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A wind speed phase transition model for the emergence of extreme storms

Fürstenau, Norbert and Mittendorf, Monika (2018) A wind speed phase transition model for the emergence of extreme storms. Meteorology and Atmospheric Physics. Springer. ISSN 0177-7971 (Submitted)

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Abstract

Based on initial analysis of two historical extreme storm local wind speed time series (Fürstenau and Mittendorf (2016) Z. Naturforsch. A, 71:1167-1173 ) we derive a model for two-state non-equilibrium phase transition dynamics between the speed levels before/after and during the storm. It is formalized by a nonlinear Bernoulli-Langevin stochastic differential equation with a single Lorentz function control parameter l(t) (Bernoulli Lorentz Langevin equation, BLL). The rate of speed change k(t) = l(t) – k0 (dissipation parameter k0 = inverse relaxation time tau0) allows for simulating and predicting the time series s(t) of the two quite different empirical speed profiles. The pre-/post storm speed is described by a weakly stationary Ornstein-Uhlenbeck (OU) process (k = -k0 < 0 with mean (reversal) speed rho and delta-correlated Gaussian noise of strength Q. Lorentz parameters are determined by start time of transition t1(k=0), duration T of disturbance k(t) > 0, and maximum rate parameter k(t1 + T/2) = kmax. Fitting of wind speed time series with an analytical solution provides speed fluctuation variances for numerical simulations and it predicts hysteresis s(k(t)). Stochastic properties are analyzed by means of numerical BLL-Monte-Carlo simulations and by integration of the corresponding Fokker-Planck equation. For extended disturbance duration T extreme asymptotic speed levels of sa > 200 km/h are predicted. The fluctuation-dissipation theorem provides the foundation for the crucial role of dissipation k0 as phase transition threshold and for the speed fluctuation dynamics. The model is proposed as extension of the OU process to support predictive filtering for control of technical infrastructures during extreme storm. Our hypothesis requires however, additional support by more empirical data .

Item URL in elib:https://elib.dlr.de/114747/
Document Type:Article
Title:A wind speed phase transition model for the emergence of extreme storms
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Fürstenau, Norbertnorbert.fuerstenau (at) dlr.deUNSPECIFIED
Mittendorf, Monikamonika.mittendorf (at) dlr.deUNSPECIFIED
Date:2018
Journal or Publication Title:Meteorology and Atmospheric Physics
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Publisher:Springer
ISSN:0177-7971
Status:Submitted
Keywords:extreme storm, wind speed, time series, nonlinear dynamics, non-equilibrium, phase transition model, stochastic differential equation, analytical model, hysteresis, data fitting, Monte Carlo simulation, Focker-Planck equation
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:air traffic management and operations
DLR - Research area:Aeronautics
DLR - Program:L AO - Air Traffic Management and Operation
DLR - Research theme (Project):L - Efficient Flight Guidance
Location: Braunschweig
Institutes and Institutions:Institute of Flight Control
Institute of Flight Control > Controller Assistance
Institute of Flight Control > Systemergonomy
Deposited By: Fürstenau, Dr.phil.nat. Norbert
Deposited On:05 Nov 2018 12:06
Last Modified:28 Nov 2018 10:02

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