Aliased power of a stochastic temperature field on a sphere

A random climate field over the globe can be decomposed into a series of spherical harmonic functions. This paper shows that the mean square sampling error for a spherical harmonic coefficient is composed of aliased powers from other spherical harmonic omponents due to the spatial gaps in sampling networks. A general formula is given for calculating the aliased powers. On the basis of the spectra derived from a noise-forced linear energy balance model (EBM) for the climate field the aliased powers are investigated in detail for the Gauss-Legendre networks and the latitude-longitude uniform networks. It is found that the GaussLegendre networks outperform the uniform networks of the same size as long as the number of stations is sufficiently large.