For each HI, the number of heat wave days was summed annually (warm season) at the NLDAS grid cell scale. To gain insight into regionalized patterns of the HI, CONUS was divided into six regions: Northwest (Washington, Oregon, Idaho), Southwest (California, Nevada, Utah, Arizona, New Mexico and Colorado), Great Plains (North Dakota, South Dakota, Montana, Wyoming, Nebraska, Kansas, Oklahoma, Texas), Midwest (Minnesota, Iowa, Missouri, Wisconsin, Illinois, Indiana, Ohio, Michigan), Southeast (Arkansas, Louisiana, Mississippi, Alabama, Tennessee, Kentucky, Georgia, Florida, South Carolina, North Carolina, Virginia) and Northeast (Pennsylvania, New Jersey, New York, Rhode Island, Connecticut, Massachusetts, Vermont, New Hampshire, Maine, Maryland, West Virginia, Delaware). These regions are depicted in Figure 1 and approximately match the six geographical regions used for regional climate change analysis in the United States Global Change Research Program (USGCRP) report Global Climate Change Impacts in the United States (2009).
For each of the fifteen HI, the total number of annual heat wave days was averaged over the 33-year timespan at the NLDAS grid cell scale. These results were then averaged over the six CONUS regions to arrive at the average number of heat wave days unique for each heat wave index and region.
These heat wave day averages were then assessed for their trends over the 1979–2011 time period using ordinary least squares (OLS) regression. As the OLS residuals exhibited non-normality for several indices (as shown by Shapiro-Wilks normality testing), significance tests were performed using the Mann-Kendall tau test. The Mann-Kendall tau test is a nonparametric test that does not assume an underlying probability distribution of the data, and is also robust to outliers (Moberg et al. 2006 ). Because of this, it is valuable when assessing trends in climate data and therefore has been used in previous studies of trends in extreme temperature indices (El Kenawy et al. 2011 ; Efthymiadis et al. 2011 ; Kuglitsch et al. 2010 ). A trend was considered statistically significant if the p-value was smaller than the significance level α of 0.05. Based on the results of the Mann-Kendall testing, all insignificant trends were masked out. The average of the resulting significant trends was computed for each of the six CONUS regions for all fifteen HI. Results are reported for trends calculated over the entire 1979–2011 period of record available at the time the study was performed. The sensitivity of trends to choice of time period was assessed by repeating the trend analysis with the beginning date shifted between 1979 and 1981 and the end date shifted between 2007 and 2012 (provisional data used for 2012). It was found that results were very similar for all analyses that included data through at least 2009. For periods that excluded recent years the geographic pattern and direction of trends was similar, but statistical significance of trends tended to be reduced.
To compliment these trend values, landmass coverage was calculated. These landmass coverage percentages represent the number of cells covered by significant trends (which were averaged) divided by the total number of cells in that region.
For each of the fifteen HI, the total number of annual heat wave days was averaged over the 33-year timespan at the NLDAS grid cell scale. These results were then averaged over the six CONUS regions to arrive at the average number of heat wave days unique for each heat wave index and region.
These heat wave day averages were then assessed for their trends over the 1979–2011 time period using ordinary least squares (OLS) regression. As the OLS residuals exhibited non-normality for several indices (as shown by Shapiro-Wilks normality testing), significance tests were performed using the Mann-Kendall tau test. The Mann-Kendall tau test is a nonparametric test that does not assume an underlying probability distribution of the data, and is also robust to outliers (Moberg et al. 2006 ). Because of this, it is valuable when assessing trends in climate data and therefore has been used in previous studies of trends in extreme temperature indices (El Kenawy et al. 2011 ; Efthymiadis et al. 2011 ; Kuglitsch et al. 2010 ). A trend was considered statistically significant if the p-value was smaller than the significance level α of 0.05. Based on the results of the Mann-Kendall testing, all insignificant trends were masked out. The average of the resulting significant trends was computed for each of the six CONUS regions for all fifteen HI. Results are reported for trends calculated over the entire 1979–2011 period of record available at the time the study was performed. The sensitivity of trends to choice of time period was assessed by repeating the trend analysis with the beginning date shifted between 1979 and 1981 and the end date shifted between 2007 and 2012 (provisional data used for 2012). It was found that results were very similar for all analyses that included data through at least 2009. For periods that excluded recent years the geographic pattern and direction of trends was similar, but statistical significance of trends tended to be reduced.
To compliment these trend values, landmass coverage was calculated. These landmass coverage percentages represent the number of cells covered by significant trends (which were averaged) divided by the total number of cells in that region.
