  The Mat{\'e}rn 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 Mat{\'e}rn 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 paper proposes a new family of isotropic
covariance functions for random fields defined over the sphere. The proposed
family has a parameter that indexes the mean square differentiability of the
corresponding Gaussian field, and allows for any admissible range of fractal
dimension. Our simulation study mimics the fixed domain asymptotic setting,
which is the most natural regime for sampling on a closed and bounded set. As
expected, our results support the analogous results (under the same asymptotic
scheme) for planar processes that not all parameters can be estimated
consistently. 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 Mat{\'e}rn model using chordal distances.
