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Velocities of a spatial-temporal stochastic field with embedded dynamics

Podgorski, Krzysztof LU and Wegener, Joerg (2012) In Environmetrics 23(3). p.238-252
Abstract
The paper investigates further an approach to modeling dynamically changing Gaussian spatio-temporal fields. In that

approach, the dynamics are introduced by embedding deterministic velocities into a stochastic spatio-temporal Gaussian

model. In this way, a dynamically inactive stochastic field with given spatial and temporal covariance structure gains

dynamics that in general follow a deterministic pattern. Here, we make an important connection between the resulting

stochastic field and underlying deterministic dynamics by demonstrating that in the case of isotropic spatial dependencies,

the observed random velocities are centered at the velocities of the underlying physical flow. Additionally,... (More)
The paper investigates further an approach to modeling dynamically changing Gaussian spatio-temporal fields. In that

approach, the dynamics are introduced by embedding deterministic velocities into a stochastic spatio-temporal Gaussian

model. In this way, a dynamically inactive stochastic field with given spatial and temporal covariance structure gains

dynamics that in general follow a deterministic pattern. Here, we make an important connection between the resulting

stochastic field and underlying deterministic dynamics by demonstrating that in the case of isotropic spatial dependencies,

the observed random velocities are centered at the velocities of the underlying physical flow. Additionally, we discuss strategies

for simulation of such fields and give foundation for fitting and prediction procedures that are based on the obtained

results. In an effort to illustrate attractiveness of the approach for modeling environmental phenomena, we consider a

parametrized specification of spatio-temporal correlation structure and embed to it the dynamics driven by the shallow

water equations. Through simulations, we show how the spatio-temporal behavior of the resulting non-stationary Gaussian

field is altered by the embedded dynamics. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Gaussian fields, nonstationary covariance, dynamical flow, isotropic covariance, Ornstein–Uhlenbeck process
in
Environmetrics
volume
23
issue
3
pages
238 - 252
publisher
John Wiley & Sons
external identifiers
  • wos:000302396600004
  • scopus:84862792606
ISSN
1099-095X
DOI
10.1002/env.1150
language
English
LU publication?
yes
id
4a8e8077-6619-4ec0-b112-8d4a798bfe90 (old id 3048401)
date added to LUP
2012-09-04 14:00:24
date last changed
2017-01-01 04:14:43
@article{4a8e8077-6619-4ec0-b112-8d4a798bfe90,
  abstract     = {The paper investigates further an approach to modeling dynamically changing Gaussian spatio-temporal fields. In that<br/><br>
approach, the dynamics are introduced by embedding deterministic velocities into a stochastic spatio-temporal Gaussian<br/><br>
model. In this way, a dynamically inactive stochastic field with given spatial and temporal covariance structure gains<br/><br>
dynamics that in general follow a deterministic pattern. Here, we make an important connection between the resulting<br/><br>
stochastic field and underlying deterministic dynamics by demonstrating that in the case of isotropic spatial dependencies,<br/><br>
the observed random velocities are centered at the velocities of the underlying physical flow. Additionally, we discuss strategies<br/><br>
for simulation of such fields and give foundation for fitting and prediction procedures that are based on the obtained<br/><br>
results. In an effort to illustrate attractiveness of the approach for modeling environmental phenomena, we consider a<br/><br>
parametrized specification of spatio-temporal correlation structure and embed to it the dynamics driven by the shallow<br/><br>
water equations. Through simulations, we show how the spatio-temporal behavior of the resulting non-stationary Gaussian<br/><br>
field is altered by the embedded dynamics.},
  author       = {Podgorski, Krzysztof and Wegener, Joerg},
  issn         = {1099-095X},
  keyword      = {Gaussian fields,nonstationary covariance,dynamical flow,isotropic covariance,Ornstein–Uhlenbeck process},
  language     = {eng},
  number       = {3},
  pages        = {238--252},
  publisher    = {John Wiley & Sons},
  series       = {Environmetrics},
  title        = {Velocities of a spatial-temporal stochastic field with embedded dynamics},
  url          = {http://dx.doi.org/10.1002/env.1150},
  volume       = {23},
  year         = {2012},
}