A method is developed for estimating the uncertainty (standard error) of observed regional, hemispheric, and global-mean surface temperature series due to incomplete spatial sampling. Standard errors estimated at the grid-box level [SE2 = S2(1 − r̄)/(1 + (n − 1)r̄)] depend upon three parameters: the number of site records (n) within each box, the average interrecord correlation (r̄) between these sites, and the temporal variability (S2) of each grid-box temperature time series. For boxes without data (n = 0), estimates are made using values of S2 interpolated from neighboring grid boxes. Due to spatial correlation, large-scale standard errors in a regional-mean time series are not simply the average of the grid-box standard errors, but depend upon the effective number of independent sites (Neff) over the region. A number of assumptions must be made in estimating the various parameters, and these are tested with observational data and complementary results from multicentury control integrations of... Abstract A method is developed for estimating the uncertainty (standard error) of observed regional, hemispheric, and global-mean surface temperature series due to incomplete spatial sampling. Standard errors estimated at the grid-box level [SE2 = S2(1 − r̄)/(1 + (n − 1)r̄)] depend upon three parameters: the number of site records (n) within each box, the average interrecord correlation (r̄) between these sites, and the temporal variability (S2) of each grid-box temperature time series. For boxes without data (n = 0), estimates are made using values of S2 interpolated from neighboring grid boxes. Due to spatial correlation, large-scale standard errors in a regional-mean time series are not simply the average of the grid-box standard errors, but depend upon the effective number of independent sites (Neff) over the region. A number of assumptions must be made in estimating the various parameters, and these are tested with observational data and complementary results from multicentury control integrations of...