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We develop methods for adjusting grid box average temperature time series for the effects on variance of changing numbers of contributing data. Owing to the different sampling characteristics of the data, we use different techniques over land and ocean. The result is to damp average temperature anomalies over a grid box by an amount inversely related to the number of contributing stations or observations. Variance corrections influence all grid box time series but have their greatest effects over data sparse oceanic regions. After adjustment, the grid box land and ocean surface temperature data sets are unaffected by artificial variance changes which might affect, in particular, the results of analyses of the incidence of extreme values. We combine the adjusted land surface air temperature and sea surface temperature data sets and apply a limited spatial interpolation. The effects of our procedures on hemispheric and global temperature anomaly series are small.