Dynamically evolving Gaussian spatial fields
Journal article, 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



Stationary second order


Spectral density


Velocity field

Covariance function


random noise


Anastassia Baxevani

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

K. Podgorski

Lund University

Igor Rychlik

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics


1386-1999 (ISSN)

Vol. 14 2 223-251

Driving Forces

Sustainable development

Areas of Advance



Basic sciences

Subject Categories

Probability Theory and Statistics



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