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Velocities of a spatial-temporal stochastic field with embedded dynamics

Publiceringsår: 2012
Språk: Engelska
Sidor: 238-252
Publikation/Tidskrift/Serie: Environmetrics
Volym: 23
Nummer: 3
Dokumenttyp: Artikel i tidskrift
Förlag: John Wiley & Sons


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.


  • Probability Theory and Statistics
  • Gaussian fields
  • nonstationary covariance
  • dynamical flow
  • isotropic covariance
  • Ornstein–Uhlenbeck process


  • ISSN: 1099-095X

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