Home/BlogIn a recent post I used our new Urban Heat Island (UHI) warming estimates at individual U.S. GHCN stations having at least 120 years of data to demonstrate that the homogenized (adjusted) GHCN data still contain substantial UHI effects. Therefore, spurious warming from UHI effects is inflating reported U.S. warming trends.
The data plots I presented had considerable scatter, though, leading to concerns that there is large uncertainty in my quantitative estimates of how much UHI warming remains in the GHCN data. So, I updated that post to include additional statistics of the regressions.
A Simple Example: High Correlation, But Low Confidence In the Regression Slope
The following plot of a small amount of data I created shows what looks like a pretty strong linear relationship between 2 variables, with a regression explained variance of 82% (correlation coefficient of 0.91).
But because there are so few data points, there is large statistical uncertainty in the resulting diagnosed regression slope (21% uncertainty), as well as the regression intercept (which is diagnosed as 0.0, but with an uncertainty of +/- 0.94).
Now let’s look at the third data plot from my previous blog post, which demonstrated that there is UHI warming in not only the raw GHCN data, but in the homogenized data as well:
Importantly, even though the regression explained variances are rather low (17.5% for the raw data, 7.6% for the adjusted data), the confidence in the regression slopes is quite high (+/-5% for the raw GHCN regressions, and +/-10% for the homogenized GHCN regressions). Confidence is also high in the regression intercepts (+/-0.002 C/decade for the raw GHCN data, +/-0.003 C/decade for the homogenized GHCN data).
Compare these to the first plot above containing very few data points, which had a very high explained variance (82%) but a rather uncertain regression slope (+/- 21%).
The points I was making in my previous blog post depended upon both the regression slopes and the regression intercepts. The positive slopes demonstrated that the greater the population growth at GHCN stations, the greater the warming trend… not only in the raw data, but in the homogenized data as well. The regression intercepts of zero indicated that the data, taken as a whole, suggested zero warming trend (1895-2023) if the stations had not experienced population growth.
But it must be emphasized that these are all-station averages for the U.S., not area averages. It is “possible” that there has (by chance) actually been more climate warming at the locations where there has been more population growth. So it would be premature to claim there has been no warming trend in the U.S. after taking into account spurious UHI warming effects. I also showed that there has been warming if we look at more recent data (1961-2023).
But the main point of this post is to demonstrate that low correlations between two dataset variables do not necessarily mean low confidence in regression slopes (and intercepts). The confidence intervals also depend upon how much data are contained in the dataset.
Could there possibly be a UHI in the Antarctic? Nature recently brought a story over strong warming there..
“A fast-warming region of Antarctica is getting greener with shocking speed”
https://www.nature.com/articles/d41586-024-03219-2
As you will know the South Pole is barely warming at all and that is a thing. So there are different strategies to cope with it. One is quote a single location with “extreme warming”.
This specific place around the small Ardley Island is interesting because it is so denesly populated. There is the “Great Wall Station”, “Villa Las Estrellas” (a permanent settlement wich ~150 residents plus airport) or the Artigas Station, all in walking distance.
If you introduce that many houses and people (including heating) into a remote location, what might be the impact on the local climate?
*** Good question! One of the things we demonstrated is that the largest rate of warming happens at the most rural locations… once you start adding a few people (and associated buildings, pavement, etc.) you get the greatest warming per increase in population. This isn’t a new finding, it was demonstrated by Oke in his original 1973 paper on UHI. So, what you are suggesting is possible. -Roy
Yes, the more points the more confidence in the slopes. I keep having to argue this on WUWT, with people who have convinced themselves that the more data the less certainty there is in the regressions line.
One question though, is whether the stated uncertainties are assuming independence of the data points. If two stations are close together they will have similar temperature and population changes. This seems likely when you look at the sparser data on the right, where there a number of stations with similar UHI and temperature deviations.