AbstractThis paper considers the mean squared error (MSE) incurred in estimating an idealized earth's global average temperature with a finite number of point gauges located in a specified or stochastic way over the globe. For a class of model earths with rotationally invariant statistics, the MSE formula can be cast into the form of a summation over spherical harmonic indices. The summand factors into a part which depends on the design of the gauge network and a second part which is the degree variance spectrum of the surface temperature field. After presenting this formalism, we provide an example spectrum for the surface temperature field derived from a simple two parameter stochastic climate model defined on the sphere. An example calculation is given for the case ofNgauges randomly arranged on the sphere. In addition, the sampling error is computed for some simple regular arrays of gauges as illustrative examples.