Nov 28 2007
Is it the Heat Island or a Linear Trend?
If one blindly plots a time series of noisy data, it is difficult to understand what is going on by visual inspection. The two plots below are fake data (soon to be submitted to The Journal of Geoclimatic Studies); one is of system that is increasing linearly with time and the other is one that has four discrete steps. In both of the fake data, random noise was added. Can you tell which is which? No guessing and no looking at the alternate text - that’s cheating.
The trend in each case is exactly the same, and it is plotted as the dark blue dashed line. The cyan line is the step function without the noise. Astute readers (aka alive) will actually notice that it is a series of 4 steps. This is explained below, so keep reading. They will also notice that the vertical scale is different in the two plots. This is because the author was stupid attempting to show how different random noise would manifest in the two plots.
|
|
The top plot is the linearly trended data and the bottom plot is the stepped data. Did you get it right?
The stepped plot is attempting to show how changing the location of surface stations preferentially from native surroundings to more urban locations will have a similar signature when looking at the time series plots. This is the argument that the folks at surfacestations.org are making; that the average surface temperature is not increasing, and it only appears to be increasing due to the fact that the stations are being moved from cooler locations to warmer locations. (Or that the hotter locations, aka cities, are getting larger and thus necessarily getting closer to the stations and warming them.)
However, as can be seen above, it is not possible to know if the trend is due to the heat island effect (steps) or because of global climate change (trend). In practice it is not this simple. The steps from changes in location are easy to find, especially if the meta data is properly maintained. The problem is due to urban sprawl. Stations at the edge of a city in 1950 are likely to be totally urbanized by now. And this urbanization does not happen in steps, it’s a gradual process. Therefore, the steps in the above plots would instead be trends that gradually transition from the initial background temperature to the current higher background temperature.
(No Ratings Yet)
Loading ...Related Posts:
3 Responses to “Is it the Heat Island or a Linear Trend?”
To reduce spam, comments are automatically closed 30 days after the last comment. If you would like to comment on any closed thread, please use the contact form at the top of this page.
“The stepped plot is attempting to show how changing the location of surface stations preferentially from native surroundings to more urban locations will have a similar signature when looking at the time series plots.” B
I would guess that if you make the noise big enough you can hide any signal. For a given station and its noise what is the minimum detectable step change? This also depends on the length of the series proceeding and following the step (it is harder to detect a recent step because you don’t have enough samples of the new level). Seems a perfect question for Tamino.
Something like,
Assume location for step..Calc means either side of step..Calc noise (standard deviation) either side of step ..check homogenous noise… t-test (corrected for multiple comparisons?) for different means.. choose next location for the step..repeat above
[Response: You're right that if the step is larger than the noise (or some fraction of the noise) then it will be easy to detect the change. But that's a pretty trivial problem.
In this example, I let the noise be randomly distributed around zero with a variance of 1. Each of the 4 steps was 2 units (deg C I guess, but the axis isn't labeled), which after averaging the four stations led to steps of 0.5. I should be able to come up with something to test the minimum step needed to detect the change. Stay tuned.]
McKitrick/Michaels have rehashed an earlier paper on this:
http://www.uoguelph.ca/~rmckitri/research/jgr07/M&M.JGR07-background.pdf
…which has gotten some play in our local Conservative rag.
Never mind. This is just an update of their 2004 piece of junk.