We thank Anne Markel for editing assistance. We also wish to thank Xungang Yin and several anonymous reviewers for their thoughtful comments.
APPENDIX A: CALCULATION OF DAILY CLIMATOLOGICAL PROBABILITIES OF OCCURRENCE. For a particular station and variable, the daily probabilities are calculated according to the following four-step procedure.
Sample selection: For each day of the year except 29 February, the sample used includes data from within +/−14 days of the day in question and from all years that have values on at least 20 calendar days within that 29-day window. A minimum of 10 such years is required for each window (Durre et al. 2013).
Calculation: The climatological probability of occurrence is then equal to the percentage of nonzero values within the pool. Due to the limited sample size for 29 February, the probability for that day is set to the average of the probabilities for 28 February and 1 March.
Smoothing: To reduce fluctuations from one calendar day to the next that are associated with sampling variability, the empirical probabilities are smoothed with a 29-day running mean. After several other types of filters had been tested, this particular filter was found to yield the desired level of smoothing while retaining variations on the time scale of weeks.
Synchronization: The use of the 29-day window and subsequent smoothing can result in small nonzero probabilities for snowfall or snow depth in months during which snow was never reported in the underlying observations. In such cases, the affected probabilities are set to zero. Similarly, at the beginning of the snow season, another check sets to zero any nonzero probabilities of snow on the ground that appear before the probability of snowfall has increased from zero.
As an example, consider the probability of snow on the ground on 25 December during 1981–2010 at Milwaukee (Table 1). For this calculation, observations were available on all of the 29 days in the window in 28 of the 30 years and on 27 of the 29 days in another year, yielding a total of 839 observations. Of these, 392 were nonzero values, resulting in an empirical probability of 46.8%, which was transformed to 47.7% by the subsequent smoothing of the raw probabilities.
APPENDIX B: COMPUTATION OF DAILY MEDIANS OF NONZERO AMOUNTS. The procedure for calculating daily medians of the nonzero amounts of one element at one station is described below.
Sample selection: The median of a particular day is calculated from the same sample of values used to compute the probability of occurrence (see #1 in appendix A).
Calculation: If at least 10% of the values in the sample for a particular calendar day are nonzero, these nonzero amounts are sorted from lowest to highest, and the median is identified (Durre et al. 2013). Otherwise, the median is set to missing. The median for 29 February is set to the average of the corresponding medians for 28 February and 1 March.
Smoothing: The resulting daily medians are smoothed with a 29-day running mean. To allow for the smoothing of even those medians that directly precede or follow a time of the year during which medians are missing, the running mean is calculated whenever medians are available on at least 15 of the 29 days. Medians that cannot be smoothed in this manner are set to missing.
Interpolation: Gaps in the resulting medians that are shorter than 15 days are filled in using linear interpolation between the corresponding medians immediately preceding and following the gap. At locations in the northern Great Plains, midwinter gaps in snowfall medians that extend over more than 15 days are also filled in since the medians before and after the gap typically do not differ significantly from each other.
Cleanup: To avoid fragmented annual cycles, continuous stretches of medians shorter than 15 days are removed, and all medians are set to missing if there is no continuous stretch of (empirical and interpolated) medians that is at least 30 days long.
For Further Reading
Arguez, A., I. Durre, S. Applequist, R. S. Vose, M. F. Squires, X. Yin, R. R. Heim Jr., and T. W. Owen, 2012: NOAA’s 1981-2010 U.S. climate normals: An overview. Bull. Amer. Meteor. Soc., 93, 1687–1697, doi:10.1175/BAMS-D-11-00197.1.
Durre, I., M. F. Squires, R. S. Vose, X. Yin, A. Arguez, and S. Applequist, 2013: NOAA’s 1981-2010 U.S. Climate Normals: Monthly precipitation, snowfall, and snow depth. J. Appl. Meteor. Climatol., 52, 2377–2395, doi:10.1175/JAMC-D-13-051.1.
Menne, M. J., I. Durre, R. S. Vose, B. E. Gleason, and T. G. Houston, 2012: An overview of the Global Historical Climatology Network-Daily Database. J. Atmos. Oceanic Technol., 29, 897–910, doi:10.1175/JTECH-D-11-00103.1.
Vose, R. S., and Coauthors, 2014: Improved historical temperature and precipitation time series for U.S. climate divisions. J. Appl. Meteor. Climatol., 53, 1232–1251, doi:10.1175/JAMC-D-13-0248.1.