  This paper proposes a sketching strategy based on spherical designs, which is
applied to the classical spherical basis function approach for massive
spherical data fitting. We conduct theoretical analysis and numerical
verifications to demonstrate the feasibility of the proposed { sketching}
strategy. From the theoretical side, we prove that sketching based on spherical
designs can reduce the computational burden of the spherical basis function
approach without sacrificing its approximation capability. In particular, we
provide upper and lower bounds for the proposed { sketching} strategy to fit
noisy data on spheres. From the experimental side, we numerically illustrate
the feasibility of the sketching strategy by showing its comparable fitting
performance with the spherical basis function approach.
  These interesting findings show that the proposed sketching strategy is
capable of fitting massive and noisy data on spheres.
