Yesterday a co-worker and I were talking about how we weren’t able to enjoy the new snow because the weather had turned cold as soon as the snow stopped falling. Along the way, she mentioned that it seemed to her that the really cold winter weather was coming later and later each year. She mentioned years past when it was bitter cold by Halloween.

The first question to ask before trying to determine if there has been a change in the date of the first cold snap is what qualifies as “cold.” My officemate said that she and her friends had a contest to guess the first date when the temperature didn’t rise above -20°F. So I started there, looking for the month and day of the winter when the maximum daily temperature was below -20°F.

I’m using the GHCN-Daily dataset from NCDC, which includes daily minimum and maximum temperatures, along with other variables collected at each station in the database.

When I brought in the data for the Fairbanks Airport, which has data available from 1948 to the present, there was absolutely no relationship between the first -20°F or colder daily maximum and year.

However, when I changed the definition of “cold” to the first date when the
daily *minimum* temperature is below -40, I got a weak (but not statistically
significant) positive trend between date and year.

The SQL query looks like this:

```
SELECT year, water_year, water_doy, mmdd, temp
FROM (
SELECT year, water_year, water_doy, mmdd, temp,
row_number() OVER (PARTITION BY water_year ORDER BY water_doy) AS rank
FROM (
SELECT extract(year from dte) AS year,
extract(year from dte + interval '92 days') AS water_year,
extract(doy from dte + interval '92 days') AS water_doy,
to_char(dte, 'mm-dd') AS mmdd,
sum(CASE WHEN variable = 'TMIN'
THEN raw_value * raw_multiplier
ELSE NULL END
) AS temp
FROM ghcnd_obs
INNER JOIN ghcnd_variables USING(variable)
WHERE station_id = 'USW00026411'
GROUP BY extract(year from dte),
extract(year from dte + interval '92 days'),
extract(doy from dte + interval '92 days'),
to_char(dte, 'mm-dd')
ORDER BY water_year, water_doy
) AS foo
WHERE temp < -40 AND temp > -80
) AS bar
WHERE rank = 1
ORDER BY water_year;
```

I used “water year” instead of the actual year because the winter is split between two years. The water year starts on October 1st (we’re in the 2013 water year right now, for example), which converts a split winter (winter of 2012/2013) into a single year (2013, in this case). To get the water year, you add 92 days (the sum of the days in October, November and December) to the date and use that as the year.

Here’s what it looks like (click on the image to view a PDF version):

The dots are the observed date of first -40° daily minimum temperature for each
water year, and the blue line shows a linear regression model fitted to the data
(with 95% confidence intervals in grey). Despite the scatter, you can see a
slightly positive slope, which would indicate that colder temperatures in
Fairbanks *are* coming later now, than they were in the past.

As mentioned, however, our eyes often deceive us, so we need to look at the
regression model to see if the visible relationship is significant. Here’s the
R `lm` results:

Call: lm(formula = water_doy ~ water_year, data = first_cold) Residuals: Min 1Q Median 3Q Max -45.264 -15.147 -1.409 13.387 70.282 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -365.3713 330.4598 -1.106 0.274 water_year 0.2270 0.1669 1.360 0.180 Residual standard error: 23.7 on 54 degrees of freedom Multiple R-squared: 0.0331, Adjusted R-squared: 0.01519 F-statistic: 1.848 on 1 and 54 DF, p-value: 0.1796

The first thing to check in the model summary is the p-value for the entire model on the last line of the results. It’s only 0.1796, which means that there’s an 18% chance of getting these results simply by chance. Typically, we’d like this to be below 5% before we’d consider the model to be valid.

You’ll also notice that the coefficient of the independent variable
(`water_year`) is positive (0.2270), which means the model predicts that the
earliest cold snap is 0.2 days later every year, but that this value is not
significantly different from zero (a p-value of 0.180).

Still, this seems like a relationship worth watching and investigating further. It might be interesting to look at other definitions of “cold,” such as requiring three (or more) consecutive days of -40° temperatures before including that period as the earliest cold snap. I have a sense that this might reduce the year to year variation in the date seen with the definition used here.