Remotely sensed data products are now routinely used to study various aspects of the Earth's atmosphere. These remote sensing datasets are typically very high dimensional, have near global coverage and exhibit nonstationary spatial correlation structures. Proper statistical analysis of these datasets should be sufficiently flexible to account for all these aspects. To this end, we develop a kernel convolution construction of spatial processes on a sphere. As is the case with kernel convolution constructions on the plane, we establish a link between stationary kernels and a stationary covariance function on the sphere via the spherical harmonic decomposition of the kernel. We also introduce the Kent distribution as an appropriate kernel with interpretable parameters to be used in the kernel convolution construction. We demonstrate the discrete kernel convolution model using a dataset of remotely sensed CO2 concentrations over the globe. Copyright © 2014 John Wiley & Sons, Ltd.