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Dynamically evolving Gaussian spatial fields

Baxevani, Anastassia; Podgorski, Krzysztof LU and Rychlik, Igor (2011) In Extremes 14(2). p.223-251
Abstract
We discuss general non-stationary spatio-temporal surfaces that involve dynamics governed by velocity fields. The approach formalizes and expands previously used models in analysis of satellite data of significant wave heights. We start with homogeneous spatial fields. By applying an extension of the standard moving average construction we obtain models which are stationary in time. The resulting surface changes with time but is dynamically inactive since its velocities, when sampled across the field, have distributions centered at zero. We introduce a dynamical evolution to such a field by composing it with a dynamical flow governed by a given velocity field. This leads to non-stationary models. The models are extensions of the earlier... (More)
We discuss general non-stationary spatio-temporal surfaces that involve dynamics governed by velocity fields. The approach formalizes and expands previously used models in analysis of satellite data of significant wave heights. We start with homogeneous spatial fields. By applying an extension of the standard moving average construction we obtain models which are stationary in time. The resulting surface changes with time but is dynamically inactive since its velocities, when sampled across the field, have distributions centered at zero. We introduce a dynamical evolution to such a field by composing it with a dynamical flow governed by a given velocity field. This leads to non-stationary models. The models are extensions of the earlier discretized autoregressive models which account for a local velocity of traveling surface. We demonstrate that for such a surface its dynamics is a combination of dynamics introduced by the flow and the dynamics resulting from the covariance structure of the underlying stochastic field. We extend this approach to fields that are only locally stationary and have their parameters varying over a larger spatio-temporal horizon. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Spectral density, Covariance function, Stationary second order, processes, Velocity field
in
Extremes
volume
14
issue
2
pages
223 - 251
publisher
Kluwer
external identifiers
  • wos:000289733600005
  • scopus:79955150995
ISSN
1572-915X
DOI
10.1007/s10687-010-0120-8
project
MERGE
language
English
LU publication?
yes
id
a34df398-968b-4278-b6f8-4eb8edd01433 (old id 1965034)
date added to LUP
2011-05-23 11:51:29
date last changed
2017-01-01 05:41:40
@article{a34df398-968b-4278-b6f8-4eb8edd01433,
  abstract     = {We discuss general non-stationary spatio-temporal surfaces that involve dynamics governed by velocity fields. The approach formalizes and expands previously used models in analysis of satellite data of significant wave heights. We start with homogeneous spatial fields. By applying an extension of the standard moving average construction we obtain models which are stationary in time. The resulting surface changes with time but is dynamically inactive since its velocities, when sampled across the field, have distributions centered at zero. We introduce a dynamical evolution to such a field by composing it with a dynamical flow governed by a given velocity field. This leads to non-stationary models. The models are extensions of the earlier discretized autoregressive models which account for a local velocity of traveling surface. We demonstrate that for such a surface its dynamics is a combination of dynamics introduced by the flow and the dynamics resulting from the covariance structure of the underlying stochastic field. We extend this approach to fields that are only locally stationary and have their parameters varying over a larger spatio-temporal horizon.},
  author       = {Baxevani, Anastassia and Podgorski, Krzysztof and Rychlik, Igor},
  issn         = {1572-915X},
  keyword      = {Spectral density,Covariance function,Stationary second order,processes,Velocity field},
  language     = {eng},
  number       = {2},
  pages        = {223--251},
  publisher    = {Kluwer},
  series       = {Extremes},
  title        = {Dynamically evolving Gaussian spatial fields},
  url          = {http://dx.doi.org/10.1007/s10687-010-0120-8},
  volume       = {14},
  year         = {2011},
}