Testing for trend in the variability of monthly and seasonal temperature using the range and the standard deviation as measures of variability

In the Climate Change literature, the range is predominantly used as a measure of variability, and the presence of trend is typically done on seasonal and/or annual basis. In this study, we used daily average temperature values at 15 spatially distributed sites across Canada to test the presence of trend in variability (using both range and standard deviation) using the bootstrap method by Woodward et al. (1997). The length of the series varied from site to site, ranging from 30 to 151 years. The analysis was done for each month, each season and the annual data. When calculating the standard deviations, supersmoother estimates of temperature were used as the means to make the results invariant to the presence of trend in the mean. The results from the monthly and seasonal analysis revealed the presence of either increasing or decreasing variability for some months and some seasons. The results for the annual data were not so revealing, especially at the sites where some months have increasing and others have decreasing trends. The significance of trend in variability by the range and the standard deviation agreed in less than 30% of the time across sites and across the monthly, seasonal and annual aggregations. The differences between median significance scores was significant in 2 of the 15 sites, and in 6 of the 17 aggregations.