Here's a map showing the results for all of North America. I created a smoothed contour map rather than showing all the points, because there are so many stations in the lower 48 that all the markers overlap. We see that Fairbanks temperatures do indeed have a modest negative correlation with temperatures in parts of the southwest US at this time of year, and there is a small positive correlation with the northern Plains and upper Midwest.
Below are the maps for each month of the year (click to enlarge). A surprising result is that the scale of very good correlations (R>0.9) across Alaska and western Canada is greatest in September; I would have expected this to occur in winter.
























Update July 2: below are the corresponding maps for monthly precipitation. Note that I've used the rank correlation coefficient rather than the Pearson correlation coefficient, because precipitation amounts can be highly nonGaussian in drier areas even on a monthly timescale.
Also note that there are far fewer stations reporting precipitation than temperature across the north (at least in the GHCN data set), so the continentwide map shows large areas of missing data, and the results of the smoothing algorithm (Cressman analysis) are not realistic in Alaska. I recommend paying attention only to the very broadscale features of the maps. But it's interesting to see that September again has a relatively good correlation of anomalies across Alaska.
























I don't understand how you are creating the correlations. Correlations are meaningless without trends. So what trends are you using?
ReplyDeleteThey are correlations over time, 19812010. So we have 30 data points for Fairbanks June temp, 30 data points for Barrow June temp, and we find the correlation coefficient. Repeat for thousands of stations.
DeleteDoes that help? Sorry for the confusion.
Forgive my confusion. I interpret your explanation in two possible ways:
Delete1. Given the 30 year period, the warmer it is in Fairbanks during any given month, the colder the blue areas are. Thus a warm January in Fairbanks is cold in Orlando, while a cold winter here is warm there.
2. Over the 30 years period, the Florida temps have been getting colder with respect to Fairbanks.
I suspect that option 1 is right but it's not clear.
Eric I think your option 1 is the closest. My understanding is that the colors are not related to specific warm/cold but instead related to the correlative relationship between Fairbanks' temps with temps elsewhere.
DeleteMy question is, what are the original data points? Are they deviation from the long term mean? For instance, if it's a day in January in Fairbanks that is 20 degrees cooler than normal, does that make a day in Tanana that is 20 degrees cooler than normal a "1.0"? And a day in Quebec City that is 20 degrees warmer than normal a "1.0"?
Option 1 and Andy's explanation are correct.
DeleteThe data points are just mean monthly temperature. The correlation calculation takes out the sample (i.e. 19812010) mean:
https://en.wikipedia.org/wiki/Pearson_productmoment_correlation_coefficient
The variance at each site doesn't matter, as we are looking at correlation. So for example the following two series are perfectly correlated (R=+1.0) even though the variance is different.
3 1 5 9 2
6 2 10 18 4
Great map set Richard! May I share?
ReplyDeleteYes, of course. It would be trivial to create similar maps for any other location if you're interested.
DeleteI like the visual presentation of correlation between different NA zones...even when it's a negative less than 0.
ReplyDeleteWhich to me means there's a relationship although opposite in temperature...when we're warm; they're cold apparently.
How about one for precipitation?
Gary
Yes, some places are inversely correlated. A ridge upstream is usually associated with a trough downstream at a certain preferred wavelength, and vice versa.
DeleteShouldn't be too difficult to add precipitation, although I'll have to use Spearman correlation rather than Pearson.
It'll be interesting to potentially compare temps and precip via your visual methods.
DeleteOr...simply regress sales of umbrellas per capita by location (smile).
I looked up Pearson/Spearman but it's been 48 yrs since Stat classes so I got the preexam shakes and quit. Now with plugin PC programs its easier than hand computation was in the age before calculators
Gary
I've added the precip correlation maps. The paucity of data makes them less informative than the temperature maps, but there are a couple of interesting features.
DeleteThank you for adding the precip correlation maps! It's a bummer that NCEI has precip (v2) and temps (v4) in separate files with separate identifiers. Makes it hard to join data.
ReplyDelete