SPECTRAL APPROACH TO OPTIMAL ESTIMATION OF THE GLOBAL AVERAGE TEMPERATURE

Making use of EOF analysis and statistical optimal averaging technique s, the problem of random sampling error in estimating the global avera ge temperature by a network of surface stations has been investigated. The EOF representation makes it unnecessary to use simplified empiric al models of the correlation structure of temperature anomalies. If an adjustable weight is assigned to each station according to the criter ion of minimum mean-square error, a formula for this error can be deri ved that consists of a sum of contributions from successive EOF modes. The EOFs were calculated from both observed data and a noise-forced E BM for the problem of one-year and five-year averages. The mean square statistical sampling error depends on the spatial distribution of the stations, length of the averaging interval, and the choice of the wei ght for each station data stream. Examples used here include four symm etric configurations of 4 X 4, 6 X 4, 9 X 7, and 20 X 10 stations and the Angell-Korshover configuration. Comparisons with the 100-yr U.K. d ataset show that correlations for the time series of the global temper ature anomaly average,between the full dataset and this study's sparse configurations are rather high. For example, the 63-station Angell-Ko rshover network with uniform weighting explains 92.7% of the total var iance, whereas the same network with optimal weighting can lead to 97. 8% explained total variance of the U.K. dataset.