Optimal Averaging for the Determination of Global Mean Temperature: Experiments with Model Data

Optimal averaging is a method to estimate some area mean of datasets with imperfect spatial sampling. The accuracy of the method is tested by application to time series of January temperature fields simulated by the NCAR Community Climate Model. Some restrictions to the application of optimal averaging are given. It is demonstrated that the proper choice of a spatial correlation model is crucial. It is shown that the optimal averaging procedures provide a better approximation to the true mean of a region than simple area-weight averaging does. The inclusion of measurement errors of realistic size at each observation location hardly changes the value of the optimal average nor does it substantially alter the sampling error of the optimal average.