Estimation of the global average temperature with optimally weighted point gauges

This paper considers the minimum mean squared error (MSE) incurred in estimating an idealized Earth's global average temperature with a finite network of point gauges located over the globe. We follow the spectral MSE formalism given by North et al. (1992) and derive the optimal weights for N gauges in the problem of estimating the Earth's global average temperature. Our results suggest that for commonly used configurations the variance of the estimate due to sampling error can be reduced by as much as 50%.