Coldest Days Trends

The coldest days are rarer than they used to be.

Is the frequency of the coldest days of the year changing? The tl;dr answer is of course yes. There are any number of ways to measure this. In this blog post, I identify the frequency of cold days during a base period (1951-2000), and then evaluate the trends of those values. The methodology and results are presented below.

Methodology:

1) Find the temperature that occurs on average 20, 15, 10, and 5 days per year during a baseline period for all long-term climate stations in the U.S. (I chose 1951 to 2000 - 50 years). For a 50-year period, the 10-day per year temperature value is found by ordering all 18,263 low temperatures (assuming no missing obs) and identifying the 500th lowest value.

2) For each year between 1950 and 2021, count the number of days that met or exceeded the temperatures identified in Step 1. Also identify the first and last occurrence of these temperatures each year. For example, if 20F is the temperature that occurred an average of 10 days per year during the 1951-2000 baseline period, count the number of days each year that 20F occurred and find the first/last 20F day each year.

3) If a station contained 65 or more complete years of temperature data (no more than 10 missing days in a year), it was kept for the final analysis. There were 609 U.S. stations that successfully met the criteria, 15 Canadian stations, and 0 Mexican stations. 

4) Fit a linear regression line to the 72-year (1950-2021) time series of the number of annual occurrences (and the first/last dates) for each station. The different between the fitted (not observed) 2021 value and the fitted (not observed) 1950 value represents the change,

Example:

In Fig. 1, we see the change in days per year for the temperature that historically occurred 20 and 10 days per year for Boise, Idaho. Those temperatures are 17F and 11F respectively. A regression line is fitted to each time series and the begin and end points of the regression lines represent the change. In the Boise example, the 17F temperature, which occurred an average of 20 days per year during the 1951-2000 period, trended from 26 days per year to 12 days per year. An decrease of 24 days per year over the 72-year period.

Fig 1. Change in the number of days per year for the temperature that historically (1951-2000) occurred 10 and 20 days per year in Boise, Idaho.

Fig. 2. Change in the length of time (days) between the first/last occurrence of the temperature that historically (1951-2000) occurred 10 and 20 days per year in Boise, Idaho.

In Fig. 2 we see the same information for Boise, except it notes the length of time between the first and last occurrences of the temperature that historically occurred 20 and 10 days per year. A low temperature of 17F historically occurred 20 days per year in Boise. The trend in the length of time between the first and last 17F day of the year decreased from 85 to 57 days per year. We interpret this as a shortening of the coldest time of year by 28 days. Specifically, the typical first occurrence for Boise of 17F changed from November 30th to November 29th (1 day later) and the typical last occurrence of 17F changed from February 21st to January 25th (27 days earlier).

Maps: Modern Days per Year Count

Figs 3-6 below show the current number of days per year for the temperatures that historically occurred 20, 15, 10, and 5 days per year. If you refer back to Fig. 1, the value at the end of the trend (dotted) lines are what we are mapping below. 

Fig 3. Current number of days per year that the historically (1951-2020) coldest 20 days per year now occur. This is the end point of the 72-year regression line.

Fig 4. Current number of days per year that the historically (1951-2020) coldest 15 days per year now occur. This is the end point of the 72-year regression line.

Fig 5. Current number of days per year that the historically (1951-2020) coldest 10 days per year now occur. This is the end point of the 72-year regression line.

Fig 6. Current number of days per year that the historically (1951-2020) coldest 5 days per year now occur. This is the end point of the 72-year regression line.

Maps: Change in the Length of the Cold Portion of the Year

As Fig. 2 shows for Boise, we can track the length of time between the first/last occurrence of particularly hot days and see how that length changed over time. Figs 7-11 below show how the length of time of peak heating has changed. 

Fig 7. Change in the length of time that the historically (1951-2020) coldest 20 days per year now occur. This is the difference between end point and beginning point of the 72-year regression line.

Fig 8. Change in the length of time that the historically (1951-2020) coldest 15 days per year now occur. This is the difference between end point and beginning point of the 72-year regression line.

Fig 9. Change in the length of time that the historically (1951-2020) coldest 10 days per year now occur. This is the difference between end point and beginning point of the 72-year regression line.

Fig 10. Change in the length of time that the historically (1951-2020) coldest 5 days per year now occur. This is the difference between end point and beginning point of the 72-year regression line.

Maps: Change in the Length of Consecutive Cold Days
This is where we will look at the changing length of coldwaves. As with before, we're using the temperature that historically occurred 20, 15, 10, and 5 days per year. Now we are looking at each year and identifying the maximum number of consecutive days that those temperatures occurred. If the 5-day per year temperature occurred 8 times in a specific year but there was at least 1 day between each occurrence, then the maximum consecutive streak would be 1 in that example. Figs. 11-14 show the change in the length of these streaks. The change is the end trend point minus the beginning trend point divided by the beginning trend point times 100. 

Fig 11. Change in the number of consecutive days at or below the temperature that historically (1951-2020) occurred 20 days per year. This is the difference between end point and beginning point of the 72-year regression line as a percentage.

Fig 12. Change in the number of consecutive days at or below the temperature that historically (1951-2020) occurred 15 days per year. This is the difference between end point and beginning point of the 72-year regression line as a percentage.

Fig 13. Change in the number of consecutive days at or below the temperature that historically (1951-2020) occurred 10 days per year. This is the difference between end point and beginning point of the 72-year regression line as a percentage.

Fig 14. Change in the number of consecutive days at or below the temperature that historically (1951-2020) occurred 5 days per year. This is the difference between end point and beginning point of the 72-year regression line as a percentage.

Mapping
The map in Fig. 15 shows the stations used in this analysis. The maps in Figs 3-10 were generated from station data using an inverse distance weighted surfacing algorithm with 50km grid cells. There is often a lot of variability in small geographical regions; therefore, a 5x5 smoothing filter was applied to all maps. No adjustment for topography was made. 

Fig 15. Map of stations used in the analysis presented in this blog post. There are 609 U.S. stations that successfully met the criteria, 15 Canadian stations, and 0 Mexican stations.

Conclusion
The frequency and duration of the coldest days of the year are dramatically decreasing in the U.S. Period. There are no locations that have escaped this trend.