIturbe I.
Publication year - 2011
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2011gl049074
Subject(s) - geophysics , poisson distribution , geology , noise (video) , seismic noise , seismology , computer science , mathematics , statistics , artificial intelligence , image (mathematics)
Threshold crossings are crucial in many geophysical processes, including soil water balance, vegetation stress, landslides, particle erosion and transport. We focus here on the crossing properties of systems with additive or multiplicative stochastic impulses having the form of a marked Poisson process. We derive exact expressions for the probability of excursions of very short duration above/below a generic threshold. These expressions, together with mean first passage times, allow for approximating the full probability density function of excursion times with two‐parameter distributions. Such approximations are effective for a wide range of stochastic processes covering relevant geophysical applications, as confirmed by the two examples provided regarding the dynamics of soil moisture content and water table depth.