Abstract
Many useful statistical properties can be derived for isotropic, stationary, homogeneous, Gaussian random fields. The field of surface pressure in the region north of 70°N is shown to approximately satisfy these conditions. Under these conditions, all properties of the field are related to the autocovariance, which is a function of time and space lag. In particular, the following quantities are derived: the time and space covariance functions for the geostrophic wind; the covariance functions for the vorticity of the geostrophic wind; the average number of highs, lows and saddles per unit area; the average number of highs, lows and saddles at which the vorticity exceeds a specified threshold; and the probability density function for the Gaussian curvature of the pressure surface. The horizontal shear in the geostrophic wind is also investigated, as is the number of umbilic points per unit area. Estimates for all these quantities are constructed using observations of surface pressure from the Arctic Basin during 1979 and 1980. The comparison between theory and observation is favorable. At least when these several quantities are considered, the isotropic, stationary, homogeneous, Gaussian random process is a good model of the actual pressure field.
