Estimation of nonstationary spatial covariance structure

We introduce a method for estimating nonstationary spatial covariance structure from space-time data and apply the method to an analysis of Sydney wind patterns. Our method constructs a process honouring a given spatial covariance matrix at observing stations and uses one or more stationary processes to describe conditional behaviour given observing site values. The stationary processes give a localised description of the spatial covariance structure. The method is computationally attractive, and can be extended to the assessment of covariance for multivariate processes. The technique is illustrated for data describing the east-west component of Sydney winds. For this example, our own methods are contrasted with a geometrically appealing though computationally intensive technique which describes spatial correlation via an isotropic process and a deformation of the geographical space.