  In this work, we describe, analyze, and implement a pseudospectral quadrature
method for a global computer modeling of the incompressible surface
Navier-Stokes equations on the rotating unit sphere. Our spectrally accurate
numerical error analysis is based on the Gevrey regularity of the solutions of
the Navier-Stokes equations on the sphere. The scheme is designed for
convenient application of fast evaluation techniques such as the fast Fourier
transform (FFT), and the implementation is based on a stable adaptive time
discretization.
