Francisco Cuevas, UQÀM

Title: A family of covariance functions for random fields on spheres

Abstract: The Matérn family of isotropic covariance functions has been central to the theoretical development and application of statistical models for geospatial data. For global data defined over the whole sphere representing planet Earth, the natural distance between any two locations is the great circle distance. In this setting, the Matern family of covariance functions has a restriction on the smoothness parameter, making it an unappealing choice to model smooth data. Finding a suitable analogue for modelling data on the sphere is still an open problem. This work proposes a new family of isotropic covariance functions for random fields defined over the sphere. The proposed family has four parameters, one of which indexes the mean square differentiability of the corresponding Gaussian field, and also allows for any admissible range of fractal dimension. We apply the proposed model to a dataset of precipitable water content over a large portion of the Earth, and show that the model gives more precise predictions of the underlying process at unsampled locations than does the Matérn model using chordal distances.