This paper describes a method that minimizes the mean squared error (MSE) in estimating the spherical harmonic components of the surface air temperature field. The ratio of the MSE to the variance of the spherical harmonic component is expressed in terms of the length scale Xo, and the positions and weights of the measurement stations. The weights are optimized by the condition of minimizing th...

A spherical t-design is a set of points on the unit sphere that are nodes of a quadrature rule with positive equal weights that is exact for all spherical polynomials of degree ≤ t. The existence of a spherical t-design with (t + 1)2 points in a set of interval enclosures on the unit sphere S2 ⊂ R3 for any 0 ≤ t ≤ 100 is proved in [17, Chen, Frommer, Lang, Computational existence proofs for sph...