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 components 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 Gauss‐Legendre networks outperform the uniform networks of the same size as long as the number of stations is sufficiently large.