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From: Bret Schichtel
Date: 11/1/2002
Time: 1:20:05 PM
Remote Name: 129.82.108.243
The slope of the trend lines is calculated from a Theil regression analysis on the 5 year running averages of the annual values. The units of the slope are provided at the bottom of each figure and are in ng/m3/year, DV/year or 1/Mm/year. The Theil regression analysis is a linear model of the data where the slope of the best fit line is an estimate of the change per year. Any other linear model will give you a different estimate of the slope. I do not think one can ascribe to any method that it is an average or median change per year, only that it is the change per year as estimated by Theil or MLS or…
The following describes how the Theil slope and significance level of the trend lines are calculated. This was taken from Malm et al. A ten-year spatial and temporal trend of sulfate across the United States to be published in JGR in 2002 or 2003.
"Characterization of trends can be a highly subjective exercise in that slopes and their significance can vary depending on the technique employed. Using ordinary least squares (OLS) regression approach is questionable with such small data sets as the results can be highly influenced by outliers. In another approach, developed by Theil [1950], outlier data points do not as significantly influence the results. Slopes of trend lines are calculated for each site by first finding the slope between all possible pairs of data points, then sorting the results from smallest or most negative to the largest. Finally, the median value in the case of an odd number of pairs is selected as the estimated slope, or in the case of even number of pairs, the average of the two slopes that straddle the median is used as the estimate. The significance of the Theil slope is found by assuming that the "true" slope is zero, then calculating the probability that the estimated slope occurred by chance."