Significant wave height, Hs, 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 Hs 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 Hs estimates may be considered stationary. Furthermore, it is reasonable to assume that the (natural) logarithms of the Hs 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 Hs 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 Hs field.