In my last post, I did some preliminary analysis of the relationship between population density and temperature. You can find links to the code and data in that post. I tried to make the code reader-friendly and flexible so I’d encourage anyone to take it and run their own tests with it.
Anyhow, in that post the largest correlation occurs when comparing: endpoint (1990 and 2000) temperature differences vs. endpoint population difference as a percentage of end year population density. While I’m not certain that theoretically this is a better approach than using the linear temperature trend from 1990 to 2000 as my y-value, I’ll proceed with this method because that’s where the signal (or spurious correlation) seems to appear. I’ll break it down by 2000 population density and we can get a hint about how the trends may differ in rural, city, and big city situations (I hope Zeke won’t mind me borrowing his idea yet again and using 10 and 100 breakdowns).
Low density stations (PopDens2000 < 10)
There are four values on the extremes of the X-axis (large relative changes in population density) that have a significant effect on the trend and correlation here. If I exclude those four observations (include only X > -.4 & X < .6), we get an even better correlation:
Medium density stations (PopDens2000 > 10 & PopDens2000 < 100)
High density stations (PopDens2000 > 100)
As was the case with low density areas, the trend and correlation seem to be greatly affected by a few points on the extremes of the relative population change axis. If I filter these out (include only X > -.25 & X < .4), I get a much better correlation below.
I would say we’re getting a significant signal in the low density (PopDens < 10) and high density (PopDens > 100) situations. What’s more, this signal seems to appear just as strong (if not stronger) in the F52 case, which I understand is supposed to correct for UHI. I don’t believe the adjustments are necessarily making the UHI effect worse, but rather that many of the corrections in the F52 data are useful and probably just help make the signal clearer. However, my impression is that these corrections fail to remove the UHI effect.
Another thing the results show is that comparing rural to urban stations may not be the way to detect UHI, since the low density stations and high density stations are both affected. This means that the TOB adjustment issue for rural stations may be a red herring.
Of course, this all comes with the caveat that we only have a small time period of population data to work with here, and my approach is somewhat questionable.
Quantifying the Effect
Here’s my little back-of-the-napkin approach for quantifying the effect of UHI between 1990 and 2000 based on the results. If someone is so inclined they can do a more correct analysis by running the code from Clear Climate Code or another temperature reconstruction, but with all the uncertainties here already present I don’t know that such a level of precision is warranted.
First, I calc the mean relative population density change between 1990 and 2000 (mean of X-axis values from F52 charts above) using R:
Mean at PopDens2000 < 10: 0.05827
Mean at PopDens2000 > 10 & < 100: 0.073120
Mean at PopDens2000 > 100: 0.05912
I then multiply these values by their respective slopes, and take a weighted average based on the number of observations (stations). (Remembers that the slope is hundredths tenths of a degree (F) per year, to we need to divide by 10 to get degrees per decade). The quick and dirty approach yields:
[(.05827 * 3.2 * 387) + (0.073120 * 1 * 432) + (0.05912 * 2.68 * 383)] / (387 + 432 + 383) / 10 = .0137 C / decade 0.137 degrees F / decade, or .076 degrees C / decade.
Since we’ve only considered data from 1990 to 2000, we may want to only look at the average US trend during that time. Once again I’ll take a quick-and-dirty approach of simply averaging all of my F52 station data together each year between 1990 and 2000, and then calculating the 10 year trend using OLS.
My years look like this:
The calculated slope is .487 hundredths tenths of a degree per year, or .0487 C / decade. 0.487 degrees F / decade, or .271 degrees C / decade.
If we take this at face value, it would suggest that UHI accounts for 28% of the warming of the 1990 to 2000 time period. However, if you look at the years above, the trend in the U.S. is lower in part because we have a peak in 1990, and so I would venture to say that this 28% is an overestimate.
My next step will likely be to run similar experiments, but with global data, and see if I get similar results.
Update (8/8): As in the last post, I should have read the README file more carefully. The reported temperatures are in tenths of degrees Fahrenheit, not hundredths of a degree Celsius.