Optimal Estimation of Spherical Harmonic Components from a Sample with Spatially Nonuniform Covariance Statistics

An optimal estimation technique is presented to estimate spherical harmonic coefficients. This technique is based on the minimization of the mean square error. This optimal estimation technique consists of computing optimal weights for a given network of sampling points. Empirical orthogonal functions (EOFs) are an essential ingredient in formulating the estimation technique of the field of which the second-moment statistics are non-uniform over the sphere. The EOFs are computed using the United Kingdom dataset of global gridded temperatures based on station data. The utility of the technique is further demonstrated by computing a set of spherical harmonic coefficients from the 100-yr long surface temperature fluctuations of the United Kingdom dataset. Next, the validity of the mean-square error formulas is tested by actually calculating an ensemble average of mean-square estimation error. Finally, the technique is extended to estimate the amplitudes of the EOFs.