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.

**Impressions**

** **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:

1990 540.1651602

1991 536.7764996

1992 527.2547247

1993 515.9013969

1994 530.0986031

1995 528.7929334

1996 519.1618735

1997 524.4864421

1998 548.5152013

1999 541.8685292

2000 532.8077239

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.**

Hi. Haven’t had time to look closely at your work, but two brief comments

1. When Spencer looked for UHI in US, he found that the greatest effects seem to occur in lower population densities and that increasing density had a ‘diminishing return’ effect.

2. Beware of autocorrelation. If AGW has a positive effect on temperature and population density increases in most regions over time, then just looking at pden isn’t giving you the whole story. That is why most such studies comparative – testing station pairs or regions pairs that are in proximity. Assuming a constant AGW signal in such regions, comparison studies tease out the difference caused by changes or differences in pden.

As I said, I’m just glancing, but I am confused by your statement regarding rural TOB adjustments as a red herring. Could you expand on what you mean?

Comment by Ron Broberg — August 7, 2010 @ 10:06 am

Thanks Ron, I”ll definitely check out Spencer’s work.

With respect to auto-correlation, I’ll definitely need to look into it further, but my impression is that while we’d expect an overall positive trend between population density and temperature with AGW, this wouldn’t explain why we get a correlation between individual station changes in population density as related to their temperature changes. That is, we would expect the dTemp/dPop to be a flat line, it would just be positive, if we merely suggested that both temperature and population density have increased with AGW.

With respect to the red herring, I just meant that at first the TOB adjustments in rural stations might have seemed suspect in Zeke’s post, since there was a large difference applied between rural vs. urban. However, based on these results, it would seem imply that that there is nothing nefarious in these TOB adjustments.

Comment by troyca — August 7, 2010 @ 12:27 pm

[…] Troy_CA's blog Troy_CA's blog Skip to content HomeAbout ← Searching for UHI in changing population densities in the US part 2 […]

Pingback by Specific Humidity, Temperature, and UHI | Troy_CA's blog — August 10, 2010 @ 11:38 am

Interesting results. Its hard to quantify using such a short time period, but it does suggest some interesting avenues for further research.

One suggestion might be to assume that near-zero population stations in the present were also near-zero in the past, and compare those areas to higher pop stations. I’ll play around with tightening my station selection and see how the implied UHI signal changes.

Comment by Zeke — August 10, 2010 @ 3:09 pm

I recently got around to trying this, and have not been having much luck. That is, the assumption of “near-zero population stations in the present were also near-zero in the past” does not necessarily seem to imply that these near-zero stations are unaffected by UHI bias (or at least there is not an obvious signal)…because at these low population densities it only takes a slight change actual change to get a large percentage change.

For instance, using F51 data from 1970-2000, I got the following results:

Case 1 (PopDens2000 0.5): average OLS trend = 0.5, number of stations = 1145

So right off the bat we see we run into an issue of lack of data when we get that small. But I also found that in Case 1, the average abs value of the percent pop density change from 1990 to 2000 was 0.16 as opposed to 0.12 in case 2, suggesting there is more volatility at those low population densities. (On the other hand, many of these population changes from 1990 to 2000 in those low pop areas were negative).

Using 1.0 as the cutoff instead of 0.5 yields almost identical results, but with about 75 more stations.

Using 0.01 as a cutoff leaves only a total of 5 stations.

Comment by troyca — August 14, 2010 @ 2:31 pm

[…] Posted on August 30, 2010 by troyca Continuing on what I’ve been doing in Part I and Part II of my U.S. analysis in terms of UHI as a function of population, I’ll now look at the global […]

Pingback by More UHI sniffing in GHCN | Troy_CA's blog — August 30, 2010 @ 10:25 pm

[…] density from 1990 to 2000 and the change in temps from 1990 to 2000 in the US. See here, here, and here. At first I took this to be a UHI signal. However, a bit more investigating has shown […]

Pingback by Explaining correlation in US UHI tests | Troy_CA's blog — November 4, 2010 @ 1:06 pm

[…] station pairs. (I should mention that Ron suggested something similar way back in an earlier comment). For now I’ve matched based on “distance” in terms of degrees, which […]

Pingback by A More Robust Method of Finding a UHI signal | Troy_CA's blog — November 8, 2010 @ 10:44 pm