A new method for modelling the space variability of significant wave height Anastassia Baxevani & Igor Rychlik & Richard J. Wilson Received: 18 December 2005 / Revised: 18 December 2005 / Accepted: 19 January 2006 / Published online: 8 June 2006 # Springer Science + Business Media, LLC 2006 Abstract Significant wave height, H s , is a measure of the variability of the ocean surface and is defined to be four times the standard deviation of the height of the ocean surface. In this paper, we present a methodology for modelling estimates of H s over space and time, using data obtained from satellite measurements. These estimates can be thought of as a random surface in space which develops over time. For each fixed time and over some limited region in space, the field consisting of the H s estimates may be considered stationary. Furthermore, it is reasonable to assume that the (natural) logarithms of the H s estimates are normally distributed. Under these assumptions and for each fixed time, the marginal distribution over space of the random field of the logarithms of the H s estimates is fitted by estimating its mean and covariance function, where the form of the covariance function is chosen to allow for correlation patterns at different spatial scales in the data. Both the mean and the covariance function of this model are allowed to be time dependent. A new methodology is developed for estimating the parameters of the chosen covariance structure. The proposed model is validated along the TOPEX-Poseidon satellite tracks by computing distributions of different quantities for the fitted model and comparing these to empirical estimates. Finally, the fitted model is used to compute the distribution of the global maximum over a certain region in the North Atlantic and to reconstruct the H s field. Keywords Significant wave height . Random surface . Satellite data . Gaussian random fields . Stationary . Total variation AMS 2000 Subject Classification Primary—60G10, 60G15, 60G60 Extremes (2005) 8: 267–294 DOI 10.1007/s10687-006-0002-2 The research of Anastassia Baxevani is partially supported by the Gothenburg Stochastic Center. A. Baxevani (*) : I. Rychlik Center for Mathematical Sciences, University of Lund, Lund, Sweden e-mail: baxevani@maths.lth.se R. J. Wilson Department of Mathematics, The University of Queensland, Brisbane, Qld, Australia