  Problems in astrophysics, space weather research and geophysics usually need
to analyze noisy big data on the sphere. This paper develops distributed
filtered hyperinterpolation for noisy data on the sphere, which assigns the
data fitting task to multiple servers to find a good approximation of the
mapping of input and output data. For each server, the approximation is a
filtered hyperinterpolation on the sphere by a small proportion of quadrature
nodes. The distributed strategy allows parallel computing for data processing
and model selection and thus reduces computational cost for each server while
preserves the approximation capability compared to the filtered
hyperinterpolation. We prove quantitative relation between the approximation
capability of distributed filtered hyperinterpolation and the numbers of input
data and servers. Numerical examples show the efficiency and accuracy of the
proposed method.
