Dynamically evolving Gaussian spatial fields
Artikel i vetenskaplig tidskrift, 2011

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.

significant wave height

seas

velocities

Stationary second order

rainfall

Spectral density

mathematical-analysis

Velocity field

Covariance function

processes

random noise

Författare

Anastassia Baxevani

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

K. Podgorski

Lunds universitet

Igor Rychlik

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Extremes

1386-1999 (ISSN)

Vol. 14 2 223-251

Drivkrafter

Hållbar utveckling

Styrkeområden

Transport

Fundament

Grundläggande vetenskaper

Ämneskategorier

Sannolikhetsteori och statistik

DOI

10.1007/s10687-010-0120-8

Mer information

Senast uppdaterat

2018-03-02