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The first four statistical moments and their trends are calculated for the average daily surface air temperature (SAT) from 1950 to 2010 using the Global Historical Climatology Network-Daily station data for each season relative to the 1961-90 climatology over the Northern Hemisphere. Temporal variation of daily SAT probability distributions are represented as generalized linear regression coefficients on the mean, standard deviation, skewness, and kurtosis calculated for each 10-yr moving time window from 1950-59 to 2001-10. The climatology and trends of these statistical moments suggest that daily SAT probability distributions are non-Gaussian and are changing in time. The climatology of the first four statistical moments has distinct spatial patterns with large coherent structure for mean and standard deviation and relatively smaller and more regionalized patterns for skewness and kurtosis. The linear temporal trends from 1950 to 2010 of the first four moments also have coherent spatial patterns. The linear temporal trends in the characterizing statistical moments are statistically significant at most locations and have differing spatial patterns for different moments. The regionalized variations specific to higher moments may be related to the climate dynamics that contribute to extremes. The nonzero skewness and kurtosis makes this detailed documentation on the higher statistical moments useful for quantifying climate changes and assessing climate model uncertainties. [ABSTRACT FROM AUTHOR]