## Abstract

This paper estimates the sampling error variances of gridded monthly U.S. Historical Climatology Network, version 2 (USHCN V2), time-of-observation-biases (TOB)-adjusted data. The analysis of mean surface air temperature (SAT) assesses uncertainties, trends, and the rankings of the hottest and coldest years for the contiguous United States in the period of 1895–2008. Data from the USHCN stations are aggregated onto a 2.5° × 3.5° latitude–longitude grid by an arithmetic mean of the stations inside a grid box. The sampling error variances of the gridded monthly data are estimated for every month and every grid box with data. The gridded data and their sampling error variances are used to calculate the contiguous U.S. averages and their trends and associated uncertainties. The sampling error variances are smaller (mostly less than 0.2°C^{2}) over the eastern United States, where the station density is greater and larger (with values of 1.3°C^{2} for some grid boxes in the earlier period) over mountain and coastal areas. In the period of 1895–2008, every month from January to December has a positive linear trend. February has the largest trend of 0.162°C (10 yr)^{−1}, and September has the smallest trend at 0.020°C (10 yr)^{−1}. The three hottest (coldest) years measured by the mean SAT over the United States were ranked as 1998, 2006, and 1934 (1917, 1895, and 1912).

*Corresponding author address:*Samuel S. P. Shen, Dept. of Mathematics and Statistics, San Diego State University, 5500 Campanile Dr., San Diego, CA 92182. E-mail: shen@math.sdsu.edu