OPTIMAL WEIGHTING SCHEME FOR AVERAGING REGIONAL TEMPERATURE .1. THEORETICAL-ANALYSIS

Inadequacy of a spatial data sampling scheme often causes confusion wh en considering global, hemispherical and regional temperature averages . Jones et al.([1,2]), Hansen et al.([3]), Vinnikov et al.([4]) used d ifferent methods in their researches for the long-term trend of global or hemispherical surface air temperatures. Optimal weighting scheme w as used by Vinnikov et al. The weight for each station at different la titude was obtained in the sense of minimum mean square error of avera ge temperature. The weights were then used to compute the global or he mispherical average temperature. Recently, using empirical orthogonal functions, Shen et al.([5]) showed that the global average temperature can be computed with quite satisfactory accuracy by using only above 60 stations distributed properly over the globe. Our research will inv estigate the influence of inadequate spatial sampling on the computati on of regional average temperature. The optimal weighting scheme is gi ven in sec, 2. Some special cases of the scheme are analyzed in sec. 3 ; sees. 4 and 5 show some results of test computations and summarize o ur conclusions. More comprehensive computational results about the com parison between the optimal weighting scheme and the ordinary arithmet ic average will be given in another article.